A die is rolled. Find the probability of the given event. Round all answers to 4 decimals. (a) The number showing is a 5; The probability is: ___
(b) The number showing is an even number; The probability is : ___
(c) The number showing is greater than 2; The probability is: ___

Answers

Answer 1

The probability of the each event is:

(a) The probability is: 0.1667

(b) The probability is: 0.5

(c) The probability is 0.6667.

Given: A die is rolled.

There are 6 outcomes when a die is rolled, from 1 to 6.

So the sample space (S) is {1, 2, 3, 4, 5, 6}.

(a) The number showing is a 5;

The probability of getting 5 on the die is 1/6 or 0.1667 (rounded to 4 decimal places).

So, the probability is: 0.1667

(b) The number showing is an even number;

The even numbers are 2, 4, and 6. So, there are three favorable outcomes.

Event is getting even number.

Therefore, P(getting an even number) = 3/6

= 1/2

= 0.5 (rounded to 4 decimal places).

Thus, the probability is: 0.5

(c) The number showing is greater than 2;

The numbers greater than 2 are 3, 4, 5, and 6.

So, there are four favorable outcomes.

Event is getting number greater than 2.

P(getting a number greater than 2) = 4/6

= 1/2

= 0.6667 (rounded to 4 decimal places).

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Related Questions

(a) (10 points) Consider the linear system X'(t) = AX(t) where A = [ 1 3 3 1]
i. Find the general solution for the system
ii. Sketch a phase portrait. iii Solve the initial value problem X'(t) = AX(t), X(0) = [1 0]

Answers

General solution for the system The given linear system is X'(t) = AX(t)The general solution for this system can be expressed as:[tex]X(t) = c1V1e^(λ1*t) + c2V2e^(λ2*t[/tex] where, V1 and V2 are the eigenvectors of matrix A, and λ1 and λ2 are the corresponding eigenvalues.

To find the eigenvectors and eigenvalues, we solve the characteristic equation of matrix [tex]A:|A - λI| = 0⇒|1 - λ 3| = 0 3 1 - λ|A - λI| = 0⇒λ² - 4λ = 0⇒λ(λ - 4) = 0[/tex] Thus, λ1 = 4 and λ2 = 0 For λ1 = 4, we have 1 - 4x + 3z = 0 and 3y + (1 - 4)z = 0 Solving these equations, we ge tV1 = [1 1]T For λ2 = 0, we have 1x + 3y + 3z = 03x + 1y + 3z = 0 Solving these equations, we get V2 = [3 -1]T Therefore, the general solution is given asX(t) = c1[1 1]T e^(4t) + c2[3 -1]T The general solution in matrix form is [tex]X(t) = c1[1e^(4t) 3e^(4t)]T + c2[1e^(0t) -1e^(0t)]T= [c1e^(4t) + c2 c1e^(4t) - c2][/tex] ii. Sketch the phase portrait The phase portrait for the given system is shown below: [tex]X = \begin{bmatrix}x_1\\x_2\end{bmatrix}[/tex] [tex]\frac{dX}{dt} = A \times X[/tex] [tex]X(0) = \begin{bmatrix}1\\0\end{bmatrix}[/tex] The arrows indicate the direction of motion of solutions in the x1-x2 plane.iii. Solve the initial value problem We have to solve X'(t) = AX(t), X(0) = [1 0] Here, A = [1 3; 3 1] is the matrix of coefficients. Let us write down the differential equation in component form: [tex]x1' = x1 + 3x2x2' = 3x1 + x2[/tex] The characteristic equation of A is given by the determinant:|[tex]A-λI| = 0⇒ |1-λ 3| = 0 3 1-λ⇒ λ²-4λ=0⇒ λ(λ-4)=0[/tex] Thus, the eigenvalues are λ1=4, λ2=0. To find the eigenvectors, we must solve the system(A-λ1I)v1 = 0, which gives us (A-4I)v1=0 and the system[tex](A-λ2I)v2 =[/tex] 0, which gives us Av2=0-4v1 Thus,[tex]v1 = [1 1]Tv2 = [3 -1][/tex]T

The general solution is given by:[tex]X(t) = c1[1e^(4t) 3e^(4t)]T[/tex] + [tex]c2[1e^(0t) -1e^(0t)]T = [c1e^(4t) + c2 c1e^(4t) - c2][/tex] Let us use the initial conditions to solve for c1 and c2: X(0) = [1 0]Thus, c1 + c2 = 1c1 - c2 = 0 Solving these equations gives us c1 = 1/2 and c2 = 1/2Therefore, the solution to the given initial value problem is [tex]X(t) = (1/2)[e^(4t) 1]T[/tex]

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Which of the following is not an assumption (condition) for a one- population mean hypothesis test. a. Random Sample b. Sample data should be either normal or have a sample size of at least 30. c. Individuals in sample should be independent d. Sample data should have at least ten successes and at least ten failures.

Answers

The correct answer is d. Sample data should have at least ten successes and at least ten failures.

The four assumptions for a one-population mean hypothesis test are:

1.Random Sample

2.Sample data should be either normal or have a sample size of at least 30.

3.Individuals in the sample should be independent

4.Sample data should have no less than ten successes and ten failures for hypothesis tests of proportions.

This assumption is related to the fourth assumption for a hypothesis test of proportion rather than a one-population mean hypothesis test.

Therefore, the answer is d.

Sample data should have at least ten successes and at least ten failures.

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We saw an example in lecture where there was a candidatate with more than 50% of the first place votes, but that candidate still lost the election when we used the Borda Count Method. Here's the preference table from the example: # of Votes 6 N 3 1st Choice A A B С 2nd Choice B с D 3rd Choice С D B 4th Choice D A A A Write a sentence or two describing why you think that this happened.

Answers

Candidate is ranked with 4,3,2,1 point for 1st, 2nd, 3rd, 4th choice vote respectively and the points are added to get the winner.

A candidate's placement in the voter's rank order affects how many points they receive. The winner is the contender with the most points. In the instance at hand, the Borda count does not meet the Condorcet requirement.

This is because in Borda count each candidate is ranked with 4,3,2,1 point for 1st, 2nd, 3rd, 4th choice vote respectively and the points are added to get the winner.

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An oak tree grows about 2 feet per year. Use dimensional analysis to find this growth rate in centimeters (cm) per day. Round to the nearest hundredth. Show your work. Include units in your work and result.

Answers

The growth rate of an oak tree in centimeters per day is 0.17 cm/day.

To convert the growth rate of an oak tree from feet per year to centimeters per day, we can use dimensional analysis to convert the units accordingly.

Growth rate of oak tree = 2 feet/year

We can set up the following conversion factors:

1 foot = 30.48 centimeters (since 1 foot is equal to 30.48 centimeters)

1 year = 365 days (approximate value)

We'll start with the given growth rate in feet per year and convert it to centimeters per day:

(2 feet/year) x (30.48 centimeters/foot) x (1 year/365 days)

Let's calculate the result:

= (2 feet/year) x (30.48 centimeters/foot) x (1 year/365 days)

= (2 x 30.48 / 365) (centimeters/day)

= 0.16739726027 centimeters/day

Rounding to the nearest hundredth, the growth rate of the oak tree in centimeters per day is approximately 0.17 cm/day.

Therefore, the growth rate of the oak tree is approximately 0.17 cm/day.

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A rectangular page is to contain 24 in^2 of print. The margins at the top and bottom of the page are each 1 1/2 inches. The margins on each side are 1 inch. What should the dimensions of the page be so that the least amount of paper is used?

Answers

To minimize the amount of paper used, the dimensions of the rectangular page should be 5 inches by 6 inches.

Let's assume the length of the page is x inches. Since there are 1-inch margins on each side, the effective printable width of the page would be (x - 2) inches. Similarly, the effective printable height would be (24 / (x - 2)) inches, considering the print area of 24 in^2.

To minimize the amount of paper used, we need to find the dimensions that minimize the total area of the page, including the printable area and margins. The total area can be calculated as follows:

Total Area = (x - 2) * (24 / (x - 2))

To simplify the equation, we can cancel out the common factor of (x - 2):

Total Area = 24

Since the total area is constant, we can conclude that the dimensions that minimize the amount of paper used are the ones that satisfy the equation above. Solving for x, we find x = 6. Hence, the dimensions of the page should be 5 inches by 6 inches, with 1 1/2-inch margins at the top and bottom and 1-inch margins on each side.

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what are the largest positive representable numbers in 32-bit ieee 754 single precision floating point and double precision floating point? show the bit encoding and the values in base 10.

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the largest positive representable number in 32-bit IEEE 754 single precision floating point format is approximately [tex]3.4028235 * 10^{38[/tex]., the largest positive representable number in 64-bit IEEE 754 double precision floating point format is approximately [tex]1.7976931348623157 * 10^{308.[/tex]

What is floting point?

A floating-point is a numerical representation used in computing to approximate real numbers.

In IEEE 754 floating-point representation, the largest positive representable numbers in 32-bit single precision and 64-bit double precision formats have specific bit encodings and corresponding values in base 10.

32-bit IEEE 754 Single Precision Floating-Point:

The bit encoding for a single precision floating-point number consists of 32 bits divided into three parts: the sign bit, the exponent bits, and the fraction bits.

Sign bit: 1 bit

Exponent bits: 8 bits

Fraction bits: 23 bits

The largest positive representable number in single precision format occurs when the exponent bits are set to their maximum value (all 1s) and the fraction bits are set to their maximum value (all 1s). The sign bit is 0, indicating a positive number.

Bit Encoding:

0 11111110 11111111111111111111111

Value in Base 10:

To determine the value in base 10, we need to interpret the bit encoding according to the IEEE 754 standard. The exponent bits are biased by 127 in single precision format.

Sign: Positive (+)

Exponent: 11111110 (254 - bias = 127)

Fraction: 1.11111111111111111111111 (interpreted as 1 + 1/2 + 1/4 + ... + [tex]1/2^{23[/tex])

Value = (+1) * [tex]2^{(127)[/tex] * 1.11111111111111111111111

Value ≈ 3.4028235 × [tex]10^{38[/tex]

Therefore, the largest positive representable number in 32-bit IEEE 754 single precision floating point format is approximately 3.4028235 × [tex]10^{38[/tex].

64-bit IEEE 754 Double Precision Floating-Point:

The bit encoding for a double precision floating-point number consists of 64 bits divided into three parts: the sign bit, the exponent bits, and the fraction bits.

Sign bit: 1 bit

Exponent bits: 11 bits

Fraction bits: 52 bits

Similar to the single precision format, the largest positive representable number in double precision format occurs when the exponent bits are set to their maximum value (all 1s) and the fraction bits are set to their maximum value (all 1s). The sign bit is 0, indicating a positive number.

Bit Encoding:

0 11111111110 1111111111111111111111111111111111111111111111111111

Value in Base 10:

Again, we interpret the bit encoding according to the IEEE 754 standard. The exponent bits are biased by 1023 in double precision format.

Sign: Positive (+)

Exponent: 11111111110 (2046 - bias = 1023)

Fraction: 1.1111111111111111111111111111111111111111111111111 (interpreted as 1 + 1/2 + 1/4 + ... + [tex]1/2^{52[/tex])

Value = (+1) * [tex]2^{(1023)[/tex] * 1.1111111111111111111111111111111111111111111111111

Value ≈ 1.7976931348623157 × [tex]10^{308[/tex]

Therefore, the largest positive representable number in 64-bit IEEE 754 double precision floating point format is approximately 1.7976931348623157 × [tex]10^{308[/tex].

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What substitution should be used to solve the integral x² dx S √4-9x² A sec u =3x/2 B tan u =2x/3 C sec u =2x/3 D) sinu=3x/2

Answers

The substitution to solve the integral ∫x²√(4-9x²)dx is B) tan u = 2x/3.

To determine the appropriate substitution, we can analyze the expression under the square root, which is 4-9x². Notice that the presence of a square root suggests that trigonometric substitutions may be useful.
Let's assume the substitution u = 2x/3, which implies that x = 3u/2. We can find the corresponding differential dx by differentiating both sides of the equation with respect to u: dx = (3/2)du.Substituting these expressions into the integral, we have:
∫(9u²/4)√(4-9(9u²/4)) * (3/2)du.
Simplifying further:
(27/8) ∫u²√(4-9u²)du.
At this point, we can use a trigonometric identity involving tan^2 u and sec^2 u to simplify the integrand. Specifically, we can express 4-9u² as (2/tan^2 u) - 9:
(27/8) ∫u²√[(2/tan^2 u) - 9] du.
By substituting tan u = 2x/3 into the expression, we obtain the integral in terms of u. Therefore, the correct substitution for this integral is B) tan u = 2x/3.

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A sample of size n=86 is drawn from a normal population whose standard deviation is o=8.5. The sample mean is x = 47.65. = Part 1 of 2 (a) Construct a 99.9% confidence interval for u. Round the answer to at least two decimal places. (b) If the population were not approximately normal, would the confidence interval constructed in part (a) be valid? Explain.

Answers

Confidence interval:a confidence interval is a statistical method used to estimate the range within which the true population parameter lies with a certain degree of confidence. The confidence interval is the interval (or range) between two numbers within which the true population parameter, such as a mean or proportion, is expected to fall with a certain level of confidence.

:Given that the sample size is n=86, the sample mean is x = 47.65, and the standard deviation is o=8.5, we need to construct a 99.9% confidence interval for u.a)

Summary:A 99.9% confidence interval for u was constructed using the sample mean of x = 47.65, a sample size of n=86, and a standard deviation of o=8.5. The confidence interval is (45.86, 49.44). If the population were not approximately normal, the confidence interval would not be valid.

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A sequence defined by a₁ = 2i an+1= √6 + an is a convergence sequence. Find lim n→[infinity]o an
a. 2√2
b. 6
c. 2.9
d. 3

Answers

The correct option is a. 2√2.

To find the limit of the sequence an as n approaches infinity, we can solve for the limit by setting an+1 equal to an:

an+1 = √6 + an

Substituting the given value a₁ = 2√2:

a₂ = √6 + 2√2

a₃ = √6 + (√6 + 2√2) = 2√6 + 2√2

a₄ = √6 + (2√6 + 2√2) = 3√6 + 2√2

By observing the pattern, we can see that an = (n-1)√6 + 2√2.

Now, as n approaches infinity, the term (n-1)√6 becomes negligible compared to 2√2. Therefore, the limit of the sequence is:

lim(n→∞) an = 2√2

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Determine the slope-intercept equation for the line through (1,1) which is perpendicular to the other line z+y = 4

Answers

Therefore, the slope-intercept equation for the line through (1,1) that is perpendicular to the other line z+y=4 is y=x+0.

We need to determine the slope-intercept equation for the line through (1,1) which is perpendicular to the other line z+y=4..

The slope-intercept form is y=mx+b, where m is the slope and b is the y-intercept, which is where the line intersects the y-axis.

If we want to write a line in slope-intercept form, we must have its slope and y-intercept.

We can determine the slope of a line by rearranging it into y=mx+b form.

y=mx+b is the slope-intercept form of a line where m represents the slope.

Let's rearrange the given equation in the slope-intercept form as follows:

y=-z+4

Let us determine the slope of the line. From the equation, the coefficient of z is -1, which represents the slope of the line.

Therefore, the slope of the line is -1.

The slope of a line perpendicular to a given line is the negative reciprocal of that line's slope.

Therefore, the slope of a line perpendicular to the given line is 1.

Let us apply point-slope form to find the equation of the line. We know that the line passes through the point (1, 1) and has a slope of 1.

y-y1=m(x-x1) y-1=1(x-1) y-1=x-1 y=x

Therefore, the equation of the line that passes through (1,1) with a slope of 1 is y=x.

We can write this equation in slope-intercept form by rearranging it as:

y=x+0

Therefore, the slope-intercept equation for the line through (1,1) that is perpendicular to the other line z+y=4 is y=x+0.

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let p be a prime and let a and b be relatively prime integers. prove that if p 2 | ab, then p 2 | a or p 2 | b.

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We need to prove that if p² divides ab, then p² divides a or p² divides b. Since a and b are relatively prime, p cannot divide both a and b. If p² divides ab, then it must have p in it twice.

Let p be a prime and let a and b be relatively prime integers. Now, we need to prove that if p² | ab, then p² | a or p² | b.Let's assume that p² does not divide a. Then, we can write a = p x c + r, where r is a positive integer less than p. Since a and b are relatively prime, p does not divide b. Thus, we can write pb = pxd + s, where s is a positive integer less than p. Therefore, ab = (pxc + r) (pxd + s) = p²xcd + pxr + pys + rs. Now, p² divides ab, thus, p² divides p²xcd, pxr and pys but p² does not divide rs. Thus, p² divides pxc or p² divides pxd. Hence, either p² divides a or p² divides b. Thus, we have shown that if p² | ab, then p² | a or p² | b.

It can be said that if p² divides the product of two relatively prime integers, then p² must divide either of the integers. Hence, we can prove the contrapositive of the statement: if p² does not divide a and p² does not divide b, then p² does not divide ab.

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Consider the following.
f(x) = { e^x if x < 1 a =1
x^3 if x ≥ 1
Find the left-hand and right-hand limits at the given value of a.
lim x -> 1 f(x) = ___________
lim x -> 1 f(x) = ___________
Explain why the function is discontinous at the given number a.

Answers

The left-hand limit of f(x) as x approaches 1 is e^1, which is approximately 2.71828. The right-hand limit of f(x) as x approaches 1 is 1^3, which is equal to 1.

The function is discontinuous at x = 1 because the left-hand limit (e^1) is not equal to the right-hand limit (1^3). In order for a function to be continuous at a specific point, the left-hand limit and the right-hand limit must be equal. However, in this case, the function takes on different values depending on whether x is less than 1 or greater than or equal to 1.

When x is less than 1, the function takes on the value of e^x, which approaches approximately 2.71828 as x approaches 1 from the left. On the other hand, when x is greater than or equal to 1, the function takes on the value of x^3, which equals 1 when x is 1. Therefore, the function has a jump discontinuity at x = 1.

The jump discontinuity occurs because the function "jumps" from one value to another at x = 1, without any intermediate values. This violates the definition of continuity, which requires the function to have a single, well-defined value at each point. Thus, the function is discontinuous at x = 1.

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Mr. Smith immediately replaced the battery on his radio after the radio died / did not work. Suppose the time required to replace the battery is neglected because the time is very small when compared to the life of the battery. Let N(t) represent the number of batteries that have been replaced during the first t years of the radio's life, without counting the batteries used when the radio was started.

a. Suppose that battery life is a random event that has an identical and independent distribution. What is the N(t) renewal process? Explain your answer.

b. If the battery life is a random variable whose iid (independent and identically distribution) follows a uniform distribution at intervals of (1.5) years. Determine the battery replacement rate in the long term

c. If Mr. Smith decided to keep replacing the battery if it had reached 3 years of use even though the battery was still functioning. The cost to replace the battery is $75 if replacement is planned (ie up to 3 years of use), and $125 if the battery is malfunctioning/damaged. Suppose C(t) represents the total cost incurred by Mr. Smith up to time t. Is the C(t) renewal reward process? Explain your answer.

d. find the average cost incurred by Mr. Smith in 1 year.

Answers

a)The N(t) renewal process represents the number of batteries that have been replaced during the first t years of the radio's life

b) The battery replacement rate in the long term is 1.33 batteries per year.

c) The cost varies based on the battery's condition, the C(t) process can be considered a renewal reward process.

d)  The formula would be: average cost per year = C(t) / t.

a. The N(t) renewal process represents the number of batteries that have been replaced during the first t years of the radio's life, without counting the batteries used when the radio was started.

This process is a renewal process because it involves replacing batteries at certain intervals (when they die) and starting with a new battery. Each replacement is considered as a renewal event.

b.In this case, the mean battery life is

= (1.5 years / 2)

= 0.75 years.

Therefore, the battery replacement rate in the long term is

=  1 / 0.75 = 1.33 batteries per year.

c. The C(t) renewal reward process represents the total cost incurred by Mr. Smith up to time t.

In this case, the cost incurred by Mr. Smith depends on whether the battery is replaced within 3 years or if it malfunctions/damages.

Since the cost varies based on the battery's condition, the C(t) process can be considered a renewal reward process.

d. To find the average cost incurred by Mr. Smith in 1 year, we need to calculate the average cost per year.

The formula would be: average cost per year = C(t) / t.

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Points G and H lie on the same line. The coordinate of G is - 3x +
5 and the coordinates of H is 5x + 4 If GH = 39 , find the
coordinate (s) of G.

Answers

The coordinate of point G on the line is found by substituting the given distance GH and the coordinates of point H into the equation of the line and solving for x.

Let's set up an equation to represent the distance between points G and H on the same line. The distance formula is given by d = √[(x₂ - x₁)² + (y₂ - y₁)²]. In this case, we have the coordinates of G as (-3x + 5) and the coordinates of H as (5x + 4), and the distance GH is given as 39.

Using the distance formula, we can set up the equation:

√[(5x + 4) - (-3x + 5)]² = 39

Simplifying the equation, we have:

√[8x + 1]² = 39

Squaring both sides of the equation, we get:

8x + 1 = 39²

Solving for x, we have:

8x = 39² - 1

x = (39² - 1) / 8

Evaluating the expression, we find x ≈ 75.75.

Substituting this value back into the coordinates of G (-3x + 5), we get:

G = (-3(75.75) + 5, 5)

G ≈ (13, 5)

Therefore, the coordinates of point G are approximately (13, 5).

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if log 2=a and log 3=b, determine the value of log 12 in terms of a and b

Answers

Log 12 will have a value of a.

An airport limousine service $3.5 for any distance up to the first kilometer, and $0.75 for each additional kilometer or part thereof. A passenger is picked up at the airport and driven 7.5 km.
a) Sketch a graph to represent this situation.
b) What type of function is represented by the graph? Explain
c) Where is the graph discontinuous?
d) What type of discontinuity does the graph have?

Answers

a) The graph representing the situation can be divided into two segments. The first segment, up to the first kilometer, is a horizontal line at a height of $3.5. This indicates that the price remains constant at $3.5 for any distance up to the first kilometer. The second segment is a linear line with a slope of $0.75 per kilometer. This represents the additional cost of $0.75 for each additional kilometer or part thereof. The graph starts at $3.5 and increases linearly with a slope of $0.75 for each kilometer.

b) The function represented by the graph is a piecewise function. It consists of two parts: a constant function for the first kilometer and a linear function for each additional kilometer. The constant function represents the fixed cost of $3.5 for distances up to the first kilometer, while the linear function represents the variable cost of $0.75 per kilometer for distances beyond the first kilometer.

c) The graph is discontinuous at the point where the transition from the constant function to the linear function occurs, which happens at the first kilometer mark. At this point, there is a sudden change in the rate of increase in the price.

d) The graph has a jump discontinuity at the first kilometer mark. This is because there is an abrupt change in the price as the distance crosses the one kilometer threshold. The price jumps from $3.5 to a higher value based on the linear function. The jump discontinuity indicates a clear distinction between the two segments of the graph.

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Solve Bernoulli's equation dy XC +y=(x dx n (x² In(x))y², x>0

Answers

The general solution to the equation is y = (c/x)^(1/(n-1))*(x^n In(x))^n, where c is an arbitrary constant.

To solve the equation, we can use the following steps:

1. Rewrite the equation in standard form. The equation can be rewritten in standard form as dy/dx + (1-n)y = x^n In(x)y^n.

2. Use the integrating factor method. The integrating factor for the equation is e^((1-n)x). Multiplying both sides of the equation by the integrating factor gives e^((1-n)x)dy/dx + (1-n)e^((1-n)x)y = x^n In(x)e^((1-n)x)y^n.

3. Integrate both sides of the equation. Integrating both sides of the equation gives e^((1-n)x)y = c*x^n In(x)y^n + K, where K is an arbitrary constant.

4. Divide both sides of the equation by y^n. Dividing both sides of the equation by y^n gives e^((1-n)x) = c*x^n In(x) + K/y^n.

5. Solve for y. Taking the natural logarithm of both sides of the equation gives (1-n)x = n In(x) + ln(K/y^n).

6. Exponentiate both sides of the equation. Exponentiating both sides of the equation gives (1-n)x^n = nx^n In(x) * K/y^n.

7. Simplify the right-hand side of the equation. Simplifying the right-hand side of the equation gives K/y^n = (1/n) * x^(n-1) In(x).

8. Solve for y. Taking the nth root of both sides of the equation gives y = (c/x)^(1/(n-1))*(x^n In(x))^n.

This is the general solution to the equation. The specific solution to the equation can be found by substituting the initial conditions into the general solution.

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Ashley earns 15 per hour define the varibles and state which quantity is a function of the other

Answers

Answer: Part 1:

Variable x - number of the hours.

Variable y - her total income.

y = f ( x ), Her total income is a function of the hours she worked.

Part 2 :

The function is: y = 15 * x

Part 3 :

f ( 35 ) = 15 * 35 = $525

f ( 29 ) = 15 * 29 = $435

Week 1 : Ashley worked 35 hours. She earned $525.

Week 2: Ashley worked 29 hours. She earned $435.

Step-by-step explanation: Hope u get an A!

12. College freshmen took a psychology exam. If the mean is 80, the SD is 10, and the scores have normal distribution, what percent of students failed the test (grade0030?
a.14% b. 2% c. 34% d. 48%
13. A factory has reported that 81% of their mechanical keyboards remain in a consumer's household over a year. Assuming a score of 1.5H, calculate the margin of amor for a hatch of 301 keyboar a.0.95% b.3.5% c.8% d.2.2% 16. What is the standard deviation, or, in the circumferences of the trees shown in the table below? Circumference of Trees (Feet) 3.18 4.20 4.89 3.29 5.28 4.96 a.a≈ 0.8185 b.a≈ 0.9403 c. a≈0.9782 d. a≈0.7982

Answers

a)The percent of students failed the test is 50%

b) The margin of error for a hatch is 3.5%

c) The standard deviation of the circumferences of the trees is 0.29278

The percentage of students who failed the test (grade < 30), we need to calculate the z-score for the grade of 30 using the given mean and standard deviation. The z-score formula is given by:

z = (x - μ) / σ

where x is the grade, μ is the mean, and σ is the standard deviation.

In this case, x = 30, μ = 80, and σ = 10. Substituting these values into the formula, we get:

z = (30 - 80) / 10 = -5

The percentage of students who failed the test, we need to find the area under the normal distribution curve to the left of the z-score -5. Looking up the z-score in the standard normal distribution table, we find that the area is approximately 0.5.

Since the normal distribution is symmetric, the area to the right of the z-score -5 is also 0.5. To find the percentage, we multiply this area by 100:

Percentage = 0.5 × 100 ≈ 50%

13. The margin of error for a hatch of 301 keyboards with a reported rate of 81%, we can use the formula for the margin of error for proportions:

Margin of Error = Z × √((p × (1 - p)) / n)

where Z is the z-score corresponding to the desired level of confidence (typically 1.96 for a 95% confidence level), p is the proportion, and n is the sample size.

In this case, p = 0.81 and n = 301. Substituting these values, we have:

Margin of Error = 1.96 × √((0.81 × (1 - 0.81)) / 301)

Rounding to two decimal places, the answer is approximately 3.5%.

16. The standard deviation of the circumferences of the trees, we can use the formula:

Standard Deviation = √(Σ(xi - x(bar) )² / (n - 1))

where:

Σ denotes the sum of the values

xi represents each individual circumference value

x(bar) is the mean (average) of the circumferences

n is the total number of data points (in this case, the number of trees)

First, let's calculate the mean of the circumferences:

x(bar) = (3.18 + 4.20 + 4.89 + 3.29 + 5.28 + 4.96) / 6 = 4.3

Next, we calculate the sum of the squared differences from the mean:

(3.18 - 4.3)² + (4.20 - 4.3)² + (4.89 - 4.3)² + (3.29 - 4.3)² + (5.28 - 4.3)² + (4.96 - 4.3)²

= 1.2544 + 0.01 + 0.3481 + 1.0201 + 0.9604 + 0.4356

= 4.0286

Now, we can substitute these values into the standard deviation formula:

Standard Deviation = √(4.0286 / (6 - 1))

= √(4.0286 / 5)

≈ √0.08572

≈ 0.29278

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2. Find the area between the curves x = = 10- y² and y=x-8.

Answers

Given the curves are x=  10- y² and y=x-8. Therefore, the area between them is x = 10 - y² and y = x - 8 is 16√10 square units.

To find the intersection points, we set the equations x = 10 - y² and y = x - 8 equal to each other:

10 - y² = x - 8

Rearranging the equation, we have:

y² + x = 18

Now, let's solve for x in terms of y:

x = 18 - y²

We can set up the integral to find the area between the curves:

Area = ∫[a, b] (x - (10 - y²)) dx

where a and b are the x-coordinates of the intersection points. From the equation x = 18 - y², we can see that the range of y is from -√10 to √10. Therefore, we can calculate the area using the definite integral:

Area = ∫[-√10, √10] (18 - y² - (10 - y²)) dx

Simplifying the integral:

Area = ∫[-√10, √10] (8) dx

Evaluating the integral, we get:

Area = 8[x]_[-√10, √10] = 8(√10 - (-√10)) = 8(2√10) = 16√10

Hence, the area between the curves x = 10 - y² and y = x - 8 is 16√10 square units.

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Find the stationary points of f(x):x^4/2- 12x³ +81x² + 3 and determine the nature of the stationary point in each case. For each point enter the x-coordinate of the stationary point (as an integer or single fraction) and then either A, B or C for maximum, minimum or point of inflection.
The 1st stationary point is x = The nature of this point is: where
A: maximum
B: minimum
C: point of inflection
The 2nd stationary point is a = The nature of this point is: where
A: maximum
B: minimum
C: point of inflection =

Answers

The stationary points of the function [tex]\(f(x) = \frac{x^4}{2} - 12x^3 + 81x^2 + 3\)[/tex] are calculated by finding the values of x where the derivative of the function equals zero.

Differentiating the function with respect to x, we obtain [tex]\(f'(x) = 2x^3 - 36x^2 + 162x\)[/tex]. To find the stationary points, we set f'(x) = 0 and solve for x.

By factoring out 2x, we have [tex]\(2x(x^2 - 18x + 81) = 0\)[/tex]. This equation is satisfied when x=0 or when [tex]\(x^2 - 18x + 81 = 0\).[/tex]

Solving the quadratic equation [tex]\(x^2 - 18x + 81 = 0\)[/tex] gives us the roots x=9, which means there are two stationary points: [tex]\(x = 0\) and \(x = 9\)[/tex].

To determine the nature of each stationary point, we examine the second derivative f''(x). Differentiating f'(x), we find [tex]\(f''(x) = 6x^2 - 72x + 162\)[/tex].

[tex]At \(x = 0\), \(f''(0) = 162 > 0\)[/tex], indicating that the function has a minimum at this point.

At [tex]\(x = 9\), \(f''(9) = 6(9)^2 - 72(9) + 162 = -54 < 0\)[/tex], suggesting that the function has a maximum at this point.

Therefore, the first stationary point is x = 0 and it is a minimum (B), while the second stationary point is x = 9 and it is a maximum (A).

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Subtract 62-26 +9 from 62-7b-5 and select the simplified answer below. a. -9b-14 b. -5b+4 c. -5b-14 d. -9b+4

Answers

The simplified answer of the expression [tex]62-7b-5 - (62-26+9)[/tex] is [tex]-7b+17[/tex]

The expression that we need to simplify is [tex]62-7b-5 - (62-26+9)[/tex].

We can simplify this expression by subtracting the bracketed expression from the given expression.

So, the value of [tex]62-26+9[/tex] is [tex]45[/tex].

Thus, the expression becomes [tex]62-7b-5 - 45[/tex].

Now, we can combine like terms to simplify it further.

[tex]-7b[/tex] and [tex]-5[/tex] are like terms, so they can be combined.

[tex]62[/tex]and [tex]-45[/tex] are also like terms as they are constants, so they can also be combined.

So, the simplified expression becomes [tex]-7b+17[/tex].

Therefore, the answer to the given problem is [tex]-7b+17[/tex].

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Part 2. Applying Math Concepts in a Presentation
a. Insert your own design. Draw using triangle concepts learned in this unit.
b. Indicate the measures (dimensions) of each side.
c. Show how triangle congruence played a role in your design.
d. The answer to the below questions should be part of your presentation
i. How much weight can the bridge carry? (people, vehicle and rain)
ii. How long will the bridge be and what materials should be used?
iii. How many years/months/weeks/days will it take to build?
iv. How many workers do you suggest being hired to build it?
e. Justify using the information you have which of the two bridge designs best fit the conditions needed by the investors.

Answers

(a) The trusses are to provide maximum support and distribute the weight evenly.(b)  Distance between truss segments. (c) congruence allows for the uniform distribution of weight and stability. (d) The optimal number is based on the project's requirements and desired completion timeframe. (e) It will help in making an informed decision that aligns with the investors' needs and goals.

a. Design: In my design, I have created a truss bridge using triangle concepts. The bridge consists of multiple triangular trusses connected together to form a strong and stable structure. The trusses are arranged in an alternating pattern to provide maximum support and distribute the weight evenly.

b. Measures (Dimensions):

Side 1: Length of each truss segment

Side 2: Height of each truss segment

Side 3: Distance between truss segments

c. Triangle Congruence: Triangle congruence plays a crucial role in the design of the bridge. Each triangular truss is congruent to one another, ensuring that they have the same shape and size. This congruence allows for the uniform distribution of weight and stability throughout the bridge structure.

d. Answers to Questions:

i. To determine the weight the bridge can carry, a structural analysis needs to be conducted considering factors such as material strength, bridge design, and safety regulations. An engineer would need to perform calculations based on these factors to provide an accurate weight capacity.

ii. The length of the bridge will depend on the span required to cross the intended gap or distance. The materials used for construction will depend on various factors, including the weight capacity required, budget, and environmental conditions. Common materials for bridges include steel, concrete, and composite materials.

iii. The construction time for the bridge will depend on several factors, such as the size and complexity of the bridge, the availability of resources, and the number of workers involved. A construction timeline can be estimated by considering these factors and creating a detailed project plan.

iv. The number of workers required to build the bridge will depend on the project's scale, timeline, and available resources. A construction manager can determine the optimal number of workers needed based on the project's requirements and the desired completion timeframe.

e. Justification: To determine which bridge design best fits the conditions needed by the investors, we need more information about the specific requirements, budget constraints, and other factors such as environmental considerations and aesthetics.

Additionally, the weight capacity, length, construction time, and workforce requirements would need to be evaluated for each design option. Conducting a thorough analysis and comparing the designs based on these factors will help in making an informed decision that aligns with the investors' needs and goals.

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C) Find the solution y(x) to the initial value problem in terms of a definite integral. 39. xy' – 3y = sin(x) y(2) = 24 SOLUTION: The equation is rewritten as y'-(3/x)y = sin(x)/x. The integrating factor = x-?. So (x-*y)' = x * sin(x). x-Py = $** sin(t)dt + c *S*:*sin(t)dt+Cx? y(2) = 24 gives 24 = 8(0) + C(8), or C = 3. So =x***sin(t)dt+3x'o. y = x y = x 45. (x*+8)y' +2x®y = 1, y(-1) = 1.

Answers

Here is the solution to the initial value problem, y(x) in terms of a definite integral: (x^2+8)y' +2x²y = 1, y(-1) = 1

The given differential equation is rewritten as y' - ( - 2x / (x^2+8) ) y = 1 / (x^2+8) Multiplying both sides by the integrating factor, e^(- ln(x^2+8) / 2), we havee^(- ln(x^2+8) / 2) y' - ( - 2x / (x^2+8) ) e^(- ln(x^2+8) / 2) y = e^(- ln(x^2+8) / 2) / (x^2+8)

\

Applying the product rule, we get (e^(- ln(x^2+8) / 2) y)' = e^(- ln(x^2+8) / 2) / (x^2+8) x e^( ln(x^2+8) / 2) = e^( ln(x^2+8) / 2) / (x^2+8)

Integrate both sides with respect to x to gete^(- ln(x^2+8) / 2) y = ∫ [ e^( ln(x^2+8) / 2) / (x^2+8) ] dx e^(- ln(x^2+8) / 2) y = ( 1 / 2 ) ln( x^2 + 8 ) + C e^( ln(x^2+8) / 2 ) y = ( x^2 + 8 )^(1/2) * ( 1 / 2 ) + C(x^2+8)^(-1/2)

Applying the initial condition, y(-1) = 1, we have 1 = ( 9 )^(1/2) * ( 1 / 2 ) + C(9)^(-1/2) => C = 1/6

Therefore, the solution of the given differential equation isy(x) = ( x^2 + 8 )^(1/2) * ( 1 / 2 ) + (1/6) * (x^2+8)^(-1/2)

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1. How does the interpretation of the regression coefficients differ in multiple regression and simple linear regression? 2. A shoe manufacturer is considering developing a new brand of running shoes. The business problem facing the marketing analyst is to determine which variables should be used to predict durability (i.e., the effect of long-term impact). Two independent variables un- der consideration are X 1 (FOREIMP), a measurement of the forefoot shock-absorbing capability, and X 2 (MIDSOLE), a measurement of the change in impact properties over time. The dependent variable Y is LTIMP, a measure of the shoe's durability after a repeated impact test. Data are collected from a random sample of 15 types of currently manufactured running shoes, with the following results: Standard Variable Coefficients Error t Statistic p-Value Intercept -0.02686 -0.39 0.7034 0.06905 0.06295 12.57 FOREIMP 0.79116 0.0000 MIDSOLE 0.60484 0.07174 8.43 0.0000 A: state the multiple regression equation b. interpret the meaning of the slopes, b1 and b2 in this problem. c. what conclusions can you reach concerning durability?

Answers

The multiple regression equation is [tex]LTIMP[/tex]= -0.027 + 0.791*[tex]FOREIMP[/tex]+ 0.605*[tex]MIDSOLE[/tex]. Both [tex]FOREIMP[/tex]and [tex]MIDSOLE[/tex] have positive and significant coefficients (0.791 and 0.605, respectively).

The multiple regression equation can be stated as:

[tex]LTIMP = -0.02686 + 0.79116FOREIMP + 0.60484MIDSOLE[/tex]

The slopes (b1 and b2) represent the change in the dependent variable ([tex]LTIMP[/tex]) for a one-unit increase in the corresponding independent variable ([tex]FOREIMP[/tex]and [tex]MIDSOLE[/tex]), holding other variables constant. Specifically, for every one-unit increase in [tex]FOREIMP[/tex], [tex]LTIMP[/tex] is expected to increase by 0.79116, and for every one-unit increase in [tex]MIDSOLE[/tex], [tex]LTIMP[/tex]is expected to increase by 0.60484.

Based on the coefficients' significance and magnitude, we can conclude that both [tex]FOREIMP[/tex] and [tex]MIDSOLE[/tex]are significant predictors of durability ([tex]LTIMP[/tex]) in running shoes. A higher value of [tex]FOREIMP[/tex] and [tex]MIDSOLE[/tex] is associated with greater durability. However, further analysis, such as assessing the p-values and confidence intervals, is necessary to determine the strength and significance of the relationships and to draw more robust conclusions about durability based on the given data.

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A rectangular plot of land adjacent to a river is to be fenced. The cost of the fence that faces the river is $10 per foot. The cost of the fence for the other sides is $3 per foot. If you have $1379, how long should the side facing the river be so that the fenced area is maximum? (Round the answer to 2 decimal places)

Answers

To maximize the fenced area with a given budget, the length of the side facing the river should be 45.70 feet. Let's denote the length of the side facing the river as "x" and the width of the rectangular plot as "y."

We want to maximize the area of the rectangular plot, which is given by the formula A = x * y. The cost of the fence along the river is $10 per foot, and the cost of the fence for the other sides is $3 per foot. Therefore, the total cost of the fence can be expressed as C = 10x + 3(2x + y), where 2x represents the sum of the other two sides.

We are given a budget of $1379, so we can set up the equation 10x + 3(2x + y) = 1379 to represent the cost constraint.

To maximize the area, we need to solve for y in terms of x from the cost equation and substitute it into the area formula. After some calculations, we arrive at y = (1379 - 16x) / 3.

Substituting this value of y into the area formula, A = x * y, we get A = x * (1379 - 16x) / 3.

To find the maximum area, we can differentiate A with respect to x, set the derivative equal to zero, and solve for x. By applying the first derivative test, we find that x = 45.70 feet maximizes the area.

Therefore, the length of the side facing the river should be approximately 45.70 feet to maximize the fenced area within the given budget.

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Giving a test to a group of students the grades and gender are
summarized below.
if one student was chosen at random find the probability that
the student got a "C" .
give your answer as a fraction o
Giving a test to a group of students, the grades and gender are summarized below A B C Total Male 18 16 14 48 Female 17 7 4 28 Total 35 23 18 76 If one student was chosen at random,
Find the probability that the student got a B:
Find the probability that the student was female AND got a "C":
Find the probability that the student was female OR got an "B":
If one student is chosen at random, find the probability that the student got a 'B' GIVEN they are male:

Answers

In conclusion:

a) The Probability of a student getting a B is 23/76.

b) The probability of a student being female and getting a C is 1/19.

c) The probability of a student being female or getting a B is 51/76.

d) The probability of a student getting a B given that they are male is 1/3.

The given probabilities, let's use the information provided:

Total number of students: 76

Number of students who received a B: 23

Number of female students who received a C: 4

Number of female students: 28

Number of male students: 48

a) Probability that the student got a B:

To find the probability of a student receiving a B, we divide the number of students who received a B by the total number of students:

P(B) = Number of students who received a B / Total number of students

P(B) = 23 / 76

P(B) = 23/76 (Answer: 23/76)

b) Probability that the student was female AND got a C:

To find the probability of a student being female and receiving a C, we divide the number of female students who received a C by the total number of students:

P(Female and C) = Number of female students who received a C / Total number of students

P(Female and C) = 4 / 76

P(Female and C) = 1/19 (Answer: 1/19)

c) Probability that the student was female OR got a B:

To find the probability of a student being female or receiving a B, we add the number of female students to the number of students who received a B and then divide by the total number of students:

P(Female or B) = (Number of female students + Number of students who received a B) / Total number of students

P(Female or B) = (28 + 23) / 76

P(Female or B) = 51/76 (Answer: 51/76)

d) Probability that the student got a B GIVEN they are male:

To find the probability of a student receiving a B given that they are male, we divide the number of male students who received a B by the total number of male students:

P(B|Male) = Number of male students who received a B / Number of male students

P(B|Male) = 16 / 48

P(B|Male) = 1/3 (Answer: 1/3)

In conclusion:

a) The probability of a student getting a B is 23/76.

b) The probability of a student being female and getting a C is 1/19.

c) The probability of a student being female or getting a B is 51/76.

d) The probability of a student getting a B given that they are male is 1/3.

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Please help!! This is a Sin Geometry question

Answers

In the given diagram, by using trigonometry, the value of sin θ is √5/5. The correct option is D) √5/5

Trigonometry: Calculating the value of sin θ

From the question, we are to determine the value of sin θ in the given diagram

First,

We will calculate the value of the unknown side length

Let the unknown side be x

By using the Pythagorean theorem, we can write that

(5√5)² = 10² + x²

125 = 100 + x²

125 - 100 = x²

25 = x²

x = √25

x = 5

Now,

Using SOH CAH TOA

sin θ = Opposite / Hypotenuse

sin θ = 5 / 5√5

sin θ = 1 / √5

sin θ = √5/5

Hence, the value of sin θ is √5/5

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5) Use the vectors v = i +4j and w = 3i - 2j to find: () -v+2w (b) Find a unit vector in the same direction of v. (c) Find the dot product v. w

Answers

-v+2w is equal to 5i - 8j. The unit vector in the same direction as v will be: u = v/|v| = (i + 4j)/√17. The dot product of v and w is equal to -5.

a) To find -v+2w, we have to substitute the given vectors in the equation:

v = i + 4j and w = 3i - 2j

Now we can write the following:-v+2w = -(i + 4j) + 2(3i - 2j) = -i - 4j + 6i - 4j = 5i - 8j

Therefore, -v+2w is equal to 5i - 8j.

b) Let v be the given vector: v = i + 4j

The magnitude of v is given by the formula:|v| = √(vi² + vj²) = √(1² + 4²) = √17

Now the unit vector in the same direction as v will be: u = v/|v| = (i + 4j)/√17

Therefore, the unit vector in the same direction as v is given by (i + 4j)/√17.

c) To find the dot product of v and w, we have to substitute the given vectors in the equation: v = i + 4j and w = 3i - 2j

The dot product of v and w is given by the formula: v·w = (vi)(wi) + (vj)(wj) = (1)(3) + (4)(-2) = -5

Therefore, the dot product of v and w is equal to -5.

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6 ✓7 08 x9 10 11 12 13 14 15 Genetics: A geneticist is studying two genes. Each gene can be either dominant or recessive. A sample of 100 individuals is categorized as follows. Write your answer as a fraction or a decimal, rounded to four decimal places.


Gene 2
Dominant Recessive
Dominant 52 28
Gene 1
Recessive 16 4

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(a) What is the probability that in a randomly sampled individual, gene 1 is dominant?
(b) What is the probability that in a randomly sampled individual, gene 2 is dominant?
(c) Given that gene I is dominant, what is the probability that gene 2 is dominant?
(d) Two genes are said to be in linkage equilibrium if the event that gene I is dominant is independent of the event that gene 2 is dominant. Are these genes in linkage equilibrium?

Part: 0 / 4 Part 1 of 4
The probability that gene 1 is dominant in a randomly sampled individual is

Answers

(a) The probability that gene 1 is dominant is 0.5200.

(b) The probability that gene 2 is dominant is 0.2800.

(c) Given gene 1 is dominant, the probability that gene 2 is dominant is 0.5385.

(d) The genes are not in linkage equilibrium since the probability of gene 2 being dominant depends on the dominance of gene 1.

(a) The probability that in a randomly sampled individual, gene 1 is dominant can be calculated by dividing the number of individuals with the dominant gene 1 by the total sample size.

In this case, the number of individuals with dominant gene 1 is 52, and the total sample size is 100. Therefore, the probability is 52/100 = 0.5200.

(b) Similarly, the probability that in a randomly sampled individual, gene 2 is dominant can be calculated by dividing the number of individuals with the dominant gene 2 by the total sample size.

In this case, the number of individuals with dominant gene 2 is 28, and the total sample size is 100. Therefore, the probability is 28/100 = 0.2800.

(c) To calculate the probability that gene 2 is dominant given that gene 1 is dominant, we need to consider the individuals who have dominant gene 1 and determine how many of them also have dominant gene 2.

In this case, out of the 52 individuals with dominant gene 1, 28 of them have dominant gene 2. Therefore, the probability is 28/52 = 0.5385.

(d) To determine if the genes are in linkage equilibrium, we need to assess if the event that gene 1 is dominant is independent of the event that gene 2 is dominant. If the two events are independent, then the probability of gene 2 being dominant should be the same regardless of whether gene 1 is dominant or recessive.

In this case, the probability that gene 2 is dominant given that gene 1 is dominant (0.5385) is different from the probability that gene 2 is dominant overall (0.2800). This suggests that the genes are not in linkage equilibrium, as the occurrence of dominant gene 1 affects the probability of gene 2 being dominant.

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Please note, that those two campuses are independent of each otherA) what is the appropriate tool to perform the hypothesis testing in this questionB) What is the test statistic? You deposit $500 into a saving account at ABC Bank near your house for 2 years. At the end of 2 years, you withdraw all your money and received a total sum of $600. The interest rate/year earned from this saving account should be? Simon Company's year-end balance sheets follow. At December 31 Current Year 1 Year Ago 2 Years Ago Assets Cash $ 36,000 $ 37,200 $ 31, 200 87,800 Accounts receivable, net 64,000 51,000 110,500 83,000 during the month of july 22 836 new cars and 57693 used cars were sold what is the residual for this data point a solution has a volume of 0.709 l and contains 7.95 mol of ammonium nitrate (nh4no3). what is the molarity of the solution could this trna conform to the nearly universal genetic code? Saved An appliance manufacturer claims to have developed a compact microwave oven that consumes a mean of no more than 250 W. From previous studies, it is believed that power consumption for microwave ovens is normally distributed with a population standard deviation of 15 W. A consumer group has decided to try to discover if the claim appears true. They take a sample of 20 microwave ovens and find that they consume a mean of 257.3 W. For a test with a level of significance of 0.01, the critical value would be 1) 1.96 2) -2.33 3) -1.96 4) -2.58 largo+company+recorded+for+the+past+year+sales+of+$730,000+and+average+operating+assets+of+$292,000.+what+is+the+margin+that+largo+company+needed+to+earn+in+order+to+achieve+an+roi+of+32.5%? 12.journalize the issuance of a stock dividend that was 5% of 50,000common shares outstanding and par value was $2 and selling pricewas $20 Find the mean, u, for the binomial distribution which has the stated values of and p. Round your answer to the nearest tenth.n=20 P=1/5 2.4 N =^R =//=0,2 d = 5 15 20.012=4 04 R Describe the circumstances that limit the liability of the auditors. In how many ways we can construct a different numbers consisting of 4 digits from odd numbers A The statistics computed below use data from a number of recent releases that includes the USGross (in $), the Budget ($), the Run Time (minutes), and the average number of stars awarded by reviewers. The multiple regression equation is shown below. A middle manager at an entertainment company, upon seeing this analysis, concludes that the longer you make a movie, the less money it will make. He argues that his company's films should all be cut by 25 minutes to improve their gross. Explain the flaw in his interpretation of this model. USGross= - 22.9898 + 1.13442Budget + 24.9724Stars - 0.403296RunTime Choose the correct answer below. A. The model says that longer films had larger gross incomes after allowing for Budget and Stars, so making a movie longer will increase its gross. B. The model says that longer films had smaller gross incomes after allowing for Budget and Stars, but it does not say that making a movie shorter will increase its gross. C. Since the coefficient for Run Time is less than one, making a movie shorter may or may not increase its gross. D. Since the coefficient for Run Time is so small, the studio should cut the films by more than 25 minutes to increase gross income. Find the rate of change with respect to t of the function f(x, y) = 5xy along the parametric curve * = 4cos, y = 3t and express your answer in terms of t. Then find f'(1) at the point t = Write the 2 exact answer. Do not round. Answer 2 Points . Keyboard Shor 16) - = the ratio of women to men in a local book club is 7 to 3. whitch combanation of women to the total could the club have 10. Find the 96% confidence interval (CI) and margin of error (ME) for the mean heights of men when: n = 28 , = 175 cm, s = 21 cm Interpret your results. (8 pts) I abia Explain 5 areas in which the concept of elasticity of de becomes useful to business and governm A good is produced using $160 in imported inputs. The current domestic price of the good is $200. For each of the following cases, find the level of effective rate of protection. The nominal tariff rate on the good is 10%, and there is no tariff on the inputs. b. The nominal tariff rate on the good is 10%, and there is a 10% tariff on the inputs. c. The nominal tariff rate on the good is 0%, and there is a 10% tariff on the inputs.