Let T be the outcome of a roll with a fair die.
a. Describe the probability distribution of T ; that is, list the outcomes and the corresponding probabilities.
b. Determine E[T] and Var(T).

The number of hours to operate the mines to minimize cost are Mine 1 hour = 30 hours and Mine 2 hour = 10 hours

The given parameters can be represented using the following table of values

                             Mine 1 (x)              Mine 2 (y)   Available

Regular grade          5                            20             350

Low grade               17                             10              610

Operating cost      7000                     29000

Time                        54                              27

From the table, we understand that we are to minimize cost

This means that:

Objective function: C = 7000x + 29000y

Subject to:

5x + 20y ≥ 350

17x + 10y ≥ 610

Next, we plot the constraints on a graph (see attachment)

From the graph, we have

(x, y) = (30, 10)

This means that

Mine 1 hour = 30 hours

Mine 2 hour = 10 hours

Hence, the number of hours are 30 and 10 hours

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For the  given  quadratic function, the  highest  point  that the object  reaches is  (5, 768).

Since we are given with the quadratic function of h(t)=−16t2+160t+368, where  Let a = -16, b = 160, and c = 368, so the vertex for the equation will be  :t = -b/2a = -(160)/2(-16) = -160/(-32) = 5, so substituting this value  in the equation for the value of t is

h(5) = -16(5)2 + 160(5) + 368 = -400 + 800 + 368 = 768

Here the highest point that the object reaches is (5, 768), which means that  at a time of 5 seconds, the object reaches the building after being launched at the height of  768 feet  

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We are standing on the top of a 368 feet tall building and launching a small object upward. The object's vertical position, measured in feet, after t seconds is

We are standing on the top of a 1200 feet tall building and launch a small object upward. The object's vertical position, measured in feet, after t seconds is  What is the highest point that the object reaches?

40 pounds of salami are purchased by a deli for its renowned grinder sandwiches. An illustration of an intermediate good is salami.

Given fill-in-the-blank;

A deli buys 40 pounds of salami for its famous grinder sandwiches. the salami is an example of___ goods.

The answer for this case is Intermediate.

A deli buys 40 pounds of salami for its famous grinder sandwiches. the salami is an example of Intermediate goods.

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The cumulative distribution function, for

a > 0 is  F((x - b)/a) and for  a < 0 is 1 -  F((x - b)/a).

What is cumulative distribution function?

The cumulative distribution function of a real-valued random variable X, or simply the distribution function of X, evaluated at x, is the probability that X will take a value less than or equal to x in probability theory and statistics.

We have to find the c.d.f  of ax + b for a > 0 and a < 0.

F(x) = P(X < x)

a>0:

P(aX + b < x) = P(aX < (x - b)) = P(X < (x - b)/a) = F((x - b)/a)

a < 0 :

P(aX + b < x) = P(aX < (x - b)) = P(X > (x - b)/a) = 1 - P(X < (x - b)/a) =

1 -  F((x - b)/a).

Hence, the cumulative distribution function, for

a > 0 is  F((x - b)/a) and for  a < 0 is 1 -  F((x - b)/a).

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The histogram that represents the data-set in this problem is given by the image shown at the end of the answer.

An histogram is a graph that shows the number of times each element of x was observed.

For this problem, the elements are divided in ranges, hence the histogram will give the number of elements in each range that was observed.

The ranges for this histogram are given as follows:

The number of elements in each range is given as follows:

Meaning that the third histogram, from the top down, is the correct option.

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Grape flavor has the smallest ratio of mix to water.

What is ratio proportion?

A ratio in mathematics is a comparison of two or more numbers that shows how big one is in comparison to the other. The dividend or number being divided is referred to as the antecedent, and the divisor or number that is dividing is referred to as the consequent. A ratio compares two numbers by division.

Here, we have

The ratios of punch mix to water for several fruit drinks as Grape mix (1 Grape flavor has the smallest ratio of mix to water.

cup to 3 cups), Cherry mix (5 cups to 12 cups), Lemon mix (7 cups to 12 cups), and Orange mix (2 cups to 3 cups).

We have to find which flavor has the smallest ratio of mix to water.

So, we compare all the given proportions by having a common base.  

Proportions of grape, cherry, lemon, and orange mixed in water = 1/3, 5/12, 7/12, 2/3

Now let us have a common denominator 12 as LCM of 3 and 12 is 12.  

Proportions of grape, cherry, lemon, and orange mixed with water = 1×4/3×4, 5/12, 7/12, 2×4/3×4

Proportions of grape, cherry, lemon, and orange mixed with water = 4/12, 5/12, 7/12, 8/12

Hence, the Grape flavor has the smallest ratio of mix to water.

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The fraction of Josh's height which is 2/3 of Josh's current height indicates that the equation that can be used to  find Josh's height and Josh's current height are;

a. (2/3) × h 4 1/2 feet

b. 6 3/4 feet

A fraction of an item is a representation of the whole or entire of the item.

Josh's height two years ago = (2/3) × Josh's height now

Hosh's height two years ago = 4 1/2  feet

a. Josh's current height, = h

An equation is mathematical statement that joins two equivalent expressions with an equal to sign.

(2/3) of Josh's current height is equivalent to Josh's initial height of 4 1/2 feet.

The equation that can be written to solve for h is therefore;

b. h = (4 1/2)/(2/3) = (4 1/2) × 3/2

4 1/2 = 9/2

Therefore;

h = 9/2 × 3/2 = 27/4 = 6 3/4

Josh's current height, h = 6 3/4 feet

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Question 1

[tex]a=1, r=1/2 \implies S_{\infty}=\frac{1}{1-(1/2)}=\boxed{2}[/tex]

Question 2

[tex]d=10, a_1+5d=52 \implies a_1=2 \\ \\ a_{15}=a_1+14d=2+14(10)=\boxed{142}[/tex]

The prime number that cannot be in the set is A . 2.

Prime number:

In math, prime number is a natural number greater than 1 that is not a product of two smaller natural numbers

Given,

Here we need to find the prime number that is not in the set, if if the sum of a set of ten different positive prime numbers is an even number.

Here we know that, all prime numbers except the first prime number are odd except 2.

And here we assume that the two prime numbers are different,

So, if one of the prime number is 2 which is even, the other prime number would be odd and hence sum of the prime numbers would be odd as sum of an even and an odd number is always odd.

Where as if none of the prime numbers are odd, then both the prime numbers would be odd and hence sum of the prime numbers would be even as sum of two odd numbers is always even.

There the correct option is A. 2.

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Answer:

(x - 3 i) (x + 3 i) (x + 3)

Step-by-step explanation:

Yes, it is possible that one-to-one function and its inverse are true. If f(f(x)) = x then function and its inverse coincide.

If each x-value corresponds to exactly one y-value, the function is said to be one-to-one.  Inverse function graphs are reflections of the y = x line. This indicates that there can be only one y-value for each x-value. One-to-one functions are those that fit this description.

Inverse of function is represented by [tex]f^{-1} (x)[/tex].

Test to check inverse function: If and only if no horizontal line intersects the graph of f at more than one location, then the function f is one-to-one and possesses an inverse function.

Example: f(x) = 5-x

f(f(x))= 5- (5-x) = x

So above function is one to one and inverse of itself.

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The types of angles include the supplementary, complementary, adjacent and vertical angles.

An angle is defined as the common point that is being formed when two straight lines meet at a common endpoint.

There are various types of angles that include the following:

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At tα/2= -1.66, we reject H0.

What is the Null hypothesis?

The null hypothesis is a standard statistical theory that contends there is no statistical relationship or significance between any two sets of observed data and measured phenomena for any given single observed variable.

Data provided

sample size is 100, and

sample mean, 52.0 for x

The standard deviation of the sample, s= 22.0

Average population, = 60.0

Level of significance, = 0.05

Theorem testing

The alternate and the null hypothesis is

H0: u = 60

Ha: u < 60

Crucial component:

value crucial at 0.05

tα/2= -1.66

Region of rejection:

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A person who watches 14 hours of TV can do 21.1 sit-ups.

The regression equation is used to predict or estimate the value of the response (or dependant) variables based on an understanding of the explanatory (or predictor) variables.

A regression equation has the following general form:

y = ax + b

Here,

y = dependent variable

x = independent variable

a = intercept

b = slope

The regression equation showing the relationship between the number of sit-ups a person can accomplish (y) and the number of hours of TV viewed each day (x) is:

y = -1.284x + 39.108

Compute the number of sit-ups a person who watches 14 hours of TV can do as follows:

y = -1.284(14) + 39.108

y = -17.976 + 39.108

y = 21.132 ≈ 21.1

Thus, a person who watches 14 hours of TV can do 21.1 sit-ups.

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The probability of a coin landing on heads 4 times in a row is 1/16 or, 6.25%, the probability of flipping a coin and it landing heads is 1/2 or, 50%, the probability that exactly four students toss heads at least 4 times each is 1/16 or, 6.25%, and the probability of getting heads both times the coin is flipped is 0.25.

There are different situations for us stated as -

(a) What is the probability of a coin landing on heads 4 times in a row?

(b) What is the probability of flipping a coin and it landing heads?

(c) What is the probability that exactly four students toss heads at least 4 times each?

(d)What is the probability of flipping a coin and getting heads both times?

We have to find out the probability of the given situations happening.

(a) It is known to us that a coin is flipped.

We have to determine the probability of this coin landing on heads 4 times in a row.

In order to get 4 heads in a row, the coin should be flipped 4 times.

For n (say) number of heads, the value of n = 0, 1, 2, 3, 4

Total number of possible outcomes = 16

It can be concluded that there is only one possible outcome that will result in the coin landing on 4 heads where each flip ends up as a head.

So, the probability = 1/16

Thus, the probability of a coin landing on heads 4 times in a row is 1/16 or, 6.25%.

(b) It is known to us that a coin is flipped.

We have to find out the probability of this flipped coin landing on heads.

When a coin is flipped in the air, there is always 50% chance of the coin landing on heads and a 50% chance of the coin landing on tails.

So, the probability = 1/2

Thus, the probability of flipping a coin and it landing heads is 1/2 or, 50%.

(c) It is known to us that exactly four students toss coins.

We have to determine the probability that exactly four students toss heads at least 4 times each.

As mentioned in the previous part of the question, there is always 50% chance of the coin landing on heads.

So, the probability of getting heads when the coin is flipped first = 1/2

=> the probability of getting two heads in a row = 1/2 * 1/2 = 1/4

=> the probability of getting three heads in a row = 1/2 * 1/4 = 1/8

=> the probability of getting four heads in a row = 1/2 * 1/8 = 1/16

Thus, the probability that exactly four students toss heads at least 4 times each is 1/16 or, 6.25%.

(d) It is known to us that a coin is flipped.

We have to find out the probability of getting heads both times.

Since, there is always 50% chance of the coin landing on heads. So, the probability of getting heads both times = 0.5 * 0.5 = 0.25

Thus, the probability of getting heads both times the coin is flipped is 0.25.

Therefore, the probability of a coin landing on heads 4 times in a row is 1/16 or, 6.25%, the probability of flipping a coin and it landing heads is 1/2 or, 50%, the probability that exactly four students toss heads at least 4 times each is 1/16 or, 6.25%, and the probability of getting heads both times the coin is flipped is 0.25.

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Answer:

1.3 to the twenty-eighth power over 1.2 to the twenty-first power

Step-by-step explanation:

The equivalent expression for 1.2 cubed over 1.3 raised to the fourth power all raised to the power of negative seven is 1.3 cubed over 1.2 raised to the fourth power.

To find the equivalent expression, we need to use the rule that x^a / x^b = x^(a-b) for any value of x except 0.

In this case, we have 1.2^3 / 1.3^4 raised to the power of -7. Applying the rule, we get:

(1.2^3 / 1.3^4)^-7 = (1.2^(-4) / 1.3^3)^7

Since the exponent of a number raised to a power is the same as the power, we can rewrite the expression as:

1.2^(-47) / 1.3^(37)

Simplifying, we get:

1.2^(-28) / 1.3^(21)

Which is the same as:

1.3^(21) / 1.2^(28)

This is the same as the expression 1.3 cubed over 1.2 raised to the fourth power. Therefore, the equivalent expression for 1.2 cubed over 1.3 raised to the fourth power all raised to the power of negative seven is 1.3 cubed over 1.2 raised to the fourth power.

It's true, any irrational number squared will result in a rational number

A real number that can NOT be made by dividing two integers (an integer has no fractional part).

"Irrational" means "no ratio", so it isn't a rational number. We aren't saying it's crazy!

Its decimal also goes on forever without repeating.

A counterpart problem in measurement would be to find the length of the diagonal of a square whose side is one unit long; there is no subdivision of the unit length that will divide evenly into the length of the diagonal. (See Sidebar: Incommensurables.) It thus became necessary, early in the history of mathematics, to extend the concept of number to include irrational numbers. Irrational numbers such as π can be expressed as an infinite decimal expansion with no regularly repeating digit or group of digits. Together the irrational and rational numbers form the real numbers.

Irrational numbers are those that cannot be expressed as a fraction of integers.

 If we square the irrational numbers then it becomes rational numbers as it can be shown as ratio of integers.

[tex]\sqrt{3}[/tex]  is a irrational number but by squaring it [tex](\sqrt{3 )^{2}[/tex] is a rational number

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The greatest common factor for the fraction is 26.

What is fraction?

A fraction represents a district of an entire or, additional typically, any range of equal components. once spoken in everyday English, a fraction describes what number components of an exact size there area unit.

Main body:

According to the question,

fraction = 52/78

to find its common factor , we need to write it in form of multiples of its factors,

52 = 2*2*13

78 = 2*3*13

from this it is clear that both 52, 78 has factor as 2*13

Hence the greatest common factor for the fraction is 26

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If On December 31, a corporation determines that they have income taxes expense of $20,000, with $15,000 currently due. the journal entry is Debit Income taxes expense $20,000, Credit income taxes payable $15,000 Credit Deferred income tax liability $5,000.

Based on the given information the appropriate journal entry to record the transaction is"

Journal entry

Debit Income taxes expense $20,000

Credit income taxes payable $15,000

Credit Deferred income tax liability $5,000

($20,000 -$5,000)

(To record income taxes)

Therefore the entry is Debit Income taxes expense ,Credit income taxes payable and Credit Deferred income tax liability.

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The four types of probability sampling methods are

1. Simple random sampling

2. Stratified sampling

3. Systematic sampling

4. Cluster sampling

Probability sampling is a sampling method that involves randomly selecting a sample, or a part of the population that you want to research.

1. Simple Random Sampling: Simple random sampling gathers a random selection from the entire population, where each unit has an equal chance of selection. This is the most common way to select a random sample.

2. Stratified Sampling: Stratified sampling collects a random selection of a sample from within certain strata, or subgroups within the population. Each subgroup is separated from the others on the basis of a common characteristic.

3. Systematic Sampling: Systematic sampling draws a random sample from the target population by selecting units at regular intervals starting from a random point. This method is useful in situations where records of target population already exist.

4. Cluster Sampling: Cluster sampling is the process of dividing the target population into groups, called clusters. A randomly selected subsection of these groups then forms the sample. It usually involves existing groups that are similar to each other in some way

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A function is a relationship between inputs and outputs, while a power is a mathematical operation that represents repeated multiplication.

In mathematics, a function is a relation between a set of inputs and a set of possible outputs with the property that each input is related to exactly one output. Functions are often represented by equations, which specify the relationship between the inputs and outputs.

A power, on the other hand, is a mathematical operation that represents repeated multiplication of a number by itself. The number that is being multiplied is called the base, and the number of times it is multiplied is called the exponent. For example, in the power 3⁴, the base is 3 and the exponent is 4, which represents 3 multiplied by itself 4 times, or 333*3.

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The long-run average resulting from repeated sampling of members of the fitness center will approach 3.12 days per week.

A variable is a quantity that could alter when used in a mathematical problem or experiment. Normally, a variable is denoted by a single letter. Common generic symbols used for variables include the letters x, y, and z.

Any traits, figure, or amount that can be gauged or counted is referred to as a variable. An alternative name for a variable is a data item. Age,  business earnings and expenses, country of birth, capital expenditures, class grades, eye color, and car kind are a few examples of variables.

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In the ellipse, the center is (-3/2,5/2) semi-major axis is 2√3 and the semi-minor axis is 2.

What is ellipse?

In addition to being drawn outside the ellipse, the directrix of the ellipse is parallel to its latus rectum. There are two directions on the ellipse that are parallel to its principal axis. The ratio of distances between any point on an ellipse and its foci, as well as the directrix of the ellipse, is used to define an ellipse's eccentricity, and it is less than 1.

6x^(2)+2y^(2)+18x-10y+2=0

[tex]\frac{\left(x-\left(-\frac{3}{2}\right)\right)^2}{2^2}+\frac{\left(y-\frac{5}{2}\right)^2}{\left(2\sqrt{3}\right)^2}=1[/tex]

[tex]\left(h,\:k\right)=\left(-\frac{3}{2},\:\frac{5}{2}\right),\:a=2,\:b=2\sqrt{3}[/tex]

[tex]\mathrm{Ellipse\:with\:center}\:\left(h,\:k\right)=\left(-\frac{3}{2},\:\frac{5}{2}\right),\:\:b=2\sqrt{3},\:\:a=2[/tex]

Hence, In the ellipse, the center is (-3/2,5/2) semi-major axis is 2√3 and the semi-minor axis is 2.

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Answer: 1980

Step-by-step explanation:

1. If 4 sessions is 330 dollars, and how much is 24 sessions you have to multiply 4 times 6 and the answer is 24.

2. If 4 times 6 is 24 you have to multiply 330 by 6

3. We break down 330 dollars, so 300 times 6 is 1800, i like to take away  the zeros so 3 times 6 is 18 and we add 2 zeros becuase 300 has 2 zeros. And we do the same think with 30, but this time add 1 zero because 30 has 1 one zero.

4. the answer is 1800 dollars, you're welcome!

Answer:

  x = √41

Step-by-step explanation:

Given a right trapezoid with bases 10 and 14, and height 5, you want the length of the angled side, x.

The length x is the hypotenuse of a right triangle with one leg 5 units and the other leg (14 -10) = 4 units. It can be found using the Pythagorean relation:

  c² = a² +b²

  x² = 5² +4² = 25 +16 = 41

  x = √41 . . . . . take the square root

If a decision maker wishes to reduce the margin of error associated with a confidence interval estimate for a population mean, she can decrease the sample size. So the option a is correct.

If a decision maker wishes to reduce the margin of error associated with a confidence interval estimate for a population mean, then we have to explain what she can:

decrease the sample size.

increase the confidence level.

increase the sample size.

increase the sample size.

As we know that;

The formula of Margin of Error is;

ME = Z(α)× √σ^2/n

where; ME = margin of error

α = confidence level

z(α) = quantile

σ = standard deviation

n = sample size

So as we can see that Margin of Error is inversely proportion to sample size.

So, if a decision maker wishes to reduce the margin of error associated with a confidence interval estimate for a population mean, she can decrease the sample size. So the option a is correct.

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The total amount that will ba paid altogether is $710.

From the information, the person borrow 500 for 6 years at an annual interest rate of 7%.

It should be noted that interest is calculated as:

= Principal × Rate × Time

= 500 × 7% × 6

= $210

The total amount will be:

= Principal + Interest

= $500 + $210

= $710

The total amount is $710

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The value of the expression on evaluation is 96π / 5.

Here we have to find the value of the expression.

∫∫∫x² dV

E is indeed the solid that exists inside the cylinder x² + y² = 4 above the surface z =0.

E's precession through into xy-plane is x² + y² ≤4 where r≤2 with Ф[0, 2π].

∫∫∫ x² dV = ∫[tex]\int\limits^2\pi _0 {} \, \int\limits^2_0{} \, \int\limits^3r_0[/tex] r² cos² Фrd dФ

             = [tex]\int\limits^2\pi _0 {} \, \int\limits^2_0 \int\limits^3r_z=0 {} \,[/tex]r³ cos²Ф dz dr dФ

            = [tex]\int\limits^2\pi _0 {} \, \int\limits^2_0 {} \,[/tex] 3[tex]r^{4}[/tex]cos²Ф dr dФ

           = 3 [tex]\int\limits^2\pi _0 {} \,[/tex] 1/2 [tex]2^{5}[/tex]/ 5 ( 1 + cos² Ф )dr dФ

           = 48 / 5 [( Ф + 1/2 sin 2Ф)[tex]]^{2\pi } _{0}[/tex]

            = 96π / 5

Therefore the value of the expression is 96π/5.

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Debit Common Dividends Payable $ 234,850 ; credit Cash $ 234,850.

What is arithmetic?

Mathematical arithmetic is the study of the properties of the standard operations on numbers, such as addi - tion, subtraction, multiplication, division, exponents, and root extraction. The Peano axioms, developed by the Italian mathematician Giuseppe Peano in the 19th century and still vital to the modern study of mathematical logic, formalised arithmetic. There are only a few ancient artefacts that can be used to date the invention of addition and subtraction. The best-known of these is the disputedly interpreted Ishango bone from africa, which dates to between 20,000 and 18,000 BC.

Main Body:

Debit Common Dividends Payable $100,100; credit Cash $100,100.

= $0.55 * (456,000 shares - 19,000 shares)

= $0.55 *427,000 shares

= $ 234,850

Hence ,debit Common Dividends Payable $ 234,850 ; credit Cash

$ 234,850.

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Although part of your question is missing, you might be referring to this full question: Use the exponential regression equation that best fits the data (10, 4), (12, 20), (13, 35), and (16, 300) to estimate y when x = 15.

The estimated y value at x = 15 is 147.

The exponential regression equation in general has form y = a*b^x.

And from the attached graph, it is shown that:

a ≈ 0.0038

b ≈ 2.0223

So, using the exponential regression calculator, the exponential model created by the data is:

y = a*b^x

y = 0.0038*(2.0223)^x

And when x = 15, thus:

y = 0.0038*(2.0223)^15

y ≈ 147

Hence, the estimated y value at x = 15 is 147.

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