What is the equation of the line in slope intercept form?

Answer:

32.5

Step-by-step explanation:

if it completes a pack per second then it’s 32.5 g per second but this question does not have much detail on what you need to do

156.25cm

Step-by-step explanation:

The area of a square is L×L

12.5×12.5=156.25cm

Answer:

The slope is 0

Step-by-step explanation:

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

y = mx + b

Using the slope-intercept form, the slope is 0.

m = 0

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The null hypothesis (H0) is that the average time spent studying is 2 hours or less, while the alternative hypothesis (H1 or Ha) is that the average time spent studying is more than 2 hours.

The null hypothesis (H0) is a statement of no effect or no difference, while the alternative hypothesis (H1 or Ha) is a statement of the opposite, suggesting that there is an effect or a difference.

In this case, the professor does not believe that his students spend 2 hours on average studying for the final exam and thinks they spend more time than that.

The null hypothesis (H0) would be that the average time spent studying for the final exam is indeed 2 hours or less:

H0: μ ≤ 2

The alternative hypothesis (H1 or Ha) would be that the average time spent studying for the final exam is more than 2 hours:

Ha: μ > 2

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No, Jenna and Henry cannot both be correct. Jenna’s answer of 614 hours is incorrect, as it is much too long for a school day. Henry’s answer of 6.25 hours is also incorrect, as it is much too short for a school day.

The part of the length of the school day that is the same in all three ways the time is given is the hours. In the first way, the school day is given as 6 hours and 15 minutes.

In the second way, the school day is given as 6.25 hours. In the third way, the school day is given as 375 minutes. In each case, the number of hours in the school day is the same: 6 hours. However, the way that the minutes are expressed differs, leading to different numerical values.

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The expression 1.05h correctly represents the total amount Sylvia will pay for the hat if it costs h dollars.

Sylvia knows that the price of the hat will increase by 5% when she pays sales tax. Let's break down the expressions to understand them better.

Expression 1: h + 0.05h

In this expression, h represents the cost of the hat. Adding 0.05h to h accounts for a 5% increase. However, this expression does not accurately represent the total amount Sylvia will pay because it only considers the increase due to sales tax, not the original cost of the hat.

Expression 2: 1.05h

In this expression, 1.05 represents the total cost multiplier, which includes the original cost of the hat and the 5% increase. Multiplying h by 1.05 accounts for both the original cost and the sales tax increase. This expression correctly calculates the total amount Sylvia will pay for the hat.

Therefore, the expression 1.05h is the correct representation of the total amount Sylvia will pay for the hat if it costs h dollars.

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The inverse of f(x) = 11x - 8 include the following: C. [tex]f^{-1}(x) = \frac{x+8}{11}[/tex]

In Mathematics and Geometry, an inverse function simply refers to a type of function that is obtained by reversing the mathematical operation in a given function (f(x)).

In this exercise, you are required to determine the inverse of the function f(x). This ultimately implies that, we would have to swap (interchange) both the independent value (x-value) and dependent value (y-value) as follows;

f(x) = y = 11x - 8

x = 11y - 8

11y = x + 8

By dividing both sides of the equation by 11, we have:

y = x/11 + 8/11

f⁻¹(x) = (x + 8)/11

[tex]f^{-1}(x) = \frac{x+8}{11}[/tex]

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The length of side a is approximately 6.0 in the triangle. The correct option is (b) 6.0.

To find the length of side a in triangle ABC, we can use the Law of Sines.

The Law of Sines states that the ratio of a side length to the sine of its opposite angle is constant for all sides of a triangle.

In this case, we have:

a/sin(A) = b/sin(B) = c/sin(C)

Given that angle A has a measure of 29°, we can substitute the known values:

a/sin(29°) = 13.5/sin(B) = 8.9/sin(C)

Solving for side a, we have:

a = sin(29°) × 13.5 / sin(B)

To find sin(B), we can use the fact that the sum of the angles in a triangle is 180°:

B = 180° - A - C = 180° - 29° - 90° (since angle C is 90° in a right triangle)

B = 61°

Now we can calculate side a:

a = sin(29°) × 13.5 / sin(61°)

a ≈ 6.0

Therefore, the length of side a is approximately 6.0. The correct option is (b) 6.0.

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To find the test statistic for a test to show that the population mean height of the school district is lower than 59 inches, we can perform a one-sample t-test.

The test statistic is calculated using the sample mean, sample standard deviation, sample size, and the hypothesized population mean.

Given the sample heights of the 11 fifth-grade boy students: 59.0, 57.2, 57.1, 58.0, 57.0, 50.1, 52.3, 55.6, 57.8, 53.9, 57.8, we can calculate the sample mean () and sample standard deviation (s).

= (59.0 + 57.2 + 57.1 + 58.0 + 57.0 + 50.1 + 52.3 + 55.6 + 57.8 + 53.9 + 57.8) / 11

Next, calculate the sample standard deviation:

s = sqrt(((59.0 - )^2 + (57.2 - )^2 + ... + (57.8 - )^2) / (11 - 1))

Once you have the sample mean and sample standard deviation, you can calculate the test statistic (t):

t = ( - μ) / (s / sqrt(n))

where μ is the hypothesized population mean (in this case, 59 inches), and n is the sample size (11).

By substituting the values into the formula, you can calculate the test statistic rounded off to the first decimal place.

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Answer:

The formula for the volume of a cone is V = (1/3)πr^2h,

r is the base radius

h is the height.

Substituting the given values, we get:

V = (1/3)π(4 yards)^2(9 yards)

V = (1/3)π(16 yards^2)(9 yards)

V = (1/3)π(144 yards^3)

V = 48π cubic yards

Therefore, the volume of the cone is 48π cubic yards.

Answer:

$9.25

Step-by-step explanation:

One box of popcorn costs $2.65 while the total cost of three boxes of popcorn and a fountain drink is $9.70.

We have,

We are given that the cost C of buying three boxes of popcorn and a fountain drink is represented by the equation C = 3x + 1.75.

Where x is the number of popcorn.

Now,

We want to find the cost of one box of popcorn when the cost is $9.70.

Let's first substitute C = 9.70 into the equation:

9.70 = 3x + 1.75

Next, we'll isolate x by subtracting 1.75 from both sides:

9.70 - 1.75 = 3x

7.95 = 3x

Finally, we'll solve for x by dividing both sides by 3:

x = 7.95/3 = 2.65

Therefore,

One box of popcorn costs $2.65 while the total cost of three boxes of popcorn and a fountain drink is $9.70.

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To use Lagrange multipliers, we first need to set up our objective function and constraint equation. Constructing a box with dimensions 12x12x6 feet will minimize the cost of construction.

Our objective is to minimize the cost of constructing the box, which is equal to:

C = 5xy + 2(3xy + 3xz + 3yz)

where x, y, and z are the dimensions of the box, and we have broken up the cost into the bottom and sides/top respectively. Our constraint is that the volume of the box must be 480 cubic feet, so:

xyz = 480

To use Lagrange multipliers, we set up the following equation:

∇C = λ∇(xyz)

where ∇C is the gradient of our objective function, ∇(xyz) is the gradient of our constraint equation, and λ is our Lagrange multiplier.

Taking the partial derivatives of our objective and constraint functions, we get:

∇C = (5y, 5x, 6x + 6y)
∇(xyz) = (yz, xz, xy)

Setting these equal and solving for λ, we get:

5y / yz = 5x / xz = (6x + 6y) / xy = λ

Simplifying, we get:

x = y = 2z

Substituting this into our constraint equation, we get:

4z^3 = 480

z = 6

Substituting this back into our dimensions, we get:

x = y = 12

So the minimum cost of constructing the box is:

C = 5(12)(12) + 2(3(12)(12) + 3(12)(6) + 3(12)(6)) = $1,296

Therefore, constructing a box with dimensions 12x12x6 feet will minimize the cost of construction.

To find the minimum cost for constructing a 480 cubic feet box with the bottom costing $5 per square foot and the top and sides costing $3 per square foot, we can use Lagrange multipliers. Let the dimensions of the box be length (x), width (y), and height (z).

First, we need to define the constraint function:
G(x, y, z) = xyz - 480 (the volume constraint)

Next, define the cost function:
C(x, y, z) = 5xy + 3(xz + yz + xy) (cost of bottom + cost of top and sides)

Now, we use the Lagrange multiplier λ and set the gradient of the cost function equal to the gradient of the constraint function multiplied by λ:
∇C(x, y, z) = λ∇G(x, y, z)

This results in a system of equations:

5y + 3z + 3y = λy
5x + 3z + 3x = λx
3x + 3y = λz

We also have the constraint equation:
xyz = 480

Solve this system of equations to find the optimal dimensions x, y, and z. Then, plug these dimensions into the cost function C(x, y, z) to find the minimum cost for constructing the 480 cubic feet box.

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The type of indeterminate form obtained by direct substitution in the given limit is 1^∞, where 1^∞ is not a determinate form and its value is not always predictable.

Applying L'Hôpital's Rule to the limit, we get:

lim_(xâ0^+) [cos(Ï/2 - x)]^x = lim_(xâ0^+) e^[x ln(cos(Ï/2 - x))]

Now, applying L'Hôpital's Rule to the exponent, we get:

= lim_(xâ0^+) e^[x (-tan(Ï/2 - x))]

= e^0 = 1

Therefore, the limit is equal to 1.

Using a graphing utility to graph the function, we can see that the limit approaches 1 as x approaches 0 from the right side. Therefore, the result obtained using L'Hôpital's Rule is verified by the graph.

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Answer:

$6.81 or 681 US Cents

Step-by-step explanation:

100 - 19 = 81

7 - 1 = 6

$7.00 - .19 = $6.81

or 681 US Cents.

Based on the information provided, the type of sample used in the research study would be a convenience sample.

A convenience sample is a non-probability sampling technique where participants are selected based on their availability and willingness to participate. In this case, the professor selected the first 55 students who arrived in class, which means the sample was not selected randomly or systematically. It is important to note that convenience samples may not represent the entire population accurately, and therefore, the results obtained from such samples may not be generalizable to the larger population. As such, caution should be taken when interpreting the findings of this research study.

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Answer:

A. [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

Slope = rise/run or (y2 - y1) / (x2 - x1)

Pick 2 points (0,2) (3,3)

We see the y increase by 1 and the x increase by 3, so the slope is

m = 1/3

So, the answer is A. [tex]\frac{1}{3}[/tex]

Answer:

To tell if a polynomial is constant, linear, quadratic, cubic or quartic, you must first look at the highest power of the variable in the polynomial. If the highest power is 0, then the polynomial is a constant. If the highest power is 1, then it is a linear polynomial. If the highest power is 2, then it is a quadratic. If the highest power is 3, then it is a cubic and finally, if the highest power of the variable is 4, then the polynomial is a quartic.

Step-by-step explanation:

The graph of the logaritmic function is on the image at the end.

So here we want to graph the function:

y = 3log₂(-x) - 9

To graph this, we can evaluate it in some values and then find some points. We can graph these points and then connect them.

if x = -1 then:

y = 3*log₂(1) - 9   = -9

So we have the point (-1, 9)

if x = -2 then:

y = 3*log₂(2) - 9   = -6

We have the point (-2, -6)

And so on, when you have enough points, you can graph them and connect them, you should get something like the graph in the image at the end.

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The domain of the function is all non-negative real numbers.

In this situation, the function F(n) is used to estimate the amount of adhesive needed to tile a floor with an area of n square feet. The expression F(n) = n√+1 represents the formula used for the estimation.

To determine the domain of the function, we need to consider the restrictions or limitations on the variable n. In this case, since we are dealing with the area of a floor, the area cannot be negative. Therefore, the domain of the function consists of all non-negative real numbers.

In other words, any non-negative value of n, including zero and all positive real numbers, can be used as input for the function. However, negative values are not applicable in this context since the area of a floor cannot be negative.

Hence, the domain of the function F(n) in this situation is all non-negative real numbers.

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Answer:

8+17+5=30

Step-by-step explanation:

Kevin spends mixing, baking, and cooling the muffins. If you add 7 and 8 you get 15 and add another 5 you get 20+10 = 30

The linear combination of u and v that gives us the vector ⟨−10,−6⟩ is (−22,−6)

To find a linear combination of the vectors u and v that results in the vector ⟨−10,−6⟩, solve the system of linear equations:

a u + b v = ⟨−10,−6⟩

where a and b are scalars.

Expanding the left-hand side using the given vectors:

a ⟨−2,−3⟩ + b ⟨−1,3⟩ = ⟨−10,−6⟩

Simplify:

⟨−2a − b, −3a + 3b⟩ = ⟨−10,−6⟩

The following system of equations is derived:

-2a - b = -10

-3a + 3b = -6

Solve for a and b by substitution. Rearrange the first equation to solve for b:

b = -10 + 2a

Substitute this expression for b into the second equation:

-3a + 3(-10 + 2a) = -6

Simplify:

-3a - 30 + 6a = -6

3a = 24

a = 8

Substitute the value for a into the expression for b:

b = -10 + 2a = -10 + 2(8) = 6

Therefore, the linear combination of u and v that gives us the vector ⟨−10,−6⟩ is:

8u + 6v = 8⟨−2,−3⟩ + 6⟨−1,3⟩ = ⟨−16,−24⟩ + ⟨−6,18⟩ = ⟨−22,−6⟩

So, 8u + 6v = ⟨−22,−6⟩ which is the desired linear combination of the vectors u and v.

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The complete question in ideal form is given as thus:

Given vector u = (-2,-3 and v (-1,3) , find a linear combination of the vectors U and v of the form au + bv that would result in the - vector (-10, -6).

Answer:

Kiera will use 15 yellow charms

Step-by-step explanation:

The pattern would look like this:

BBYYYBBYYYBBYYYBBYYYBBYYY

B = Blue Charms

Y = Yellow Charms

The unconditional expectation of y (E(y)) equals β0 + (β1 * E(x)), derived using the Law of Iterated Expectations.

To simplify the expression for the unconditional expectation E(y), we can apply the properties of expected value and the Law of Iterated Expectations. The Law of Iterated Expectations states that the unconditional expectation of a conditional expectation is equal to the unconditional expectation itself.

Starting with the expression for E(y):

E(y) = E(β0 + β1x + u)

We can break down this expression using the linearity of expectation:

E(y) = E(β0) + E(β1x) + E(u)

Since β0 and β1 are constants, their expected values are equal to themselves:

E(y) = β0 + β1E(x) + E(u)

Now, since u is the error term and it is assumed to have a mean of zero (E(u) = 0), the expression simplifies to:

E(y) = β0 + β1E(x)

Therefore, we can conclude that the unconditional expectation of y (E(y)) is equal to the constant term β0 plus the product of the slope coefficient β1 and the unconditional expectation of x (E(x)). This result follows from the Law of Iterated Expectations, which allows us to simplify the expression by considering the expected values of the individual terms separately.

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Answer: 60

Step-by-step explanation:

Lowest common multiple is the smallest number that 5 10 and 12 can all multiply too

Multiples of 10 are easy, any number ending in 0

So you need to find a number that 5 and 12 go into that ends in 0

We can do this by doing 5*12 which gives us 60 which is divisible by 10

This means the Probability of drawing a star is now 4/8 or 1/2, which is equal to the probability of drawing a card without a star. Thus, the game is now fair.

To make the game fair, we need to ensure that the probability of drawing a card with a star is the same as the probability of drawing a card without a star.

Currently, there are 4 cards with stars and 6 cards without stars, which means the probability of drawing a star is 4/10 or 2/5, while the probability of drawing a card without a star is 6/10 or 3/5.

To make the game fair, we need to adjust the number of cards with stars and without stars so that the probabilities are equal.

Option A is not correct because the game is not currently fair.

Option B is not correct because adding 2 cards with stars will increase the probability of drawing a star to 6/12 or 1/2, which is not equal to the probability of drawing a card without a star.

Option C is also not correct because adding a star to 1 of the blank cards will still result in a probability of drawing a star that is not equal to the probability of drawing a card without a star.

Therefore, the correct answer is option D: take away 2 blank cards. If we remove 2 blank cards, we are left with 4 cards with stars and 4 cards without stars. This means the probability of drawing a star is now 4/8 or 1/2, which is equal to the probability of drawing a card without a star. Thus, the game is now fair.

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No, the Vaughns do not qualify for Chapter 7 bankruptcy.

Filing petition under chapter 7 stops most collection actions against the debtor or the debtor's property.

In the field of bankruptcy, the means test is used to determine whether an individual or family qualifies for Chapter 7 bankruptcy. This test compares the debtor's income to the median income in their state.

In this case, the Vaughns make $58,000 a year which is above Florida's median annual income of $47,778. Therefore, this stipulates they are not eligible for Chapter 7 bankruptcy.

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The value of the acute angles are 67.4° and 22.6° respectively

The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

sin(tetha) = opp/hyp

cos( tetha) = adj/hyp

tan(tetha) = opp/adj

Here the longest side which is the hypotenuse is 13 and the other legs of the right triangle are 12 and 13.

Represent the acute angle by A and B. If 12 is that opposite and 5 is the adjascent

sin A = 12/13

A = sin^-1( 0.923)

A = 67.4°

sinB = 5/13

B = sin^-1( 0.385)

B = 22.6°

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Answer:

The correct answer is: A. If many different samples of size 250 were selected and, based on each sample, a confidence interval were constructed, in the long run 99% of the confidence intervals would contain the true value of p.

Step-by-step explanation:

A confidence interval is a range of values that is likely to contain the true value of a population parameter. In this case, the population parameter is the proportion of voters who favor a tax on e-commerce. The confidence interval is constructed from a sample of voters, and it is based on the assumption that the sample is representative of the population.

The 99% confidence interval means that if we were to take many different samples of size 250 and construct a confidence interval for each sample, 99% of the confidence intervals would contain the true value of the population proportion. This does not mean that there is a 99% chance that the true value of the population proportion lies between 0.113 and 0.171. It means that if we were to take many different samples of size 250 and construct a confidence interval for each sample, 99% of the confidence intervals would contain the true value of the population proportion.

The other answer choices are incorrect because they do not correctly interpret the meaning of a confidence interval.