A theater is selling tickets to a ''preview night'' of their new musical. The tickets cost $12 per adult and $7. 50 per child. Due to limit on seating, they can sell no more than 150 tickets. However, they would like to make at least $675 from ticket sales

To determine whether the function f(x) = a^x-a^(-x)+sinx is even or odd, we need to check if it satisfies the properties of even and odd functions.

An even function is a function that satisfies the property f(x) = f(-x) for all x in the domain of the function. This means that if we reflect the graph of the function across the y-axis, we get the same graph.

An odd function is a function that satisfies the property f(x) = -f(-x) for all x in the domain of the function. This means that if we reflect the graph of the function across the origin (both x and y-axis), we get the same graph.

Let's start by checking whether f(x) is even:

f(-x) = a^(-x)-a^(x)+sin(-x)  (since sin(-x) = -sin(x))

       = -a^x+a^(-x)-sin(x)

Comparing f(-x) with f(x), we can see that f(-x) = -f(x) only when sin(x) = 0.

This means that f(x) is an even function only when sin(x) = 0, which occurs when x = nπ (where n is an integer).

Now, let's check whether f(x) is odd:

f(-x) = a^(-x)-a^(x)+sin(-x)  (since sin(-x) = -sin(x))

       = -a^x+a^(-x)-sin(x)

Comparing f(-x) with -f(x), we can see that f(-x) = -f(x) only when a^x = -a^x, which is not possible for any real value of a.

Therefore, f(x) is neither an even nor an odd function.
To determine whether the function f(x) = a^x - a^(-x) + sin(x) is even or odd, we can evaluate f(-x) and compare it to f(x).

An even function satisfies the condition f(-x) = f(x), while an odd function satisfies the condition f(-x) = -f(x).

Let's evaluate f(-x):
f(-x) = a^(-x) - a^(-(-x)) + sin(-x)
f(-x) = a^(-x) - a^x - sin(x)

Now, let's compare f(-x) to f(x):
f(-x) ≠ f(x) because f(x) = a^x - a^(-x) + sin(x)
f(-x) ≠ -f(x) because -f(x) = -a^x + a^(-x) - sin(x)

Since f(-x) is neither equal to f(x) nor -f(x), the function f(x) = a^x - a^(-x) + sin(x) is neither even nor odd.

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The formula to calculate surface area is 2(Length × Width) + 2(Length × Height) + 2(Width × Height) and the length, width, and height of the sandbox is required to calculate rectangular area.

To determine how much sand your cousin will need to fill the rectangular prism-shaped sandbox, we first need to calculate its volume. To do this, we need the dimensions of the sandbox (length, width, and height). The formula for the volume of a rectangular prism is:

Volume = Length × Width × Height

Once we have the volume, we can determine the amount of sand needed to fill the sandbox in cubic units.

To find out how much paint is needed to paint all six surfaces of the sandbox, we need to calculate its surface area. The formula for the surface area of a rectangular prism is:

Surface Area = 2(Length × Width) + 2(Length × Height) + 2(Width × Height)

Once we have the surface area, we can determine the amount of paint required, usually measured in square units. Note that the amount of paint needed also depends on the coverage rate of the paint, which is typically listed on the paint container.

Please provide the dimensions of the sandbox (length, width, and height) so I can provide specific calculations for the sand and paint required.

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If Katie started with $40, the remaining balance after purchasing the supplies is $20.

To determine how much money Katie had left after purchasing the supplies, we'll consider the fraction "1/5" for the storybook and "3/10" for the calculator.

1: Calculate the amount spent on the storybook.

Katie spent 1/5 of her initial $40 on the storybook. To find this amount, multiply the fraction by the total amount:

(1/5) x $40 = $8

2: Calculate the amount spent on the calculator.

Katie spent 3/10 of her initial $40 on the calculator. To find this amount, multiply the fraction by the total amount:

(3/10) x $40 = $12

3: Add the amounts spent on both the storybook and calculator.

$8 (storybook) + $12 (calculator) = $20

4: Subtract the total amount spent from Katie's initial amount of money to find the remaining balance.

$40 (initial amount) - $20 (total spent) = $20

After purchasing the supplies, Katie had $20 left.

Note: The question is incomplete. The complete question probably is: Katie started with $40. He spent 1/5 of the money on a storybook and 3/10 on a calculator. how much money did she have left after purchases the supplies.

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The expression that shows how many beads are on the necklace in all is:

b + 12.

An expression in mathematics is a combination of numbers, variables, and/or operators that represents a mathematical relationship or quantity. It may contain constants, variables, coefficients, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. Expressions are often used to describe or represent real-world situations, and can be simplified, evaluated, or manipulated using algebraic rules and properties.

In the given question,

To write an expression that shows how many beads are on Josie's necklace in all after adding b more beads:

Start with the initial number of beads on the necklace, which is 12.

To this, add the number of beads Josie added, which is b.

Combine the two terms to form the final expression: 12 + b.

Therefore, the expression that shows how many beads are on Josie's necklace in all after adding b more beads is 12 + b.

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Answer:

8/10

Step-by-step explanation:

Formula

Cosine A = Adjacent side / Hypotenuse

Here,

Adjacent side = 8

Hypotenuse = 10

Answer

Cosine A = 8/10

The amount of popcorn the bigger box holds than the smaller box depends on the dimensions of the two containers, so it cannot be determined without additional information.

The difference in the amount of popcorn the two containers hold depends on the volume of each container. Let's assume the volume of Amanda's popcorn container is V1 and the volume of Mary's popcorn container is V2.

If we know the dimensions of both containers, we can calculate their volumes using the formula V = l × w × h, where l is the length, w is the width, and h is the height of the container. Then, we can find the difference in the volumes of the two containers by subtracting V1 from V2.

However, the question does not provide any information about the dimensions of the two containers, so we cannot determine the difference in their volumes. Therefore, the main answer is that the amount of popcorn the bigger box holds than the smaller box cannot be determined without additional information.

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Answer:

I think it's 8...

Step-by-step explanation:

8x8 = 64

since each side is the same.

sorry if I'm wrong though-

Answer: 16 cm long

Step-by-step explanation:

Since we already have given the Area of the Square i.e. 64cm²

So, putting values into the Formulae, we get-

Area of the Square = side X side

64 = 8 x 8

since the sides have to be equal because the square has 4 equal sides, we multiply it by 4, it has to be 4 x 4 = 16

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Each cook made 109 pizzas.

The total number of pizzas ordered is 4 + 97 + 335 = 436.

If the 4 cooks each made an equal number of pizzas, then we can divide the total number of pizzas by the number of cooks to find out how many pizzas each cook made.

436 pizzas / 4 cooks = 109 pizzas per cook.

Therefore, each cook made 109 pizzas.

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Answer:

x = 13

Step-by-step explanation:

We Know

(5x - 6) + (8x + 17) must equal 180°

Find the value of x.

Let's solve

5x - 6 + 8x + 17 = 180

13x + 11 = 180

13x = 169

x = 13

So, the value of x is 13.

The approximate surface area of the glass prism is approximately 1986.66 square millimeters.

To find the surface area of the glass prism, we need to determine the area of each of its faces and then add them together. The prism consists of two congruent equilateral triangles and three rectangular faces.

The area of an equilateral triangle with side length s and height h is given by:

A = (√(3)/4) * s²

Using this formula, we can find the area of each of the two equilateral triangles in the prism:

A = (√(3)/4) * 7² ≈ 21.22 mm²

Next, we need to find the area of each of the three rectangular faces. The length of each rectangular face is equal to the side length of the equilateral triangle (7 mm), and the height is equal to the length of the prism (93 mm). Therefore, the area of each rectangular face is:

A = length x height = 7 mm x 93 mm = 651 mm²

To find the total surface area of the prism, we add the areas of the two equilateral triangles and the three rectangular faces:

Total surface area ≈ 2 x 21.22 mm² + 3 x 651 mm² ≈ 1986.66 mm²

Therefore, the approximate surface area of the glass prism is approximately 1986.66 square millimeters.

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The value of x is -4.

We have,

(3x + 25) and (6x - 2) makes one angle.

So,

(9x + 23) is the angle.

Now,

It is bisected in two angles.

So,

9x + 23 = 1/2 x (6x - 2)

9x + 23 = 3x - 1

9x - 3x = -1 - 23

6x = -24

x = -4

Thus,

The value of x is -4.

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we have the first eight terms, let's analyze the sequence. There doesn't appear to be a clear pattern or convergence towards a single value. The values are fluctuating, suggesting that the series may be divergent.

To find the first eight terms of the sequence of partial sums for the series sin(n), we will calculate the sum of the series for each term up to n=8, and then determine whether the series appears to be convergent or divergent.

1. sin(1)

2. sin(1) + sin(2)

3. sin(1) + sin(2) + sin(3)

4. sin(1) + sin(2) + sin(3) + sin(4)

5. sin(1) + sin(2) + sin(3) + sin(4) + sin(5)

6. sin(1) + sin(2) + sin(3) + sin(4) + sin(5) + sin(6)

7. sin(1) + sin(2) + sin(3) + sin(4) + sin(5) + sin(6) + sin(7)

8. sin(1) + sin(2) + sin(3) + sin(4) + sin(5) + sin(6) + sin(7) + sin(8)

Now, let's calculate these sums up to four decimal places:

1. 0.8415

2. 0.8415 + 0.9093 = 1.7508

3. 1.7508 + 0.1411 = 1.8919

4. 1.8919 - 0.7568 = 1.1351

5. 1.1351 - 0.9589 = 0.1762

6. 0.1762 - 0.2794 = -0.1032

7. -0.1032 + 0.6569 = 0.5537

8. 0.5537 + 0.9894 = 1.5431

Now that we have the first eight terms, let's analyze the sequence. There doesn't appear to be a clear pattern or convergence towards a single value. The values are fluctuating, suggesting that the series may be divergent.

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Volumes of the cylinder are given by:

(A) (1) Volume = 2486.88 cubic in.

(2) Volume = 108518.4 cubic ft.

(3) Volume = 47608.68 cubic yd.

(B) (4) Volume = 508.68 cubic ft.

(5) Volume = 8490.56 cubic yd.

(6) Volume = 43407.36 cubic in.

(7) Volume = 9420 cubic ft.

(8) Volume of cylindrical flower vase = 1105.28 cubic in.

Surface Area of the Cylinder are given by:

(1) Surface Area = 113.04 square in.

(2) Surface Area = 1444.4 square ft.

(3) Surface Area = 678.24 square yd.

(4) Surface Area = 1130.4 square yd.

(5) Surface Area = 602.88 square in.

(6) Surface Area = 1055.04 square ft.

(7) Surface Area = 1570 square ft.

(8) Surface Area = 791.28 square yd.

(9) Surface Area = 326.56 square in.

We know that the volume of a cylinder with radius 'r' and height 'h' is given by,

V = 2πr²h

(A) (1) From the figure, radius = 6 in and height = 11 in.

So the volume = 2π(6)²*11 = 2486.88 cubic in.

(2) Radius = 24 ft. and height = 30 ft.

Hence, the volume of cylinder = 2π(24)²*30 = 108518.4 cubic ft.

(3) Radius = 19 yd. and height = 21 yd.

Hence, the volume of cylinder = 2π(19)²*21 = 47608.68 cubic yd.

(B) (4) Radius = 3 ft. and height = 9 ft.

Hence, the volume of cylinder = 2π(3)²*9 = 508.68 cubic ft.

(5) Radius = 13 yd. and height = 8 yd.

Hence, the volume of cylinder = 2π(13)²*8 = 8490.56 cubic yd.

(6) Radius = 16 in. and height = 27 in.

Hence, the volume of cylinder = 2π(16)²*27 = 43407.36 cubic in.

(7) Radius = 10 ft. and height = 15 ft.

Hence, the volume of cylinder = 2π(10)²*15 = 9420 cubic ft.

(8) Cylindrical flower vase is 11 inch tall and radius of vase is 4 inches.

The volume of flower vase = 2π(4)²*11 = 1105.28 cubic in.

   Now we know that the surface area of a Cylinder with radius 'r' and height 'h' is given by,

S = 2πrh + 2πr²

(1) Radius = 2 in. and Height = 7 in.

Hence the surface area = 2π*2*7 + 2π(2)² = 113.04 square in.

(2) Radius = 10 ft. and Height = 13 ft.

Hence the surface area = 2π*10*13 + 2π(10)² = 1444.4 square ft.

(3) Radius = 6 yd. and Height = 12 yd.

Hence the surface area = 2π*6*12 + 2π(6)² = 678.24 square yd.

(4) Radius = 9 yd. and Height = 11 yd.

Hence the surface area = 2π*9*11 + 2π*9² = 1130.4 square yd.

(5) Radius = 6 in. and Height = 10 in.

Hence the surface area = 2π*6*10 + 2π(6)² = 602.88 square in.

(6) Radius = 8 ft. and Height = 13 ft.

Hence the surface area = 2π*8*13 + 2π(8)² = 1055.04 square ft.

(7) Radius = 10 ft. and Height = 15 ft.

Hence the surface area = 2π*10*15 + 2π(10)² = 1570 square ft.

(8) Radius = 6 yd. and Height = 15 yd.

Hence the surface area = 2π*6*15 + 2π(6)² = 791.28 square yd.

(9) Radius = 4 in. and Height = 9 in.

Hence the surface area = 2π*4*9 + 2π(4)² = 326.56 square in.

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Infectious diseases, chronic conditions, mental health, healthcare access, health disparities. Vaccination campaigns, disease prevention, healthcare access, mental health support, social determinants. Increased disease burden, higher costs, reduced quality of life, higher mortality, strained healthcare systems, hindered socio-economic development.

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The average amount of books read per student according to the histogram is given as follows:

1.27 books.

The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations, which is also called the cardinality of the data-set.

The histogram shows the number of times for each observation, hence:

Hence the mean is calculated as follows:

M = (7 x 0 + 9 x 1 + 6 x 2 + 4 x 3)/(7 + 9 + 6 + 4) = 1.27 books.

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The service should wax approximately 233 cars daily to maximize profit.

To maximize profit, we need to find the number of cars (q) that would result in the highest profit. Profit function P(q) can be calculated as:

P(q) = Revenue - Cost
P(q) = 65q - (0.06q² + 37q + 360)

Now, to find the optimal value of q, we can calculate the derivative of the profit function with respect to q and set it to zero:

dP(q)/dq = 65 - (0.12q + 37)
0 = 65 - 0.12q - 37

Solve for q:

0.12q = 28
q = 28 / 0.12
q ≈ 233.33

Since the number of cars must be a whole number, we can round q to the nearest integer. Therefore, the service should wax approximately 233 cars daily to maximize profit.

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The length of the actual car is 10.8 feet.

The scale of 1 inch: 4 feet means that every inch on the model car corresponds to 4 feet on the actual car. Therefore, to find the length of the actual car, we need to multiply the length of the model car in inches by the scale factor of 4 feet/inch.

Length of actual car = Length of model car x Scale factor

Length of actual car = 2.7 inches x 4 feet/inch

Length of actual car = 10.8 feet

Therefore, the length of the actual car is 10.8 feet.

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Where every student offer at least one of the subjects, there are 4 students who offer all three subjects.

To find the number of students who offer only one subject, we can use the formula:

number of students offering only one subject = total number of students offering the subject - number of students offering both subjects

For math, there are 22 students offering math and 5 offering both math and biology, so the number of students offering math only is:

22 - 5 = 17

Similarly, for physics and biology, the numbers of students offering the subjects only are:

14 - 7 = 7 (physics)
16 - 5 = 11 (biology)

To find the number of students offering all three subjects, we can use the formula:

number of students offering all three subjects = total number of students offering at least one subject - number of students offering only one subject in each subject + number of students offering no subject

We know that there are 7 students offering at least one subject. To find the number of students offering no subject, we can subtract this from the total number of students:

39 - 7 = 32

Now we can plug in the numbers:

number of students offering all three subjects = 7 - 17 - 7 - 11 + 32
= 4

Therefore, there are 4 students who offer all three subjects.

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The z scοre is negative the actual probability would be

1-0.7995 = 0.2005

What is the probability?

A number that expresses hοw likely it is that an event will occur is called the probability of οccurrence. It is written as a number from 0 to 1, or frοm 0% to 100%, in percentage notation. The probability of an event occurring increases with probability.

here,

mean = 20.20

standard deviatiοn = 2.60

we knοw that,

Z scοre = (X-mean)/standard deviation

fοr X = 18:

Z scοre = (18-20.20)/2.6 = -0.8461

nοte that the z score is negative because the measured value is less than the mean value.

fοr Z score 0.8461 probability is 0.7995

and since the z scοre is negative the actual probability would be

1-0.7995 = 0.2005

a. For nοt within 1 hour of the population mean

We apply the formula here and we get the value οf P.

P(19.20>x>21.20) = P(19.20-20.20/2.60√18) > X-μ/σ√n >21.20-20.20/2.60√18

P(19.20>x>21.20) = P(-1.63>z>1.63)

Now, we find the value οf z.

P(19.20>x>21.20) = P(z>1.63) + P(z<-1.63)

P(19.20>x>21.20) = 0.0516 + 0.0516

P(19.20>x>21.20) = 0.1032

b. Fοr 20. 0 to 20. 5 hours

P(20<x<20.5) = P(20-20.20/2.60√18) < X-μ/σ√n<20.50-20.20/2.60√18

P(20<x<20.5) = P(-0.33<z<0.49)

Nοw, we find the value of the z-score and we get

P(20<x<20.5) = P(z<0.49) - P(z<-0.33)

P(20<x<20.5)  = 0.6879 - 0.2707

P(20<x<20.5)  = 0.3172

c. Fοr at least 22 hours

We apply the t-test fοrmula here and we get

P(x≥22) = P(X-μ/σ√n≥22-20.20/2.60√18)

Nοw, we find the value of z.

P(x≥22) = P(z≥2.94)

P(x≥22) = 0.0016

d. Fοr not more than 21 hours.

P(x<21) = P(X-μ/σ√n<21-20.20/2.60√18)

We find here the value οf P for x<21 and we get

P(x<21) = P(z<1.31)

Now, we find the value οf the z- score.

P(x<21) = 0.9049

Hence, a. 0.1032

b.  0.3172

c. 0.0016

d. 0.9049

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Complete question is,

Among college students who hold part-time jobs during the school year, the distribution of the time spent working per week is approximately normally distributed with a mean of 20.20 hours and a standard deviation of 2.60 hours. Find the probability that the average time spent working per week of 18 randomly selected college students who old part-time jobs during the school year is.

Answer:

1/3

Step-by-step explanation:

It would be 2 options out of 6 total which means 2/6. 2/6 reduces down to 1/3

If you let z be a random variable with a standard normal distribution, the indicated probability is 0.0793. So, the probability P(z ≥ 1.41) = 0.0793

To find the probability P(z ≥ 1.41) for a standard normal distribution, you can use a Z-table or calculator to find the area to the right of z = 1.41.

Using a Z-table or calculator, you will find the value of P(z ≥ 1.41) is approximately 0.0793. So, the probability P(z ≥ 1.41) = 0.0793. Remember to round your answer to four decimal places.

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The quadratics that would not have 5 and -7 as zeros are (1) and (3)

From the question, we have the following parameters that can be used in our computation:

Zeros: 5 and -7

This means that

x = 5 and x = -7

Rewrite as

x - 5 = 0 and x + 7 = 0

Multiply both equation

This gives

(x - 5)(x + 7) = 0

Rewrite as

f(x) = (x - 5)(x + 7)

When expanded, we have

f(x) = x² + 2x - 35

So, we have

(2) f(x) = x² + 2x - 35

(4) f(x) = 2(x + 7)(x - 5)

Hence, the quadratics that would not have 5 and -7 as zeros are (1) and (3)

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Answer: There are two solutions to X.. x = -3 and x = 2

Step-by-step explanation:

In this case, a = 1, b = 1, and c = -6, so we have:

x = (-1 ± sqrt(1^2 - 4(1)(-6))) / 2(1)

x = (-1 ± sqrt(1 + 24)) / 2

x = (-1 ± sqrt(25)) / 2

The two solutions are x = (-1 + 5) / 2 = 2 and x = (-1 - 5) / 2 = -3. Therefore, the solutions to the equation X^2 + x - 6 = 0 are x = 2 and x = -3.

The closest amount to the total balance is option B, 695.00.

For Account A, the interest earned after 2 years is:

Interest = Principal * Rate * Time = 400 * 0.035 * 2 = 28

So the total balance in Account A after 2 years is:

Total A = Principal + Interest = 400 + 28 = 428

For Account B, the interest earned after 2 years is:

Interest = Principal * (1 + Rate/100)^Time - Principal = 250 * (1 + 3.25/100)^2 - 250 = 25.95

The total balance in Account B after 2 years is:

Total B = Principal + Interest = 250 + 25.95 = 275.95

The total balance in both accounts after 2 years is:

Total Balance = Total A + Total B = 428 + 275.95 = 703.95

The closest amount to the total balance is option B, 695.00.

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Answer:

A = P(1 + r/n)^(nt)

Where:

A = the future balance

P = the present balance ($1430.00)

r = the annual interest rate (2% or 0.02)

n = the number of times the interest is compounded per year (since it's compounded annually, n = 1)

t = the number of years (8 years in this case)

Plugging in the values into the formula:

A = 1430(1 + 0.02/1)^(1*8)

Simplifying the equation:

A = 1430(1.02)^8

Using a calculator or performing the calculations manually:

A ≈ 1430(1.171661)

A ≈ 1674.02

the balance after 8 years will be approximately $1674.02.

Answer:

X = 2² * 3² * 5³ * 7.

Step-by-step explanation:

140 = 2*2*5*7

15^2 = 3*5*3*5

So X = 2² * 3² * 5³ * 7

To find the prime factorization of X, we first need to simplify the expression.

Now, we can factor 140 and 225 into their prime factors:

So,

We can now use the distributive property to multiply these factors together:

Therefore, the prime factorization of X is:

The least-squares regression line for predicting the 2016 budget from the 2006 budget is y = 18.18 + 0.9365x, their budgets to differ in 2016 is 9.365 million and the budget for organization is 111.83 million.

In a regression graph, the regression line closest to the data points is shown. By replacing alternative values of x in the regression equation, this statistical technique can assist analyse the behaviour of a dependent variable y when the independent variable x changes.

The corporation can identify the optimal asset price in relation to the cost of capital by using regression. It is used in the stock market to calculate the impact of stock price movements on the price of underlying commodities.

Regression analysis may be used in marketing to understand how pricing fluctuations affect the rise or reduction in products sales. It is particularly successful in forecasting future sales by correlating market factors, weather forecasts, economic situations, and prior sales.

a) Here we find the least square regression line for predicting the 2016 budget :

Regression line y = a+bx

b = [tex]\frac{n(Exy)-(Ex*Ey)}{n(Ex)^r-(Ey)^r}[/tex]

= [tex]\frac{2216256 - 1219050}{2220421-1155625}[/tex]

= [tex]\frac{997206}{1064796}[/tex]

= 0.9365

a= y-bx

= [tex]\frac{Ey}{n} -b\frac{Ex}{n}[/tex]

162 - (0.9635 x 153.5714286)

= 162 - 143.819

= 18.18

y = 18.18 + 0.9365x

b) For 10 million change in 2006, there will be

= 10 x 0.9365 = 9.365 million change in 2016

c) If x = 100,

y = 18.18 + 0.9365(100) = 111.83 million.

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Complete question:

Organization 2006 2016

Corporation for Public Broadcasting 460 445

Institute of Museum and Library Services 247 237

National Endowment for the Humanities 142 148

National Endowment for the Arts 124 148

National Gallery of Art 95 147

Commission of Fine Arts 2 3

Advisory Council on Historic Preservation 5 6

Source: National Endowment for the Arts

a. Compute the least-squares regression line for predicting the 2016 budget from the 2006 budget.

b. If two institutions have budgets that differ by 10 million dollars in 2006, by how much would you predict their budgets to differ in 2016?

c.Predict the 2016 budget for an organization whose 2006 budget was 100 million dollars.

The expected population proportion,  with 95% confidence, that prefers to shop at places with loyalty cards is between 54.6% and 61.4%.

Based on the survey results, we know that 58% of the sample respondents prefer to shop at places with loyalty cards. If the margin of error is 3.4%, we can calculate the expected range of the population proportion as follows:

Upper bound: 58% + 3.4% = 61.4%
Lower bound: 58% - 3.4% = 54.6%

Therefore, we can say with 95% confidence that the expected population proportion that prefers to shop at places with loyalty cards is between 54.6% and 61.4%.

More on population proportion: https://brainly.com/question/15087042

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