Movie studios often release films into selected markets and use the reactions of audiences to plan further promotions. In these data, viewers rate the film on a scale that assigns a score from 0 (dislike) to 100 (great) to the movie. The viewers are located in one of three test markets: urban, rural, and suburban.
Fit a multiple regression of rating on two dummy variables that identify the urban and suburban viewers.
Predicted rating = ( 49.50) + ( 14.45) D_urban + ( 19.67) D_Suburban (Round to two decimal places as needed.)

The length and the width are 12 yards and 16 yards

The formula for calculating the perimeter of a rectangle is expressed as;

Perimeter =2( l + w)

Given that the parameter are;

Length = 4 + w

Substitute the values into the formula

52 = 2( 4 + w + w)

collect like terms

52 = 2(4 + 2w)

expand the bracket

52 = 8 + 4w

collect like terms

4w = 52 - 8

subtract the values

4w = 48

Make 'x' the subject of formula

w = 12 yards

L = 16 yards

Hence, the values are 12 yards and 16 yards

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Answer:

A line segment

Step-by-step explanation:

(a) For Jack, with the utility function u(1) = 1, u(2) = 2, and u(3) = 3, the indifference curve represents combinations of probabilities (p1, p3) that yield the same utility level for Jack. Since Jack's utility increases with the outcome value, the indifference curve will be upward sloping.

To sketch the indifference curve for Jack, we connect the points (p1, p3) that yield the same utility level. The specific shape of the indifference curve depends on the utility function and the values of p1 and p3. However, since the utility values increase linearly, the indifference curve will be a straight line. The slope of this indifference curve can be calculated as the change in p3 divided by the change in p1. Since the utility function is linear, the slope will be constant. The slope of the indifference curve is given by (change in p3)/(change in p1) = (u(3) - u(1))/(u(2) - u(1)) = (3 - 1)/(2 - 1) = 2.

(b) For Alice, with the utility function u(1) = 1, u(2) = 4, and u(3) = 6, we can compare the expected utilities to determine her preference.

The expected utility of receiving 2 for sure is u(2) = 4.

The expected utility of a 50:50 gamble between 1 and 3 is (1/2)u(1) + (1/2)u(3) = (1/2)(1) + (1/2)(6) = 3.5.

Since the expected utility of receiving 2 for sure (4) is greater than the expected utility of the 50:50 gamble (3.5), Alice prefers receiving 2 for sure.

(c) To sketch the indifference curve for Alice, we connect the points (p1, p3) that yield the same utility level according to her utility function u(1) = 1, u(2) = 4, and u(3) = 6. Similar to Jack, the indifference curve will be upward sloping since Alice's utility increases with the outcome value.

The slope of this indifference curve can be calculated as (u(3) - u(1))/(u(2) - u(1)) = (6 - 1)/(4 - 1) = 5/3.

(d) For Bob, with the utility function u(1) = 9, u(2) = 12, and u(3) = 18, we can compare the expected utilities.

The expected utility of receiving 2 for sure is u(2) = 12.

The expected utility of a 50:50 gamble between 1 and 3 is (1/2)u(1) + (1/2)u(3) = (1/2)(9) + (1/2)(18) = 13.5.

Since the expected utility of the 50:50 gamble (13.5) is greater than the expected utility of receiving 2 for sure (12), Bob prefers the 50:50 gamble.

(e) To sketch the indifference curve for Bob, we connect the points (p1, p3) that yield the same utility level according to his utility function u(1) = 9, u(2) = 12, and u(3) = 18. Similar to Jack and Alice, the indifference curve will be upward sloping.

The slope of this indifference curve can be calculated as (u(3) - u

(1))/(u(2) - u(1)) = (18 - 9)/(12 - 9) = 3.

(f) The findings in parts (a) to (e) demonstrate that individuals' attitudes toward risk differ based on their utility functions. The slope of the indifference curve represents the marginal rate of substitution between the probabilities of different outcomes. Steeper indifference curves indicate a higher marginal rate of substitution and imply a higher aversion to risk.

In general, for a person with a utility function u(x1), u(x2), u(x3) and outcome values x=(x1, x2, x3), the equation for the curve of constant expected value is:

x1p1 + x2p2 + x3p3 = E

where E is the expected value.

The equation for the curve of constant expected utility is:

\(u(x1)p1 + u(x2)p2 + u(x3)p3 = U\)

where U is the constant expected utility level.

The condition for the indifference curve to be steeper, indicating higher risk aversion, is:

u''(x) > 0

This condition implies that the second derivative of the utility function with respect to the outcome values is positive, indicating diminishing marginal utility and higher risk aversion.

Please note that the equations and conditions provided are based on general principles and can be applied to utility functions and outcomes in various decision-making scenarios.

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\((\stackrel{x_1}{1}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{k}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{k}-\stackrel{y1}{3}}}{\underset{run} {\underset{x_2}{5}-\underset{x_1}{1}}}~~ = ~~\stackrel{\stackrel{m}{\downarrow }}{2} \\\\\\ \cfrac{k-3}{4}=2\implies k-3=8\implies k=11\)

Answer:

yuhhhh thanks brah hehehejejejne

Answer:

y = 28

Step-by-step explanation:

0.5y + y/ 3 = 0.25y + 7

1.5y / 3 = 0.25y + 7

y/2 = 0.25y + 7

y = ( 0.25y + 7)*2

y = 0.5y + 14

y - 0.5y = 14

0.5y = 14

y = 14/0.5

y = 28

The approximate amount of interest earned on the investment is c. $720.37.

The formula to calculate compound interest is given by:

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

Where:

A = the final amount (including principal and interest)

P = the principal amount (initial investment)

r = annual interest rate (as a decimal)

n = number of times interest is compounded per year

t = number of years

In this case, the principal amount (P) is $2,000, the annual interest rate (r) is 6.2% (or 0.062 as a decimal), the interest is compounded quarterly (n = 4), and the investment is held for 5 years (t = 5).

Plugging these values into the formula, we can calculate the final amount (A):

\(A = 2000(1 + 0.062/4)^{4*5}\\A ≈ $2,720.37\)

To calculate the interest earned on the investment, we subtract the principal amount from the final amount:

Interest = A - P

Interest ≈ $2,720.37 - $2,000

Interest ≈ $720.37

Therefore, the approximate amount of interest earned on the investment is $720.37. So the correct answer is c. $720.37.

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Answer:

200cm cubed

Step-by-step explanation:

Remember that volume of a rectangular prism is length x width x height

Answer: A) 200

Step-by-step explanation: The volume of a prism is length x width x height. Substitute the variables in this given prism into the equation.

Length = 10

Width = 5

Height = 4

V = 10 x 5 x 4 = 200

The percent of bags with a weight of more than 134 grams is approximately 5%.

To solve this problem using the empirical rule, we need to first calculate the z-score associated with a weight of 134 grams, using the formula:

z = (x - μ) / σ

where x is the weight of interest (134 grams in this case), μ is the mean (120 grams), and σ is the standard deviation (7 grams).

Substituting the values, we get:

z = (134 - 120) / 7 = 2

This means that a weight of 134 grams is 2 standard deviations above the mean.

According to the empirical rule:

About 68% of the population falls within one standard deviation of the mean.

About 95% of the population falls within two standard deviations of the mean.

About 99.7% of the population falls within three standard deviations of the mean.

Since a weight of 134 grams is 2 standard deviations above the mean, we can conclude that approximately 5% of bags should have a weight more than 134 grams, based on the 95% of the population within two standard deviations of the mean.

Therefore, the percent of bags with a weight of more than 134 grams is approximately 5%.

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The leader of the campfire girls troop can appoint 3 out of 14 members to clean up the camp in 364 ways.

The number of members in the campfire girls troop

= 14

The number of members the leader of the campfire girls troop can appoint at a time = 3

The number of ways to appoint r members out of n members

= nCr = n!/(r)!×(n-r)!

Therefore, the number of ways in which the leader of the campfire girls troop can appoint 3 out of 14 members to clean up the camp

= 14C3 = 14!/(3)!×(14-3)! = 364 ways

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Answer:

C.

Step-by-step explanation:

-1/4(12x+8)<=-2x+11

Distribute:

-3x-2<=-2x+11

Add 2x on both sides:

-1x-2<=0+11

Additive identity property applied:

-1x-2<=11

Add 2 on both sides:

-1x+0<=13

Additive identity property applied:

-1x<=13

Divide both sides by -1:

x>=-13 (dividing or multiplying both sides of an inequality by a negative means we must flip inequality sign)

Answer x>=-13

So the solution set includes any number greater than or equal to -13. That means we have everything to right of -13 including -13.

Answer:

0.25

Step-by-step explanation:

Probability is the chance you get a certain thing when you pick randomly. In this case, it's asking the probablility of picking someone from a whole student survey that does music or drama.

Looking at the two way table is easy! Out of all grades, 65 are in sports, 25 have music or drama, and 10 has work. Add them all up and get 100.

However, we only found the people in the survey. We need to find the probability of someone in music and drama. So we divide the number of people in all grades who take that class and divide it by the total amount- 25/100, this turns out for the probability to be 0.25.

[0] = { x ∈ Z | x^2 is even } is the set of all even integers, and [1] = { x ∈ Z | x^2 + 1 is even } is the set of all odd integers.

To prove that R is an equivalence relation on Z, we need to show that it satisfies the following three properties:

Reflexivity: For all x in Z, xRx.

Symmetry: For all x, y in Z, if xRy then yRx.

Transitivity: For all x, y, z in Z, if xRy and yRz then xRz.

Reflexivity: For all x in Z, x^2 + x^2 = 2x^2 is even. Therefore, xRx and R is reflexive.

Symmetry: For all x, y in Z, if xRy, then x^2 + y^2 is even. This means that y^2 + x^2 is also even, since even + even = even. Therefore, yRx and R is symmetric.

Transitivity: For all x, y, z in Z, if xRy and yRz, then x^2 + y^2 and y^2 + z^2 are both even. This means that (x^2 + y^2) + (y^2 + z^2) = x^2 + 2y^2 + z^2 is even. Since the sum of two even numbers is even, x^2 + 2y^2 + z^2 is also even, so xRz and R is transitive.

Since R is reflexive, symmetric, and transitive, it is an equivalence relation on Z.

The equivalence classes of R are the subsets of Z that contain all the integers that are related to each other by R. For any integer n in Z, the equivalence class [n] of n is the set of all integers that are related to n by R, i.e., [n] = {x ∈ Z | xRn}.

In this case, if n is even, then [n] contains all even integers because if x is even, then x^2 + n^2 is even. If n is odd, then [n] contains all odd integers because if x is odd, then x^2 + n^2 is even. So the set of equivalence classes of R is:

{ [n] | n ∈ Z }

where [n] = { x ∈ Z | x^2 + n^2 is even }.

For example, [0] = { x ∈ Z | x^2 is even } is the set of all even integers, and [1] = { x ∈ Z | x^2 + 1 is even } is the set of all odd integers.

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The numbers that could be added to 1/12 to make the sum greater than 1/2 are 9/24 and 4/9.

To make the sum greater than 1/2, we need to find the number that, when added to 1/12, gives a result greater than 1/2.

1/2 is the same as 6/12, so we need to find the number that, when added to 1/12, gives a result greater than 6/12.

1/12 + 5/12 = 6/12, which is not greater than 1/2.

1/12 + 9/24 = 1/12 + 3/8 = 11/24, which is greater than 1/2.

1/12 + 1/3 = 1/12 + 4/12 = 5/12, which is not greater than 1/2.

1/12 + 4/9 = 3/36 + 16/36 = 19/36, which is greater than 1/2.

Therefore, the numbers that could be added to 1/12 to make the sum greater than 1/2 are 9/24 and 4/9.

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To find the number of ternary strings of length n that have at least four 0s, we need to consider two cases: strings with exactly four 0s and strings with more than four 0s.

The total number of ternary strings of length n is 3^n, and the number of strings with exactly four 0s is given by the binomial coefficient C(n, 4). Therefore, the number of strings with at least four 0s is the sum of these two cases: C(n, 4) + C(n, 5) + C(n, 6) + ... + C(n, n).

A ternary string of length n can have 0, 1, 2, ..., or n 0s. To count the number of strings with exactly four 0s, we need to choose four positions out of the n positions to place the 0s, and the remaining positions can be filled with either 1s or 2s. The number of ways to choose four positions out of n is given by the binomial coefficient C(n, 4).

Similarly, for strings with more than four 0s, we need to choose five positions, six positions, and so on, up to n positions for the 0s. The number of ways to choose k positions out of n is given by C(n, k), where k ranges from 5 to n.

Therefore, the total number of ternary strings of length n with at least four 0s is the sum of all these cases: C(n, 4) + C(n, 5) + C(n, 6) + ... + C(n, n).

Note that C(n, k) represents the number of ways to choose k items out of n, and it is computed as C(n, k) = n! / (k!(n-k)!).

By summing up these binomial coefficients, we obtain the final answer for the number of ternary strings of length n that have at least four 0s.

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for every 60 grams of nuts, Babajan uses 40 grams of raisins and 100 grams weight of oats to make the breakfast cereal.

Raisins: 40 grams

Oats: 100 grams

Babajan makes breakfast cereal by mixing nuts, raisins and oats in the ratio 3 : 2 : 5 by weight. To work out the weight of raisins and the weight of oats she uses, we first need to determine the total weight of the ingredients. On Monday, Babajan uses 60 grams of nuts, so the total weight of the ingredients is 60 + (2/3) x 60 = 100 grams. The weight of raisins is then 2/5 x 100 = 40 grams, and the weight of oats is 5/5 x 100 = 100 grams. Therefore, for every 60 grams of nuts, Babajan uses 40 grams of raisins and 100 grams weight of oats to make the breakfast cereal.

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Answer

linear

nonproportional

Step-by-step explanation:

Since for each equal change in time (1 week), there is an equal change in weight (5 lb), the situation is linear.

At time zero, the first week, the weight was not zero. It was 60 lb, so it is not proportional.

Answer:

linear

nonproportional

Therefore, the value of n that makes the system of equations true is n = 10.

Given:

p = 2n

p - 5 = 1.5n

Substituting the value of p from the first equation into the second equation, we have:

2n - 5 = 1.5n

Next, we can solve for n by subtracting 1.5n from both sides of the equation:

2n - 1.5n - 5 = 0.5n - 5

Simplifying further:

0.5n - 5 = 0

Adding 5 to both sides of the equation:

0.5n = 5

Dividing both sides by 0.5:

n = 10

Therefore, the value of n that makes the system of equations true is n = 10.

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The volume common to two spheres, each with radius r, if the distance between their centres is r/2 is V = (11/12)×π×r³.

The attached diagram shows 2 circumferences with radius r and separated centres by r/2.

Let´s call circumferences  1 and 2; by symmetry, rotating area A will produce a volume V₁ identical to a V₂, Obtained by rotating area B ( both around the x-axis), then the whole volume V will be:

V = 2× V₁

V₁ = ∫π×y²×dx         (1)

Now

( x - r/2)²  +  y² = r²       the equation of circumference 1

y² = r² - ( x - r/2)²

Plugging this value in equation (1)

V₁ = ∫π×[  r² - ( x - r/2)²]×dx        with integrations limits    0 ≤ x ≤ r/2

V₁ = π×∫ ( r² - x² + (r/2)² - r×x )×dx

V₁ = π× [  r²×x - x³/3 + (r/2)²×x - (1/2) × r × x²]    evaluate between 0 and r/2

V₁ = π× [(5/4)×r²×x - x³/3 - (1/2) × r × x²]

V₁ =  π× [(5/4)×r² × ( r/2 - 0 ) - (1/3)×(r/2)³ -  (1/2) × r × (r/2)²]

V₁ =  π× [ (5/8)×r³ - r³/24 - r³/8]

V₁ =  π× (11/24)×r³

Then

V = 2× V₁

V = 2×π×11/24)×r³

V = (11/12)×π×r³

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Taylor bought 5 cupcakes and 8 muffins from the bakery costing $22.00

An equation is an expression that shows the relationship between two or more numbers and variables using mathematical operations. An equation can be linear, quadratic, cubic and so on, depending on the degree of the variable.

The slope intercept form of the linear equation is:

y = mx + b

where m is the slope and b is the initial value.

Let m represent the number of muffins and c represent the number of 2 cupcakes. Cupcakes cost $2.00 and muffins cost $1.50.

Taylor bought 13 cupcakes and muffins from the bakery, hence:

c + m = 13      (1)

Also, Taylor spent a total of $22.00, therefore:

2c + 1.5m = 22    (2)

From both equations:

c = 5, m = 8

Taylor bought 5 cupcakes and 8 muffins

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Answer:

Im pretty sure it's  D

Step-by-step explanation:

Srry if Im wrong.

Plz mark brainliest

The simple interest will be $36 and the amount will be $236

Given, the principal = $200

Rate of interest = 6%

Time = 3 years

Now, on using the formula of Simple Interest,

SI = (P×R×T)/100

SI = (200×6×3)/100

SI = $36

Now, the amount will be

Amount = 200 + 36

Amount = $236

Hence, the simple interest will be $36 and the amount will be $236

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Answer:

c) $43.81

Step-by-step explanation:

= $25.00 + ($0.09 × 209)

= $25.00 + $18.81

= $43.81

The error between the exponential function e^x and its third degree Taylor polynomial p3(x) = 1 + x + (x^2)/2 + (x^3)/6 can be computed by subtracting p3(x) from e^x. The error depends on the value of x and can be determined using the Taylor series remainder formula.

1. The error is generally smaller for values of x closer to zero, as the Taylor series approximation becomes more accurate near the expansion point. As x increases, the error tends to grow, indicating that the approximation becomes less accurate further away from the expansion point.

2. To compute the error ex−p3(x) for various values of x, we subtract the Taylor polynomial p3(x) from the exponential function e^x. The third degree Taylor polynomial is given by p3(x) = 1 + x + (x^2)/2 + (x^3)/6. Subtracting p3(x) from e^x gives us the error term ex−p3(x).

3. The error between the approximation and the actual value depends on the value of x. The Taylor series approximation becomes more accurate as x approaches zero, as the higher degree terms in the polynomial become relatively smaller compared to the lower degree terms. Thus, for values of x close to zero, the error is relatively small.

4. However, as x increases, the error tends to grow. This is because the Taylor series approximation is centered around the expansion point (in this case, x = 0), and as we move further away from the expansion point, the approximation becomes less accurate. Higher degree terms in the Taylor polynomial become relatively larger and contribute more to the error.

5. In conclusion, the error ex−p3(x) between the exponential function and its third degree Taylor polynomial depends on the value of x. The error is generally smaller for values of x closer to zero and tends to increase as x moves further away from the expansion point.

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Answer:

w = 25

Step-by-step explanation:

The 180-degree system and the axis of action are fundamental principles of filmmaking that help create a cohesive and engaging visual experience for the viewer.

The axis of action is a fundamental principle in film and video production, which is used to ensure that the continuity of a scene is maintained and that the viewer's spatial orientation is not disrupted.

It is also known as the 180-degree system because it is based on a visual guideline that involves maintaining a consistent spatial relationship between the camera and the subjects within the scene.

The 180-degree system establishes an imaginary line, also known as the axis of action, between two subjects or objects in a scene. The camera is then positioned on one side of this line, and the subjects are positioned on the other side, allowing the viewer to maintain their spatial orientation throughout the scene.

By maintaining a consistent axis of action, filmmakers can avoid disorienting the viewer and maintain continuity throughout the scene. This technique is especially important in dialogue scenes where the interaction between characters is a critical component of the story.

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Answer:

No

Step-by-step explanation:

It is not being multiplyed evenly on both sides with each other