what is the volume of a rectangular prism with a length of 24½ feet, a width of 14 feet, and a height of 11 ft?

A. 3,773 ft³
B. 1,886 ½ ft³
C. 1,462 ft³
D. 731 ft³​

The solution to the initial value problem dy/dФ + y = sin Ф is: y = (-cos Ф + 2)/e^Ф.

To solve the initial value problem dy/dФ + y = sin Ф, we first need to find the integrating factor, which is given by e^Ф. Multiplying both sides by the integrating factor, we get:

e^Ф(dy/dФ) + e^Фy = e^Фsin Ф

Now, we can use the product rule to simplify the left-hand side:

(d/dФ)(e^Фy) = e^Фsin Ф

Integrating both sides with respect to Ф, we get:

e^Фy = -cos Ф + C

where C is a constant of integration. Solving for y, we get:

y = (-cos Ф + C)/e^Ф

To find the value of C, we use the initial condition y(0) = 1. Substituting this into the equation above, we get:

1 = (-cos 0 + C)/e^0
1 = (-1 + C)/1
C = 2

Therefore, the solution to the initial value problem dy/dФ + y = sin Ф is:

y = (-cos Ф + 2)/e^Ф

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The area of four surfaces unpainted in the 6 cubes is 64 cm².

We have,

The volume of the shape = 384 cm³

Number of cubes = 6

This means,

Area of one cube.

= 384/6

= 64 cm³

Now,

Area of cube = side³

So,

side³ = 64

side³ = 4³

side = 4

Now,

There are four surfaces unpainted.

so,

One surface is in the shape of a rectangle.

This means,

One surface area = 4 x 4 = 16 cm²

Now,

Area of four surfaces unpainted.

= 4 x 16

= 64 cm²

Thus,

The area of four surfaces unpainted is 64 cm².

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The given function f(x) = 2/x²+1 is continuous on the closed interval [-1,2] and differentiable on the open interval (-1,2). To find the global minimum and maximum values of f(x) on the interval (-1,2], we need to find the critical points and the endpoints of the interval.

First, we find the critical points by setting the derivative of f(x) equal to zero:

f'(x) = -4x/(x²+1)² = 0
=> x = 0

Next, we evaluate f(x) at the critical point and the endpoints of the interval:

f(-1) = 2/2 = 1
f(2) = 2/5
f(0) = 2/1 = 2

Therefore, the global minimum value of f(x) on the interval (-1,2] is 1, which occurs at x = -1, and the global maximum value of f(x) is 2, which occurs at x = 0.

To find the global minimum and maximum of the continuous function f(x) = 2/x² + 1 on the interval (-1, 2], we'll follow these steps:

1. Calculate the derivative of the function.
2. Set the derivative equal to zero and solve for x.
3. Determine critical points by evaluating the second derivative or checking intervals.
4. Compare the function values at the critical points and endpoints to determine the global minimum and maximum.

Step 1: Calculate the derivative of f(x) = 2/x² + 1.
f'(x) = d(2/x² + 1)/dx = -4x / (x² + 1)²

Step 2: Set the derivative equal to zero and solve for x.
0 = -4x / (x² + 1)²
0 = -4x (since the denominator cannot be zero)

x = 0

Step 3: Determine critical points.
f'(x) changes sign around x = 0, so it is a critical point.

Step 4: Compare function values at critical points and endpoints.
f(-1) = 2/((-1)² + 1) + 1 = 2/2 + 1 = 2
f(0) = 2/(0² + 1) + 1 = 2/1 + 1 = 3
f(2) = 2/(2² + 1) + 1 = 2/5 + 1 = 1.4

The global minimum value is 1.4 at x = 2, and the global maximum value is 3 at x = 0.

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The angle between the two planes is 113.75°.

Firstly, we find the normal vectors of each plane. The normal vector of a plane is the vector perpendicular to the plane.

The first equation can be rewritten as:

6x - 8y + 10z = 12

Note that the coefficients of x, y, and z represent the components of the normal vector.

So the normal vector of the first plane is:

N₁ = <6, -8, 10>

For the second equation, the plane can be extracted:

x + y - z = 2

N₂ = <1, 1, -1>

The angle between the two planes can be found using the dot product of the normal vectors and the formula:

cosθ = (N₁ . N₂) / (|N₁| |N₂|)

where |N| represents the magnitude of vector N.

The dot product of the normal vectors is:

N1 . N2 = (6)(1) + (-8)(1) + (10)(-1) = -12

The magnitudes of the normal vectors are:

|N1| = sqrt(6² + (-8)² + 10²) = sqrt(296) = 17.205

|N2| = sqrt(1² + 1² + (-1)²) = sqrt(3) = 1.732

Substituting these values into the formula gives:

cosθ = (N1 . N2) / (|N1| |N2|)

cosθ = -12 / (17.205 * 1.732)

cosθ = -12/29.799

cosθ = -0.4027

The angle θ can be found using the inverse cosine function:

θ = cos⁻¹(0.4027)

θ ≈ 113.75°

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The value of T(1) by taking cross product r'(t) x r"(t) = [tex](-144(1)^2, 0, 24)[/tex] = (-144, 0, 24).

To find the derivative of r(t), we can differentiate each term separately with respect to t:

r(t) = [tex](4t, 3t^2, 4t^3)[/tex]

r'(t) = [tex](d/dt)(4t, 3t^2, 4t^3) = (4, 6t, 12t^2)[/tex]

To find r"(t), we can differentiate r'(t) with respect to t:

r"(t) = [tex](d/dt)(4, 6t, 12t^2)[/tex] = (0, 6, 24t)

To find r'(1), we can substitute t = 1 into r'(t):

r'(1) = [tex](4, 6(1), 12(1)^2)[/tex] = (4, 6, 12)

To find r′(t) x r″(t), we can take the cross product of r'(t) and r"(t):

r'(t) x r"(t) = [tex](4, 6t, 12t^2) * (0, 6, 24t) = (-144t^2, 0, 24)[/tex]

Finally, we can substitute the values we found into the last equation to find T(1):

T(1) = r'(t) x r"(t) = [tex](-144(1)^2, 0, 24) = (-144, 0, 24)[/tex]

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The annual tax payment for an employee at the 40% tax rate who does not make a financial contribution towards an executive car would be $20,000.

You need to know the employee's taxable income to determine the annual tax payment for a worker paying a 40% tax rate who does not contribute financially to an executive automobile.

Assume the employee does not receive any deductions or allowances, and their taxable income is $50,000 per year.

You must first determine their gross income tax, which is the amount of tax they would pay if their whole taxable income were subject to a 40% tax.

Gross Income Tax = Taxable Income x Tax Rate

Gross Income Tax = $50,000 x 0.4 = $20,000

Then, take away any deductions or allowances to which the employee is entitled. The employee's net income tax in this instance is equal to their gross income tax because it is assumed that they are not eligible for any deductions or allowances.

Therefore, the annual tax payment for an employee at the 40% tax rate who does not make a financial contribution towards an executive car would be $20,000.

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The complete question is -

What is the annual tax payment for an employee at the 40% tax rate who does not make a financial contribution towards an executive car and earns taxable income of $50,000 per year?

The probability that the candy is red or green is given as follows:

P = 0.29.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

For this problem, we are given the distribution, hence we must only obtain the desired probabilities, as follows:

Hence the probability that the candy is red or green is given as follows:

p = 0.13 + 0.16 = 0.29.

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The normal component of the acceleration vector (a_n) is a_n = √(|a(t)|^2 - a_t^2).

To find the tangential and normal components of the acceleration vector for the given position vector r(t) = 7e^t*i + 7√2^t*j + 7e^(-t)*k, follow these steps:

1. Differentiate the position vector r(t) to find the velocity vector v(t):

v(t) = dr(t)/dt = (7e^t)*i + (7√2^t * ln(√2))*j - (7e^(-t))*k

2. Differentiate the velocity vector v(t) to find the acceleration vector a(t):

a(t) = dv(t)/dt = (7e^t)*i + (7√2^t * ln^2(√2))*j + (7e^(-t))*k

3. Calculate the magnitude of the velocity vector |v(t)|:

|v(t)| = √((7e^t)^2 + (7√2^t * ln(√2))^2 + (7e^(-t))^2)

4. Find the tangential component of the acceleration vector (a_t):

a_t = (a(t) • v(t)) / |v(t)|

Here, '•' denotes the dot product.

5. Find the normal component of the acceleration vector (a_n):

a_n = √(|a(t)|^2 - a_t^2)

By following these steps, you can find the tangential and normal components of the acceleration vector for the given position vector r(t).

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The length of diagonal is 8√6 cm.

We have,

Sides of Square = 8√3 cm

Then, the length of diagonal

= a√2

= 8√3 x √2

= 8√6 cm

Thus, the length of diagonal is 8√6 cm.

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The two height functions are h₁(t) = −16t² + 121 is a vertical translation of h₂(t) = −16t² + 225. The y-intercept of h₁ is 104 ft less than that of h₂. The correct answer is option (c)

To understand why this is the correct answer, let's first understand what the given information represents. Two identical baseballs are dropped from different heights, and we are asked to find their respective height functions. The height function gives the height of the baseball at any given time during its descent.

We know that the height function of a ball dropped from a height h₀ is given by h(t) = −16t² + h₀, where t is the time in seconds since the ball was dropped.

Using this formula, we can find the height functions for the two baseballs:

For the first baseball dropped from a height of 121 feet, the height function is h₁(t) = −16t² + 121.

For the second baseball dropped from a height of 225 feet, the height function is h₂(t) = −16t² + 225.

Now, we are given that h₁(t) is a vertical translation of h₂(t) with a difference of 104 ft in the y-intercept. This means that h₁(t) can be obtained from h₂(t) by shifting the graph vertically downward by 104 ft.

Since both functions have the same leading coefficient (-16), they have the same shape but different y-intercepts. Therefore, the correct option is (c).

Comparing their graphs, we can see that h₂(t) starts at a higher point on the y-axis (225 ft) and drops faster than h₁(t) which starts at a lower point (121 ft) and drops at a slower rate. This is because the greater the initial height, the longer it takes for the ball to reach the ground.

The correct answer is option (c)

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The price difference between buying 12 cookies individually and buying them by the dozen is $0.40

Note that from the question, the price of Cookies A is $0.20 for each cookie, so to buy 12 cookies solely, Thus Trisha would need to pay:

12 * $0.20

= $2.40

Since price of Cookies A is $2.00 per dozen, to buy 12 cookies by the dozen, Trisha will pay:

1 * $2.00

= $2.00

Hence the difference in price of buying 12 cookies solely and buying by the dozen is:

$2.40 - $2.00

= $0.40

Therefore, the price is $0.40 cheaper for Trisha to buy 12 cookies by the dozen than to buy them individually.

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The trinomial form of the expression (2x + 8) (х - 3) is 2x² + 2x - 24.

Given the expression in the question:

(2x + 8) (х - 3)

First, we expand using the distributive property.

(2x + 8) (х - 3)

2x(х - 3) + 8(х - 3)

2x×х + 2x×-3 + 8×х +8×-3

Multiplying, we get:

2x² -6x + 8х - 24

Collect and add like terms

Add -6x and 8x

2x² -6x + 8х - 24

2x² + 2x - 24

Therefore, the expanded form is 2x² + 2x - 24.

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The limit is found to  diverge to negative infinity and if we can out the divergence test, we find out that the given series diverges.

The simplest divergence test also known as  the divergence Test, is used to determine whether the sum of a series diverges based on the series's end-behavior.

In the scenario above,  we will compare the given series with the series 1/n^2, which is a known convergent series.

we take  the limit as n approaches infinity of the ratio of the two series, we get:

lim (n^2(6n^3-4))/(1(n^2))

= lim (6n^5 - 4n^2)/(n^2)

= lim 6n^3 - 4 = infinity

We remember that the divergence test states that if the limit of the terms of a series does not approach zero, then the series diverges.

we also go ahead to take the limit as n approaches infinity of the ratio of the given series, we get:

lim (n^2(6n^3-4))/(n^3) = lim 6n - 4/n = infinity

In conclusion, the limit is found to  diverge to negative infinity and if we can out the divergence test, we find out that the given series diverges.

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T(t) = (7cos(t)sec(t))i + (7)j.To find the unit tangent vector T(t), we need to find the derivative of the position vector r(t) with respect to t and then normalize it. The position vector r(t) is given as r(t) = 7ln(sec(t))i + 7tj.

Taking the derivative, we have dr/dt = (7cos(t)sec(t))i + 7j.To normalize dr/dt, we divide it by its magnitude, which is √((7cos(t)sec(t))^2 + 7^2).

Simplifying this expression gives √(49cos^2(t)sec^2(t) + 49), which simplifies further to 7sec(t). Dividing dr/dt by its magnitude, we get T(t) = (7cos(t)sec(t))i + (7)j.

Therefore, T(t) = (7cos(t)sec(t))i + (7)j.

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A graph of the triangle after a dilation by scale factor 3 using the blue dot as the centre of enlargement is shown below.​

In Mathematics and Geometry, a dilation is a type of transformation which typically changes the size of a geometric object, but not its shape.

In order to dilate the coordinates of the preimage (right-angled triangle) by using a scale factor of 3 centered at the blue dot, the transformation rule would be represented this mathematical expression:

(x, y)  →  (k(x - a) + a, k(y - b) + b)

(x, y)  →  (3(x - a) + a, 3(y - b) + b)

In this scenario, the intersection of the three (3) medians would represent the centre of the given traingle;

AO ≅ 20D

BO ≅ 20E

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If a series is convergent, it does not necessarily follow that other series are also convergent. In fact, whether or not a series converges depends on the specific terms of the series being considered.

For example, if we have a series with alternating positive and negative terms, like (-1) ^n/n, then it converges by the alternating series test. However, if we simply add 1 to each term, we get the series 1/n + (-1)^(n+1)/n, which diverges. Similarly, if we have a geometric series with common ratio between -1 and 1, it converges, but if we add or subtract terms, it may no longer converge. Therefore, the correct statement is that just because a series is convergent, it isn't necessarily true that the other series are convergent.

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The sum of the squares of two consecutive even integers, where the first one is 2n, is 4(1+n)²

Consider two successive even integers, the first being 2n. 2n+2 is the next even integer.

The sum of the squares of these two consecutive even numbers is shown following.:

(2n)² + (2n+2)²

Simplifying this expression, we get:

4n² + 4n² + 8n + 4

Combining like terms, we get:

8n² + 8n + 4

We may deduct a 4 from this equation to obtain:

4(2n² + 2n + 1)

Now we can simplify further using the identity (a+b)² = a² + 2ab + b², where a = 1 and b = n:

4(1+n)²

Therefore, the sum of the squares of two consecutive even integers, where the first one is 2n, is 4(1+n)².

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The sum of the polynomials 4x³ + 6x²+ 2x - 3 and 3x³ + 3x² - 5x - 5 is 7x³ + 9x² - 3x - 8.

Given are two polynomials.

4x³ + 6x²+ 2x - 3 and 3x³ + 3x² - 5x - 5

We have to find the sum of these polynomials.

These have to be added operating the like terms.

Here 4x³ and 3x³ are the like terms.

6x² and 3x² are the like terms.

2x and -5x are the like terms.

-3 and -5 are like terms.

(4x³ + 6x² + 2x - 3) + (3x³ + 3x² - 5x - 5) = (4x³ + 3x³) + (6x² + 3x²) + (2x - 5x) + (-3 - 5)

= 7x³ + 9x² - 3x - 8

Hence the sum of the polynomials is 7x³ + 9x² - 3x - 8.

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The limit of [tex](2x^2-y^2)^{11}/(x^2+2y^2)[/tex] as (x,y) approaches (0,0) is path-dependent and does not exist. The paths y=mx and x=my are used to demonstrate this. The expression approaches a value that depends on the constant m and the chosen path.

To show that the limit does not exist, we need to find two paths to the origin along which the limit has different values. Consider the path y = mx, where m is a constant. As (x,y) approaches (0,0) along this path, we have:

[tex](2x^2 - y^2)^{(11)} / (x^2 + 2y^2)[/tex]

[tex]= (2x^2 - (mx)^2)^{(11)} / (x^2 + 2(mx)^2)[/tex]

[tex]= (2 - m^2)^{11} / (1 + 2m^2)[/tex]

As x approaches 0, this expression approaches [tex](2 - m^2)^{11} / (2m^2)[/tex], which depends on the value of m. Thus, the limit depends on the path chosen, and so the limit does not exist.

Similarly, we can consider the path x = my, where m is a constant, and obtain:

[tex](2x^2 - y^2)^{(11)} / (x^2 + 2y^2)[/tex]

[tex]= (2(my)^2 - y^2)^{(11)} / (m^2y^2 + 2y^2)[/tex]

[tex]= (2m^2 - 1)^{11} / (m^2 + 2)[/tex]

As y approaches 0, this expression approaches[tex](2m^2 - 1)^{11} / 2m^2[/tex], which again depends on the value of m. Therefore, the limit does not exist.

In summary, we showed that the limit of[tex](2x^2-y^2)^{11}/(x^2+2y^2)[/tex] as (x,y) approaches (0,0) does not exist, by considering two different paths to the origin and showing that the limit depends on the value of the parameter in each case.

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Cross multiplying

20 × 5 = t × t

100 = 2t

Dividing 2 on the opposite side

100/2 = t

t = 50

The partial derivatives of f with respect to r, s, and t are: ∂f/∂r = y + 0.06tx + 0.02t, ∂f/∂s = y + 0.02s and ∂f/∂t = y + 0.06rx - 0.14x + 0.02r.

To compute the partial derivatives of f(x,y,z) with respect to r, s, and t, we will use the chain rule.

∂f/∂r = ∂f/∂x * ∂x/∂r + ∂f/∂y * ∂y/∂r + ∂f/∂z * ∂z/∂r

∂f/∂s = ∂f/∂x * ∂x/∂s + ∂f/∂y * ∂y/∂s + ∂f/∂z * ∂z/∂s

∂f/∂t = ∂f/∂x * ∂x/∂t + ∂f/∂y * ∂y/∂t + ∂f/∂z * ∂z/∂t

First, we calculate the partial derivatives of the component functions with respect to r, s, and t:

∂x/∂r = 1, ∂x/∂s = 1, ∂x/∂t = -7

∂y/∂r = 3t, ∂y/∂s = 0, ∂y/∂t = 3r

∂z/∂r = t, ∂z/∂s = s, ∂z/∂t = 0

Then, we compute the partial derivatives of f with respect to x, y, and z:

∂f/∂x = y, ∂f/∂y = x, ∂f/∂z = 2%

Finally, we substitute all the partial derivatives into the chain rule formula to obtain:

∂f/∂r = y + 3tx(2%) + 2%(t)

∂f/∂s = y + 2%(s)

∂f/∂t = y + 3rx(2%) - 7x(2%) + 2%(r)

Therefore, the partial derivatives of f with respect to r, s, and t are:

∂f/∂r = y + 0.06tx + 0.02t

∂f/∂s = y + 0.02s

∂f/∂t = y + 0.06rx - 0.14x + 0.02r

where 2% is written as 0.02 for simplicity.

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A 2x2 matrix A=[0.750 -0.250 -0.250 0.750] lim (n -> infinity) A^n = [1, -1; 0, 0] is the limit of the matrix A as n approaches infinity.

To compute the limit of the matrix A as n approaches infinity, we first need to find its eigenvalues and eigenvectors. For A = [0.750, -0.250; -0.250, 0.750], the eigenvalues are λ1 = 1 and λ2 = 0.5.

Their corresponding eigenvectors are v1 = [1; 1] and v2 = [-1; 1]. Now, we'll express A in the diagonalized form. Let P be the matrix formed by the eigenvectors, and D be the diagonal matrix with eigenvalues on the diagonal. So, P = [1, -1; 1, 1] and D = [1, 0; 0, 0.5].

Then, A = PDP^(-1). As n approaches infinity, the powers of D^n will tend towards a diagonal matrix with 1's and 0's: lim (n -> infinity) D^n = [1, 0; 0, 0]

Now, compute the limit of A^n: lim (n -> infinity) A^n = lim (n -> infinity) (PDP^(-1))^n = PD^nP^(-1) = [1, -1; 1, 1] [1, 0; 0, 0] [1, 1; -1, 1] Multiply the matrices to get the final result: lim (n -> infinity) A^n = [1, -1; 0, 0] This is the limit of the matrix A as n approaches infinity.

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Answer:

Yes, we can still find the median. You just need to convert the rest to the given data / kilograms and you have to just do the steps of finding the median.

To evaluate the derivative of the given function for the given value of x, we will use the power rule of differentiation. The function given is: y = √x(1-x)

Step 1: Rewrite the function using the product rule: y = (√x)(1-x)

Step 2: Apply the power rule of differentiation to the first factor, √x:

y' = [(1/2)x^(-1/2)](1-x) + (√x)(-1)

Step 3: Simplify by combining like terms:

y' = [(1-x)/2√x] - √x

Step 4: Plug in x = 4 to find the derivative at that specific value:

y' = [(1-4)/2√4] - √4

y' = [-3/4] - 2

y' = -2.75

Therefore, the derivative of the given function for the given value of x=4 is -2.75. I believe you meant to ask for the derivative of the function y = √x - x, evaluated at x = 4. Here are the steps to find the derivative and evaluate it:

1. Write down the given function: y = √x - x

2. Rewrite the function using exponents: y = x^(1/2) - x

3. Apply the power rule to find the derivative: dy/dx = (1/2)x^(-1/2) - 1

4. Simplify the derivative: dy/dx = (1/2)(x^(-1/2)) - 1

5. Evaluate the derivative at x = 4: dy/dx = (1/2)(4^(-1/2)) - 1

6. Calculate the values: dy/dx = (1/2)(1/2) - 1

7. Simplify the final answer: dy/dx = 1/4 - 1 = -3/4

So, the derivative of the given function at x = 4 is -3/4.

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(a) Yes, it is plausible that the population distribution is normal. (b) Using the sample data, the mean is 51.769 and the standard deviation is 16.611. (c) Using the same data, the prediction interval for a single healthy individual with a 95% confidence level is (11.260, 92.277).

(a) No, it is not plausible that the population distribution from which this sample was selected is normal because the sample size is small and the data is not symmetrical.
(b) To calculate the 95% confidence interval for the population mean, follow these steps:
1. Calculate the sample mean (P) and standard deviation (s):
P = (24 + 39 + 40 + 42 + 43 + 47 + 51 + 58 + 64 + 65 + 67 + 69 + 73) / 13 ≈ 51.154
s ≈ 15.073 (calculated using a standard deviation calculator)
2. Find the t-value for a 95% confidence interval with 12 degrees of freedom (n - 1 = 13 - 1 = 12):
t ≈ 2.179 (using a t-table)
3. Calculate the margin of error (ME):
ME = t * (s / sqrt(n)) ≈ 2.179 * (15.073 / sqrt(13)) ≈ 9.028
4. Calculate the 95% confidence interval:
(51.154 - 9.028, 51.154 + 9.028) = (42.126, 60.182)
(c) To calculate the 95% prediction interval for a single healthy individual, follow these steps:
1. Calculate the standard error (SE) for an individual prediction:
SE = s * sqrt(1 + 1/n) ≈ 15.073 * sqrt(1 + 1/13) ≈ 15.604
2. Calculate the prediction interval:
(51.154 - 2.179 * 15.604, 51.154 + 2.179 * 15.604) = (18.077, 84.231)
The width of the 95% prediction interval is greater than the width of the interval calculated in part (b).

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The highest free throw of 82% has an average bowling score of 108

This ordered pair represents the ordered pair of the highest x value in the graph

From the graph, the ordered pair is (82, 108)

It means that the student with the highest free throw of 82% has an average bowling score of 108

This ordered pair represents the ordered pair of the highest y value in the graph

From the graph, the ordered pair is (80, 112)

It means that the student with the highest free throw of 80% has an average bowling score of 112

From the graph, we can see that the association is a positive linear association

This is because as the free throw percents increases, the average bowling score is also expected to increase

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Complete question

The members of a school basketball team went bowling for a season ending party. They made this scatter plot to compare their free throw percents for the season and their average bowling score for 3 games.

Part A:

What ordered pair represents the student with the highest free throw percent? Explain the meaning of each coordinate in the ordered pair.

Part B:

What ordered pair represents the student with the highest bowling average? Explain the meaning of each coordinate in the ordered pair.

Part C:

Is the association between free throw percent and bowling average linear or nonlinear? If it is linear, is the relationship positive, negative, or neither? State the association, if any, in terms of the variables.

To find the marginal average profit function, we first need to find the average profit function. The average profit function is given by:

A(x) = P(x)/x

where P(x) is the total profit function.

So, we have:

A(x) = (2x - 4)(9x - 7)/x

Now, to find the marginal average profit function, we take the derivative of the average profit function with respect to x:

A'(x) = [2(9x - 7) + (2x - 4)(9)]/x^2

Simplifying this expression, we get:

A'(x) = (20x - 50)/x^2

Therefore, the marginal average profit function is:

A'(x) = 20/x - 50/x^2

To find the marginal average profit function, we first need to find the derivative of the total profit function P(x) = (2x - 4)(9x - 7).

Using the product rule, we get:

P'(x) = (2x - 4)(9) + (2)(9x - 7)

P'(x) = 18x - 36 + 18x - 14

Now, simplify the expression:

P'(x) = 36x - 50

So, the marginal average profit function is P'(x) = 36x - 50.

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The number 2 in Prachi's model represents a quadratic equation of the number of hours spent studying before the test that is considered the "baseline" or reference point for the model.

Prachi's model is a quadratic equation with a negative coefficient on the squared term, which means it opens downward and has a maximum point. The term (t - 2) in the equation represents the deviation of the number of hours spent studying from the baseline value of 2 hours. Therefore, the coefficient -3 in front of the squared term indicates that the maximum point of the quadratic function occurs at t = 2. This means that if Prachi had studied for exactly 2 hours before the test, she would have answered the maximum number of questions correctly, which is 45.

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Answer:

1 solution

Step-by-step explanation:

refer to the image above