Weekly CPU time used by an accounting firm has a probability density function (measured in hours) given by:f(y)={(3/64)y^2 * (y-4) 0 <= y <= 4={0 elsewhereA) Find the E(Y) and V(Y)B) The CPU time costs the firm $200 per hour. Find E(Y) and V(Y) of the weekly cost for CPU time. C) Would you expect the weekly cost to exceed $600 very often? Why?I'm good on part A, but am having a difficult time with B and C

If x = x1(t) and y = y1(t) and x = x2(t) and y = y2(t) are any two solutions of the linear nonhomogeneous system given by x' = p11(t)x + p12(t)y + g1(t), y' = p21(t)x + p22(t)y + g2(t), then x = x1(t) - x2(t) and y = y1(t) - y2(t) is a solution of the corresponding homogeneous system given by x' = p11(t)x + p12(t)y, y' = p21(t)x + p22(t)y.

To show that x = x1(t) - x2(t) and y = y1(t) - y2(t) is a solution of the corresponding homogeneous system, we need to verify that it satisfies the differential equations x' = p11(t)x + p12(t)y and y' = p21(t)x + p22(t)y with g1(t) = g2(t) = 0. Using the properties of derivatives, we can calculate that x' = x1'(t) - x2'(t) and y' = y1'(t) - y2'(t). Substituting these expressions and the expressions for x and y into the differential equations, we get:

x' = p11(t)x + p12(t)y

==> x1'(t) - x2'(t) = p11(t)(x1(t) - x2(t)) + p12(t)(y1(t) - y2(t))

==> p11(t)x1(t) + p12(t)y1(t) = p11(t)x2(t) + p12(t)y2(t)

y' = p21(t)x + p22(t)y

==> y1'(t) - y2'(t) = p21(t)(x1(t) - x2(t)) + p22(t)(y1(t) - y2(t))

==> p21(t)x1(t) + p22(t)y1(t) = p21(t)x2(t) + p22(t)y2(t)

Since x1(t), y1(t), x2(t), and y2(t) all satisfy the original nonhomogeneous system, we know that the expressions on the right-hand sides of the above equations are equal to g1(t) and g2(t), which are both zero in the corresponding homogeneous system. Therefore, x = x1(t) - x2(t) and y = y1(t) - y2(t) satisfy the differential equations x' = p11(t)x + p12(t)y and y' = p21(t)x + p22(t)y with g1(t) = g2(t) = 0, and hence they are a solution of the corresponding homogeneous system.

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The differential of the function z = x^6 ln(y^4) is dz = 6x^5 ln(y^4) dx + 4x^6 (1/y) dy.

To find the differential of the function z = x^6 ln(y^4), we use the rules of partial differentiation.

Taking the partial derivative of z with respect to x, we get ∂z/∂x = 6x^5 ln(y^4).

Taking the partial derivative of z with respect to y, we get ∂z/∂y = (4x^6/y) ln(y^4).

Then, using the differential notation, we can write dz = (∂z/∂x) dx + (∂z/∂y) dy.

Substituting the values we calculated for ∂z/∂x and ∂z/∂y, we get dz = 6x^5 ln(y^4) dx + 4x^6 (1/y) dy.

This represents the differential of the function z = x^6 ln(y^4).

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Answer:

X= 95 Y=55

Step-by-step explanation:

95X5= 475

2X55= 110

475+110= 585

I hope this helps! : )

The correlation coefficient between x and y is 0.61. The formula for the correlation coefficient (r) between two variables x and y is:

r = covariance(x, y) / (standard deviation(x) * standard deviation(y))

We are given that the covariance between x and y is 1225, the variance of x is 1600, and the variance of y is 2500. Since variance is the square of standard deviation, we can calculate the standard deviations of x and y as:

standard deviation(x) = sqrt(variance(x)) = √(1600) = 40

standard deviation(y) = sqrt(variance(y)) = √(2500) = 50

Plugging in these values into the formula for the correlation coefficient, we get:

r = 1225 / (40 * 50) = 0.61

r = 1225/(2000) = 0.61

Therefore, the correlation coefficient between x and y is 0.61.

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To draw a line and measure it to the nearest quarter inch, you will need a ruler or tape measure marked in inches.

Place the ruler or tape measure at one end of the line and align it so that the 0 mark lines up with the beginning of the line. Then, count the number of quarter inches to the end of the line and record the measurement.

Measuring to the nearest quarter inch means that you are rounding the measurement to the nearest multiple of 0.25 inches. For example, if the line measures between 3 and 3.24 inches, it would be rounded down to 3 inches; if it measures between 3.25 and 3.49 inches, it would be rounded up to 3.5 inches. This level of precision is commonly used in construction, woodworking, and other fields where precise measurements are important.

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The p-value for the given t-statistic falls between 0.005 and 0.01.

o find the p-value for the given t statistic of -2.63 with degrees of freedom of 24, we need to consult the t-distribution table or use statistical software.

Since the alternative hypothesis is μ < 100, we are conducting a one-tailed test in the left tail of the t-distribution. We want to find the area under the t-distribution curve to the left of -2.63.

Using the t-distribution table or software, we can determine that the p-value falls between 0.005 and 0.01. This means that the p-value for the statistic falls between 0.005 and 0.01.

Therefore, the p-value for the given t-statistic falls between 0.005 and 0.01.

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The perimeter of the triangle is 170 inches.

To solve for the perimeter, we first need to find the length of the perpendicular height. We can do this using the sine function:

sin(35°) = 46/x

x = 46/sin(35°) = 65 inches

Now that we know the length of the perpendicular height, we can find the length of the base of the triangle using the cosine function:

cos(35°) = 65/x

x = 65/cos(35°) = 75 inches

The perimeter of the triangle is the sum of the lengths of the three sides, so the perimeter is:

P = 65 + 75 + 30

= 170 inches

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Thus, we can find nonzero matrices a, b, and c such that ac = bc and a is not equal to b by using the distributive property of matrix multiplication. One example of such matrices is provided above.

The problem statement requires us to find three matrices - a, b, and c, such that their product ac is equal to bc but a is not equal to b. To solve this problem, we need to use the properties of matrix multiplication. One such property is the distributive property, which states that a(b + c) = ab + ac, where a, b, and c are matrices.

Let's assume that a, b, and c are all 2x2 matrices. One example of such matrices could be:

a = [1 0]
   [0 2]

b = [2 0]
   [0 1]

c = [1 2]
   [3 4]

Using these matrices, we can verify that ac = bc, as follows:

ac = [1 0]  [1 2] = [1 2]
    [0 2]  [3 4]   [6 8]

bc = [2 0]  [1 2] = [2 4]
    [0 1]  [3 4]   [3 4]

As we can see, both products result in the same matrix. However, a and b are not equal, as a(1,1) = 1 and b(1,1) = 2. Therefore, we have found an example of three nonzero matrices such that ac = bc but a is not equal to b.

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The integral of sin^4(8q)cos(8q) with respect to q is (1/40)sin^5(8q) + C or (3/8)cos(32q) - (1/64)cos(16q) + C, where C is the constant of integration.

Using the product-to-sum identity for cosine, we can rewrite the integrand as sin(2x+2x+2x+2x)cos(2x+2x) = [sin(2x+2x)cos(2x+2x) + sin(2x)cos(2x+2x+2x)]cos(2x+2x).

We can then use the double angle formula for sine and cosine to simplify the integrand to (3/8)sin(16x) - (1/8)sin(8x) + C. Therefore, the integral of sin4(8q)cos(8q) is (3/8)cos(16q) - (1/64)cos(8q) + C.

To evaluate the integral ∫sin4(8q)cos(8q)dq, we start by using the product-to-sum identity for cosine:

cos(a)sin(b) = 1/2[sin(a+b) + sin(a-b)]

We can rewrite the integrand as:

sin(8q)cos(8q)sin(8q)cos(8q) = [sin(8q+8q)cos(8q+8q) + sin(8q)cos(8q+8q+8q)]cos(8q+8q)

Using the double angle formula for sine and cosine, we can simplify the first term as:

sin(16q)cos(16q) = (1/2)sin(2*16q) = (1/2)sin(32q)

For the second term, we can apply the product-to-sum identity for sine:

sin(a)cos(b) = 1/2[sin(a+b) - sin(a-b)]

sin(8q)cos(8q+8q+8q) = 1/2[sin(8q+24q) - sin(8q-16q)] = 1/2[sin(32q) + sin(8q)]

Putting everything together, we have:

∫sin4(8q)cos(8q)dq = ∫[sin(16q)/2 + sin(32q)/2 + sin(8q)/2]cos(16q)dq

Using the substitution u = 16q, we have:

(1/16)∫[sin(u)/2 + sin(2u)/2 + sin(u/2)/2]cos(u)du

We can then integrate each term separately:

∫sin(u)cos(u)du = (1/2)sin^2(u) + C1

∫sin(2u)cos(u)du = (1/2)[(1/2)sin(3u)] + C2

∫sin(u/2)cos(u)du = -2cos(u/2) + C3

Substituting back, we get:

(1/16)[(1/2)sin^2(16q) + (1/4)sin^2(32q) - 2cos(8q) + C4]

Simplifying, we get:

(3/8)sin^2(16q) - (1/8)sin^2(8q) + C5

Using the identity sin^2(x) = (1-cos(2x))/2, we can rewrite this as:

(3/8)(1-cos(32q))/2 - (1/8)(1-cos(16q))/2 + C6

= (3/8)

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The length of the curve is approximately 0.873 units.

To find the length of the curve, we use the formula:

L = ∫a^b ||r'(t)|| dt

where r'(t) is the derivative of r(t), and ||r'(t)|| is the magnitude of r'(t).

First, let's find the derivative of r(t):

r'(t) = -5sin(5t) i + 5cos(5t) j - (5sin(t)/cos(t)) k

= -5sin(5t) i + 5cos(5t) j - 5tan(t) k

Next, let's find the magnitude of r'(t):

||r'(t)|| = sqrt[(-5sin(5t))^2 + (5cos(5t))^2 + (-5tan(t))^2]

= sqrt[25 + 25tan^2(t)]

Now, we can find the length of the curve:

L = ∫0^(π/4) sqrt[25 + 25tan^2(t)] dt

To solve this integral, we make the substitution u = tan(t), du/dt = sec^2(t), dt = du/sec^2(t), and rewrite the integral as:

L = ∫0^1 sqrt[25 + 25u^2] du/[(1 + u^2)^(1/2)]

Next, we make the substitution v = u/5, dv = du/5, and rewrite the integral as:

L = 5 ∫0^0.2 sqrt[1 + v^2] dv

Using the formula for the integral of the square root of a quadratic, we get:

L = 5/2 [(1/2)(1 + (0.2)^2)^(3/2) - (1/2)(1 + 0^(2))^(3/2)]

= 5/2 [(1.04)^(3/2) - 1]

≈ 0.873

Therefore, the length of the curve is approximately 0.873 units.

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Therefore, The double integral in polar coordinates involves integrating the function that defines the height of the solid over the region of the polar plane that defines the base of the solid.

To find the volume V of the solid bounded by the graphs of the equations using a double integral in polar coordinates, we first need to determine the limits of integration. This can be done by finding the intersection points of the curves. Once we have the limits, we can set up the integral as follows:
V = ∬R f(r,θ) rdrdθ
where R is the region in the polar plane bounded by the curves, and f(r,θ) is the height of the solid at each point (r,θ). We then evaluate the integral using the appropriate limits to obtain the volume of the solid.
The double integral in polar coordinates allows us to calculate the volume of a three-dimensional solid bounded by two or more surfaces defined in polar coordinates. It involves integrating the function that defines the height of the solid over the region of the polar plane that defines the base of the solid. The limits of integration are determined by finding the intersection points of the curves that bound the region. Once the limits are established, the integral is evaluated to find the volume of the solid.

Therefore, The double integral in polar coordinates involves integrating the function that defines the height of the solid over the region of the polar plane that defines the base of the solid.

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The given order of integration is dx first, then dy, and finally dz. To change the order of integration to dz first, then dx, and finally dy, we need to identify the new limits of integration. We can do this by using the given limits of integration and setting up the new integrals. The equivalent integral with the new order of integration is ∫0^1 ∫0^2x ∫0^20 f(x,y,z)dzdxdy.

To change the order of integration, we need to identify the new limits of integration. We can do this by looking at the given limits of integration and setting up the new integrals. First, we need to integrate with respect to z, so we set the limits of integration for z from 0 to 1 - 2x.

Next, we integrate with respect to x, so we set the limits of integration for x from 0 to 2y. Finally, we integrate with respect to y, so we set the limits of integration for y from 0 to 1/4.

Putting it all together, we get the equivalent integral with the new order of integration: ∫0^1 ∫0^2x ∫0^20 f(x,y,z)dzdxdy.

To change the order of integration, we need to identify the new limits of integration. We can do this by setting up the new integrals based on the given limits of integration. The equivalent integral with the new order of integration is ∫0^1 ∫0^2x ∫0^20 f(x,y,z)dzdxdy.

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The probability that 4 or more students score 85 percent or higher on the exam is 0.1209 or approximately 12.09 percent.

To solve this problem, we need to use the binomial distribution formula. We know that the probability of each student scoring 85 percent or higher on the exam is p = 0.2 (since 20 percent is equivalent to 85 percent or higher). We also know that n = 10 students took the exam.

Now we need to find the probability that 4 or more students score 85 percent or higher. We can use the binomial probability formula to calculate this:

P(X ≥ 4) = 1 - P(X < 4)

= 1 - (P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3))

= [tex]1 - [(10 choose 0) * 0.2^0 * (0.8)^10 + (10 choose 1) * 0.2^1 * (0.8)^9 + (10 choose 2) * 0.2^2 * (0.8)^8 + (10 choose 3) * 0.2^3 * (0.8)^7][/tex]
= 1 - (0.1074 + 0.2684 + 0.3020 + 0.2013)

= 0.1209

Therefore, the probability that 4 or more students score 85 percent or higher on the exam is 0.1209 or approximately 12.09 percent.

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Here, the outer sum is over the variable $i$ and it ranges from $1$ to $n$. For each value of $i$, the inner sum is over the variable $j$ and it ranges from $1$ to $3$.

The expression $j^2$ is the summand, which is added for each value of $j$.

The given sigma notation is:

n

___

\    j^2

/___

j=1

Expanding this sigma notation, we have:

= 1^2 + 2^2 + 3^2 + ... + (n-1)^2 + n^2

= (1 + 4 + 9 + ... + (n-1)^2) + n^2

The sum of squares up to n-1 can be expressed using the formula:

1^2 + 2^2 + 3^2 + ... + (n-1)^2 = n(n-1)(2n-1)/6

Substituting this in the above expression, we get:

= n(n-1)(2n-1)/6 + n^2

= (2n^3 - 3n^2 + n)/6

Therefore, the expanded form of the given sigma notation is (2n^3 - 3n^2 + n)/6.

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There are 96 different possible combos.

The principle used to calculate the number of possible combos is called the multiplication principle.

We have,

(a)

The number of possible combos, when you select a popcorn, a candy, and a soda.

= 8 (choices of candy) x 6 (choices of soda) x 2 (choices of popcorn)

= 96

(b)

The principle used to calculate the number of possible combos is called the multiplication principle.

Thus,

There are 96 different possible combos.

The principle used to calculate the number of possible combos is called the multiplication principle.

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Answer:

0.375 gallons

Step-by-step explanation:

Answer:

9749

Step-by-step explanation:

45000·(1+4%)5-45000

9749.38061

rounded to the nearest penny

9749

The equation of the tangent line:

y = (-x - sqrt(2)/2) - (π/2)(x - sqrt(2)/2)

To find the equation of the line tangent to the curve at the point corresponding to t = π/4, we need to find the first derivatives of x and y with respect to t, evaluate them at t = π/4, and then use these values to find the slope of the tangent line.

The first derivative of x with respect to t is:

dx/dt = -sint + tcost

The first derivative of y with respect to t is:

dy/dt = cost + tsint

Evaluating these at t = π/4, we get:

dx/dt|t=π/4 = -sqrt(2)/2

dy/dt|t=π/4 = (sqrt(2)/2) + (π/4)(sqrt(2)/2)

The slope of the tangent line is the ratio of the change in y to the change in x. So, the slope of the tangent line at t = π/4 is:

m = dy/dt|t=π/4 / dx/dt|t=π/4 = -1 - π/2

Now, we can use the point-slope form of the equation of a line to find the equation of the tangent line. Using the point (x(π/4), y(π/4)) = (sqrt(2)/2, sqrt(2)/2), we get:

y - (sqrt(2)/2) = (m)(x - sqrt(2)/2)

Substituting the value of m, we get:

y - (sqrt(2)/2) = (-1 - π/2)(x - sqrt(2)/2)

Expanding and simplifying, we get the equation of the tangent line:

y = (-x - sqrt(2)/2) - (π/2)(x - sqrt(2)/2)

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Answer: To compare the final amounts, we need to calculate the compound interest for Brianna and the simple interest for Audra.

For compound interest, the formula to calculate the future value is:

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

Where:

A = the future value/amount

P = the principal amount (initial investment)

r = the annual interest rate (as a decimal)

n = the number of times that interest is compounded per year

t = the number of years

For Brianna:

P = $16,500

r = 8% = 0.08

n = 1 (compounded annually)

t = 13 years

A = 16500(1 + 0.08/1)^(1*13)

A = 16500(1.08)^13

A ≈ $42,159.84

After 13 years, Brianna will have approximately $42,159.84.

For simple interest, the formula to calculate the future value is:

A = P(1 + rt)

Where:

A = the future value/amount

P = the principal amount (initial investment)

r = the annual interest rate (as a decimal)

t = the number of years

For Audra:

P = $16,500

r = 8% = 0.08

t = 13 years

A = 16500(1 + 0.08*13)

A = 16500(1 + 1.04)

A ≈ $39,720

After 13 years, Audra will have approximately $39,720.

To determine who will have more and by how much, we subtract Audra's amount from Brianna's amount:

Difference = Brianna's amount - Audra's amount

Difference = $42,159.84 - $39,720

Difference ≈ $2,439.84

Therefore, at the end of 13 years, Brianna will have approximately $2,439.84 more than Audra.

Step-by-step explanation: :)

Answer:

Brianna will have approximately $2,439.84 more than Audra.

hope it helps u

Step-by-step explanation:

After considering all the data we conclude that the area of the region enclosed by the astroid is (3/8) π a⁴, under the condition that  x = a cos3θ, y = a sin3θ.

The astroid curve is given by x = a cos³θ, y = a sin³θ. The area enclosed by the astroid curve is given by the integral of ½ y dx from θ = 0 to θ = 2π ².

Staging x = a cos³θ and y = a sin³θ in ½ y dx, we get:

½ y dx = ½ a sin³θ (−3a sin²θ dθ) = −3/2 a⁴ cos⁶θ sin⁴θ dθ

Applying Integration to this expression from θ = 0 to θ = 2π provides us the area enclosed by the astroid curve:

A = ∫₀²π −3/2 a⁴ cos⁶θ sin⁴θ dθ

A = (3/8) π a⁴

Therefore, the area enclosed by the astroid curve is (3/8) π a⁴.
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Answer:

Step-by-step explanation:

Side A has a length of 80 ft, side b has a length of 150 ft, and side c (the hypotenuse) has a length of 170 ft. Side A will represent a in the pythagorean theorem, side B will represent b, and side C (hypotenuse) will represent c in the equation. If the equation holds true, then the triangle is a right triangle.

So, we plug it in. a^2 + b^2 = c^2 becomes (80)^2 + (150)^2 = (170)^2

(80)^2 + (150)^2= 28,900

(170)^2= 28,900

since the answers are the same, we know the equation holds true, and thus the triangle is a right triangle. Hope this helps!!

Answer:

it will take 9 hours to empty the pool.

Step-by-step explanation:

The minimum order of the Taylor polynomial centred at O for cos x required to approximate cos (-0.85) with an absolute error no greater than 10-4 is 5.

The Taylor series for cos x centred at O is given by:

cos x = 1 - x^2/2! + x^4/4! - x^6/6! + ...

The nth-order Taylor polynomial for cos x centred at O is given by the first n terms of the Taylor series. We want to find the minimum n such that the absolute error between cos (-0.85) and the nth-order Taylor polynomial is no greater than 10-4.

The error term for the nth-order Taylor polynomial is given by:

Rn(x) = cos (c) * xn+1 / (n+1)!

where c is some value between 0 and x.

To find the minimum n, we need to find the value of n such that the error term is no greater than 10-4 for x = -0.85.

Substituting x = -0.85 into the error term and using the fact that |cos (c)| <= 1, we have:

|Rn(-0.85)| <= |(-0.85)^(n+1) / (n+1)!|

We want to find the minimum n such that the right-hand side is no greater than 10-4.

We can use a computer or calculator to find that n = 5 is the smallest integer that satisfies this condition. Therefore, the minimum order of the Taylor polynomial centred at O for cos x required to approximate cos (-0.85) with an absolute error no greater than 10-4 is 5.

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To determine the number of passes required to sort the elements using insertion sort, we need to first understand how insertion sort works. It involves comparing each element with the previous elements in the list and inserting it into the correct position.

So for this particular list of elements: 14, 12, 16, 6, 3, 10, we can see that the first pass would involve comparing the second element (12) with the first element (14) and swapping them to get: 12, 14, 16, 6, 3, 10.

The second pass would involve comparing the third element (16) with the second element (14) and leaving it in place, then comparing it with the first element (12) and swapping them to get: 12, 14, 16, 6, 3, 10.

Similarly, the third pass would involve comparing the fourth element (6) with the previous elements and inserting it into the correct position, resulting in: 6, 12, 14, 16, 3, 10.

The fourth pass would involve comparing the fifth element (3) with the previous elements and inserting it into the correct position, resulting in: 3, 6, 12, 14, 16, 10.

Finally, the fifth pass would involve comparing the sixth element (10) with the previous elements and inserting it into the correct position, resulting in the fully sorted list: 3, 6, 10, 12, 14, 16.

Therefore, the answer to this question would be 5, which is one of the answer choices given.

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The probability that a random sample of 20 pies will have a mean baking time that exceeds 48 minutes is approximately 0.0037 or 0.37%

We can use the central limit theorem to approximate the distribution of the sample mean baking time. Since the sample size is large enough (20 pies) and the population standard deviation is known, we can use the normal distribution to approximate the distribution of the sample mean.

The mean of the sample mean baking time is the same as the population mean, which is 45 minutes.

To find the probability that a random sample of 20 pies will have a mean baking time that exceeds 48 minutes, we can standardize the sample mean using the formula:

[tex]z=\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]

= (48-45)/(5/√20)

= 2.68

Using a standard normal distribution table or calculator, we can find that the probability of a standard normal random variable being greater than 2.68 is approximately 0.0037. Therefore, the probability that a random sample of 20 pies will have a mean baking time that exceeds 48 minutes is approximately 0.0037 or 0.37%

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The expression that is equivalent to (2x² + 7x - 15)/(3x² + 16x + 5) * (3x² - 2x - 1)/(2x² - x - 3) is (D) (x - 1)/(x + 1)

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

(2x² + 7x - 15)/(3x² + 16x + 5) * (3x² - 2x - 1)/(2x² - x - 3)

When the expressions are factored, we have:

(2x² + 7x - 15)/(3x² + 16x + 5) * (3x² - 2x - 1)/(2x² - x - 3) = (2x - 3)(x + 5)/(3x + 1)(x + 5) * (3x + 1)(x - 1)/(x + 1)(2x - 3)

Cancelling out the common factors, we have

(2x² + 7x - 15)/(3x² + 16x + 5) * (3x² - 2x - 1)/(2x² - x - 3) = (x - 1)/(x + 1)

This means that the equivalent expression is (D) (x - 1)/(x + 1)

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The 74th apple will be placed in second basket of apples.

Apples are distributed, one at a time, into six baskets. the first apple goes into basket one, the second into basket two, the third into basket three, and so on, until each basket has one apple.  

This pattern is repeated, beginning each time with basket one

Since there are 6 baskets, the pattern of distribution repeats every 6 apples.

Hence, to determine which basket the 74th apple will be placed in, we need to find the remainder when 74 is divided by 6:

=> 74 ÷ 6 = 12 remainder 2

This means that the 74th apple will be placed in the second basket, since it follows the pattern of distributing apples starting with the first basket.

Therefore,

The 74th apple will be placed in second basket of apples.

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The cooling rate of the turkey is 0.45°F per minute. This means that every minute, the temperature of the turkey decreases by 0.45°F.

The cooling rate of a roasted turkey can be determined by the rate at which it loses heat to its surroundings. In this case, the temperature of the turkey was 191°F when it was taken out of the oven and placed on a table in a room with a temperature of 75°F. After half an hour, the temperature of the turkey had decreased to 155°F.

To calculate the cooling rate, we can use Newton's law of cooling, which states that the rate of heat loss of an object is proportional to the difference in temperature between the object and its surroundings. The equation for Newton's law of cooling is:

dT/dt = -k (T - Ts)

where dT/dt is the rate of change of temperature with respect to time, T is the temperature of the turkey at time t, Ts is the temperature of the surroundings (75°F), and k is a constant that depends on the specific heat of the turkey, its surface area, and other factors.

To solve for k, we can use the data given:

dT/dt = -k (T - Ts)

-36 = -k (155 - 75)

-36 = -k (80)

k = 0.45

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