Find the volume of a sphere with a radius of 8 cm.

-5° F represents the change in the temperature of the park city.

Given that the temperature of a park city has been decreased or dropped by 5° F,

We need to represent this as an integer,

So, here dropped means decrease in temperature, that mean whatever was the temperature it is decreased by 5° F.

That mean the change is in negative.

Hence -5° F represents the change in the temperature of the park city.

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Riemann sum with right endpoints and n = 8 is -93

We can divide [0,4] into 8 subintervals with right endpoints

The widths of those smaller intervals is 0.5

We get the following right subinterval endpoints: 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0

Remember, this is a right Riemann sum.

Now we evaluate the function x²- 5x at those right endpoints and we get the heights of our 8 little rectangles of -2.25, -4.00, -5.25, -6.00, -6.25, -6.0,-5.25, -4.00

f(x) = x²- 5x when x = 0.5

f(x) = (0.5)² - 5(0.5)

f(x) = -2.25

f(x) = x²- 5x when x = 1.0

f(x) = (1)² - 5(1)

f(x) = -4

f(x) = x²- 5x when x = 1.5

f(x) = (1.5)² - 5(1.5)

f(x) = -5.25

f(x) = x²- 5x when x = 2

f(x) = (2)² - 5(2)

f(x) = - 6

f(x) = x²- 5x when x = 2.5

f(x) = (2.5)² - 5(2.5)

f(x) = -6.25

f(x) = x²- 5x when x = 3

f(x) = (3)² - 5(3)

f(x) = -6

f(x) = x²- 5x when x = 3.5

f(x) = (3.5)² - 5(3.5)

f(x) = -5.25

f(x) = x²- 5x when x = 4

f(x) = (4)² - 5(4)

f(x) = -4

To find the area we multiply the width of each rectangle times its height and we get the areas of our 8 rectangles:

Area = L × B when L = 0.5 B = -2.25

Area = - 1.125

Area = L × B when L = 1 B = - 4

Area = - 4

Area = L × B when L = 1.5 B = - 5.25

Area = -7.875

Area = L × B when L = 2.0 B = -6

Area = -12

Area = L × B when L = 2.5 B = -6.25

Area = -15.625

Area = L × B when L = 3.0 B = -6

Area = -18

Area = L × B when L = 3.5 B = -5.25

Area = - 18.375

Area = L × B when L = 4 B = -4

Area = - 16

By adding all the values we get our desired Reimann sum of -93

This is an approximation to the integral of the same function with the same limits which is the limit of Riemann sum if we let delta_x go to 0 and the number of rectangles therefore approach infinity.

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The volume of the solid generated when the region r is revolved about the x-axis is 4π (5^(1/4) - 3^(1/4) + 1/5^(1/4) - 1/3^(1/4)).

To find the volume of the solid generated when the region r is revolved about the x-axis, we can use the method of cylindrical shells.

First, we need to determine the limits of integration. The region r is bounded by the curves y=e^(x/2) , y=e^(-x/2), x=ln3, and x=ln5. Since we are revolving the region about the x-axis, we need to integrate with respect to x. The lower limit of integration is ln3 and the upper limit is ln5.

Next, we need to find the radius of each cylindrical shell. The radius is the distance from the x-axis to the curve. For this region, the radius is e^(x/2) - e^(-x/2).

Finally, we need to find the height of each cylindrical shell. The height is the differential dx.

Thus, the integral that gives the volume of the solid is:

V = ∫[ln3, ln5] 2π (e^(x/2) - e^(-x/2)) dx

Simplifying the integrand:

V = 2π ∫[ln3, ln5] (e^(x/2) - e^(-x/2)) dx

Evaluating the integral:

V = 2π (2e^(x/2) + 2e^(-x/2)) |[ln3, ln5]

V = 4π (e^(ln5/2) - e^(ln3/2) + e^(-ln5/2) - e^(-ln3/2))

V = 4π (5^(1/4) - 3^(1/4) + 1/5^(1/4) - 1/3^(1/4))

Therefore, the volume of the solid generated when the region r is revolved about the x-axis is 4π (5^(1/4) - 3^(1/4) + 1/5^(1/4) - 1/3^(1/4)).

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The second plan would be more cost-effective for Chris if he drives less than 300 miles over the weekend.

Chris will rent a car for the weekend and can choose between two plans. The first plan has an initial fee of $60 and costs an additional $0.60 per mile driven, while the second plan has no initial fee but costs $0.80 per mile driven.

Let's say Chris plans to drive a total of m miles over the weekend.

Under the first plan, the total cost, C1, would be:

C1 = 60 + 0.60m

Under the second plan, the total cost, C2, would be:

C2 = 0.80m

To determine which plan is more cost-effective for Chris, we can set the two expressions for cost equal to each other and solve for m:

60 + 0.60m = 0.80m

60 = 0.20m

m = 300

So, if Chris drives more than 300 miles over the weekend, the second plan would be more cost-effective, and if he drives less than 300 miles, the first plan would be more cost-effective.

For example, if Chris plans to drive 250 miles over the weekend, the total cost under the first plan would be:

C1 = 60 + 0.60(250) = $210

And under the second plan, the total cost would be:

C2 = 0.80(250) = $200

Therefore, the second plan would be more cost-effective for Chris if he drives less than 300 miles over the weekend.

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Answer:

Set your calculator to degree mode.

tan B = 5/2

B = tan^-1 (5/2) = 68.20°

Answer:

22

Step-by-step explanation:

As we know the basic rule to solve an expression is BODMAS, the full form is Brackets, Orders, Division, Multiplication, Addition, and Subtraction.

So first, we will solve the first bracket, and as we know if we multiply a negative integer with another negative integer then the result is a positive value ( - * - =  + ), and the expression becomes

-4(-8)+(-10) = 32+(-10)

Now we solve another bracket, and as we know positive multiplied by negative results in a negative sign ( + * - = - ), and the expression becomes

32+(-10) = 32 - 10

And now we subtract 10 from 32, so our final answer is

32 - 10 = 22

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Answer:

--------------------------

Let's denote the cost of one rose bush as r and the cost of one pot of ivy as i.

We can write two equations based on the information provided:

Solve the system by elimination, double the first equation and subtract the second one:

Pot of ivy costs $8.

Find r by substituting 8 for i:

Rose bush costs $12.

So we get the option B provided as a choice.

Option B is correct, the cost of rose bush is $12 and cost of pot of ivy is $8.

Given that Elisa spent $124 on 7 rose bushes and 5 pots of ivy.

7R+5I=124...(1)

Kathryn spent $176 on 14 rose bushes and 1 pot of ivy.

14R+I=176

I=176-14R...(2)

We have to find the cost of rose and pot of ivy

Substitute equation (2) in (1)

7R+5(176-14R)=124

7R+5(176)-5(14R)=124

7R+880-70R=124

880-63R=124

880-124=63R

756=63R

R=$12

Now let us find the cost of I

I=176-14R

I=176-14(12)

I=176-168

I=$8

Hence, option B is correct, the cost of rose bush is $12 and cost of pot of ivy is $8.

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To solve the expression -25 x (84/21) + (-3) x (-6), follow these steps:

Step 1: Perform the division inside the parentheses.
(84/21) = 4

Step 2: Replace the terms and rewrite the expression.
-25 x (4) + (-3) x (-6)

Step 3: Perform the multiplications.
-25 x 4 = -100
-3 x -6 = 18

Step 4: Rewrite the expression and perform the addition.
-100 + 18

Step 5: Calculate the final result.
-100 + 18 = -82

Your answer is -82.

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To determine whether the linear transformation T is one-to-one, onto, or neither, we need to analyze the rank and nullity of the transformation.

The rank of T is the dimension of the image space, which is the span of the columns of the transformation matrix. To find the matrix, we can write T(X, Y, Z, W) = (V, W, X, Z) as a matrix equation:

|V|   |0 0 1 0||X|
|W| = |0 1 0 0||Y|
|X|   |1 0 0 0||Z|
|Z|   |0 0 0 1||W|

From this matrix, we can see that the columns are linearly independent, so the rank of T is 4.

The nullity of T is the dimension of the kernel, which is the set of all solutions to the equation T(X, Y, Z, W) = (0, 0, 0, 0). We can set up the augmented matrix for this equation:

|0 0 1 0 0|
|0 1 0 0 0|
|1 0 0 0 0|
|0 0 0 1 0|

Row-reducing this matrix gives:

|1 0 0 0 0|
|0 1 0 0 0|
|0 0 1 0 0|
|0 0 0 1 0|

The only solution is the trivial one, so the nullity of T is 0.

Since the rank of T is equal to the dimension of the domain and the codomain, T is onto. And since the nullity of T is 0, T is also one-to-one. Therefore, the correct answer is "one-to-one and onto".
Hi! To determine whether the linear transformation T: R4 → R4, T(X, Y, Z, W) = (V, W, X, Z) is one-to-one, onto, or neither, let's analyze the properties of this transformation.

1. One-to-one: A linear transformation is one-to-one if different input vectors produce different output vectors.

In this case, T(X, Y, Z, W) = (V, W, X, Z). Observe that every input vector (X, Y, Z, W) uniquely determines the output vector (V, W, X, Z). Thus, this transformation is one-to-one.

2. Onto: A linear transformation is onto if every output vector can be produced by some input vector.

For this transformation, T(X, Y, Z, W) = (V, W, X, Z), every output vector (V, W, X, Z) can be produced by the input vector (X, Y, Z, W). So, the transformation is onto as well.

In conclusion, the linear transformation T: R4 → R4, T(X, Y, Z, W) = (V, W, X, Z) is both one-to-one and onto.

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In a boxplot, potential outliers are data points that are more than 1.5 Interquartile Ranges (IQRs) from the edges of the box. A boxplot visually represents the distribution of a dataset, with the box containing the middle 50% of the data and the edges representing the lower and upper quartiles.

To answer your question, potential outliers in a boxplot are points that are more than 1.5 times the interquartile range (IQR) away from the edges of the box. The IQR is the difference between the third quartile (75th percentile) and the first quartile (25th percentile) of the data. The box in a boxplot represents the IQR, with the median (50th percentile) marked by a line inside the box. The whiskers of the boxplot extend to the minimum and maximum values that fall within 1.5 times the IQR from the edges of the box. Any points outside this range are considered potential outliers and are plotted as individual points beyond the whiskers. However, it is important to note that potential outliers do not necessarily indicate errors or incorrect data, and further investigation may be needed to determine their validity. Overall, boxplots are a useful tool for visualizing the spread and distribution of numerical data.

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Answer:31.4

Step-by-step explanation: tan=oppisite/adjacent, so just plug it in.
tan e=square root 22/square root 59
tan^-1=(square root 22/square root 59) < Use arc tan to find the missing angle.

M<E= 31.4

The inequality is solved to give the value of x as x≤ 4

Inequalities are defined as those expressions with unequal comparison of numbers, expressions, variables or even terms.

It is important to note the different signs of inequalities. They are;

From the information given, we have that;

9-7.25x ≤-20

Now, collect the like terms, we have;

-7. 25 ≤ - 20- 9

subtract the values given, we get;

-7.25x ≤ -29

Divide both sides by the coefficient of x, we get;

x ≤ - 29/7.25

Divide the values, we get;

x ≤ 4

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Hi!
You make $15 per day.
60 divided by 4 (The number of days you work per month since you work once weekly.) is 15.

Hope this helps!

We cannot find the correlation coefficient between x and y for this bivariate distribution.

To find the correlation coefficient between x and y, we need to first calculate the expected value of x, denoted E(x), the expected value of y, denoted E(y), and the expected value of xy, denoted E(xy).

Using the given distribution, we can calculate:

E(x) = ∑x * p(x,y) = ∑x * 0.5(x y) = 0.5(1+2+3+...) = ∞ (diverges)

E(y) = ∑y * p(x,y) = ∑y * 0.5(x y) = 0.5(1+2+3+...) = ∞ (diverges)

E(xy) = ∑x*y * p(x,y) = ∑x*y * 0.5(x y) = 0.5(1*1 + 2*1 + 2*2 + 3*1 + 3*2 + 3*3 + ...) = ∞ (diverges)

Since the expected values of both x and y diverge, we cannot use the formula for the correlation coefficient that involves standard deviations. Instead, we can use the formula:

[tex]\rho = [E(xy) - E(x)E(y)] / [(E(x^2) - E(x)^2) * (E(y^2) - E(y)^2)]^{(1/2)}[/tex]

Since E(x²) and E(y²) also diverge, we cannot use this formula either.

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The Area of glass needed for the window is approximately 200.97 square inches.

The area of the glass needed for the circular window can be found using the formula for the area of a circle, which is given by:

A = πr^2

where A is the area of the circle and r is the radius.

In this case, the radius of the window is 8 inches, so we can substitute this value into the formula:

A = π(8)^2

Simplifying the expression inside the parentheses, we get:

A = π(64)

Using a calculator or estimating π as 3.14, we can evaluate the expression to find:

A ≈ 200.96

Rounding to the nearest hundredth, we get:

A ≈ 200.97 square inches

Therefore, the area of glass needed for the window is approximately 200.97 square inches.

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The probability that a randomly sampled household has more than $16,000 in credit card debt is approximately 0.4726 or 47.26%.

The question asks us to find the probability that a randomly sampled household has more than $16,000 in credit card debt, given that the distribution of household debt is somewhat right skewed with a mean of $15,355 and a standard deviation of $10,000.

To solve this problem, we can use the standard normal distribution, which allows us to calculate probabilities for any normal distribution by standardizing the variable of interest (in this case, credit card debt) to a standard normal distribution with a mean of 0 and a standard deviation of 1.

To standardize the value of $16,000, we use the formula:

z = (x - μ) / σ

where x is the value we want to standardize, μ is the mean, σ is the standard deviation, and z is the corresponding z-score. Substituting the given values, we get:

z = (16000 - 15355) / 10000 = 0.0655

This means that $16,000 is 0.0655 standard deviations above the mean. To find the probability that a randomly sampled household has more than $16,000 in credit card debt, we need to find the area to the right of this z-score under the standard normal curve. We can use a standard normal table or calculator to find this probability, which is approximately 0.4726.

It's important to note that this probability is based on the assumptions made about the distribution of household debt, and may not accurately reflect the true probability in practice. Additionally, credit card debt is influenced by a variety of factors beyond just household income and spending habits, so it's important to consider the limitations of this analysis when interpreting the results.

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[tex]\sin( 54^o )=\cfrac{\stackrel{opposite}{22}}{\underset{hypotenuse}{x}} \implies x=\cfrac{22}{\sin(54^o)}\implies x\approx 27.2[/tex]

Make sure your calculator is in Degree mode.

Answer:

X= 27.19 approximate to 27.2

Step-by-step explanation:

To answer x use sin (54°)

Sin(54°) = 22/X

Sin(54°) × X = 22

X = 22 / Sin(54°)

X= 27.19 approximate to 27.2 .

The given series converges to 4/3.

The given series is:

4/5 - 4/7 + 4/9 - 4/11 + 4/13 - ...

We can rewrite this series as:

4(1/5 - 1/7 + 1/9 - 1/11 + 1/13 - ...)

Now, we can use the alternating series test, which states that an alternating series converges if the absolute values of its terms decrease monotonically to zero.

In this case, the absolute values of the terms are:

|4/5|, |4/7|, |4/9|, |4/11|, |4/13|, ...

These terms do decrease monotonically to zero, so we can apply the alternating series test. Therefore, the series converges.

To find the sum of the series, we can use the formula for the sum of an alternating series:

S = a - a1 + a2 - a3 + ...

where S is the sum of the series, a is the first term, and ai is the ith term.

In this case, a = 4/5 and the common difference d = -2/5, since we are subtracting 2/5 from each term to get the next one. So, we have:

S = 4/5 - 4/7 + 4/9 - 4/11 + 4/13 - ...

S = a/(1 + d) = (4/5)/(1 - 2/5) = 4/3

Therefore, the given series converges to 4/3.

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a. The standard error of the mean can be determined using the formula:

Standard error of the mean = population standard deviation / square root of sample size

Plugging in the given values, we get:

Standard error of the mean = 25 / square root of 250
Standard error of the mean = 25 / 15.8114
Standard error of the mean = 1.579 (rounded to 3 decimal places)


The standard error of the mean measures the amount of variability or error that is expected in the sample mean when compared to the true population mean. It is calculated by dividing the population

by the square root of the sample size. In this case, the standard error of the mean is 1.579, indicating that the sample mean of 20 is expected to be off by around 1.579 units from the true population mean.

c. To determine the 95% confidence interval for the population mean, we can use the formula:

Confidence interval = sample mean +/- (critical value) x (standard error of the mean)

The critical value can be obtained from a t-distribution table with n-1 degrees of freedom, where n is the sample size. For a 95% confidence interval and 249 degrees of freedom, the critical value is 1.96.

Plugging in the given values, we get:

Confidence interval = 20 +/- (1.96) x (1.579)
Confidence interval = 20 +/- 3.095
Confidence interval = (16.905, 23.095) (rounded to 3 decimal places)


The confidence interval is a range of values that is expected to contain the true population mean with a certain degree of confidence. In this case, we are 95% confident that the true population mean falls within the range of 16.905 to 23.095. This means that if we were to repeat this sampling process many times, 95% of the resulting confidence intervals would contain the true population mean.

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All closed intervals of length 1 in which a function has a unique zero, we need to find all pairs of zeros that are exactly 1 unit apart and consider the intervals between them as described above.

To find all closed intervals of length 1 in which a function has a unique zero, we need to look for intervals where the function changes sign exactly once. This is because if a function has a unique zero, it must change sign from positive to negative or negative to positive at that point.

Let's call the function f(x). To find these intervals, we can use the Intermediate Value Theorem. This theorem states that if a function is continuous on a closed interval [a, b] and takes on values f(a) and f(b) at the endpoints, then it must also take on every value between f(a) and f(b) somewhere on the interval.

So, to apply this theorem, we need to find values of x such that f(x) = 0. Then, we can look at the intervals between these values and see if f(x) changes sign exactly once on any of them.

Let's say we find two zeros of the function at x = a and x = b, where a < b. Then, we can consider the intervals [a, a+1] and [b-1, b] (assuming these intervals have length 1). If f(x) is positive on the interval [a, a+1] and negative on the interval [b-1, b], or vice versa, then f(x) must change sign exactly once on each of these intervals and therefore has a unique zero in each interval.

In general, to find all closed intervals of length 1 in which a function has a unique zero, we need to find all pairs of zeros that are exactly 1 unit apart and consider the intervals between them as described above.

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The correct options for the parts of the circle are:

A circle is a spherical plane figure whose edge is made up of points spaced equally apart from a fixed point.

The fixed point from which every point on the circle's edge is equally distant is the center of the circle.

The parts of a circle include the following:

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The notations and the terms that correctly defines them is matched below:

1.)GCB = Major arc. Option I.

2.)CE = Chord. Option B.

3.)AB= Radius. Option C.

4.)CB= Minor arc. Option A.

5.)BAD= central angle. Option F.

6.)A = Center. Option J.

7.)DGC = Minor arc. Option A.

8.)CD = Diameter. Option G.

The circle has the following parts with their various properties described below;

Major arc: This is part of the circle that has an angle which measures more that 180°.

Minor arc: This is part of the circle that has an angle which measures less than 180°.

Diameter: This is defined as the distance across a circle which must pass through its central point.

Radius: This is defined as half the diameter of a circle.

Chord:. This is defined as the line that joins two point on the circumference of a circle.

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The given equation is (tan²(θ) - 9)(2cos(θ) + 1) = 0. To solve it, we can set each factor equal to 0: 1) tan²(θ) - 9 = 0 2) 2cos(θ) + 1 = 0 Solving each equation: 1) tan²(θ) - 9 = 0 tan²(θ) = 9 tan(θ) = ±3 θ = arctan(±3) 2) 2cos(θ) + 1 = 0 2cos(θ) = -1 cos(θ) = -1/2 θ = arccos(-1/2) The solutions for θ are the angles where either tan(θ) = ±3 or cos(θ) = -1/2.

To solve the equation (tan2(θ) − 9)(2 cos(θ) + 1) = 0, we need to use the zero product property, which states that if the product of two factors is equal to zero, then at least one of the factors must be zero.
First, let's solve for tan2(θ) − 9 = 0. We can add 9 to both sides to get tan2(θ) = 9. Then, we can take the square root of both sides to get tan(θ) = ±3.
Next, let's solve for 2 cos(θ) + 1 = 0. We can subtract 1 from both sides to get 2 cos(θ) = -1. Then, we can divide both sides by 2 to get cos(θ) = -1/2.
Therefore, our solutions are θ = arctan(±3) and θ = arccos(-1/2). Note that the ± sign in the first solution gives us two different angles, since tangent is periodic with a period of π.
In conclusion, the equation (tan2(θ) − 9)(2 cos(θ) + 1) = 0 has solutions at θ = arctan(±3) and θ = arccos(-1/2).

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This limaçon is symmetrical along the y-axis. The horizontal intercepts are (4,0) and (-4,0). The vertical intercepts are (0,-2) and (0,6).

To determine the type of shape, we look at the value of the constant versus the value of the term with the sign.

As 4>2, this is a dimpled limacon.

We have y-intercepts where θ = [tex]\pi/2[/tex] and [tex]3\pi /2[/tex]

Then, our polar equation is r = 4 + 2 sinθ.

r = 4 + 2 sin θ= 6 if θ = [tex]\pi /2[/tex] and

r = 4 + 2 sin θ = 2 if θ = [tex]3\pi /2[/tex]

Therefore, y-intercepts or vertical intercepts are (0,-2) and (0,6)

We have x-intercepts where θ = 0 and [tex]\pi[/tex]

Then

r = 4 + 2sin θ = 4 for θ = 0 and

r = 4 + 2 sin θ = 4

Therefore, x-intercepts or horizontal intercepts are (4,0) and (-4,0)

This is symmetric about the y-axis.

As we already know that sin θ = sin ( [tex]\pi[/tex] - θ) and

cos θ = cos ([tex]\pi[/tex] - θ)

Therefore, we replace θ with [tex]\pi[/tex] - θ, and thus we prove symmetry about the y-axis.

r = 4 + 2sin([tex]\pi[/tex] - θ)= 4 + 2 sin θ

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A box of 30 pieces of chocolate candies contains approximately 424.11 cubic units of chocolate.

The volume of a sphere can be calculated using the formula:

V = (4/3) * π * r^3

where V is the volume, π is pi (approximately 3.14), and r is the radius of the sphere.

Since the diameter of each candy is 3, the radius is half of that, or 1.5. We can plug this value into the formula to find the volume of one piece of candy:

V = (4/3) * π * r^3

V = (4/3) * 3.14 * 1.5^3

V ≈ 14.137

So one piece of candy has a volume of approximately 14.137 cubic units. To find the total amount of chocolate in a box of 30 candies, we can simply multiply the volume of one candy by the number of candies in the box:

Total volume = 14.137 * 30

Total volume = 424.11

Therefore, a box of 30 pieces of chocolate candies contains approximately 424.11 cubic units of chocolate.

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The standard deviation of the sampling distribution of sample means is 2.5.

The standard deviation of the sampling distribution of sample means (also known as the standard error of the mean) can be calculated using the formula:

σM = σ / sqrt(n)

where σ is the population standard deviation, n is the sample size, and σM is the standard deviation of the sampling distribution of sample means.

Substituting the given values, we get:

σM = 20 / sqrt(64) = 20 / 8 = 2.5

Therefore, the standard deviation of the sampling distribution of sample means is 2.5.

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Super Fast Food drive-thru is able to estimate their wait time more consistently because it has a smaller IQR.

Super Fast Food is able to estimate their wait time more consistently because it has a smaller IQR (interquartile range). The IQR is the range of the middle 50% of the data and is a measure of variability. In this case, the IQR for Super Fast Food is 7 (15.5 - 8.5), while the IQR for Burger Quick is 14.5 (24 - 9.5).

This means that the wait times at Super Fast Food are more tightly clustered around the median of 12 minutes, indicating that their estimate of wait time is more consistent. The range, which is the difference between the maximum and minimum values, is not as informative in this case because both ranges are fairly large and do not give insight into the spread of the data within that range.

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The investment with the greater amount of interest is Investment X which earns $50.40 more.

Hence the correct option for first position is (A) and for second position is option (C).

For Investment X:

Given that the principle amount of investment (P) = $ 6000

Time period (t) = 2 years

Rate of Interest (r) = 4.5% (simple interest rate)

So the interest gained over 2 years = (6000*2*4.5)/100 = $540.

For Investment Y:

Given that the principle amount of investment (P) = $ 6000

Time period (t) = 2 years

Rate of Interest (r) = 4% (compound interest rate)

so the amount after 2 years is given by

= 6000(1 + 4/100)²

= 6000*(1.04)²

= $6489.6

so the interest gained over 2 years = 6489.6 - 6000 = $489.6

So the difference between the interests = 540 - 489.6 = $50.40

Hence the Investment X gives greater interest.

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The correct answer is C) rectangular prism trash can by $0.50.

To determine which trash can design will cost the company less to manufacture, weneed to calculate the cost of material for each design.

For the rectangular prism-shaped trash can:

The base dimensions are 1.5 ft and 2.0 ft, which gives a base area of 1.5 ft * 2.0 ft = 3.0 sq ft.

The total volume is given as 7.85 cubic ft.

To find the height of the rectangular prism, we divide the total volume by the base area:

Height = Total volume / Base area = 7.85 cubic ft / 3.0 sq ft = 2.617 ft

The cost of material for the rectangular prism-shaped trash can is the product of the base area and the cost per square foot:

Cost = Base area * Cost per square foot = 3.0 sq ft * $3.60/sq ft = $10.80

For the cylindrical trash can:

The base area is given as 3.14 sq ft.

To find the height of the cylindrical trash can, we divide the total volume by the base area:

Height = Total volume / Base area = 7.85 cubic ft / 3.14 sq ft ≈ 2.5 ft

The cost of material for the cylindrical trash can is the product of the base area and the cost per square foot:

Cost = Base area * Cost per square foot = 3.14 sq ft * $3.60/sq ft = $11.30

Comparing the costs, we can see that the rectangular prism-shaped trash can costs $10.80, and the cylindrical trash can costs $11.30. Therefore, the rectangular prism-shaped trash can design will cost the company less to manufacture.

The cost difference is:

$11.30 - $10.80 = $0.50

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