Greg is recovering one of his couch cushions. The cushion is in the shape of a rectangular prism. Greg drew a net of the cushion below.



Note: Figure is not drawn to scale.

If the length of the cushion measures 12 in, the width measures 7 in, and the height measures 4 in, how much fabric does Greg need to cover the cushion?
A.
160 sq in
B.
336 sq in
C.
672 sq in
D.
320 sq in
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There are 7920 ways to seat 14 people in a circle such that every man is diametrically opposite a woman.

In this problem, we want to find the number of ways to seat 14 people in a circle such that every man is diametrically opposite a woman.

Since every man must be diametrically opposite a woman, we can pair each man with one woman. There are 5 men and 9 women, so there are 5 pairs. We need to find the number of ways to seat these 5 pairs of people in a circle.

To do this, we can first seat one pair in any position. Then, we can seat the second pair anywhere but opposite the first pair. This gives us 11 positions for the second pair. Continuing in this way, we see that there are 11 * 6 * 5 * 4 * 3 = 7920 ways to seat the 5 pairs of people in a circle.

So, there are 7920 ways to seat 14 people in a circle such that every man is diametrically opposite a woman.

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Assuming 14 people, 5 men and 9 women, how many ways can they sit in a circle such that every man is diametrically opposite a woman?

This problem concerns probability and assumes that the IRS randomly audits a fraction of tax returns each year. The query is about a married couple that filed separate returns, and it wants to know how likely it is that both will be audited, just one will be audited, neither will be audited, and at least one will be audited. The problem assumes that the percentage of audited tax returns is set at 20%.

(a) The probability that both the husband and wife will be audited is equal to the product of the individual probabilities:

P(both audited) = 0.2 * 0.2 = 0.04

(b) The probability that only one of them will be audited is the sum of the probabilities that the husband is audited and the wife is not, and vice versa:

P(only one audited) = 0.2 * 0.8 + 0.8 * 0.2 = 0.32

(c) The probability that neither one of them will be audited is the complement of the probability that at least one of them will be audited:

P(neither audited) = 1 - P(at least one audited) = 1 - (0.2 * 0.8 + 0.8 * 0.2 + 0.2 * 0.2) = 0.36

(d) The probability that at least one of them will be audited is equal to one minus the probability that neither of them will be audited:

P(at least one audited) = 1 - P(neither audited) = 1 - 0.36 = 0.64

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Given:

A roofer earns ​$25 per hour for regular hours worked and ​$30 per hour for overtime hours worked. He puts in 40 hours of regular time during a certain week and he wishes to earn ​$1140​.

Required:

To find how many hours of overtime should he​ work.

Explanation:

Let he should work x hours overtime.

Then the equation becomes:

He should work approximately 5 hours.

Final Answer:

He should work approximately 5 hours overtime.

Answer:

5

Step-by-step explanation:

50  by divded 5 is 10 90 divided by 5 is 18 and 110 divded  by 5 is 22 hope this helps!

Answer:

50.6°

Step-by-step explanation:

complementary angles sum to 90° , that is

complementary angle + 39.4° = 90° ( subtract 39.4° from both sides )

complementary angle = 90° - 39.4° = 50.6°

Answer:

opposite - hypotenuse

Using the surface area of the rectangular prism we know that the dimensions of the base are 2in * 2in.

A three-dimensional solid form with six faces, including rectangular bases, is called a rectangular prism.

A rectangular prism also refers to a cuboid.

A cuboid and a rectangular prism have the same cross-section.

The surface area of the rectangular prism:

A=2(wl+hl+hw)

Insert values:

A=2(wl+l+hw)

232=2(wl+28l+28w)

232 = 2wl + 56l + 56w

We know that w and l are equal as: w = l as the base is square:
So, we can write:

232 = 2wl + 56l + 56w

232 = 2w² + 56w + 56w

232 = 2w² + 112w

2w² + 112w - 232 = 0

2w²  + w(116 - 4) -232

2w² + 116w - 4w - 232

2w(w+58) -4(w+58)

Then, we have:
w+58 = 0 ⇒ w = -58

2w-4 = 0 ⇒ w = 2

Since the base measurements cannot be negative.

Then, the dimensions of the base are: 2in * 2 in

Therefore, using the surface area of the rectangular prism we know that the dimensions of the base are 2in * 2in.

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The graph of the equation x^2/49 + (y + 1)^2/4 = 1 is added as an attachment

The expression that represents the function in words is given as

StartFraction x squared Over 49 EndFraction + StartFraction (y + 1) squared Over 4 EndFraction = 1

Express the equation properly

So, we have

x^2/49 + (y + 1)^2/4 = 1

The above equation is an ellipse

Next, we plot the graph on a coordinate plane using a graphing tool

See attachment for the graph of the equation

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We can conclude that -

The exponential function is of the form -

f(x) = eˣ

Given is to write the exponential growth and exponential decay equation.

{ 1 } -

The general exponential growth equation is -

\($f(x)=a(1+r)^{x}\)

{ 2 } -

The general exponential decay equation is -

\($\frac {dN}{dt}= -\lambda N\)

Option {A} and option {E} represent the exponential decay. Option {B}, {E} and {D} represent exponential growth.

Therefore, we can conclude that -

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The information about your sample data is summarized and provided by summary statistics.It provides information regarding the values in your data set.This covers the distribution of the mean and the skewness of your data.

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so your problem is 2x+y=18 and y=4x+6

solution

solve for the first variable in one of the equations then substitute the result into the other equation

point form:

(2,14)

equation form

x=2, y=14

Answer: y = (3^(x-1))*1500

Step-by-step explanation:

We want the relationship

y = f(x)

where y is the number of songs, and x is the number of years.

We know that in the first year, x = 1, the site has 1,500 songs.

The next year, x = 2, the number of songs is tripled, then we will have:

1,500*3 = 4500 songs.

The next year, x = 3, we will have: 3*(3*1500) = (3^2)*1500.

when x = 4, the number is tripled again:

3*(3^2)*1500 = (3^3)*1500

We already can see the pattern, for the year x, the site will have:

y = (3^(x-1))*1500 songs.

This is the equation we are looking for.

The probability that at least one sensor detects the pollutant is 0.9.The probability that either only S1 or only S2 detects the pollutant is 0.5.The probability that S1 does not detect the pollutant, and S2 detects the pollutant is 0.2.The probability that S2 fails to detect the pollutant is 0.3.

The event "at least one sensor detects the pollutant" refers to the scenario where either S1 or S2 (or both) detect the excessive pollution. This can be visualized as the union of the two events: S1 detecting the pollutant (event A) and S2 detecting the pollutant (event B). The probability of event A is 0.7, the probability of event B is 0.8, and the probability of both events A and B occurring together is 0.6. By applying the principle of inclusion-exclusion, we can calculate the probability of the union as P(A ∪ B) = P(A) + P(B) - P(A ∩ B) = 0.7 + 0.8 - 0.6 = 0.9.

The event "either only S1 or only S2 detects the pollutant" can be represented as the exclusive OR (XOR) of the two events: S1 detecting the pollutant without S2 detecting it (event A) and S2 detecting the pollutant without S1 detecting it (event B). Since the probabilities of events A and B are not explicitly given, we assume that they are equal. Let's denote this probability as p. Therefore, the probability of either event A or event B occurring is 2p. Given that the sum of probabilities of all possible outcomes is equal to 1, we have 2p + P(A ∩ B) = 1. We are also given that P(A ∩ B) = 0.6. Solving these equations simultaneously, we find that p = 0.2. Hence, the probability of the event "either only S1 or only S2 detects the pollutant" is 2p = 2 × 0.2 = 0.4.

The event "S1 does not detect, and S2 detects the pollutant" is the complement of S1 detecting the pollutant (event A) intersected with S2 detecting the pollutant (event B). The probability of event A is 1 - P(S1 detects) = 1 - 0.7 = 0.3. The probability of event B is P(S2 detects) = 0.8. The probability of both events A and B occurring together is given as P(A ∩ B) = 0.6. Therefore, the probability of the event "S1 does not detect, and S2 detects the pollutant" is P(A' ∩ B) = P(A ∩ B') = P(A) - P(A ∩ B) = 0.3 - 0.6 = 0.2.

The event "S2 fails to detect the pollutant" is the complement of S2 detecting the pollutant. Therefore, the probability of this event is 1 - P(S2 detects) = 1 - 0.8 = 0.2.

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Answer:

(-2.5,2)

Step-by-step explanation:

Answer:

The first group has 20 and the second group has 8.

Step-by-step explanation:

1. Twice as many as 8 is 16  (8x2)

2. If you add four to the total it's 20 (16+4=20)

3. So group one has four more than twice as many as group 2.

The Taylor series for f centered at 9, given f^(n)(9) = (-1)^n n!/6^n (n + 2), is f(x) = f(9) - (x-9)/2 + (x-9)^2/12 - (x-9)^3/432 + (x-9)^4/10368 - ... .

To find the Taylor series for f centered at 9, we need to use the formula

f(x) = f(a) + f'(a)(x-a)/1! + f''(a)(x-a)^2/2! + f'''(a)(x-a)^3/3! + ...

where f'(x) represents the first derivative of f(x) with respect to x, f''(x) represents the second derivative of f(x) with respect to x, and so on.

In this case, we are given the nth derivative of f(x) evaluated at x = 9, so we can plug in the values and simplify the formula

f(9) = f(9) (since we're centering the series at 9)

f'(9) = (-1)^1 (1!/6^1)(1 + 2) = -1/2

f''(9) = (-1)^2 (2!/6^2)(2 + 2) = 1/6

f'''(9) = (-1)^3 (3!/6^3)(3 + 2) = -1/36

f''''(9) = (-1)^4 (4!/6^4)(4 + 2) = 1/216

and so on. So the Taylor series for f centered at 9 is

f(x) = f(9) - (x-9)/2 + (x-9)^2/2! * 1/6 - (x-9)^3/3! * 1/36 + (x-9)^4/4! * 1/216 - ...

or, simplifying the coefficients

f(x) = f(9) - (x-9)/2 + (x-9)^2/12 - (x-9)^3/432 + (x-9)^4/10368 - ...

This is the Taylor series for f centered at 9, based on the given information.

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The given question is incomplete, the complete question is:

Find the Taylor series for f centered at 9 if f^(n)(9) = (-1)^n n!/6^n (n + 2)

PreAlg students spend significantly less time doing homework compared to ElemAlg and InterAlg students, while there is no significant difference in homework time between ElemAlg and InterAlg students.

What is significantly ?

Significantly" is the keyword that indicates a notable or meaningful difference or result in the context of statistical analysis. It is often used to describe findings that have a high level of confidence and statistical significance, indicating that the observed difference or relationship is unlikely to have occurred by chance.

Based on the given data and statistical analysis, the conclusion is as follows:

PreAlg compared to ElemAlg:

The sample mean for PreAlg (1.32) is significantly different from the sample mean for ElemAlg (3.18) with a t-value of 5.08 and a p-value of 0.000. Therefore, we can conclude that PreAlg students spend significantly less time doing homework compared to ElemAlg students.

PreAlg compared to InterAlg:

The sample mean for PreAlg (1.32) is significantly different from the sample mean for InterAlg (4.42) with a t-value of 3.64 and a p-value of 0.003. Hence, we can conclude that PreAlg students spend significantly less time doing homework compared to InterAlg students.

ElemAlg compared to InterAlg:

The sample mean for ElemAlg (3.18) is not significantly different from the sample mean for InterAlg (4.42) with a t-value of 1.49 and a p-value of 0.163. Therefore, we fail to reject the null hypothesis, and we cannot conclude a significant difference in homework time between ElemAlg and InterAlg students.

In summary, the PreAlg students have significantly lower homework time compared to both ElemAlg and InterAlg students. However, there is no significant difference in homework time between ElemAlg and InterAlg students.

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The number of ways 9 yellow marbles can be divided among 4 distinguishable cups is 126.

Dividing 9 marbles among 4 cups is a combination problem. The number of combinations is given by the formula C(n + r - 1, r - 1), where n is the number of items (marbles) and r is the number of groups (cups). In this case, n = 9 and r = 4. Plugging these values into the formula, we get:

C(9 + 4 - 1, 4 - 1) = C(12, 3) = (12 * 11 * 10) / (3 * 2 * 1) = 220

This means that there are 220 ways to divide 9 yellow marbles into 4 distinguishable cups. However, since the cups are distinguishable, each combination is counted multiple times, once for each permutation of the cups. The number of permutations of n items taken r at a time is given by the formula n! / (n - r)!. In this case, the number of permutations is 4! = 4 * 3 * 2 * 1 = 24.

So, the total number of ways to divide 9 yellow marbles into 4 distinguishable cups is 220 / 24 = 9. This means that there are 126 distinct ways to divide 9 yellow marbles among 4 distinguishable cups.

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Answer:

6(x+2y)

Step-by-step explanation:

An essay on " God's Not Dead " would include the date it was made, some of the events in the movie, and the lessons the movie teaches.

"God's Not Dead" is a 2014 American Christian drama film that tells the story of a college student named Josh Wheaton who is challenged by his philosophy professor to defend his belief in God. The film explores the idea that faith in God is being threatened by a secular culture and highlights the struggles that people of faith face in a world that is becoming increasingly hostile to religion.

The movie centers around Josh's decision to stand up for his beliefs in the face of opposition from his professor, who gives him an ultimatum: either deny the existence of God or face a failing grade in the class. The film raises important questions about the role of religion in society and the importance of standing up for one's beliefs.

One of the key themes of the film is the idea that faith is not just a personal belief, but a vital part of our society and culture. Another important theme of the film is the importance of intellectual curiosity and critical thinking.

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Answer:

5

Step-by-step explanation:

(I'm assuming that by m2 and n2 you mean m to the power of 2 and n to the power of 2)

Whenever you have a number to a power, it is the same as that number times itself that power number of times. For example, 3 to the power of 4 is equal to 3 times itself 4 times, which is 3 * 3 * 3 * 3. If we use this and substitute the values in for m and n, we get that 3^2 - 2^2, and since 3^2 is 3 * 3 and 2^2 is 2 * 2 and 3 times 3 is 9 and 2 times 2 is 4, we get that 9 - 4 is 5.

Note: This symbol means to the power of ----> ^

Answer:

4w  −  14

Step-by-step Explanation:

This is the answer because:

1) First, we have to multiply the 4 with the -2. This equals -8

2) Now, we have the equation 4w - 8 - 6

3) Finally, do -8 - 6 which is -14

4) We simplified the equation to 4w - 14

Therefore, the answer is 4w - 14

Hope this helps!

Answer: 5

Step-by-step explanation: A cube has all lengths equal.

Volume is 125 find the cube root

Answer:

9

Step-by-step explanation:

Answer:

9 Is the answer

Step-by-step explanation:

Can i have brainliest??? thx

An exponential function can represent growth or decay.

The graph represents an exponential growth function is given by  \(y = ab^{x}\).

An exponential function is represented as:

\(y = ab^{x}\)

Where:

a represents any constant value.

b represents the growth or decay rate of the function

When the value of b is greater than 1, then the exponential function represents growth

Graph shown below represents an exponential growth function.

Hence, the graph representing an exponential growth function is graph traced by \(y = ab^{x}\).

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To find the joint density function, we need to calculate the Jacobian determinant of the transformation from (x, y) to (u, v)

The joint distribution of (u, v), where u and v are defined as

\(u = \frac{x}{{\sqrt{x^2 + y^2}}}\)  and \(v = \frac{y}{{\sqrt{x^2 + y^2}}}\), is given by:

\(f_{U,V}(u,v) = \frac{1}{{2\pi}} \cdot e^{-\frac{1}{2}(u^2 + v^2)}\)

To find the joint density function, we need to calculate the Jacobian determinant of the transformation from (x, y) to (u, v):

\(J = \frac{{du}}{{dx}} \frac{{du}}{{dy}}\)

\(\frac{{dv}}{{dx}} \frac{{dv}}{{dy}}\)

Substituting u and v in terms of x and y, we can evaluate the partial derivatives:

\(\frac{{du}}{{dx}} &= \frac{{y}}{{(x^2 + y^2)^{3/2}}} \\\frac{{du}}{{dy}} &= -\frac{{x}}{{(x^2 + y^2)^{3/2}}} \\\frac{{dv}}{{dx}} &= -\frac{{x}}{{(x^2 + y^2)^{3/2}}} \\\frac{{dv}}{{dy}} &= \frac{{y}}{{(x^2 + y^2)^{3/2}}}\)

Therefore, the Jacobian determinant is:

\(J &= \frac{y}{{(x^2 + y^2)^{\frac{3}{2}}}} - \frac{x}{{(x^2 + y^2)^{\frac{3}{2}}}} \\&= -\frac{x}{{(x^2 + y^2)^{\frac{3}{2}}}} + \frac{y}{{(x^2 + y^2)^{\frac{3}{2}}}} \\J &= \frac{1}{{(x^2 + y^2)^{\frac{1}{2}}}}\)

Now, we can find the joint density function of (u, v) as follows:

\(f_{U,V}(u,v) &= f_{X,Y}(x,y) \cdot \left|\frac{{dx,dy}}{{du,dv}}\right| \\&= f_{X,Y}(x,y) / J \\&= f_{X,Y}(x,y) \cdot (x^2 + y^2)^{\frac{1}{2}}\)

Substituting the standard normal density function

\(f_{X,Y}(x,y) &= \frac{1}{2\pi} \cdot e^{-\frac{1}{2}(x^2 + y^2)} \\f_{U,V}(u,v) &= \frac{1}{2\pi} \cdot e^{-\frac{1}{2}(x^2 + y^2)} \cdot (x^2 + y^2)^{\frac{1}{2}} \\&= \frac{1}{2\pi} \cdot e^{-\frac{1}{2}(u^2 + v^2)}\)

Therefore, the joint distribution of (u, v) is given by:

\(f_{U,V}(u,v) &= \frac{1}{2\pi} \cdot \exp\left(-\frac{1}{2}(u^2 + v^2)\right)\)

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To find the joint density function, we need to calculate the Jacobian determinant of the transformation from (x, y) to (u, v)

The joint distribution of (u, v) is a bivariate normal distribution with mean (0,0) and variance-covariance matrix

\(\begin{bmatrix}2 & 0 \0 & 2\end{bmatrix}\)

The joint distribution of (u, v) can be found by transforming the independent random variables x and y using the following formulas:

\( u = x + y\)
\( v = x - y \)

To find the joint distribution of (u, v), we need to find the joint probability density function (pdf) of u and v.

Let's start by finding the Jacobian determinant of the transformation:

\(J = \frac{{\partial (x, y)}}{{\partial (u, v)}}\)

\(= \frac{{\partial x}}{{\partial u}} \cdot \frac{{\partial y}}{{\partial v}} - \frac{{\partial x}}{{\partial v}} \cdot \frac{{\partial y}}{{\partial u}}\)

\(= \left(\frac{1}{2}\right) \cdot \left(-\frac{1}{2}\right) - \left(\frac{1}{2}\right) \cdot \left(\frac{1}{2}\right)\)

\(J = -\frac{1}{2}\)

Next, we need to express x and y in terms of u and v:

\(x = \frac{u + v}{2}\)

\(y = \frac{u - v}{2}\)

Now, we can find the joint pdf of u and v by substituting the expressions for x and y into the joint pdf of x and y:

\(f(u, v) = f(x, y) \cdot |J|\)

\(f(u, v) = \left(\frac{1}{\sqrt{2\pi}}\right) \cdot \exp\left(-\frac{x^2}{2}\right) \cdot \left(\frac{1}{\sqrt{2\pi}}\right) \cdot \exp\left(-\frac{y^2}{2}\right) \cdot \left|-\frac{1}{2}\right|\)

\(f(u, v) = \frac{1}{2\pi} \cdot \exp\left(-\frac{u^2 + v^2}{8}\right)\)

Therefore, the joint distribution of (u, v) is given by:

\(f(u, v) = \frac{1}{2\pi} \cdot \exp\left(-\frac{{u^2 + v^2}}{8}\right)\)

In summary, the joint distribution of (u, v) is a bivariate normal distribution with mean (0,0) and variance-covariance matrix

\(\begin{bmatrix}2 & 0 \0 & 2\end{bmatrix}\)

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Answer:

410 is the outlier.

What is an outlier?

An outlier is an observation that lies an abnormal distance from other values in a random sample from a population. In a sense, this definition leaves it up to the analyst (or a consensus process) to decide what will be considered abnormal.

In simpler words, it is the number that is significantly bigger or smaller than the rest of the numbers, and 410 is it.

Step-by-step explanation:

Hope it helps! =D