Identify the volume of the composite figure. The figure shows a rectangular prism with a cube removed. The prism is 9 meters long, 8 meters wide, and 3 meters high. The cube has a side of 4 meters

wAnswer:

e

Step-by-step explanation:

Answer:

$2 per pen

Step-by-step explanation:

mechanical pencils: 5.25

all pens: 8

5.25+8= $13.25

:)

The sampling distribution of a mean will be approximately normal even when the population is not exactly normal as long as the sample is representative, large, or small. Therefore, options (a), (b), and (c) are correct.

(a) When the sample is representative, it means that it accurately reflects the characteristics of the population. In this case, the Central Limit Theorem states that regardless of the shape of the population distribution, as long as the sample is representative, the sampling distribution of the mean will approach a normal distribution.

(b) When the sample is large, typically considered to be greater than 30 observations, the Central Limit Theorem holds true. This theorem states that as the sample size increases, the sampling distribution of the mean becomes increasingly normal. The larger the sample size, the closer the sampling distribution of the mean will approximate a normal distribution.

(c) Even when the sample size is small, as long as certain conditions are met, the sampling distribution of the mean can still be approximately normal.

These conditions include the absence of extreme outliers and the population not being heavily skewed. In such cases, the Central Limit Theorem can still apply, allowing for an approximately normal sampling distribution of the mean.

In summary, the sampling distribution of a mean will approximate a normal distribution regardless of the population's exact distribution, as long as the sample is representative, large, or small under certain conditions.

The Central Limit Theorem plays a crucial role in establishing this approximation. Therefore, options (a), (b), and (c) are correct.

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Answer:

x = -9, 3

Step-by-step explanation:

you cross multiply

Answer:

 \(x=-9\) or \(x=3\)

Step-by-step explanation:

Cross multiply:

\(3/x+6=x/9\\\\\\(3) * (9)=x*(x+6)\\\\\\27=x^{2} +6x\)

Subtract x^2 +6x from both sides:

\(27-(x^{2}+6x )=x^{2} +6x-(x^{2} +6x)\\\\\\-x^{2} -6x+27=0\)

Factor left side of the equation:

\((-x+3)(x+9)=0\)

Set factors equal to 0:

\(-x+3=0\) or \(x+9=0\)

Therefore, \(x=3\) or \(x=-9\)

hope this helps.....

both expressions 2m - 4 and 6(m - 2) represent the same area of the shaded rectangle. However, 6(2-m) does not represent the area of the rectangle, since the width of the rectangle is (m-2), not (2-m).

To determine whether the area of the shaded rectangle is 6(2-m) or 6(m-2), we need to first identify the dimensions of the rectangle.

Looking at the diagram, we see that the rectangle has a height of 2 units and a width of (m - 2) units. Therefore, the area of the rectangle is given by:

Area of rectangle = height x width

Area of rectangle = 2 x (m - 2)

Simplifying this expression, we get:

Area of rectangle = 2m - 4

So, the area of the shaded rectangle is 2m - 4, which is equivalent to 6(m-2) since:

2m - 4 = 2(m - 2) = 6(m - 2)/3 = 6(m - 2)

what is rectangle?

A rectangle is a quadrilateral with four sides and four right angles. It is a type of parallelogram where opposite sides are equal in length, and it has two pairs of parallel sides. The length of a rectangle is typically longer than its width, and the opposite sides are parallel and equal in length.

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The answers to each part is mentioned above.

Given is that Aiko works in the fish department of a pet store. She must drain, clean, and refill two reef tanks. The first tank hold 175 gallons of water and drains at a rate of 25 gallons per hour. The second tank holds 200 gallons of water and drains at a rate of 30 gallons per hour.

Equation for tank {1} -

y = 175 - 25x

Equation for tank {2} -

y = 200 - 30x

For the solution we can write -

175 - 25x = 200 - 30x

- 25x + 30x = 200 - 175

5x = 25

x = 5

and

y = 200 - 150

y = 50

For the same amount of water we can write -

175 - 25x = 200 - 30x

- 25x + 30x = 200 - 175

5x = 25

x = 5 hours

In tank (1), there is : 175 - 25 x 5 = 50 gallons

In tank (2), there is : 200 - 30 x 5 = 50 gallons

Therefore, the answers to each part is mentioned above.

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Consider the same figure as given above. It is observed that DP/PE = DQ/QF and also in the triangle DEF, the line PQ is parallel to the line EF.

So, ∠P = ∠E and ∠Q = ∠F.

Hence, we can write: DP/DE = DQ/DF= PQ/EF.

The above expression is written as

DP/DE = DQ/DF=BC/EF.

It means that PQ = BC.

Hence, the triangle ABC is congruent to the triangle DPQ.

(i.e) ∆ ABC ≅ ∆ DPQ.

Thus, by using the AAA criterion for similarity of the triangle, we can say that

∠A = ∠D, ∠B = ∠E and ∠C = ∠F.

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The population variance is approximately 16.41 and the population standard deviation is approximately 4.05. These values indicate the spread or dispersion of the children's ages around the mean age of 7.71 in the given family.

To find the population variance and standard deviation for the ages of children in a family, follow these steps:

Calculate the mean (average) of the ages by adding all the ages and dividing by the total number of children, which is 7 in this case.

Mean = (1 + 3 + 5 + 7 + 8 + 11 + 14) / 7 = 7.71 (approximately)

Calculate the squared difference of each age from the mean.

Find the sum of the squared differences.

Divide the sum by the number of data points (7) to calculate the population variance.

Finally, take the square root of the variance to get the population standard deviation (σ).

After performing the calculations, the population variance is approximately 16.41 and the population standard deviation is approximately 4.05.

These values indicate the spread or dispersion of the children's ages around the mean age of 7.71 in the given family.

The standard deviation measures the average amount by which each age deviates from the mean, providing a useful metric to understand the variability within the age distribution.

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The equation that represents the inverse function b(a) in this case is:

C. b(a) = 7

Answer:

The y-intercept of this line is 2.

Step-by-step explanation:

To find where this line reaches the y axis, you simply need to assign the value 0 to x, and solve for y:

\(2x + 3y = 6\\2(0) + 3y = 6\\3y = 6\\y = 6/3\\y = 2\)

So the y intercept of that line is 2

In a game theory situation that results in a Prisoners' Dilemma, the following statement must be true: Each player has a dominant strategy that leads to a suboptimal outcome for both players

A Prisoners' Dilemma is a classic example in game theory where two individuals face a situation where cooperation would lead to the best outcome for both, but individual self-interest and the absence of trust lead to a non-cooperative outcome.

In a Prisoners' Dilemma, each player has a dominant strategy, which means that regardless of the other player's choice, each player's best move is to act in their own self-interest. This dominant strategy leads to a suboptimal outcome for both players.

The dilemma arises from the fact that if both players choose to cooperate and trust each other, they can achieve a better overall outcome. However, due to the lack of trust and the fear of being taken advantage of, both players choose the non-cooperative strategy, resulting in a suboptimal outcome for both.

Therefore, in a Prisoners' Dilemma, it is necessary for each player to have a dominant strategy and for cooperation to lead to a better outcome, but individual self-interest prevents them from choosing the cooperative option.

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Note that the IRS Installment Agreement form 433-D can be mailed to

Internal Revenue Service

ACS Support

PO Box 8208

Philadelphia, PA 19101-8208.

Please note   that you will need to include a copyof your most recent tax return with your Form 433-D.

You can also   include any other documentation that you think would be helpful in your request foran installment agreement.

Here are some additional tips for mailing Form 433-D -

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a) The probability of obtaining k heads when one of two coins is randomly selected and tossed three times can be calculated using the binomial distribution.

b) The probability that coin 1 was tossed given k heads can be found using Bayes' theorem, considering the conditional probabilities of selecting each coin and the probability of getting k heads with each coin.

c) In part b, the coin that is more probable when k heads have been observed depends on the specific value of k and the corresponding probabilities calculated.

d) To determine the threshold value T where coin 1 becomes more probable for k > T heads observed, and coin 2 is more probable for k < T heads observed, a generalization of the solution from part b can be used by considering the probabilities of selecting each coin and the probability of obtaining k heads with each coin when tossed m times.

a) To find the probability of obtaining k heads, we can use the binomial distribution formula: P(k heads) = C(n, k) * p^k * (1 - p)^(n - k), where n is the number of tosses (in this case, 3), p is the probability of getting heads for the selected coin, and C(n, k) represents the number of combinations of n items taken k at a time.

b) To find the probability that coin 1 was tossed given k heads, we can apply Bayes' theorem: P(Coin 1 | k heads) = P(k heads | Coin 1) * P(Coin 1) / P(k heads), where P(Coin 1) is the probability of selecting coin 1, P(k heads | Coin 1) is the probability of getting k heads with coin 1, and P(k heads) is the overall probability of getting k heads (calculated in part a).

c) Comparing the probabilities calculated in part b for different values of k, we can determine which coin is more probable when k heads have been observed.

d) To find the threshold value T, we can generalize the solution from part b to the case where the selected coin is tossed m times. By considering the probabilities of selecting each coin and the probability of obtaining k heads with each coin when tossed m times, we can find the value of k where the probabilities switch, indicating which coin is more likely. This threshold value T can then be used to determine which coin is more probable for k > T and k < T heads observed.

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Answer

C. 49 fl oz

Step-by-step explanation:

I took the quiz.

Product Property of Roots The product property of roots states that the square root of the product of two numbers is equal to the product of their square roots. In other words, for any non-negative numbers a and b, the square root of the product of a and b equals the product of the square roots of a and b.

The equivalent expression to √(ab) using the product property of roots is √a * √b. The reason is that by definition of the product property of roots, the square root of the product of a and b is equal to the square root of a multiplied by the square root of b, that is, √(ab) = √a * √b. Therefore, the correct answer is option A, which is √(ab).

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The solution to the expression given as 5x + 3y > 12 has the ordered pair of (3, 0)

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

5x + 3y > 12

Solving further, we need to collect the like terms

So, the expression becomes

3y > 12 - 5x

Next, we divide through the inequality by 3

So, we have the following representation

y > 12/3 - 5/3x

Evaluate

The equation becomes

y > 4 - 5/3x

At this point, we assume any value for x and then solve for y

Assume that the value of x is 3

So, we have the following representation

y > 4 - 5/3 * 3

Evaluate the products

y > -1

A value greater than -1 is 0

So, we have

x = 3 and y = 0

Express as ordered pairs

(x, y) = (3, 0)

Hence, the ordered pair of the solution is (3, 0)

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Answer:

0.04

Step-by-step explanation:

The sensors made by Breaker's have a 4% defect rate

Randomly selecting one adult from a residence when conducting a sample survey on residential telephone numbers is a good idea for several reasons.

Firstly, this method helps ensure a diverse and representative sample. By selecting a random adult from each household, the survey aims to capture a wide range of perspectives and demographics. This increases the validity and reliability of the survey results, as it reduces the chances of bias or skewed outcomes.
Secondly, asking about the adults who live in the residence rather than the person who picks up the phone helps to avoid selection bias. If the survey only asked the person who answered the call, it may inadvertently exclude certain demographics, such as households with multiple adults or those with different schedules.

By randomly selecting one adult, the survey takes into account the possibility of multiple residents and provides a more comprehensive view.
Furthermore, this approach helps to maintain confidentiality and privacy.

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Solution

We can create the solution with the following tree diagram:

Part 2

For this case we want this probability:

P(rain and accident)

And we can do this operation:

P(rain and accident) = 0.75 *0.5 = 0.375

Part 3

For this case we want this probability:

P( no rain and accident)

And we can do this operation:

P(no rain and accident) = 0.25 *0.25 = 0.0625

Part 4

P(Accident) = 0.5*0.75 + 0.25*0.25= 0.4375

Answer:

x<1

Step-by-step explanation:

Pretend the sign is an equal sign and solve:

-11x-4=-15

-11x=-15+4

-11x=-11

If you divide a negative, the sign switches, so the sign is now less than, not greater than

x<1

Answer:

x<1

Step-by-step explanation:

-11x-4>-15

-11x>-15+4

-11x>-11

11x>11

x>11/11

x>1

x<1

Answer:

A

brainliest is much appreciated!

Step-by-step explanation:

hope this helps!

Answer:

x = -5

Step-by-step explanation:

(2/3)x - (1/2) = (1/3) + (5/6)x

we observe that the denominators are 3, 2 and 6 and the lowest common multiple between the 3 numbers is 6.

Therefore we multiply each term of the equation of the equation by 6 in order to remove the fractions:

(2/3)x - (1/2) = (1/3) + (5/6)x    (multiply all terms by 6)

(6)(2/3)x - (6)(1/2) = (6)(1/3) + (6)(5/6)x     (simplify)

4x - 3 = 2 + 5x     (add 3 to both sides)

4x = 2 + 5x + 3

4x = 5 + 5X   (subtract 5x from btoh sides)

4x - 5x = 5

-x = 5 (multiply both sides by -1)

x = -5  (answer)

The measures of the larger angles are 130°, and the measures of the smaller angles are 50°

Vertically opposite angles are angles that shares the same vertex point . Vertically opposite angles are congruent.

Therefore, the angles 3y + 11 and 4x - 22 are vertical angles and 10y and 7x + 4 are vertical angles.

Hence,

10y = 7x + 4

10y - 7x = 4

3y + 11 = 4x - 22

3y - 4x = - 33

Combine the equation

10y - 7x = 4

3y - 4x = - 33

multiply equation(ii) by 1.75

10y - 7x = 4

5.25y - 7x = - 57.75

subtract the equation

4.75y = 61.75

y = 61.75 / 4.75

y = 13

Therefore, let's find x

10(13) = 7x + 4

130 - 4 = 7x

7x = 126

x = 126 / 7

x = 18

Hence,

10y = 10(13) = 130 degrees

(3(13) + 11) = 50 degrees

Therefore,

larger angle = 130°

smaller angle = 50°

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210 orders are possibe to pass across a bridge.

The number of orders in which 7 cars can cross a bridge that can only accommodate 4 cars at a time can be calculated using the permutation formula.

The formula for permutation is n!/(n-r)! where n is the total number of items and r is the number of items being selected at a time. In this case, n = 7 cars and r = 4 cars at a time.

Thus, the number of orders in which 7 cars can cross the bridge is 7!/(7-4)! = 7!/(3)! = 765 = 210. This means that there are 210 possible orders in which 7 cars can cross the bridge.

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—————————————————

Margi has 6 square tiles of equal size. each side of each tile is 0.8 inch long. If Margi places all the tiles in a row with sides touching, how long is the row?

—————————————————

\(\mathrm{N = 6×0.8 \: inch}\)

\({\boxed{\mathrm\green{N = 4.8 \: inch}}}\)

—————————————————

\(\purple{\boxed{\boxed{\tt\pink{➢4.8 \: inch}}}}\)

Answer:

The awnser to this equation is 120 cents

The cost of using a 200-watt television for 30 days, turned on for 2 hours per day, would be $1.20.  

To calculate the cost of using a 200-watt television for 30 days with 2 hours of daily usage at 10 cents per kilowatt-hour, we need to find the total energy consumption and then multiply it by the cost per kilowatt-hour.

First, let's find the total energy consumption:

1. Daily energy usage: 200 watts * 2 hours = 400 watt-hours
2. Monthly energy usage: 400 watt-hours * 30 days = 12,000 watt-hours

Now, we need to convert watt-hours to kilowatt-hours:
3. Monthly energy usage in kilowatt-hours: 12,000 watt-hours / 1,000 = 12 kWh

Finally, let's calculate the cost:
4. Cost of using the television for 30 days: 12 kWh * 10 cents per kWh = 120 cents

So, the cost of using a 200-watt television for 30 days with 2 hours of daily usage at 10 cents per kilowatt-hour is 120 cents.

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-0.05 is the average rate of change in median age per year from 1930 to 1960.

The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.

Given,  a data set that gives the median age of an American man at the time of his first marriage.

Year                             Median age

1910                              25.1

1920                             24.6

1930                             24.3

1940                             24.3

1950                             22.8

1960                             22.8

1970                             23.2

1980                             24.7

1990                             26.1

2000                             26.8

The average rate of change from 1930 to 1960 = (-24.3 + 22.8) / (1960-1930)

The average rate of change from 1930 to 1960 = -0.05

Therefore, the average rate of change in median age per year from 1930 to 1960 is -0.05.

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True. A recursive function can have two base cases, such as n == 0 returning 0, and n == 1 returning 1.

Having multiple base cases in a recursive function allows for handling different scenarios and terminating the recursion based on those specific conditions.

In the case you mentioned, where the first base case is n == 0 returning 0, and the second base case is n == 1 returning 1:

When the input value of n is 0, the recursive function reaches the first base case (n == 0) and returns the value 0. This provides a stopping condition to prevent further recursive calls and allows the function to unwind back through the call stack.

When the input value of n is 1, the recursive function does not match the first base case (n != 0), but it matches the second base case (n == 1), which returns the value 1. Again, this terminates the recursion and allows the function to exit.

Having multiple base cases is useful when the recursive problem has different possible outcomes or when there are specific values that need to be handled separately. Each base case defines a condition under which the recursion should stop and allows the function to return a specific value.

If none of the base cases match for a given input, the recursive function will continue making recursive calls until a base case is reached and the recursion can be terminated.

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Answer:

  2 m

Step-by-step explanation:

You want the height of the triangular base of a triangular prism that has a volume of 12.6 m³. The base of the triangle is 2.8 m, and the height of the prism is 4.5 m.

The volume formula for the triangular prism is ...

  V = Bh . . . . the product of the triangle area and the base–base distance

  12.6 = B·4.5

  2.8 = B . . . . . . . area of the triangular base

The area of the triangular base is given by ...

  A = 1/2bh

The area is shown above to be 2.8 m², and the base of the triangle is given as 2.8 m, so we have ...

  2.8 = 1/2(2.8)h

  2 = h . . . . . . . . . . . . divide by 1.4, the coefficient of h

The center height of the tent is 2 meters.

__

Additional comment

If you combine the formulas, you see that a triangular prism has half the volume of a rectangular prism with the same overall dimensions.

  V = 1/2LWH

  12.6 = 1/2(4.5)(2.8)h = 6.3h

  2 = h . . . . meters

Answer:

Equation is y = 3

Step-by-step explanation:

\((x_1, y_1) = ( -2, 3) \ , \ (x_2, y_2) = (8, 3 )\)

\(Slope,m = \frac{y_2 - y_1}{x_2-x_1} = \frac{3-3}{8 -- 2} = 0\)

\(Equation : (y - y_1) = m (x - x_1)\)

               \(y - 3 = 0 (x -- 2)\\y - 3 = 0\\y = 3\)