The headquarters of the United States Department of Defense is the Pentagon,
which has 5 sides that are all the same length. If the perimeter (all sides added
together) of the Pentagon is 1,600 meters, what is the length of each side?

A system of equation is 1680mi3hr = p−w×600×2hr -p + w  for a jet airliner travels 1680 miles in 3hours with a tail wind.

Let p be  the speed of the jet airliner

and w  be the speed of the tail wind

It takes the plane 3 hours to go 1680 miles when a jet airliner travels with a tail wind and and 3.5 hours to go 1680 miles against the wind.. So, using system of equations we get

1680mi3hr = p−w×600×2hr = p + w

Solving for the left sides we get:

200mph = p - w

300mph = p + w

Now solve for one variable in either equation, we use

200mph = p - w

Add w to both sides:

p = 200mph + w

Using the value of x, we can found the value of w using system of equations.

300mph = (200mph + w) + w

Combine like terms:

300mph = 200mph + 2w

Subtract 200mph on both sides:

100mph = 2w

On dividing by 2:

50mph = w

So the speed of the tail wind is 50mph.

Therefore, 200mph = p - 50mph

Add 50mph on both sides:

250mph = p

Hence, speed of jet airliner is 250mph.

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The sample space for tossing a fair coin eight times is: There are 256 possible scenarios for tossing a coin flip eight times.

A probability event's sample space is indeed the collection of all possible outcomes.

HHHH HHHH

HHHH HHHT

HHHH HHTH

HHHH HHTT

HHHH HTHH

HHHH HTHT

HHHH HTTH

HHHH HTTT

HHHH THHH

HHHH THHT

HHHH THTH

HHHH THTT

HHHH TTHH

:

:

TTTT TTTT

Thus, the sample space for tossing a fair coin eight times is: There are 256 possible scenarios for tossing a coin flip eight times.

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The statement If a simple random sample is chosen with replacement, each individual has the same chance of selection on every draw is True.

If a simple random sample is chosen with replacement, it means that after each selection, the chosen individual is placed back into the population before the next selection is made. In this case, each individual in the population has the same chance of being selected for every draw.

The process of replacing the selected individual ensures that the selection probabilities remain constant throughout the sampling process. As a result, each individual has an equal probability of being chosen on each draw, making the statement true.

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Answer:

85 because if you do the math

The points that he average on the last two tests will be 93 points.

A mean is the average of the set of numbers that are given.

On the first five tests that he took, he averaged 86 points. The total points will be:

= 86 × 5

= 430 points

He averaged 88 points on all seven tests. The total will be:

= (88 × 7)

= 616 points

The point average on the last two tests will be:

= (616 - 430)/2

= 186/2

= 93 points

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Horizontal asymptote of c(x) is 450.

A horizontal asymptote is a line that guides the graph of a function for x-values but is not itself a part of the graph. "far," either "far" to the right or "far" to the left. Eventually, whether the graph is large enough or little, it may intersect.

Since we have given that

Cost to produce one refrigerator = $450

Fixed monthly cost = $200,000

Thus, the following formula represents the average cost to produce x refrigerators:

C(x) = (200000 + 450x)/x

Horizontal asymptote of c(x) would be

= 450x/x

= 450

Hence, Horizontal asymptote of c(x) is 450

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Answer:

$3h

Step-by-step explanation:

w=$44+$12h

w=$35+$15h

$44+$12h=$35+$15h

         -12              -12

$44=$35+$3h

-35    -35

$9=3h

/3   /3

$3=h

Answer:

anything to the power of 0 is always going to be 1 so the problem isnt as hard as it seems. so 1 million to the power of 0 will still be 1. so instead of the problem being 10,324 to the power of 0 by 8,576 to the power of 0 its really 1 x 1.

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

If you have a number with the exponent 0, then you should know that the exponent 0 always means 1. So, 10,324^0 is 1 and 8,576^0 is also 1.

Now, you have 1 times 1.  

1 times 1 = 1

So, the answer is 1.

Answer:

0.25 pints

Step-by-step explanation:

Hehe, i used goo. gle

The weight of the first basket full of apples is 8.66 kilograms more as compare to weight of the second basket.

Number of full of apples basket with Tommy = 2

Weight of first basket full of apples = 18.63 kilograms

Weight of second basket full of apples = 9.97 kilograms

Weight of first basket is greater than the weight of the second basket.

More weight in first basket

= Subtract the weight of the second basket from the weight of the first basket

⇒ More weight in first basket  = Weight of first basket - Weight of second basket

⇒ More weight in first basket = ( 18.63 - 9.97 ) kilograms

⇒ More weight in first basket = 8.66 kilograms

Therefore, the first basket weighed 8.66 kilograms more than the second basket.

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The mode is 5.ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

Answer:

The mode is 5, hope this helps!

The magnitude of the number of the minutes in the school is 2.

Although the order of magnitude of zero is not specified, it is occasionally stated to have a magnitude of. Zero is less than any other positive number, and so is its order of magnitude, according to this infinitely negative order of magnitude.

There can be no negative magnitude. The component of the vector that lacks direction is its length (positive or negative).

The order of magnitude is the approximate representation of the logarithmic of the order's value and is typically considered to be 10 taken as the base.

On a scale of 10 logarithmic, the difference in the order of magnitude can be quantified.

The value storage is where you may find the number into the various magnetic.

As a result, the number of minutes spent in school is 2.

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Complete question -

What is the Order of Magnitude of the number of minutes in a school day?

Answer: step 2

Step-by-step explanation:

Answer:

(-5, -6)

Step-by-step explanation:

Solve this by doing x- and y- separately.

For the x-axis:

Let right be the positive direction, so x = 2 -7

x = -5

For the y-axis:

Let up be the positive direction, so x = -4 -2

x = -6

Hope that helps!

You can find the coefficient of variation for your data set using a TI-84 calculator by following the below steps.

To find the coefficient of variation (CV) using a TI-84 calculator, follow these steps:

1. Enter the data set values into a list on your calculator. For example, if your data is stored in the list L1, enter the values into L1.

2. Calculate the mean of the data set using the calculator's statistical functions. Press the [STAT] button and navigate to the "Calc" menu. Choose the appropriate mean function (e.g., "1-Var Stats" or "mean") and select the list that contains your data (e.g., L1).

3. Calculate the standard deviation of the data set using the calculator's statistical functions. Press the [STAT] button, navigate to the "Calc" menu, and choose the appropriate standard deviation function (e.g., "1-Var Stats" or "stdDev"). Select the list containing your data (e.g., L1).

4. Divide the standard deviation by the mean and multiply by 100 to calculate the coefficient of variation. Store the standard deviation and mean values in variables if necessary. Use the formula CV = (stdDev / mean) * 100 to calculate the coefficient of variation.

By following these steps, you can find the coefficient of variation for your data set using a TI-84 calculator.

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To find the coefficient of variation on a TI-84 Plus calculator, enter the dataset into a list, calculate the mean and standard deviation, and then divide the standard deviation by the mean and multiply by 100.

To find the coefficient of variation on a TI-84 Plus calculator, follow these steps:

By following these steps, you can find the coefficient of variation for a dataset using a TI-84 Plus calculator.

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   "

Answer:

The answer should be B C and E!Thank me later.Don worry i took this question!Good luck!

Step-by-step explanation:

Answer:

the guy above me correct thank u

Step-by-step explanation:

Answer:

11 h

Step-by-step explanation:

1/2 h

11h 1/2 will be need for a bike

Given that <A and <B are complementary angles, the measure of angle B is: \(41^{\circ}\)

Apply the knowledge of what complimentary angles are to solve for x then find the measure of <B.

Since <A and <B are both complimentary angles, therefore:

m<A = (6x+1)

m<B = (8x-23)

\((6x+1) + (8x-23) = 90\)

\(6x+1 + 8x-23 = 90\)

\(6x+1 + 8x-23 = 90\\\\14x - 22 = 90\)

\(14x = 90 + 22\\\\14x = 112\)

\(x = 8\)

\(m \angle B = 8x-23\\\\m \angle B = 8(8) - 23\\\\m \angle B = 41^{\circ}\)

Therefore, given that <A and <B are complementary angles, the measure of angle B is: \(41^{\circ}\)

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We are 99% confident that the true average stance duration among elderly individuals lies within the range of 744.56 ms to 857.44 ms.

To test whether the true average stance duration is larger among elderly individuals than among younger individuals, we can perform a one-tailed independent samples t-test. The null hypothesis (H0)

Using the t-test, we compare the means and standard deviations of the two samples and calculate the test statistic

a) To calculate a 99% confidence interval for the true average stance duration among elderly individuals, we can use the sample mean, sample standard deviation, and the t-distribution.

Given:

Older adults: n = 28, sample mean = 801, sample standard deviation = 117

Using the formula for a confidence interval for the mean, we have:

Margin of error = t * (sample standard deviation / √n)

Since the sample size is relatively large (n > 30), we can use the z-score instead of the t-score for a 99% confidence interval. The critical z-value for a 99% confidence level is approximately 2.576.

Calculating the margin of error:

Margin of error = 2.576 * (117 / √28) ≈ 56.44

The confidence interval is then calculated as:

Confidence interval = (sample mean - margin of error, sample mean + margin of error)

Confidence interval = (801 - 56.44, 801 + 56.44) ≈ (744.56, 857.44)

b) To test whether the true average stance duration is larger among elderly individuals than among younger individuals, we can perform a one-tailed independent samples t-test.

The null hypothesis (H0): The true average stance duration among elderly individuals is equal to or less than the true average stance duration among younger individuals.

The alternative hypothesis (Ha): The true average stance duration among elderly individuals is larger than the true average stance duration among younger individuals.

. With the given data, perform the t-test and obtain the p-value.

c) To construct a 95% confidence interval for the difference in means between older and younger adults, we can use the formula for the confidence interval of the difference in means.

Given:

Older adults: n1 = 28, sample mean1 = 801, sample standard deviation1 = 117

Younger adults: n2 = 16, sample mean2 = 780, sample standard deviation2 = 72

Calculating the standard error of the difference in means:

Standard error = √((s1^2 / n1) + (s2^2 / n2))

Standard error = √((117^2 / 28) + (72^2 / 16)) ≈ 33.89

Using the t-distribution and a 95% confidence level, the critical t-value (with degrees of freedom = n1 + n2 - 2) is approximately 2.048.

Calculating the margin of error:

Margin of error = t * standard error

Margin of error = 2.048 * 33.89 ≈ 69.29

The confidence interval is then calculated as:

Confidence interval = (mean1 - mean2 - margin of error, mean1 - mean2 + margin of error)

Confidence interval = (801 - 780 - 69.29, 801 - 780 + 69.29) ≈ (-48.29, 38.29)

Comparison with part (b): In part (b), we performed a one-tailed test to determine if the true average stance duration among elderly individuals is larger than among younger individuals. In part (c), the 95% confidence interval for the difference in means (-48.29, 38.29) includes zero. This suggests that we do not have sufficient evidence to conclude that the true average stance duration is significantly larger among elderly individuals compared to younger individuals at the 95% confidence level.

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Answer:

x = 5

Step-by-step explanation:

Because the red-marked lines are parallel, we know that the ratios are the same

5x : 45 = 20 : 36

5x/45 = 20/36

5x * 36 = 20 * 45

5x * 4 = 20 * 5

5x * 1 = 5 * 5

x = 5

Answer:

The first equation should be multiplied by - 7 and the second equation by 3

Step-by-step explanation:

Given

\(9x + 3y = -18\) -- (1)

\(8x + 7y = 10\) -- (2)

Required

How to eliminate y

In (1), the coefficient of y = 3

In (2), the coefficient of y = 7

Multiply the first equation by -7

\(-7(9x + 3y = -18)\)

\(-63x -21y = 126\) --- (3)

Multiply the second by 3

\(3(8x + 7y = 10)\)

\(24x + 21y = 30\) -- (4)

Add the results together:

\(-63x -21y = 126\)

\(24x + 21y = 30\)

\(-------------------------\)

\(-63x + 24x -21y +21y = 126+30\)

\(-63x + 24x = 126+30\)

See that y is eliminated

Answer:

Step-by-step explanation:

34/35  is much larger than 2/5

1/12 is smaller than 2/5

A number that is the same as 2/5 is 2*5/5*5 = 10/25

There is a common factor in both the numerator and denominator. The common factor is the same (that's what common means in this case)

To determine the proportion that proves the relationship involving the tangent of angle D in the dilated triangles, we need more information about the angles and sides involved in triangles BAC and BDE. Specifically, we need the measures of the angles and the lengths of the sides to establish a proportion.

Without the specific measurements or relationships between angles and sides, we cannot provide a proportion that directly involves the tangent of angle D in this scenario. Dilations with a scale factor of 2 generally result in corresponding sides being twice as long, but the angles may or may not maintain the same measures. To establish a proportion involving the tangent of angle D, we would need more specific information about the triangle's properties, such as angle measures, side lengths, or additional relationships between angles and sides.

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A) the three inequalities that must be satisfied are:

B) Graph shaded and satisfying all conditions is attached.

An inequality in mathematics is a relationship that makes a non-equal comparison between two integers or other mathematical expressions.

It is most commonly used to compare the sizes of two numbers on a number line.

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The value of f(8.1) using the tangent line approximation is k + 0.2 where f(8) = k.

Tangent line approximation is the approximation of any function using a linear function. It is also called as linear approximation.

It allows us to approximate the value of a general function with amore simpler linear function.

Tangent line approximation can be found as,

L(x) = f(a) + f'(a) (x - a)

Here x = 8.1, at which we have to find the function value.

a = 8

f'(8) = 2

f(8) is not given in the question, Let it be k.

f(8.1) ≈ L(8.1) = k + 2(8.1 - 8)

                    = k + 0.2

Hence the approximate value of the function at x = 8.1 is k + 0.2, where f(8) = k.

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Answer:

In triangle XYZ, we are given that YZ = 9ft, XZ = 13ft, and angle X = 111 degrees.

To find the remaining side and angles of the triangle, we can use the Law of Cosines and the Law of Sines.

First, we can use the Law of Cosines to find the length of side XY:

XY^2 = XZ^2 + YZ^2 - 2(XZ)(YZ)cos(X)

XY^2 = 13^2 + 9^2 - 2(13)(9)cos(111)

XY^2 ≈ 5.98

XY ≈ 2.44 ft (rounded to two decimal places)

Next, we can use the Law of Sines to find the measure of angles Y and Z:

sin(Y)/YZ = sin(X)/XY

sin(Y)/9 = sin(111)/2.44

sin(Y) ≈ 0.39

Y ≈ 23.4 degrees (rounded to one decimal place)

sin(Z)/XZ = sin(X)/XY

sin(Z)/13 = sin(111)/2.44

sin(Z) ≈ 0.87

Z ≈ 60.6 degrees (rounded to one decimal place)

Therefore, in triangle XYZ, we have:

• XY ≈ 2.44 ft

• Y ≈ 23.4 degrees

• Z ≈ 60.6 degrees

The concept of ratio is used here to determine the number of boys in the school. Here the in a school of 425 pupils, the total number of boys in the school is 200.

Here there are 425 pupils, If the ratio of boys to girls is 8 to 9, then 8 out of 17 are boys and 9 out of every 17 are girls. Set up a proportion for the boys, where b = the total number of boys.

8 / 17 = b / 425

17 b = 8 × 425

b = 8 × 425 / 17

b = 200

So the number of boys are 200 and the number of girls are 425 - 200 = 225.

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Answer:

Reflection across x = -5