Given the similar triangles below find the missing length

Because of safety considerations, in May 2003 the Federal Aviation Administration (FAA) changed its guidelines for how small com

Rasek [7]

Answer:

a) The 95% confidence interval for the mean summer weight (including carry-on luggage) of Frontier Airlines passengers is between 179 and 187 pounds. This means that we are 95% sure that the mean summer weight of all Frontier Airlines passengers is between these two values.

b)

The 95% confidence interval for the mean winter weight (including carry-on luggage) of Frontier Airlines passengers is between 185.4 pounds and 194.6 pounds. This means that we are 95% sure that the mean winter weight of all Frontier Airlines passengers is between these two values.

c) They are respected, as the upper bound of both intervals is below the new FAA recommendations.

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve these questions.

Question a:

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 100 - 1 = 99

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 99 degrees of freedom(y-axis) and a confidence level of $1 - \frac{1 - 0.95}{2} = 0.975$ . So we have T = 1.9842

The margin of error is:

$M = T\frac{s}{\sqrt{n}} = 1.9842\frac{20}{\sqrt{100}} = 4$

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 183 - 4 = 179 pounds.

The upper end of the interval is the sample mean added to M. So it is 183 + 4 = 187 pounds.

The 95% confidence interval for the mean summer weight (including carry-on luggage) of Frontier Airlines passengers is between 179 and 187 pounds. This means that we are 95% sure that the mean summer weight of all Frontier Airlines passengers is between these two values.

Question b:

Critical value is the same(same sample size and confidence level).

The margin of error is:

$M = T\frac{s}{\sqrt{n}} = 1.9842\frac{23}{\sqrt{100}} = 4.6$

The lower end of the interval is the sample mean subtracted by M. So it is 190 - 4.6 = 185.4 pounds.

The upper end of the interval is the sample mean added to M. So it is 190 + 4.6 = 194.6 pounds.

The 95% confidence interval for the mean winter weight (including carry-on luggage) of Frontier Airlines passengers is between 185.4 pounds and 194.6 pounds. This means that we are 95% sure that the mean winter weight of all Frontier Airlines passengers is between these two values.

c. The new FAA recommendations are 190 pounds for summer and 195 pounds for winter. Comment on these recommendations in light of the confidence interval estimates from Parts (a) and (b).

They are respected, as the upper bound of both intervals is below the new FAA recommendations.

7 0

3 years ago

The diagram below shows a shaded parallelogram drawn inside a rectangle. Using Pythagoras, find the hypotenuse of triangle A and

Julli [10]

Answer: 5.9 cm for both triangles.

Step-by-step explanation:

Hi, since the situation forms 2 right triangles we have to apply the Pythagorean Theorem:

c^2 = a^2 + b^2

Where c is the hypotenuse of a triangle (the longest side of the triangle) and a and b are the other sides.

Replacing with the values given:

c^2 = 3^2 + 5^2

c^2 = 9+25

c^2 = 34

c = √34

c = 5.9 cm

Since both triangles are identical ( same side lengths) the hypotenuse is the same for both, 5.9 cm.

Feel free to ask for more if needed or if you did not understand something.

5 0

3 years ago

A two-digit number becomes 5/6 of the reversed number obtained when the digits are interchanged. The difference between the digi

stealth61 [152]

<h3>Answer: 54</h3>

==============================================

Work Shown:

T = tens digit

U = units digit (aka ones digit)

A number like 27 is really 20+7 = 2*10 + 7*1 = 10*2 + 1*7. We have 2 in the tens digit and 7 in the units digit. So 27 can be written in the form 10T + U where T = 2 and U = 7. Reversing the digits gives 72, so T = 7 and U = 2 now. Clearly the difference between the digits 7 and 2 is not 1, so 27 or 72 is not the answer (as it's just an example).

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

Let T be larger than U. This doesn't work if T = U.

Because T is larger, saying "The difference between the digits is 1" means T - U = 1. We can isolate T to get T = U+1. We'll use this later.

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

If T > U, then the original number 10T+U reverses to the new number 10U+T and it becomes smaller. We are told that it becomes 5/6 of what it used to be.

So,

new number = (5/6)*(old number)

10U + T = (5/6)(10T + U)

6(10U + T) = 5(10T + U)

60U + 6T = 50T + 5U

60U + 6(U+1) = 50(U+1) + 5U ... plug in T = U+1

60U + 6U + 6 = 50U + 50 + 5U

66U + 6 = 55U + 50

66U - 55U = 50-6

11U = 44

U = 44/11

U = 4 is the units digit of the original number

T = U+1

T = 4+1

T = 5 is the tens digit of the original number

The original number is therefore 10T + U = 10*5+4 = 54.

We see the difference in their digits is T-U = 5-4 = 1

The reverse of 54 is 45. The number 45 is 5/6 of 54

45 = (5/6)*54

7 0

3 years ago

What is the length of JM

Sloan [31]

Answer:

JM .................???????

8 0

3 years ago

Read 2 more answers

Please help me with this question.

Rasek [7]

The answer is 4,000 ft squared because since the sides are 100 ft and 80ft then we need to multiply them which is 8,000 then divide that by 2 since it’s a triangle which is 4,000 ft squared.

6 0

3 years ago