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2 years ago

In the trapezoid at the right, BE= 2x-8, DE= x-4, and AC= x+2

Mathematics

1 answer:

Marta_Voda [28]2 years ago

5 0

Answer:

A. x = 5 (Equation below)

B. AC = 9 | BD = 9

Step-by-step explanation:

A. Since we know the diagonals of an isosceles trapezoid are congruent, we know that the two bottom parts of the diagonal BD (2x - 8 and x - 4) are congruent to the diagonal AC (x + 2) . This means you can just equal them together and get the value of x:

2x - 8 + x - 4 = x + 2

3x - 12 = x + 2

3x = x + 14

2x = 14

x = 7

B. Just plug in 5 for x:

AC = x + 2 = 7 + 2 = 9

BD = 2x - 8 + x -4 = 3x - 12 = 21 - 12 = 9

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Answer:

For this case the 95% confidence interval is given (63.5 , 74.4) and we want to conclude about the result. For this case we can say that the true mean of heights for male students would be between 63.5 and 74.4. And the best answer would be:

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Step-by-step explanation:

Notation

$\bar X$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

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The confidence interval for the mean is given by the following formula:

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In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=40-1=39$

b. The doctor can be 95% confident that the mean height of male students at the college is between 63.5 inches and 74.4 inches.

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