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Mashcka [7]
2 years ago
11

The formula for a trapezoid relates the area A, the two bases, a and b, and the height, h. Solve for a

Mathematics
1 answer:
den301095 [7]2 years ago
8 0

Answer:

a=\frac{2A}{h}-b

Step-by-step explanation:

we know that

The formula to calculate the area for a trapezoid is equal to

A=\frac{1}{2}(a+b)h

where

a and b are the parallel bases

h is the height of trapezoid

A is the area

<em>Solve for a</em>

That means ----> isolate the variable a

Multiply by 2 both sides to remove the fraction in the right side

2A=(a+b)h

Divide by h both sides

\frac{2A}{h}=a+b

Subtract b both sides

\frac{2A}{h}-b=a

Rewrite

a=\frac{2A}{h}-b

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A study of the amount of time it takes a mechanic to rebuild the transmission for a 1992 Chevrolet Cavalier shows that the mean
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B) 0.0069

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

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For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question, we have that:

\mu = 8.4, \sigma = 1.8, n = 40, s = \frac{1.8}{\sqrt{40}} = 0.2846

Find the probability that their mean rebuild time exceeds 9.1 hours.

This is 1 subtracted by the pvalue of Z when X = 9.1. So

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{9.1 - 8.4}{0.2846}

Z = 2.46

Z = 2.46 has a pvalue of 0.9931

1 - 0.9931 = 0.0069

So the answer is B.

6 0
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