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3 years ago

13

A contractor digs a hole for the basements of a new house that is 40 feet long and 10 1/2 feet deep. What is the width of the ho

le if 6,510 cubic feet of dirt are removed?
A.80 feet
B.81 1/4 feet
C.16 Feet
D.15 1/2 feet

1 answer:

34kurt3 years ago

7 0

D. 15.5

40*10.5 = 420

6510/420 = 15.5

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$32.39

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So the equation should be 12 times $2.699.

12 × 2.699 = 32.388

Then, round to the nearest cent.

32.388 = $32.39

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$y = 2$

Step-by-step explanation:

This answer is easily found using the Pythagorean Theorem:

${a}^{2} + {b}^{2} = {c}^{2}$

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Vlad1618 [11]

Basically the question is asking you for the area of the triangle.
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3 years ago

The quality control manager of a chemical company randomly sampled twenty 100-pound bags of fertilizer to estimate the variance

lisabon 2012 [21]

Answer:

The 95% confidence interval for the variance in the pounds of impurities would be $3.829 \leq \sigma^2 \leq 14.121$ .

Step-by-step explanation:

1) Data given and notation

$s^2 =6.62$ represent the sample variance

s=2.573 represent the sample standard deviation

$\bar x$ represent the sample mean

n=20 the sample size

Confidence=95% or 0.95

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population mean or variance lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

The Chi square distribution is the distribution of the sum of squared standard normal deviates .

2) Calculating the confidence interval

The confidence interval for the population variance is given by the following formula:

$\frac{(n-1)s^2}{\chi^2_{\alpha/2}} \leq \sigma^2 \frac{(n-1)s^2}{\chi^2_{1-\alpha/2}}$

On this case the sample variance is given and for the sample deviation is just the square root of the sample variance.

The next step would be calculate the critical values. First we need to calculate the degrees of freedom given by:

$df=n-1=20-1=19$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical values.

The excel commands would be: "=CHISQ.INV(0.025,19)" "=CHISQ.INV(0.975,19)". so for this case the critical values are:

$\chi^2_{\alpha/2}=32.852$

$\chi^2_{1- \alpha/2}=8.907$

And replacing into the formula for the interval we got:

$\frac{(19)(6.62)}{32.852} \leq \sigma^2 \frac{(19)(6.62)}{8.907}$

$3.829 \leq \sigma^2 \leq 14.121$

So the 95% confidence interval for the variance in the pounds of impurities would be $3.829 \leq \sigma^2 \leq 14.121$ .

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3 years ago