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Ivan
3 years ago
7

A patio is in the shape of a trapezoid. The length of the longer base is 17 feet. The length of the shorter base is two feet les

s than half the longer base. The height is 4 feet. What is the area of the patio?

Mathematics
1 answer:
erma4kov [3.2K]3 years ago
5 0

Answer:

The area of the patio is 43 square feet

Step-by-step explanation:

In this question, we have a trapezoid and we are asked to calculate the area of the patio which is in the form of the trapezoid.

Please check attachment for possible trapezoid picture.

Mathematically, the area of the trapezoid can be calculated using the mathematical formula below;

A = 1/2 (a+b) h

where a and b are the lengths of the parallel sides.

Now, let’s say a is 17 feet

b was stated explicitly to be 2 feet half the length of the longer base. That would be 1/2(17) - 2 = 8.5 -2 = 6.5 feet

Now let’s calculate the area of the patio;

A = 1/2(6.5+17) * 4 = 2(23.5) = 47 square feet

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A local bottler in Hawaii wishes to ensure that an average of 22 ounces of passion fruit juice is used to fill each bottle. In o
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Answer:

(a) Null Hypothesis, H_0 : \mu = 22 ounces  

    Alternate Hypothesis, H_A : \mu\neq 22 ounces

(b) The value of the test statistic is -2.687.

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Step-by-step explanation:

We are given that a local bottler in Hawaii wishes to ensure that an average of 22 ounces of passion fruit juice is used to fill each bottle.

He takes a random sample of 65 bottles. The mean weight of the passion fruit juice in the sample is 21.54 ounces. Assume that the population standard deviation is 1.38 ounce.

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Alternate Hypothesis, H_A : \mu\neq 22 ounces     {means that the average different from 22 ounces of passion fruit juice is used to fill each bottle}

The test statistics that would be used here <u>One-sample z test statistics</u> as we know about the population standard deviation;

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where, \bar X = sample mean weight of the passion fruit juice = 21.54 ounces

            \sigma = population standard deviation = 1.38 ounce

            n = sample of bottles = 65

So, <u><em>test statistics</em></u>  =  \frac{21.54-22}{\frac{1.38}{\sqrt{65} } }  

                               =  -2.687

(b) The value of z test statistics is -2.687.

(c) Since, in the question we are not given with the level of significance so we assume it to be 5%. Now, at 5% significance level the z table gives critical values of -1.96 and 1.96 for two-tailed test.

<em>Since our test statistics does not lie within the range of critical values of z, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which </em><u><em>we reject our null hypothesis</em></u><em>.</em>

Therefore, we conclude that Reject H_0 since the value of the test statistic is less than the negative critical value which means that the average different from 22 ounces of passion fruit juice is used to fill each bottle.

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