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liubo4ka [24]
3 years ago
13

A trapezoid has an area of 184 in^2. The height is 8 in and the length of one base is 16 in. Write and solve an equation to find

the length of the other base.
Mathematics
1 answer:
inna [77]3 years ago
3 0

Answer:

The length of other base is <u>30 in</u>.

Step-by-step explanation:

Given:

A trapezoid has an area of 184 in^2. The height is 8 in and the length of one base is 16 in.

Now, to get the length of other base.

Let the length of other base be  (b).

Area of trapezoid (Area) = 184 in².

Height of trapezoid (h) = 8 in.

Length of one base (a) = 16 in.

Now, to get the length of other base of trapezoid we solve an equation:

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

184=\frac{(16+b)}{2}\times 8

184=(16+b)\times 4

<em />184=64+4b<em />

<em>Subtracting both sides by 64 we get:</em>

<em />120=4b<em />

<em>Dividing both sides by 4 we get:</em>

30=b\\\\b=30\ in.

Therefore, the length of other base is 30 in.

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Answer:

z=\frac{0.694 -0.75}{\sqrt{\frac{0.75(1-0.75)}{180}}}=-1.735  

p_v =P(z  

If we compare the p value obtained and the significance level given \alpha=0.05 we have p_v so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the proportion of americans between 17 to 24 that not qualify for the military is significantly less than 0.75 or 75% .  

Step-by-step explanation:

1) Data given and notation  

n=180 represent the random sample taken  

X=125 represent the number of americans between 17 to 24 that not qualify for the military

\hat p=\frac{125}{180}=0.694 estimated proportion of americans between 17 to 24 that not qualify for the military

p_o=0.75 is the value that we want to test  

\alpha=0.05 represent the significance level  

Confidence=95% or 0.95  

z would represent the statistic (variable of interest)  

p_v represent the p value (variable of interest)  

2) Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that less than 75% of Americans between the ages of 17 to 24 do not qualify for the military :  

Null hypothesis: p\geq 0.75  

Alternative hypothesis:p < 0.75  

When we conduct a proportion test we need to use the z statistic, and the is given by:  

z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}} (1)  

The One-Sample Proportion Test is used to assess whether a population proportion \hat p is significantly different from a hypothesized value p_o.  

3) Calculate the statistic  

Since we have all the info requires we can replace in formula (1) like this:  

z=\frac{0.694 -0.75}{\sqrt{\frac{0.75(1-0.75)}{180}}}=-1.735  

4) Statistical decision  

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The significance level provided \alpha=0.05. The next step would be calculate the p value for this test.  

Since is a left tailed test the p value would be:  

p_v =P(z  

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Answer:

a. a = 1, b = -5, c = -14

b. a = 1, b = -6, c = 9

c. a = -1, b = -1, c = -3

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Step-by-step explanation:

a. x-ints at 7 and -2

this means that our quadratic equation must factor to:

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FOIL and you will get:

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