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balandron [24]
3 years ago
5

The area of a circle is found with the formula A = The expression is pi times r squared., where pi represents 3.14. If a tile ar

tist is laying down tiles in a circular mosaic pattern and the area of the circle is 706.5 square feet, what is the radius of the circle in feet?
Mathematics
1 answer:
lana [24]3 years ago
7 0
Okay. The formula for the area of the circle is A = πr². To find the radius, we would first do the steps in reverse. Let's divide the area by pi (3.14) 706.5/3.14 is 225. With that, the square root of 225 is 15, because 15² is 225. There. The radius of the circle is 15 feet.
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A genetic experiment involving peas yielded one sample of offspring consisting of 420 green peas and 174 yellow peas. Use a 0.01
slavikrds [6]

Answer:

a) z=\frac{0.293 -0.23}{\sqrt{\frac{0.23(1-0.23)}{594}}}=3.649  

b) For this case we need to find a critical value that accumulates \alpha/2 of the area on each tail, we know that \alpha=0.01, so then \alpha/2 =0.005, using the normal standard table or excel we see that:

z_{crit}= \pm 2.58

Since the calculated value is higher than the critical value we have enough evidence to reject the null hypothesis at 1% of significance.

Step-by-step explanation:

Data given and notation

n=420+174=594 represent the random sample taken

X=174 represent the number of yellow peas

\hat p=\frac{174}{594}=0.293 estimated proportion of yellow peas

p_o=0.23 is the value that we want to test

\alpha=0.01 represent the significance level

Confidence=99% or 0.99

z would represent the statistic (variable of interest)

p_v represent the p value (variable of interest)  

Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that the true proportion of yellow peas is 0.23:  

Null hypothesis:p=0.23  

Alternative hypothesis:p \neq 0.23  

When we conduct a proportion test we need to use the z statisitc, 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.

Calculate the statistic  

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

z=\frac{0.293 -0.23}{\sqrt{\frac{0.23(1-0.23)}{594}}}=3.649  

Statistical decision  

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.  

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

Since is a bilateral test the p value would be:  

p_v =2*P(z>3.649)=0.00026  

So the p value obtained was a very low value and using 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.

b) Critical value

For this case we need to find a critical value that accumulates \alpha/2 of the area on each tail, we know that \alpha=0.01, so then \alpha/2 =0.005, using the normal standard table or excel we see that:

z_{crit}= \pm 2.58

Since the calculated value is higher than the critical value we have enough evidence to reject the null hypothesis at 1% of significance.

5 0
3 years ago
What is -1/3 minus 5/8
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- 1/3 -5/8
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The first step is to find the least common denominator. The LCD of 3 and 8 is 24. Now, mulitply -1/3 by 8/8 and -5/8 by 3/3. This will give you fractions with equal denominators which you need to find before subtracting. Finally, you simplify the equation. Since this cannot be simplified, -23/24 is the answer
5 0
3 years ago
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Answer:

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Step-by-step explanation:

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This was used, together with the given limits:

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lim x => 0 f(x)/x = 5,

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f(x + y) = [f(x) + f(y)]/[1 - f(x)f(y)].

The workings are shown in the attachments.

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3 years ago
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