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bearhunter [10]
3 years ago
15

The two prisms below are similar. What is the value of x? A. 30 B. 1 C. 9 D. 3

Mathematics
2 answers:
UNO [17]3 years ago
5 0

Answer:

D. 3

Step-by-step explanation:

If the prisms are said to the similar, that means that the ratio/relation between their corresponding sides have to equal, so

\frac{x}{1} = \frac{9}{3} = \frac{30}{10}

We can easily use the part x/1 = 9/3 to make a cross-multiplication that would give us:

x = (1 * 9) / 3 = 9/3 = 3

So, the green prism is a dilated version of the blue one by a dilation/scale factor of 3.

Lynna [10]3 years ago
4 0

I believe it's D - 3....

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Read 2 more answers
The number of events is 29​, the number of trials is 298​, the claimed population proportion is​ 0.10, and the significance leve
Nina [5.8K]

Answer:

z=\frac{0.0973 -0.1}{\sqrt{\frac{0.1(1-0.1)}{298}}}=-0.155  

p_v =2*P(Z  

And we can use excel to find the p value like this: "=2*NORM.DIST(-0.155;0;1;TRUE)"

So the p value obtained was a very high value and using the significance level given \alpha=0.05 we have p_v>\alpha so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of interest is not significantly different from 0.1 .  

Step-by-step explanation:

1) Data given and notation

n=298 represent the random sample taken

X=29 represent the events claimed

\hat p=\frac{29}{298}=0.0973 estimated proportion

p_o=0.1 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 the proportion is 0.1 or no.:  

Null hypothesis:p=0.1  

Alternative hypothesis:p \neq 0.1  

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{0.0973 -0.1}{\sqrt{\frac{0.1(1-0.1)}{298}}}=-0.155  

4) 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 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  

And we can use excel to find the p value like this: "=2*NORM.DIST(-0.155;0;1;TRUE)"

So the p value obtained was a very high value and using the significance level given \alpha=0.05 we have p_v>\alpha so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of interest is not significantly different from 0.1 .  

We can do the test also in R with the following code:

> prop.test(29,298,p=0.1,alternative = c("two.sided"),conf.level = 1-0.05,correct = FALSE)

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