Find the prime factorization of the number.<br><br> 168

Determine whether each of the following triangles is a right-angled triangle

Fantom [35]

Answer:

Yes

Step-by-step explanation:

To determine if this is a right triangle, use the pythagorean theorem and see if a^2 + b^2 is equal to c^2.

a^2 + b^2 = c^2

12^2 + 16^2 = 20^2

Evaluate the exponents.

144 + 256 = 400

Add them together.

400 = 400

Since a^2 and b^2 add up to equal c^2, this is a right triangle.

4 0

2 years ago

What is your favorite color? A larger survey of countries, including the United States, China, Russia, France, Turkey, Kenya, an

prohojiy [21]

Answer:

$z=\frac{0.253 -0.24}{\sqrt{\frac{0.24(1-0.24)}{75}}}=0.264$

$p_v =2*P(z>0.264)=0.792$

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 students said that blue is their favorite color is not different from 0.24

Step-by-step explanation:

Data given and notation

n=75 represent the random sample taken

X=19 represent the students said that blue is their favorite color

$\hat p=\frac{19}{75}=0.253$ estimated proportion of students said that blue is their favorite color

$p_o=0.24$ 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)

Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that the true proportion is different from 0.24.:

Null hypothesis: $p=0.24$

Alternative hypothesis: $p \neq 0.24$

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:

$z=\frac{0.253 -0.24}{\sqrt{\frac{0.24(1-0.24)}{75}}}=0.264$

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:

$p_v =2*P(z>0.264)=0.792$

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 students said that blue is their favorite color is not different from 0.24

7 0

3 years ago

If 3/4 of the class likes soda and 3/5 of those who like soda prefer Coke, what PERCENT of the whole class that likes Coke?

katen-ka-za [31]

Answer:

For soda =3/4

For coke= 3/5 X 3/4=9/20

Whole class is 1....

Therefore X% of 1 =9/20

Solving :

X/100 X 1 =9/20

X/100=9/20