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3 years ago

Simplify the following expression.

Mathematics

1 answer:

Nitella [24]3 years ago

7 0

Answer:

Step-by-step explanation:

So to make it look simpler, rewrite it as this:

$\frac{4^{5} 7^{3} }{4^27^4}$

Now, you can cross out the 4^2 and 7^3

You're left with:

$\frac{4^3}{7}$

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How many meters are in a exameter?

xz_007 [3.2K]

Answer:

1E18 OR 10^18

Step-by-step explanation:

The formula is multiply the length by 1e+18

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3 years ago

What is the correct order of the fractions from least to greatest? Point A: −11 3 Point B: −2 3 Point C: 1 3 Point D: −12 3 The

Otrada [13]

Answer

-12/3, -11/3, -2/3, 1/3

Step-by-step explanation:

sorry if im wrong

6 0

3 years ago

Read 2 more answers

A sample of 200 observations from the first population indicated that x1 is 170. A sample of 150 observations from the second po

igor_vitrenko [27]

Answer:

a) For this case the value of the significanceis $\alpha=0.05$ and $\alpha/2 =0.025$ , we need a value on the normal standard distribution thataccumulates 0.025 of the area on each tail and we got:

$z_{\alpha/2} =1.96$

If the calculated statistic $|z_{calc}| >1.96$ we can reject the null hypothesis at 5% of significance

b) Where $\hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{170+110}{200+150}=0.8$

c) $z=\frac{0.85-0.733}{\sqrt{0.8(1-0.8)(\frac{1}{200}+\frac{1}{150})}}=2.708$

d) Since the calculated value satisfy this condition 2.708>1.96 we have enough evidence at 5% of significance that we have a significant difference between the two proportions analyzed.

Step-by-step explanation:

Data given and notation

$X_{1}=170$ represent the number of people with the characteristic 1

$X_{2}=110$ represent the number of people with the characteristic 2

$n_{1}=200$ sample 1 selected

$n_{2}=150$ sample 2 selected

$p_{1}=\frac{170}{200}=0.85$ represent the proportion estimated for the sample 1

$p_{2}=\frac{110}{150}=0.733$ represent the proportion estimated for the sample 2

$\hat p$ represent the pooled estimate of p

z would represent the statistic (variable of interest)

$p_v$ represent the value for the test (variable of interest)

$\alpha=0.05$ significance level given

Concepts and formulas to use

We need to conduct a hypothesis in order to check if is there is a difference between the two proportions, the system of hypothesis would be:

Null hypothesis: $p_{1} = p_{2}$

Alternative hypothesis: $p_{1} \neq p_{2}$

We need to apply a z test to compare proportions, and the statistic is given by:

$z=\frac{p_{1}-p_{2}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{1}}+\frac{1}{n_{2}})}}$ (1)

a.State the decision rule.

For this case the value of the significanceis $\alpha=0.05$ and $\alpha/2 =0.025$ , we need a value on the normal standard distribution thataccumulates 0.025 of the area on each tail and we got:

$z_{\alpha/2} =1.96$

If the calculated statistic $|z_{calc}| >1.96$ we can reject the null hypothesis at 5% of significance

b. Compute the pooled proportion.

Where $\hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{170+110}{200+150}=0.8$

c. Compute the value of the test statistic.

z-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.

Replacing in formula (1) the values obtained we got this:

$z=\frac{0.85-0.733}{\sqrt{0.8(1-0.8)(\frac{1}{200}+\frac{1}{150})}}=2.708$

d. What is your decision regarding the null hypothesis?

Since the calculated value satisfy this condition 2.708>1.96 we have enough evidence at 5% of significance that we have a significant difference between the two proportions analyzed.

5 0

3 years ago

Classify the following triangle

jek_recluse [69]

Acute-The angle is less than 90 degrees

Equilateral-All sides are equal in length

Isosceles-Two of the sides are equal in length

Scalene-None of the sides are equal in length

Right-The angle is 90 degrees

Obtuse-The angle is greater than 90 degrees

We can see that none of the sides are the same length, so we know that it must be scalene. We can also see that every angle is less than 90 degrees, so we know that is must be acute.

The triangle is scalene and acute.

Hope this helps!!

3 0

3 years ago

Veronica is saving money to by a saddle for her horse that costs 175 . She plans to save $10 the first month and then increased

Anon25 [30]

You will start off with $175-$10=$165. Then you will take your $165 and divide by $15 to get the answer. $165÷$15=11 months to save the money.

6 0

3 years ago