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3 years ago

(4^p*4^1)^3 simplifies to 4^15 what does p equal?

Mathematics

1 answer:

zzz [600]3 years ago

6 0

When an exponent is outside the parentheses, you "distribute" it to the other exponents inside the parentheses.

(4^p)^3 would become 4^3p

(4^1)^3 would become 4^3

When the bases are the same, you just simply add the exponents.

Let's just ignore the bases so it'll look less confusing.

3p + 3 = 15

Subtract 3 from both sides.

3p = 12

Divide both sides by 3.

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A.) find the test statistic

Arada [10]

Regarding the hypothesis tested in this problem, it is found that:

a) The test statistic is: t = 0.49.

b) The p-value is: 0.6297..

c) The null hypothesis is not rejected, as the p-value is greater than the significance level.

d) It appears that the students are legitimately good at estimating one minute, as the sample does not give enough evidence to reject the null hypothesis.

<h3>What is the test statistic?</h3>

The test statistic of the t-distribution is given by the equation presented as follows:

$t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}$

In which the variables of the equation are given as follows:

$\overline{x}$ is the sample mean.

$\mu$ is the value tested at the hypotheses.

s is the standard deviation of the sample.

n is the sample size.

The value tested at the hypothesis is:

$\mu = 60$

From the sample, using a calculator, the other parameters are given as follows:

$\overline{x} = 62.47, s = 19.2, n = 15$

Hence the test statistic is obtained as follows:

$t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}$

$t = \frac{62.47 - 60}{\frac{19.2}{\sqrt{15}}}$

t = 0.49.

<h3>What are the p-value and the conclusion?</h3>

The p-value is obtained using a t-distribution calculator, with a two-tailed test, as we are testing if the mean is different a value, in this case 60, with:

15 - 1 = 14 df, as the number of degrees of freedom is one less than the sample size.

t = 0.49, as obtained above.

Hence the p-value is of 0.6297.

Since the p-value is greater than the significance level of 0.01, the null hypothesis is not rejected, attesting to the ability of the students to estimate one minute.

More can be learned about the test of an hypothesis at brainly.com/question/13873630

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1 year ago

Find the x-intercept of the graph of the linear equation<br> y = - 2 x + 3.

Lina20 [59]

The answer is y= -6.

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3 years ago

7. Jena has a triangular garden with a perimeter that can be represented by 25r ^ 2 - 9r + 14 . The sum of two sides of the gard

galben [10]

Answer: $15r^2-21r+5$

Step-by-step explanation:

Given: Perimeter of triangular garden = $25r^2 - 9r + 14$

The sum of two sides of the garden = $10r^2 + 12r + 9$

Perimeter is the sum of all sides of a triangle.

Third side = Perimeter of triangular garden - sum of two sides of the garden

$=25r ^ 2 - 9r + 14-(10r ^ 2 + 12r + 9)\\\\=25r ^ 2 - 9r + 14-10r ^ 2 - 12r - 9\\\\=15r^2-21r+5$

The expression represent the third side = $15r^2-21r+5$ .

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3 years ago

A factory made about 75,000 robots last year. The actual number of robots made was rounded to the nearest thousand. What is the

Alex777 [14]

The greatest number of robots: 74999
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3 years ago

Read 2 more answers

Someone help pretty please!

Nonamiya [84]

The answer is choice B
y > (2/3)x + 1

The boundary line is the equation y = (2/3)x + 1 which can be found through the slope formula to get m = 2/3. Then you use one of the two points on the line to find b = 1.

The equal sign in y = (2/3)x + 1 changes to a "greater than" sign to indicate two things
A) The shaded region is above the boundary line
B) The boundary line itself is a dashed line to indicate "no solution points on this line"

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3 years ago