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antoniya [11.8K]
3 years ago
11

Write each power as a product of factors 2^4 4^2 9^2 8^5 5^3 7^3

Mathematics
1 answer:
snow_lady [41]3 years ago
5 0
<em><u>2^{4}⇒2×2×2×2⇒16</u></em>
<em><u>4^{2}⇒4×4⇒16</u></em>
<em><u>9^{2}⇒9×9⇒81</u></em>
<em><u>8^{5}⇒8×8×8×8×8⇒32.768</u></em>
<em><u>5^{3}⇒5×5×5⇒125</u></em>
<em><u>7^{3}⇒7×7×7⇒343</u></em>
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Bill bought a new cellular phone. His monthly bill will be $32.99 each month which includes 100 minutes of use. Additional minut
Sunny_sXe [5.5K]

Answer: option D is the correct answer.

Step-by-step explanation:

Let m represent the total number of minutes that the phone is used in a month.

Let C represent the amount of the bill for using m minutes.

His monthly bill will be $32.99 each month which includes 100 minutes of use. Additional minutes will cost $0.19 per minute. It means that the cost of additional minutes is

0.19(m - 100). Therefore, the linear model representing the amount of the bill would be

C = 0.19(m - 100) + 32.99

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3 years ago
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URGENT HELP Graph f(x) = 3|x - 5| + 1 (please put picture of the answer graphed)
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Answer:

Step-by-step explanation:

I uploaded a picture of the graph, but you can go to the site, Desmos. Just plug in your equation, and you will get the equation graphed.

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2 years ago
What is the length of the diagonal of a rectangle that is 12 inches long and 6 inches wide?​
lakkis [162]
To find the diagonal of the rectangle we have to use Pythagorean theorem!

Pythagorean theorem is used to find the length of a missing angle such as the hypotenuse or the sides a and b.

Steps to solve:

1. 12 in is the length or the base of the right triangle, and 6 in is the wide or the side a.
2. Now use the formula: a^2+b^2=c^2, and plug in the numbers!
3. 6^2+12^2=c^2, now just solve the squared numbers.
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5. 180=c^2
6. Find the square root of 180.

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3 years ago
The CEO of a large manufacturing company is curious if there is a difference in productivity level of her warehouse employees ba
blsea [12.9K]

Answer:

The test statistic is z = -2.11.

Step-by-step explanation:

Before finding the test statistic, we need to understand the central limit theorem and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

Group 1: Sample of 35, mean of 1276, standard deviation of 347.

This means that:

\mu_1 = 1276, s_1 = \frac{347}{\sqrt{35}} = 58.6537

Group 2: Sample of 35, mean of 1439, standard deviation of 298.

This means that:

\mu_2 = 1439, s_2 = \frac{298}{\sqrt{35}} = 50.3712

Test if there is a difference in productivity level.

At the null hypothesis, we test that there is no difference, that is, the subtraction is 0. So

H_0: \mu_1 - \mu_2 = 0

At the alternate hypothesis, we test that there is difference, that is, the subtraction is different of 0. So

H_1: \mu_1 - \mu_2 \neq 0

The test statistic is:

z = \frac{X - \mu}{s}

In which X is the sample mean, \mu is the value tested at the null hypothesis and s is the standard error.

0 is tested at the null hypothesis:

This means that \mu = 0

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X = \mu_1 - \mu_2 = 1276 - 1439 = -163

s = \sqrt{s_1^2+s_2^2} = \sqrt{58.6537^2+50.3712^2} = 77.3144

Test statistic:

z = \frac{X - \mu}{s}

z = \frac{-163 - 0}{77.3144}

z = -2.11

The test statistic is z = -2.11.

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