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3 years ago

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Find the exact solution to the equation. (2 points) five to the power of quantity nine minus three x equals one hundred and twen

ty five.

1 answer:

Anna35 [415]3 years ago

8 0

Answer:

x = 2

Step-by-step explanation:

Five to the power of quantity nine minus three x equals one hundred and twenty five.

----------------------

5^(9 - 3x) = 125
5^(9 - 3x) = 5^3
9 - 3x = 3
3x = 9 - 3
3x = 6
x = 6/3
x = 2

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Answer:

468 ways

Step-by-step explanation:

Given: A catering service offers 5 appetizers, 4 main courses, and 8 desserts

To find: number of ways a customer is to select 4 appetizers, 2 main courses,and 3 desserts.

Solution:

A permutation is an arrangement of elements such that order of elements matters and repetition is not allowed.

Number of appetizers = 5

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Number of ways of choosing k terms from n terms = $nPk=\frac{n!}{(n-k)!}$

Number of ways a customer is to select 4 appetizers, 2 main courses,and 3 desserts = $5P4+4P2+8P3$

$=\frac{5!}{(5-4)!}+\frac{4!}{(4-2)!}+\frac{81}{(8-3)!}\\=5!+\frac{4!}{2!}+\frac{8!}{5!}\\=5!+(4\times 3)+(8\times 7\times 6)\\=120+12+336\\=468$

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A truck is rented at $40 per day plus a charge per mile of use. The truck traveled 15 miles in one day, and the total was $115.

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Nationally, patients who go to the emergency room wait an average of 7 hours to be admitted into the hospital. Do patients at ru

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For this study, we should use t-test and the null and alternative hypotheses would be given by H₀: μ = 7 and H₁: μ < 7.
The test statistic is -1.941 and the p-value (0.0381) is <u>greater than</u> α = 0.01.
Based on this, we should <u>fail to reject</u> the null hypothesis.
Thus, the final conclusion is that the data suggest the population mean is not significantly lower than 7 at α = 0.01, so there is statistically insignificant evidence to conclude that the population mean waiting time to be admitted into the hospital from the emergency room for patients at rural hospitals is equal to 7 hours.

<h3>What is a null hypothesis?</h3>

A null hypothesis (H₀) can be defined the opposite of an alternate hypothesis (H₁) and it asserts that two (2) possibilities are the same.

<h3>How to calculate value of the test statistic?</h3>

The test statistics can be calculated by using this formula:

$t=\frac{x\;-\;u}{\frac{\delta}{\sqrt{n} } }$

<u>Where:</u>

x is the sample mean.

u is the mean.

is the standard deviation.

n is the number of hours.

For this study, we should use t-test and the null and alternative hypotheses would be given by:

H₀: μ = 7

H₁: μ < 7

$t=\frac{6.3\;-\;7}{\frac{1.3}{\sqrt{13} } }\\\\t=\frac{-0.7}{\frac{1.3}{3.6056 } }$

t = -0.7/0.3606

t = -1.941.

For the p-value, we have:

P-value = P(t < -1.9412)

P-value = 0.0381.

Therefore, the p-value (0.0381) is <u>greater than</u> α = 0.01. Based on this, we should <u>fail to reject</u> the null hypothesis.

Thus, the final conclusion is that the data suggest the population mean is not significantly lower than 7 at α = 0.01, so there is statistically insignificant evidence to conclude that the population mean waiting time to be admitted into the hospital from the emergency room for patients at rural hospitals is equal to 7 hours.

Read more on null hypothesis here: brainly.com/question/14913351

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