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3 years ago

Describe the rule for multiplying powers with the same base and give an example please

1 answer:

6 0

When multiplying powers with the same base you write the result as a base raised to the power that is the sum of previous two powers:

$a^m\cdot a^n=a^{m+n}.$

For example,

$2^5\cdot 2^7=2^{5+7}=2^{12};$

$3^5\cdot 3^4=3^{5+4}=3^9.$

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Factor the polynomial

Art [367]

Find the GCF (Greatest Common Factor)

GCF = 2x

Factor out the GCF (Write the GCF first and then, in parentheses, divide each term by the GCF.)

2x (2x^3/2x + 4x^2/2x + 6x/2x)

Simplify each term in parentheses

-2x(x^2 + 2x + 3)

<u>Answer D. -2(x^2 + 2x + 3)</u>

7 0

3 years ago

The sum of the ages of Mr Lin and his son Ethan is 38 years. In three years' time, Mr Lin will be three times as old as his son.

Sati [7]

Answer:

Mr.Lin's present age is 30 years now. His son is 8 years old now.

Step-by-step explanation:

Let L = Mr.Lin's present age,

S = his son's present age.

First equation is

L + S = 38. (1)

The second equation is

L + 3 = 3*(S+3) (2) ("In three years' time, Mr.Lin will be three times as old as his son.")

From (1), express S = 38-L and substitute it into (2). You will get

L + 3 = 3*((38-L)+3), or

L + 3 = 114 - 3L + 9,

4L = 114 + 9 - 3,

4L = 120,

L = 30.

8 0

3 years ago

Which substances dissolve in water? Check all of

Arturiano [62]

Answer:

polar liquids and polar solids

Step-by-step explanation:

6 0

4 years ago

Read 2 more answers

If y = kx, and x = 3 and y = 15, calculate k.

kenny6666 [7]

Answer:

k = 5

Step-by-step explanation:

Since the equation is y = kx and x equals 3 while y equals 15, in order to solve this equation we are going to have to substitute the variables with their answers:

x = 3

y = 15

15 = 3k

Now we divide 3 from both 3x and 15 to segregate the variable x:

15/3 = 3k/3

5 = k

Now to check our work we are going to substitute 5 for the variable k, 3 for the variable x and 15 for the variable y.

y = kx

15= (5)(3)

15 = 15

Tada, I hope this helps you!

6 0

3 years ago

Read 2 more answers

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

valina [46]

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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4 0

2 years ago