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valina [46]
3 years ago
13

What is the simplest form of 4 square root 81x^8y^5?

Mathematics
1 answer:
olasank [31]3 years ago
5 0
Firstly,
thanks for posting this.

81 = 9x9 or 9 squared so at this stage I'm guessing the last two. 
x^ 8 = (x^ 4) x (x^ 2) (its called the multiplication rule of indices). 
Okay I have approx 14 mins to answer.
No panic
√ 81.x^8 x <span>√ y^5
</span>√ (9x^2 x 9x^6) x <span>√ y^5
</span>= 9x x <span>√ 9x^6 x  </span><span>√ y^5
</span>did I just gain time?
√ 9x^6 = <span>√ </span>3x ^3 x <span>√ 3x ^ 3
</span>or 2 . √ 3x^3. <span>√ y^5
</span>more time
okay, so that wasnt successful. 
√ 9x^6 =<span>√ </span> (3x^2) x <span>√ </span>(3x^4)




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A laptop producing company also produces laptop batteries, and claims that the batteries
gregori [183]

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There is enough evidence to support the claim that the batteries power the laptops for significantly less than 4 hours. (P-value = 0).

The null and alternative hypothesis are:

H_0: \mu=4\\\\H_a:\mu< 4

Step-by-step explanation:

<em>The question is incomplete: To test this claim a sample or population standard deviation is needed.</em>

<em>We will estimate that the sample standard deviation is 2 hours, and use a t-test to test that claim.</em>

<em> NOTE (after solving): The difference between the sample mean and the mean of the null hypothesis is big enough to reject the null hypothesis, even when we have a sample standard deviation of 3.5 hours, which can be considered bigger than the maximum standard deviation for the sample.</em>

This is a hypothesis test for the population mean.

The claim is that the batteries power the laptops for significantly less than 4 hours.

Then, the null and alternative hypothesis are:

H_0: \mu=4\\\\H_a:\mu< 4

The significance level is 0.05.

The sample has a size n=500.

The sample mean is M=3.5.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=2.

The estimated standard error of the mean is computed using the formula:

s_M=\dfrac{s}{\sqrt{n}}=\dfrac{2}{\sqrt{500}}=0.0894

Then, we can calculate the t-statistic as:

t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{3.5-4}{0.0894}=\dfrac{-0.5}{0.0894}=-5.5902

The degrees of freedom for this sample size are:

df=n-1=500-1=499

This test is a left-tailed test, with 499 degrees of freedom and t=-5.5902, so the P-value for this test is calculated as (using a t-table):

P-value=P(t

As the P-value (0) is smaller than the significance level (0.05), the effect is  significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the batteries power the laptops for significantly less than 4 hours.

5 0
3 years ago
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