Direct Variation: If y = 22, when x=-11, find x when y = 88.

A laptop producing company also produces laptop batteries, and claims that the batteries

gregori [183]

Answer:

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:

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

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

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.

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

Plssss help in need of answers soon

vfiekz [6]

My guess is that you're doing the Law of Cosines? You have everything you need for that except the angle theta, which is the thing you need to find. It's set up like this: (8)^2 = (10)^2 + (5)^2 -[2(10)(5)cos A] I used A instead of theta. Doing that math, you have: 64 = 100 + 25 -[ 100 cos A]; 64 = 125 - 100 cos A;
-61 = - 100 cos A; -61 / -100 = cos A; .61 = cos A. Now use your inverse function on your calculator to find cos^-1(.61) and that equals 52.4

5 0

3 years ago

Read 2 more answers

20 is what present of 30?

tia_tia [17]

66.6667

20=x/100•30
Solve this equation and you will get your answer (66.6667)

6 0

3 years ago

The weight of 1000 identical samples of a substance is 1 pound. What is the weight of 100 samples?

alex41 [277]

The answer is 0.1 lbs. Or 1/10 lbs.

Hope this helps!

8 0

3 years ago

Read 2 more answers

In London today, four times the high temperature was more than twice the high temperature plus

4vir4ik [10]

Answer:

Let's define the high temperature as T.

We know that:

"four times T, was more than 2*T plus 66°C"

(i assume that the temperature is in °C)

We can write this inequality as:

4*T > 2*T + 66°C

Now we just need to solve this for T.

subtracting 2*T in both sides, we get:

4*T - 2*T > 2*T + 66°C - 2*T

2*T > 66°C

Now we can divide both sides by 2:

2*T/2 > 66°C/2

T > 33°C

So T was larger than 33°C

Notice that T = 33°C is not a solution of the inequality, then we should use the symbol ( for the set notation.

Then the range of possible temperatures is:

(33°C, ...)

Where we do not have an upper limit, so we could write this as:

(33°C, ∞°C)

(ignoring the fact that ∞°C is something impossible because it means infinite energy, but for the given problem it works)

4 0

3 years ago