If 2x^3=y, then log y equals

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

At what point is the function y=(x+3)/(x^(2)-7x+12) continuous

nika2105 [10]

If a function is defined as

$h(x)=\dfrac{f(x)}{g(x)}$

where both $f(x),g(x)$ are continuous functions, then $h(x)$ is also continuous where defined, i.e. where $g(x)\neq0$

So, in your case, this function is continous everywhere, except where

$x^2-7x+12=0$

To solve this equation, we can use the formula $x^2-sx+p=0$

It means that, if the leading terms is 1, then the x coefficient is the opposite of the sum of the roots, and the constant term is the product of the roots.

So, we're looking for two terms whose sum is 7, and whose product is 12. These numbers are easily found to be 3 and 4.

So, this function is continuous for every real number different than 3 or 4.

3 0

2 years ago

What is the equaiton of the line that goes through the point (6,-1) and is parallel to the line represented by the equautions y=

mixas84 [53]

parallel lines have the same slope

The slope-intercept form of a linear equatio is y=mx+b, where m stands for the "slope of the line" and b stands for the "y-intercept of the line"

They give you the equation y= -5/6x+3 Notice this is already on the slope-intercept form, so in this case the slope is -5/6 and the y-intercept is 3

You want an equation of the line that is parallel to the given line. The slopes must be the same, so m=-5/6

So far we have y=-5/6x + b

We don't have b yet but that can be found using the given point (6,-1) which tells you that "x is 6 when y is -1"

Replace that on the equation y=-5/6x + b and you get

-1 = (-5/6)(6) + b

-1 = -5 +b

4 = b

b = 4

We found b, or the y-intercept

Go back to the equation y = -5/6 x + b and replace this b with the b we just found

y = -5/6x + 4

6 0

2 years ago

Jordan is mixing water and flour to make tortillas. The number cups of water, w needed for f cups of flour is described by the e

Tresset [83]

Answer:

$1\frac{1}{3}$ cups of flour.

Step-by-step explanation:

Given that:

$w$ is the number of cups of water to be mixed with flour for making tortillas.

$f$ is the number of cups of flour to be mixed with water for making tortillas.

Relation between $w$ and $f$ is given by the equation:

$w=0.75f$

To find:

Number of cups of flour to be added if number of cups of water to be used is 1.

Solution:

We are given an equation with two variables.

Value of one variable is given and we have to find the value of other variable.

$1=0.75f\\\Rightarrow f = \dfrac{1}{0.75}\\\Rightarrow f = 1.33$

Number of cups of flour to be added = $1\frac{1}{3}$

6 0

2 years ago

PLEASE HELP PEOPLE!!!!!

Pavel [41]

4 rectangles are 6 x 4

4 triangles are 4x 4

1 square is 6x 6

Area :

6 x 4 = 24 x 4 = 96

1/2 x 4 x 4 = 8 x 4 = 32

6 x 6 = 36

96 + 32 + 36 = 164 square inches.

The answer is A

7 0

3 years ago