$y=8x+5\\\\\\\text{Swap the x's and y's. Then solve for y:}\\x=8y+5\\\\\\\text{Subtract 5 from both sides:}\\x-5=8y\\\\\\\text{Divide both sides by 8:}\\\dfrac{x-5}{8}=y$

3 0

2 years ago

What is the first step in solving ln(x − 1) = ln6 − lnx for x?

Marizza181 [45]

First step would be using this logarithm rule $\ln\left(\dfrac ab\right) = \ln(a) - \ln(b)$ on right side.

Hope this helps.

6 0

3 years ago

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An electronics company just finished designing a new tablet computer and is interested in estimating its battery-life. A random

Alika [10]

Answer:

$6 \pm 2.861(0.3354)$

Step-by-step explanation:

We have the standard deviation for the sample, so we use the t-distribution to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 20 - 1 = 19

99% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 19 degrees of freedom(y-axis) and a confidence level of $1 - \frac{1 - 0.99}{2} = 0.995$ . So we have T = 2.861.

The margin of error is:

$M = T\frac{s}{\sqrt{n}} = 2.861\frac{1.5}{\sqrt{20}} = 2.861(0.3354)$

In which s is the standard deviation of the sample and n is the size of the sample.

The format of the confidence interval is:

$S_{M} \pm M$

In which $S_{M}$ is the sample mean

$6 \pm 2.861(0.3354)$

7 0

2 years ago