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3 years ago

Complete the third step to solve the equation.

Mathematics

2 answers:

blondinia [14]3 years ago

8 0

Answer:

Step-by-step explanation:

I got <u>100%</u> on this assignment.

Flauer [41]3 years ago

7 0

Answer:

$x = \frac{1}{8}$

Step-by-step explanation:

You need to get the X by itself and the only way to do that is to get rid of the 8. Since the X is being multiplied by the 8 you need to do the opposite and divide to get rid of it. Since you divide one side by 8 you must do it to the other, leaving the answer as 1/8

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A student carried out an experiment to determine the amount of vitamin C in a tablet sample. He performed 5 trials to produce th

ivolga24 [154]

Answer:

There is not enough evidence to support the claim that the amount of vitamin C in a tablet sample is different from 500 mg.

P-value = 0.166.

Step-by-step explanation:

We start by calculating the mean and standard deviation of the sample:

$M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{5}(490+502+505+495+492)\\\\\\M=\dfrac{2484}{5}\\\\\\M=496.8\\\\\\s=\sqrt{\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{4}((490-496.8)^2+(502-496.8)^2+(505-496.8)^2+(495-496.8)^2+(492-496.8)^2)}\\\\\\s=\sqrt{\dfrac{166.8}{4}}\\\\\\s=\sqrt{41.7}=6.5\\\\\\$

Then, we can perform the hypothesis t-test for the mean.

The claim is that the amount of vitamin C in a tablet sample is different from 500 mg.

Then, the null and alternative hypothesis are:

$H_0: \mu=500\\\\H_a:\mu< 500$

The significance level is 0.05.

The sample has a size n=5.

The sample mean is M=496.8.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=6.5.

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

$s_M=\dfrac{s}{\sqrt{n}}=\dfrac{6.5}{\sqrt{5}}=2.907$

Then, we can calculate the t-statistic as:

$t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{496.8-500}{2.907}=\dfrac{-3.2}{2.907}=-1.1$

The degrees of freedom for this sample size are:

$df=n-1=5-1=4$

This test is a left-tailed test, with 4 degrees of freedom and t=-1.1, so the P-value for this test is calculated as (using a t-table):

$\text{P-value}=P(t$

As the P-value (0.166) is bigger than the significance level (0.05), the effect is not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the amount of vitamin C in a tablet sample is different from 500 mg.

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2 years ago

Lisa purchases a professional racing bicycle that sells for $3,000, including tax. It requires an 18.5% down payment. How much i

matrenka [14]

Answer: 3,0080

Step-by-step explanation:

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3 years ago

The manager of a department store uses the given function to model the monthly opening inventory of down comforters at the store

tangare [24]

Answer: $d(x)=-750x^2-3750x-10500$

Step-by-step explanation:

Given: The manager of a department store uses the given function to model the monthly opening inventory of down comforters at the store, in dollars, where x represents the number of months from September.

$d(x)=-750(x^2-5x-14)$

To rewrite this hat reveals the store's opening inventory of down comforters in the month of September, multiply -750 on the bracket, we get

$d(x)=-750x^2-3750x-10500$

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2 years ago

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The graph of the function f(x) = -(x+3)(x - 1) is shown below. What is true about the domain and range of the function? у The do

Nataly_w [17]

Answer:

The domain will be all real numbers, range will be all real numbers below -3

Step-by-step explanation:

its quadratic so it goes forever left and right. but the vertex has a y value of -3. It is a negative sloped graph, so anything below that is in the range

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3 years ago

Jocelyn needs to place a 7 meter ladder against a house so that the base of the ladder is 6.5 meters from the building. I want a

GrogVix [38]

Answer:

21.787°

Step-by-step explanation:

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