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Naya [18.7K]
3 years ago
10

Solve the equation. | 2z - 3| = 4z - 1

Mathematics
1 answer:
svet-max [94.6K]3 years ago
6 0
Keeping in mind that, an absolute value expression is in effect a piece-wise, then

\bf |2z-3|=4z-1\implies 
\begin{cases}
+(2z-3)=4z-1\\
\qquad 2z-3=4z-1\\
\qquad -2=2z\\
\qquad \frac{-2}{2}=z\\
\qquad -1=z\\
----------\\
-(2z-3)=4z-1\\
\qquad -2z+3=4z-1\\
\qquad 4=6z\\
\qquad \frac{4}{6}=z\\\\
\qquad \frac{2}{3}=z
\end{cases}
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Answer:

Yes you are correct.

Step-by-step explanation:

The best way to check theese types of questions is go back in plug in X with your answer so 88+97+80+90(which is x)=360 then divide by 4 and get 90! So yes you are correct good job!

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3 years ago
872.4 mm equals how many cm?
blagie [28]
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7 0
3 years ago
Read 2 more answers
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alina1380 [7]

Using the t-distribution, it is found that the correct option is:

0.005 < P-value < 0.01, reject the null hypothesis.

<h3>What are the hypothesis tested?</h3>

At the null hypothesis, it is tested if the mean of a given population is equal to 85, that is:

H_0: \mu = 85

We have a left-tailed test, hence, at the alternative hypothesis, it is tested if the mean of the population is less than 85, that is:

H_1: \mu < 85

<h3>What is the decision?</h3>

The test statistic is of t = -3.018.

Using a t-distribution calculator, with test statistic t = -3.018, 13 - 1 = 12 df and a significance level of 0.01, it is found that the p-value for a left-tailed test is of 0.0051.

The p-value is <u>less than 0.01</u>, hence the null hypothesis is rejected and the correct option is:

0.005 < P-value < 0.01, reject the null hypothesis.

More can be learned about the t-distribution at brainly.com/question/16313918

5 0
2 years ago
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Step-by-step explanation:

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