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ANEK [815]
3 years ago
12

|c- 24| = 7c :D :D :D

Mathematics
2 answers:
nignag [31]3 years ago
8 0

Start by making this absolute value equation into two equations; one positive and one negative equation. The two equations will be: c - 24 = 7c and c - 24 = -7c.

Start by solving the positive equation first: c - 24 = 7c. Add 24 to both sides and subtract 7c from both sides of the equation.

-6c = 24, now divide both sides by -6 to find your first c value.

c = -4

Solve the negative equation next: c - 24 = -7c. Add 24 to both sides and add 7c to both sides of the equation.

8c = 24, divide both sides by 8 to isolate c and find your second c value.

c = 3

Substitute to see if these values actually work with the given absolute value equation. Substitute -4 for c.

|c - 24| = 7c ==> |(-4) - 24| = 7(-4)

Solving this equation gives us 28 = -28, and this is a false statement so -4 cannot be part of the solutions. Now check 3 by substituting it for c.

|c - 24| = 7c ==> |(3) - 24| = 7(3)

Solving this equation we get 21 = 21, and this is a true statement so our only possible solution is c = 3.

Ivanshal [37]3 years ago
3 0

c\geq0\\\\\\ |c- 24| = 7c\\\\c-24=7c \vee c-24=-7c\\\\6c=-24 \vee -8c=-24\\\\c=-4 \vee c=3\\\\-4\not \geq0\\\\\boxed{c=3}

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Using the z-distribution, since the p-value of the test is of 0.057 > 0.05, there is not enough evidence that the population proportion of successes does not equal 0.50.

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

At the null hypotheses, we test if the proportion of successes equals 0.5, hence:

H_0: p = 0.5

At the alternative hypotheses, we test if it does not equal, hence:

H_1: p \neq 0.5

<h3>What is the test statistic?</h3>

The test statistic is given by:

z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}

In which:

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For this problem, the parameters are given by:

n = 40, \overline{p} = \frac{14}{40} = 0.35, p = 0.5

Hence the test statistic is given by:

z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}

z = (0.35 - 0.5)/(0.5/sqrt(40))

z = -1.9.

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

Using a z-distribution calculator, considering a two-tailed test, as we are testing if the proportion is different of a value, with z = -1.9, we get that the p-value of the test is of 0.057.

Since the p-value of the test is of 0.057 > 0.05, there is not enough evidence that the population proportion of successes does not equal 0.50.

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

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