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Degger [83]
2 years ago
6

Solve 2x - 16 ≥ 32 - 6x.

Mathematics
1 answer:
sergij07 [2.7K]2 years ago
8 0

Hello!

\mathcal{SOLUTION:}

  • Move all the x's to the left, using the opposite operation:
  • 2x+6x-16≥32
  • Now, move all the numbers to the right, using the opposite operation:
  • 2x+6x≥32+16
  • Combine Like Terms:
  • 8x≥48
  • Divide both sides by 8:
  • x≥6

Final Answer:

x≥6

I hope it helps.

Good luck & enjoy your day!

-SnowFlake

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3 years ago
Suppose a consumer product researcher wanted to find out whether a highlighter lasted less than the manufacturer's claim that th
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Answer:

The null hypothesis is H_0: \mu = 14

The alternate hypothesis is H_a: \mu < 14

The test statistic is t = -1.95.

The p-value is of 0.0292. This means that for a level of significance of 0.0292 and higher, there is sufficient evidence to conclude that the  highlighters wrote for less than 14 continuous hours.

Step-by-step explanation:

Suppose a consumer product researcher wanted to find out whether a highlighter lasted less than the manufacturer's claim that their highlighters could write continuously for 14 hours.

At the null hypothesis, we test if the mean is 14 hours, that is:

H_0: \mu = 14

At the alternate hypothesis, we test if the mean is less than 14 hours, that is:

H_a: \mu < 14

The test statistic is:

t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}

In which X is the sample mean, \mu is the value tested at the null hypothesis, s is the standard deviation of the sample and n is the size of the sample.

14 is tested at the null hypothesis:

This means that \mu = 14

X = 13.6 hours, s = 1.3 hours. Sample of 40:

In addition to the values of X and s given, we have that n = 40

Test statistic:

t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}

t = \frac{13.6 - 14}{\frac{1.3}{\sqrt{40}}}

t = -1.95

The test statistic is t = -1.95.

P-value:

The p-value of the test is the probability of finding a sample mean lower than 13.6, which is a left tailed test, with t = -1.95 and 40 - 1 = 39 degrees of freedom.

Using a calculator, the p-value is of 0.0292. This means that for a level of significance of 0.0292 and higher, there is sufficient evidence to conclude that the  highlighters wrote for less than 14 continuous hours.

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Step-by-step explanation:

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Step-by-step explanation:

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Step-by-step explanation:

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