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Dennis_Churaev [7]
2 years ago
10

Given m||n, find the value of x.

Mathematics
2 answers:
vladimir1956 [14]2 years ago
6 0

Answer:

x=23

Step-by-step explanation:

5x+16=6x-7

Solve.

-x=-23

x=23

Nonamiya [84]2 years ago
3 0

Answer:

x = 23

Step-by-step explanation:

5x + 16 = 6x - 7

They are congruent, because m and n are parallel, as stated, "m||n"

5x + 16 - 16 = 6x - 7 - 16

5x = 6x - 23

23 = 6x - 5x

23 = x

x = 23

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Morgarella [4.7K]

Answer:

(a) We reject our null hypothesis.

(b) We fail to reject our null hypothesis.

(c) We fail to reject our null hypothesis.

Step-by-step explanation:

We are given that a certain pen has been designed so that true average writing lifetime under controlled conditions (involving the use of a writing machine) is at least 10 hr.

A random sample of 18 pens is selected.

<u><em>Let </em></u>\mu<u><em> = true average writing lifetime under controlled conditions</em></u>

So, Null Hypothesis, H_0 : \mu \geq 10 hr   {means that the true average writing lifetime under controlled conditions is at least 10 hr}

Alternate Hypothesis, H_A : \mu < 10 hr    {means that the true average writing lifetime under controlled conditions is less than 10 hr}

<u>The test statistics that is used here is one-sample t test statistics;</u>

                           T.S. = \frac{\bar X -\mu}{\frac{s}{\sqrt{n} } }  ~ t_n_-_1

where, \bar X = sample mean

             s = sample standard deviation

             n = sample size of pens = 18

          n - 1 = degree of freedom = 18 -1 = 17

<u>Now, the decision rule based on the critical value of t is given by;</u>

  • If the value of test statistics is more than the critical value of t at 17 degree of freedom for left-tailed test, then <u>we will not reject our null hypothesis</u> as it will not fall in the rejection region.
  • If the value of test statistics is less than the critical value of t at 17 degree of freedom for left-tailed test, then <u>we will reject our null hypothesis</u> as it will fall in the rejection region.

(a) Here, test statistics, t = -2.4 and level of significance is 0.05.

<em>Now, at 0.05 significance level, the t table gives critical value of -1.74 at 17 degree of freedom.</em>

Here, clearly the value of test statistics is less than the critical value of t as -2.4 < -1.74, so we reject our null hypothesis.

(b) Here, test statistics, t = -1.83 and level of significance is 0.01.

<em>Now, at 0.051 significance level, the t table gives critical value of -2.567 at 17 degree of freedom.</em>

Here, clearly the value of test statistics is more than the critical value of t as -2.567 < -1.83, so we fail to reject our null hypothesis.

(c) Here, test statistics, t = 0.57 and level of significance is not given so we assume it to be 0.05.

<em>Now, at 0.05 significance level, the t table gives critical value of -1.74 at 17 degree of freedom.</em>

Here, clearly the value of test statistics is more than the critical value of t as  -1.74 < 0.57, so we fail to reject our null hypothesis.

8 0
3 years ago
Stan had 15 apples and gave 10 to his sister. If he had 21 apples and wanted to give the same percentage to his sister, how many
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10 x

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The sum of three consecutive even integers is 126. Let x represent the first integer, x + 2 represent the second integer, and x
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We have that (x) + (x+2) + (x+4) = 126 so 3x + 6 = 126 can be used to find the first integer.

3x + 6 = 126
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Answer:

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Step-by-step explanation:

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Answer:

Step-by-step explanation:

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