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4 years ago

M is between L and N. LM= 7x -1 MN = 2x 4, and LN =12. Find the value of x an determine if M is a bisector

Mathematics

1 answer:

Mademuasel [1]4 years ago

7 0

12/2 = 6, so;
7x-1 = 6
7x = 7
x = 1
Because both sides are equal, you do the same for 2x+4
2x+4 = 6
2x = 2
x = 1

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for the data values below construct a 95 confidence interval if the sample mean is known to be 12898 and the standard deviation

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A 95% confidence interval for the population mean is [3315.13, 22480.87] .

Step-by-step explanation:

We are given that for quality control purposes, we collect a sample of 200 items and find 24 defective items.

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P.Q. = $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

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Here for constructing a 95% confidence interval we have used a One-sample t-test statistics as we don't know about population standard deviation.

So, 95% confidence interval for the population mean, $\mu$ is ;

P(-2.776 < $t_4$ < 2.776) = 0.95 {As the critical value of t at 4 degrees of

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P(-2.776 < $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ < 2.776) = 0.95

P( $-2.776 \times {\frac{s}{\sqrt{n} } }$ < ${\bar X-\mu}$ < $2.776 \times {\frac{s}{\sqrt{n} } }$ ) = 0.95

P( $\bar X-2.776 \times {\frac{s}{\sqrt{n} } }$ < $\mu$ < $\bar X+2.776 \times {\frac{s}{\sqrt{n} } }$ ) = 0.95

95% confidence interval for $\mu$ = [ $\bar X-2.776 \times {\frac{s}{\sqrt{n} } }$ , $\bar X+2.776 \times {\frac{s}{\sqrt{n} } }$ ]

= [ $12,898-2.776 \times {\frac{7,719}{\sqrt{5} } }$ , $12,898+2.776 \times {\frac{7,719}{\sqrt{5} } }$ ]

= [3315.13, 22480.87]

Therefore, a 95% confidence interval for the population mean is [3315.13, 22480.87] .

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