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cupoosta [38]
3 years ago
7

LM is a perpendicular bisector of NP The length of LN is 12w +7, and the length of LP is 15w 5. What is the length of LN?

Mathematics
1 answer:
Mazyrski [523]3 years ago
8 0

Answer:

LN = 55

Step-by-step explanation:

Given

LN = 12w + 7

LP = 15w - 5

Required

Determine LN

Since LM is a bisector, then we have:

LP = LN (See attachment for illustration)

15w - 5 = 12w + 7

Collect Like Terms

15w - 12w = 5 +7

3w = 12

Solve for w

w = 12/3

w = 4

LN is calculated as thus:

LN = 12w + 7

Substitute 4 for w

LN = 12 * 4 + 7

LN = 48 + 7

LN = 55

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Step-by-step explanation:

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In a large midwestern university (the class of entering freshmen is 6000 or more students), an SRS of 100 entering freshmen in 1
Serga [27]

Answer:

The p-value of the test is 0.0228, which is less than the standard significance level of 0.05, which means that there is evidence that the proportion of freshmen who graduated in the bottom third of their high school class in 2001 has been reduced.

Step-by-step explanation:

Before solving this question, we need to understand the central limit theorem and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

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p_1 = \frac{20}{100} = 0.2

s_1 = \sqrt{\frac{0.2*0.8}{100}} = 0.04

2001:

10 out of 100 in the bottom third, so:

p_2 = \frac{10}{100} = 0.1

s_2 = \sqrt{\frac{0.1*0.9}{100}} = 0.03

Test if proportion of freshmen who graduated in the bottom third of their high school class in 2001 has been reduced.

At the null hypothesis, we test if the proportion is still the same, that is, the subtraction of the proportions in 1999 and 2001 is 0, so:

H_0: p_1 - p_2 = 0

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The test statistic is:

z = \frac{X - \mu}{s}

In which X is the sample mean, \mu is the value tested at the null hypothesis, and s is the standard error.

0 is tested at the null hypothesis:

This means that \mu = 0

From the two samples:

X = p_1 - p_2 = 0.2 - 0.1 = 0.1

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z = \frac{X - \mu}{s}

z = \frac{0.1 - 0}{0.05}

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