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2 years ago

45°

Mathematics

1 answer:

ioda2 years ago

7 0

Answer:

$x = \sqrt{\frac{7}{2} }$

Step-by-step explanation:

Explanation

From given graph

AC = √7

Given angle ∝ = 45°

$cos\alpha = \frac{adjacentside}{Opposite side}$

$cos45 = \frac{x}{\sqrt{7} }$

$\frac{1}{\sqrt{2} } = \frac{x}{\sqrt{7} }$

$x = \frac{\sqrt{7} }{\sqrt{2} }$

$x = \sqrt{\frac{7}{2} }$

x = 1.8708

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Assume that the random variable X is normally distributed with mean u = 45 and standard deviation o = 14.

larisa86 [58]

Answer:

P(57 < X < 69) = 0.1513

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 45, \sigma = 14$

Find P(57 < X < 69):

This is the pvalue of Z when X = 69 subtracted by the pvalue of Z when X = 57. So

X = 69

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{69 - 45}{14}$

$Z = 1.71$

$Z = 1.71$ has a pvalue of 0.9564

X = 57

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{57 - 45}{14}$

$Z = 0.86$

$Z = 0.86$ has a pvalue of 0.8051

0.9564 - 0.8051 = 0.1513

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3 years ago

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jek_recluse [69]

Answer:

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Step-by-step explanation:

PART A

slope of the line passing through AC : (6-1)/(1-2) = 5/-1 = -5

equation of the line passing through B and perpendicular to AC:

y-3 = 1/5(x-3)

y-3 = 1/5x -3/5

y = 1/5 x - 3/5 + 3

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Interception of the lines

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y = -5x + 11

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BD = $\sqrt{(3-1.65)^2 + (3-2.73)^2}$ = 1,376735

PART D

AREA = (5,09902 * 1.376735)/2 = 3,509999

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