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Minchanka [31]
2 years ago
15

If you know how to do it, please help me out :)

Mathematics
1 answer:
Artemon [7]2 years ago
8 0

Answer:

Answer in explanation.

Step-by-step explanation:

Lets take

y =  \frac{3}{4} x - 5

as L1.

Take L2 the line perpendicular to L1.

Standard form of equation of line:

y=mx+c, where m = slope and c = y-intercept.

Since L1 and L2 are perpendicular,

mL1 x mL2 = -1

Substitute mL1 into the equation,

3/4 x mL2 = -1

mL2 = -1 ÷ 3/4

mL2 = -4/3

L2 : y = mx+ c

Substitute y = 6, x = 8 and m = -4/3 into the equation,

6 =  -  \frac{4}{3} (8) + c \\ 6 = -  \frac{32}{3}  + c \\ c = 6 +  \frac{32}{3}  \\  = 16 \frac{2}{3}

therefore L2:

y =  -  \frac{4}{3}x   + 16 \frac{2}{3}

Lets take L3 as the line parallel to L1.

Since L3 and L1 are parallel,

mL3 = mL1 = 3/4

equation of line: y = mx+c

substitute y = 6, x = 8 and m = 3/4 into equation.

6 = ( \frac{3}{4} )(8) + c \\ 6 = 6 + c \\ c = 6 - 6 \\  = 0

therefore L3:

y =  \frac{3}{4} x

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Assume that the empirical rule is a good model for the time it takes for all passengers to board an airplane. The mean time is 4
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Answer:

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Step-by-step explanation:

Problems of normally distributed samples can be 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.

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\mu = 48, \sigma = 4.

Which interval describes how long it takes for passengers to board the middle 95% of the time?

This is between the 2.5th percentile and the 97.5th percentile.

So this interval is the value of X when Z has a a pvalue of 0.025 and the value of X when Z has a pvalue of 0.975

Lower Limit

Z has a pvalue of 0.025 when Z = -1.96. So

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

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Upper Limit

Z has a pvalue of 0.975 when Z = 1.96. So

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

1.96 = \frac{X - 48}{4}

X - 48 = 1.96*4

X = 55.84

The interval that describes how long it takes for passengers to board the middle 95% of the time is between 40.16 minutes and 55.84 minutes.

7 0
3 years ago
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