MATHEMATICS COLLEGE

Prove that the diagonals of a rectangle bisect each other.Plan: Since midpoints will be involved, use multiples of __ to name the coordinates for B, C, and D.

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Answer 1

Answer:

Answer:

Step-by-step explanation:

example A(2a,0),B(2b,0)

C(2b,2c),D(2a,2c)

mid point of AC=((2a+2b)/2,(0+2c)/2)=(a+b,c)

mid point of BD=((2b+2a)/2,(0+2c)/2)=(a+b,c)

∴midpoint of diagonals same or diagonals bisect each other.

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What are the coordinates of the point on the directed line segment from (-6, -3) to(5,8) that partitions the segment into a ratio of 6 to 5?

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Given:

A point divides a directed line segment from (-6, -3) to (5,8) into a ratio of 6 to 5.

To find:

The coordinates of that point.

Solution:

Section formula: If point divides a line segment in m:n, then the coordinates of that point are

$Point=\left((mx_2+nx_1)/(m+n),(my_2+ny_1)/(m+n)\right)$

A point divides a directed line segment from (-6, -3) to (5,8) into a ratio of 6 to 5. Using section formula, we get

$Point=\left((6(5)+5(-6))/(6+5),(6(8)+5(-3))/(6+5)\right)$

$Point=\left((30-30)/(11),(48-15)/(11)\right)$

$Point=\left((0)/(11),(33)/(11)\right)$

$Point=\left(0,3\right)$

Therefore, the coordinates of the required point are (0,3).

(a) For a normal distribution, find the z-score that cuts off the bottom 55.76% of all the z-scores. Round to 2 decimal places after the decimal point. answer: (b) For a normal distribution, find the z-score that cuts off the top 77.52% of area. Round to 2 decimal places after the decimal point. answer:

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Answer:

a) Z = 0.15

b) Z = -0.76

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:

$Z = (X - \mu)/(\sigma)$

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.

(a) For a normal distribution, find the z-score that cuts off the bottom 55.76% of all the z-scores.

Bottom 55.76% of the scores are the z-scores with a pvalue of 0.5576 and less. So the z-score that cuts off these scores is Z when X has a pvalue of 0.5576, which is Z = 0.145, rounded to two decimal places, Z = 0.15.

(b) For a normal distribution, find the z-score that cuts off the top 77.52% of area.

The top 77.52% of the scores are the z-scores with a pvalue of 1-0.7752 = 0.2248 and higher. So Z = -0.764 and higher. So the value that cuts off the top 77.52% is Z = -0.76.

Don’t understand please help

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The lowest value of the range of the function would be -2, as this is the lowest the y value goes

Write an equation of the passing through point p that is perpendicular to the given line .p(3,1) y= 1/3x -5

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Answer:

y = -3x + 10

Step-by-step explanation:

slope of perpendicular line = -3

y-1 = -3(x-3)

y-1 = -3x + 9

y = -3x + 9 + 1

y = -3x + 10

the answer is y=-3x+10! :)

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All possible random samples of 200 middle managers are selected from a population for a study concerning their mean annual income. The population standard deviation is computed to be $2,248.5. What is the standard deviation of the sampling distribution of the means?

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Answer:

158.993

Step-by-step explanation:

We have to find the standard deviation of the sampling distribution of the means.

We are given that population standard deviation=σ=2248.5 and sample size=n=200.

Standard deviation of sampling distribution of means=σxbar=σ/√n

σxbar=2248.5/√200

σxbar=2248.5/14.1421

σxbar=158.993

Thus, the standard deviation of the sampling distribution of the means is $158.993.

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Prove that the diagonals of a rectangle bisect each other.Plan: Since midpoints will be involved, use multiples of __ to name the coordinates for B, C, and D.2413

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Prove that the diagonals of a rectangle bisect each other.Plan: Since midpoints will be involved, use multiples of __ to name the coordinates for B, C, and D.

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4

1

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