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2 years ago

The lines graphed below are perpendicular. The slope of the red line is -1/3. What is the slope of the green line?

Mathematics

1 answer:

Serggg [28]2 years ago

7 0

Answer:

The slope of the green line is 3.

Step-by-step explanation:

<em><u>Definition: </u></em>If the two lines are said to be perpendicular, than the multiplication of their slope is -1.

In other words, the slope of the perpendicular line is the negative reciprocal of the given slope of the line.

Here we are slope of the red line, which is -1/3

Let's take it as "m1"

Let's take "m2" the slope of the green line.

By the above definition,

$m_1 *m_2 = -1$

Given: $m_1 = -\frac{1}{3}$

Now plug m1 value in the above statement, we get

$-\frac{1}{3} *m_2 = -1$

Multiply both sides by reciprocal of -1/3. The reciprocal of -1/3 = -3

$-3*-\frac{1}{3} *m_2 = -3*-1$

$m_2 = 3$

Therefore, the slope of the green line is 3.

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it will take 2 cans to fill the go cart gas tank.

Step-by-step explanation:

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2 years ago

According to the U.S. Census Bureau (2016), a substantial pay gap still exists. The average American man, with an advanced colle

Leokris [45]

Answer:

The difference in earnings, over a 30-year career, for men vs women, is $1,200,150

Step-by-step explanation:

Per year.

The average man earns $90,761.

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So, per year, the difference is:

90,761 - 50,756 = 40,005

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The difference in earnings, over a 30-year career, for men vs women, is $1,200,150

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2 years ago

A population of butterflies grows in such a way that each generation is simply 1.5 times the previous generation. There were 350

kap26 [50]

Answer:

378.5 or just 378

Step-by-step explanation:

This is a linear model with x representing the number of generations that's gone by, y is the number of butterflies after x number of generations has gone by, and the 350 represents the number of butterflies initially (before any time has gone by. When x = 0, y = 350 so that's the y-intercept of our equation.)

The form for a linear equation is y = mx + b, where m is the rate of change and b is the y-intercept, the initial amount when x = 0.

Our rate of change is 1.5 and the initial amount of butterflies is 350, so filling in the equation we get a model of y = 1.5x + 350.

If we want y when x = 19, plug 19 in for x and solve for y:

y = 1.5(19) + 350

y = 378.5

Since we can't have .5 of a butterfly we will round down to 378

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2 years ago

Imagine you have a data set with 9,987 names. The data set is sorted alphabetically. You want to find out if the name "David Joy

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Answer:

Step-by-step explanation:

David Joyner might be the first name, so you may only have to check 1 name.

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2 years ago

In a survey of men aged 20-29 in a certain country, the mean height is 73.4 inches with a standard deviation of 2.7 inches. Find

satela [25.4K]

Answer:

The minimum height in the top 15% of heights is 76.2 inches.

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:

$\mu = 73.4, \sigma = 2.7$