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3 years ago

Which equation represents a line that passes through (–2, 4) and has a slope of 2/5 ?

1 answer:

3 0

$\bf \begin{array}{lllll}
&x_1&y_1\\
% (a,b)
&({{ -2}}\quad ,&{{ 4}})
\end{array}
\\\\\\
% slope = m
slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{2}{5}
\\\\\\
% point-slope intercept
\stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-4=\cfrac{2}{5}[x-(-2)]
\implies 
y-4=\cfrac{2}{5}(x+2)
\\\\\\
y-4=\cfrac{2}{5}x+\cfrac{4}{5}\implies y=\cfrac{2}{5}x+\cfrac{4}{5}+4\implies y=\cfrac{2}{5}x+\cfrac{24}{5}$

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2. Use the Distributive Property to determine which of the following statements is equivalent to 5(6-2).

frez [133]

Answer:

30 - 10

Step-by-step explanation:

When you distribute, that means you multiply everything on the outside of the parentheses by everything on the inside.

5 (6-2)

is really

5*6 - 5*2

30 - 10

3 0

2 years ago

Evaluate the difference quotient for the given function. Simplify your answer.

IgorC [24]

Answer:

-5 - h

Step-by-step explanation:

ƒ(x) = 1 + 5x - x²

[f(5 + h) -f(5)]/h

= [1 + 5(5 + h) - (5 + h)² - 1 - 5(5) +5²]/h

= (25 + 5h - 25 - 10h - h² - 25 + 25)/h

= (-5h - h²)/h

= -5 - h

The difference quotient is -5 - h.

7 0

3 years ago

What is 90 percent of 35

monitta

Answer:

31.50

Step-by-step explanation:

All you have to do is multiply 35 by 90% or .90

35 x .90 = 31.5

4 0

2 years ago

The distribution of results from a cholesterol test has a mean of 180 and a standard deviation of 20. A sample size of 40 is dra

olga2289 [7]

Using the normal distribution, there is a 0.2148 = 21.48% probability that the sum of the 40 values is less than 7,100.

<h3>Normal Probability Distribution</h3>

The z-score of a measure X of a normally distributed variable with mean $\mu$ and standard deviation $\sigma$ is given by:

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

The z-score measures how many standard deviations the measure is above or below the mean.

Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.

By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For this problem, these parameters are given as follows:

$\mu = 180, \sigma = 20, n = 40, s = \frac{20}{\sqrt{40}} = 3.1623$

A sum of 7100 is equivalent to a sample mean of 7100/40 = 177.5, which means that the probability is the <u>p-value of Z when X = 177.5</u>, hence:

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

By the Central Limit Theorem:

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