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2 years ago

Find the equation of the line with the given slope and containing the given point. slope -7/10; through (-8,0)

Mathematics

1 answer:

Kisachek [45]2 years ago

5 0

Answer:

$y = -\frac{7}{10}(x + 8)$

Step-by-step explanation:

To write the equation of a line, substitute m = -7/10 and the point (-8,0) into the point slope formula.

$y - y_1=m(x-x_1)\\y - 0 = -\frac{7}{10}(x --8)\\y = -\frac{7}{10}(x + 8)$

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The points (9, 9) and (5, 1) fall on a particular line. What is its equation in slope-intercept form?

Ilia_Sergeevich [38]

Your equation would be y= 2x-9

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2 years ago

How does the slope intercept form compare to the point slope form

polet [3.4K]

Slope intercept = y=mx+b
m is the slope
b is the y int

point slope =y2-y1=m(x1-x2)

3 0

3 years ago

By using the remainder theorem, determine the remainder when

Greeley [361]

Answer:

-123

Step-by-step explanation:

The remainder theorem says that when a polynomial is divided by a linear factor x - c (note the minus sign), the remainder is the value of the polynomial at x = c.

When a polynomial P(x) is divided by x - c, the remainder is P(c). In other words, to find the remainder, plug in c for x.

You're dividing by x + 4 which is the same thing as x - (-4) -- the role of c is being played by -4.

3(–4)^3 – (–4)^2 – 20(–4) + 5 = –123

3 0

3 years ago

Read 2 more answers

Matt bought a home in 2001 and paid $150,000 for it. He sold the home for $450,000. How much of the profit on his home will be t

butalik [34]

Answer:

profit to be taxable will be $300,000

Step-by-step explanation:

Matt home cost = $150,000

Matt sold his home for = $450,000

so,

cost price will be $150,000

selling price will be $450,000

profit = selling price - cost price

profit = $450,000 - $150,000

profit = $300,000

hence the taxable amount for his home this year will be $300,000

7 0

3 years ago

Assume that 24.5% of people have sleepwalked. Assume that in a random sample of 1478 adults, 369 have sleepwalked. a. Assuming t

solniwko [45]

Answer:

a) 0.3483 = 34.83% probability that 369 or more of the 1478 adults have sleepwalked.

b) 369 < 403.4, which means that 369 is less than 2.5 standard deviations above the mean, and thus, a result of 369 is not significantly high.

c) Since the sample result is not significant, it suggests that the rate of 24.5% is a good estimate for the percentage of people that have sleepwalked.

Step-by-step explanation:

We use the normal approximation to the binomial to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

A result is considered significantly high if it is more than 2.5 standard deviations above the mean.

Normal probability distribution

Problems of normally distributed distributions 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.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

Assume that 24.5% of people have sleepwalked.

This means that $p = 0.245$

Sample of 1478 adults:

This means that $n = 1478$

Mean and standard deviation:

$\mu = 1478*0.245 = 362.11$

$\sigma = \sqrt{1478*0.245*0.755} = 16.5346$

a. Assuming that the rate of 24.5% is correct, find the probability that 369 or more of the 1478 adults have sleepwalked.

Using continuity correction, this is $P(X \geq 369 - 0.5) = P(X \geq 368.5)$ , which is 1 subtracted by the p-value of Z when X = 368.5.

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

$Z = \frac{368.5 - 362.11}{16.5346}$

$Z = 0.39$

$Z = 0.39$ has a p-value of 0.6517

1 - 0.6517 = 0.3483

0.3483 = 34.83% probability that 369 or more of the 1478 adults have sleepwalked.

b. Is that result of 369 or more significantly high?

362.11 + 2.5*16.5346 = 403.4

369 < 403.4, which means that 369 is less than 2.5 standard deviations above the mean, and thus, a result of 369 is not significantly high.

c. What does the result suggest about the rate of 24.5%?

Since the sample result is not significant, it suggests that the rate of 24.5% is a good estimate for the percentage of people that have sleepwalked.

3 0

3 years ago