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3 years ago

write an equation in point slope form for the line through the given point with the given slope (-4, -3); m=8

Mathematics

1 answer:

Ne4ueva [31]3 years ago

4 0

Answer:

An equation in point-slope form for the line will be:

$y - (-3) = 8 (x - (-4))$

Please check the attached line graph also.

Step-by-step explanation:

Given

The point (-4, -3)

The slope m = 8

To determine

Write an equation in point slope form for the line.

Using the point-slope form of the line equation

$y-y_1=m\left(x-x_1\right)$

where

m is the slope of the line

(x₁, y₁) is the point

In our case,

(x₁, y₁) = (-4, -3)

The slope m = 8

substituting the values m = 8 and the point (-4, -3)

$y-y_1=m\left(x-x_1\right)$

$y - (-3) = 8 (x - (-4))$

Therefore, an equation in point-slope form for the line will be:

$y - (-3) = 8 (x - (-4))$

Please check the attached line graph also.

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g A psychic was tested for extrasensory perception (ESP). The psychic was presented with cards face down and asked to determine

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Answer:

Step-by-step explanation:

Hello!

The objective is to test ESP, for this, a psychic was presented with cards face down and asked to determine if each of the cards was one of four symbols: a star, cross, circle, square.

Be X: number of times the psychic identifies the symbols on the cards correctly is a size n sample.

p the probability that the psychic identified the symbol on the cards correctly

You have to calculate the sample size n to estimate the proportion with a confidence level of 95% and a margin of error of d=0.01

The CI for the population proportion is constructed "sample proportion" ± "margin of error" Symbolically:

p' ± $Z_{1-\alpha /2} * (\sqrt{\frac{p'(1-p')}{n} } )$

Where $d= Z_{1-\alpha /2} * (\sqrt{\frac{p'(1-p')}{n} } )$ is the margin of error. As you can see, the formula contains the sample proportion (it is normally symbolized p-hat, in this explanation I'll continue to symbolize it p'), you have to do the following consideration:

Every time the psychic has to identify a card he can make two choices:

"Success" he identifies the card correctly

"Failure" he does not identify the card correctly

If we assume that each symbol has the same probability of being chosen at random P(star)=P(cross)=P(circle)=P(square)= 1/4= 0.25

Let's say, for example, that the card has the star symbol.

The probability of identifying it correctly will be P(success)= P(star)= 1/4= 0.25

And the probability of not identifying it correctly will be P(failure)= P(cross) + P(circle) + P(square)= 1/4 + 1/4 + 1/4= 3/4= 0.75

So for this experiment, we'll assume the "worst case scenario" and use p'= 1/4 as the estimated probability of the psychic identifying the symbol on the card correctly.

The value of Z will be $Z_{1-\alpha /2}= Z_{0.975}= 1.96$