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3 years ago

Find the equation for the linear function that passes through the points ( see photo)

Mathematics

2 answers:

Sidana [21]3 years ago

6 0

Answer:

f(x) = (-4/5)*x + 4

Step-by-step explanation:

The line which passes through these points will decrease y by 12 for every x increase of 15. This is the same as decreasing y by 4 for every x increase of 5. This means the slope (rise over run) is -4/5. If this is applied to the first point to find what y is at 0, then the point (0, 4) is on the line.

This means that f(x) = (-4/5)*x + 4

Scorpion4ik [409]3 years ago

3 0

Answer:

$\large\boxed{y=-\dfrac{4}{5}x+4}$

Step-by-step explanation:

The slope-intercept form of an equation of a line:

$y=mx+b$

m - slope

b - y-intercept

The formula of a slope:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

We have the points (-5, 8) and (10, -4). Substitute:

$m=\dfrac{-4-8}{10-(-5)}=\dfrac{-12}{15}=-\dfrac{12:3}{15:3}=-\dfrac{4}{5}$

Put it to the equation of a line:

$y=-\dfrac{4}{5}x+b$

Put the coordinates of the point (-5, 8) to the equation, and solveit for b:

$8=-\dfrac{4}{5\!\!\!\!\diagup_1}(-5\!\!\!\!\diagup^1)+b$

$8=4+b$ subtract 4 from both sides

$4=b\to b=4$

Finally we have:

$y=-\dfrac{4}{5}x+4$

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3 years ago

In a region, 90% of the population have brown eyes. If 15 people are randomly selected, find the probability that at least 13

Andrew [12]

Answer:

a) $P(X \geq 13) = P(X=13) +P(X=14) +P(X=15)$

$P(X=13)=(15C13)(0.9)^{13} (1-0.9)^{15-13}=0.267$

$P(X=14)=(15C14)(0.9)^{14} (1-0.9)^{15-14}=0.343$

$P(X=15)=(15C15)(0.9)^{15} (1-0.9)^{15-15}=0.206$

And replacing we got:

$P(X \geq 13) = P(X=13) +P(X=14) +P(X=15)=0.267+0.343+0.206=0.816$

b) D. No, because the probability of this occurring is not small.

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Part a

If 15 people are randomly selected, find the probability that at least 13 of them have brown eyes.

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n=15, p=0.90)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

And we want to find this probability:

$P(X \geq 13) = P(X=13) +P(X=14) +P(X=15)$

$P(X=13)=(15C13)(0.9)^{13} (1-0.9)^{15-13}=0.267$

$P(X=14)=(15C14)(0.9)^{14} (1-0.9)^{15-14}=0.343$

$P(X=15)=(15C15)(0.9)^{15} (1-0.9)^{15-15}=0.206$

And replacing we got:

$P(X \geq 13) = P(X=13) +P(X=14) +P(X=15)=0.267+0.343+0.206=0.816$

Part b

Is it unusual to randomly select 15 people and find that at least 13 of them have brown eyes? Note that a small probability is one that is less than 0.05.

Since our calculated probability is too higher compared to 0.05 we can conclude this:

D. No, because the probability of this occurring is not small.

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4 years ago