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grin007 [14]
3 years ago
11

Describe the key features of polynomial function

Mathematics
1 answer:
Oksi-84 [34.3K]3 years ago
3 0

Answer:

Zeros: x = 1 , − 2 , 2 End Behavior: Falls to the left and rises to the right.

Y-intercept: (0,4)

Step-by-step explanation:

mark me brainliest

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A varies directly as b. If A = 3 when b = 24, find b when A = 10
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The equation y = 2x + 1 is changed to y = 2x - 1. How does this change the graph of the line?
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Y = 2x + 1
y = 2x - 1

so the 1st one has a y int of 1 and the second one has a y int of -1...so the original line will shift down 2 units
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Leakage from underground gasoline tanks at service stations can damage the environment. It is estimated that 25% of these tanks
Gnesinka [82]

Answer:

a) 3.75

b) 23.61% probability that fewer than 3 tanks will be found to be leaking

c) 0% the probability that at least 600 of these tanks are leaking

Step-by-step explanation:

For each tank there are only two possible outcomes. EIther they leak, or they do not. The probability of a tank leaking is independent of other tanks. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

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)}

To solve question c), i am going to approximate the binomial distribution to the normal.

Normal probability distribution

Problems of normally distributed samples 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)}.

It is estimated that 25% of these tanks leak.

This means that p = 0.25

15 tanks chosen at random

This means that n = 15

a.What is the expected number of leaking tanks in such samples of 15?

E(X) = np = 15*0.25 = 3.75

b.What is the probability that fewer than 3 tanks will be found to be leaking?

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 0) = C_{15,0}.(0.25)^{0}.(0.75)^{15} = 0.0134

P(X = 1) = C_{15,1}.(0.25)^{1}.(0.75)^{14} = 0.0668

P(X = 2) = C_{15,2}.(0.25)^{2}.(0.75)^{13} = 0.1559

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0134 + 0.0668 + 0.1559 = 0.2361

23.61% probability that fewer than 3 tanks will be found to be leaking

c.Now you do a larger study, examining a random sample of 2000 tanks nationally. What is the probability that at least 600 of these tanks are leaking?

Now we have n = 2000. So

\mu = E(X) = np = 2000*0.25 = 500

\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{2000*0.25*0.75} = 19.36

This probability is 1 subtracted by the pvalue of Z when X = 600. So

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

Z = \frac{600 - 500}{19.36}

Z = 5.16

Z = 5.16 has a pvalue of 0.

0% the probability that at least 600 of these tanks are leaking

4 0
3 years ago
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timofeeve [1]

Answer:

If you divided the hours they worked and then add that to what they got all together and u should get the answer

Step-by-step explanation:

i hope this helps a little

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Find the coordinates of the points of intersection of the graphs with coordinate axes: y=− 1/4 x+2
bearhunter [10]

Answer:


Step-by-step explanation:

Here, you can use a simple formula.

To find the point of intersection you just put x=0 or y=0.

Because, if a graph intersects x-axis, then at this point  y=0

Similarly, if a graph intersects y-axis, then at this point  x=0


So, for our given line.

y=-1/4 x +2

when , x=0 , y=-1/4 (0)+2=2

So, the graph intersects y-axis at   y=2


when , y=0 ,

then    0=-1/4 x+2

       or, 1/4 x=2

       or, x=8    [multiplying by  4]

So, the graph intersects x-axis at   x=8

3 0
3 years ago
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