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Pavel [41]
2 years ago
14

Is a graph of a slanted line a one-to-one function? Justify your answer.

Mathematics
1 answer:
kkurt [141]2 years ago
7 0

Answer:

Yes

Step-by-step explanation:

A slanted straight line is one-to-one:  It passes the "horizontal ilne test."  This means that any line drawn horizontally through the given line intersects that line only once.  The significance of this is that the given line/function has an inverse.  y = x is one-to-one and has the inverse y = x.  y = 2x is one-to-one and has the inverse y = (1/2)x.

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23% of college students say they use credit cards because of the rewards program. You randomly select 10 college students and as
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Answer:

a) There is a 29.42% probability that the number of college students who say they use credit cards because of the rewards program is exactly two.

b) There is a 41.37% probability that the number of college students who say they use credit cards because of the rewards program is more than two.

c) There is a 69.49% probability that the number of college students who say they use credit cards because of the rewards program is between two and five, inclusive.

Step-by-step explanation:

There are only two possible outcomes. Either the student use credit cards because of the rewards program, or they use for other reason. So, we can solve this exercise using the binomial probability distribution.

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}.\pi^{x}.(1-\pi)^{n-x}

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

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

And \pi is the probability of X happening.

In this problem, we have that:

10 students are randomly selected, so n = 10.

23% of college students say they use credit cards because of the rewards program. This means that \pi = 0.23

(a) exactly two

This is P(X = 2).

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

P(X = 2) = C_{10,2}.(0.23)^{2}.(0.77)^{8} = 0.2942

There is a 29.42% probability that the number of college students who say they use credit cards because of the rewards program is exactly two.

(b) more than​ two

This is P(X > 2).

Either a value is larger than two, or it is smaller of equal. The sum of the decimal probabilities of these events must be 1. So:

P(X \leq 2) + P(X > 2) = 1

P(X > 2) = 1 - P(X \leq 2)

In which

P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)

So

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

P(X = 0) = C_{10,0}.(0.23)^{0}.(0.77)^{10} = 0.0733

P(X = 1) = C_{10,1}.(0.23)^{1}.(0.77)^{9} = 0.2188

P(X = 2) = C_{10,2}.(0.23)^{2}.(0.77)^{8} = 0.2942

P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0733 + 0.2188 + 0.2942 = 0.5863

P(X > 2) = 1 - P(X \leq 2) = 1 - 0.5863 = 0.4137

There is a 41.37% probability that the number of college students who say they use credit cards because of the rewards program is more than two.

(c) between two and five inclusive.

This is

P = P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)

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

P(X = 2) = C_{10,2}.(0.23)^{2}.(0.77)^{8} = 0.2942

P(X = 3) = C_{10,3}.(0.23)^{3}.(0.77)^{7} = 0.2343

P(X = 4) = C_{10,4}.(0.23)^{4}.(0.77)^{6} = 0.1225

P(X = 5) = C_{10,3}.(0.23)^{5}.(0.77)^{5} = 0.0439

So

P = P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) = 0.2942 + 0.2343 + 0.1225 + 0.0439 = 0.6949

There is a 69.49% probability that the number of college students who say they use credit cards because of the rewards program is between two and five, inclusive.

8 0
3 years ago
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