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3 years ago

Which of the following is an even function?

Mathematics

2 answers:

ycow [4]3 years ago

5 0

An even function is a function that is symmetrical over the y axis. With that said, D is the answer.

anyanavicka [17]3 years ago

4 0

Answer:

The correct answer is D) f(x) = 7

Step-by-step explanation:

A function is even when f(-x) = f(x) for all x in the domain of f. We can say that the function is simetrical over x axis.

To get which is the correct answer , we try the same function for -x and x and we have to find the same answer. We are going to try with -5 and 5

A) f(x) = (x – 1)^2

f(5) = (5 – 1)^2 =16

f(-5) = (-5 – 1)^2 =36

Not even funtion

B) f(x) = 8x

f(-5) = 8 *-5 =-40

f(5) = 8*5 =40

Not even funtion

C) f(x) = x^2 – x

f(-5) = -5^2 – -5=30

f(5) = 5^2 – 5 =20

Not even funtion

D) f(x) = 7

f(-5) = 7

f(5) = 7

Even

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Using the binomial distribution, it is found that there is a 0.056 = 5.6% probability that more than 7 will make a purchase.

<h3>What is the binomial distribution formula?</h3>

The formula is:

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

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

The parameters are:

x is the number of successes.

n is the number of trials.

p is the probability of a success on a single trial.

In this problem:

There are 12 customers, hence n = 12.

The probability of any of them making a purchase is of p = 0.4.

The probability that more than 7 will make a purchase is given by:

P(X > 7) = P(X = 8) + P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12).

Hence:

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

$P(X = 8) = C_{12,8}.(0.4)^{8}.(0.6)^{4} = 0.042$

$P(X = 9) = C_{12,9}.(0.4)^{9}.(0.6)^{3} = 0.012$

$P(X = 10) = C_{12,10}.(0.4)^{10}.(0.6)^{2} = 0.02$

$P(X = 11) = C_{12,11}.(0.4)^{11}.(0.6)^{1} \approx 0$

$P(X = 12) = C_{12,12}.(0.4)^{12}.(0.6)^{0} \approx 0$

Then:

P(X > 7) = P(X = 8) + P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12) = 0.042 + 0.012 + 0.02 + 0 + 0 = 0.056.

0.056 = 5.6% probability that more than 7 will make a purchase.

More can be learned about the binomial distribution at brainly.com/question/24863377

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