If f(x) =5x-1 , then f(3)=

coldgirl [10]

No explenation, but m is 25

5 0

3 years ago

The proportion of high school seniors who are married is 0.02. Suppose we take a random sample of 300 high school seniors; a.) F

cricket20 [7]

Answer:

a) Mean 6, standard deviation 2.42

b) 10.40% probability that, in our sample of 300, we find that 8 of the seniors are married.

c) 14.85% probability that we find less than 4 of the seniors are married.

d) 99.77% probability that we find at least 1 of the seniors are married

Step-by-step explanation:

For each high school senior, there are only two possible outcomes. Either they are married, or they are not. The probability of a high school senior being married is independent from other high school seniors. 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:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

In this problem, we have that:

$n = 300, p = 0.02$

a.) Find the mean and standard deviation of the sample count X who are married.

Mean

$E(X) = np = 300*0.02 = 6$

Standard deviation

$\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{300*0.02*0.98} = 2.42$

b.) What is the probability that, in our sample of 300, we find that 8 of the seniors are married?

This is P(X = 8).

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

$P(X = 8) = C_{300,8}.(0.02)^{8}.(0.98)^{292} = 0.1040$

10.40% probability that, in our sample of 300, we find that 8 of the seniors are married.

c.) What is the probability that we find less than 4 of the seniors are married?

$P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)$

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

$P(X = 0) = C_{300,0}.(0.02)^{0}.(0.98)^{300} = 0.0023$

$P(X = 1) = C_{300,1}.(0.02)^{1}.(0.98)^{299} = 0.0143$

$P(X = 2) = C_{300,2}.(0.02)^{2}.(0.98)^{298} = 0.0436$

$P(X = 3) = C_{300,3}.(0.02)^{3}.(0.98)^{297} = 0.0883$

$P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0023 + 0.0143 + 0.0436 + 0.0883 = 0.1485$

14.85% probability that we find less than 4 of the seniors are married.

d.) What is the probability that we find at least 1 of the seniors are married?

Either no seniors are married, or at least 1 one is. The sum of the probabilities of these events is decimal 1. So

$P(X = 0) + P(X \geq 1) = 1$

From c), we have that $P(X = 0) = 0.0023$ . So

$0.0023 + P(X \geq 1) = 1$

$P(X \geq 1) = 0.9977$

99.77% probability that we find at least 1 of the seniors are married

3 0

3 years ago

How do you simplify 3445 over 15?

andreev551 [17]

Divide Numerator and Denominator by 5
3445 / 5 = 689
15 / 5 = 3

689/3

3 0

3 years ago

If the expression x^{-\frac{3}{2}}y\sqrt{36xy^2}x − 2 3 y 36xy 2 is written in the form ax^by^cax b y c , then what is the p

Mekhanik [1.2K]

Answer:

-12

Step-by-step explanation:

The given expression is

$x^{-\frac{3}{2}}y\sqrt{36xy^2}$

We have to rewrite the given function in the form of

$ax^{b}y^c$ ....(i)

then we have to find the product of a,b and c.

The given expression can be rewritten as

$x^{-\frac{3}{2}}y\sqrt{36}\sqrt{x}\sqrt{y^2}$

Using properties of exponents we get

$x^{-\frac{3}{2}}y6x^{\frac{1}{2}}y$ $[\because \sqrt[n]{a}=a^{\frac{1}{n}}]$

$6x^{-\frac{3}{2}+\frac{1}{2}}y^{1+1}$ $[\because a^ma^n=a^{m+n}]$

$6x^{-1}y^{2}$ ...(ii)

On comparing (i) and (ii), we get

$a=6,b=-1,c=2$

Product of a,b and c is

$abc=(6)(-1)(2)=-12$

Therefore, the product of a,b, and c is -12.

7 0

4 years ago

what is the mathematical expression for the problem withdrawing $10 every week from an outstanding $400?

Fofino [41]

Answer:

40

Step-by-step explanation:

because if you do 400 divided by 10, it gives you 40

4 0

4 years ago