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3 years ago

7

Please help me with this question step by step. A rectangle has a width of 2x exponent 2 +4x+1) and a length of (8-x). What is t

he function for the area of the rectangle?

1 answer:

timurjin [86]3 years ago

6 0

Answer:

A = (2x² + 4x + 1) (8 − x)

A = -2x³ + 12x² + 31x + 8

Step-by-step explanation:

W = 2x² + 4x + 1

L = 8 − x

Area is width times length.

A = (2x² + 4x + 1) (8 − x)

If you wish, you can simplify with distribution.

A = 8 (2x² + 4x + 1) − x (2x² + 4x + 1)

A = 16x² + 32x + 8 − 2x³ − 4x² − x

A = -2x³ + 12x² + 31x + 8

You might be interested in

The probability that your call to a service line is answered in less than 30 seconds is 0.75. Assume that your calls are indepen

vfiekz [6]

Answer:

a) 0.2581

b) 0.4148

c) 17

Step-by-step explanation:

For each call, there are only two possible outcomes. Either they are answered in less than 30 seconds. Or they are not. The probabilities for each call are independent. 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.

In this problem we have that:

$p = 0.75$

a. If you call 12 times, what is the probability that exactly 9 of your calls are answered within 30 seconds? Round your answer to four decimal places (e.g. 98.7654).

This is $P(X = 9)$ when $n = 12$ . So

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

$P(X = 9) = C_{12,9}.(0.75)^{9}.(0.25)^{3} = 0.2581$

b. If you call 20 times, what is the probability that at least 16 calls are answered in less than 30 seconds? Round your answer to four decimal places (e.g. 98.7654).

This is $P(X \geq 16)$ when $n = 20$

So

$P(X \geq 16) = P(X = 16) + P(X = 17) + P(X = 18) + P(X = 19) + P(X = 20)$

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

$P(X = 16) = C_{20,16}.(0.75)^{16}.(0.25)^{4} = 0.1897$

$P(X = 17) = C_{20,17}.(0.75)^{17}.(0.25)^{3} = 0.1339$

$P(X = 18) = C_{20,18}.(0.75)^{18}.(0.25)^{2} = 0.0669$

$P(X = 19) = C_{20,19}.(0.75)^{19}.(0.25)^{1} = 0.0211$

$P(X = 20) = C_{20,20}.(0.75)^{20}.(0.25)^{0} = 0.0032$

So

$P(X \geq 16) = P(X = 16) + P(X = 17) + P(X = 18) + P(X = 19) + P(X = 20) = 0.1897 + 0.1339 + 0.0669 + 0.0211 + 0.0032 = 0.4148$

c. If you call 22 times, what is the mean number of calls that are answered in less than 30 seconds? Round your answer to the nearest integer.

The expected value of the binomial distribution is:

$E(X) = np$

In this question, we have $n = 22$

So

$E(X) = 22*0.75 = 16.5$

The closest integer to 16.5 is 17.

7 0

3 years ago

These are the round-trip distances that city buses traveled on different routes each month. Calculate the distance, in miles, th

prohojiy [21]

I think you have to use the distance formula

4 0

3 years ago

Suppose that six individuals are interested in taking part in a study relating BMI to a number of health outcomes. The following

posledela

Answer:

a) Mean = 27.65

Median = 27.645

b) Relative Frequency = 33.33%

Step-by-step explanation:

We are given the following data set:

25.78, 21.06, 36.54, 29.51, 18.96, 34.05

a) Mean and Median

$Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}$

$Mean =\displaystyle\frac{165.9}{6} = 27.65$

$Median:\\\text{If n is odd, then}\\\\Median = \displaystyle\frac{n+1}{2}th ~term \\\\\text{If n is even, then}\\\\Median = \displaystyle\frac{\frac{n}{2}th~term + (\frac{n}{2}+1)th~term}{2}$

Sorted data: 18.96, 21.06, 25.78, 29.51, 34.05, 36.54

$\text{Median} = \displaystyle\frac{25.78 +29.51}{2} = 27.645$

b) BMI above 30 is considered obese

Frequency of obese in the given sample = 2

Relative Frequency =

$\displaystyle\frac{\text{Frequency of obese}}{\text{Total number}} = \frac{2}{6} = 0.3333 = 33.33\%$

5 0

3 years ago

what is the square root of 98 what is the square root of y to the 6th what is the square root of a to the 7th what is the square

Bogdan [553]

1. sqrt(98) = 7 sqrt(2)
2. sqrt(y^6) = y^3
3. sqrt(a^7) = a^7/2
4. sqrt(12x^3y^2) = 2xy sqrt(3x)
5. sqrt(36x^2y^4) = 6xy^2
6. sqrt(48ab^3) = 4b sqrt(3ab)
7. sqrt(10a^5b^2) = a^2b sqrt(10a)
8. sqrt(20x^3y^10 = 2xy^5 sqrt(5x)

7 0

3 years ago

Y=5x+2 <br> 4x-y=0<br> is (2,12) a solution of the system?

Svetach [21]

Answer:

The point (2,12) is not a solution of the system

see the explanation

Step-by-step explanation:

we have

$y=5x+2$ ----> equation A

$4x-y=0$ ----> equation B

Solve the system by elimination

Adds equation A and equation B

$y=5x+2\\4x-y=0\\------\\y+4x-y=5x+2+0\\4x=5x+2\\5x-4x=-2\\x=-2$

Find the value of y

substitute the value of x in the equation A

$y=5(-2)+2=-8$

The solution of the system is the point (-2,-8)

The system has only one solution, because the intersection point both lines is only one point

therefore

The point (2,12) is not a solution of the system

6 0

3 years ago