Hey guys I just wanted to put this out there-

First we find the zeroes so we don't take the integral of negative bits

4x-x²
x(4-x)
zeroes at x=0 and x=4
it opens down
so the part we are interested in is the bit between x=0 and x=4

$\int\limits^4_0 {4x-x^2} \, dx =[2x^2- \frac{1}{3}x^3]^4_0=(32- \frac{64}{3})-(0)= 10.6666666666$ or aout 10 and 2/3

C is answer

6 0

3 years ago

If you are currently making $8.75 per hour and you are offered a new job that pays $9.47 per hour, how much more would you make

andreev551 [17]

Do you mean the percentage or just total value? 9.47-8.75=$0.72

7 0

3 years ago

Read 2 more answers

The amount of calories consumed by customers at the Chinese buffet is normally distributed with mean 2617 and standard deviation

Eduardwww [97]

Answer:

a) N(2617, 586)

b) 0.3613 = 36.13% probability that the customer consumes less than 2409 calories.

c) 0.4013 = 40.13% of the customers consume over 2764 calories

d) 3981 calories.

Step-by-step explanation:

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.

In this question, we have that:

$\mu = 2617, \sigma = 586$

a. What is the distribution of X?

Here we first place the mean, then the standard deviation.

N(2617, 586)

b. Find the probability that the customer consumes less than 2409 calories.

This is the pvalue of Z when X = 2409. So

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

$Z = \frac{2409 - 2617}{586}$

$Z = -0.355$

$Z = -0.355$ has a pvalue of 0.3613

0.3613 = 36.13% probability that the customer consumes less than 2409 calories.

c. What proportion of the customers consume over 2764 calories?

This is 1 subtracted by the pvalue of Z when X = 2764. So

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

$Z = \frac{2764 - 2617}{586}$

$Z = 0.25$

$Z = 0.25$ has a pvalue of 0.5987

1 - 0.5987 = 0.4013

0.4013 = 40.13% of the customers consume over 2764 calories

d. The Piggy award will given out to the 1% of customers who consume the most calories. What is the fewest number of calories a person must consume to receive the Piggy award?

Top 1%, so the 100-1 = 99th percentile.

The 99th percentile is the value of X when Z has a pvalue of 0.99. So it is X when Z = 2.327. So

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

$2.327 = \frac{X - 2617}{586}$

$X - 2617 = 2.327*586$

$X = 3980.6$

Rounding to the nearest calorie, 3981 calories.

7 0

2 years ago