Inequality’s of (0,3) (2,-3)

Find the shaded region of the figure below

lilavasa [31]

Answer:

-x³ + 3x² - 14x + 12

Step-by-step explanation:

Area of outer rectangle = (x² + 3x - 4) * (2x - 3)

= (x² + 3x - 4) * 2x + (x² + 3x - 4) * (-3)

=x²*2x + 3x *2x - 4*2x + x² *(-3) + 3x *(-3) - 4*(-3)

=2x³ + 6x² - 8x - 3x² - 9x + 12

= 2x³ + <u>6x² - 3x²</u> <u>- 8x - 9x</u> + 12 {Combine like terms}

= 2x³ + 3x² - 17x + 12

Area of inner rectangle = (x² - 1)* 3x

= x² *3x - 1*3x

= 3x³ - 3x

Area of shaded region = area of outer rectangle - area of inner rectangle

= 2x³ + 3x² - 17x + 12 - (3x³ - 3x)

= 2x³ + 3x² - 17x + 12 -3x³ + 3x

= 2x³ - 3x³ + 3x² - 17x + 3x + 12

= -x³ + 3x² - 14x + 12

4 0

3 years ago

The operation manager at a tire manufacturing company believes that the mean mileage of a tire is 30,393 miles, with a standard

Pie

Answer:

52.84% probability that the sample mean would differ from the population mean by less than 339 miles in a sample of 37 tires if the manager is correct

Step-by-step explanation:

To solve this question, we have to understand the normal probability distribution and the central limit theorem:

Normal probability distribution:

Problems of normally distributed samples are 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.

Central limit theorem:

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$ , a large sample size can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$

In this problem, we have that:

$\mu = 30393, \sigma = 2876, n = 37, s = \frac{2876}{\sqrt{37}} = 472.81$

What is the probability that the sample mean would differ from the population mean by less than 339 miles in a sample of 37 tires if the manager is correct

This probability is the pvalue of Z when X = 30393 + 339 = 30732 subtracted by the pvalue of Z when X = 30393 - 339 = 30054. So

X = 30732

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

By the Central Limit Theorem

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

$Z = \frac{30732 - 30393}{472.81}$

$Z = 0.72$

$Z = 0.72$ has a pvalue of 0.7642.

X = 30054

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

$Z = \frac{30054 - 30393}{472.81}$

$Z = -0.72$

$Z = -0.72$ has a pvalue of 0.2358

0.7642 - 0.2358 = 0.5284

52.84% probability that the sample mean would differ from the population mean by less than 339 miles in a sample of 37 tires if the manager is correct

4 0

3 years ago

2. Help ASAP!!!!!!!!!!!!!!!!

ch4aika [34]

ANSWER

$2 \times 2$