F(x)=4x squared −7x+7, Find f(2)

Help please. This is due tomorrow

Ray Of Light [21]

Answer:

96 is accortinaded to x therefore x - 76 = 89 x = 13

Step-by-step explanation:

3 0

2 years ago

The sum of the interior angles of a hexagon is equal to the sum of six consecutive integers. What is the measure of the smallest

kipiarov [429]

Answer:

Look to the explanation

Step-by-step explanation:

* Lets explain how to solve the problem

- The consecutive integers are the integers after each other like

1 , 2 , 3 , ......

- The rule of the sum of the interior angles of any polygon is:

(n - 2) × 180° , where n is the number of the sides of the polygon

- The sum of the interior angles of a hexagon is equal to the sum of

six consecutive integers

* Lets find the sum of the interior angle of the hexagon

∵ The hexagon has 6 sides

∴ n = 6

∴ The sum of its interior angles = (6 - 2) × 180° = 720°

* Lets find the sum of six consecutive integers

- Assume that the smallest integer is x

∴ The numbers are x , x + 1 , x + 2 , x + 3 , x + 4 , x + 5

∵ Their sum = x + (x + 1) + (x + 2) + (x + 3) + (x + 4) + (x + 5)

- Add like terms

∴ Their sum = 6x + 15

- Equate the sum of the 6 numbers by the sum of the angles of

the hexagon

∴ 6x + 15 = 720

- Subtract 15 from both sides

∴ 6x = 705

- Divide both sides by 6

∴ x = 117.5

- But 117 .5 not integer

∴ The sum of the interior angles of a hexagon can not equal the

sum of six consecutive integers

- But it can be if the numbers are consecutive odd integers

because the consecutive odd numbers are

x , x + 2 , x + 4 , x + 6 , x + 8 , x + 10

∴ Their sum = 6x + 30

∵ 6x + 30 = 720

- Subtract 30 from both sides

∴ 6x = 690

- Divide both sides by 6

∵ x = 115

∵ x represents the measure of the smallest angle

∴ The measure of the smallest interior angle of the hexagon is 115°

7 0

4 years ago

A population of plastic chairs in a factory has a weight's mean of 1.5 kg and a standard deviation of 0.1 kg . Suppose a sample

Firlakuza [10]

Answer:

0.9544 = 95.44% probability that the sample mean will be within +0.02 of the population mean.

Step-by-step explanation:

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

Normal probability distribution

When the distribution is normal, we use 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 normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question, we have that:

$\mu = 1.5, \sigma = 0.1, n = 100, s = \frac{0.1}{\sqrt{100}} = 0.01$

What is the probability that the sample mean will be within +0.02 of the population mean?

Sample mean between 1.5 - 0.02 = 1.48 kg and 1.5 + 0.02 = 1.52 kg, which is the pvalue of Z when X = 1.52 subtracted by the pvalue of Z when X = 1.48. So

X = 1.52

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

By the Central Limit Theorem

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