Factor and simplify: (a^2+2a)^2-2(a^2+2a)-3

The scores for a certain test of intelligence are normally distributed with mean 85 and standard deviation 11. Find the 90th per

jonny [76]

Answer:

99.1 is the 90th percentile of these scores.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 85

Standard Deviation, σ = 11

We are given that the distribution of score is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

We have to find the value of x such that the probability is 0.90

$P( X < x) = P( z < \displaystyle\frac{x - 85}{11})=0.90$

Calculation the value from standard normal z table, we have,

$P(z \leq 1.282) = 0.90$

Putting values, we get,

$\displaystyle\frac{x - 85}{11} = 1.282\\\\x = 99.1$

Thus, 99.1 is the 90th percentile of these scores.

5 0

3 years ago

Which set of numbers could represent the lengths of the sides of a right triangle?

DiKsa [7]

Answer:

The first set: 8, 15, and 17.

Step-by-step explanation:

By the pythagorean theorem, a triangle is a right triangle if and only if

$\text{longest side}^2 = \text{first shorter side}^2 + \text{second shorter side}^2$ .

In this case,

$\text{longest side}^2 = 17^2 = 289$ .

$\begin{aligned}&\text{first shortest side}^2 + \text{second shortest side}^2 \\ &= 8^2 + 15^2\\ &=64 + 225 = 289 \end{aligned}$ .

In other words, indeed $\text{hypotenuse}^2 = \text{first leg}^2 + \text{second leg}^2$ . Hence, 8, 15, 17 does form a right triangle.

Similarly, check the other pairs. Keep in mind that the square of the longest side should be equal to the sum of the square of the two

Factor out the common factor $2$ to simplify the calculations.

$\text{longest side}^2 = 20^2 = 400$

$\begin{aligned}&\text{first shortest side}^2 + \text{second shortest side}^2 \\ &= 10^2 + 15^2\\ &=100 + 225 = 325 \end{aligned}$ .

$\text{longest side}^2 \ne \text{first shorter side}^2 + \text{second shorter side}^2$ .

Hence, by the pythagorean theorem, these three sides don't form a right triangle.

$\text{longest side}^2 = (2\times 11)^2 = 2^2 \times 121$ .

$\begin{aligned}&\text{first shortest side}^2 + \text{second shortest side}^2 \\ &= (2 \times 6)^2 + (2 \times 9)^2\\ &=2^2 \times(36 + 81) = 2^2 \times 117 \end{aligned}$ .

$\text{longest side}^2 \ne \text{first shorter side}^2 + \text{second shorter side}^2$ .

Hence, by the pythagorean theorem, these three sides don't form a right triangle.

$\text{longest side}^2 = 11^2 = 121$ .

<h3> $\begin{aligned}&\text{first shortest side}^2 + \text{second shortest side}^2 \\ &= 7^2 + 9^2\\ &=49+ 81 = 130 \end{aligned}$ .</h3>

$\text{longest side}^2 \ne \text{first shorter side}^2 + \text{second shorter side}^2$ .

Hence, by the pythagorean theorem, these three sides don't form a right triangle.

6 0

4 years ago

Solve the rational equation (3x^2+1)/(x-1) + x =4 + 4/(x-1)

natita [175]

Answer:

The answer to your question is letter D

Step-by-step explanation:

Rational equation

$\frac{3x^{2} + 1}{x - 1} + x = 4 + \frac{4}{x - 1}$

Simplify

$\frac{3x^{2} + 1 + x(x - 1)}{x - 1} = \frac{4(x - 1) + 4}{x - 1}$

Cancel the denominators and expand

3x² + 1 + x² - x = 4x - 4 + 4

Simplify

4x² - x + 1 - 4x = 0

4x² - 5x + 1 = 0

Factor

4x² - 4x - 1x + 1 = 0

4x(x - 1) - 1(x - 1) = 0

(4x - 1)(x - 1) = 0

x₁ = 1/4 x₂ = 1

4 0

3 years ago

The ideal width of a safety belt strap for a certain automobile is 7 cm. An actual width can vary by at most 0.3 cm. Write an ab

tester [92]

<span>
</span> $(7-.3) \leq w \leq (7+.3)
$

$6.7 \leq w \leq 7.3$

$w - 7 = -0.3$

$w = 6.7$

So the answer is

<span>C. |w – 7| ≤ 0.3</span>

6 0

3 years ago

Find the area of the following kite:

muminat

Answer:64

Step-by-step explanation:

2×2=4

4×2=8

8×8=64

7 0

3 years ago