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3 years ago

5

Factoring Quadratic Expressions: 7x^2 -32x -60

2 answers:

krek1111 [17]3 years ago

6 0

$7 x^{2} -32x-60$

$7 x^{2} -42x+10x-60$

$7x(x-6)+10(x-6)$

$(x-6)(7x+10)$

Gnoma [55]3 years ago

3 0

$7x^{2} -32x-60$
factors into this:
$(7x+10)(x-6)$

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Assume that adults have IQ scores that are normally distributed with a mean of mu equals 105 and a standard deviation sigma equa

Sindrei [870]

Answer:

0.7698

Step-by-step explanation:

If you call your random variable $X$ , then what you are looking for is

$P(87 \leq X \leq 123)$

because you want the probability of $X$ being <em>between 87 and 123.</em>

We need a table with of the normal distribution. But we can only find the table with $\mu = 0$ and $\sigma = 1$ . Because of that, first we need to <em>normalize </em>our random variable:

$Z = \frac{X - \mu}{\sigma} = \frac{X - 105}{15}$

(you can always normalize your variable following the same formula!)

now we can do something similar to our limits, to get a better expression:

$\frac{87 - 105}{15} = \frac{-18}{15} = -1.2$

$\frac{123 - 105}{15} = \frac{18}{15} = 1.2$

And we transform our problem to a simpler one:

$P(87 \leq X \leq 123) = P(-1.2 \leq Z \leq 1.2) = P(Z \leq 1.2) - P(Z \leq -1.2)$

(see Figure 1)

From our table we can see that $P(Z \leq 1.2) = 0.8849$ (this is represented in figure 2).

Remember that the whole area below the curve is exactly 1. So we can conclude that $P(Z \geq 1.2) = 0.1151$ (because 0.8849 + 0.1151 = 1). We also know the normal distribution is symmetric, then

$P(Z \leq -1.2)= P(Z \geq 1.2) = 0.1151$ .

FINALLY:

$P(Z \leq 1.2) - P(Z \leq -1.2) = 0.8849 - 0.1151 = 0.7698$

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3 years ago

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elena55 [62]

Answer:

We obtain same product by both the methods.

Step-by-step explanation:

We are given the following in the question:

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$\dfrac{3}{4}\times 4 =4\times \dfrac{3}{4}$

Different ways to find the product:

1. First way

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2. Second way

$\dfrac{3}{4}\times 4\\\\=\dfrac{12}{4}\\\\=3$

We get the same product for both the calculations.

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MA_775_DIABLO [31]

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Answer:

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