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3 years ago

Which of the following is the correct factorization of the polynomial below? x3 + 14x2 + 49x

Mathematics

2 answers:

Naddika [18.5K]3 years ago

7 0

For this case we must factor the following polynomial:

$x ^ 3 + 14x ^ 2 + 49x\\$

We can take common factor x:

$x(x ^ 2+ 14x + 49)$

To factor the expression within the parenthesis, we must find two numbers that when multiplied give 49 and when added together, 14 are obtained. These are: 7 and 7.

$7*7=49,7+7=14$

Thus, the expression is factored as:

$x(x + 7)(x +7)$

Answer:

$x (x + 7) ^ 2$

loris [4]3 years ago

4 0

The answer is x(x+7)^2

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A nationwide census is conducted and it is found that the mean number of hours of television watched per year by Americans is 35

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Answer:

Probability that a group of 4 Americans watch more than 400 hours of television per year is 0.3264.

Step-by-step explanation:

We are given that a nationwide census is conducted and it is found that the mean number of hours of television watched per year by Americans is 350 with a standard deviation of 220.

A group of 4 Americans is selected.

Let $\bar X$ = sample mean number of hours of television watched per year

The z score probability distribution for sample mean is given by;

Z = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\mu$ = population mean = 350

$\sigma$ = standard deviation = 220

n = sample of Americans = 4

Now, the probability that a group of 4 Americans watch more than 400 hours of television per year is given by = P( $\bar X$ > 400 hours)

P( $\bar X$ > 400) = P( $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ > $\frac{400-350}{\frac{220}{\sqrt{4} } }$ ) = P(Z > 0.45) = 1 - P(Z $\leq$ 0.45)

= 1 - 0.6736 = 0.3264

The above probability is calculated by looking at the value of x = 0.45 in the z table which has an area of 0.6736.

Hence, the probability that a group of 4 Americans watch more than 400 hours of television per year is 0.3264.

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