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ehidna [41]
3 years ago
14

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
Ber [7]

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 = <u><em>sample mean number of hours of television watched per year</em></u>

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 = <u>0.3264</u>

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.

6 0
3 years ago
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