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olchik [2.2K]
3 years ago
9

We want to factor the following expression:

Mathematics
1 answer:
Pie3 years ago
5 0

Answer:

U = x + 3 and V = 7

Step-by-step explanation:

Let U = x + 3 and V = 7, then:

=> (x + 3)^2 + 14(x + 3) + 49

= (x + 3)^2 + 2*7*(x + 3) + 7^2

= U^2 + 2UV + V^2

= (U + V)^2

(correct)

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Zanzabum

Answer:

I have no idea

Step-by-step explanation:

4 0
3 years ago
You are asked to do a study of shelters for abused and battered women to determine the necessary capacity in your city to provid
ohaa [14]

Answer:

Using the normal probability distribution, with a capacity of 350, it is enough for all abused on 90.82% of nights.

274 shelters will be needed.

Step-by-step explanation:

Problems of normally distributed samples are solved using 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.

In this problem, we have that:

\mu = 250, \sigma = 75

If the city’s shelters have a capacity of 350, will that be enough places for abused women on 95% of all nights?

What is the percentile of 350?

This is the pvalue of Z when X = 350.

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

Z = \frac{250 - 150}{75}

Z = 1.33

Z = 1.33 has a pvalue of 0.9082.

Using the normal probability distribution, with a capacity of 350, it is enough for all abused on 90.82% of nights.

If not, what number of shelter openings will be needed?

The 95th percentile, which is X when Z = 1.645. So

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

1.645 = \frac{X - 150}{75}

X - 150 = 1.645*75

X = 274

274 shelters will be needed.

5 0
3 years ago
Population lottery numbers: 56, 42, 19, 8, 24, 13 find the total number of samples of size 4 that can be drawn from this populat
statuscvo [17]

Answer:

The correct answer is there are 15 samples each of size 4 to choose from the population and the population mean is 27.

Step-by-step explanation:

Total number of lottery tickets = 6

Number of samples of size 4 that can be drawn from this population of 6 lottery numbers are = \left[\begin{array}{ccc}6\\4\end{array}\right] = 15.

Now the population mean is given by \frac{1}{n} × ∑ x , where n is the number of lottery tickets and ∑ x  is the sum of the lottery numbers.

Summation of the lottery ticket numbers is 162

Thus the population mean is given by \frac{162}{6} = 27.

8 0
3 years ago
How do u know if a like is linear?
Sever21 [200]

Answer:

Step-by-step explanation:

Linear means strait but what are you asking ?

7 0
3 years ago
Simplify completely quantity 4 x squared minus 32 x plus 48 all over quantity 3 x squared minus 17 x minus 6. (1 point)
Galina-37 [17]

Given rational expression is:


\frac{(4x^2-32x+48)}{(3x^2-17x-6)}

Now we can simplify this by factoring as shown below:


=\frac{4(x^2-8x+12)}{(3x^2-17x-6)}


=\frac{4(x-2)\left(x-6\right)}{(3x^2-18x+1x-6)}


=\frac{4(x-2)\left(x-6\right)}{3x\left(x-6\right)+1\left(x-6\right)}


=\frac{4(x-2)\left(x-6\right)}{(3x+1)\left(x-6\right)}


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



Hence final answer is \frac{4(x-2)}{(3x+1)}




8 0
3 years ago
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