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algol [13]
3 years ago
12

Complete the factorization of 3x ^ 2 - 10x + 8 3x^ 2 -10x+8=(x- Box x-4)

Mathematics
1 answer:
aniked [119]3 years ago
5 0

Answer:

3x^2-10x+8=(x-x_1)(x-x_2)=(x-2)(x-\frac{4}{3})

Step-by-step explanation:

The general form of a quadratic polynomial is given by:

ax^2+bx+c    (1)

You have the following polynomial:

3x^2-10x+8    (2)

In order to complete the factorization you can use the quadratic formula, to obtain the roost of the polynomial. The quadratic formula is given by:

x_{1,2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}    (3)

By comparing the equation (1) with the equation (2) you obtain:

a = 3

b = -10

c = 8

Then, you replace these values in the equation (3):

x_{1,2}=\frac{-(-10)\pm \sqrt{(-10)^2-4(3)(8)}}{2(3)}\\\\x_{1,2}=\frac{10\pm2}{6}\\\\x_1=2\\\\x_2=\frac{4}{3}

Then, the factorization of the polynomial is:

3x^2-10x+8=(x-x_1)(x-x_2)=(x-2)(x-\frac{4}{3})

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<h3>Answer:</h3>
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<h3>Step-by-step explanation:</h3>

Part A

At the end of the year, the value of the computer system is ...

... (beginning value) - 15% · (beginning value) = (beginning value) · (1 - 0.15)

... = 0.85 · (beginning value)

Since the same is true for the next year and the next, the multiplier after x years will be 0.85^x. Then the value after x years is ...

... f(x) = (beginning value) · 0.85^x

The beginning value is given as $3000, so this is ...

... f(x) = 3000·0.85^x

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Part B

For x=4, this is ...

... f(4) = 3000·0.85^4 = 3000·0.52200625 ≈ 1566.02

The value after 4 years is $1566.02.

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A company is manufacturing highway emergency ares. Such ares are sup- posed to burn for an average of 20 minutes. Every hour a s
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Complete question :

A company is manufacturing highway emergency ares. Such ares are sup- posed to burn for an average of 20 minutes. Every hour a sample of ares is collected, and their average burn time is determined. If the manufacturing process is working cor- rectly, there is a 68% chance that the average burn time of the sample will be between 14 minutes and 26 minutes. The quality engineer in charge of the process believes that if 4 of 5 samples fall outside these bounds then this is a signal that the process might not be performing as expected. Each morning the sampling begins anew. Let X denote the number of samples drawn in order to obtain the fourth sample whose average value is outside of the above bounds. Find the probability that for a given morning X = 5, hence there seems to be a problem right away.

Answer:

0.0285

Step-by-step explanation:

We are to find the probability for a given morning that X = 5

From the question, we could see that there is a 68% chance that the average burn time of the sample will be between 14 minutes and 26 minutes and the success of the process is obtained after the fourth or fifth sample.

Thus, r = 4; q = 0.68

The probability average burn time falls outside p will be:

p = 1 - 0.68 = 0.32

The random variable X follows negative binomial distribution.

Therefore,

f(x) = \left[\begin{array}{ccc}x-1\\r-1\end{array}\right] (1-p)^x^-^r) (p)^r

Where, x = 5

r = 4

p = 0.32

Substituting figures in the equation, we have:

P(x=5) = \left[\begin{array}{ccc}5-1\\4-1\end{array}\right] (1-0.32)^5^-^4 (0.32)^4

P(x=5) = \left[\begin{array}{ccc}4\\3\end{array}\right] (0.68)(0.01048576)

= 0.0285

The probability that for a given morning X = 5 is 0.0285

4 0
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