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Dennis_Churaev [7]
3 years ago
14

Which of the following is a factor of 2x^4 22x^3 60x^2? 2x^3 x^4 x 4 x 5

Mathematics
1 answer:
zavuch27 [327]3 years ago
8 0
The factor theorem says that for a function f(x), if f(a) = 0, then (x - a) is a factor of f(x).
For f(x) = 2x^4 + 22x^3 + 60x^2
f(-5) = 2(-5)^4 + 22(-5)^3 + 60(-5)^2 = 2(625) + 22(-125) + 60(25) = 1250 - 2750 + 1500 = 0
Therefore, x - (-5) = x + 5 is a factor of f(x).
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chris is 3 years older than jacob. Nathan is 18 years old. two years ago the sum of all their ages was 59 years old how old is j
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           <u>Today</u>          <u>2 years ago</u>

Chris:   x + 3            (x + 3) - 2   = x + 1

Nathan: 18               (18) - 2       = 16

Jacob:   x                (x) - 2          = x - 2

Chris + Nathan + Jacob = sum

x + 1  +     16     +   x - 2   = 59

                            2x - 15 = 59   <em>added like terms (x and x) and (1, 16, and -2)</em>

                                   2x = 74   <em>added 15 to both sides</em>

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A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 419 gram setting. It
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Answer:

We reject the null hypothesis, and accept the alternative hypothesis.

So, it means that the machine is under filling the bags

Step-by-step explanation:

Given

Null Hypothesis

H_0:\mu = 419 --- works correctly at 419g

Alternate Hypothesis

H_0:\mu < 419 --- under fills the bag

n =15 --- the sample

\bar x = 409 --- the mean

\sigma = 22 --- the standard deviation

\alpha = 0.05 --- the significance level

Required

What is the decision rule

Since n is less than 30, we make use of t test

t = \frac{\bar x - \mu}{\sigma/\sqrt n}

t = \frac{409 - 419}{22/\sqrt{15}}

t = \frac{-10}{22/ 3.87}

t = \frac{-10}{5.58}

t = -1.792

Calculate df

df = n-1

df = 15-1

df = 14

Calculate the p value from the Student's t-distribution  at df = 14 and t = -1.792

p =0.047  

Given that: \alpha = 0.05

Since p < \alpha

So, it means that the machine is under filling the bags

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