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3 years ago

What is the greatest common factor of 5x^7+30x^4+10x^4 ?

Mathematics

1 answer:

yan [13]3 years ago

7 0

Answer:

5x^4

Step-by-step explanation:

When you need to find the GCF where there is multiple terms and variables, start by looking at them one at a time and break the terms apart.

GCF of 5, 30, and 10: 5

Factors of 5: 1*5

Factors of 30: 1*30, 2*15, 3*10, 5*6

Factors of 10: 1*10, 2*5

The greatest factor that those numbers all have in common is 5.

GCF of the variables: x^4

(5)x^7: x*x*x*x*x*x*x

(30)x^4: x*x*x*x

(10)x^4: x*x*x*x

The greatest number of x's that those variables have in common is 4.

Therefore, the answer is 5x^4.

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a. The test statistic for this hypothesis would be z=1.71

b. Critical value at α = 0.10: z=1.282

c. Reject H0, the television network should not keep its current lineup.

d. H0: p ≤ 0.50; HA: p > 0.50

Step-by-step explanation:

We have to performa an hypothesis test on a proportion.

The claim is that the proportion of viewers that prefer the new show is bigger than 50% (meaning that most viewers prefer the new show).

The null hypothesis will state that both shows have the same proportion.

Then, the null and alternative hypothesis are:

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Then, the z-statistic can be calculated as:

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The critical value for a right tailed test at a significance level of 0.10 is zc=1.282. This value can be looked up in a standard normal distribution table.

As the statistic is bigger than the critical value, it lies in the rejection region. The null hypothesis is rejected. There is evidence to support the claim that the proportion of viewers which support the new show is larger than 0.50.

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