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Mrac [35]
2 years ago
13

Given the expression: 6x10 − 96x2

Mathematics
1 answer:
Anettt [7]2 years ago
5 0

Step-by-step explanation:

Part A:

I'm going to assume you meant to write 6x^10 - 96x^2. Based off that assumption you can factor out 6 from both equations as well as x^2.

This is going to give you

6x^2(x^8-16). I

Part B:

if you look at the inside, both of the values are perfect squares (if the exponent is even, it's a perfect square). So the equation can further be rewritten using the difference of squares

6x^2(x^4-4)(x^4+4)

If you look at the expression, you'll notice one of the equations can further be rewritten as the difference of squares (x^4 - 4).

6x^2(x^2-2)(x^2+2)(x^4+4)

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D. H0​: p ≤0.36 H1​: p>0.36

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D. Reject H0. There is sufficient evidence to support the hypothesis that the proportion of admissions officers who visit an applying​ students' social networking page has increased in the past year

Step-by-step explanation:

To solve this problem, we run a hypothesis test about the population proportion.

$$Sample proportion: $\bar P=0.47\\Sample size n=100$\\Significance level \alpha=0.10$\\(Left tail test) Z_{1-\alpha}=Z_{0.90}=-1.28155$\\(Right tail test) Z_{\alpha}=Z_{0.1}=1.28155$\\(Two-tailed test) $Z_{1-\alpha/2}=Z_{0.95}=-1.64485$ and $ Z_{\alpha/2}=Z_{0.05}=1.64485\\\\

The appropriate hypothesis system for this situation is:

H_0:\pi_0=0.35\\H_a:\pi_0 > 0.35\\\\$Proportion in the null hypothesis is:\\\pi_0=0.35\\\\

$$The test statistic is $Z=\frac{(\bar P-\pi_0)\sqrt{n}}{\sqrt{\pi_0(1-\pi_0)}}\\$The calculated statistic is Z_c=\frac{(0.47-0.35)\sqrt{100}}{\sqrt{0.35(1-0.35)}}=-0.25516\\p-value = P(Z \geq Z_c)=0.01620\\\\

Since, the calculated statistic Z_c is greater than critical Z_{\alpha}, the null hypothesis should be rejected. There is enough statistical evidence to state that the proportion of admissions officers who visit an applying​ students' social networking page has increased in the past year.

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