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natita [175]
3 years ago
7

The value of x varies directly with the value of y, and when x=20, y=18. What is the value of “k”, the constant of proportionali

ty?
Mathematics
1 answer:
stealth61 [152]3 years ago
8 0

Answer:

In this case, y=30 and x=6, so 30=k*5<=> k=30/6=5.

Step-by-step explanation:

The constant of proportionality is the ratio between two directly proportional quantities. Two quantities are directly proportional when they increase and decrease at the same rate. The constant of proportionality k is given by k=y/x where y and x are two quantities that are directly proportional to each other.

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A television network is deciding whether or not to give its newest television show a spot during prime viewing time at night. If
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Answer:

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.

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

Then, the null and alternative hypothesis are:

H_0: \pi\leq0.50\\\\H_a: \pi>0.5

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The standard error of the proportion is:

\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.5*0.5}{827}}= 0.017

Then, the z-statistic can be calculated as:

z=\dfrac{p-\pi-0.5/n}{\sigma_p}=\dfrac{0.53-0.50-0.5/827}{0.017}=\dfrac{ 0.029 }{0.017} =1.706

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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9)2405.364

steps for 7) attached

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