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1 year ago

If a ∝ b and a = 18 when b = 3, then find a when b = 5.

Mathematics

1 answer:

Elden [556K]1 year ago

4 0

"a ∝ b" means "a is proportional to b", which in turn means there is some constant k such that

a = kb

We're given that a = 18 and b = 3, so that

18 = 3k ⇒ k = 6

Then when b = 5, we would have

a = 6 × 5 = 30

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The Bureau of the Census reports the average commuting time for citizens of both Baltimore, Maryland, and Miami, Florida. To see

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Answer:

$z=\frac{28.5-35.2}{\sqrt{\frac{7.2^2}{40}+\frac{9.1^2}{40}}}}=-3.652$

Now we can calculate the p value since we are conducting a bilateral test the p value would be:

$p_v =2*P(z$

Since the p value is very low we have enough evidence to reject the null hypothesis that the true means are equal at 5% of significance.

Step-by-step explanation:

Information provided

$\bar X_{1}=28.5$ represent the mean for Miami

$\bar X_{2}=35.2$ represent the mean for Baltimore

$\sigma_{1}=7.2$ represent the population standard deviation for Miami

$\sigma_{2}=9.1$ represent the population standard deviation for Baltimore

$n_{1}=40$ sample size selected for Miami

$n_{2}=10$ sample size selected for Baltimore

$\alpha=0.05$ represent the significance level

z would represent the statistic (variable of interest)

$p_v$ represent the p value for the test

Hypothesis to analyze

We want to check if the commiting times are different in the winter for the two cities, so then the system of hypothesis are:

Null hypothesis: $\mu_{1} = \mu_{2}$

Alternative hypothesis: $\mu_{1} \neq \mu_{2}$

Since we know the population deviations the statistic for this case is given by:

$z=\frac{\bar X_{1}-\bar X_{2}}{\sqrt{\frac{\sigma^2_{1}}{n_{1}}+\frac{\sigma^2_{2}}{n_{2}}}}$ (1)

Replacing the info provided we got:

$z=\frac{28.5-35.2}{\sqrt{\frac{7.2^2}{40}+\frac{9.1^2}{40}}}}=-3.652$

Now we can calculate the p value since we are conducting a bilateral test the p value would be:

$p_v =2*P(z$

Since the p value is very low we have enough evidence to reject the null hypothesis that the true means are equal at 5% of significance.

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3 years ago

A town has two sneaker factories, Sneakerheadz and Nukicks. While Nukicks was closed on Sunday, Sneakerheadz made 900 pairs of s

Scilla [17]

Answer:

Sneakerheadz produced 900 pairs on Sunday. And on Monday, they produced shoes at a rate of 300 per hour.

Then the total number of pairs produced is:

S(t) = 900 + 300*t

where t represents the number of hours worked on Monday.

We know that Nuckicks only worked on Monday, and the same amount of time as Sneakerheadz, but at a rate of 480 sneakers per hour.

We can write the total number of pairs as:

N(t) = 480*t

Now we know that Nukcicks produced in Monday the sane number of pairs than Sneakerheadz produced in the two days, then we have that:

S(t) = N(t)

900 + 300*t = 480*t

900 = 480*t - 300*t = 180*t

900/180 = t

5 = t

So the factories operated 5 hours on Monday.

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3 years ago