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2 years ago

The cost of a gym membership is $25 per month. There is an initial fee of $40

Mathematics

2 answers:

Lina20 [59]2 years ago

6 0

Let the total cost of a gym membership be y, with the number of months as x.

The total cost would be 40 dollars, the initial fee, plus 25 times the number of months (x).

y = 40 + 25x

IceJOKER [234]2 years ago

5 0

Answer:

y = 25x + 40

Step-by-step explanation:

Using the formula, y = mx + b we can find out what this equation would be.

m = the rate of change/slope

b = the y- intercept

25 per month is telling us that this is the rate of change.

Since the $40 is only paid once, you can tell that this is the y intercept.

The equation will look like:

y = 25x + 40

On a graph it would look like:

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My brother wants to estimate the proportion of Canadians who own their house.What sample size should be obtained if he wants the

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a) $n=\frac{0.675(1-0.675)}{(\frac{0.02}{1.64})^2}=1475.07$

And rounded up we have that n=1476

b) $n=\frac{0.5(1-0.5)}{(\frac{0.02}{1.64})^2}=1681$

And rounded up we have that n=1681

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{\hat p(1-\hat p)}{n}})$

The margin of error for the proportion interval is given by this formula:

$ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$ (a)

If solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

Part a

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 90% of confidence, our significance level would be given by $\alpha=1-0.9=0.1$ and $\alpha/2 =0.05$ . And the critical value would be given by: