Assume that lines that appear to be tangent are tangent.

Suppose you have entered an 85-mile biathlon that consists of a run and a bicycle race. during your run, your average velocity

belka [17]

X= number of hours in run
y = number of hours in bike race

9x+29y=85
x+y=5, and y=5-x

Substituting 5-x for y in the first equation, we have 9x+ 29(5-x)=85 and 9x+145-29x=85, then subtracting 145 from both sides to get -20x=-60 and x=3, which is the amount of hours in the running race. Multiply that by 9 miles per hour to get 27 miles

7 0

3 years ago

PLEASE HELP AND LEAVE A SMALL EXPLANATION

Fofino [41]

Answer:

A

Step-by-step explanation:

Because Alternative Exterior angle

4 0

3 years ago

Suppose that a researcher is designing a survey to estimate the proportion of adults in your state who oppose a proposed law tha

irinina [24]

Answer:

$n=\frac{0.5 (1-0.5)}{(\frac{0.02}{1.96})^2}= 2401$

So without prior estimation for the population proportion, using a confidence level of 95% if we want a margin of error about 2% we need al least a sample size of 2401.

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

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

Solution to the problem

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)

The margin of error desired for this case is $ME= \pm 0.02$ equivalent to 2% points

For this case we need to assume a confidence level, let's assume 95%. And since we don't have prior estimation for the population proportion of interest the best value to do an approximation is $\hat p =0.5$

In order to find the critical value we need to take in count that we are finding the margin of error for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical value would be given by:

$z_{\alpha/2}=\pm 1.96$

Now we have all the values needed and if we replace into equation (b) we got:

$n=\frac{0.5 (1-0.5)}{(\frac{0.02}{1.96})^2}= 2401$

So without prior estimation for the population proportion, using a confidence level of 95% if we want a margin of error about 2% we need al least a sample size of 2401.

5 0

4 years ago

Selena can make 5 pancakes in 12 minutes. which equation can be used to find m the number of minutes needed to make 20 pancakes

Tamiku [17]

I hope this helps you

5 0

4 years ago

A population of caribou in a forest grows at a rate of 2% every year. If there are currently 273 caribou, which function represe

Feliz [49]

Answer:

Step-by-step explanation:

D

C (t)= 273 (0.02)t

6 0

3 years ago