Write an equation in slope-intercept form for the following line:

What fraction of 1 litre is 10 millilitres

tia_tia [17]

$l-litre\\ml-mililitre\\\\1l=1,000ml\\\\therefore\\\\\frac{1l}{10ml}=\frac{1,000ml}{10ml}=\frac{1,000}{10}=\frac{100}{1}=100\to\boxed{1l=100ml}$

4 0

3 years ago

If the track makes 30 miles in 25 minutes, find the time it will need to cover 25 miles

dimulka [17.4K]

Answer:

About 21 min

Explanation:

Distance and time are directly related, meaning that distance / time = constant.

In this case the constant is the rate or speed.

Thus you can write:

speed = distance / time

And, given that covering 30 miles requires 25 minutes, to calculate the time needed to cover 25 miles, you can set this proportion:

30 miles / 25 min = 25 miles / t

To clear t you do cross multiplication:

t × 30 miles = 25 miles × 25 min

Divide both sides by 30 miles:

t = 25 miles × 25 min / 30 miles = 20.8 min ≈ 21 min ← answer

8 0

3 years ago

A student was asked to find a 90% confidence interval for the proportion of students who take notes using data from a random sam

Scorpion4ik [409]

Answer:

After use the formula we got the following result for the 90% confidence interval (0.13 <p<0.34)

And the conclusion for this case would be:

e. With 90% confidence, the proportion of all students who take notes is between 0.13 and 0.34.

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".

Description in words of the parameter p

$p$ represent the real population proportion of students who take notes

$\hat p$ represent the estimated proportion of students who take notes

n is the sample size required

$z_{\alpha/2}$ represent the critical value for the margin of error

The population proportion have the following distribution

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

Numerical estimate for p

In order to estimate a proportion we use this formula:

$\hat p =\frac{X}{n}$ where X represent the number of people with a characteristic and n the total sample size selected.

Confidence interval

The confidence interval for a proportion is given by this formula

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

For the 90% confidence interval the value of $\alpha=1-0.90=0.1$ and $\alpha/2=0.05$ , with that value we can find the quantile required for the interval in the normal standard distribution.