John runs 4 miles in 30 minutes. at the same rate, how many miles would he run in 48 minutes?

Use the inequality 18 < -3(4x - 2)<br> Solve the inequality for x. <br> Show your work.

IrinaVladis [17]

Answer:

x > -1

Step-by-step explanation:

Simplify the inequality using the distributive property (multiply the term outside the bracket with each number inside the bracket). Then, isolate 'x' by performing the reverse operations for every number that's on the same side as 'x'. (Reverse operations 'cancel out' a number.)

18 < -3(4x - 2) Expand this to simplify

18 < (-3)(4x) - (-3)(2) Multiply -3 with 4x and -2

18 < -12x + 6 Start isolating 'x'

18 - 6 < -12x + 6 - 6 Subtract 6 from both sides

18 - 6 < -12x '+ 6' is cancelled out on the right side

12 < -12x Subtracted 6 from 18 on the left side

12/-12 < -12x/-12 Divide both sides by -12

12/-12 < x 'x' is isolated. Simplify left side

-1 < x Answer

x > -1 Standard formatting puts variable on the left side

6 0

2 years ago

Determine the sample size needed to construct a 90% confidence interval to estimate the population proportion when p = 0.65 and

WINSTONCH [101]

Answer:

n=170

Step-by-step explanation:

1) Notation and definitions

$n$ random sample taken (variable of interest)

$\hat p=0.65$ estimated proportion.

$p$ true population

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

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

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 $\alpha=1-0.90=0.1$ and $\alpha/2 =0.05$ . And the critical value would be given by: