Write the equations included in the same set of related facts as 6×8=48

Jackson buys a grape snow cone on a hot day. By the time he eats all the "snow" off the top, the paper cone is filled with 27\pi

anyanavicka [17]

Question:

Jackson buys a grape snow cone on a hot day. By the time he eats all the "snow" off the top, the paper cone is filled with 27\pi27π27, pi cm^3 3 start superscript, 3, end superscript of melted purple liquid. The radius of the cone is 333 cm. What is the height of the cone?

Answer:

The height of the cone is $9 \ cm$

Explanation:

It is given that the radius of the cone is $3 \ cm$

The volume of the cone is $27\pi$

The height of the cone can be determine using the formula,

$V=\frac{1}{3} \pi r^{2} h$

Substituting the values $V=27 \pi$ and $r=3$ , we get,

$27 \pi=\frac{1}{3} \pi(3)^{2} h$

Multiplying both sides by 3, we have,

$81 \pi= 9\pi h$

Dividing both sides by $9 \pi$ , we have,

$9=h$

Thus, the height of the cone is $9 \ cm$

4 0

3 years ago

In a sample of 70 stores of a certain company, 62 violated a scanner accuracy standard. It has been demonstrated that the condi

uysha [10]

Answer:

We need at least 243 stores.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

The margin of error of the interval is:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

For this problem, we have that:

$n = 70, p = \frac{62}{70} = 0.886$

95% confidence level

So $\alpha = 0.05$ , z is the value of Z that has a pvalue of $1 - \frac{0.05}{2} = 0.975$ , so $Z = 1.96$ .

Determine the number of stores that must be sampled in order to estimate the true proportion to within 0.04 with 95% confidence using the large-sample method.

We need at least n stores.

n is found when M = 0.04. So

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.04 = 1.96\sqrt{\frac{0.886*0.114}}{n}}$