All categories

3 years ago

How do you find the smallest positive integer k such that 1350k is a perfect cube?

1 answer:

3 0

A cube is x*x*x
prime factor 1350
1350*k
5*270*k
5*3*90*k
5*3*3*30*k
5*3*3*3*10*k
5*3*3*3*2*5*k
what value does k have to be to have three of each prime factor?
k = 5*2*2 = 20

Then 1350*20 = 27,000 = (5*3*2)^3

You might be interested in

Please help me

Georgia [21]

Answer:

This may well be you! No matter where you are on the road to being a critical thinker, you can always more fully develop and finely tune your skills. Doing so will help you develop more balanced arguments, express yourself clearly, read critically, and glean important information efficiently.

Step-by-step explanation:

3 0

2 years ago

Find the measure of the indicated angle to the nearest degree.

fredd [130]

Step-by-step explanation:

Let the measure of required angle be x degree

$\therefore \tan \: x = \frac{33}{56} \\ \\ \therefore \tan \: x = 0.589285714 \\ \\ \therefore \: x = {\tan}^{ - 1} (0.589285714) \\ \\ \therefore \: x = {\tan}^{ - 1} ( \tan \: 30.510237394 \degree) \\ \\ \huge \red{ \boxed{\therefore \: x = 31\degree}}$

Thus, first option is the correct answer.

3 0

3 years ago

Enter an equation that gives the cost y of renting a car for x days from Rent-All.

Lelechka [254]

Answer:At the time of rental, an authorized hold will be secured on your credit/debit card provided to cover the estimated rental charges plus an additional $200.00 to cover additional charges that may be incurred.

Step-by-step explanation:

3 0

3 years ago

When 0.5(20x – 50y + 36) – 0.25(–100x + 40y – 12) is simplified, what is the resulting expression?

alisha [4.7K]

0.5(20x - 50y + 36) - 0.25(-100x + 40y - 12)
10x - 25y + 18 + 25x - 10y + 3
35x - 35y + 21

7 0

3 years ago

An article regarding interracial dating and marriage recently appeared in the Washington Post. Of the 1,709 randomly selected ad

VMariaS [17]

Answer:

The 95% confidence interval for the percent of all black adults who would welcome a white person into their families is (0.8222, 0.8978).

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 $1 - \frac{\alpha}{2}$ .

For this problem, we have that:

323 blacks, 86% of blacks said that they would welcome a white person into their families. This means that $n = 323, p = 0.86$

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 $Z = 1.96$ .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.86 - 1.96\sqrt{\frac{0.86*0.14}{323}} = 0.8222$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.86 + 1.96\sqrt{\frac{0.86*0.14}{323}} = 0.8978$

The 95% confidence interval for the percent of all black adults who would welcome a white person into their families is (0.8222, 0.8978).

5 0

3 years ago