1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
elixir [45]
3 years ago
10

Which expression is equivalent to (5x^3)(2x)^3

Mathematics
2 answers:
Whitepunk [10]3 years ago
4 0

For this case we have the following expression:

5x ^ 3 * (2x) ^ 3

Rewriting we have:

5x ^ 3 * (2x * 2x * 2x) =\\5x ^ 3 * 8x ^ 3 =

For properties of multiplication of power of the same base we have that:

a ^ m * a ^ n = a ^ {m + n}

So:

5x ^ 3 *8x ^ 3 = 40x ^ 6

Answer:

40x ^ 6

Elanso [62]3 years ago
3 0

Answer:

\large\boxed{(5x^3)(2x)^3=40x^6}

Step-by-step explanation:

(5x^3)(2x)^3\qquad\text{use}\ (ab)^n=a^nb^n\\\\(5x^3)(2^3x^3)=(5x^3)(8x^3)\qquad\text{use commutative law}\\\\=(5\cdot8)(x^3x^3)\qquad\text{use}\ a^na^m=a^{n+m}\\\\=40x^{3+3}=40x^6

You might be interested in
Experian would like to test the hypothesis that the average credit score for an adult in Virginia is different from the average
aliya0001 [1]

Answer:

a. We fail to reject the hypothesis that the average credit score for an adult in Virginia is different from the average credit score for an adult in North Carolina at the significance level of 0.05.

b. The 95% confidence interval for the true difference of means is -2.2468 and 36.2468. There is a probability of 95% that the true difference of means \mu_{1}-\mu_{2} is between -2.2468 and 36.2468. This confidence interval contains the number 0, this is consistent with the results we got in a. Because we fail to reject the hypothesis that the average credit score for an adult in Virginia is different from the average credit score for an adult in North Carolina at the significance level of 0.05.

Step-by-step explanation:

Let \mu_{1}-\mu_{2} be the true difference between the average credit score for an adult in Virginia and the average credit score for an adult in North Carolina. We have the large sample sizes n_{1} = 40 and n_{2} = 35, the unbiased point estimate for \mu_{1}-\mu_{2} is \bar{x}_{1} - \bar{x}_{2}, i.e., 699-682 = 17.

The standard error is given by \sqrt{\frac{\sigma^{2}_{1}}{n_{1}}+\frac{\sigma^{2}_{2}}{n_{2}}}, i.e.,

\sqrt{\frac{(44)^{2}}{40}+\frac{(41)^{2}}{35}} = 9.8198.

a. We want to test H_{0}: \mu_{1}-\mu_{2} = 0 vs H_{1}: \mu_{1}-\mu_{2} \neq 0 (two-tailed alternative). The rejection region is given by RR = {z | z < -1.96 or z > 1.96} where -1.96 and 1.96 are the 2.5th and 97.5th quantiles of the standard normal distribution respectively. The test statistic is Z = \frac{\bar{x}_{1} - \bar{x}_{2}-0}{\sqrt{\frac{\sigma^{2}_{1}}{n_{1}}+\frac{\sigma^{2}_{2}}{n_{2}}}} and the observed value is z_{0} = \frac{17}{9.8198} = 1.7312. Because 1.7312 does not fall inside RR, we fail to reject the null hypothesis.

b. The endpoints for a 95% confidence interval for \mu_{1}-\mu_{2} is given by 17\pm (z_{0.05/2})9.8198, i.e., 17\pm (z_{0.025})9.8198 where z_{0.025} is the 2.5th quantile of the standard normal distribution, i.e., -1.96, so, we have 17-(1.96)(9.8198) and 17+(1.96)(9.8198), i.e., -2.2468 and 36.2468. There is a probability of 95% that the true difference of means \mu_{1}-\mu_{2} is between -2.2468 and 36.2468. This confidence interval contains the number 0, this is consistent with the results we got in a. Because we fail to reject the hypothesis that the average credit score for an adult in Virginia is different from the average credit score for an adult in North Carolina at the significance level of 0.05.

3 0
3 years ago
Bertha and Vernon are competing in a diving competition. Bertha's dive ended -54 m from the starting platform. Vernon's dive end
irinina [24]
.bertha dived 8 times more then vernon 54/8 = 6
8 0
2 years ago
Mr. Gubareff gave his class 15 minutes to read. Sabira read 6 ¼ pages in that time. At what rate, in pages per hour, did Sabira
creativ13 [48]

Answer:

I think its 25 (proceed with caution)

Step-by-step explanation:

15×4=60 so basically 6.25×4=25

6.25 = 6 1/4

4 0
2 years ago
Read 2 more answers
What is the remainder of x^4-6x^3-10x^2+20x+15
sergejj [24]

Answer:

0 - 1

Step-by-step explanation:

U can do by simple division method to get the answer

8 0
3 years ago
Help please
andre [41]
I am pretty sure that it is B
6 0
3 years ago
Other questions:
  • Find the whole. 60% of what is 24
    14·2 answers
  • Forty students are in the science club. Of those, 45% are girls. This percents increases to 56% after new girls join the club. H
    6·1 answer
  • What is the range of the following numbers: 12,8,17,12,15,18,30
    6·2 answers
  • What is the result of multiplication of complex numbers -square root 3. +i and<br> (cos y + i sin )?
    9·1 answer
  • Which of the following is the correct formula that can be used to find the surface area of a prism?
    7·1 answer
  • The National Coffee Association reported that of U.S. adults drink coffee daily. A random sample of U.S. adults is selected. Rou
    7·1 answer
  • If misty has been traveling for 9hours how many miles of the trip does she have remaining
    13·1 answer
  • Suppose a study estimated the population mean for a variable of interest using a ​% confidence interval. If the width of the est
    14·1 answer
  • I really need help ... I need a tutor or someone who’s willing to help me bc I’m struggling in math
    13·1 answer
  • Use cramer's rule of x-3y+z=13,3x+2y-z=1,5x+7y+2z=9​
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!