Rewrite the expression with the given base. 125^2x with a base of 5

1 answer:

6 0

We should know that
$(a^{m} )^{n} = a^{m*n}$
125 = 5 * 5 * 5

so, the given expression can be rewritten as following 
$125^{2x} = (5*5*5)^{2x} = ( 5^{3} )^{2x} = 5^{3*2x} =5^{6x}$

You might be interested in

How to solve it and step to show how u got it

gulaghasi [49]

Name if a b and c are opposite adjacent or hypotenuse

5 0

3 years ago

A bag of candy contains 300 pieces and 25% of the pieces in the bag are red

taurus [48]

Answer:

75 of them are red

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

The International Air Transport Association surveys business travelers to develop quality ratings for transatlantic gateway airp

motikmotik

Answer:

The 95% confidence interval for the population mean rating is (5.73, 6.95).

Step-by-step explanation:

We start by calculating the mean and standard deviation of the sample:

$M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{50}(6+4+6+. . .+6)\\\\\\M=\dfrac{317}{50}\\\\\\M=6.34\\\\\\s=\sqrt{\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{49}((6-6.34)^2+(4-6.34)^2+(6-6.34)^2+. . . +(6-6.34)^2)}\\\\\\s=\sqrt{\dfrac{229.22}{49}}\\\\\\s=\sqrt{4.68}=2.16\\\\\\$

We have to calculate a 95% confidence interval for the mean.

The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.

The sample mean is M=6.34.

The sample size is N=50.

When σ is not known, s divided by the square root of N is used as an estimate of σM:

$s_M=\dfrac{s}{\sqrt{N}}=\dfrac{2.16}{\sqrt{50}}=\dfrac{2.16}{7.071}=0.305$