All categories

2 years ago

Simplify the exponential problem 7b^5/b^4

Mathematics

2 answers:

fredd [130]2 years ago

6 0

7b is the simplified answer

Norma-Jean [14]2 years ago

5 0

Solution:

If the numerator and the denominator have like bases in exponents, then the exponents subtract.

$\frac{7b^5}{b^4} = 7b^5^{-4}$
=> $7b$

Thus, 7b is the simplified expression.

You might be interested in

Tim installs 50 square feet of his floor in 45 minutes. At this rate, how long does it take him to install 495 square feet?

77julia77 [94]

Answer:

99.5 minutes

Step-by-step explanation:

50=45

495=?

495×45÷50=99.5

6 0

3 years ago

Read 2 more answers

Twenty years ago, you began investing $3,000 a year. Because your investments earned an average of 8 percent a year, your invest

Ulleksa [173]

Answer:

$32,000

Step-by-step explanation:

Yearly investment = $3,000

Number of years = 20

Investments earned an average of 8 percent a year.

Total invested amount = $3,000 × 20 = $60,000

Current value of investment = $92,000.

We need to find the total earnings on the investment.

Earnings = Current value of investment - Total invested amount

Earnings = $92,000 - $60,000

Earnings = $32,000

Therefore, the total earnings is $32,000.

6 0

3 years ago

Michmoo Computer Company sells computers and computer parts by mail. The company assures its customers that products are mailed

Anastaziya [24]

Answer: (60.858, 69.142)

Step-by-step explanation:

The formula to find the confidence interval for mean :

$\overline{x}\pm z_c\dfrac{\sigma}{\sqrt{n}}$ , where $\overline{x}$ is the sample mean , $\sigma$ is the population standard deviation , n is the sample size and $z_c$ is the two-tailed test value for z.

Let x represents the time taken to mail products for all orders received at the office of this company.

As per given , we have

Confidence level : 95%

n= 62

sample mean : $\overline{x}=65$ hours

Population standard deviation : $\sigma=18$ hours

z-value for 93% confidence interval: $z_c=1.8119$ [using z-value table]

Now, 93% confidence the mean time taken to mail products for all orders received at the office of this company :-

$65\pm (1.8119)\dfrac{18}{\sqrt{62}}\\\\ 65\pm4.142\\\\=(65-4.142,\ 65+4.142)\\\\= (60.858,\ 69.142)$

Thus , 93% confidence the mean time taken to mail products for all orders received at the office of this company : (60.858, 69.142)

8 0

3 years ago

Mathematically verify the outlier(s) in the data set using the 1.5 rule.

statuscvo [17]

Given:

The data values are:

7, 8, 11, 13, 14, 14, 14, 15, 16, 16, 18, 19

To find:

The outliers of the given data set.

Solution:

We have,

7, 8, 11, 13, 14, 14, 14, 15, 16, 16, 18, 19

Divide the data set in two equal parts.

(7, 8, 11, 13, 14, 14), (14, 15, 16, 16, 18, 19)

Divide each parenthesis in two equal parts.

(7, 8, 11), (13, 14, 14), (14, 15, 16), (16, 18, 19)

Now,

$Q_1=\dfrac{11+13}{2}$

$Q_1=\dfrac{24}{2}$

$Q_1=12$

And

$Q_3=\dfrac{16+16}{2}$

$Q_3=\dfrac{32}{2}$

$Q_3=16$

The interquartile range is:

$IQR=Q_3-Q_1$

$IQR=16-12$

$IQR=4$

The data values lies outside the interval $[Q_1-1.5IQR,Q_3+1.5IQR]$ are known as outliers.

$[Q_1-1.5IQR,Q_3+1.5IQR]=[12-1.5(4),16+1.5(4)]$

$[Q_1-1.5IQR,Q_3+1.5IQR]=[12-6,16+6]$

$[Q_1-1.5IQR,Q_3+1.5IQR]=[6,22]$

All the data values lie in the interval [6,22]. So, there are no outliers.

Hence, the correct option is 4.

3 0

3 years ago

If f(x) = 5x − 3, which expression represents its inverse function?

tangare [24]

Answer:

$f ^{-1}(x)=\frac{x+3}{5}$

Step-by-step explanation:

To find the inverse of a function f (x) follow the steps below:

1) Make y = f (x)

$y= 5x - 3$

2) Solve for the variable x

$y+3= 5x - 3+3$

$y+3= 5x$

$x=\frac{y+3}{5}$

3) Exchange the variable x with the variable y

$y=\frac{x+3}{5}$

4) Make $y = f ^{-1}(x)$

$f ^{-1}(x)=\frac{x+3}{5}$

Finally, the inverse of the function f (x) is: $f ^{-1}(x)=\frac{x+3}{5}$

5 0

3 years ago