The question is about sequences

The circle with center O has a minor arc BSA with a length of

tangare [24]

Answer:

D. $\frac{27\pi}{2}$ inches.

Step-by-step explanation:

We have been given that the circle with center O has a minor arc BSA with a length of $3\pi^{2}$ inches. The central angle is 40°.

To find the circumference of circle we will use formula:

$\frac{\text{Central angle}}{2\pi}=\frac{\text{Arc length}}{2\pi r}$ , where $2\pi$ = measure of 360 degrees in radians and $2\pi r$ = circumference of circle.

Let us convert measure of central angle into radians.

$40^{o}=\frac{40*\pi}{180} =\frac{2\pi}{9}$

Upon substituting our given value in the formula we will get,

$\frac{\frac{2\pi}{9}}{2\pi}=\frac{\frac{3\pi}{2}}{2\pi r}$

$\frac{2\pi}{18\pi}=\frac{3\pi}{4\pi r}$

$\frac{1}{9}=\frac{3}{4r}$

Cross multiplying we will get,

$4r=27$

$r=\frac{27}{4}$

Hence, the radius of our circle is 27/4 inches.

Since the circumference of circle is $2\pi r$ . Upon substituting $r=\frac{27}{4}$ we will get,

$2\pi r=2\pi* \frac{27}{4}=\frac{27\pi}{2}$

Therefore, circumference of our given circle will be $\frac{27\pi}{2}$ inches and option D is the correct choice.

6 0

3 years ago

John's parents purchased their first home in the 1980s with a 30-year

slega [8]

Answer:

Option A,$ 1,832.91 is correct

Step-by-step explanation:

The monthly payment can be computed using the below pmt formula i excel shown below:

=pmt(rate,nper,-pv,fv)

rate is the monthly rate on the mortgage which is 17.5%/12=0.014583333

nper is the number of months of payment i.e 30*12=360

pv is the amount of the loan which is $125,000

fv is the total amount of repayment which is unknown

=pmt(0.014583333 ,360,-125000,0)=$ 1,832.91

The correct option is A,$ 1,832.91 which is the amount of money they need to pay back on the mortgage for 360 months

7 0

3 years ago

Linda can bicycle 48 miles in the same time as it takes her to walk 12 miles. She can ride 9 mph faster than she can walk. How f

Marrrta [24]

Answer:

$\frac{48}{r+9}=\frac{12}{r}$

Step-by-step explanation:

Let r represent Linda's walking rate.

We have been given that Linda can ride 9 mph faster than she can walk, so Linda's bike riding rate would be $t+9$ miles per hour.

$\text{Time}=\frac{\text{Distance}}{\text{Rate}}$

We have been given that Linda can bicycle 48 miles in the same time as it takes her to walk 12 miles.

$\text{Time while riding}=\frac{48}{r+9}$

$\text{Time taken while walking}=\frac{12}{r}$

Since both times are equal, so we will get:

$\frac{48}{r+9}=\frac{12}{r}$

Therefore, the equation $\frac{48}{r+9}=\frac{12}{r}$ can be used to solve the rates for given problem.

Cross multiply:

$48r=12r+108$

$48r-12r=12r-12r+108$

$36r=108$

$\frac{36r}{36}=\frac{108}{36}$

$r=3$

Therefore, Linda's walking at a rate of 3 miles per hour.

Linda's bike riding rate would be $t+9\Rightarrow 3+9=12$ miles per hour.

Therefore, Linda's riding the bike at a rate of 12 miles per hour.

7 0

3 years ago

Sadie has 8 quarts of lemon lime juice and 8 cups of orange juice how many more quarts of lemon lime juice will she use than ora

AnnZ [28]

Answer:

8-2=6 the answer is 6 because there are 4 cps in 1 quart

Step-by-step explanation:

4 0

3 years ago

A sample of 16 ATM transactions shows a mean transaction time of 67 seconds with a standard deviation of 12 seconds. Find the te

vredina [299]

Answer:

b. 2.333

Step-by-step explanation:

Test if the mean transaction time exceeds 60 seconds.

At the null hypothesis, we test if the mean transaction time is of 60 seconds, that is:

$H_0: \mu = 60$

At the alternate hypothesis, we test if it exceeds, that is:

$H_1: \mu > 60$

The test statistic is:

$t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}$

In which X is the sample mean, $\mu$ is the value tested at the null hypothesis, s is the standard deviation of the sample and n is the size of the sample.