Answer:
The best approximation for the area of the shaded region is 
Step-by-step explanation:
<u><em>The complete question is</em></u>
The diameter of the larger circle is 12.5 cm. The diameter of the smaller circle is 8.5 cm.
What is the best approximation for the area of the shaded region?
Use 3.14 to approximate pi.
Small circle inside big circle, shaded region outside smaller circle and inside larger circle
we know that
To find out the area of the shaded region subtract the area of the smaller circle from the area of the larger circle
Remember that
The area of the circle is
so
![A=\pi [r_1^{2}-r_2^{2}]](https://tex.z-dn.net/?f=A%3D%5Cpi%20%5Br_1%5E%7B2%7D-r_2%5E%7B2%7D%5D)
where
r_1 is the radius of the larger circle
r_2 is the area of the smaller circle
we have
---> the radius is half the diameter
---> the radius is half the diameter
substitute
![A=3.14[6.25^{2}-4.25^{2}]](https://tex.z-dn.net/?f=A%3D3.14%5B6.25%5E%7B2%7D-4.25%5E%7B2%7D%5D)
let's first off, convert the mixed fractions to improper fractions, and then, let's multiply both sides by the LCD, notice, the LCD will be hmmmm 4, so we'll multiply both sides by 4, to do away with the denominators.
![\bf \stackrel{mixed}{3\frac{1}{2}}\implies \cfrac{3\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{7}{2}}~\hfill \stackrel{mixed}{3\frac{1}{4}}\implies \cfrac{3\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{13}{4}} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \cfrac{7}{2}w+8=\cfrac{13}{4}w+10\implies \stackrel{\textit{multiplying by }\stackrel{LCD}{4}}{4\left( \cfrac{7}{2}w+8 \right)=4\left( \cfrac{13}{4}w+10 \right)} \\\\\\ 14w+32=13w+40\implies w=40-32\implies \boxed{w=8}](https://tex.z-dn.net/?f=%5Cbf%20%5Cstackrel%7Bmixed%7D%7B3%5Cfrac%7B1%7D%7B2%7D%7D%5Cimplies%20%5Ccfrac%7B3%5Ccdot%202%2B1%7D%7B2%7D%5Cimplies%20%5Cstackrel%7Bimproper%7D%7B%5Ccfrac%7B7%7D%7B2%7D%7D~%5Chfill%20%5Cstackrel%7Bmixed%7D%7B3%5Cfrac%7B1%7D%7B4%7D%7D%5Cimplies%20%5Ccfrac%7B3%5Ccdot%204%2B1%7D%7B4%7D%5Cimplies%20%5Cstackrel%7Bimproper%7D%7B%5Ccfrac%7B13%7D%7B4%7D%7D%0A%5C%5C%5C%5C%5B-0.35em%5D%0A%5Crule%7B34em%7D%7B0.25pt%7D%5C%5C%5C%5C%0A%5Ccfrac%7B7%7D%7B2%7Dw%2B8%3D%5Ccfrac%7B13%7D%7B4%7Dw%2B10%5Cimplies%20%5Cstackrel%7B%5Ctextit%7Bmultiplying%20by%20%7D%5Cstackrel%7BLCD%7D%7B4%7D%7D%7B4%5Cleft%28%20%5Ccfrac%7B7%7D%7B2%7Dw%2B8%20%5Cright%29%3D4%5Cleft%28%20%5Ccfrac%7B13%7D%7B4%7Dw%2B10%20%5Cright%29%7D%0A%5C%5C%5C%5C%5C%5C%0A14w%2B32%3D13w%2B40%5Cimplies%20w%3D40-32%5Cimplies%20%5Cboxed%7Bw%3D8%7D)
Answer:
the annual interest rate is 7.583%
Step-by-step explanation:
We are given
Summer has an offer to buy an item with a sticker price of $13,200
so, we have
P=13200
paying $460 a month for 36 months
so, we can find total amount
Let's assume
annual interest is r
total time =36 months
so, total number of years =3
Since, it is compounded monthly
so, n=12
now, we can use formula
now, we can plug values
now, we can solve solve for r
So, the annual interest rate is 7.583%
C.
90 + 2x = 180
Solve that and x is answer
