let's notice something, we have a circle with a radius of 12 and one 90° sector is cut off, so only three 90° sectors of the circle are left shaded, so namely the cone will be using 3/4 of that circle.
think of it as, this shaded area is some piece of paper, and you need to pull it upwards and have the cutoff edges meet, and when that happens, you'll end up with a cone-shaped paper cup, and pour in some punch.
now, once we have pulled up the center of the circle to make our paper cup, there will be a circular base, its diameter not going to be 24, it'll be less, but whatever that base is, we know that is going to have the same circumference as those in the shaded area. Well, what is the circumference of that shaded area?
![\bf \textit{circumference of a circle}\\\\ C=2\pi r~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=12 \end{cases}\implies C=2\pi 12\implies C=24\pi \implies \stackrel{\textit{three quarters of it}}{24\pi \cdot \cfrac{3}{4}} \\\\\\ 6\pi \cdot 3\implies 18\pi](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Bcircumference%20of%20a%20circle%7D%5C%5C%5C%5C%20C%3D2%5Cpi%20r~~%20%5Cbegin%7Bcases%7D%20r%3Dradius%5C%5C%5B-0.5em%5D%20%5Chrulefill%5C%5C%20r%3D12%20%5Cend%7Bcases%7D%5Cimplies%20C%3D2%5Cpi%2012%5Cimplies%20C%3D24%5Cpi%20%5Cimplies%20%5Cstackrel%7B%5Ctextit%7Bthree%20quarters%20of%20it%7D%7D%7B24%5Cpi%20%5Ccdot%20%5Ccfrac%7B3%7D%7B4%7D%7D%20%5C%5C%5C%5C%5C%5C%206%5Cpi%20%5Ccdot%203%5Cimplies%2018%5Cpi)
well then, the circumference of that circle at the bottom will be 18π, so, what is the diameter of a circle with a circumferenc of 18π?
![\bf \textit{circumference of a circle}\\\\ C=2\pi r~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ C=18\pi \end{cases}\implies 18\pi =2\pi r\implies \cfrac{18\pi }{2\pi }=r\implies 9=r \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \stackrel{\textit{diameter is twice the radius}}{d=18}~\hfill](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Bcircumference%20of%20a%20circle%7D%5C%5C%5C%5C%20C%3D2%5Cpi%20r~~%20%5Cbegin%7Bcases%7D%20r%3Dradius%5C%5C%5B-0.5em%5D%20%5Chrulefill%5C%5C%20C%3D18%5Cpi%20%5Cend%7Bcases%7D%5Cimplies%2018%5Cpi%20%3D2%5Cpi%20r%5Cimplies%20%5Ccfrac%7B18%5Cpi%20%7D%7B2%5Cpi%20%7D%3Dr%5Cimplies%209%3Dr%20%5C%5C%5C%5C%5B-0.35em%5D%20%5Crule%7B34em%7D%7B0.25pt%7D%5C%5C%5C%5C%20~%5Chfill%20%5Cstackrel%7B%5Ctextit%7Bdiameter%20is%20twice%20the%20radius%7D%7D%7Bd%3D18%7D~%5Chfill)
Step-by-step explanation:
It is parallel to the third side and has a length equal to half the length of the third side.
so
x= 34/2= 17
x= 17
Answer:
y = 3x - 4
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (0, - 4) and (x₂, y₂ ) = (2, 2) ← 2 points on the line
m = 
= 
= 3
Note the line crosses the y- axis at (0, - 4) ⇒ c = - 4
y = 3x - 4 ← equation of line
Answer:
Volume= 216 cubic yards
Surface area: 276 square yards
Step-by-step explanation:
Find volume of rectangular prism:
V= lxwxh
V= 3x18x4
= 216 cubic yards
Find surface area:
SA= 2 x (front/back area) + 2 x (right/left area) and 2 x ( bottom/top area)
Front and Back Area:
A= l x w
A = 18 x 3
= 54 square yards
Right/ left Area:
4 x 3
= 12 square yards
Top/ Bottom Area:
18 x 4
= 72 square yards
54^2+12^2+72^2
= 108+24+144
=276 square yards
Answer:
I’m pretty sure it’s B)- Z
Step-by-step explanation:
18. The correct table must display the following information.
38% prefer turkey with mayonnaise 20% prefer turkey with mustard 24% prefer ham with mayonnaise 18% prefer ham with mustard
In tables Z and W, each table totals 50 people.
To find the relative frequencies of the data in these tables, divide each number in the table by 50.
In tables X and Y, each table totals 100 people.
To find the relative frequencies of the data in these tables, divide each number in the table by 100.
The only table which is a possible representation of the data collected is table Z.
Likes Baseball
Does Not Like Baseball
Total
Likes Football Does Not Total Like Football
0.50 0.64 0.54
0.50 0.36 0.46 1.00 1.00 1.00
Mayonnaise Mustard
Total
Turkey
19 ÷ 50 = 0.38
10 ÷ 50 = 0.20
29 ÷ 50 = 0.58
Ham
12 ÷ 50 = 0.24
9 ÷ 50 = 0.18
21 ÷ 50 = 0.42
Total
31 ÷ 50 = 0.62
19 ÷ 50 = 0.38
50 ÷ 50 =1.00
