Answer:
Part a) 119 cups
Part b) 30 cups
Step-by-step explanation:
Part a)
step 1
Find the volume of the conical cup with a diameter of 4 in. and a height of 8 in
The volume of the cone (cup) is equal to
![V=\frac{1}{3}\pi r^{2}h](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B1%7D%7B3%7D%5Cpi%20r%5E%7B2%7Dh)
we have
----> the radius is half the diameter
![h=8\ in](https://tex.z-dn.net/?f=h%3D8%5C%20in)
assume
![\pi =3.14](https://tex.z-dn.net/?f=%5Cpi%20%3D3.14)
substitute
![V=\frac{1}{3}(3.14)(2^{2})8=33.49\ in^3](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B1%7D%7B3%7D%283.14%29%282%5E%7B2%7D%298%3D33.49%5C%20in%5E3)
step 2
Find out how many cups of water must Carissa scoop out of the sink
Divide the volume of the sink by the volume of the cup
so
![\frac{4,000}{33.49}= 119\ cups](https://tex.z-dn.net/?f=%5Cfrac%7B4%2C000%7D%7B33.49%7D%3D%20119%5C%20cups)
Part b)
step 1
Find the volume of the conical cup with a diameter of 8 in. and a height of 8 in
The volume of the cone (cup) is equal to
![V=\frac{1}{3}\pi r^{2}h](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B1%7D%7B3%7D%5Cpi%20r%5E%7B2%7Dh)
we have
----> the radius is half the diameter
![h=8\ in](https://tex.z-dn.net/?f=h%3D8%5C%20in)
assume
![\pi =3.14](https://tex.z-dn.net/?f=%5Cpi%20%3D3.14)
substitute
![V=\frac{1}{3}(3.14)(4^{2})8=133.97\ in^3](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B1%7D%7B3%7D%283.14%29%284%5E%7B2%7D%298%3D133.97%5C%20in%5E3)
step 2
Find out how many cups of water must Carissa scoop out of the sink
Divide the volume of the sink by the volume of the cup
so
![\frac{4,000}{133.97}= 30\ cups](https://tex.z-dn.net/?f=%5Cfrac%7B4%2C000%7D%7B133.97%7D%3D%2030%5C%20cups)
In an isosceles triangle, the base angles are congruent. The third angle is called the vertex angle.
Here, the vertex angle is <A.
Therefore, m<C = m<B.
m<A = 3m<B + 20
m<A + m<B + m<C = 180
3m<B + 20 + m<B + m<B = 180
5m<B + 20 = 180
5m<B = 160
m<B = 32
m<C = m<B = 32
Answer: m<C = 32 deg
Answer:
he purchased 5 movies bro
Step-by-step explanation:
917 - 67 = 850 (subtract the difference)
850 / 2 = 425 (divide the cost of the washer/dryer)
425 + 67 = 492 (add the difference)
The dryer costs $492.
Answer: Option C.
Step-by-step explanation:
You need to find the distance AB with the formula for calculate the distance between two points:
![d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%28x_2-x_1%29%5E2%2B%28y_2-y_1%29%5E2%7D)
Then, substituting the coordinates of the points A(1,1) and B(4,1), you get:
![AB=\sqrt{(4-1)^2+(1-1)^2}=3](https://tex.z-dn.net/?f=AB%3D%5Csqrt%7B%284-1%29%5E2%2B%281-1%29%5E2%7D%3D3)
You know that A'B'=6, then the scale factor of dilation can be calculated with:
![k=\frac{A'B'}{AB}](https://tex.z-dn.net/?f=k%3D%5Cfrac%7BA%27B%27%7D%7BAB%7D)
Substituting values, you get:
![k=\frac{6}{3}\\\\k=2](https://tex.z-dn.net/?f=k%3D%5Cfrac%7B6%7D%7B3%7D%5C%5C%5C%5Ck%3D2)
This matches with the option C.