Answer:
Yes, your answers are correct.
The volume of a cone is given by V = 1/3πr²h. Since the diameter of the first cone is 4, the radius is 2; therefore the volume is
V = 1/3π(2²)(8) = 32π/3
We divide the volume of the sink, 2000π/3, by the volume of the cone:
2000π/3 ÷ 32π/3 = 2000π/3 × 3/32π = 6000π/96π = 62.5 ≈ 63.
The diameter of the second conical cup is 8, so the radius is 4. The volume then is:
V = 1/3π(4²)(8) = 128π/3
Dividing the volume of the sink, 2000π/3, by 128π/3:
2000π/3 ÷ 128π/3 = 2000π/3 × 3/128π = 6000π/384π = 15.625 ≈ 16
Answer:
The answer is D. 12 children, 147 adults.
Step-by-step explanation:
I solved all of the possibilities and only D was the answer.
A. 16 children, 143 adults = $1,367
B. 6 children, 153 adults = $1,407
C. 9 children, 150 adults = $1,395
D. 12 children, 147 adults = $1,383
So, the answer is D.
Hope this helps! :)
Answer:
Y = 6 I’m pretty sure if its not 6 it’s -6
Step-by-step explanation:
Answer: x = {-1, -3, 2}
<u>Step-by-step explanation:</u>
x³ + 2x² - 5x - 6 = 0
Use the rational root theorem to find the possible roots: ±1, ±2, ±3, ±6
Use Long division, Synthetic division, or plug them into the equation to see which root(s) work <em>(result in a remainder of zero)</em>.
I will use Synthetic division. Let's try x = 1
1 | 1 2 -5 -6
|<u> ↓ 1 3 -2 </u>
1 3 -2 -8 ← remainder ≠ 0 so x = 1 is NOT a root
Let's try x = -1
- 1 | 1 2 -5 -6
|<u> ↓ -1 -1 6 </u>
1 1 -6 0 ← remainder = 0 so x = -1 is a root!
The coefficients of the reduced polynomial are: 1, 1, -6 --> x² + x - 6
Factor: x² + x - 6
(x + 3)(x - 2)
Set those factors equal to zero to solve for x:
x + 3 = 0 --> x = -3
x - 2 = 0 --> x = 2
Using Synthetic Division and Factoring the reduced polynomial, we found
x = -1, -3, and 2
4/10 × 1/6 = 2/30
You can cross cancel 4 and six...then multiply 2/10 × 1/3 which equals 2/30
If you want you can simplify 2/30 to 1/15
