Answer:
6840
Step-by-step explanation:
Here, the order matters (1st, 2nd, and 3rd), so we need to use permutations.
There are 20 people who can get in first place. After that, there are 19 people who can get in second place. Finally, there are 18 people who can get in third place. So:
20 * 19 * 18 = 6840
we know that
A <u>geometric sequence</u> is a sequence of numbers in which the ratio between consecutive terms is constant
so
Let







therefore
The common ratio is equal to 
<u>the answer is</u>
The common ratio is 1.02
The factors of this polynomial would be (x + 4)(x + 2)(x - 1).
To find these, you first have to start with long division to find the first factor. If you use x + 4 it would look like this.
= 
Now we are left with only
. We can factor this by looking for numbers that multiply to the last number and add to the middle number. 2 and -2 multiply to -2 and add to 1. Therefore, we'll use those in parenthesis in their place.
(x + 4)(x + 2)(x - 1)
9514 1404 393
Answer:
- maximum: 15∛5 ≈ 25.6496392002
- minimum: 0
Step-by-step explanation:
The minimum will be found at the ends of the interval, where f(t) = 0.
The maximum is found in the middle of the interval, where f'(t) = 0.
![f(t)=\sqrt[3]{t}(20-t)\\\\f'(t)=\dfrac{20-t}{3\sqrt[3]{t^2}}-\sqrt[3]{t}=\sqrt[3]{t}\left(\dfrac{4(5-t)}{3t}\right)](https://tex.z-dn.net/?f=f%28t%29%3D%5Csqrt%5B3%5D%7Bt%7D%2820-t%29%5C%5C%5C%5Cf%27%28t%29%3D%5Cdfrac%7B20-t%7D%7B3%5Csqrt%5B3%5D%7Bt%5E2%7D%7D-%5Csqrt%5B3%5D%7Bt%7D%3D%5Csqrt%5B3%5D%7Bt%7D%5Cleft%28%5Cdfrac%7B4%285-t%29%7D%7B3t%7D%5Cright%29)
This derivative is zero when the numerator is zero, at t=5. The function is a maximum at that point. The value there is ...
f(5) = (∛5)(20-5) = 15∛5
The absolute maximum on the interval is 15∛5 at t=5.
1 pound = 16 ounces
3 pounds = 3*16 ounces
3 pounds= 48 ounces
So, he can make 48 one-ounce bags