What are the zeros of the function?
1 answer:
You might be interested in
Answer:
See explanation
Step-by-step explanation:
Paul has three cube-shaped boxes. Each box is a different size and they are stacked from the largest to the smallest. Some information about the boxes is given below.
- The combined volume of the three boxes is 1,197 cubic inches.
- The area of one face of the medium box is 49 square inches.
- The volume of the smallest box is 218 cubic inches less than the volume of the medium box.
1. The medium box has the area of one face of 49 square inches, then
is the side length.
The volume of the medium box is
2. The volume of the smallest box is 218 cubic inches less than the volume of the medium box, then the volume of the smallest box is
Ib is the side length, then
The area of one face is
3. The volume of the largest box is
then if c is the side length,
4. The total height of the stack is the sum of all sides lengths:
5. Find the surface area of each box:
- small
- medium
- large
In total, Paul needs
of wrapping paper. He has 1,000 square inches, so Paul has enough paper to wrap all 3 boxes.
Answer:
a) There are 11,881,336 of these words in total.
b) There are 7,893,600 of these words with no repeated letters.
c) 896,376 of these words start with an a or end with a z or both
Step-by-step explanation:
Our words have the following format:
L1 - L2 - L3 - L4 - L5
In which L1 is the first letter, L2 the second letter, etc...
There are 26 letters in the English alphabet.
(a) How many of these words are there total?
Each of L1, L2, L3, L4 and L5 have 26 possible options.
So there are of these words total
(b) How many of these words contain no repeated letters?
The first letter can be any of them, so L1 = 26.
At the second letter, the first one cannot be repeated, so L2 = L1 - 1 = 25.
At the third letter, nor the first nor the second one can be repeated, so L3 = L1 - 2 = 24
This logic applies until L5
So we have
26-25-24-23-22
In total there are
of these words with no repeated letters.
(c) How many of these words start with an a or end with a z or both (repeated letters are allowed)?
is the number of words that start with an a and do not end with z. So we have
1 - 26 - 26 - 26 - 25
The first letter can only be a, and the last one cannot be z. So:
is the number of words that start with any letter other than a and end with z. So we have
25 - 26 - 26 - 25 - 1
The first letter can be any of them, other than a, and the last can only be z. So:
is the number of words that both start with a and end with z. So:
1 - 26 - 26 - 26 - 1
The first letter can only be a, and the last can only be z. The other three letters could be anything. So:
896,376 of these words start with an a or end with a z or both