2/9 • 3/4 • 2/5 = 1/15
1/15 of of the students are girl sopranos in chorus.
Answer:
6; 22; 20 (ft.)
Step-by-step explanation:
1) if the length of the each side are: n; 4n-2 and 4n-4, then the expression of the perimeter can be written: P=n+4n-2+4n-4 or P=9n-6.
2) if according to the condition perimeter is 48 (ft.), then
9n-6=P; ⇔ 9n-6=48; n=6.
3) if n=6, then the required lengths of the sides are:
n=6 (ft.);
4n-2=22 (ft.);
4n-4=20 (ft.)
Answer:
The probability is 0.503
Step-by-step explanation:
If the ghost appearances occur in the house according to a Poisson process with mean m, the time between appearances follows a exponential distribution with mean 1/m. so, the probability that the next ghost appearance happens before x hours is equal to:
Then, replacing m by 1.4 ghosts per hour we get:
Additionally, The exponential distribution have a memoryless property, so if it is now 1:00 p.m. and we want the probability that ghost appear before 1:30 p.m., we need to find the difference in hours from 1:00 p.m and 1:30 p.m. no matter that the last ghost appearance was at 12:35 p.m.
Therefore, there are 0.5 hours between 1:00 p.m. and 1:30 p.m, so the probability that the 7th ghost will appear before 1:30 p.m is calculated as:
4. To solve this problem, we must simply subtract the volume of the smaller box from the volume of the larger box. The formula for volume of a rectangular prism is length * width * height. So we know that the bigger box has a height of 20 inches, a length of 15 inches, and a height of 9 inches. We can multiply these together to get the volume.
20 * 15 = 300
300 * 9 = 2700
The bigger box has a volume of 2,700 cubic inches.
Now for the smaller box. This box has a length of 12 inches, a width of 8 inches, and a height of 4 inches. Let us multiply this together:
12 * 8 = 96
96 * 4 = 384
The smaller box has a volume of 384 cubic inches.
Now, we just need to subtract.
2700 - 384 = 2316
There are 2,316 cubic inches of space left in Jeff's bigger box.
5. Mrs. Nelson has plans for a flower box that has two constant side lengths, the length and height (5 feet and 2 feet). The width can be any whole number (counting number) only up to 5 feet, so there are 5 different volumes she could have. Those are:
5 * 2 * 1 = 10 cubic feet
5 * 2 * 2 = 20 cubic feet
5 * 2 * 3 = 30 cubic feet
5 * 2 * 4 = 40 cubic feet
and
5 * 2 * 5 = 50 cubic feet
The possible volumes for Mrs. Nelson's flower box are 10, 20, 30, 40, and 50 cubic feet.
So there you have it!
Hope that helped! =)
