3.2 is the Length of y 7.5 is the length of z and the length of x is 12.5
Answer:
Mrs. Etercsid
Step-by-step explanation:
One thing we can do is just multiply the averages by the percents in each class and compare from there.
To get from percentages to decimals, we can divide by 100.
For Mr. Tats:
Homework: 25 % -> 0.25
Participation: 10% -> 0.1
Test: 40% -> 0.4
Final: 0.25 -> 0.25
For Mrs. Etercsid:
Homework: 15% -> 0.15
Participation: 10% -> 0.1
Test: 60% -> 0.6
Final: 15% -> 0.15
We can then multiply the averages by the decimals for each teacher and add them up.
Mr. Tats:
0.25 * 81 + 0.1 * 57 + 0.4 * 93 + 0.25 * 87 = 84.9
Mrs. Etercsid:
0.15 * 81 + 0.1 * 57 + 0.6 * 93 + 0.15 * 87 = 86.7
You would get the higher grade with Mrs. Etercsid
Answer: a) 3 2/3, b) 5 2/5
Explanation:
a) 5/3 + 6/3 = 11/3 = 3 2/3
b) 12/5 + 15/5 = 27/5 = 5 2/5
Answer:
128
Step-by-step explanation:
Answer and Step-by-step explanation:
(a) Given that x and y is even, we want to prove that xy is also even.
For x and y to be even, x and y have to be a multiple of 2. Let x = 2k and y = 2p where k and p are real numbers. xy = 2k x 2p = 4kp = 2(2kp). The product is a multiple of 2, this means the number is also even. Hence xy is even when x and y are even.
(b) in reality, if an odd number multiplies and odd number, the result is also an odd number. Therefore, the question is wrong. I assume they wanted to ask for the proof that the product is also odd. If that's the case, then this is the proof:
Given that x and y are odd, we want to prove that xy is odd. For x and y to be odd, they have to be multiples of 2 with 1 added to it. Therefore, suppose x = 2k + 1 and y = 2p + 1 then xy = (2k + 1)(2p + 1) = 4kp + 2k + 2p + 1 = 2(kp + k + p) + 1. Let kp + k + p = q, then we have 2q + 1 which is also odd.
(c) Given that x is odd we want to prove that 3x is also odd. Firstly, we've proven above that xy is odd if x and y are odd. 3 is an odd number and we are told that x is odd. Therefore it follows from the second proof that 3x is also odd.
