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.
Answer:
0.25 or 1/4
Step-by-step explanation:
2 negatives equal a positive
Answer:
monthly payment is $377
C is the correct option.
Step-by-step explanation:
The formula for the monthly payment is given by
Given that,
P = $20,000
n = 5 years = 60 months
r = 0.05
Substituting these values in the formula
On simplifying, we get
Therefore, the monthly payment is $377
C is the correct option.
Answer: 0.046
Step-by-step explanation:
From the question,
orange jelly beans= 7
Cherry jelly beans =9
Lemon jelly beans = 3
Licorice jelly beans = 15
Blueberry jelly beans = 6
Total jelly beans = 40
The probability of choosing the first cherry jelly beans will be = 9/40
After the first one is chosen, there'll be 8 cherry jelly beans and total of 39 left. The probability of choosing the second one will be = 8/39
The probability of choosing two cherry jelly beans in a row will be:
= 9/40 × 8/39
= 72/1560
= 0.046
