Answer:
Step-by-step explanation:
Let
be the greater number and
be the smaller number. We know that their difference is 15, so we have
![x-y=15](https://tex.z-dn.net/?f=%20x-y%3D15%20)
Then, we have the following information: if we add twice the greater (2x) and 8 (2x+8), the result is 3 times the lesser (3y) minus four (3y-4). So, we have
![2x+8 = 3y-4 \iff 2x-3y = -12](https://tex.z-dn.net/?f=%202x%2B8%20%3D%203y-4%20%5Ciff%202x-3y%20%3D%20-12%20)
So, we have the follwing system:
![\begin{cases} x-y=15\\2x-3y = -12\end{cases}](https://tex.z-dn.net/?f=%20%5Cbegin%7Bcases%7D%20x-y%3D15%5C%5C2x-3y%20%3D%20-12%5Cend%7Bcases%7D%20)
From the first equation, we can derive
, and substitute this expression in the second equation to get
![2(y+15)-3y = -12 \iff 2y + 30 -3y = -12 \iff -y = -42 \iff y = 42](https://tex.z-dn.net/?f=%202%28y%2B15%29-3y%20%3D%20-12%20%5Ciff%202y%20%2B%2030%20-3y%20%3D%20-12%20%5Ciff%20-y%20%3D%20-42%20%5Ciff%20y%20%3D%2042%20)
Substitute this value for y in the first equation to get
![x-42=15 \iff x=15+42 \iff x = 57](https://tex.z-dn.net/?f=%20x-42%3D15%20%5Ciff%20x%3D15%2B42%20%5Ciff%20x%20%3D%2057%20)
Answers: 0.286
Explanation:
Let E → major in Engineering
Let S → Play club sports
P (E) = 28% = 0.28
P (S) = 18% = 0.18
P (E ∩ S ) = 8% = 0.08
Probability of student plays club sports given majoring in engineering,
P ( S | E ) = P (E ∩ S ) ÷ P (E) = 0.08 ÷ 0.28 = 0.286
Can you please take another picture that is closer to the diagram, it's quite blurry.
Answer:
I think there 1 and 1/2 quarts of lemonade left in the pitcher because in 1 quart there is 4 cups of something. In one gallon there are 4 quarts. So in one gallon there are 16 cups. How I got 16 cups it’s easy (4+4+4+4) . So they drank 5 glasses and each glass is 2 cups. So it will be 10 cups. (2+2+2+2+2). So in one gallon 16 cups they drank 10 cups. 6 cups left. 4 cups one quart and 2 cups is 1/2 of one quart. So the answer is 1 and 1/2 quarts of lemonade. Thank you
Step-by-step explanation: