5y(2x-1)=y(x+2)+20, x=3
2 answers:
5y(2x-1)=y(x+2)+20, x=3
Step 1: Substitute x with 3
5y(2(3) - 1) = y(3 + 2) + 20
Step 2: Combine like terms in the parentheses
5y(6 - 1) = y(3 + 2) + 20
5y(5) = y(3 + 2) + 20
5y(5) = y(5) + 20
Step 2: Distribute the number outside the parentheses to the numbers inside the parentheses
25y = 5y + 20
Step 3: Combine like terms by subtracting 5y to both sides
25y-5y = (5y-5y) + 20
20y = 20
Step 4: Divide 20 to both sides to isolate y
y = 1
Check:
5(1) (2(3) - 1) = 1(3+2) + 20
5(6-1) = 1(5) + 20
5(5) = 5 + 20
25 = 25
Hope this helped!
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Answer: a) P = 0.5, b) P = 0.07
Step-by-step explanation:
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Lets call X₁ the time at which you arrive, and X₂ the time at which Bob arrives. Both are random variables with uniform density in the interval [0, 60] (in minutes). Their joint distribuition is uniform over the square in the image, with value P = 1/(60*60) = 1/3600.
a) For you to get more cake than Bob, you should arrive earlier. This event is A = { X₁ < X₂ }, the shaded triangle in the figure.The area of this event (set) is half the total area of the square, so P(A) = 0.5.
It makes sense, beacuse its equally probable for you or Bob to arrive earlier, as both have uniform density over the time interval.
b) In this case you arrive later than Bob, but less than 5 minutes later. So the event is B = { X₂ < X₁ < (X₂ + 5) } . This is the gray shaded area in b) part of the image. Its area is the difference two triangles (half square - blue triangle), then the probability is:
