aliviadushane

14.04.2020 • 

Mathematics

(15 points) You and your brother will play a certain game 900 times. You bet one dollar per game. If you win, you win 5 dollars. If you lose, you lose the dollar. You have a 1 in 8 chance to win. (a) (3 points) On average, what is the net gain OF YOUR FRIEND of playing one game? Round your answer to the nearest cent. Think of this game as YOUR FRIEND picking a ticket from a box of 8 tickets. There is one ticket that will cause him to lose 5 dollars and 7 tickets that will cause him to win 1 dollar. Find the average of this box. (b) (6 points) How much does your friend expect to win/lose in 900 games? What is the standard error? (c) (6 points) Find the probability that your friend will win at least $200 in 900 games.

Ответ:

leah1386

25.06.2022

Mathematics

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The slope of the given line y=-(2/3)x+2
is m1=-2/3
The slope of any line perpendicular to it is m2=-1/m1=3/2

Since it passes through point (6,3) and the slope m2=3/2 is known, we use the point-slope form to define the new line:
y-y1=m(x-x1)   where (x1,y1)=(6,3).
Substituting x1=6, y1=3 into the point slope form,
y-y1=m2(x-x1)
y-3=(3/2)(x-6)
simplify
y=(3/2)x-9+3, =>

y=(3/2)x-6
is the line perpendicular to y=-(2/3)x+2 passing through (6,3)

Check: y=(3/2)6-6=3 ok, and
m1m2=-2/3*(3/2)=-1 ok

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