At a school fair, each student spins the spinner, which is equally likely to land on each of the four sectors. The spinner shows
how many tokens the student wins or loses. What is the expected number of tokens that a student will win on each spin
1 answer:
Answer:
3 tokens.
Step-by-step explanation:
We need the roulette image, therefore we will suppose one that I will leave as an attached image:
The main thing to keep in mind in this case is that the probabilities are the same, therefore you don't have to take that into account, just operate with the values of each sector, therefore the expected value would be:
expected value = profit - loss
expected value = (5 + 5) - (4 + 3)
expected value = 10 - 7 = 3
This means that the number of tokens waiting for the student to earn for each spin is 3 tokens.
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Answer:
- 168.25 ft
- 3.125 s
Step-by-step explanation:
It is almost too easy to let a graphing calculator show you the solution. (See attached)
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You may be expected to use some actual algebra (or even calculus) to find the solution.
If you've spent any time with quadratics, you know the vertex of ax²+bx+c is located at x=-b/(2a). Here, that means the time to get to the highest point is ...
... t = -100/(2·(-16)) = 100/32 = 3.125 . . . . seconds
Then the highest point is ...
... h(3.125) = -16·3.125² +100·3.125 +12 = 168.25 . . . . feet
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Or, you can put the equation into vertex form.
... h(t) = -16t² +100t +12
... = -16(t² +6.25t) +12
... = -16(t² +6.25t +3.125²) +12 +16·3.125² . . . . . add the square of half the t coefficient inside parentheses; add the opposite of the same amount outside parentheses
... = -16(t +3.125)² +168.25 . . . . . simplify
This tells us the peak of the travel of the bullet is at 168.25 ft after 3.125 seconds.
