Answer:
6 6/7
Explanation:
You want the expected value of a spinner to be 3.5, when it has a 90° section valued at 4, a 60° section valued at -9, and the remaining section valued at x.
Expected value
The expected value of the spinner is the sum of the section values, each multiplied by its probability. The 360° of the spinner have a probability of 1, so the probability of a section is its degree measure divided by 360°.
expected value = 4(90/360) +(-9)(60/360) +x((360 -90 -60)/360)
3.5 = 1 -3/2 +7x/12
42 = -6 +7x . . . . . . . . . multiply by 12
48 = 7x . . . . . . add 6
x = 48/7 = 6 6/7
The value of x so the expected value of the spinner is 3.5 is 6 6/7.
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Additional comment
The unfortunate line break in the problem statement means the problem is a bit ambiguous. We assume the desired expected value is 3.5. If it is 3, then the value of x needs to be 6. (If the expected value is 3, then we don't know the meaning of the "5." on the second line.)