The wording of your question suggests that there were answer choices. Mind sharing them?
The system <span>y=-2x^2 y=x-2 would be best written as:
</span><span>y=-2x^2
y=x-2 If you subst. x-2 for y in the first equation, you'll get:
x-2 = -2x^2, or 2x^2 + x - 2 = 0.
</span>
Answer:
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Explanation:
The figure attached shows the <em>Venn diagram </em>for the given sets.
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<em><u>a) What is the probability that the number chosen is a multiple of 3 given that it is a factor of 24?</u></em>
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From the whole numbers 1 to 15, the multiples of 3 that are factors of 24 are in the intersection of the two sets: 3, 6, and 12.
There are a total of 7 multiples of 24, from 1 to 15.
Then, there are 3 multiples of 3 out of 7 factors of 24, and the probability that the number chosen is a multiple of 3 given that is a factor of 24 is:
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<em><u>b) What is the probability that the number chosen is a factor of 24 given that it is a multiple of 3?</u></em>
The factors of 24 that are multiples of 3 are, again, 3, 6, and 12. Thus, 3 numbers.
The multiples of 3 are 3, 6, 9, 12, and 15: 5 numbers.
Then, the probability that the number chosen is a factor of 24 given that is a multiple of 3 is:
We can let r be the number of food tickets and f be the number of food tickets.
Since Alana can spend at most $40, that means the total of price bought for r and f must be less than or equal to $40. In addition, since Alana buys at least 16 tickets, this also means that the total of r and f is 16. Mathematically, we have these inequalities:
(1) 4r + 2f ≤ 40 and
(2) r + f ≥ 16
Multiplying -2 in (2), we have
4r + 2f ≤ 40
-2r - 2f ≤ 32
Adding both inequalities,
2r ≤ 8
r ≤ 4
Since r must be less than or equal to 4.Thus the answer is <span>A.</span>