Answer:
He gets 32, $10 bills.
Step-by-step explanation:
He puts in $630.
3 times $50 equals $150.
8 times $20 equals $160.
$150 plus $160 equals $310.
$630 minus $310 equals $320.
$320 divided by 10 equals 32.
So he gets 32, $10 bills.
Answer: 
Step-by-step explanation:
given data:
number of balls = 65.
special black ball that is picked from 10 other balls = numbered 0-9.
<u><em>Solution:</em></u>
<em>probability that a single lottery ticket will match 2 balls and the special black ball.</em>
The area of an equilateral triangle of side "s" is s^2*sqrt(3)/4. So the volume of the slices in your problem is
(x - x^2)^2 * sqrt(3)/4.
Integrating from x = 0 to x = 1, we have
[(1/3)x^3 - (1/2)x^4 + (1/5)x^5]*sqrt(3)/4
= (1/30)*sqrt(3)/4 = sqrt(3)/120 = about 0.0144.
Since this seems quite small, it makes sense to ask what the base area might be...integral from 0 to 1 of (x - x^2) dx = (1/2) - (1/3) = 1/6. Yes, OK, the max height of the triangles occurs where x - x^2 = 1/4, and most of the triangles are quite a bit shorter...
Answer:
C. Triangle BAC is congruent to triangle FDE by AAS
Step-by-step explanation:
BAC names the vertices in the order longest-side, shortest-side. That same order is FDE in the other triangle, eliminating choiced B and D. The triangles are not right triangles, eliminating choice A.
The only viable answer choice is C.
No specific sides are shown as being congruent, but two angles are, so we could claim congruence by ASA or AAS. Answer choice C uses the latter.
Based on lifelike statistics, I would say they got more sleep than about 8-10 hours.
