Answer:
b = 15°
Step-by-step explanation:
The base angles (c = ∠QRP) of ΔQPR are such that the sum of angles of the triangle is 180°. Since the triangle isosceles, the base angles are equal:
2c +60 = 180
2c = 120
c = 60 . . . . . . degrees; the base angle of ΔQPR
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Likewise, the base angle (∠SRP) of ΔSPR is ...
a = (180 -90)/2 = 45 . . . . . degrees
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The measure of angle b is the difference between the larger and smaller base angles:
b = c -a = 60° -45°
b = 15°
Answer:
8/11.
Step-by-step explanation:
There are a total of 11 balls.
At least one of those picked is green means that 1 or 2 green balls are picked in the two trials.
Prob (First one picked is green) = 5/11.
Prob( second one picked is green) = 4/10 = 2/5.
Therefore Prob ( Green then green) = 5/11 * 2/5 = 10/55 = 2/11.
The other possibilities are Green then Yellow OR Yellow then Green.
The probabilities of these are worked out as above and come to
5/11 * 6/10 and 6/11 * 5/10
= 300/110 and 30/110
= 3/11 and 3/11.
Finally the Prob ( 2G OR G&Y OR Y&G) = 2/11 + 3/11 + 3/11
= 8/11.
I just realised there is an easier way to do this. Much less work.
The only other thing that can happen other than ' at least one green' is '2 yellows' so the required probability is
1 - prob(2 yellows)
= 1 - (6/11 * 5/10)
= 1 - 30 /110)
= 1 - 3/11
= 8/11.
But never mind. I hope the above is instructive and helps you understand.
I think that the answer would be -3/5 because when you turn 1/3 into 2/6, you can do 2/6 - 5/6 which is -3/6 or -1/2. To divide, you would flip the reciprocal and do 6/5 multiplied by -1/2, which is -6/10, or -3/5.
Its B..............,,,,,,,,..........
By the product rule,
By the power and chain rules,
When , the first and last term vanish, and we're left with