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Bumek [7]
3 years ago
14

PLEASE GEOMETRY HELP!! FIND THE LENGTH OF ARC PQR. EXPLAIN PLEASE!! BOGUS ANSWERS REPORTED

Mathematics
1 answer:
deff fn [24]3 years ago
8 0

First we need to find the measurement of arc PQ.

And sum of measurement of all arc angles is 360 degree.

Let measurement of arc PQ is x degree.

Therefore, we get

150+73+x+65=360
\\
288+x =360
\\
x =360-288=72

So measurement of arc PQ is 72.

And measurement of arc PQR is the sum of the measurement of arc PQ and QR.

That is

m \ PQR = 72 +65 = 137

measurement of Arc PQR = 137 degree= 2.39 radian

And radius is 6.48 inches

And arc length is the product of radius and central angle in radians .

That is

PQR= 6.48*2.39=15.5 inches

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pantera1 [17]

Answer:

The probability of winning directly is, as you calculated, 8/36, and the probability of losing directly is (1+2+1)/36=4/36.

For the remaining cases, you need to sum over all remaining rolls. Let p be the probability of rolling your initial roll, and q=6/36=1/6 the probability of rolling a 7. Then the probability of rolling your initial roll before rolling a 7 is p/(p+q), and the probability of rolling a 7 before rolling your initial roll is q/(p+q). Thus, taking into account the probability of initially rolling that roll, each roll that doesn't win or lose directly yields a contribution p2/(p+q) to your winning probability.

For p=5/36, that's

(536)25+636=2511⋅36,

and likewise 16/(10⋅36) and 9/(9⋅36) for p=4/36 and p=3/36, respectively. Each of those cases occurs twice (once above 7 and once below), so your overall winning probability is

836+236(2511+1610+99)=244495=12−7990≈12−0.007.

Step-by-step explanation:

Suppose you throw a 4 and let p(4) your winning probability. At your next roll you have a probability 3/36 of winning (you throw a 4), a probability 6/36 of losing (you throw a 7) and a probability 27/36 of repeating the whole process anew (you throw any other number). Then:

p(4)=336+2736p(4),so thatp(4)=13.

Repeat this reasoning for the other outcomes and then compute the total probability of winning as:

ptot=836+336p(4)+436p(5)+…

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