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lesya692 [45]
3 years ago
15

Angle C is an inscribed angle of circle P. Angle C measures (5x – 7)° and arc AB measures (2x)° . Find x.

Mathematics
1 answer:
cluponka [151]3 years ago
7 0

m∠C = (1/2)(m arc AB), because ∠C is an inscribed angle.

(5x-7) = (1/2)(2x)

5x-7 =x

4x = 7

x= 7/4 or 1.75

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Complete answer:

Fulfill the requirements for a certain degree, a student can choose to take any 7 out of a list of 20 courses, with the constraint that at least 1 of the 7 courses must be a statistics course. Suppose that 5 of the 20 courses are statistics courses.

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(b) Explain intuitively why the answer to (a) is not \binom{5}{1}\binom{19}{6}

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a) 71085 choices

b) See below

Step-by-step explanation:

a) First we're going to calculate in how many ways you can take 7 courses from a list of 20 without the constraint that at least 1 of the 7 courses must be a statistics course, that's simply a combination of elements without repetition so it's: \binom{20}{7}, but now we should subtract from that all the possibilities when none of the courses chose are a statistic course, that's is \binom{15}{7} because 15 courses are not statistics and 7 are the ways to arrange them. So finally, the choices for which 7 courses to take with the constraint that at least 1 of the 7 courses must be a statistics course are:

\binom{20}{7}-\binom{15}{7}=71085

b) It's important to note that the constraint at least 1 of the 7 courses must be a statistics course make the possible events dependent, we can not only fix an statistic course and choose the others willingly ( that is what \binom{5}{1}\binom{19}{6} means) because the selection of one course affect the other choices.

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