Answer:Since the integers are closed under addition, . m C n C 1/ is an integer, and hence the last equation shows that x C y is even. Therefore, we Page 3 Appendix C. Answers for Exercises 539 have proven that if x and y are odd integers, then x C y is an even integer. P1 There exists an integer k m D 2k.
Step-by-step explanation:
The probability that the 10th will be able to sit on his/her original seat when the 1st person has randomly changed his/her seat is 7/9
Probability :
In Mathematics, Probability stands for the ratio of the number of favorable outcomes to the total number of outcomes in a random experiment. It is used to predict how likely an event can happen.
Probability of an event,
P(E) = No of favorable outcomes / total number of outcomes
Here we have,
10 people always get on a bus in the same order and sit in the same places.
The 1st person has randomly changed his/her seat
Except for 1 remaining number of seats is 9
If 1st person changes his/her place with the remaining 9 seats the number of ways that 1st person can be seated is 9
In 9 ways 10th will be able to sit on his/her original seat when the 1st person is seated in 2 to 9 seats i.e 7 seats
Therefore,
The number of favorable outcomes that the 10th person will be able to seat in his/her original seat = 7
From the above observations,
The probability that the 10th will be able to sit on his/her original seat
= 7 / 9
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Answer:
6.5 cm
Step-by-step explanation:
Here, <em>the tangent line squared is equal to the secant line times the secant line outside the circle</em>.
That is <em>20.2² = 14.7 * (14.7 + 2x)</em> --> it is 2x because the secant goes through <em>the whole circle</em>.
Simplify: <em>408.04 = 216.09 + 29.4x</em>
Subtract: <em>191.95 = 29.4x</em>
Divide: <em>x = 6.528911565</em> ≈ 6.5 cm
