Pemdas helps so first you do Parentheses Exponet multiply divide add and subtract
Part A)
The coin landed on heads 9 times out of 30 flips, so the experimental probability is 9/30, which reduces to 3/10 probability.
Part B)
Theoretically a coin has a 1/2 probability of landing on heads each flip
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32x + 53 = 501
-53 - 53
<u>32x</u> = <u>448</u>
32 32
x = 14
Answer:
P(3) is true since 2(3) - 1 = 5 < 3! = 6.
Step-by-step explanation:
Let P(n) be the proposition that 2n-1 ≤ n!. for n ≥ 3
Basis: P(3) is true since 2(3) - 1 = 5 < 3! = 6.
Inductive Step: Assume P(k) holds, i.e., 2k - 1 ≤ k! for an arbitrary integer k ≥ 3. To show that P(k + 1) holds:
2(k+1) - 1 = 2k + 2 - 1
≤ 2 + k! (by the inductive hypothesis)
= (k + 1)! Therefore,2n-1 ≤ n! holds, for every integer n ≥ 3.
