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.
Answer:
X=15
Step-by-step explanation:
Ignore the increase for equasion. This is factored in but irellevent. Orignal x value is 13, but increases to 15, and orignal x value is not needed for this equasion. (its there to confuse you)
L+L+W+W=66.
(w+3) +(w+3) +w +w = 66
(4xw) + 3 +3= 66
4 x w = 66 -3 -3
4 x w =60
60/4= 15.
L= 15+ 3 =18
W = 15.
W + W + L + L
15 + 15 + 18 +18 =66
Answer:
Shift 8 units up
Step-by-step explanation:
The given function is;
f(x)=x
and
g(x)=x+8
The function f(x) has its y-intercept at y=0.
The function g(x)=x+8 has its y-intercept at y=8
This implies that; the linear parent function f(x)=x is shifted up 8 units to obtain g(x)=x+8.
Answer:
Recycling
Step-by-step explanation:
because i see recyling bins everywhere
