X+y+z=92
y=3x
z=2x-10
subsitute
x+3x+2x-10=92
6x-10=92
add 10 to both sdies
6x=102
divide by 6
x=17
subsitute
y=3x
y=3(17)
y=51
z=2x-10
z=2(17)-10
z=34-10
z=24
x=17
y=51
z=24
the numbers are 17,51,24
Answer:
In Exercises 1-15 use mathematical induction to establish the formula for n ≥ 1.
1. 1
2 + 22 + 32 + · · · + n
2 =
n(n + 1)(2n + 1)
6
Proof:
For n = 1, the statement reduces to 12 =
1 · 2 · 3
6
and is obviously true.
Assuming the statement is true for n = k:
1
2 + 22 + 32 + · · · + k
2 =
k(k + 1)(2k + 1)
6
, (1)
we will prove that the statement must be true for n = k + 1:
1
2 + 22 + 32 + · · · + (k + 1)2 =
(k + 1)(k + 2)(2k + 3)
6
. (2)
The left-hand side of (2) can be written as
1
2 + 22 + 32 + · · · + k
2 + (k + 1)2
.
In view of (1), this simplifies to:
87.5 per year put how ever many years since 1975 in as t...2016 would be 41 so 41 times 87.5 equals 3587.5
The answer is -72. I added an attachment below for the steps.
Answer:
Step-by-step explanation:
Let the outcome from the two dice be (x,y) where x is the outcome from the red die and y is the outcome from the green die.
Event A: the red die shows 2
Event B: the numbers add to 5
Event C: at least one of the numbers is 2;
Event D: the numbers do not add to 9;
Therefore: