Answer:
You need the combinations formula:
Combinations = n! / (r! * (n-r)!)
where n = total # of choices (8) and r = # of choices (4)
Combinations = 8 * 7 * 6 * 5 * 4! / (4! * 4 * 3 * 2 * 1)
Combinations = 8 * 7 * 6 * 5 / 4 * 3 * 2 * 1
Combinations = 7 * 2 * 5
Combinations = 70
Step-by-step explanation:
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There are 57 variations that are above and then times that by 9 because the various will never repeat the same number like when you move onto 2's you'd replace all the 2 with 1's and so on and so forth
The answer is 513 variations
Step-by-step explanation:
a2 = a1×r
a3 = a1×r²
a1×r + a1×r² = 6×a4 = 6×a1×r³
1.
r + r² = 6r³
6r³ - r² - r = 0
r×(6r² - r - 1) = 0
the first solution is obvious : r = 0.
but this is no useful ratio for a geometric sequence.
the other 2 solutions are in
6r² - r - 1 = 0
the general solutions for a quadratic equation are
(-b ± sqrt(b² - 4ac))/(2a)
in our case
a = 6
b = -1
c = -1
so,
(1 ± sqrt(1 - 4×6×-1))/12
r = (1 ± sqrt(25))/12
r = (1 ± 5)/12
r1 = (1+5)/12 = 6/12 = 1/2
r2 = (1-5)/12 = -4/12 = -1/3
2.
we can ignore r2 (negative) and just focus on r1 (1/2).
the second term is 8. that means
a2 = 8 = a1×r = a1×1/2
a1 = 2×a2 = 16
so, we have
a1 = 16
a2 = 8
a3 = a2×1/2 = 8×1/2 = 4
a4 = a3×1/2 = 4×1/2 = 2
a5 = a4×1/2 = 2×1/2 = 1
a6 = a5×1/2 = 1×1/2 = 1/2
a7 = a6×1/2 = 1/2 × 1/2 = 1/4
Answer: -4
Step-by-step explanation:
Answer:
Jane is a liar. :)
Jane is incorrect. John has the greater amount of money.
Step-by-step explanation:
5 nickels (5 cents) = 25 cents
3 dimes (10 cents) = 30 cents