Answer:
a₅ = 96
Step-by-step explanation:
We know that:
a₁ = 6
aₙ = -2*aₙ₋₁
Then we want to find the value of a₅
We can do it in two ways, we can use the relation to find the terms as:
a₂ = -2*a₁ = -2*6 = -12
a₃ = -2*a₂ = -2*(-12) = 24
a₄ = -2*a₃ = -2*24 = -48
a₅ = -2*a₄ = -2*(-48) = 96
Then we have a₅ = 96
And we know that this is a geometric sequence, where the ratio between terms is -2, then the n-th term can be written as:
aₙ = a₁*r^(n - 1)
where r is the ratio, in this case, r = -2 and a₁ = 6
Then:
aₙ = 6*(-2)^(n -1)
then:
a₅ = 6*(-2)^(5 - 1) = 6*(-2)^4 = 96
She makes 15 bowls every 5 days so the answer whould be 15.
Answer:
24 multi-scented candles
10 single-scented candles
Step-by-step explanation:
There was no question, so I am going to assume that you want to know how many of each type of candles were sold.
Let m = no. of multi-scented candles
s = no. of single-scented candles
(1) m + s = 34 (2) 3m + 2s = 92
s = 34 - m 3m + 2(34 - m) = 92
3m + 68 - 2m = 92
m + 68 = 92
m = 24
s = 34 - 24 = 10
Conversion: 9 1/6 = 9 · 6 + 1
6
= 55
6
Conversion: 6 1/4 = 6 · 4 + 1
4
= 25
4
Add: 55
6
+ 25
4
= 55 · 2
6 · 2
+ 25 · 3
4 · 3
= 110
12
+ 75
12
= 110 + 75
12
= 185
12
The common denominator you can calculate as the least common multiple of the both denominators - LCM(6, 4) = 12
Conversion: 4 5/6 = 4 · 6 + 5
6
= 29
6
Add: 185
12
+ 29
6
= 185
12
+ 29 · 2
6 · 2
= 185
12
+ 58
12
= 185 + 58
12
= 243
12
= 81
4
The common denominator you can calculate as the least common multiple of the both denominators - LCM(12, 6) = 12
Answer:
Step-by-step explanation:
We are given the equation
a) T=6b+2w
T is the total cost
b is the no of bath towels
w is the no of washcloths
so the final equation becomes when T=85
6b+2w=85
b) given budget is $85
6b+2w 
85
the maximum no of bath towels will be when wash clothes will be zero
6b + 2(0) 85
6b 85
b 85/6
b 14.16
that means the maximum no of baths towels we can buy is 14
similarly for the maximum no of wash clothes it will be when bath towels will be zero
6(0) + 2w 85
upon solving we get
w 42.5
That means we can buy at most 42 wash clothes.
c) when w = 20
6b + 2(20) 85
6b 45
b 7.5
That means we can buy 7 bath towels when 20 wash clothes are bought to stay in the budget.
Note: omitting the decimal values because a particular objects can't be bought in decimals.
