(1) (2) 790 + 172 What is the answer
1 answer:
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Answer:
The cost of six magnets is $1.10
Step-by-step explanation:
The cost of 1 magnet = $ 0.20
Cost of 2 Magnets = $ 0.38
Now, the series of the cost of magnets is:
0.20 , 0.38, 0.56 , 0.74,...
Now, the above series forms an Arithmetic Progression as
0. 38 - 0. 20 = 0.18
and 0. 56 - 0. 38 = 0.18
Hence, the common difference of the series = 0.18
and first term of the series = 0.20
By , A.P a(n) = a + (n-1) d
⇒
or, a(6) = 0.20 + 0.9 = 1.1
or, the sixth term in the sequence is $1.1
Hence, the cost of six magnets is $1.1
Answer:
1) The number of compact fluorescent light bulbs to buy = 120 bulbs
The number of square feet of insulation to be purchased = 2,800 sqft
2) The amount of savings in energy cost per year = $800
Step-by-step explanation:
The cost of each compact fluorescent bulb = $4
The average amount saved by each bulb per year = $ 2
The cost of each square foot of wall insulation = $ 1
The amount saved by each square foot of wall insulation = $ 0.20
The number of light fittings in the mansion = 300 fittings
The area of uninsulated exterior wall of the mansion = 2,800 ft.²
The maximum amount saved in energy cost = $800
1) Let 'x' represent the number of compact fluorescent bulb used and let 'y' represent the number of square feet of insulation purchased
We have;
2·x + 0.2·y ≤ 800
∴ y ≤ 4,000 - 10·x
Total Cost, P = 4·x + y
From the combined graph of the total cost and cost savings, we have the highest total cost is given when the wall insulation area, y is maximum, that is y = 2,800 and x = 120
Therefore, we have;
Total Cost, P = 4·x + y
∴ P = 4 × 120 + 2,800 = 3,280
Therefore, the number of compact fluorescent light bulbs and the number of square feet of insulation to be purchased are 120 bulbs and 2,800 square feet of insulation respectively
2) The amount of savings in energy cost per year, = 2·x + 0.2·y
Where;
x = 120, and y = 2,800
∴ = 2 × 120 + 0.2 × 2,800 = 800
The amount of savings in energy cost per year, = $800