Mackenzie has enough paint to paint 108 square feet she wants to pay her garage door which has the height of 12 feet the garage
2 answers:
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Answer:
height = 14.5 ft
width = length = 3.2 ft
Step-by-step explanation:
Let the side of the square base is a and the height of the box is h.
The material required to make the box is equal to the total surface area of the box.
Area of base = a²
Cost of square base is $ 2 per ft²
So, the cost of making base = 2a²
Area of four walls + area of top = 2 (a² + ah + ah) + a² = 3a² + 2ah
Cost of making walls and the top is $ 1 per ft²
So, the cost of making walls and the top = 1 x ( 3a² + 2ah)
Total cost of making the box = 2a² + 3a² + 2ah = 5a² + 2ah
According to the question
144 = 5a² + 2ah
.... (1)
The volume of the box is V = length x width x height
V = a x a x h
V = 72 a - 2.5 a³ from equation (1)
Differentiate both sides with respect to a.
dV/da = 72 - 7.5 a²
Put, it equal to zero for maxima and minima
7.5 a² = 72
a = 3.2 ft
Put in equation (1)
h = 14.5 ft
So, the dimensions of the box are
height = 14.5 ft
width = length = 3.2 ft
Answer:
Insufficient data.
Step-by-step explanation:
Given,
Total number of games = 100,
(1) The team won 60% of its first 65 games last season.
So, the number of winning games in 65 games = 60% of 65
But we do not know about the data for last 35 games,
Thus, the data is insufficient.
(2) The team won 60% of its last 65 games last season.
So, the number of winning games in last 65 games = 60% of 65 =39,
Thus, the total winning games = 45 + 45 = 90,
But we do not know about the data for first 35 games,
Thus, the data is insufficient.
When we combined both (1) and (2) statements,
we found that the maximum number of games won by the team = 39 + 39 = 78,
But there is a overlap of 30 games,
i.e. an unknown number will be subtract from 78 to find the exact number of winning games.
Hence, even after combining statements (1) and (2),
The data is insufficient.