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andrezito [222]

3 years ago

12

Eight students are painting 2 boards for a project. The students want to divide the work equally. How much of the board should e

ach student paint

1 answer:

barxatty [35]3 years ago

7 0

Each student should do 1/4 of one board or 1/8 of both boards. This is because 8÷2 is 4, which means 4 people need to work together on one board.

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Katrina is building a deck. She cuts 3 lengths of wood from a 72-inch board. The first length is inches. The second length is in

kap26 [50]

Rewriting the question, the given lengths that were cut from the board were 30 3/4 inches, 12 1/4 inches, and 16 1/4 inches. To obtain the remaining length of the board, all of the measurements cut are to be added and subtracted from 72 inches. This is shown below:

30 3/4 + 12 1/4 + 16 1/4 = 237/4 = 59.25 inches.

Remaining length of board = 72 - 59.25 = 12.75 inches.

Therefore, there will be 12.75 inches remaining of the board.

8 0

3 years ago

Read 2 more answers

Which rule best represents the dilation that was

NemiM [27]

Answer:

B

Step-by-step explanation:

Count the units

5 0

2 years ago

Read 2 more answers

N is the set of integers that are greater than - 3 and less than 2.

Schach [20]

The given set is {-1,0,1,2,3,4,5}
(notice the -2 and 6 are excluded)

the subset which contain positive factors of 5 is {1,5}

so the complement set would be
{-1,0,2,3,4) which matches with b)

4 0

3 years ago

A rectangular field with one side along a river is to be fenced. Suppose that no fence is needed along the river, the fence on t

Andreas93 [3]

Answer:

a) Side Parallel to the river: 200 ft

b) Each of the other sides: 400 ft

Step-by-step explanation:

Let L represent side parallel to the river and W represent width of fence.

The required fencing (F) would be $F=L+2W$ .

We have been given that field must contain 80,000 square feet. This means area of field must be equal to 80,000.

$LW=80,000...(1)$

We are told that the fence on the side opposite the river costs $20 per foot, and the fence on the other sides costs $5 per foot, so total cost (C) of fencing would be $C=20L+5(2W)\Rightarrow 20L+10W$ .

From equation (1), we will get:

$L=\frac{80,000}{W}$

Upon substituting this value in cost equation, we will get:

$C=20(\frac{80,000}{W})+10W$

$C=\frac{1600,000}{W}+10W$

$C=1600,000W^{-1}+10W$

To minimize the cost, we need to find critical points of the the derivative of cost function as:

$C'=-1600,000W^{-2}+10$

$-1600,000W^{-2}+10=0$

$-1600,000W^{-2}=-10$

$-\frac{1600,000}{W^2}=-10$

$-10W^2=-1,600,000$

$W^2=160,000$

$\sqrt{W^2}=\pm\sqrt{160,000}$

$W=\pm 400$

Since width cannot be negative, therefore, the width of the fencing would be 400 feet.

Now, we will find the 2nd derivative as:

$C''=-2(-1600,000)W^{-3}$

$C''=3200,000W^{-3}$

$C''=\frac{3200,000}{W^3}$

Now, we will substitute $W=400$ in 2nd derivative as:

$C''(400)=\frac{3200,000}{400^3}=\frac{3200,000}{64000000}=0.05$

Since 2nd derivative is positive at $W=400$ , therefore, width of 400 ft of the fencing will minimize the cost.

Upon substituting $W=400$ in $L=\frac{80,000}{W}$ , we will get:

$L=\frac{80,000}{400}\\\\L=200$

Therefore, the side parallel to the river will be 200 feet.

4 0

3 years ago

Ms. Johnson owns a cabinet business that installs cabinets in kitchens. Her employees can install 2/3 of a kitchen cabinet set i

dmitriy555 [2]

Answer:

I don't know

Step-by-step explanation:

hi

8 0

3 years ago