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shutvik [7]
3 years ago
15

Jones has a 100-acre farm. he sells it to a developer who is going to build houses. the developer will use 10% of the land for s

treets, sewers, and parks. he will divide the rest of the land into 120 lots. how many square feet will be in each lot?
Mathematics
1 answer:
Sholpan [36]3 years ago
6 0
The first thing we must do is find the amount of land that will be used for the 120 lots.
 We must remember that 10% of the land will not be used for the lots.
 We have then:
 100 - (0.10) * (100) = 100 - 10 = 90 acres.

 Then, we must consider the following conversion of units:
 1 acre = 43560 ft ^ 2

 Applying the conversion we have:
 (90) * (43560) = 3920400 ft ^ 2

 Then, the amount of square feet for each lot is given by:
 3920400/120 = 32670 ft ^ 2

 Answer:
 
There will be 32670 square feet in each lot.
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The perimeter of a rectangular deck measured 130 m. What are the possible
fomenos

Answer:

The possible dimensions of the deck can be anything that adds up to be 130 m.

Step-by-step explanation:

<em>The perimeter could be 1m x 64m.</em>

Two sides would be 1m each (so 2m total) and the other two sides would be 64m each (128m total). 2 + 128 = 130m.

<em>The perimeter could be 15m x 50m.</em>

Two sides would be 15m each (so 30m total) and the other two sides would be 50m each (100m total). 30 + 100 = 130m.

8 0
3 years ago
6.7.37
posledela

Answer:

a. The start-up cost for the teenagers company is $50

b. The number of mugs the teenager must sell to break even are 5 mugs or 25 mugs

c. The number of mugs that will give maximum profit is 15 mugs

d. The profit if she sells 10 mugs is $30

Step-by-step explanation:

The given profit function for selling <em>x</em> number of mugs is presented as follows;

f(x) = -0.4·x² + 12·x - 50

a. The start-up cost in dollars is given by the value of the profit function at the start, where, x = 0, as follows;

Start-up cost = f(0) = -0.4×0² + 12×0 - 50 = -50

The negative sign represents amount put in the business

The start-up cost = (The initial) $50 put into the business.

b. The break even point is the point where, the revenue and costs are equal

At break even point; Revenue = Cost

∴ Profit, at break even point, f(x) = Revenue - Cost = 0

From the profit function, we get;

At the break even point, f(x) = 0 = -0.4·x² + 12·x - 50

Dividing by -0.4 gives;

0/(-0.4) = 0 = (-0.4·x² + 12·x - 50)/(-0.4) = x² - 30 + 125

0 = x² - 30 + 125

∴ (x - 25)·(x - 5) = 0

The number of mugs the teenager must sell before she breaks even, x = 5 mugs or x = 25 mugs.

c. From the general form of a quadratic equation,  which is; y = a··x² + b·x + c, the formula for the x-values at the maximum point is; x = -b/(2·a)

Comparing the profit function to the general form of the quadratic equation we have at the maximum point;

x = -12/(2×(-0.4)) = 15

Therefore, the number of mugs that will give maximum profit, x = 15 mugs.

d. The profit from selling 10 mugs, f(10) is given as follows;

f(10) = -0.4 × 10² + 12 × 10 - 50 = 30

The profit from selling 10 mugs, f(10) = $30

4 0
3 years ago
The volume of a box that is the shape of a cube is 343 in3. What is the perimeter (distance around a figure) of one face (side)?
VLD [36.1K]
A^3=343 in^3
take the cubic root
a=7
Perimeter= 7in+7in+7in+7in=28inch
4 0
3 years ago
1.How much taller Porter is than Henry, given that Porter is n inches tall and Henry is m inches tall. 2.How many times as tall
EleoNora [17]

Answer:

Porter is n-m inches taller than Henry.

Porter is \frac{n}{m} times taller than henry.

Step-by-step explanation:

The difference in height can be found using subtraction.

Since Porter is taller than Henry, we'll subtract away Henry's height from Porter's height. This will leave us with only the difference between the heights.

n = Porter's height

m = Henry's height

Difference in height is thus:

n-m

Answer: Porter is n-m inches taller than Henry.

To find out how many times taller Porter is than Henry, we can use division.

An example: if Porter was 200cm, and Henry was 100cm, Porter is obviously 2 times as tall.

If we divide Porter's height by Henry's height...

\frac{200}{100}=2

..we'll get 2. This is because Henry's height "fits in twice" in Porter's height. 100 fits twice in 200.

Using our values, n and m, we'll divide n by m.

\frac{n}{m}

Answer: Porter is \frac{n}{m} times taller than henry.

3 0
3 years ago
Prove that the product of any two consecutive natural numbers is even.
Vitek1552 [10]

Answer with Step-by-step explanation:

Let us assume the 2 consecutive natural numbers are 'n' and 'n+1'

Thus the product of the 2 numbers is given by

Product=n(n+1)\\\\

We know that the sum of 'n' consecutive natural numbers starting from 1 is

S_n=\frac{n(n+1)}{2}\\\\\therefore n(n+1)=2\times S_n............(i)

Thus from equation 'i' we can write

Product=2\times S_n

As we know that any number multiplied by 2 is even thus we conclude that the product of 2 consecutive numbers is even.

6 0
3 years ago
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