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8090 [49]
3 years ago
14

Divide $500 in these ratios using the unitary method. A. 2:3 B. 3:7 C. 1:1

Mathematics
1 answer:
zysi [14]3 years ago
3 0

Answer:

A) 200 is to 300 dollars

B)150 is to 350 dollars

C) 250 is to 250

Step-by-step explanation:

Part A) We want to divide $500 in the ratio 2:3 using the unitary method.

The total ratio is 2+3=5.

This means one unit is \frac{500}{5}=$100

Therefore $500 in the ratio 2:3 is 2*100=200 to 3*100=300

Part B) We want to divide $500 in the ratio 3:7 using the unitary method.

The total ratio is 3+7=10.

This means one unit is \frac{500}{10}=$50

Therefore $500 in the ratio 3:7 is 3*50=150 to 7*50=350

Part C) We want to divide $500 in the ratio 1:1 using the unitary method.

The total ratio is 1+1=2.

This means one unit is \frac{500}{2}=$250

Therefore $500 in the ratio 1:1 is 1*250=250 to 1*250=250

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An open box is to be made from a 3 ft by 8 ft rectangular piece of sheet metal by cutting out squares of equal size from the fou
Burka [1]

Answer:

Maximum volume of the box will be 7.41 cubic feet.

Step-by-step explanation:

Open box has been made from a metal sheet measuring 3 ft and 8 ft.

Let four square pieces were removed from the four corners with one side measurement x ft.

Volume of the open box = Length × width × height

Length of the box = (3 - 2x) ft

Width of the box = (8 - 2x) ft

Height of the box = x ft

Volume of the box = (3 - 2x)(8 - 2x)x

V = (24 - 6x - 16x + 4x²)x

V = 24x - 22x² + 4x³

Now we take the derivative of V with respect to x and equate the derivative to zero,

\frac{d}{dx}(V)=\frac{d}{dx}(24x - 22x^{2}+4x^{3})

V' = 24 - 44x + 12x²

V' = 0

12x² - 44x + 24 = 0

3x² - 11x + 6 = 0

3x² - 9x - 2x + 6 = 0

3x(x - 3) - 2(x - 3) = 0

(3x - 2)(x - 3) = 0

(3x - 2) = 0

and (x - 3) = 0

Therefore, x = 3, \frac{2}{3}

For x = 0.67

Length of the box = (3 - 2x) = 3 - 1.34

                              = 1.66 ft

Width of the box = (8 - 2x) = 8 - 1.34

                            = 6.66 ft

Volume of the box = 0.67 × 1.66 × 6.66

V = 7.41 cubic feet.

Similarly, for x = 3,

Length of the box = (3 - 2\times 3) = -3

which is negative but the length of the box can not be negative.

Therefore, maximum volume of the box will be 7.41 cubic feet.

6 0
3 years ago
Can somebody please help to answer the above question and explain please
Elza [17]
The correct answer is 11.3
7 0
3 years ago
Read 2 more answers
PLEASE HELPP MEE!!!!
Artemon [7]

does the answer help you.

5 0
2 years ago
on one day, 4 plumbers and 5 helpers earned $182. On another day, working the same number of hours and at the same rate of pay,
Elanso [62]
I hope this helps you



4plumbers +5helpers =182

5plumbers +6helpers =224



-24plumbers -30helpers =1092


25plumbers+30helpers =1120



1plumbers =28


4.28+5helpers =182



5helpers =70


1helpers=14
7 0
3 years ago
What are the two representations of the conversion factor used to convert between inches and feet? Select all that apply.
ipn [44]
B and C are the same thing and they would be the two representations of the conversion that shows 12 inches is equivalent to 1 foot, so B and C are your answers
6 0
3 years ago
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