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mrs_skeptik [129]
3 years ago
8

Choose the expression that would equal the number of hours in the following question.

Mathematics
1 answer:
Minchanka [31]3 years ago
5 0
<span>B. 285/302. This is the correct answer because it is the only choice which is roughly the same ratio as 47.5/50.5 which is the ratio needed to determine how long it would take to go 47 1/2 miles in a car that averages 50 1/2 miles per hour. The mathematical equation which represents the problem is: 50.5/1 = 47.5/A (A = hours) which is the same as 50.5 A = 47.5 which means A = 47.5/50.5 which means A = .94 hours. 285/302 also equals .94.</span>
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A jet fighter is capable of reaching speeds up to 1.5 x 10^3 miles per hour. A typical passenger plane can reach speeds of appro
Volgvan

Answer:

3 times faster

Step-by-step explanation:

\frac{1.5(10)^{3} }{5.0(10)^{2}} = \frac{1.5(10)}{5} = \frac{15}{5}  = 3 times faster

5 0
3 years ago
One number is 3 less than a second number. Twice the second number is 12 more than 3 times the first. Find the two numbers.
Verdich [7]
6 and 3, 3 and 6, or 2 and 6
7 0
3 years ago
The length of a rectangular field is 4 m longer than its width.
Artyom0805 [142]
We know the perimeter is the sum of all sides. So lenght+length+width+width = 2length+2width.
Let's call the width x. If the length is 4m longer, then it's x+4.
We know the perimeter, so we can make an equation:
56=2x+2(x+4)
And solve from there:
56=2x+2x+8
56=4x+8
48=4x
48/4=x
x=12

The width, which is x, is 12 m. And the length, x+4, is 16 m.
You can check this is correct by calculating the perimeter using those values: 12+12+16+16=56.
7 0
3 years ago
Which of the following would be equivalent to Use the variable n as the unknown number.
romanna [79]

Answer:

C.

Step-by-step explanation:

"Two more than three times a number is seven"

Add 2 to 3n and set it equal to 7.

8 0
3 years ago
A closed box with a square base is to have a volume of 171 comma 500 cm cubed. The material for the top and bottom of the box co
Zepler [3.9K]

Answer:

C(x)=\dfrac{20x^3+1715000}{x}\\$Minimum cost, C(35)=\$29,400

The dimensions that will lead to minimum cost of the box are a base length of 35 cm and a height of 140 cm.

Step-by-step explanation:

Volume of the Square-Based box=171,500 cubic cm

Let the length of a side of the base=x cm

Volume =x^2h

x^2h=171,500\\h=\dfrac{171500}{x^2}

The material for the top and bottom of the box costs ​$10.00 per square​ centimeter.

Surface Area of the Top and Bottom =2x^2

Therefore, Cost  of the Top and Bottom =\$10X2x^2=20x^2

The material for the sides costs ​$2.50 per square centimeter.

Surface Area of the Sides=4xh

Cost of the sides=$2.50 X 4xh =10xh

\text{Substitute h}$=\dfrac{171500}{x^2} $into 10xh\\Cost of the sides=10x(\dfrac{171500}{x^2})=\dfrac{1715000}{x}

Therefore, total Cost of the box

= 20x^2+\dfrac{1715000}{x}\\C(x)=\dfrac{20x^3+1715000}{x}

To find the minimum total cost, we solve for the critical points of C(x). This is obtained by equating its derivative to zero and solving for x.

C'(x)=\dfrac{40x^3-1715000}{x^2}\\\dfrac{40x^3-1715000}{x^2}=0\\40x^3-1715000=0\\40x^3=1715000\\x^3=1715000\div 40\\x^3=42875\\x=\sqrt[3]{42875}=35

Recall that:

h=\dfrac{171500}{x^2}\\Therefore:\\h=\dfrac{171500}{35^2}=140cm

The dimensions that will lead to minimum costs are base length of 35cm and height of 140cm.

Therefore, the minimum total cost, at x=35cm

C(35)=\dfrac{20(35)^3+1715000}{35}=\$29,400

8 0
3 years ago
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