Set up an equation and solve for x

Write this number in standard notation. 1.986 x 106

Eduardwww [97]

Assuming this is supposed to say 1.986x10^6 , it is 1,986,000

6 0

3 years ago

1. A college newspaper, The College Spy, has a fixed production cost of $70 per edition and it costs 40¢ per copy to print and d

Mars2501 [29]

a. What is the cost expression for the newspaper?

The cost would be the sum of fixed cost and the variable cost. The fixed cost is 70 while the variable cost is 0.40 x, where x stands for the number of copies made. That is:

Cost = 70 + 0.40 x

where x = number of copies made

b. What is the revenue expression for the newspaper?

The revenue would simply be the product of selling price and number of copies sold or made, that is:

Revenue = 0.50 x

c. Put the cost and revenue expressions into an inequality that would represent a successful newspaper.

To have a successful newspaper, the difference of revenue and cost must be greater than 0, that is:

Revenue – Cost > 0

0.50 x – (70 + 0.40 x) > 0

d. How many copies should be sold to make a profit? Show all work! An answer with no work will receive 0 points.

From the above equation, we solve for x.

0.50 x – (70 + 0.40 x) > 0

0.50 x – 70 – 0.40 x > 0

0.10 x > 70

x > 700

Number of copies made should be more than 700 copies

e. Now go back to your answer for d. On every line of your solution write what property of math you would use to justify the transformation that occurred.

0.50 x – (70 + 0.40 x) > 0 Distribution property

0.50 x – 70 – 0.40 x > 0 Addition property

0.10 x > 70 Addition property

x > 700 Division property

4 0

3 years ago

A piece of wire 28 ft long is cut into two pieces. One piece is used to form a square, and the remaining piece is used to form a

marusya05 [52]

Answer:

Wire should be cut in two parts with the length = 15.69 ft and 12.31 ft

Step-by-step explanation:

Length of the wire = 28 ft has been cut in two pieces.

One piece is used to form a square and remaining piece to form a circle.

Let the length of the wire which forms the square is 'l' ft.

Area of the square = (side)²

Perimeter of the square = 4(side) = l

Length of one side = $\frac{l}{4}$

So, the area of the square = $\frac{l^{2}}{16}$ ft²

Now length of the remaining part = perimeter of the circle = (28 - l) ft

2πr = (28 - l)

r = $\frac{28-l}{2\pi }$

Area of the circle formed = πr²

= $\frac{\pi(28-l)^{2} }{4(\pi )^{2} }$

= $\frac{(28-l)^{2}}{4\pi }$

Combined area of the square and circle

= $\frac{l^{2}}{16}$ + $\frac{(28-l)^{2}}{4\pi }$

Now to maximize the area we will find the derivative of the area with respect to l.

$\frac{dA}{dl}=\frac{d}{dl}[\frac{l^{2}}{16}+\frac{(28-l)^{2}}{4\pi}]$

= $\frac{d}{dl}[\frac{l^{2}}{16}+\frac{(28)^{2}+l^{2}-56l }{4\pi }]$

= $\frac{2l}{16}+\frac{(2l-56)}{4\pi }$

Now equate the derivative to zero.

$\frac{2l}{16}+\frac{(2l-56)}{4\pi }$ = 0

$(2l-56)=-\frac{2l}{16}\times 4\pi$

$(2l-56)=-\frac{\pi l}{2}$

$2l+\frac{\pi l}{2}=56$

$\frac{(4l+l\pi )}{2}=56$

l(4 + π) = 112

l(4 + 3.14) = 112

l = $\frac{112}{7.14}$

l = 15.69 ft

Length of the other part = 28 - 15.69 = 12.31 ft

Therefore, wire should be cut in two parts with the length = 15.69 ft and 12.31 ft

8 0

3 years ago

The temperature was 75° Fahrenheit. The temperature dropped at a rate of 10° per hour.

Zigmanuir [339]

Answer:

-5 degrees

Step-by-step explanation:

you started at 75 degrees. it dropped at a rate of 10 degrees per hour. It's been eight hours. 8 times 10 equals 80. It dropped a total of 80 degrees. the starting 75 degrees minus the current 80 degrees equals -5 degrees.

3 0

3 years ago

The heights of four boys

MariettaO [177]

Please elaborate........

3 0

3 years ago