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Liono4ka [1.6K]
3 years ago
7

The planning department of Abstract Office Supplies has been asked to determine whether the company should introduce a new compu

ter desk next year. The department estimates that bsp $ 14 comma 000 of new manufacturing equipment will need to be purchased and that the cost of constructing each desk will be $ 150. The department also estimates that the revenue from each desk will be $ 500.
Mathematics
1 answer:
Zina [86]3 years ago
3 0

Answer:

The complete question is to: <em>Find the company's break-even point for the desk. </em>

<em>Answer: </em><u><em>400 desks</em></u><em> to break-even.</em>

Step-by-step explanation:

<em>Let's let x = the number of desks.</em>

Therefore:

k(x) = 150x + 14 000 and;

q(x) = 500x

<em>In conclusion:</em>

k(x) = q(x)

150x + 14 000 = 500x

14 000 = 350x

<em>400 = x</em>

<em>400 desks should be sold for the company to break-even</em>

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4 0
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A new movie is released each year for 8 years to go along with a popular book series. Each movie is 5 minutes longer than the la
Georgia [21]

Answer:

The total length of all 8 movies is 740 minutes

Step-by-step explanation:

* Lets revise the arithmetic series

- In the arithmetic series there is a constant difference between  

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- Ex:  

# 2 , 5 , 8 , 11 , ………………………. (constant difference is 3)

# 5 , 10 , 15 , 20 , ………………………… (constant difference is 5)

# 12 , 10 , 8 , 6 , …………………………… (constant difference is -2)

* General term (nth term) of an Arithmetic series:  

- If the first term is a and the common diffidence is d, then

 U1 = a , U2 = a + d , U3 = a + 2d , U4 = a + 3d , U5 = a + 4d  

 So the nth term is Un = a + (n – 1)d, where n is the position of the

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- The formula to find the sum of n terms is

  Sn = n/2 [a + l] , where l is the last term in the series

* Lets solve the problem

- A new movie is released each year for 8 years to go along with a

 popular book series

∴ n = 8

- Each movie is 5 minutes longer than the last

∴ d = 5

- The first movie is 75 minutes long

∴ a = 75

- To find the total length of all 8 movies find the sum of the 8 terms

∵ Un = a + (n - 1)d

∵ The last term l is u8

∵ a = 75 , d = 5 , n = 8

∴ l = 75 + (8 - 1)(5) = 75 + 7(5) = 75 + 35 = 110

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∵ Sn = n/2 [a + l]

∴ S8 = 8/2 [75 + 110] = 4 [185] = 740 minutes

* The total length of all 8 movies is 740 minutes

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Write the equation: 5 more than 3 times a number is 20
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What is the equation of the line that passes through the point (8, -4) and<br> has a slope of 1/2
Eva8 [605]

Answer:

y = \frac{1}{2}x - 8

Step-by-step explanation:

1. Approach,

For this problem, the format of a line that will be used is, slope-intercept form;

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Where (m) is the slope of the line, also known as the change in the line and (b) is the y-intercept, or where the graph of the line intersects the y-axis. Since, in this problem, the slope of the line is given, all one has to do is substitute in a point on the given line and solve.

2. Finding the equation,

In this problem, the slope of the line is given. Therefore, to solve this problem, all one has to do is substitute in a point on the given line and solve.

y = mx + b

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Substitute in the point,

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Simplify,

-4 = 4 + b

Inverse operations,

-4 = 4 + b\\-4\\\\-8 = b

3. Putting it all together,

Now, that one has y-intercept, (-8); use the given slope and the formula y = mx + b,  substitute in all the information.

y = \frac{1}{2}x - 8

7 0
3 years ago
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