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andre [41]
4 years ago
15

Jingle Corporation produces toy footballs. Each football sells for $9.95 with a variable unit cost of $7.10. Assuming a fixed co

st of $11,400 what is Jingle's breakeven point?
Mathematics
1 answer:
____ [38]4 years ago
5 0
Each football is sold for $9.95. To make one of these football costs $7.10.
There is a profit of $2.85. Divide 11,400 by 2.85 to see how many footballs would have to sell to break even.

11,400 / 2.85 = 4000. 

4000 footballs would have to be sold to break even.
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The sum of two consecutive natural numbers is 525.<br> Find the numbers.
Luda [366]

Answer:

262 and 263 are consecutive natural numbers whose sum is 525.

Step-by-step explanation:

Natural number are a subset of real numbers consisting in positive integers (i.e. 1, 2, 3, 525) and two natural numbers are consecutive when distance between each other is equal to 1. (|x-y| = 1, \forall\,x,y \in \mathbb{N}) We can interpret the statement mathematically by means of the following expression:

x + y = 525

x = n

y = n+1

Where x, y, n \in \mathbb{N}.

This system is reduced to a single equation and solved afterwards:

n +(n+1) = 525

2\cdot n + 1 = 525

2\cdot n = 524

n = 262

Now we evaluate x and y to obtain the natural numbers:

x = 262

y = 263

262 and 263 are consecutive natural numbers whose sum is 525.

3 0
4 years ago
Find the equation of the line that is parallel to x=5y-8 and pass through (6, -5) in slope intercept form
DochEvi [55]

Answer:

y=1/5x-31/5 (or y=0.2x-6.2 in decimals)

Step-by-step explanation:

x=5y-8     (original equation)

x+8=5y <u>(Addition Property of Equality)</u>

1/5x+8/5=y <u>(Division Property of Equality, </u><u>slope </u><u>of </u><u><em>original equation </em></u><u>is </u><u>1/5</u><u>)</u>

<u />

y-y1=m(x-x1)    <u>(point-slope formula)</u>

y-(-5))=1/5(x-(6)) <u>(plug in the slope that was found earlier and the point given in the question)</u>

y+5=1/5(x-6)

y+5=1/5x-6/5   (Distributive Property of Multiplication)   Note:  5 = 25/5

<u>y=1/5x-31/5</u> (Subtraction Property of Equality, and there's your answer)

<u>y=0.2x-6.2</u><em> </em>(This is the same answer, but written with decimals)

5 0
3 years ago
What is the sum of the first 70 consecutive odd numbers? Explain.
expeople1 [14]

The sum of the first n odd numbers is n squared! So, the short answer is that the sum of the first 70 odd numbers is 70 squared, i.e. 4900.

Allow me to prove the result: odd numbers come in the form 2n-1, because 2n is always even, and the number immediately before an even number is always odd.

So, if we sum the first N odd numbers, we have

\displaystyle \sum_{i=1}^N 2i-1 = 2\sum_{i=1}^N i - \sum_{i=1}^N 1

The first sum is the sum of all integers from 1 to N, which is N(N+1)/2. We want twice this sum, so we have

\displaystyle 2\sum_{i=1}^N i = 2\cdot\dfrac{N(N+1)}{2}=N(N+1)

The second sum is simply the sum of N ones:

\underbrace{1+1+1\ldots+1}_{N\text{ times}}=N

So, the final result is

\displaystyle \sum_{i=1}^N 2i-1 = 2\sum_{i=1}^N i - \sum_{i=1}^N 1 = N(N+1)-N = N^2+N-N = N^2

which ends the proof.

5 0
3 years ago
A phone is 35 percent off which is now worth 78 pounds what was the original price
Black_prince [1.1K]

Answer:

120 pounds

Step-by-step explanation:

65% of y= 78 pounds

\frac{65}{100} × y = 78 pounds

65y = 78  × 100=7800

y= 7800/65= 120 pounds

7 0
3 years ago
In an ore, 9.8% of its total weight is metal. How many pounds of metal are in 1,950 lb of ore?
Fudgin [204]

Answer

Find out the  how many pounds of metal are in 1,950 lb of ore .

To proof

let us assume that the pounds of metal are in 1,950 lb of ore be x .

As given

In an ore, 9.8% of its total weight is metal.

ore weight = 1,950 lb

9.8% is written in the decimal form

= \frac{9.8}{100}

= 0.098

Than the equation becomes

x = 0.098 × 1950

x = 191.1 pounds

Therefore the 191.1 pounds of metal are in 1,950 lb of ore .

Hence proved



5 0
3 years ago
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