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Novosadov [1.4K]
3 years ago
15

Printing a newsletter costs $1.50 per copy plus $450 in printer's fees. The copies are sold for $3 each.How many copies of the n

ewsletter must be sold to break even?
Mathematics
1 answer:
alekssr [168]3 years ago
8 0

Answer:

300 Copies

Step-by-step explanation:

Break even Units = Fixed Costs / (Price - Variable Cost)

Fixed Costs = $450

Variable Cost = 1.5

Price = 3

Break Even Units = 450 / (3 - 1.5)

Break Even Units = 450 / 1.5

Break Even Units = 300

300 Copies must be sold to break even.

I hope this helps!

-The BusinessMan

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Answer:

f(x) = 1 + x + (x²/2!) + (x³/3!) + ....... = Σ (xⁿ/n!) (Summation from n = 0 to n = ∞)

Step-by-step explanation:

f(x) = eˣ

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The Taylor's expansion based around any point b, is given by the infinite series

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<em>                       </em><u><em>SOLVING QUESTIONS FROM 1ST PAGE</em></u>

  • Given the point B(-5, 0)

y = -3x - 5

Putting x = -5, and y = 0 in y = -3x - 5

0 = -3(-5) - 5

0 = 15 - 5

0 = 10         ∵Putting B(-5, 0) in y = -3x - 5 does not equate the equation.

As L.H.S ≠ R.H.S

So,

Does this check?

Answer: no        ∵ L.H.S ≠ R.H.S

  • Given the point C<em>(-2, 1)</em>

y = -3x - 5

Putting x = -2, and y = 1 in y = -3x - 5

1 = -3(-2) - 5

1 =  6 - 5

1 = 1         ∵Putting C(-2, 1) in y = -3x - 5 rightly equates the equation.

As L.H.S = R.H.S

So,

Does this check?

Answer: yes      ∵ L.H.S = R.H.S

  • Given the point D<em>(-1, -2)</em>

y = -3x - 5

Putting x = -1, and y = -2 in y = -3x - 5

-2 = -3(-1) - 5

-2 =  3 - 5

-2 = -2       ∵Putting D(-1, -2) in y = -3x - 5 rightly equates the equation.

As L.H.S = R.H.S

So,

Does this check?

Answer: yes       ∵ L.H.S = R.H.S

<em>                          </em><u><em>SOLVING QUESTIONS FROM 2ND PAGE</em></u>

  • Given the point B(6, 18)

y = -2x + 18

Putting x = 6, and y = 18 in y = -2x + 18

18 = -2(6) + 18

18 = -12 + 18

18 = 6         ∵Putting B(6, 18) in y = -2x + 18 does not equate the equation.

As L.H.S ≠ R.H.S

So,

Does this check?

Answer: no       ∵ L.H.S ≠ R.H.S

  • Given the point C(9, 24)

y = 2x + 6

Putting x = 9, and y = 24 in y = 2x + 6

24 = 2(9) + 6

24 = 18 + 6

24 = 24      ∵Putting C(9, 24) in y = 2x + 6 rightly equates the equation.

As L.H.S = R.H.S

So,

Does this check?

Answer: yes       ∵ L.H.S = R.H.S

<em>               </em><u><em>SOLVING QUESTIONS FROM 3RD PAGE</em></u>

  • Given the point D(2, 7)

y = 3x + 4

Putting x = 2, and y = 7 in y = 3x + 4

7 = 3(2) + 4

7 = 6 + 4

7 = 10         ∵Putting D(2, 7) in y = 3x + 4 does not equate the equation.

As L.H.S ≠ R.H.S

So,

Does this check?

Answer: no       ∵ L.H.S ≠ R.H.S

<em>                       </em><u><em>SOLVING QUESTIONS FROM 4th PAGE</em></u>

<em>b. Which function could have produced the values in the table.</em>

<em>A. y = 3x + 4                            </em>

<em>B. y = -2x + 18</em>

<em>C. y = 2x + 6</em>

<em>D. y = x + 9</em>

<em>The Table:</em>

<em>x             y</em>

3            12

6            18

9            24

<em>Checking A) y = 3x + 4</em>

<em>Putting (3, 12), (6, 18) and (9, 24) in y = 3x + 4</em>

For (3, 12)

y = 3x + 4

12 = 3(3) + 4

<em>12 = 13   </em>∵ L.H.S ≠ R.H.S

Does this check?

Answer: no       ∵ L.H.S ≠ R.H.S

For (6, 18)

18 = 3(6) + 4

18 = 18 + 4

<em>18 = 22   </em>∵ L.H.S ≠ R.H.S

Does this check?

Answer: no       ∵ L.H.S ≠ R.H.S

For (9, 24)

24 = 3(9) + 4

24 = 27 + 4

<em>24 = 31   </em>∵ L.H.S ≠ R.H.S

Does this check?

Answer: no       ∵ L.H.S ≠ R.H.S

So, the equation y = 3x + 4 could have not produced the all values in the table as the the ordered pairs in table do not satisfy(equate) the equation.

<em>Checking B) y = -2x + 18</em>

<em>Putting (3, 12), (6, 18) and (9, 24) in y = -2x + 18</em>

  • <em>For (3, 12) </em>⇒ y = -2x + 18 ⇒ 12 = -2(3) + 18 ⇒ 12 = 12 ⇒<em> L.H.S = R.HS</em>
  • <em>For (6, 18)</em> ⇒ y = -2x + 18 ⇒ 18 = -2(6) + 18 ⇒ 18 = 6 ⇒ <em>L.H.S ≠ R.HS</em>
  • <em>For (9, 24)</em> ⇒ y = -2x + 18 ⇒ 24 = -2(9) + 18 ⇒ 18 = 0 ⇒ <em>L.H.S ≠ R.HS</em>

So, y = -2x + 18 could have not produced all the values in the table, as (6, 18) does not equate the equation.

<em>Checking C) y = 2x + 6</em>

<em>Putting (3, 12), (6, 18) and (9, 24) in y = 2x + 6</em>

  • <em>For (3, 12) </em>⇒ y = 2x + 6 ⇒ 12 = 2(3) + 6 ⇒ 12 = 12 ⇒<em> L.H.S = R.HS</em>
  • <em>For (6, 18) </em>⇒ y = 2x + 6 ⇒ 18 = 2(6) + 6 ⇒ 18 = 18 ⇒<em> L.H.S = R.HS</em>
  • <em>For (9, 24) </em>⇒ y = 2x + 6 ⇒ 24 = 2(9) + 6 ⇒ 24 = 24 ⇒<em> L.H.S = R.HS</em>

So, y = 2x + 6 could have produced the values of in the table as all the orders pairs in the table satisfy/equate the equation.

<em>Checking D) y = x + 9</em>

<em>Putting (3, 12), (6, 18) and (9, 24) in y = x + 9</em>

  • <em>For (3, 12) </em>⇒ y = x + 9 ⇒ 12 = 3 + 9 ⇒ 12 = 12 ⇒<em> L.H.S = R.HS</em>
  • <em>For (6, 18) </em>⇒ y = x + 9 ⇒ 18 = 6 + 9 ⇒ 18 = 15 ⇒ <em>L.H.S ≠ R.HS</em>
  • <em>For (9, 24) </em>⇒ y = x + 9 ⇒ 24 = 9 + 9 ⇒ 24 = 18 ⇒<em> L.H.S ≠ R.HS</em>

So, y = x + 9 could have also not produced all the values in the table, as (6, 18) and (9, 24) do not satisfy/equate the equation.

So, from all the verification we conclude that:

<u>HENCE, ONLY </u><u>y = 2x + 6</u><u> COULD HAVE PRODUCED THE VALUES IN THE TABLE AS ALL THE ORDERED PAIRS OF THE TABLE SATISFY/EQUATE THE EQUATION.</u>

<em>                  </em><u><em>SOLVING QUESTIONS FROM 5th PAGE</em></u>

<em>What is the domain and range of the relation?</em>

{(-3, 7), (6, 2), (5, 1), (-9, -6)}

  • Domain: Domain is the set of all the x-coordinates of the ordered pairs of  the relation, meaning the all first elements of the ordered pairs in a relation include in the domain of the relation.
  • Range: Range is the set of all the y-coordinate of the ordered pairs of the relation, meaning the all second elements of the ordered pairs in a relation include in the range of the relation.

As the given relation is {(-3, 7), (6, 2), (5, 1), (-9, -6)}

The <em>domain</em> is: {-3, 6, 5, -9}

<em>Note: generally, we write the numbers in ascending order for both the domain and range.</em>

The domain could also be written in order as: {-9, -3, 5, 6}

The <em>range</em> is: {7, 2, 1, -6}

The range could also be written in order as: {-6, 1, 2, 7}

Keywords: equation, point, ordered pair, domain, range

Learn more about points and equation from brainly.com/question/12597810

<em>#learnwithBrainly</em>

8 0
3 years ago
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