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GuDViN [60]
2 years ago
8

It takes one machine 25 minutes to pick a bale of cotton and another machine 30 minutes to compete the same job. If both machine

s are used, how long will it take them to pick a bale of cotton?
Mathematics
1 answer:
gladu [14]2 years ago
6 0
The first machine works at the rate x = 1 bale/ 25 min.
The second machine works at the rate y = 1 bale/30 min.

The combined rate is
x + y = 1/25 + 1/30 bales/min
         = (30 + 25)/(25*30) = 55/750
         = 11/150 bales/min

The time for both machines to pick 1 bale of cotton is
(1 bale)/(11/150 bales/min) = 150/11 min = 13.64 min

Answer: 13.6 minutes
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Answer:

Step-by-step explanation:

$27.63 / 2 = $13.82

$13.82 * 0.20 = $2.76

$13.82 + $2.76 = $16.58

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Susan and jim each own a lawn care business. The amount susan charges for lawn care is shown in the table. The amount him charge
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D)$40 because you divide 2 and 48 then multiply 10 then you do 20 x 10 then subtract the two answers
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A high school wants to sell postage stamps with the school logo on them. The fundraising group have purchased 500 sheets of stam
erma4kov [3.2K]

Answer:

a) Cost

C(q) = 50+16q\\\\C(500)=50+16(500)=50+8,000=8,050

b) Sales income

S(q)=20q\\\\S(500)=20\cdot 500 = 10,000

c) Table of values

\left[\begin{array}{ccc}q&C(q)&S(q)\\0&50&0\\250&4,050&5,000\\500&8,050&10,000\end{array}\right]

d) Attached

e) Breakeven point = 12.5 sheets

f) Profit at 550 sheets = $1,950

Step-by-step explanation:

a) We have a fixed cost for the image, at $50.

We also have a variable cost of $16 a sheet.

The purchased quantity is 500 sheets.

Then, the cost function is:

C(q) = 50+16q\\\\C(500)=50+16(500)=50+8,000=8,050

b) The price for each sheet is $20, so the income from sales are:

S(q)=20q\\\\S(500)=20\cdot 500 = 10,000

c) Table of values

\left[\begin{array}{ccc}q&C(q)&S(q)\\0&50&0\\250&4,050&5,000\\500&8,050&10,000\end{array}\right]

d) Attached

e) The minimum number of sheets the group must sell so they don't lose any money is the breakeven point (BEP) and can be calculated making the income sales equal to the cost:

S(q)=C(q)\\\\20q=50+16q\\\\(20-16)q=50\\\\4q=50\\\\q=50/4=12.5

f) This profit can be calculated as the difference between the sales income and the cost:

P(500)=S(500)-C(500)\\\\P(500)=20\cdot 500-(50+16\cdot 500)=10,000-8,050=1,950

3 0
1 year ago
ABCD is a rectangle and A and B are the points (4,2) and (2,8) respectively. Given that the equation of AC is y=x-2, find a) Equ
Rudik [331]

A(4,2), B(2,8)

AC: y=x-2

Point point form for a line through (a,b) and (c,d) is (c-a)(y-b)=(d-b)(x-a)

AB is  (2 - 4)(y - 2) = (8-2)(x-4)

-2(y - 2)=6(x-4)

y - 2 = -3(x-4)

y = -3x + 14

BC is perpendicular through B, so slope 1/3 and we calculate the constant as y-(1/3)x:

y = (1/3) x  + (8 - (1/3)(2) ) = (1/3) x + 22/3

a)Answer:  BC is  y =  (1/3) x + 22/3

C is the meet of AC and BC,

x - 2 = (1/3) x + 22/3

3x - 6 = x + 22

2x = 28

x = 14

y = x-2 = 12

Check: y = (1/3)x + 22/3 = (14+22)/3 = 36/3 = 12  good

C(14,12)

The remaining corner is D.   We have A-B=D-C or

D = A+C-B+C = (4,2)+(14,12)-(2,8) = (16, 6)

b)Answer: B(2,8) [given, but asked for]  C(14,12), D(16,6)

8 0
1 year ago
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mixas84 [53]

Answer:

<h3>The best interpretation of this equation 4x=3x is that the equation has no solution</h3>

Step-by-step explanation:

Given that Kate begins solving the equation

\frac{2}{3}(6x-3)=\frac{1}{2}(6x-4)

<h3>To find the best interpretation of the given equation :</h3><h3>Katie's steps are</h3>
  • \frac{2}{3}(6x-3)=\frac{1}{2}(6x-4)
  • \frac{2}{3}(3(2x-1))=\frac{1}{2}((2(3x-4))
  • 2(2x-1)=1(3x-2)
  • 2(2x)+2(-1)=1(3x)+1(-2)
  • 4x-2=3x-2

When she adds 2 to both sides, the equation becomes

  • 4x-2+2=3x-2+2
  • 4x=3x

Therefore 4\neq 3

<h3>Therefore the given equation has no solution </h3><h3>The best interpretation of this equation 4x=3x is that the equation has no solution.</h3><h3>Therefore the option no solution is correct</h3>
8 0
1 year ago
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