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cestrela7 [59]
3 years ago
12

One conveyor belt can move 1000 boxes in 9 minutes. Another can move 1000 boxes in 11 minutes. If another conveyor belt is added

and all three are used, the boxes are moved in 3 minutes. How long would it take the third conveyor belt alone to do the same job?
Mathematics
1 answer:
Ugo [173]3 years ago
5 0

Answer:

It would take 7.62 minutes for the third conveyor belt alone to do the same job

Step-by-step explanation:

The together rate is the sum of each separate rate.

In this question:

First conveyor: Rate of 1/9.

Second: Rate of 1/11.

Third: Rate of 1/x.

Total: 1/3

So

\frac{1}{9} + \frac{1}{11} + \frac{1}{x} = \frac{1}{3}

\frac{11x + 9x + 99}{99x} = \frac{1}{3}

\frac{20x + 99}{99x} = \frac{1}{3}

3(20x + 99) = 99x

60x + 297 = 99x

39x = 297

x = \frac{297}{39}

x = 7.62

It would take 7.62 minutes for the third conveyor belt alone to do the same job

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Dale works at a mattress store, and makes a salary plus commission. He has a $500 weekly salary and makes a 5% commission for sa
Anni [7]

Answer:

1.  \( f\circ g(x)=0.05x-150

2. \( g\circ f(x)=0.05x-3000

3. The first one represents Dale's commission

Explanation:

1. The composition of the function

                                                             \( f\circ g(x)=f(g(x)) \)    

means that you first apply the function g(x) and then f(x) on the output of g(x).

That is:

  • f(x) = 0.05x
  • g(x) = x - 3000

       f(g(x)=0.05(x - 3000)

       f(g(x))=0.05x-150

2. The composition of the function

                                                             \( g\circ f(x)=g(f(x)) \)                                                                  

means that you first apply the function f(x) and then g(x) on the output of f(x).

That is:

      g(f(x))=((0.05x)-3000)=0.05x-3000

3. Which one represents Dale's commission

To calculate Dales's commision you must subtract $3,000 from the sales, to find the sales over $3000. That is: x - 3,000, which is the function g(x).

Therefore, you first use g(x).

Then, you must multiply the output of g(x) by 0.05 to find the 5% of the sales over $3,000. That is: 0.05(g((x)) = 0.05(x - 3000) = 0.05x - 150.

Therefore, the composition that represents Dale's commission is the first one:

  f(g(x)=0.05(x - 3000)

       f(g(x))=0.05x-150

4 0
3 years ago
-4.8=1.2s+2s+4<br><br><br>Please help me <br>​
nikdorinn [45]
Simplify both sides of the equation
-4.8=1.2s+2s+4
Combine like terms
-4.8=(1.2s+2s)+(4)
-4.8=3.2s+4
Flip the equation
3.2s+4=-4.8
Subtract both sides by 4
3.2s+4-4=-4.8-4
3.2s=-8.8
Divide both sides by 3.2
3.2s/3.2= -8.8/3.2
S=-2.75 will be the answer hope it helps
6 0
3 years ago
On your wedding day you leave for the church 34 minutes before the ceremony is to begin, which should be plenty of time since th
Schach [20]

Answer:

Average speed   is 37.35 mi/h

Step-by-step explanation:

given data

leave =  34 minutes before

church distance =  12.0 miles

average speed first 17 minutes =  5.0 mi/h

solution

so we find Total distance travel in first 17 minutes = speed × time

Total distance travel in first 17 minutes = 5 × \frac{17}{60}

Total distance travel in first 17 minutes = 1.416 mi

and

Distance Remaining = 12 - 1.416 = 10.584 mi

Time Remaining = 34 - 17 min = 17 min

so

remaining distance Average speed  = \frac{distance}{time}

Average speed  = \frac{10.584}{\frac{17}{60}}

Average speed   is 37.35 mi/h

3 0
3 years ago
Given that LM and LN are tangent to the circle and that the measure of angle MLN = 75.86, find the measure of arc MN.
siniylev [52]

we know that

The measure of the external angle is the semidifference of the arcs that it covers

so

∠MLN=(1/2)*(mayor arc MN-minor arc MN)

Let

x------> minor arc MN

major arc MN=360-x

substitute in the formula above

∠MLN=(1/2)*(mayor arc MN-minor arc MN)

75.86=(1/2)*(360-x-x)------> 151.72=(360-2x)------>360-151.72=2x

x=104.14°

therefore

the answer is

the measure of arc MN (minor arc) is 104.14°

7 0
3 years ago
Write an equation of the line that passes through the points (-8, -1) and (-6, 9).
larisa [96]

Answer:

y=5x+21

Step-by-step explanation:

I included the work in the picture. lmk if you need more explaining

7 0
3 years ago
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