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vagabundo [1.1K]
2 years ago
14

Fred spent half of his allowance going to the movies. he washed the family car and earned six dollars. what is his weekly allowa

nce if he ended with sixteen dollars?
please show work and answer.
Mathematics
1 answer:
yulyashka [42]2 years ago
5 0

Answer: 20

Step-by-step explanation:

20 - 1/2 = 10 + 6 = 16

Hope this helps! C:

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An empty cylindrical vase with a radius of 8 cm and a height of 9 cm is filled with 6 cm^3 of sand every 15 seconds. At the same
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General Idea:

The volume of cylinder is given by \pi r^{2} h, where r is the radius and h is the height of the cylinder.

Applying the concept:

Step 1: We need to find the volume of full cylinder with the given dimensions using the formula.

Volume of full cylinder =\pi r^{2} h=\pi* 8^{2} *9=576\pi cm^{3}

Volume of half cylinder =\frac{576\pi }{2} =288\pi cm^{3}

Step 2: Let x be the number of minutes of filling the sand.

6 cm^{3} of sand filled every 15 seconds, there are four 15 seconds in a minute.

So volume of sand filled in 1 minute= 6*4 cm^{3} = 24 cm^{3}.

8 cm^{3} of sand taken out of cylindrical vase every minute.

Net volume of sand filled in 1 minute = Volume of sand filled in the vase in one minute - Volume of sand taken out in 1 minute

Net volume of sand filled in 1 minute=24 cm^{3} - 8cm^{3}=16cm^{3}

Volume of sand filled in x minutes = 16x.

We need to set up an equation to find the number of minutes need to fill half the volume in cylindrical vase.

16x = 288\pi \\ \\ x=\frac{288\pi}{16}  \\ \\ x=18\pi \\ \\ x=57 minutes

Conclusion:

The number of minutes required for the base be half filled with sand is 57

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Step-by-step explanation:

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