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Lerok [7]
3 years ago
14

If 1/4 gallons of water are enough to fill 7/10 of the pool how much water is nessacary to fill in the entire pool

Mathematics
1 answer:
anyanavicka [17]3 years ago
8 0
<h3>Answer:  5/14 gallons</h3>

============================================================

Work Shown:

1/4 = 0.25

7/10 = 0.70 = 70%

We are told that 0.25 gallons of water fills 70% of the pool

We want to find how many gallons of water (call it x) are needed to fill 100% of the pool.

Set up the proportion below and solve for x

(0.25 gallons)/(70% filled) = (x gallons)/(100% filled)

0.25/70 = x/100

0.25*100 = 70x ....... cross multiply

25 = 70x

70x = 25

x = 25/70

x = (5*5)/(5*14)

x = 5/14 gallons

----------------------------------------

An alternate method:

1/4 gallons = 7/10 pools filled

(10/7)*(1/4 gallons) = (10/7)*(7/10 pools filled)

(10*1)/(7*4) gallons = (10*7)/(7*10) pools filled

10/28 gallons = 1 pool filled

(5*2)/(14*2) gallons = 1 pool filled

5/14 gallons = 1 pool filled

In the second step, I multiplied both sides by 10/7 so that the "7/10" turns into "1".

----------------------------------------

Yet another alternate method:

1/4 = 10/40

7/10 = 28/40

We need 10/40 gallons of water to fill 28/40 of one pool. We can multiply both fractions by 40 to indicate that 10 gallons of water will fill up 28 pools.

So we have this ratio

10 gallons : 28 pools

Dividing both parts by 28 tells us how many gallons are needed for one pool

10 gallons : 28 pools

10/28 gallons : 28/28 pools

10/28 gallons : 1 pool

5/14 gallons : 1 pool

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Answer:

The amount invested in funds that earned 12% profit is 31000

The amount invested in stock that suffered 5% loss is 6,000.

Step-by-step explanation:

Let x be the amount invested in funds that earned 12%.

Then the amount invested in stock that suffered 5% loss is 37000 - x.

The profit from investment in funds is = 12% of x

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The loss from investment in stock is = 5% of (37000 - x)

                                                            = 0.05 × (37000 - x)

The net profit is 0.12·x - 0.05 × (37000 - x)

As the net profit given in the problem is $3420, we have :

0.12·x - 0.05 × (37000 - x) = 3420

Solving for x, we have :

12·x - 5 × (37000 - x) = 342000 (multiply both sides by 100)

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17·x = 527000

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Hence, The amount invested in funds that earned 12% profit is 31000 and the amount invested in stock that suffered 5% loss is 37000 - x = 37000 - 31000 = 6,000.

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3 years ago
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3 years ago
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Mice21 [21]

Answer: {5, -7, -19, -27, -35}

Step-by-step explanation:

In order solve this, we need to plug in the values of x into the table.

For spaces on the left of the equals sign, you need to write each x from the domain. You can then match that x-value with its function value by putting that on the right side.

For each equation, we are simply plugging a number from the domain into the function and replacing the x-value:

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I hope this helps. If you need any extra explanation on how the functions are set up, please let me know.

5 0
1 year ago
What are the possible values of x if (4x – 5)2 = 49?
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Step-by-step explanation:

5 0
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