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2 years ago

Choose the correct fraction and decimal equivalent for 78%.

Mathematics

2 answers:

vazorg [7]2 years ago

8 0

Answer: 0.78 and 39/50

<h3>Explanation:</h3>

What we know:

We need to find 78% as a fraction and decimal

How to solve:

The decimal is easy enough, and then the fraction can be found from there. D will represent decimal, p will represent percentage, and F will represent fraction.

<h3>Process:</h3>

Decimal

Set up equation D = p / 100

Substitute D = 78% / 100

Simplify D = 0.78%

Remove % sign D = 0.78

Fraction

Set up equation F = p / 100

Substitute F = 78% / 100

Remove % sign F = 78 / 100

Simplify if needed F = /2 /2

F = 39 / 50

Solution: 0.78 and 39/50

Check:

Multiply the decimal by 100 to check the decimal

0.78 x 100 = 78; 78%

Divide the fraction to check the fraction

39/50 = 0.78; see above

PilotLPTM [1.2K]2 years ago

6 0

The two answers would be .78 and 39/50.

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Two numbers total 63 and have a difference of 31. Find the two numbers

Anastaziya [24]

Answer: 47 and 16

Step-by-step explanation:

- Make Two Equations

x + y = 63

x - y = 31

- Set one of the equations equal to one of the variables

x + y = 63

x = 31 + y

- Substitute the equation back into the other one

(31 + y) + y = 63

31 + 2y = 63

2y = 32

y = 16

- Substitute the answer back into the equation

x + y = 63

x + 16 = 63

x = 47

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3 years ago

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lutik1710 [3]

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3 years ago

Ann is adding water to a swimming pool at a constant rate. The table below shows the amount of water in the pool after different

N76 [4]

Answer:

(a) As time increases, the amount of water in the pool increases.

11 gallons per minute

(b) 65 gallons

Step-by-step explanation:

From inspection of the table, we can see that <u>as time increases, the amount of water in the pool increases</u>.

We are told that Ann adds water at a constant rate. Therefore, this can be modeled as a linear function.

The rate at which the water is increasing is the <em>rate of change</em> (which is also the <em>slope </em>of a linear function).

Choose 2 ordered pairs from the table:

$\textsf{let}\:(x_1,y_1)=(8, 153)$

$\textsf{let}\:(x_2,y_2)=(12,197)$

Input these into the slope formula:

$\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{197-153}{12-8}=\dfrac{44}{4}=11$

Therefore, the rate at which the water in the pool is increasing is:

<u>11 gallons per minute</u>

To find the amount of water that was already in the pool when Ann started adding water, we need to create a linear equation using the found slope and one of the ordered pairs with the point-slope formula:

$y-y_1=m(x-x_1)$