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USPshnik [31]
2 years ago
15

It takes 8 minutes for Byron to fill the kiddie pool in the backyard using only a handheld hose. When his younger sister is impa

tient, Byron also uses the lawn sprinkler to add water to the pool so it is filled more quickly. If the hose and sprinkler are used together, it takes 5 minutes to fill the pool. Which equation can be used to determine r, the rate in parts per minute, at which the lawn sprinkler would fill the pool if used alone?
Mathematics
2 answers:
Sveta_85 [38]2 years ago
7 0

Answer:

Rate at which sprinkler will fill the pool is \frac{3}{40} per minute.

Step-by-step explanation:

It takes 8 minutes for Byron to fill the kiddie pool in the backyard with the use of handheld hose only.

So part of kiddie pool filled in one minute = \frac{1}{8}

When lawn sprinkler and handheld hose both were used to fill the pool,it took 5 minute to fill the pool together.

Now the part of pool filled in one minute = \frac{1}{5}

If the sprinkler fills the pool alone in r minutes then the pool filled per minute will be = \frac{1}{r}

Now we combine these three facts to form the equation.

\frac{1}{8}+\frac{1}{r}=\frac{1}{5}

\frac{1}{r}=\frac{1}{5}-\frac{1}{8}

\frac{1}{r}=\frac{8-5}{40}

\frac{1}{r}=\frac{3}{40}

r = \frac{40}{3}

Therefore, time taken by sprinkler alone will be 13.33 minutes and the rate per minute at which sprinkler will fill the pool is \frac{3}{40}.

lana66690 [7]2 years ago
6 0
Since you know that the hose will fill the whole pool in 8 minutes you know it will fill 1/8 of the pool per minute. In 5 minutes it will fill up 5/8 of the pool. This will make your equation 5/8 +5r=1. Solving for r will give you 3 parts/40 minutes
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Chain referral sampling

Step-by-step explanation:

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5 0
2 years ago
Indicate the general rule for the arithmetic sequence with a3 = -12 and a8 = -37
Mandarinka [93]

Answer:

The general rule is a_n = -2 - 5(n-1)

Step-by-step explanation:

Arithmetic sequence:

In an arithmetic sequence, the difference between consecutive terms is always the same, and this difference is called common difference.

The general rule of an arithmetic sequence is given by:

a_{n} = a_1 + (n-1)d

In which a_1 is the first term and d is the common difference.

We can also find the nth term as a function of a term m, using:

a_n = a_m + (n-m)d

a3 = -12 and a8 = -37

First we find the common difference. So

a_n = a_m + (n-m)d

a_8 = a_3 + (8-3)d

-37 = -12 + 5d

5d = -25

d = -\frac{25}{5}

d = -5

So

a_n = a_1 - 5(n-1)

Finding the first term:

a_n = a_1 - 5(n-1)

Since a_3 = -12

a_n = a_1 - 5(n-1)

a_3 = a_1 - 5(3-1)

a_1 = a_3 + 10 = -12 + 10 = -2

So the general rule is:

a_n = a_1 - 5(n-1)

a_n = -2 - 5(n-1)

6 0
2 years ago
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