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3 years ago

Suppose it takes 18 hours for a pipe to fill a tank of water, if the tank

Mathematics

1 answer:

Lemur [1.5K]3 years ago

4 0

Answer:

Step-by-step explanation:

Let the volume of tank be x

In 18 hours volume of tank filled = x

we have to find the volume of tank which is filled in 1 hours.

For that we divide LHS and RHS by 18

In 18/18 hours volume of tank filled = x/18

In 1 hours volume of tank filled = x/18

In 30 hours volume of tank emptied = x

we have to find the volume of tank which is emptied in 1 hours.

For that we divide LHS and RHS by 30

in 30/30 hours volume of tank filled = x/30

In 1 hours volume of tank filled = x/30

If tank is empty and one starts to fill it, two things will happen

it will start filling at rate of x/18 hours

But there is leak which will start to empty the tank at x/30 hours

So , at any given time rate if filling of water will be rate of filling the tank- rate of emptying the tank

In 1 hour volume of tank filled if both filling and leaking takes place simultaneously = x/18 -x/30 = (30-18)x/18*30 = 12x/18*30 = x/3*15 = x/45

In 1 hour volume of tank filled = x/45

in 1*45 hour volume of tank filled = x/45*45 = x

Thus, it will take 45 hours to fill the leaky tank .

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40% of what number is 18?

vladimir1956 [14]

Answer:

40 percent (calculated percentage %) of what number equals 18? Answer: 45.

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2 years ago

Read 2 more answers

a chef has 5 blocks of butter. Each weights 1 pound. she cuts each block into fourths. how many 1/4 pound pieces of butter does

lianna [129]

The answer would be 20 because you have 5 blocks that are cut into 1/4. It doesn't say anything about any of the pieces disappearing or being used yet so you multiply 4*5 and then you get the answer.

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2 years ago

Two athletic teams play a series of games; the first team to win 4 games is declared the overall winner. Suppose that one of the

kodGreya [7K]

Answer:

p=0.7103 (4-game series)
p=0.6480 (2-game series)

Step-by-step explanation:

Let X be the random variable equal the the first 4 straight wins. An overall win for the stronger team implies a negative binomial function with the parameters n=4, p=0.6:

$P(X=4)={{i-1}\choose {4-1}}0.6^40.4^{i-4},\ i=4,5,6,7$

#We find probabilities for the different values of i:

$P(X=4)={3\choose 3}0.6^4=0.1296\\\\P(X=5)={4\choose 3}0.6^40.4^1=0.2074\\\\P(X=6)={5\choose 3}0.6^40.4^2=0.2074\\\\P(X=4)={6\choose 3}0.6^40.4^3=0.1659$

Hence, probability of the stronger team winning overall is:

$=P(X=4)+P(X=5)+P(X=6)+P(X=7)\\\\=0.7103$

#Define Y as the random variable for winning 2/3 games.:

$P(Y=2)={1\choose 1}0.6^2=0.3600\\\\P(Y=3)={2\choose3}0.6^20.4=0.2880\\\\P(win)=0.2880+0.3600=0.6480$

Hence, probability of the stronger team winning in 2 out 3 game series is 0.6480

The stronger team has a higher chance of winning in a 4-game series(0.7103>0.6480)

8 0

2 years ago

Which function represents a reflection of f(x) = 5(0.8)^x across the x-axis?

Vikki [24]

Answer: The correct option is second.

Explanation:

The given function is,

$f(x)=5(0.8)^x$

If we graph a function is f(x), then its coordinates is defined as (x,f(x)).

When the graph of f(x) is reflect across the x-axis, then the the x-coordinate remains the same and the sign of y-coordinate is changed. It means after reflecting across the x-axis,

$(x,y)\rightarrow(x,-y)$