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Working together to palms can drain a certain pool in three hours if it takes the older pump nine hours to drain the pool by its

andreyandreev [35.5K]

Answer:

It would take the newer pump 4.5 hours to drain the pool

Step-by-step explanation:

Let's investigate first what is the fraction of the job done in the unit of time (hour in this case) by each pump if the work individually:

older pump: if it takes it 9 hours to complete the job, it does $\frac{1}{9}$ of the job in one hour.

newer pump: we don't know how long it takes (this is our unknown) so we call it "x hours". Therefore, in the unit of time (in one hour) it would have completed $\frac{1}{x}$ of the total job.

both pumps together: since it takes both 3 hours to complete the job, in one hour they do $\frac{1}{3}$ of the job.

Now, we can write the following equation about fractions of the job done:

<em>The fraction of the job done by the older pump plus the fraction of the job done by the newer pump in one hour should total the fraction of the job done when they work together.</em> That is in mathematical terms:

$\frac{1}{9} +\frac{1}{x} =\frac{1}{3}$

and solving for x:

$\frac{1}{9} +\frac{1}{x} =\frac{1}{3} \\x+9=3x\\2x=9\\x=\frac{9}{2} \,\,hours\\x = 4.5\,\,hours$

4 0

3 years ago

Where is the transverse axis for the hyperbola?

Dmitrij [34]

This is what I got. The standard equation for a hyperbola with a horizontal tranverse axis is - = 1. The center is at (h,k). The distance between the vertices is a 2a. The distance between the foci is 2c. I hope that helped :\

6 0

4 years ago

Can someone give me the correct answer for this.

Minchanka [31]

Answer:

The correct answer is option C that is graph X.

Step-by-step explanation:

Given : 1 sack lunch has 3 sandwiches

x axis = Number of sack lunches

y axis = Number of sandwiches

The coordinate from the given data will be: (1,3)

So, from the given graphs the graph with coordinate point (1,3) is correct. It will also show change in number of sandwiches with respect to change in number of sack lunches.

7 0

3 years ago

The product of a number, x, and 18 is 113.4. Which equation and value of x represent this relationship?

KIM [24]

Answer:

42

Step-by-step explanation:

5 0

3 years ago

Consider a sample with data values of 27, 25, 20, 15, 30, 34, 28, and 25. Compute the range, interquartile range, variance, and

Valentin [98]

So we have a set of integers,

$X=\{15,20,25,25,27,28,30,34\}$

And we need to compute some stats.

First the range,

The range of data set is difference between the maximum and the minimum of the data set.

So the minimum is 15 and maximum is 34 therefore the range is 34 - 15 = 19.

Second the interquartile range,

The interquartile range of data set is the difference of the first and third quartiles.

First quartile is the value separating the lower quarter and higher three - quarters of the set. The first quartile is computed by taking median of the lower half of the sorted set. This is 15, 20, 25, 25 and it's median is 22.5

Third quartile is therefore the median of 27, 28, 30, 34 which is 29.

Next up, variance.

The variance of set measures how much data is spread out. For data set $x_1,\dots, x_n$ with an average $a$ ,