A sample of size 400 was drawn and sample mean was found t

Mathematics

1 answer:

Nostrana [21]2 years ago

5 0

Answer:

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Write an equivalent equation that does not contain parentheses for 3(k-x) = -3x-9

amm1812

3(k-x)= -3x-9
3k - 3x = -3x - 9 ← equation without parentheses
3k - 3x + 3x = - 9
3k = -9
k = -9/3
k = -3 ← simplest form

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4 years ago

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Brums [2.3K]

Answer: 1/3

Step-by-step explanation:

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3 years ago

Officials begin to release water from a full man-made lake at a rate that would empty the lake in 10 weeks, but a river that can

Romashka [77]

Answer:

It takes 20 weeks to empty the lake

Step-by-step explanation:

Some rate, let's call it $R_{empty}$ empties the lake in 10 weeks and a river (with rate $R_{river}$ can fill the lake in 20 weeks. The idea behind the solution of this type of problem is always set the rate to the same units. Let's see this:

$R_{empty}=\frac{1\ lake}{10\ weeks}$ which implies that this rate empties 0.1 of the lake per week, thus, $R_{empty}=0.1/week$ .

Using the same idea, we can obtain that the filling rate of the river is:

$R_{river}=\frac{1\ lake}{20\ weeks} = 0.05 /week$

Since both rates are acting at the same time, the total rate of flowing water (either in or out the lake) would be given by:

$R_{total}=R_{empty}+R_{river}\\R_{total}= -0.1 + 0.05=-0.05/week$ , which means that the lake is being empty at a rate of -0.05 week and using the rule of three: