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2 years ago

A solution of salt and water is 20% salt. If 25% of the water is removed, what is the percentage of salt in the new solution?

1 answer:

4 0

So lets say that this salt and water solution consists of 100 liters.

Then that means 20 liters is salt, and 80 liters out of the 100 is water.

Now, we remove 25% of the water. 25% of 80 liters is 20 liters. So, we are left with 80-20, or 60 liters.

Now in all we have 20 liters of salt, and 60 liters of water.

The percentage of salt in the new mixture will be 20/(20+60) = 20/80 = 25%.

Your answer is 25%

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In this diagram, which equation could you prove to be true in order to conclude that the lines are parallel?

Sladkaya [172]

THE ANSWER:

c−ab=de

THIS IS WHY:

4 0

3 years ago

If <img src="https://tex.z-dn.net/?f=%5Crm%20%5C%3A%20x%20%3D%20log_%7Ba%7D%28bc%29" id="TexFormula1" title="\rm \: x = log_{a}(

timama [110]

Use the change-of-basis identity,

$\log_x(y) = \dfrac{\ln(y)}{\ln(x)}$

to write

$xyz = \log_a(bc) \log_b(ac) \log_c(ab) = \dfrac{\ln(bc) \ln(ac) \ln(ab)}{\ln(a) \ln(b) \ln(c)}$

Use the product-to-sum identity,

$\log_x(yz) = \log_x(y) + \log_x(z)$

to write

$xyz = \dfrac{(\ln(b) + \ln(c)) (\ln(a) + \ln(c)) (\ln(a) + \ln(b))}{\ln(a) \ln(b) \ln(c)}$

Redistribute the factors on the left side as

$xyz = \dfrac{\ln(b) + \ln(c)}{\ln(b)} \times \dfrac{\ln(a) + \ln(c)}{\ln(c)} \times \dfrac{\ln(a) + \ln(b)}{\ln(a)}$

and simplify to

$xyz = \left(1 + \dfrac{\ln(c)}{\ln(b)}\right) \left(1 + \dfrac{\ln(a)}{\ln(c)}\right) \left(1 + \dfrac{\ln(b)}{\ln(a)}\right)$

Now expand the right side:

$xyz = 1 + \dfrac{\ln(c)}{\ln(b)} + \dfrac{\ln(a)}{\ln(c)} + \dfrac{\ln(b)}{\ln(a)} \\\\ ~~~~~~~~~~~~+ \dfrac{\ln(c)\ln(a)}{\ln(b)\ln(c)} + \dfrac{\ln(c)\ln(b)}{\ln(b)\ln(a)} + \dfrac{\ln(a)\ln(b)}{\ln(c)\ln(a)} \\\\ ~~~~~~~~~~~~ + \dfrac{\ln(c)\ln(a)\ln(b)}{\ln(b)\ln(c)\ln(a)}$

Simplify and rewrite using the logarithm properties mentioned earlier.

$xyz = 1 + \dfrac{\ln(c)}{\ln(b)} + \dfrac{\ln(a)}{\ln(c)} + \dfrac{\ln(b)}{\ln(a)} + \dfrac{\ln(a)}{\ln(b)} + \dfrac{\ln(c)}{\ln(a)} + \dfrac{\ln(b)}{\ln(c)} + 1$

$xyz = 2 + \dfrac{\ln(c)+\ln(a)}{\ln(b)} + \dfrac{\ln(a)+\ln(b)}{\ln(c)} + \dfrac{\ln(b)+\ln(c)}{\ln(a)}$

$xyz = 2 + \dfrac{\ln(ac)}{\ln(b)} + \dfrac{\ln(ab)}{\ln(c)} + \dfrac{\ln(bc)}{\ln(a)}$

$xyz = 2 + \log_b(ac) + \log_c(ab) + \log_a(bc)$

$\implies \boxed{xyz = x + y + z + 2}$

(C)

6 0

1 year ago

A sprinkler system uses 800 gallons of water in 5 days. The system uses ___ gallons of water in 1 day

slamgirl [31]

Answer:

160

Step-by-step explanation:

800 gallons in 5 days. The days is the denominator and the gallons are the numerator, whatever you do the the bottom you do to the top, so you divide the denominator by 5 and the numerator by 5 and you get 160 gallons per day. If you want to know how your answer is right, multiply 160 by 5

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2 years ago

Use the distributive property to write an expression for the area

LUCKY_DIMON [66]

Answer:

10x+15

Step-by-step explanation:

area of the two rectangles combined is one big rectangle

area of rectange= base*height

base length: 2x+3

height: 5

(2x+3)*5

=(2x*5)+(3*5)

=10x+15

8 0

2 years ago

At a competition with 5 runners

ankoles [38]

Answer:

B: Permutation; Number of ways = 60

Step-by-step explanation:

First we have to decide if this is a problem of permutation or combination. The rule is:

If the order matters, permutations will be used
If order does not matter, combinations will be used

In this problem, they order of awarding the medals matters, so this is a permutation problem.

We have to award 3 medals among 5 runners. So this can be done in 5P3 ways:

$nPr=\frac{n!}{(n-r)!}\\ \\ so\\ \\ 5P3=\frac{5!}{(5-3)!}=60$

Therefore, there are 60 ways to award the medal. Therefore, the correct answer is B.

5 0

2 years ago

Read 2 more answers