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Vinvika [58]
3 years ago
8

The fish tank in Paul's bedroom has a pump that will recirculate 75 gallons of water in 1/4 of an hour. Find the unit rate in ga

llons per hour.
a. 5 gallons per hour
b. 18.75 gallons per hour
c. 300 gallons per hour
d. 187.5 gallons per hour
Mathematics
1 answer:
m_a_m_a [10]3 years ago
6 0
We know that
(1/4) hour---------> 0.25 hour
if the pump r<span>ecirculate 75 gallons of water in -------------> 0.25  hour
 X </span>gallons of water in-----------------------------------------> 1 hour

X=75/0.25----------> x=300 gallons /hour

the answer is 300 gallons /hour
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Answer:x<1/7 (5 - sqrt(130))

Step-by-step explanation:

4 0
3 years ago
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Simplify the equation given in the image
IRINA_888 [86]

Answer:

b^20/a^12

Step-by-step explanation:

b to the power of 20 over a to the power of 12

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3 years ago
Find the value of k so that 48x-ky=11 and (k+2)x+16y=-19 are perpendicular lines.
Rufina [12.5K]

Answer: k = -1 +/- √769

<u>Step-by-step explanation:</u>

48x - ky = 11

<u>-48x        </u>  <u> -48x</u>

         -ky = -48x + 11

         \frac{-ky}{-k} = \frac{-48x}{-k} + \frac{11}{-k}    

           y =\frac{48x}{k} - \frac{11}{k}

Slope: \frac{48}{k}

*************************************************************************

 (k + 2)x + 16y = -19

<u>- (k + 2)x          </u>   -<u>(k + 2)x </u>

                 16y = -(k + 2)x - 19

                  \frac{16y}{16} = -\frac{(k + 2)x}{16} - \frac{19}{16}

                  y = -\frac{(k + 2)x}{16} - \frac{19}{16}

Slope: -\frac{(k + 2)}{16}

**********************************************************************************

\frac{48}{k} and -\frac{(k + 2)}{16} are perpendicular so they have opposite signs and are reciprocals of each other.  When multiplied by its reciprocal, their product equals -1.

-\frac{(k + 2)}{16} *  \frac{k}{48} = -1

\frac{(k + 2)k}{16(48)} = 1

Cross multiply, then solve for the variable.

(k + 2)(k) = 16(48)

k² + 2k - 768 = 0

Use quadratic formula to solve:

k = -1 +/- √769



5 0
4 years ago
In the 2012 presidential election, exit polls from the critical state of Ohio provided the following results:
neonofarm [45]

Answer:

50% probability that a randomly selected respondent voted for Obama.

Step-by-step explanation:

We have these following probabilities:

60% probability that an Ohio resident does not have a college degree.

If an Ohio resident does not have a college degree, a 52% probability that he voted for Obama.

40% probability that an Ohio resident has a college degree.

If an Ohio resident has a college degree, a 47% probability that he voted for Obama.

What is the probability that a randomly selected respondent voted for Obama?

This is the sum of 52% of 60%(non college degree) and 47% of 40%(college degree).

So

P = 0.52*0.6 + 0.47*0.4 = 0.5

50% probability that a randomly selected respondent voted for Obama.

8 0
3 years ago
Divide 3.7÷0.006 round the answer the nearest hundredth?
Julli [10]
First divide 3.7 by 0.006
Which is 616.666
The last 6 is the thousandths place. If it is 5 or bigger then the number to the left is rounded up. If its lower than 5 you round down

Since 6 is over 5 we tound up
616.67
6 0
3 years ago
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