1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
natita [175]
3 years ago
9

A water tank holds 486 gallons but leaking at a rate 4 gallons per week. A second water tank holds 648 gallons but is leaking at

a rate of 7 gallons per week. After how many weeks will the amount of water in the 2 tanks? The amount of water that holds the two tanks will be the same in _ weeks.
Mathematics
1 answer:
notka56 [123]3 years ago
6 0

The first tank contains

486 gal - (4 gal/week) <em>t</em>

gal of water after <em>t</em> weeks.

Similarly, the second tank contains

648 gal - (7 gal/week) <em>t</em>

gal of water.

The tanks hold the same amount of water when these two amounts are equal:

486 gal - (4 gal/week) <em>t</em> = 648 gal - (7 gal/week) <em>t</em>

(7 gal/week) <em>t</em> - (4 gal/week) <em>t</em> = 648 gal - 486 gal

(3 gal/week) <em>t</em> = 162 gal

<em>t</em> = (162 gal) / (3 gal/week)

<em>t</em> = 54 weeks

You might be interested in
A runner charted how long it took her to run certain distances. Here is the
Serga [27]

Answer:

Step-by-step explanation:8

7 0
3 years ago
How many solutions does the system of equations below have?
soldier1979 [14.2K]

Answer:

One solution                    

Step-by-step explanation:

5x + y = 8

15x + 15y = 14

Lets solve using substitution, first we need to turn "5x + = 8" into "y = mx + b" or slope - intercept form

So we solve for "y" in the equation "5x + y = 8"

5x + y = 8

Step 1: Subtract 5x from both sides.

5x + y − 5x = 8 − 5x

Step 2: 5x subtracted by 5x cancel out and "8 - 5x" are flipped

y = −5x + 8

Now we can solve using substitution:

We substitute "-5x + 8" into the equation "15x + 15y = 14" for y

So it would look like this:

15x + 15(-5x + 8) = 14

Now we just solve for x

15x + (15)(−5x) + (15)(8) = 14(Distribute)

15x − 75x + 120 = 14

(15x − 75x) + (120) = 14(Combine Like Terms)

−60x + 120 = 14

Step 2: Subtract 120 from both sides.

−60x + 120 − 120 = 14 − 120

−60x = −106

Divide both sides by -60

\dfrac{ -60x  }{ -60  }   =   \dfrac{ -106  }{ -60  }

Simplify

x =   \dfrac{ 53  }{ 30  }

Now that we know the value of x, we can solve for y in any of the equations, but let's use the equation "y = −5x + 8"

\mathrm{So\:it\:would\:look\:like\:this:\ y =  -5 \left(  \dfrac{ 53  }{ 30  }    \right)  +8}

\mathrm{Now\:lets\:solve\:for\:"y"\:then}

y =  -5 \left(  \dfrac{ 53  }{ 30  }    \right)  +8}

\mathrm{Express\: -5 \times   \dfrac{ 53  }{ 30  }\:as\:a\:single\:fraction}

y =   \dfrac{ -5 \times  53  }{ 30  }  +8

\mathrm{Multiply\:-5 \:and\:53\:to\:get\:-265 }

y =   \dfrac{ -265  }{ 30  }  +8

\mathrm{Simplify\:  \dfrac{ -265  }{ 30  }    \:,by\:dividing\:both\:-265\:and\:30\:by\:5} }

y =   \dfrac{ -265 \div  5  }{ 30 \div  5  }  +8

\mathrm{Simplify}

y =  - \dfrac{ 53  }{ 6  }  +8

\mathrm{Turn\:8\:into\:a\:fraction\:that\:has\:the\:same\:denominator\:as\: - \dfrac{ 53  }{ 6  }}

\mathrm{Multiples\:of\:1: \:1,2,3,4,5,6}

\mathrm{Multiples\:of\:6: \:6,12,18,24,30,36,42,48}

\mathrm{Convert\:8\:to\:fraction\:\dfrac{ 48  }{ 6  }}

y =  - \dfrac{ 53  }{ 6  }  + \dfrac{ 48  }{ 6  }

\mathrm{Since\: - \dfrac{ 53  }{ 6  }\:have\:the\:same\:denominator\:,\:add\:them\:by\:adding\:their\:numerators}

y =   \dfrac{ -53+48  }{ 6  }

\mathrm{Add\: -53 \: and\: 48\: to\: get\:  -5}

y =  - \dfrac{ 5  }{ 6  }

\mathrm{The\:solution\:is\:the\:ordered\:pair\:(\dfrac{ 53  }{ 30  }, - \dfrac{ 5  }{ 6  })}

So there is only one solution to the equation.

5 0
2 years ago
You bought 15 apples and 2 bags of Carmel for $16.00. The bags of caramel costs $5.35. How much does each apple cost? Write an e
OLga [1]

Answer:

5.35*2+x=16 and the answer is $.35

Step-by-step explanation:

5.35*2+x=16

10.70+x=16

-10.70     -10.70

x=5.30

5.30/15= about .35

6 0
3 years ago
Read 2 more answers
2m = 1 + m what do I need to do to solve
devlian [24]

So all you need to do is subtract m from both sides.

Then you have your answer

m = 1

I hope this helps

-ayden

4 0
3 years ago
Read 2 more answers
A sample is selected from a population with μ = 46, and a treatment is administered to the sample. After treatment, the sample m
Georgia [21]

Answer:

0.5

Step-by-step explanation:

Solution:-

- The sample mean before treatment, μ1 = 46  

- The sample mean  after treatment, μ2 = 48

- The sample standard deviation σ = √16 = 4

- For the independent samples T-test, Cohen's d is determined by calculating the mean difference between your two groups, and then dividing the result by the pooled standard deviation.

                           Cohen's d = \frac{u2 - u1}{sd_p_o_o_l_e_d}

- Where, the pooled standard deviation (sd_pooled) is calculated using the formula:

                          sd_p_o_o_l_e_d =\sqrt{\frac{SD_1^2 +SD_2^2}{2} }

- Assuming that population standard deviation and sample standard deviation are same:

                          SD_1 = SD_2 =  σ = 4

- Then,

                           sd_p_o_o_l_e_d =\sqrt{\frac{4^2 +4^2}{2} } = 4

- The cohen's d can now be evaliated:

                          Cohen's d = \frac{48 - 46}{4} = 0.5

6 0
3 years ago
Other questions:
  • Math help? 1-2 please and thank you.
    12·1 answer
  • Mia hired a moving company . The company charged $500 for its services and Mia gives the movers a 16% tip. How much does Mia tip
    11·1 answer
  • whats another way to write (s-6)(s+1) when s represents the side of a square and the equation represents the area of a rectangle
    8·1 answer
  • Value times frequency equals product.<br> True or False
    9·2 answers
  • Bobby Joe and Billy ray went fishing at the local watering hole and caught a total of 51 fish. Billy Rat caught 17 fewer fish th
    5·1 answer
  • Translate the phrase into a math expression.
    15·2 answers
  • Which statement about the function is true?
    10·1 answer
  • Joe has read 30% of a book. He has 49 more pages to finish. How many pages are there in the book?
    14·1 answer
  • The diameter of a £1 coin is 22.5 mm. Work out its circumference to the nearest centimetre.Required to answer. Single choice.
    7·1 answer
  • 6(y + 8) = I need help please :)
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!