A tank that holds 6000 gallons of water may be filled by two pipes. One pipe pours water into the tank at the rate of 80 gallons per minute. The other fills the tank at the rate of 120 gallons per minute.

(a) If the pipes run simultaneously, how long will it take to fill the tank?

(b) The small pipe is opened and water is run into the tank for a certain length of time. Then this pipe is shut off and the large one is used to finish filling the tank. How long was each pipe used if it took 60 minutes to fill the tank?

(c) The large pipe alone is opened for a certain time and then both pipes together are used to finish filling the tank. If it takes 34 minutes to fill the tank in this manner, how long was the small pipe used?

Answers

Answer 1

Answer:

Below.

Step-by-step explanation:

Working together the rate is 80 + 120 = 200 gallons per minute.

(a) Time to fill tank = 6000 / 200 = 30 minutes.

(b) Let length of time the small pipe was used be x minutes , the the large pipe was used for is 60-x minutes.

Volume delivered by small pipe = y gallons, and by large pipe =  6000-y gallons.

Rate for small pipe = 80 = y/x.

Rate for large pipe = 120 = (6000-y) / 60-x.

y/x = 80

(6000-y) / 60-x = 120

From first equation y = 80x so:

6000 - 80 x =  7200  - 120x

40x = 1200

x = 30

So time for small pipe = 30 and time for large on = 30 minutes also.

C. In a similar way to part B:

y/x = 120  

(6000-y) / 34 - x = 200

(6000-120x) / 34 - x = 200

6000 - 120x = 6800 - 200x

80x = 800  so the large pipe on its own took 10 minutes and the small pipe was used for 34 - 10 = 24 minutes.


Related Questions

three times the sum of a number squared and 4​

Answers

Answer:

2

Step-by-step explanation:

3(N² + 4)

3N² = 12

3N² ÷ 3 = 12 ÷ 3

N² = 4

√N² = √4

N = 2

(2x+3y)²+(2x-3y)²

a) 4(2x)(3y)
b) 4(2x)(4y)
c) 6(3x)(5y)
d) 2((2x)²+(3y)²)
e) 2((x)²+(y)²)

Answers

Answer:

d) [tex]2 ({(2x)}^{2} + {(3y)}^{2} ) \\ [/tex]

Step-by-step explanation:

[tex] {(2x + 3y)}^{2} + {(2x - 3y)}^{2} \\ (2x + 3y)(2x + 3y) + (2x - 3y)(2x - 3y) \\ 2x(2x + 3y) + 3y(2x + 3y) + 2x(2x - 3y) - 3y(2x - 3y) \\ {4x}^{2} + 6xy + 6xy + {9y}^{2} + {4x}^{2} - 6xy - 6xy + {9y}^{2} \\ {4x}^{2} + 12xy + {9y}^{2} + {4x}^{2} - 12xy + {9y}^{2} \\ {4x}^{2} + {9y}^{2} + {4x}^{2} + {9y}^{2} \\ {8x}^{2} + {18y}^{2} \\ 2( {4x}^{2} + {9y}^{2} ) \\ 2( {2}^{2} {x}^{2} + {3}^{2} {y}^{2} ) \\ 2({(2x)}^{2} + {(3y)}^{2}) \\[/tex]

Step-by-step explanation:

d num i think 2((2x)^2+(3y)^2)

what is an equation of the line in the slope- intersepct is (0,3)

Answers

Answer:

using the formula x/a + y/b =1

a: slope intercept on the x axis

b:slope intersect on the y axis

x/0 + y/3 = 1 (since x/0 is undefined ,the slope doesn't exist and it is impossible for a slope to be linear)

The question is in the pic! Please help :)

Answers

The answer is D.

If you go to point E and count back 4 units, you will land on point B.

Hope this helps! :)

The measure of the third angle in an isosceles triangle is 55.5 more than the measure of either of the two equal angles. Find the measure of the third angle

Answers

Answer:

The third angle is 97º

Step-by-step explanation:

a triangle has 180º total

so 180-55.5=124.5

124.5÷3=41.5

then add the 55.5 back

41.5+55.5=97

97º

Enter the polynomial function with the least degree and a leading coefficient of 1 that has the given zeros. Enter your answer in standard form. 1,-1(multiplicity 3), and 3i

Answers

Answer:

0

Step-by-step explanation:

Write the equation of a parabola in vertex form.  vertex (2,3) point (3,-2). F(x)= ?

Answers

For these you would need the app “desmos” you need a table for that so first you put for the y-axis as 2 and 3 and then for the y-axis you put 3 and -2 after you do that you need to put y1~mx1+b then you get the answer as -5

During a hot summer week, Mr. Singh sold 60 watermelons. On Monday, he sold
he sold half the number of watermelons he sold on Monday. On Thursday, Mr. Singh sold 18
watermelons. On Tuesday, he sold twice as many watermelons than Monday. On Wednesday,
watermelons. On Friday, he sold four more than twice the amount he sold on Monday and
Tuesday combined. How many watermelons did he sell on Friday?


Help please

Answers

what's half 60? 30. hope that helps!

Find the total cost of a $32 Uber ride with a 15% tip.

Answers

Answer:

$36.8

Step-by-step explanation:

i just calculated it!

32*15% = 4.8

32+4.8= 36.8

whats 3+6÷2



PLEASE EXPLAIN

Answers

Answer:

6

Step-by-step explanation:

6 devide 2 is 3. 3 plus 3 is 6

Answer:6

Step-by-step explanation: It is solved by BODMAS

BODMAS is a code which means

B= brackets

O=of(*)

D=division

M=multiplication

A=addition

S=subtraction

So first of all 6 divide by 2 then add 3 you will get answer 6

Can someone help me with part B?? I already did part A

Thank you so much :)

Answers

Answer:

-150

Step-by-step explanation:

this is because you do 250 - 100 which equals -150

In part A you subtracted 100 from 100 giving you 0.

Continuing to part B you would subtract 100 from 250 leaving you with 150.

-19=-14v+14v
Solve for V
:) gets brainliest

Answers

[tex]▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ { \huge \mathfrak{Answer}}▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ [/tex]

Let's solve for v :

[tex] - 19 = - 14v + 14v[/tex]

here, the the terms associated with v, that us -14v and 14v gets cancel out, so there's no solution for v and hence it's value can't be determined.

Which property of addition is shown here? (4+5)+6=4+(5+6)

Answers

Answer:

I am pretty sure it is Associative property of addition

Step-by-step explanation:

Which fraction is equal to 0.7 repeating

Answers

Answer:7/9

Step-by-step explanation:

Answer:

7/9

Step-by-step explanation:

I hope this helps you.

( BRAINLIEST QUEATION)
Find the HCF and LCM of 72 and 56

Answers

for detailed and showed working my answer is in the picture above

lcm = 504

hcf = 8

Answer:

The HCF of 72 and 56 is 8

and, the LCM is 504

If two angles add up to 180 how many angles are there?

Answers

Answer:

Step-by-step explanation:

According to Supplementary Angles rules: two angles add up to 180

Help this is due tmr!!

Answers

Answer:

A is correct

Step-by-step explanation:

ind all natural numbers n such that 1+3+5+7+...+(2n-1) sum is divisible by 4

Answers

Answer:

All even natural numbers

Step-by-step explanation:

This is an AP with:

The first term = 1Number of terms = nCommon difference = 2

Find the sum of the first n terms:

[tex]S_n= n(1+2n-1)/2=n^2[/tex]

The sum is divisible by 4 if n is even number:

n = 2k ⇒ n² = 4k² ≡ 0 mod 4

What is the weight, in kg, shown by the arrow on the scale below?

See pic attached

Answers

Step-by-step explanation:

according to arrow the weight is 1400 g.

we know,

1 kg = 1000 g

so,

1 g = 1/1000 kg

so,

1400/1000 = 1.4 kg ans

hope this answer helps you dear!

Answer:

1.4 kg

Step-by-step explanation:

1400 grams, to find kg you have to divide by 1000

What are the coordinates of the office? Enter the coordinates like this: (x,y) without any spaces. *

Answers

Answer:

Step-by-step explanation:

(6,9) it think its that

4 2/3x4=something/3x4/1=

Answers

Answer:

4 2/3x4= 14x^4/3

3x4/1 = 3^4

Step-by-step explanation:

It took Valerie 80 minutes to drive 120 miles. Which of the following unit rates expresses how fast Valerie was traveling?
60 miles per hour 70 miles per hour
80 miles per hour 90 miles per hour

Answers

Answer:

90 miles per hour

Step-by-step explanation:

Divide distance by time to get speed.

[tex]\frac{120}{80}[/tex]=1.5 miles per minute

60 minutes in an hour

1.5(60)=90 miles an hour

17. Determine if the following segments can or cannot be a triangle.

3 m., 4 m., and 1 m.
⬜ Yes ⬜ No


12 ft., 3 ft., and 11 ft.
⬜ Yes ⬜ No
24 in., 13 in., and 5 in.
⬜ Yes ⬜ No


9.81 m., 16 m., and 6.19 m.
⬜ Yes ⬜ No
5 yds., 13 yds., and 10 yds.
⬜ Yes ⬜ No


2.5 cm., 2.5 cm., and 2.5 cm.
⬜ Yes ⬜ No
6 mm., 4 mm., and 9 mm.
⬜ Yes ⬜ No


7 ft., 7 ft., and 7 ft.
⬜ Yes ⬜ No

Answers

Answer:

Step-by-step explanation:

1. 5 cm, 7 cm, 10 cm

SOLUTION:  

The sum of the lengths of any two sides of a triangle

must be greater than the length of the third side.

5 + 7 > 10, 5 + 10 > 7, and 7 + 10 > 5

Thus, you can form a triangle with side lengths 5 cm,

7 cm, and 10 cm.  

ANSWER:  

Yes; 5 + 7 > 10, 5 + 10 > 7, and 7 + 10 > 5

2. 3 in., 4 in., 8 in.

ANSWER:  

No;

3. 6 m, 14 m, 10 m

ANSWER:  

Yes; 6 + 14 > 10, 6 + 10 > 14, and 10 + 14 > 6

4. MULTIPLE CHOICE If the measures of two

sides of a triangle are 5 yards and 9 yards, what is

the least possible measure of the third side if the

measure is an integer?

A 4 yd

B 5 yd

C 6 yd

D 14 yd

The correct option is B.

ANSWER:  

B

PROOF Write a two-column proof.

5. Given:

Given:

Prove: YZ + ZW > XW

Proof:

Statements (Reasons)

1.  (Given)

2. XW = YW (Def. of segments)

3. YZ + ZW > YW ( Inequal. Thm.)

4. YZ + ZW > XW (Substitution Property.)

ANSWER:  

Given:

Prove: YZ + ZW > XW

Proof:

Statements (Reasons)

1.  (Given)

2. XW = YW (Def. of segments)

3. YZ + ZW > YW ( Inequal. Thm.)

4. YZ + ZW > XW (Subst.)

Is it possible to form a triangle with the given

side lengths? If not, explain why not.

6. 4 ft, 9 ft, 15 ft

ANSWER:  

No;

7. 11 mm, 21 mm, 16 mm

ANSWER:  

Yes; 11 + 21 > 16, 11 + 16 > 21, and 16 + 21 > 11

8. 9.9 cm, 1.1 cm, 8.2 cm

No;

9. 2.1 in., 4.2 in., 7.9 in.

ANSWER:  

No;

10.  

No;

11.  

ANSWER:  

Yes;

Find the range for the measure of the third side

of a triangle given the measures of two sides.

12. 4 ft, 8 ft

ANSWER:  

4 ft < n < 12 ft

13. 5 m, 11 m

ANSWER:  

6 m < n < 16 m

14. 2.7 cm, 4.2 cm

ANSWER:  

1.5 cm < n < 6.9 cm

15. 3.8 in., 9.2 in.

13.

ANSWER:  

5.4 in. < n < 13 in.

16.  

ANSWER:  

17.  

 

ANSWER:  

Proof:

Statements (Reasons)

1.  (Given)

2.  (Conv. Isos.  Thm.)

3. BC = BD (Def. of  segments)

4. AB + AD > BD ( Inequal. Thm.)

5. AB + AD > BC (Subst.)

19. Given:

Prove: KJ +KL> LM  

Proof:

Statements (Reasons)

1.  (Given)

2. JL = LM (Def. of  segments)

3. KJ + KL > JL ( Inequality Thm.)

4. KJ + KL > LM (Substitution Property)

ANSWER:  

Proof:

Statements (Reasons)

1.  (Given)

2. JL = LM (Def. of  segments)

3. KJ + KL > JL ( Inequal. Thm.)

4. KJ + KL > LM (Subst.)

SENSE-MAKING Determine the possible

values of x.

20.  

   

     

Notice that  is always true for any whole  

number measure for x.The range of values that

would be true for the other two inequalities is

and  , which can be written as

.

ANSWER:  

6 < x < 17

21.  

ANSWER:  

22. TRAVEL Keyan wants to take the most efficient

route from his hotel to the hockey game at The

Sportsplex. He can either take Highway 521 or

take Highway 3 and Route 11 from his hotel to the

arena.

a. Which of these two possible routes is the shorter?

Explain your reasoning.

b. Suppose Keyan always drives the speed l

Is it possible to form a triangle with the given

side lengths? If not, explain why not.

1. 5 cm, 7 cm, 10 cm

ANSWER:  

Yes; 5 + 7 > 10, 5 + 10 > 7, and 7 + 10 > 5

2. 3 in., 4 in., 8 in.

ANSWER:  

No;

3. 6 m, 14 m, 10 m

ANSWER:  

Yes; 6 + 14 > 10, 6 + 10 > 14, and 10 + 14 > 6

4. MULTIPLE CHOICE If the measures of two

sides of a triangle are 5 yards and 9 yards, what is

the least possible measure of the third side if the

measure is an integer?

A 4 yd

B 5 yd

C 6 yd

D 14 yd

ANSWER:  

B

Given:

Prove: YZ + ZW > XW

Proof:

Statements (Reasons)

1.  (Given)

2. XW = YW (Def. of segments)

3. YZ + ZW > YW ( Inequal. Thm.)

4. YZ + ZW > XW (Subst.)

Is it possible to form a triangle with the given

side lengths? If not, explain why not.

6. 4 ft, 9 ft, 15 ft

ANSWER:  

No;

7. 11 mm, 21 mm, 16 mm

SOLUTION:  

ANSWER:  

Yes; 11 + 21 > 16, 11 + 16 > 21, and 16 + 21 > 11

8. 9.9 cm, 1.1 cm, 8.2 cm

SOLUTION:  

T

No;

9. 2.1 in., 4.2 in., 7.9 in.

No;

10.  

ANSWER:  

No;

11.  

.  

ANSWER:  

Yes;

Find the range for the measure of the third side

of a triangle given the measures of two sides.

12. 4 ft, 8 ft

4 ft < n < 12 ft

13. 5 m, 11 m

6 m < n < 16 m

14. 2.7 cm, 4.2 cm

ANSWER:  

1.5 cm < n < 6.9 cm

15. 3.8 in., 9.2 in.

13.

ANSWER:  

5.4 in. < n < 13 in.

16.  

   

 

Proof:

Statements (Reasons)

1.  (Given)

2. JL = LM (Def. of  segments)

3. KJ + KL > JL ( Inequal. Thm.)

4. KJ + KL > LM (Subst.)

SENSE-MAKING Determine the possible

values of x.

20.  

SOLUTION:  

Set up and solve each of the three triangle

inequalities.

   

     

ANSWER:  

6 < x < 17

21.  

 

ANSWER:  

Yes; 5 + 7 > 10, 5 + 10 > 7, and 7 + 10 > 5

2. 3 in., 4 in., 8 in.

ANSWER:  

No;

3. 6 m, 14 m, 10 m

ANSWER:  

Yes; 6 + 14 > 10, 6 + 10 > 14, and 10 + 14 > 6

4. MULTIPLE CHOICE If the measures of two

sides of a triangle are 5 yards and 9 yards, what is

the least possible measure of the third side if the

measure is an integer?

A 4 yd

B 5 yd

C 6 yd

D 14 yd

 

The correct option is B.

ANSWER:  

B

ANSWER:  

No;

7. 11 mm, 21 mm, 16 mm

SOLUTION:  

ANSWER:  

Yes; 11 + 21 > 16, 11 + 16 > 21, and 16 + 21 > 11

8. 9.9 cm, 1.1 cm, 8.2 cm

 

ANSWER:  

No;

9. 2.1 in., 4.2 in., 7.9 in.

Given f(x) and g(x)
f(x) + k, use the graph to determine the value of k.

Answers

Answer:

k =4

k is the amplitude of f(x)

what is the average hourly pay of someone making $45,000per year. Assuming wage growth of 5% a year, how much would he make the second year

Answers

Answer:

When it’s time for annual performance reviews, if you plan on including pay raises, you need to know the simple math behind calculating pay increases correctly. Raises can be based on any number of things including a worker’s piers, standard industry rates, length of time on the job, the amount of work to do, and even whether or not the boss likes the employee or not. There are few, if any, laws that govern how and when increases are granted, so it’s up to you to determine what you’re willing to give.

Answer:

See below

Step-by-step explanation:

Assume the person works 40 hours a week and 52 weeks a year.

The hourly pay would be:

$45000 ÷ (40*52) = $45000 ÷ 2080 =$21.63

The yearly income the second year:

$45000 + 5% = $45000*1.05 = $47250

help me please please




Answers

Answer:

9875 dollars I believe is your answer

Answer:

9,875

Step-by-step explanation:

u just multiply the number of boxes by 395

Which equation best represents the line graphed above?

Answers

Answer: x=2 because for any y value the x value is always 2.

A house was originally listed for sale at $250,00. After 3 months, the seller dropped the price to $235,000. What percent of decrease in the price

Answers

the correct answer is 6%

Explain why x2+7x+4=7x has no solutions.

Answers

[tex]x^2+7x+4=7x[/tex]

[tex]x^2+4=0[/tex]

[tex]x^2=-4[/tex]

Square of any real number cannot be negative because - * - = + so this equation has no solutions

Trey is taking his friends out to dinner to celebrate graduation. It will cost him $72 to reserve a table, and another $5 per guest. How many people can he invite if he can only spend up to $130?​

Answers

Answer:

11 people

Step-by-step explanation:

first, youd subtract the table reservation price from the max price.

130 - 72 = 58

then, since each person costs $5, you find the highest multiple of 5.

in this case, its 55, which has 11 groups of 5 in it.

to make sure:

you can then subtract 55 from 58 to make sure there isnt any extra 5's.

58 - 55 = 3.

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