A large tank is partially filled with a solution. The tank has a faucet that allows solution to enter the tank at a rate of 16 3/4 liters per minute. The tank also has a drain that allows solution to leave the tank at a rate of 19 4/5 liters per minute. (a) What expression represents the change in volume of solution in the tank in 1 minute? (b) Simplify and give your answer as a simplified mixed number. (c) What is the change in volume of the solution after 10 minutes? Show necessary work. Give your answer as a simplified mixed number.

Answers

Answer 1

The change in volume per minute and the total change in the volume of the solution after 10 minutes will be [tex] - 3 \frac {1}{20} \: litres [/tex] and [tex]- 30 \frac {1}{2} \: litres [/tex] respectively.

Entry rate = [tex] 16 \frac{3}{4} [/tex] per minute

Discharge rate = [tex] 19 \frac{4}{5} [/tex] per minute

Change in the volume of solution in the tank per minute can be calculated thus :

Change in volume = (Entry rate - Discharge rate) × time

[tex] 16 \frac{3}{4} - 19 \frac{4}{5} = \frac{67}{4} - \frac{99}{5} = \frac{(335 - 396)}{20} = \frac{-61}{20} = - 3\frac{1}{20} \: litres \: per \: minute [/tex]

The total change in the volume of solution in the tank after 10 minutes can be calculated thus :

Change in volume per minute × time

[tex] - \frac{61}{20} \times 10 = - \frac{610}{20} = - 30 \frac {1}{2} \: litres [/tex]

Therefore, the solution in the tank decreases by [tex] 30 \frac {1}{2} \: litres [/tex] after 10 minutes

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Related Questions

What makes an equation false?

Answers

Answer:

When ever you can’t solve it it considered false like 4 - 12

Step-by-step explanation:

A false equation is an incorrect equation; it says something erroneous or untrue. For example, 2 = 3 is a false equation, because 2 and 3 are different numerical values. To make a true equation, check your math to make sure that the values on each side of the equals sign are the same.

help please , i need it asap ! ty

Answers

Answer:

7.5

Step-by-step explanation:

Answer:

Step-by-step explanation:

If the one side = 3 and the other side (4.5) is supposed to be the same all it is is 4.5/3 which is 1.5. 1.5 times 5 ( the bottom side) is 7.5! X=7.5

Kelly purchased a t-shirt
for 9.99 and a pair of
jeans for $21.50. The
sales tax rate is 8.25%.
What was the total cost
of Kelly's purchase
(including sales tax)?


PLEASE HELP

Answers

Answer:

34.09

Step-by-step explanation:

Answer: $34.09

Step-by-step explanation:

Find the size of the final unknown exterior angle in a polygon whose other exterior angles are:

57°, 68°, 32°, 59° and 72°.

Answers

Answer:

=72

Step-by-step explanation:

57+68+32+59+72=288

360-288=72

The slope of the line below is 3. Write the equation of the line in point-slope
form, using the coordinates of the labeled point. Do not use parenthesis on
the y-side.
(-1,1)
-5
5
-5

Answers

Answer:

The equation of the line in point-slope form is [tex]y - 1 = m(x + 1)[/tex]

Step-by-step explanation:

Equation of a line:

The equation of a line, in point-slope form, is given by:

[tex]y - y_0 = m(x - x_0)[/tex]

In which the point is given by [tex](x_0,y_0)[/tex] and m is the slope.

The slope of the line below is 3.

This means that [tex]m = 3[/tex]

(-1,1)

This means that [tex]x_0 = -1, y_0 = 1[/tex].

Equation of the line:

[tex]y - y_0 = m(x - x_0)[/tex]

[tex]y - 1 = m(x - (-1))[/tex]

[tex]y - 1 = m(x + 1)[/tex]

The equation of the line in point-slope form is [tex]y - 1 = m(x + 1)[/tex]

Use the diagram to complete the statement!
Due in 10 min! Please help!
Will give brainliest!

Answers

Answer:

m>NQR=30°

m<LNS=61°

RQ=7

Step-by-step explanation:

m>NQR=180-89-61=30°

m<LNS=61°

RQ= 8/4=x/3.5 = 7

A merry go around has a radius of 18 ft. If a passenger gets on a horse located at the edge of the wheel and travels 38ft, find the angle of rotation to the nearest degree

Answers

Answer:

121 degrees

Step-by-step explanation:

Given

Radius r = 18ft

Length of the arc = 38ft

Required

angle of rotation

Using the formula

Length of an arc = theta/360 * 2πr

Substitute the given data

38 = theta/360 * 2π(18)

38 = theta/360 * 113.04

theta/360 = 38/113.04

theta/360 = 0.33616

theta = 0.33616 * 360

theta = 121.02

Hence the angle of rotation to the nearest degree is 121 degrees

Perimeter = 26 yards

Answers

Answer:

There isn’t a answer

Step-by-step explanation:

Where is the question? I’ll edit the message if there is something that needs to be solved otherwise this doesn’t make sense.

QUESTION 5 of 10: Throughput is the number of units a machine or process can produce in a given time. Cycle time is the time to produce
one unit. If the cycle time of your machine is 35 seconds and it runs 24/7, what is the throughput for a year period?
O a) 901,029
Ob) 969,623
c) 1,180,336
d) 1,173,322

Answers

9514 1404 393

Answer:

  a) 901,029

Step-by-step explanation:

The production volume for 1 year is ...

  1 unit/(35 s) × (3600 s)/(1 h) × (24 h)/(1 day) × (365 day)/(1 year)

  = 3600×24×365/35 unit/year = 901,029 unit/year

8. An isosceles triangle includes two 56' angles. Which equation could be
used to find the measure of the third angle?

Answers

Answer:

B. x=180-2(56)

Step-by-step explanation:

Isosceles triangles have 2 angles of equal measure and 1 different measure. we add both measures or multiply them by 2 and then subtract them from 180 (sum of all angle measurements in a triangle) to find the missing measure

A line includes the points (1,9) and (4,24). What is the equation in slope-intercept form?

Answers

Answer:

y = 5x+4

Step-by-step explanation:

The slope-intercept form of an equation is like this:

y= mx+b

M stands for the slope and b for the y-intercept.

First, we need to find the slope:

m= slope= y1-y2/ x1-x2m= slope= 9-24/1-4m= 5

Now we know: y= 5x+b

Now, to find b we have to choose one of your points. Let's use the first given point: (1, 9)

With the slope-intercept form equation I showed before, substitute x and y with the values of one point.

9= 5(1)+b9= 5+b9- 5= 5-5+b4= b

Substitute the b in the equation, and that's your answer:

y= 5x+4

What is the vertical distance from the origin to the point (8, 1)?

Answers

Answer:

The vertical distance is 1.

Explanation:

Coordinates are structured as ( x , y )

The "x" is horizontal and the "y" is vertical, when placed onto a graph.

In the question, 8 is "x" and 1 is "y". Meaning the vertical number is 1.

can someone please help me? I really need help

Answers

Answer:

x=49

<A=90

<E=147

Step-by-step explanation:

1. Name an example of a real-world data set, not yet mentioned in the course, where you would typically expect to see a normal distribution. Be sure to describe what the labels would be for the horizontal and vertical axis of the display. Then explain why you would expect a normal distribution. What range of data values would you expect to represent 1 standard deviation from the mean? (15 points; 10 for your answer, 5 for response to others' comments.)​

Answers

Answer:

1.The heights of students in a class, for example, would have a normal distribution. We expect a few students to be extremely tall and a few to be extremely short, but the majority will be in the middle. On the x-axis, we'll have heights, and on the y-axis, we'll have the frequency of the number of students with heights. According to the empirical rule, 68 percent of the data could fall within one standard deviation of the mean.

7. Newton buys a board game for $9.99
and a pack of trading cards for $2.99.
He gives the cashier a $20 bill. How
much change does he receive?
AWNSER ASAPP

Answers

Answer: Hello, there!  Your Answer is Below^^

7.O2 Would be The Correct Answer.

Step-by-step explanation:

So I Subtracted 20 - 12.98 And Got the Answer $ 7.02

To Add Or subtract Decimals Here's what you can do to find your Answer

Line up the numbers vertically so that the decimal points all lie on a vertical line.  

Add extra zeros to the right of the number so that each number has the same number of digits to the right of the decimal place. Step 3: Subtract the numbers as you would whole numbers.

Hope this Helps!!

Have a great day!!!

Rule 1: Add 7 starting from 0. Rule 2: Multiply by 2 starting from 8. Select the option that correctly shows the first 5 terms of each sequence.
Question 5 options:

First sequence: 0, 6, 12, 18, 24 and second sequence: 0, 8, 16, 32, 64

First sequence: 0, 7, 14, 21, 28 and second sequence: 8, 16, 32, 64, 128

First sequence: 0, 7, 14, 21, 28 and second sequence: 8, 14, 28, 56, 112

First sequence: 14, 21, 28, 35, 42 and second sequence: 8, 16, 32, 64, 128

Answers

Answer:

First sequence: 0, 7, 14, 21, 28 and second sequence: 8, 16, 32, 64, 128

Answer:

First sequence: 0, 7, 14, 21, 28 and second sequence: 8, 16, 32, 64, 128

Step-by-step explanation:

A square playground is covered with pebbles, except for two equal size triangular portions that have grass. How many square feet do the pebbles cover? 7ft 14ft

Answers

Answer:

The anser is 14 times 7 = 98ft

Step-by-step explanation:

-67.2-61.5−67.2−61.5

Answers

Answer:

-257.4

Step-by-step explanation:

-257.4 trust meh

Answer:

-257.4

mark as brainliest

Find the surface area of the prism.

Answers

Answer:

The surface area of the prism is 386m²

Step-by-step explanation:

The surface area of a box is equal to the sum of the areas of each side of the box.

[tex]2 \times (lenght) \times (widht) + 2 \times (lenght) \times (height) + 2 \times (width) \times (height)[/tex]

Substitute the values of the length l=15, the width w=7, and the height h=4 into the formula.

[tex]2 \times 15 \times 7 + 2 \times 15 \times 4 + 2 \times 7 \times 4[/tex]

Simplify each term.

[tex]210 + 120 + 56[/tex]

Simplify by adding numbers.

[tex]386m ^{2} [/tex]

Hence, the Surface area of this prism is 386m².

find the length of x


help please i need it asap

Answers

Step-by-step explanation:

[tex] \frac{6}{4.5} = \frac{4}{x} \\x \times 6 = 4 \times 4.5 \\ x = \frac{4 \times 4.5}{6} \\ x = \frac{18}{6} \\ x = 3[/tex]

#CMIIW

Find the area of the white region in the diagram shown.

Answers

Answer:

Option 4

Step-by-step explanation:

Area of shaded region = Area of the circle - Area of the shaded triangles

Area of the circle = πr²

r = Radius of the circle

Therefore, area of the circle = π(4)²

                                               = 16π

Area of the given triangles = [tex]2[\frac{1}{2}(\text{Base})(\text{Height})][/tex]

                                             = Base × Height

                                             = (4 × 4)

                                             = 16

Area of the shaded region = 16π - 16

Option 4 will be the correct option.

Thousands of people are going to a Grateful dead concert in Pauley Pavillion at UCLA. They park their the foot cars on several of the long streets near the arena. There are no lines to tell the drivers where to park, so they park at random locations, and end up leaving spacings between the cars that are independent and uniform on .0; 10/. In the long run, what fraction of the street is covered with cars

Answers

This question is incomplete, the complete question is;

Thousands of people are going to a Grateful dead concert in Pauley Pavilion at UCLA. They park their 10 foot cars on several of the long streets near the arena. There are no lines to tell the drivers where to park, so they park at random locations, and end up leaving spacings between the cars that are independent and uniform on ( 0, 10 ). In the long run, what fraction of the street is covered with cars?.

Answer:

in the long run, the fraction of street that will be covered with cars is 0.6667

Step-by-step explanation:

 given the data in the question;

the gaps between two cars follows uniformly ) 0, 10 )

therefore in the long run, average gap will be;

⇒ (0 + 10) / 2 = 10 / 2 = 5 feet

meaning that, in the long run a single car will occupy;

⇒ length of car + gap

⇒ 10 + 5 = 15 feet

∴ the fraction of road covered with cars will be;

⇒ length of car / space or length of road occupied by one car

⇒ 10 / 15

0.6667

Therefore, in the long run, the fraction of street that will be covered with cars is 0.6667

can someone please help me and not jsut want points ebcause i relaly need help..
y=9x
y=2x+63

Answers

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ANSWER THE QUESTION FOR BRAINLIEST

Answers

A speed rate….=constant of proportionality

A number, k……=unit rate

A ratio…………….=slope


Answer:

Step-by-step explanation:

A speed rate = constant of proportionality

A number, k = unit rate

A ratio = slope

Okay Ju|ian Foley simplifies this polynomial and then write it in standard form if Ju|ian wrote it the last term

Answers

Answer:

the second choice

Step-by-step explanation:

Find the sum of these polynomials.
(4x2 + 3x - 1) + (x2 - 5x - 6) =

Answers

Answer:      5x2-2x-7

Step-by-step explanation:

(4x2 + 3x - 1) + (x2 - 5x - 6)

=4x2+3x-1+x2-5x-6

=5x2-2x-7

Genies is making cookies. She needs 1 2/3 cups of flour for one batch, but she wants to make 2 1/3 batches. Write an equation that can be used to find how many cups of flour genies will need

Answers

Equation:  (1 2/3)(2 1/3) = x

Answer:  3 8/9 cups

Step-by-step explanation:

x represents the amount of flour she will need in cups.

To solve, convert the mixed numbers to improper fractions and multiply...

1 2/3 becomes 5/3

2 1/3 becomes 7/3

Now we have

(5/3)(7/3) = x

  35/9 = x

35/9 is 3 8/9 as a mixed number

helpppppppppppp meee

Answers

Answer:

-8

Step-by-step explanation:

Plz give brainliest

i dont have any

-8 is the correct answer!-1 - 7is the same as-1 + -7

How -15 + 8 gives me 7 ????????

Answers

it doesn’t give you 7
it gives you -7
because when you add 8 to negative 15, you’re just basically subtracting it to give you -7

Answer:

It gives you -7

Step-by-step explanation:

Think of the problem as 8 - 15, because 8 is a smaller number and 15 is bigger, you'll get a negative number.

The next step is use the rule**a-b = -(b-a)**which is - (15 - 8)

Then when you simplify it, it will be - (15 - 8)= - 7**(which is the answer)

Hope this helps:)

The length of a rectangular swimming pool is exactly three times as long
as its width. If the pool has a perimeter of 472m find the width of the pool

Answers

Answer:

59m

Step-by-step explanation:

Length= 3 × ( width)

But perimeter= 2width + 2 Lenght= 472

Let length= X

Width= Y

X= 3Y.........eqn(1)

2X + 2Y= 472........eqn(2)

Substitute X= 3Y in eqn(2)

2(3Y) + 2Y = 472

6Y + 2Y= 472

8Y= 472

Y= 59 m

Hence, the width of the pool is 59 m

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