The cold water tap can fill a container two hours faster than the hot water tap. The two taps together can fill a container in 80 minutes. How long does it take each tap to fill the container on its own?

Using the shell method, the volume is

[tex]\displaystyle 2\pi \int_0^1 (2-x) \cdot 8x^3 \, dx = 16\pi \int_0^1 (2x^3 - x^4) \, dx[/tex]

Each cylindrical shell has radius [tex]2-x[/tex] (the horizontal distance from the axis of revolution to the curve [tex]y=8x^3[/tex]); has height [tex]8x^3[/tex] (the vertical distance between a point on the [tex]x[/tex]-axis in [tex]0\le x\le1[/tex] and the curve [tex]y=8x^3[/tex]).

Compute the integral.

[tex]\displaystyle 16 \pi \int_0^1 (2x^3 - x^4) \, dx = 16\pi \left(\frac{x^4}2 - \frac{x^5}5\right) \bigg|_{x=0}^{x=1} \\\\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ = 16\pi \left(\frac12 - \frac15\right) \\\\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ = \frac{24}5\pi = \boxed{4.8\pi}[/tex]

Answer:

6%

Step-by-step explanation:

First, let's break this down:

60% of arenas sold out

Out of those arenas that did NOT sell out

We want to know the joint relative frequency of area that were sold out AND NOT on the previous tour schedule, therefore all the information about areas that did NOT sell out is irrelevant.

Because 90% of the areas that were sold out had been on the previous tour, 10% had NOT been on the previous tour.

Therefore, considering all the arenas, 10% of 60% of the arenas were sold out and not on the previous tour.

Let x equal the total number of arenas:

[tex](.10)(.60)x=0.06x[/tex]

Convert to percent

6%

Therefore, the joint relative frequency of sold out arenas that were not on the previous tour is 6%.

Answer:

x = -26

Step-by-step explanation:

[tex](f-g)(x)=\frac{4}{x-3}-\frac{3}{x+5}=\frac{3}{x^2 +2x-15} \\ \\ \frac{4(x+5)-3(x-3)}{x^2 +2x-15} \\ \\ =\frac{4x+20-3x+9}{x^2 +2x-15}=\frac{3}{x^2 +2x-15} \\ \\ \frac{x+29}{x^2 +2x-15}=\frac{3}{x^2+2x-15} \\ \\ x+29=3 \\ \\ x=-26[/tex]

This is in the domain of the equation, and is thus a solution.

Answer:

  47.4°, 132.6°

Step-by-step explanation:

Given the difference of two angles is 85.2° and their sum is 180°, you want to find their measures.

Let the smaller angle be represented by x. Then the larger angle is (x +85.2). Their sum is ...

  x +(x +85.2) = 180

Simplifying the equation, we get ...

  2x +85.2 = 180

  2x = 94.8 . . . . . . . . subtract 82.5

  x = 47.4 . . . . . . . divide by 2

  x +85.2 = 132.6

The two angles are 47.4° and 132.6°.

Answer:

c

Step-by-step explanation:

C

Using a Number Line to Add Fractions

Slide the green dot from 0 to plot the number at the correct

location.

Plot

-3.5 -3 -2.5 -2 -1.5 -1 -0.5 0

0.5 1

Use the number line to find

O

19

4

O

19

8

O-2

21

¹()+(-3¹)

8

21

8

Thus standard daviation is x~N(4400,6500)

Let X denote the salaries for all the teachers in a particular alimentary school.

As per the generation X is commonly distinguished with a mean of u=44,000

standard daviation of €=$6500

The answer is x~N(44000,6500)

Since the 10 teachers are survived randomly from the district

The site of n=10

Variable€x present salary of all 10 teachers in a particular alimentary sel.

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Answer: $15.75

Step-by-step explanation:

$78.75/5 hr=$15.75/hr

Answer:

He earns $15.75 an hour

Step-by-step explanation:

You have to divide $78.75 by 5 to get the unit rate(earnings for 1 hour).

Daunte is incorrect. After 4 weeks, the price would be 68.5 percent off.

An exponential function is a mathematical function that has the form : f(x) = a^x

Where:

An exponential function indicates that the quantity is either increasing at a faster rate or reducing at a faster rate. This is true because an exponential increase or decrease is faster than a linear increase or decrease. In a linear increase or decrease, the function is either increasing or decreasing at a constant value.

The price of the video games would reduce by 25% of the previous weeks' price. Thus, the function that would represent this is an exponential function.

The form of the exponential equation would be:

Price after 4 weeks = Initial price x (1 - percentage decrease)^number of years

Let's assume that the initial price is 100

100 x (1 - 0.25)^4

100 x (0.75)^4 = 31.64

The total percentage decrease in the price of the good: (current price initial price) - 1

(31.64 / 100) - 1 = 0.684 = 68.4%

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The solution to the system of equations is x = -8/7, y = 4/7 and z = -2/7

The system of equations is given as

2x - y + 2z = -6

-3y + z = -2

2x - 3z = -4

Subtract 2x - 3z = -4 from 2x - y + 2z = -6

This is represented as

(2x - y + 2z = -6) - (2x - 3z = -4)

This gives

- y + 5z = -2

Multiply - y + 5z = -2 by 3

-3y + 15z = -6

Subtract -3y + 15z = -6 from -3y + z = -2

This is represented as

(-3y + z = -2) - (-3y + 15z = -6)

This gives

-14z = 4

Divide by -14

z = -2/7

Substitute z = -2/7 in - y + 5z = -2

- y - 5 * 2/7 = -2

This gives

- y - 10/7 = -2

Rewrite as:

y = 2 - 10/7

Evaluate

y = 4/7

Substitute z = -2/7 in 2x - 3z = -4

2x - 3 * 4/7 = -4

This gives

2x - 12/7 = -4

So, we have:

2x = 12/7 - 4

Evaluate

2x = -16/7

Divide by 2

x = -8/7

Hence, the solution to the system of equations is x = -8/7, y = 4/7 and z = -2/7

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The number of gallons that must be needed to antifreeze 50% solution is 105.

Given that 50% antifreeze solution must be mixed with 70 gallons of Strength 25% antifreeze to get a mixture that is 40% antifreeze.

The six-step method involves a few steps that need to perform. These are defining the problem, determining the root cause, finding the alternative solution to solve the problem, selecting the solution, implementing the solution, and finally evaluating the outcome.

Let's consider x be the number of gallons of a 50% antifreeze solution.

As we know we need to make an antifreeze solution by adding the given quantities.

Hence,

x×50%+70×25%=40%×(x+70)

x×0.5+70×0.25=0.4×(x+70)

Now, we will multiply the numbers, we get

0.5x+17.5=0.4(x+70)

Now, we will multiply both sides by 10, we get

0.5x×10+17.5×10=0.4(x+70)×10

5x+175=4(x+70)

5x+175=4x+280

Further, we will subtract 175 from both sides, we get

5x+175-175=4x+280-175

5x=4x+105

Furthermore we will subtract 4x from both sides, we get

5x-4x=4x+105-4x

x=105

Hence, 105 gallons of 50% antifreeze solution must be needed.

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Answer:

  A  irrational

  B  real

Step-by-step explanation:

Given the value π/7, you want to classify it as whole, integer, real, and/or irrational.

Any number that does not have an imaginary part is a real number. Real numbers include integers, whole numbers, and natural numbers, none of which have any fractional part.

Any ratio of integers (with a non-zero denominator) is a rational number. All other real numbers are irrational numbers. Pi (π) is an irrational number.

When rational numbers are written as decimal numbers, their fractional part will either terminate or repeat. When the fractional part of a decimal number does not terminate or repeat, but continues indefinitely, the number is irrational.

As we said, pi is an irrational number. Multiplying it by a rational number (1/7) does not change its classification.

  π/7 is irrational and real

Answer: debit Cash for​ $8,500, debit Accumulated Depreciation− Truck for​ $50,000, credit Truck for​ $56,000, and credit Gain on Disposal for​ $2,500.

The book in real life is 7 times larger than the one on the website. When you divide 10.5/1.5 you get 7. So multiplying 3 by 7 will get you 21.

Therefore, the real book is 21 inches tall

Given the given task content, the answer to the sums are:

The subtraction of numbers is difference between two or more numbers

(a) -237 + 359

= 122

(b) 87 + (-163)

= 87 - 163

= -76

(c) - 35.7 + 22.9

= -12.8

(d) 8.79 + 6.41

= 15.20

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Answer: 60 square feet

Step-by-step explanation: 5 times 4= 20 yards 20 times 3=60 feet

5*3=15

4*3=12

15*12= 180square feet

Answer:

Step-by-step explanation:

64 pi cm2

Answer:

201.1 = 8^2 pi cm2 = 64 pi cm2

Step-by-step explanation:

The area of a circle with a radius 8 is 201.1

Hope it helps!!!

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Answer: See below

Step-by-step explanation:

a. 3(4)= 12

b. 4+11+(-4)

   =15+(-4)

Answer=11

c. 3.2(2)= 6.4

d. I (-2)+(-2)+(-2) I=  6

e. I 2(-7.5) I = 15

f. [tex]10\frac{1}{5}[/tex](-5)= -51

Colin paid the loan at a ten percent annual interest rate.

Simple interest is the form of interest calculation in which the principal amount remains the same for the entire duration for which the loan is taken.

It is also assumed that Colin will repay $35 per month for the next two years.

We must calculate a simple interest rate on Colin's borrowings.

As a result, Colin's total payment to his parents for two years is $35.

We are required to find simple interest rate on Colin's borrowings

Therefore, total amount paid by Colin to his parents= 35$ for 2 years

        =35*24=840

The amount paid by Colin is principal + interest

Thus, the simple interest amount= 840-700=140$

We know that the simple interest formula is principal*rate*time/100.

We know that the simple interest is 140, the principal is 700, the time is two years, and we need to find the rate of interest.

SI= P*R*T/100

140= 700*R*2/100

140/7*2=R

R=140/14=10

Therefore, The Rate of interest on which Colin paid the loan is 10 per cent per annum

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The real number that should be subtracted from - 5 to get 0 is -5 (option b).

A real number is a quantity that can be written as an infinite decimal expansion. A real number is made up of both rational numbers and irrational numbers.

Rational numbers are numbers that can be expressed as a fraction of two integers. An example is 5, -5.  Irrational numbers cannot be expressed as a fraction of two integers. An example is 22/7, 1/3.

In mathematics, the following rules exist:

-5 - (-5)

= -5 + 5

= 0

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[tex]D=\frac{1}{5}kf \\ \\ 5D=kf \\ \\ \boxed{f=\frac{5D}{k}}[/tex]

Answer:

Step-by-step explanation:

Let x be the sweater

Let y be the shirt

Equation1:    x+4y=47

Equation2:    4x+3y=84

Now solve for x in the first equation:

x+4y=47

x=47-4y

Now that we've solved for x, substitute the value for x which is 47-4y into Equation2 as follows:

4x+3y=84

4(47-4y)+3y= 84

188-16y+3y= 84

188-13y= 84

-13y= 84-188

-13y= -104

y= -104/-13

y= 8

Now plug in the value for y which is 8 into Equation 1 and solve for x:

x+4y=47

x+4(8)=47

x+32=47

x=47-32

x=15

You can perform a check by plugging in the x and y values into equations 1 and 2 which should yield true statements.

The answer is: 1 sweater costs $15 and 1 shirt costs $8

The exact value that is 98% of 2330 is 2283

The value is 98% of 2330

98% of 2330 is 98/100×2330=2283.4≅2283

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Answer:

y = 3x + 14

See the work below.

Step-by-step explanation:

The greatest number of groups that can be formed is 7.

It should be noted that there are 56 dancers wearing green outfits and 42 dancers wearing yellow outfits.

The greatest number of groups that can be formed will the highest common factor between the numbers.

It should be noted that the highest common factor between 42 and 56 is 7.

Therefore, the greatest number of groups that can be formed is 7.

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