Which of these equations represent functions where x is the input and y is the
output
y = 2x-A
y = 2-B
y = 2y-C
x+y = 2-D
x-2-E

Answer:

There are 10 students

Step-by-step explanation:

69.55-(5.35*3)= 53.5

53.5/10=5.35 which is what each ticket costed

So the answer is 10 students

Substitute [tex]x=1-y[/tex] and [tex]dx=-dy[/tex].

[tex]\displaystyle \int_0^{1/2} \frac{\ln^2(1-x)}x \, dx = \int_{1/2}^1 \frac{\ln^2(y)}{1-y} \, dy[/tex]

Since [tex]|y|<1[/tex], we can expand into a power series and interchange the integral with the sum.

[tex]\displaystyle \int_{1/2}^1 \frac{\ln^2(y)}{1-y} \, dy = \int_{1/2}^1 \ln^2(y) \sum_{n=0}^\infty y^n \, dy \\\\ ~~~~~~~~~~~~~~~~~~~ = \sum_{n=0}^\infty \int_{1/2}^1 y^n \ln^2(y) \, dy[/tex]

Let

[tex]\displaystyle I_n = \int_{1/2}^1 y^n \ln^2(y) \, dy[/tex]

Integrate by parts with

[tex]u=\ln^2(y) \implies du = \dfrac{2\ln(y)}y \, dy[/tex]

[tex]dv = y^n\,dy \implies v = \dfrac{y^{n+1}}{n+1}[/tex]

[tex]\implies \displaystyle I_n = -\frac{\left(\frac12\right)^{n+1} \ln^2\left(\frac12\right)}{n+1} - \frac2{n+1} \int_{1/2}^1 y^n \ln(y) \, dy[/tex]

Integrate by parts again, now with

[tex]u = \ln(y) \implies du = \dfrac{dy}y[/tex]

[tex]dv = y^n \, dy \implies v = \dfrac{y^{n+1}}{n+1}[/tex]

[tex]\implies \displaystyle I_n = -\frac{\ln^2(2)}{2^{n+1}(n+1)} - \frac2{n+1} \left(-\frac{\left(\frac12\right)^{n+1}\ln\left(\frac12\right)}{n+1} - \frac1{n+1} \int_{1/2}^1 y^n \, dy\right) \\\\ ~~~~~~~~~~~ = \frac2{(n+1)^3} - \frac{\ln^2(2)}{2^{n+1}(n+1)} - \frac{\ln(2)}{2^n (n+1)^2} - \frac1{2^n (n+1)^3}[/tex]

Taking the sum over all [tex]n[/tex] gives

[tex]\displaystyle \int_0^{1/2} \frac{\ln^2(1-x)}x \, dx = \sum_{n=0}^\infty I_n \\\\ ~~~~~~~~ = \sum_{n=0}^\infty \left(\frac2{(n+1)^3} - \frac{\ln^2(2)}{2^{n+1}(n+1)} - \frac{\ln(2)}{2^n (n+1)^2} - \frac1{2^n (n+1)^3}\right) \\\\ ~~~~~~~~ = 2 \sum_{n=1}^\infty \frac1{n^3} - \ln^2(2) \sum_{n=1}^\infty \frac1{2^n n}-2\ln(2)\sum_{n=1}^\infty \frac1{2^n n^2}- 2 \sum_{n=1}^\infty \frac1{2^n n^3}[/tex]

Now recall the definition of the so-called polylogarithm function, given by

[tex]\displaystyle \mathrm{Li}_\nu(z) = \sum_{n=1}^\infty \frac{z^n}{n^\nu}[/tex]

which immediately gives us a "closed" form for the integral of

[tex]\displaystyle \int_0^{1/2} \frac{\ln^2(1-x)}x \, dx \\\\ ~~~~~~~~ = 2\,\mathrm{Li}_0(1) - \ln^2(2)\,\mathrm{Li}_1\left(\frac12\right) - 2\ln(2)\,\mathrm{Li}_2\left(\frac12\right) - 2\,\mathrm{Li}_3\left(\frac12\right)[/tex]

But we can do better. The first sum is [tex]2\zeta(3)[/tex] (by definition of Riemann zeta) and the second is [tex]\ln^2(2)\cdot\ln(2)=\ln^3(2)[/tex] (using the series expansion of [tex]\ln(1+x)[/tex]). The other two polylogs have exact values of

[tex]\displaystyle \mathrm{Li}_2\left(\frac12\right) = \frac{\pi^2}{12} - \frac12 \ln^2(2) \\\\ \mathrm{Li}_3\left(\frac12\right) = \frac{\ln^3(2)}6 - \frac{\pi^2}{12} \ln(2) + \frac78 \zeta(3)[/tex]

(according to what I found when searching "polylogarithm at half integers"). Putting all the results together, we end up with

[tex]\displaystyle \int_0^{1/2} \frac{\ln^2(1-x)}x \, dx = \boxed{\frac{\ln^3(2)}3 + \frac74 \zeta(3)}[/tex]

Answer(s): Reading your answers from top left, top right, bottom left, bottom right;

Circle A: 110, 70, 70, 110

Circle B: 127, 53, 53, 127

Step-by-step explanation:

Each circle will add up to 360 degrees.

Both acute and obtuse angles are congruent (the same or identical).

If you have an acute angle of 70 for circle 'A', your other acute angle is 70 as well since they are congruent.

Your other two angles will have to equal 220 because you already have 140 degrees and your circle needs to equal 360 degrees. Both of your unknown angles are identical, so divide 220 by 2 to get 110 for both your obtuse angles.

Do the same for your second circle.

Multiply 53 by two to get 106, then subtract 360 by 106 to get 254.

Divide 254 by 2 to get 127 for both of your obtuse angles.

I hope I managed to help. If not, DM me.

Answer:

No

Step-by-step explanation:

I'm not 100% sure that this was the question but I hope so

2170+2570=$4740 per month

4740*12=$56880 per year

Food: 56880*0.5=$28440

Entertainment: 56880*0.3=$17064

Educational: 56880*0.15=$8532

28440+17064+8532=$54036

56880-54036=$2844

Or a quicker method: 1-0.5-0.3-0.15=0.05

0.05*56880=$2844

Answer:

can you show us the table please.

Step-by-step explanation:

Answer: The third one Edg 2020

Step-by-step explanation:

Answer: 2/5 liters

Step-by-step explanation: This is because you need to add 1/10 and 3/10. The answer is 4/10, which can be simplified to 2/5.

The cost that should be included in the cost of land is C. cost to clear the land of old buildings.

The  cost of land can be described as the cost of all the items as well as the cost of the labor that is been used in making the land to be available for the erection of the building on it, it should be noted that this cost will include the cost that is required to clear the land as well as well as the cost of those that supervise the clearing activities.

In this case we can come into conclusion that  cost that should be included in the cost of land is C. cost to clear the land of old buildings.

Therefore, option C is correct.

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Answer:

1809.6 cubic feet

Step-by-step explanation:

Use the formula for the volume of a cylinder, V = [tex]\pi[/tex]r²h

Plug in the height and radius:

V = [tex]\pi[/tex]r²h

V = [tex]\pi[/tex](8²)(9)

V = 1809.6

So, the volume of the cylinder is 1809.6 cubic feet

Answer:

648

Step-by-step explanation:

45+35=80

100-80=20

360×20/100

72 so the answer is this and the formula E=T×%/100

Answer:

315.0

Step-by-step explanation:

31.50x10 is just moving the digits up one place

Answer:

$76.50

Step-by-step explanation:

To find out how much he makes each hour, we do

31.5/7

resulting in 4.5

if he works for 17 hours

17 * 4.5

He would earn $76.50

Answer:

a=20

Step-by-step explanation:

Answer:

Step-by-step explanation:

4a-2a+8-3=45

2a+5=45

2a+5-5=45-5

2a/2=40/2

a=20

Mr. Arnett will pay $207 for all the trail mix bought by his children.

Here, we are given that Mr. Arnett allowed each of his children to fill their own bag as follows-

Child                 Ava   Grayson   Mason   Tyler

Amount of

Trail Mix (oz)      15        14            10            7

Further, cost of trail mix = $4.50 per pound

The total amount of trail mix collected by all 4 children will be-

15 + 14 + 10 + 7

= 46

Thus, in total the children put 46 pounds of trail mix in their bags.

Hence, the total cost will be-

46 × 4.5

= 207

Thus, Mr. Arnett will pay $207 for all the trail mix.

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Answer:

3500

Step-by-step explanation:

I got it right

Using mathematical operations, the number of balloons that Masha bought for the party was 100, made up of red, green, and yellow balloons.

Mathematical operation includes the use of basic math operators, including addition, subtraction, division, and multiplication to determine and express mathematical values.

Red balloons = 40 balloons

Green balloons = 3/5 (40) = 24 balloons

Green balloons = 24 = 2/3 of yellow balloons

Yellow balloons = 24÷ 2/3 = 24 x 3/2 = 36 balloons

Total ballons bought:

Red = 40

Green = 24

Yellow = 36

Total = 100 (40 + 24 + 36)

Thus, using mathematical operations, the total number of balloons that Masha bought for the party was 100 balloons.

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Masha bought red, green, and yellow balloons for a party. She bought 40 red balloons. The number of green balloons Masha bought is 3/5 of the number of red balloons. The number of green balloons is also 2/3 of the number of yellow balloons.  How many balloons did Masha buy for the party?

Answer:

b

Step-by-step explanation:

Answer:-5.675

Step-by-step explanation:

Answer:

The answer is -227/40 or -5 27/40

Step-by-step explanation:

Easiest way to explain this is to first get the common denominator of the denominators of 5 and 8

This will equal 40 and we have to multiply the numerators as well so this will look like....

-35/40 - 4 32/40

Now we need to convert the whole number in -4 32/40 into a fraction

4 multiplied by 40 is 160 so we will need to add 160 and 32 making the equation now say -35/40 -192/40 which will equal -227/40

So this will make the answer -227/40 in fraction form and in a compound fraction it will be -5 27/40

Answer:

top is 13 gallons left

bottom is 7.8 gallons left

Step-by-step explanation:

30=1 gallon

90= 3 gallons

246/30= 8.2

8.2*1=8.2

16-8.2=7.8

Rajesh own a plot of rectangular shape he has fenced it with a wire of length 750 ft . the length of the plot exceeds the breadth by 5ft.

Given that

To find

So, according to the question

We have,

Let's assume

He fenced this plot with a wire. So we can say this wire length is a perimeter of this plot of rectangular shape.

In mathematical form

           2 (length + breadth) = length of fenced wire

                               2 ( l + x) = W -------------------(1)

From question

                                          l = x +5 ------------------(2)

Now, putting the value of equation (2) and W in equation (1)

Then, we get

                               2 ( l + x) = W -------------------(1)

                      2 [( x + 5) + x] = 750

                        2 [ x + 5 + x] = 750/2

                               [ 2x + 5] = 375

                                        2x = 375-5

                                        2x = 370

                                          x = 370/2

                                          x = 185ft

Now, putting the value of x in equation (2)

Then, we get

                                          l = x +5 ------------------(2)

                                          l = 185 +5

                                          l = 190ft

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Answer:

-13

Step-by-step explanation:

Because

To write the equation of the line, we will use the point-slope formula.

To do this, we need a point and a slope.

We can find out slope by using the slope formula.

m = y₂ - y₁ / x₂ - x₁

So we have 5 - 9 / 3 - 1 or -4/2 which is -2.

Now let's use the point-slope formula.

y - y₁ = m(x - x₁)

Now substitute one of our points (x₁, y₁) into our formula.

So we have y - 5 = -2(x - 3).

Distributing the -2 gives us y - 5 = -2x + 6.

Moving the -5 to the right, we have y = -2x + 11.

So y = -2x + 11 is our equation.

The correct solution of Laurie's inequality expression is y ≥ 2x - 4

Laurie's inequality expression is given as

y > 2x - 4

The graph of the inequality expression that completes this question is added as an attachment

From the attached graph, we can see that the line of the inequality is a thick or closed line

Thick and closed line are represented by the inequality signs ≤ and ≥

Since the upper region is shaded, we make use of ≥ inequality sign

Hence, the correct solution of Laurie's inequality expression is y ≥ 2x - 4

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The Quotient and remainder of the polynomial is  x² + x -6 and 2 respectively

Synthetic division method is one of the method used to divide the polynomial equations.

The polynomial equation given here is

x³ + 3x² - 4x - 10

We need to divide this polynomial equation with x - 2

Thus by dividing the polynomial x³ + 3x² - 4x - 10 with x - 2, we get

the quotient as x² + x -6 and

     Remainder as 2

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For a function to have an inverse, it must be one-to-one_. To define the inverse sine function, we restrict the domain of the sine function to the interval [-pi, pi].

Two functions f(x) and g(x) are inverses if:

f(x) = y

g(y) = x

This means that the two functions need to be one-to-one, because if there are two values of x such that:

f(x₁) = y = f(x₂)

f(x) can't have an inverse because g(y) would give two different outputs, and then g(x) is not a function.

For the case of the sine (and all periodic functions) we restrict to the region where the function is one to one, which can be any interval of 2 pi radians (the common example is the interval [-pi, pi])

Then:

For a function to have an inverse, it must be one-to-one_. To define the inverse sine function, we restrict the domain of the sine function to the interval [-pi, pi].

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