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PLEASE HELP MEEEEEEEEEEEEEEEEEEEEEE
There are 360 people in a movie theater. Of these people, 35% bought student tickets, and 45% bought adult tickets. The rest bought senior-citizen tickets. how many people bought senior tickets?
Answers
45+35=80
100-80=20
360×20/100
72 so the answer is this and the formula E=T×%/100
[tex] \sf \int_0^ \frac{1}{2} \frac{ ln {}^{2} (1 - x) }{x} \: dx \\ [/tex]
Answers
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]
What is the volume of a cylinder, in cubic ft, with a height of 9ft and a base diameter
of 16ft? Round to the nearest tenths place
Answers
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
Can someone help me with this question? It's due tomorrow :(
Answers
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.
Kapow liquid detergent was on sale for $4.59 a gallon. If the sale price was 85% of the regular price, how much does one gallon of Kapow liquid detergent regularly cost?
(A)$5.28
(B)$5.40
(C)$6.09
(D)$8.49
Answers
The pressure, P (in lbs/ft2 ), in a pipe varies over time. Five times an hour, the pressure oscillates from a low of 90 to a high of 230 and then back to a low 90. The pressure at t = 0 is 90.
Question: Find a possible formula for P=f(t)
Answers
P=160-70*cos(2π*(1/12)*t)
• Pressure in mathematics or physics is defined as force per unit area. The pressure exerted by a solid object which is resting on top of a solid surface is the weight divided by the area of the object . SI unit of force is Newton (N).
First, we find the amplitude by taking the difference between the peak values and dividing by two:
Amplitude=(230+90)/2=70
We can find the center value by either adding 70 to the minimum or subtracting 70 from the maximum:
90+70=160
230-70=160
This tells us that the Center Value=160
The frequency that we are operating at is given as:
f = 5/hour
so in minutes
f=5*(1/60)/minute=5/60=1/12 per minute
So, combining everything we get
P=160-70*cos(2π*(1/12)*t)
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What is: -7/8 - 4 4/5
Answers
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
Which of the following should be included in the cost of land?
OA. cost of installing fences
B. cost of installing signage
OC. cost to clear the land of old buildings
OD. cost to build sidewalks on the land
Answers
The cost that should be included in the cost of land is C. cost to clear the land of old buildings.
What is the cost of land ?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 this question correctly and i'll give u brainliest pls
Answers
Answer:
Corresponding angles
Step-by-step explanation:
They have the same relative position to the parallel lines (in blue)
8. A skateboard ramp is 5ft tall and is 12ft from the base of the ramp to the end. What is the length from the top of the ramp to the end?
Answers
Answer:
3500
Step-by-step explanation:
I got it right
Sean bought 3/7 of a pound of cherries and then he ate 1/4 of a pound of them. When he got home, he saw that he still had 2/3 of a pound of cherries in his cupboard. How many total pounds of cherries does he have? Give your answer as an exact simplified improper fraction, not as a mixed number. Do not include units.
Answers
Answer:
71 /84
answer is not in imporper fraction.
Step-by-step explanation:
fractions need to be changed or converted to equivalent fractions inorder to solve them.
1.Total amount of cherries he bought and he already had in cupboard= 3/7 + 2/3
convert them to equivalent fractions inorder to add them by using LCM of the denominators.Which in this case is 21 (LCM of 7 and 3 is 21)
2. Now the common denominator is 21
change 3/7 to a fraction with 21 as denominator by multiplying the numerator to 3 and denominator also by 3 which will give you 3×3=9/ 7×3=21 or 9/21
note: you have to multiply both numerator and denominator by the same number which is used to convert the denominator to the number given by LCM.
3)Now change the second fractions denominator to 21 by multiplying the denominator 3 by 7 and numerator 2 to 7 :
2×7/3×7 = 14/21
4) Now the fractions have same denominator which means they can be added or subtracted.
5) Total amount of cherries he had= 9/21+14/21 = 23/21
6) The amount of cherries he ate = 1/4
7) Amount of cherries he has now with him after he ate 1/4 from 23/21 = 23/21 - 1/4
8) Again the fractions need to be changed to equivalent fractions inorder to subtract them.So,Take the LCM of the denominators (LCM 21 and 4 is 84).Now change the denominator of each fraction to 84.
9) 23/21 becomes 23× 4/21×4 = 92/84
1/4 becomes 1×21/4×21 = 21/84
now subtract them
92/84 - 21/84 = 71/84
71/84 cannot be properly divided so, 71/84 is the answer.
He has 71/84 pounds of cherries with him.
Use synthetic division to divide x³ + 3x² - 4x - 10 by x - 2
2
1
1
The quotient is:
The remainder is: 2
2
5
3
10
6
-4
>
>
Note: Enter only a number for the remainder, no fraction.
12
2
-10
Answers
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 _____. To define the inverse sine function, we restrict the _____ of the sine function to the interval _____.
Answers
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].
When a function can be invertible?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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Ravi owns a plot of rectangular shape. He has fenced it with a length of 750ft. Length x= the breath by 5m find l and b
Answers
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.
The length of his plot is 190ft and breadth is 185ft.Given that
Ravi owns a plot of rectangular shape. He has fenced it with a length of 750ft.The length of the plot exceeds the breadth by 5ft.To find
The length and breadth of the plot ?So, according to the question
We have,
The length of fenced wire is 750ft.Let's assume
Breadth of plot = x.Length of plot = l.Length of fenced wire = WHe 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
the length of the plot = breadth + 5ft.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
Length of this rectangular shaped plot = 190ft, andBreadth of this rectangular shaped plot = 185ft.
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At the grocery store, Mr. Arnett allowed each of his
children to fill their own bag with trail mix for their hike.
The table shows the amount of trail mix for each child.
Child
Ava
Grayson
Mason
Tyler
Amount of
Trail Mix (oz)
15
14
10
17
The trail mix costs $4.50 per pound. How much will Mr.
Arnett pay for all the trail mix?
Answers
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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can someone help me with this
Answers
k = constant
k = (m√x) / D^2 = 20√16 / 5^2 ≅ 3.2
m(D,x) = 3.2 D^2 / √x
Toni decided to build a rectangular concrete patio 6 feet wide all around her pool.
See diagram below. What is the area of the concrete patio?
1
6ft
6ft
10ft
32ft
Answers
Answer:
648
Step-by-step explanation:
A group of adults and students buy tickets for a dance performance.
*Each ticket costs $5.35
*The total cost of the tickets for the group is $69.55
*There are exactly 3 adults in the group.
What is the number of students in the group?
Explain your steps on how you solved this problem.
Answers
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
i will give brainlest
Answers
Answer:
b
Step-by-step explanation:
joey mows the back of his neighbors lawn. if he is rewarded 31.50 in 7 hours. how much does he make in 17 hours?
help!
Answers
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
Her teacher asked her to write the correct equation or inequality that matches the graph. Laurie wrote the following:y>2x-4 . Her teacher marked her answer incorrect. Explain the error that Laurie made and then write the correct solution.
Answers
The correct solution of Laurie's inequality expression is y ≥ 2x - 4
How to explain the error that Laurie made and then write the correct solution?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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please help me!! due in 15 mins
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Amanda has 2/3 apples. Make an equation to find how many 2/3 can go into 6.
Answers
Answer:
6 apples.
How I solved it:
2/3+ 2/3+ 2/3+ 2/3+ 2/3+ 2/3+ 2/3+ 2/3+ 2/3=
18/3
18/3=6
3/3=1
6/1= 6 apples.
Plz help me with this?!?! I will mark you brainliest!!!
Answers
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.
which table represents the statement "di runs at a rate of 4 meters per second"
Answers
Answer:
can you show us the table please.
Step-by-step explanation:
Answer: The third one Edg 2020
Step-by-step explanation:
A project consists of three tasks: A, B, and C. Task A is known to take five days for sure. Tasks B and C are each dependent on A. B takes five days. C takes seven days with a probability of 0.5 and three days with a probability of 0.5. What is the expected completion time of the project
Answers
Answer:
The expected completion time of the project is:
10 days.
Step-by-step explanation:
Duration of Task A = 5 days
Task B and C depend on Task A
This implies that Task A must be completed before Task B and C can be started.
To complete Task B will take 5 days
To complete Task C will take 5 days (7 * 0.5) + (3 * 0.5)
Since Task A takes 5 days and Tasks B and C depend on Task A and Task B takes 5 days and Task C takes expected time of 5 days, it means that the project can be completed in 10 days (5 + 5) if tasks B and C are simultaneously carried out.
The expected completion time of the project is
(i)10 days if B&C are mutually independent
(ii)15 days if B &C are mutually dependent
What is the expected completion time of a task?Expected completion time of a task= p1x1 + p2x2
Where
p1 & p2 are probabilities.
x1 and x2 are samples.
p1=p2=0.5
x1=7
x2=3
Expected completion time of task C= 0.5*7+0.5*3 = 5 days
Task B and C will be due till task A is not accomplished.
Total time to accomplish task A = 5 days
Total time to accomplish task B= 5 days
Expected time to accomplish task C = 5 days
If tasks B and C are mutually independent
expected time to complete the project = 5+5=10days
If task C depends on task B
Expected time to complete the project = 5+5+5 = 15 days.
Therefore
The expected completion time of the project is
(i)10 days if B&C are mutually independent
(ii)15 days if B and C are mutually dependent
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how do you solve this equation step-by-step? (below)
4a + 8 - 2a - 3 = 45
Answers
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
PLEASE HELP ILL MARK BRAINLIEST
Answers
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
How you express the average of five quizzes is 85 in mathematical expression
Answers
y = (x1 + x2 + x3 + x4 + x5) / 5
since y = 85:
(x1 + x2 + x3 + x4 + x5) / 5 = 85
Fred and Winnie O'Callahan have put themselveson a very strict budget. Their goal at the end of the year is to buy a car for $14,200 in
cash. Their budget includes the following per dollar:
0.50 Food and lodging
0.30 entertainment
0.15 educational
Fred earns $2,170 per month and Winnie earns $2,570 per month. After 1 year will Fred and Winnie have enough cash to buy the car?
Yes or no
Answers
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