Pre- Calculus

21,152 results, page 16

Pre calculus

1. Reference angle for -280 degrees? I do not understand why you add 360???? 2. Theta=? If reference angle =60 and theta terminates in quadrant 3. What does terminate mean? Please show work and explain why. My priority is to understand the concept ... 3. Exact value for sec ...

Pre Calculus.

Can someone check my answers please!!! Simplify (tan ^2 theta csc^2 theta-1)/(tan^2 theta). My answer: 1 Simplify ((cos x)/(sec x-1)) + ((cos x) /(sec x +1) My answer: 2cot^2 x Find a numerical value of one trigonometric function of x if (tan x/cot x )– (sec x/cos x ) = (2/...

pre calculus

If you are driving down a 10% grade, you will always be 10% below where you would have been if you could have driven on flat ground from where you started. Suppose you descend to where you are 20 feet below your starting point. What concept does the “grade” relate to, and ...

Probability (Pre-Calculus)

A class is given a list of eight study problems from which five will be part of an upcoming exam. If a given student knows how to solve six of these problems, find the probability that the student will be able to answer: (a) all five questions on the exam. (b) exactly eight ...

pre-calculus

(tan^2x-9)(2cosx+1)=0 Find one period 4cos^2x-4cosx+1=0 find all angles and name 8 angles 7sin^2x-22sinx+3=0 find all angles and name 8 angles 2cos^2x-7cosx=-3 find one period sinx(2sinx+1)=0 find one period

PRE-CALCULUS

. Sam won $150,000 in the Michigan lottery and decides to invest the money for retirement in 20 years. Find the accumulated value for Sam’s retirement for each of his options: (a) a certificate of deposit paying 5.4% compounded yearly (b) a money market certificate paying 5....

Pre Calculus

For a vector $\bold{v}$, let $\bold{r}$ be the reflection of $\bold{v}$ over the line \[\bold{x} = t \begin{pmatrix} 2 \\ -1 \end{pmatrix}.\] [asy] unitsize(1 cm); pair O, V, R; O = (0,0); V = (3,1); R = reflect(O,(2,-1))*(V); xaxis(-2,4); yaxis(-3,1); draw((-1)*(2,-1)--2*(2,-...

pre calculus

Cot 495 degrees... a) -tan 135 degrees b) -cot 135 degrees c) cot 135 degrees d) -cot 315 degrees

Pre-Calculus

At time t hours after taking the cough suppressant hydrocodone bitartrate, the amount A, in mg, remaining in the body is given by A=13(0.82)^t. a) What was the initial amount taken? b) What percent of the drug leaves the body each hour? c) How much of the drug is left in the ...

Pre-Calculus

The cost of sending a package overnight is $14.40 for the first pound and $3.90 for each additional pound or portion of a pound. A plastic mailing bag can hold up to 3 pounds. The cost f(x) of sending a package in a plastic mailing bag is given by the following function, where...

Pre-calculus-ck answers

Identify the graph of the equation 4x^2-25y^2=100. Then write the equation of the translated graph for T(5,-2) in general form. Answer: hyperbola; 4(x-5)^2 -25(y+2)^2=100 2)Find the coordinates of the center, the foci, and the vertices, and the equations of the asymptotes of ...

calculus

hello here, Please can i get direction on website to practice calculus (both differential & integral) objectives based online. thanks.

Calculus

How do I determine the area of a region bounded by a function and the x-axis if given y=cosx and interval is [0,ð/2]. This has to do with the Fundamental Theorem of Calculus. Thanks in advance!

Calculus.......plz help! =)

Use any calculus method to determine extrema, intervals where the function is increasing or decreasing, asymptotes, and points of inflection for y = -x(x+1)^3

college pre-calculus

simplify: square root (4/3)-square root (3/4) A. 2-sqaure root(3)/2 square root (3) B. square root (7/12) C. square root (3)/6 D. 2/square root (3) which answer? this is what i got square root (16/12)- square root (9/12)= square root (7/12)

College Algebra/pre-calculus

The Pointless Pencil Company purchases a new stamping machine for the production line that cost $8000. The equipment will be replaced in 10 years at which time its salvage value is expected to be $1000. Write a linear equation giving the value, y, of the machine during the ...

Pre Calculus 12

Graphing trigonometric functions A sinusoidal function has a maximum at (2,10) and its next minimum (5,-2) find an equation that represents this situation A sinuosoidal function has a zero at (5,0) and its next minimum is (7,-4). find an equation that represents this situation...

Pre calculus/ Advanced Functions

Samuel is investigating the rate of change of the function f(x) = cos x on the interval xE[0, 2pi]. He notices that the graph of f(x) passes through the x-axis at pi/2. He also determines the instantaneous rate of change at x = 0, pi and 2pi by inspection. Based on this ...

pre-calculus

y=tanx -2π≤x≤2π y=cotx -2π≤x≤2π y=cscx -2π≤x≤2π y=secx -2π≤x≤2π

Software Engineering

Consider the following program (written in pseudo-code) begin x:= 0; y:= 1; z:= 1; while y <= n do x:= x+1; z:= z+2; y:= y+z; od sqrt := x; end Prove the partial correctness of the program with respect to the following predicates: Pre: {n>=0} Post: {sqrt2 <= n and n &...

Pre-calculus

On a chicken farm, the poultry is given a healthy diet to gain weight. The chickens have to consure a minimum of 15 units of substance A and another 15 units of substance B. In the market there are only two classes of compounds: Type 1, with a compoistion of one unit of A to ...

pre-calculus

An urn contains 7 red marbles labeled (1,2,3,4,5,6,7) and 5 green marbles labeled (1,2,3,4,5) four marbles are pulled out at once. what is the probability. A. all four marbles are red B. more of the marbles are green than red C. both red and green marbles are present D. two of...

Pre-calculus

You are given a pair of equations, one representing a supply curve and the other representing a demand curve, where p is the unit price for x items. 80 p + x - 380 = 0 and 84 p - x - 40 = 0 Identify which is the supply curve and demand curve and the appropriate domain. Put the...

Pre calculus

Your computer supply store sells two types of laser printers. The first type, A, has a cost of $86 and you make a $45 profit on each one. The second type, B, has a cost of $130 and you make a $35 profit on each one. You expect to sell at least 100 laser printers this month and...

Pre-Calculus

A ball is thrown up at the edge of a 364 foot cliff. The ball is thrown up with an initial velocity of 72 feet per second. Its height measured in feet is given in terms of time t, measured in seconds by the equation h=−16t2+72t+364. How high will the ball go? To get how ...

Pre-Calculus

Laws of Logarithms Without using a calculator use the change of base rule to evaluate 1. a) log(subscript8)32(hint use base 2) =log(subscript2 32)/log(subscript2 8) = 5/3 b) log(subscript36)1296. This one doesnt even give you a hint, so how do you know which base to use? Does ...

Pre-Calculus (Check)

Please tell me what I'm doing wrong... The side lengths of tops of three squares tables can be described as three consecutive integers. The combined area of the table tops is 677 sq in. Algebraically, determine the roots of the quadratic equation. (I'll use quadratic, but if ...

Pre-Calculus

For the function f(x)=12x^3+4x^2-27x-9 describe the end behavior. Find the real zeros of f and determine whether the graph crosses or touches the x-axis at each x-intercept. Use the zeros of f and test numbers to find the intervals over which the graph of f is above or below ...

Pre-Calculus

Use the CALC features of the TI to answer the following. Show what you put into the calculator & what CALC feature you used. Round to the nearest tenths. The equation h = 20 cos (π/4 (t-3)) + 23 tells how high above the ground a ferris wheel car is at any given time. h is...

GOVERNMENT

Which group would be more likely to approve of a pre-emptive strike to rid the world of a terrorist friendly country (government)? Today, the Republicans seem to be more in favor of a pre-emptive strike -- but I think we may see a change because almost everyone is tired of ...

Spanish

Answer the following questions what does pre viernes el pescado o el bonyo mean what does que co mis parlemis i duno mean? what does pre viernes la liche o el hugo mean in spanish? what does que te gusta comer parde e la guarso mean? I know some of these are spelled wrong, but...

Pre-Calculus

A population of 20 rabbits is introduced to a small island. The population increase at a rate of 60% per year. (A) Find a function of F(t) that represents the number of rabbits on the island after t years. (B) Suppose 100 rabbits were introduced to the island and G(t) is the ...

Pre-calculus (Trigonometry)

The rotating spotlight from the Coast Guard ship can illuminate up to a distance of 250 m. An observer on the shore is 500 m from the ship. HIs line of sight to the ship makes an angle of 20 degrees with the shoreline. What length of shoreline is illuminated by the spotlight...

Pre-Calculus

Need help with this question, don't get it. Given the relation x^2+3x=y^2-2y, what is the new relation if it has undergone: A. vertical expansion by 2 B. Horizontal expansion by 3 C. Vertical compression by 4/5 D. Horizontal compression by 1/5 E. Reflection over yaxis, ...

calculus

Calculus A, Evaluate the following integral : ç (x^2+3x-2)dx

Pre-Calculus

A rectangular garden with an area of 250 square meters is to be located next to a building and fenced on three sides, with the building acting as a fence on the fourth side. Let x be the length of the side parallel to the building. 1. Find T(x), the total amount of the fence ...

Pre-Calculus

Hi! I have three questions that I need checked over just to make sure I understand it. Thanks! :) 1.) What is the slope of the line that passes through (5, 8) and (-2, 6)? My answer: -2/7 2.) If Segment AB || Segment CD and the slope of Segment AB = 1/2, what is the slope of ...

Pre-Calculus

I need help with this problem: The bearing from the Pine Knob fire tower to the Colt Station fire tower is N 65 degrees E, and the two towers are 30 kilometers apart. A fire spotted by rangers in each tower has a bearing of N 80 degrees E from Pine Knob and S 70 degrees E from...

Pre-calculus help

I have two problems I am stuck on, if you could show me how to solve the problems it would be much appreciated. 1) Find sin 2x, cos 2x, and tan 2x from the given information. tan x = − 1/6, cos x > 0 sin 2x = cos 2x = tan 2x = 2) Find sin 2x, cos 2x, and tan 2x from ...

Pre-Calculus

The cup on the 9th hole of a golf course is located dead center in the middle of a circular green that is 70 ft in diameter. You ball is located 50 feet south, and 40 feet west of the cup. The ball follows a straight line path and exits the green at the right most edge. Assume...

Pre-Calculus

Please check: 1.Find polar equation of x^2 + y^2 = 10y r^2 for x^2 + y^2 and sin(theta sin for y =r^2=10sin(theta) 2.Find polar equation: y=5 r=5/sin 3.Polar equation is r=2costheta + 3 sin theta Find rectangular equation x^2+y^2 =x^2 + y^2 =2x+3y

calculus

Does anyone know of any free calculus websites? I'm taking a college class in the fall and would like to build my confidence since I am somewhat weak in math. Thank you in advance.

Calculus Please Need Urgent3 :/

Find the derivative of the following function using the appropriate form of the Fundamental Theorem of Calculus. F(x)= (s^2)/(1+3s^4)ds from sqrtx to 1 F'(x)=? Thank you so much guys!

Pre-Calculus Graphs expansions/compressions

Need help with this question, don't get it. Given the relation x^2+3x=y^2-2y, what is the new relation if it has undergone: A. vertical expansion by 2 B. Horizontal expansion by 3 C. Vertical compression by 4/5 D. Horizontal compression by 1/5 E. Reflection over yaxis, ...

Pre Calculus

Two forces with magnitudes of 150 and 75 pounds act on an object at angles of 30° and 150°, respectively. Find the direction and magnitude of the resultant force. Round to two decimal places in all intermediate steps and in your final answer. Having lots of trouble with this...

law-major help?

Hi, my friend and I both want to be lawyers. we finally talked after a long time of not seeing each other and we got on the topic of college. and majors. etc. i asked her what do u want to major in? she goes "history.. for LAw" i'm like you want to major in history law!? i was...

Pre-Calculus

Cost,Revenue,and Profit: Estimate the number of scanners that would produce a maximum profit when p is the price per scanner and x is the number of scanners. p= 100-0.0001x and the cost for producing x scanners is C= 350,000+30x and the profit for producing and selling x ...

Easy Pre-calculus Questions?

What is the value of x in the right triangle below? If needed, round your answer to two decimal places. 32 angle, 15 inches. A 10-foot ladder is leaning up against the side of a building so that the top of the ladder reaches the top of the building. If the ladder meets the ...

Pre-Calculus-Trig

A woman on the top of a 448 foot high building spots a small plane. As she views the plane, its angle of elevation is 62 degrees. At the same instant a man at the ground-level entrance to the entrance to the building sees the plane and notes that its an angle of elevation is ...

pre-calculus

the spread of oil leaking from a tanker is in the shape of a circle. If the radius r (in feet) of the spread after t hours is r(t)= 200 square root of t, find the area A of the oil slick as a function of the time t. You know that the area of a circle is A=pi*r^2. You're told ...

Pre-Calculus

This is application question. Bacterial Control. If t days after treatment the bacteria count per cubic centimeter in a body of water is given by C(t) = 10t^2 - 120x + 800 0 <= t <= 9 Thn in how many days will the jcount be a minimum? I got this result: 20(t^2 - 6 + 40) ...

Pre Calculus 12

Modelling with sine/cosine A Ferris wheel has a diameter of 30m. The bottom of the wheel is 1.5m off the ground it takes 3.5min to make one complete revolution. a person gets on ferris wheel at its lowest point at time = 0. write an equation that represents persons height ...

Pre calculus

A 100 foot tall antenna sits part way up a hill. The hill makes an angle to 12 degrees with the horizontal. In other words, if you were going to walk up the hill, you would walk at an angle of 12 degrees. To keep the antenna stable, it must be anchored by 2 cables.The distance...

Pre calculus

A 100 foot tall antenna sits part way up a hill. The hill makes an angle to 12 degrees with the horizontal. In other words, if you were going to walk up the hill, you would walk at an angle of 12 degrees. To keep the antenna stable, it must be anchored by 2 cables.The distance...

Pre-Calculus

Driving down Bald Mountain in Wyoming, Bob dean finds that he descends 1600 feet in elevation by the time he is 2.5 miles (horizontally) away from the high point on the mountain road. Find the slope of his descent (Hint: 1 mile = 5280 feet) After converting the miles to feet I...

Pre-Calculus

A corpse was discovered in a motel room at midnight and uts temperature was 82°F. The temperature dropped to 80.5°F two hours later. Given k is a constant for the object in question, S is the surrounding temperature, t represents the time and theta(of time) is the ...

Calculus

In calculus, the sum of an infinite geometric series whose first term is 1/20 is given by the complex fraction 1/20 _____ 1-r where r is the common ratio between the terms. Simplify this expression.

Pre-Calculus

1) For tax purposes a manufacturer is allowed to depreciate the value of a machine by 10% each year. If the original value of the machine was $10,000, what would be its value for tax purposes at the end of 6 years. (Assume the depreciation is computed at the end of each year...

CDA

4. Signature software systems are primarily used by A. children and providers. B. parents and children. C. parents and other authorized individuals. D. parents and providers. 5. A software program features an electronic coloring book, in which children get to paint characters ...

Pre-Calculus

I posted earlier and didn't get an answer so I'm posting again-hoping someone could please check these two-I think they're correct Please check my answer: I think it's correct? 1.Find polar form of (-3,2) r=sqrt of (-3)^2 + 2^2)=sqrt (13) = 3.61 tan^-1(2/-3) = 33.79 180-33.79...

Math HELPPP

In a survey of 2000 adults 50 years and older of whom 40% were retired and 60% were pre-retired, the following question was asked: Do you expect your income needs to vary from year to year in retirement? Of those who were retired, 33% answered no, and 67% answered yes. Of ...

Pre-Calculus

Consider the chemical reaction aC2H6 + bCO2 + cH2O → dC2H5OH, where a, b, c, and d are unknown positive integers.? The reaction must be balanced; that is, the number of atoms of each element must be the same before and after the reaction. For example, because the number ...

PRE - CALCULUS

A woman works out by running and swimming. When she runs, she burns 7 calories per minute. When she swims, she burns 8 calories per minute. She wants to burn at least 336 calories in her workout. Write an inequality that describes the situation. Let x represent the number of ...

Pre-Calculus

An indoor physical fitness room consists of a rectangular region with a semicircle on each end. The perimeter of the room is to be a 200-meter running track. a) Draw a figure that visually represents the problem. Let x and y represent the length and width of the rectangular ...

Math (Pre-Calculus)

9t^4 + 6t^2 + 2 the problem is asking for the value of t at which the graph is at it's minimum. what i did was set t^4 to x^2 and t^2 to x. So that means I have 9x^2 + 6x + 2. Completing the square and the vertex formula gave me the same answer of -1/3 as x. So setting that ...

Pre-Calculus

Water is spraying from a nozzle in a fountain forming a parabolic path. The nozzle is 10 cm above the service of the water. The water achieves a max height of 100 cm above the waters surface and lands in the pool. The water spray is again 10 cm above the surface of the water ...

Pre-Calculus

The profit in dollars in producing x items of some commodity is given by the equation P=−11x2+346.5x−2612.5. How many items should be produced to break even?(If there are two break-even points, then enter the smaller value of x. Your solution may not be an integer...

Pre-Calculus

A local photocopying store advertises as follows. " We charge 14 cents per copy for 150 copies or less, 6 cents per copy for each copy over 150 but less than 230, and 3 cents per copy for each copy 230 and above. " Let x be the number of copies ordered and C(x) be the cost of ...

Pre-calculus

So a computer virus has been created via Corporate e-mail. Let t=0 be the time of the first 100 infections, and at t=17 minutes the population of infected computers grows to 200. Assume the anti-virus companies arent able to identify the virus or slow its progress for 24 hours...

COLLEGE CALCULUS. HELP!

the fundamental theorem of calculus, f(x)=∫(0,x) t^3+2t^2+ 2 dt, and find f"(x). my answer was: f'(x)=x^3+x^2 f"(x)=3x^2+2x it said its wrong. i don't know how solve with interval, ∫(0,x)

Calculus - Fundamental Thm of Calc

Suppose F(t) is an antiderivative of t^{3}. Then F'(t)= t^3. According to the Second Fundamental Theorem of Calculus, x ∫ (t^3)dt = ??? 1 Answer using the function F

Calculus

Need an answer to this Calculus Question. I keep getting this type of question wrong. Thanks. Differentiate the Function: y = (3x-1)^2(2-x^4)^2 y =

Calculus

Apply the concepts of calculus (limits and derivatives) to describe the graph y = sec(x). Include a quality graph

Pre-Calculus

The paddle wheel of a boat measures 16 feet in diameter and is revolving at a rate of 20 rpm. The maximum depth of the paddle wheel under water is 1 foot. Suppose a point is located at the lowest point of the wheel at t=0. 1) Write a cosine function with phase shift 0 for the ...

Pre-Calculus

The paddle wheel of a boat measures 16 feet in diameter and is revolving at a rate of 20 rpm. The maximum depth of the paddle wheel under water is 1 foot. Suppose a point is located at the lowest point of the wheel at t=0. 1) Write a cosine function with phase shift 0 for the ...

Pre-Calculus

The paddle wheel of a boat measures 16 feet in diameter and is revolving at a rate of 20 rpm. The maximum depth of the paddle wheel under water is 1 foot. Suppose a point is located at the lowest point of the wheel at t=0. 1) Write a cosine function with phase shift 0 for the ...

Pre-Calculus

The paddle wheel of a boat measures 16 feet in diameter and is revolving at a rate of 20 rpm. The maximum depth of the paddle wheel under water is 1 foot. Suppose a point is located at the lowest point of the wheel at t=0. 1) Write a cosine function with phase shift 0 for the ...

Pre-Calculus

The surface ares S (in square meters) of a hot air ballon is given by s(r)=4 pi r^2 where r is radius of balloon (in meters). If the radius r is increasing with time (in seconds) according to the formula r(t) = 2/3t^3, t is greater than or equal to 0, find the surface area S ...

History. Please Help!!

Which of the following was the most significant development in the evolution of pre-historic Native American cultures? a. The development of fire based technology because it allowed prehistoric people to invent pottery. b. The development of agriculture because it allowed pre-...

Math- Pre calculus

A community bird-watching society makes and sells simple bird feeders to raise money for its conservation activities. The materials for each feeder cost $5, and the society sells an average of 20 per week at a price of $9 each. The society has been considering raising the ...

Pre-Calculus

A local photocopying store advertises as follows. " We charge 14 cents per copy for 150 copies or less,6 cents per copy for each copy over 150 but less than 230, and 3 cents per copy for each copy 230 and above. " Let x be the number of copies ordered and C(x) be the cost of ...

Calculus

estimate the absolute maximum and minimum values of f if any, on the stated interval, and then use calculus methods to find the exact values: f(x)=10ln(x^2+1)-8x; [0,3]

calculus

Verify the identity: arctanx + arctan(1/x)=∏/2 using calculus theory. (Hint: Differentiate the left hand side of the identity)

Calculus

I need help with these two review calculus problems for my final exam. What is the derivative of a). (5x^2+9x-7)^5 b). Lne^x^3 For a. I got 50x+45(5x^5+9x-7)^4 For b. I got 3x^2 Can you verify please?

pre calculus

1.)A utility company has the following rate schedule for natural gas usage in a city’s business district: Monthly service charge: $8.80 Per therm service charge 1st 25 therms : $0.6686/therm Over 25 therms: $0.85870/therm (a) What is the charge for using 25 therms in one ...

calculus

using the fundamental theorem of calculus what is the derivative of the definite integral from x^3 to sqrt x of (sqrt t) sin t dt

Calculus

use te fundamental theorem of calculus to evaluate the integral Integral [0, pi/3] sin^2(x)dx I'm confused on what F(x) should be

statistics

Given the ensuing well drilling data, answer the following. [Reference: #4.78, page 172] • .30 (30%) probability of a productive well absent test information • Pre-drilling ballistics test ‘s affirmative result correctly predicts a productive well .70 of the time • Pre...

Pre-Calculus

Carmen rides her bicycle at a constant rate to the market. When she rides her bicycle back home along the same route, she bikes at three-quarters the rate she biked to the market. At any given time, t, the distance biked can be calculated using the formula d = rt, where d ...

Calculus I Theorem

I factored and simplified dy/dx of 192x^5 + 96x^3 + 12x all the way down to x^2 = u = (-1/2) and (-1/6). How does the result illustrates part 1 of the Calculus Fundamental Theorem?

Calculus - Find volume of cylinder

There is a cylindrical tank lying horizontally on the ground, its diameter is 8 feet, and length is 25 feet, the depth of the water currently in the tank is 2 feet. (1 gallon=231 cubic inches) How many gallons of water are in the tank? How many gallons of water will it take to...

Math - Two-Step Inequalities - Please Help

I need help with this one, please. Which of the following is in the solution set of the inequality –3 > –3t + 6? A. -1/3 B. 1/3 C. 4 D. -4 I did a Pre-Test for my lesson, and it says I got this one wrong. However, it doesn't say which one I picked. For this one, is C ...

Calculus: Derivatives

I'm having trouble understanding what derivatives in calculus (instantaneous speed) is. Can someone please explain it to me, or provide some easy links to learn from? Thanks!

Calculus

for the function F(t)=ln(t^2), let f(t)=F'(t). Write the integral from a to b of f(t) dt and evaluate it with the fundamental theorem of calculus. the integral from 1 to 3 ___ dt= __

Calculus - Fundamental thm of Calc

Use the Fundamental Theorem of Calculus to find the derivative of f(x)=∫[4,x^2]((1/4)t^2−1)^15 dt

statistics

Pre- study scores versus post- study scores for a class of 120 college freshman english students were considerated. The residual plot for the least squares regression line showed no pattern. The least squares regression line was y^=0.2+0.9x withwith a correlation coefficient r...

Pre calculus

A 100 foot tall antenna sits part way up a hill. The hill makes an angle to 12 degrees with the horizontal. In other words, if you were going to walk up the hill, you would walk at an angle of 12 degrees. To keep the antenna stable, it must be anchored by 2 cables.The distance...

Pre-calculus; urgent ! Please help !

1.Graph the polar equation r=3-2sin(theta) 2. Find the polar coordinates of 6 radical 3,6 for r > 0. 3. Find the rectangular coordinates of (7, 30°). 4. Write the rectangular equation in polar form. (x – 4)2 + y2 = 16 5. Write the equation –2x + 6y = 7 in polar form. 6...

Pre-Calculus

You are taking a flight from Daytona Beach to St. Louis. There is a stopover in Atlanta. The bearing from Daytona Beach to Atlanta is N 38.3 degrees W. The bearing from Dayton directly to St. Louis is N 43.4 degrees W. The distance of the first leg of the trip from Daytona to ...

Math

Eight people are put into pairs and enter a room with a large table with four pairs of chairs (2 chairs and a lot of space then 2 more chairs and a lot of space and so on) Though they could sit anywhere they had to sit with there assigned partner. In How Many ways could the ...

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