
Math
What is 5/8 + 4/7 1 ? I can't understand this math problem.... Please help me....  Problem: In a boys' school, 5/8 of the boys play football and 4/7 play rugby. If every boy plays at least one of the two games, find the fraction of the
asked by bobpursley on July 6, 2007 
Physics
Suppose a 68kg boy and a 40kg girl use a massless rope in a tugofwar on an icy, resistancefree surface. If the acceleration of the girl toward the boy is 3.0 m/s^2, find the magnitude of the acceleration of the boy toward the girl.
asked by Sasha on January 3, 2010 
math
If there is a bench at first and every fourth sign after that.there is water at seconed sign and fifth after that. at which sign can i find both bench and water. my answer is i subtract 41=3 and i subtract52=3 i added 3+3=6,so ami correct to say that
asked by Keisha on March 20, 2011 
Probability 2
Between 11 P.M. and midnight on Thursday night, Mystery Pizza gets an average of 4.2 telephone orders per hour. Find the probability that, a. at least 30 minutes will elapse before the next telephone order b. less than 15 minutes will elapse c. between 15
asked by Janice on November 2, 2009 
physics
A car travels a distance of 100m per second with a constant acceleration and average velocity of 20m per second .The final velocity acquired by the car is 25m per second .Find The initial velocity and acceleration of car
asked by Anonymous on July 2, 2013 
Ap chemistry
15 ml of .325 M NaOH is delivered into a 35 ml HObr solution of unknown concentration.The pH of the final solution is measured to be 7.48.Ka for HOBr is 2.0 * 10^9 at 25C. Find the number of moles of OBr and HOBr in the final solution
asked by Jdawg on February 18, 2012 
Math
The resistance of the motionof a vechincle is partly constant and partly constant and partly varies to the square of its speed.At 30km/h the resistance is 496, and at 50km/h is 656N.Find the resistance at 60km/h
asked by Adekunle Adebola on October 9, 2018 
Algebra 2
Use Cramer's rule to find the number of items the company must sell each week to break even. y= 20x + 200 y= 25x D= 20 1. 20  (25) . 25 1 D= 5 Dx= 200 1. 200  0 . 0 1 Dx= 200 Dy= 20 200. 0  5000 . 25 0  Dy= 5000 x= Dx/D x= 200/5 x=
asked by Jacqueline on October 29, 2014 
physics
Suppose a 65kg boy and a 45kg girl use a massless rope in a tugofwar on an icy, resistancefree surface. If the acceleration of the girl toward the boy is 3.0 m/s2, find the magnitude of the acceleration of the boy toward the girl.
asked by Liz on October 28, 2009 
electrical
A 20v battery with an internal resistance of 5ohm is connected to a resistance of x ohm if an additional 6ohm resistance is connected across the battery find the value of x so that the power supplied externally by the battery remains the same
asked by Anonymous on March 6, 2017 
6th grade math
Find the value fir each expression. Show your work. (13.28  7.8) divided by 4. I have the answer in the back of my book and when I try to work the problem out I keep getting the wrong answer. The answer is supposed to be 1.345 I can get the 1.34 but I get
asked by Mad(: on January 23, 2012 
physics
A car travels a distance of 100m per second with a constant acceleration and average velocity of 20m per second .The final velocity acquired by the car is 25m per second .Find The initial velocity and acceleration of car
asked by Anonymous on July 2, 2013 
physics
Suppose a 64kg boy and a 49kg girl use a massless rope in a tugofwar on an icy, resistancefree surface. If the acceleration of the girl toward the boy is 3.0 m/s2, find the magnitude of the acceleration of the boy toward the girl.
asked by Anonymous on June 10, 2010 
Math
The distance covered by a moving particle through point O is given by the equation, s = t^3 15t^2+ 63t 10. Find: (a) distance covered when t = 2 (b) the distance covered during the 3rd second; (c) the time when the particle is momentarily at rest; (d)
asked by Kd on May 9, 2019 
trigonometry
A guy wire from the top of a telephone post touches the ground at a point 7 meters from the foot of the post. If the wire and the post make an angle of 56°40', find the length of the guy wire.
asked by maniru on January 11, 2015 
Maths
A flay pole is placed at the top of a tower.the angle of elevation of the bottom and top of the flay pole from a point on the ground 10M away and 40 degrees and 50degrees respectively.find the length of the flay pole.
asked by Patrick on March 6, 2016 
math
A printer knows that a page of print contains 1273 words if large type is used and 1773 words if small type is used. A document containing 16521 words fills exactly 10 pages. Find how many pages are in each type.
asked by Anonymous on November 28, 2013 
physics
A car travels a distance of 100m per second with a constant acceleration and average velocity of 20m per second .The final velocity acquired by the car is 25m per second .Find The initial velocity and acceleration of car
asked by Anonymous on July 2, 2013 
Physics
Suppose a 68kg boy and a 40kg girl use a massless rope in a tugofwar on an icy, resistancefree surface. If the acceleration of the girl toward the boy is 3.0 m/s2, find the magnitude of the acceleration of the boy toward the girl.
asked by Sasha on January 5, 2010 
English and Language Arts
Which of the following would you find in the new English and Language Arts curriculum guidelines? A: An oral language program only at the primary grades B: A phonics program at all grades C: A writing program at all grades D: A study of core literacy works
asked by Bree on April 28, 2015 
Calculus
A solid has as its base a circular region in the xy plane bounded by the graph of x^2 + y^2 = 4. Find the volume of a solid if every cross section by a plane perpendicular to the xaxis is an isosceles triangle with base on the xy plane and altitude equal
asked by Denise on September 11, 2010 
Statistics
Assume a population of any 4 numbers(suppose: 4,8,15,19). Select a random sample of size 2 with replacement from the population. List all the possible samples and their corresponding values of x̄ “xbar” and then find the probability distribution of
asked by Ali on November 16, 2010 
physics
The large blade of a helicopter is rotating in a horizontal circle. The length of the blade is 6.60 m, measured from its tip to the center of the circle. Find the ratio of the centripetal acceleration at the end of the blade to that which exists at a point
asked by Cassandra on February 28, 2012 
Maths urgent help needed!
A rectangular tank measures 60cm by 40cm by 30cm. It is half filled with water. Water is added to the tank at a rate of 13litres per minute and drained out at 9litres per minute. Find the volume of water in the tank after 7 minutes.
asked by joi on October 23, 2011 
Algebra
Mattie Evans drove 300 miles in the same amount of time that it took a turbo propeller plane to travel 1300 miles. The speed of the plane was 200 mph faster than the speed of the car.Find the speed of the plane.
asked by Roxy on February 25, 2013 
statistics
the breaking distance of a Honda CRV can be approximated by a normal distribution, where the mean is 53 meters and the standard deviation is 3.8 meters. Let x be a random variable that represents a braking distance. Find the probability that a randomly
asked by katie on February 25, 2013 
calculus
A rectangular box is to be constructed from two different materials. The box will have a square base and open top. The material for the bottom costs $4.25/m2. The material for the sides costs $2.50/m2. Find the dimensions of the box with the largest volume
asked by j on April 9, 2011 
Physics
The large blade of a helicopter is rotating in a horizontal circle. The length of the blade is 6.7m, measured from its tip to the center of the circle. Find the ratio of the centripetal acceleration at the end of the blade to that which exists at a point
asked by Natasha on February 18, 2012 
Maths
A water tank has the shape of a rectangular prism of base 50 cm2. This tank is being filled at the rate of 12 liters per minutes. Find the rate at which the height of the water in the water tank increases; express your answer in millimeters per second. I
asked by Elise on July 14, 2015 
math
Romy invested $5,000 into an account that pays 5% compound semiannually. He intended to keep the account untouched for five years. However, after three years he had to withdraw $3,000. Find the amount left in the account five years from the time he made
asked by Lula on May 5, 2018 
chemisrty
A solid acid is dissolved in enough water to make 200 ml of a solution. 40.0ml of the solution is titrated to a phenolphthalein en point with an NaOH solution. The neutralized solution and the remainder of the acid solution are then mixed and the PH of the
asked by Aria on April 16, 2014 
physics
The large blade of a helicopter is rotating in a horizontal circle. The length of the blade is 6.07 m, measured from its tip to the center of the circle. Find the ratio of the centripetal acceleration at the end of the blade to that which exists at a point
asked by heather on February 23, 2011 
fnu
The length of country and western songs is normally distributed and has a mean of 200 seconds and a standard deviation of 30 seconds. Find the probability that a random selection of 9 songs will have mean length of 186.30 seconds or less. Assume the
asked by giovanny on June 10, 2014 
Algebra
Let P0 = $1000.00. • k = 0.5% = _____0.005______ as a decimal. Compute and explain how to find the doubling time. Then, write the compound interest equation for this value of k and the 3 values for t. Number of years Equation New Value 1
asked by Brittany on June 28, 2016 
statistics
The length of country and western songs is normally distributed and has a mean of 200 seconds and a standard deviation of 30 seconds. Find the probability that a random selection of 9 songs will have mean length of 186.30 seconds or less. Assume the
asked by Anonymous on July 29, 2013 
physics
The large blade of a helicopter is rotating in a horizontal circle. The length of the blade is 7.0 m, measured from its tip to the center of the circle. Find the ratio of the centripetal acceleration at the end of the blade to that which exists at a point
asked by jyothi on February 16, 2015 
math
Question 1 of 5 Multiple Choice The rate of change is constant in the table. Find the rate of change. Explain what the rate of change means for the situation. The table shows the cost of a ski rental package for a given number of people.
asked by yeeeeet on November 29, 2018 
Physics Circular Motion
The large blade of a helicopter is rotating in a horizontal circle. The length of the blade is 7.0 m, measured from its tip to the center of the circle. Find the ratio of the centripetal acceleration at the end of the blade to that which exists at a point
asked by Jayesh on February 20, 2015 
essay cont.: mrs. sue
The next step for a student to do is to take all of the information he or she learned in the class, and apply it to his or her future. For example, when one buys a house in the future, it is necessary to take out a loan. To do this, one has to consider
asked by julie on November 28, 2007 
Calculus derivative
find the slope m and an equation of the tangent line to the graph of the function f at the specified point. original: x^2/x+10 point: (3,9/13) After I found the derivative: (x+10)(2x)(x^2)(1)/((x+10))^2 How do I get the slope? Should I put 3 into the
asked by Eve on September 17, 2013 
math
A rectangular solid has a base with length 6 cm and width 5 cm. If the volume of the solid is 300 cm3, find the height of the solid. [Hint: The volume of a rectangular solid is given by V = LWH.]
asked by Brenda on January 29, 2008 
value
A Body Is In Equilibrium When Three Forces Act On It,two Of The Forces Are F1 Of Magnitude 8n Acting Dud East And F2 Which Is 5n Acting N60degree East.Find The Magnitude And Direction Of The Third Force.
asked by value on October 8, 2016 
Physics
A man using 80kg garden tractor on a level surface exert a force of 50N at 65^0 to the ground. Find the vertical force of the garden tractor on the ground
asked by Eric on November 4, 2018 
Physics
Find the tension in each of the two ropes supporting a hammock if the first one is at an angle of 19.4° above the horizontal and the second is at an angle of 35.3° above the horizontal. The person sleeping in the hammock (unconcerned about tensions and
asked by Tesia on July 7, 2015 
Algebra 2
The angular speed of a larger pulley wheel (radius=15cm) is 50 rev./min. Find the angular speed of the smaller wheel (radius=6cm).
asked by Mary on April 22, 2012 
math
A candidate believes that 2/3 of the registered voters in his district will vote for him in the next election. If two registered voters are independently selected at random, find the probability that neither will vote for him in the next election.
asked by ALAINI on May 31, 2011 
Calculus
Find the limit lim as x approaches (pi/2) e^(tanx) I have the answer to be zero: t = tanx lim as t approaches negative infi e^t = 0 Why is tan (pi/2) approaching negative infinity is my question?
asked by NYCalc on March 23, 2011 
math
calvin buys 3/5 pound of ground beef. he divides the beef into 6 equal portions. a)find the weight of 1 portion of beef. b)fin the weight of 4 portions of beef.
asked by Shohanur on February 8, 2013 
math
A tugboat goes upstream 120 miles in 20 hours. The return trip downstream takes 10 hours. Find the speed of the tugboat without the current and the speed of the current.
asked by Lori on August 1, 2012 
Science
I need to find out if sucrose, sucrose solution, sodium chloride, sodium chloride solution, water, vinegar, and aluminum are electrolytes and what type of bond they are but I don't know where to look.
asked by Anonymous on December 20, 2009 
Trigonometry
Suppose *u* is a quadrant IV angle with cos(u) = 3/5. Suppose *v* is a quadrant IV angle with cos(v) = 12/13. Find the exact value of sin(uv) I have gotten to sin120cos150  sin150cos120 but I am not sure I am correct up to that point and I don't know
asked by Lydia on April 17, 2016 
Algebra
A store mixes red fescue worth $10 per pound and ryegrass worth $13 per pound. The mixture is to sell for $12 per pound. Find how much of each should be used to make a 120 pound mixture.
asked by Chad on June 29, 2015 
physics
A bat flying in a cave emits a sound and receives its echo 0.5 s later. How far away is the cave wall? I answered this below. If you cant find it, search on bat flying in the search window above.
asked by Barry on November 5, 2006 
math
The bases of trapezoid ABCD are \overline{AB} and \overline{CD}. Let P be the intersection of diagonals \overline{AC} and \overline{BD}. If the areas of triangles ABP and CDP are 8 and 18, respectively, then find the area of trapezoid ABCD.
asked by Robert on December 8, 2013 
PreCalculus
Rational Functions y = (x^2+7x4)/(x2) Since the degrees of both the numerator and denominator are the same, I would use the leading coefficient, and both the rational functions start with 1, so would the horizontal asymptote be 1? Also don't get how to
asked by Shreya on October 2, 2012 
algebra
Marcel brought in 40 cookies to share equally with his classmates. Let t represent the number of classmates Marcel has. Which expression could be used to find the number of cookies each classmate received?
asked by kinley on December 14, 2018 
geometry
round to the nearest tenth. a rectangular plot of land is 80 meters wide and 98 meters long. Find the length of the diagonal and if necessary, round to the nearest tenth.
asked by Ariana on September 1, 2013 
English
What is the meter of the following line from “A Sybil” by Rilke? “Her age became too much to say” Im confused and cant find an answer. Iambic pentameter Iambic tetrameter Trochaic pentameter Trochaic tetrameter
asked by Anonymous on December 15, 2014 
Math
The perimeter of a rectangle is 110 inches. The length exceeds the width by 41 inches. Find the length and the width. I can't seem to figure out this last question. Don;t know where to start. Please help it is my last question.
asked by Flossie on August 29, 2010 
statistics
I need to find the class midpoint, boundaries and class with for the following problem Tar Cigarette Filter Frequency 25 2 69 2 1013 6 1417 15 I did the midpoint and boundaries 3.5 5.5 7.5 9.5 11.5 13.5 15.5 17.5 But for the width I got an answer of
asked by ALFREDA on April 19, 2012 
Calculus,reaction rates
A car starting at 12:00 noon travels west at a speed of 30 kph. Another car starting from the same point at 2:00 PM travels north at 45 kph. Find how fast the two are separating at 4:00 PM?
asked by @jayr on November 30, 2014 
Geometry
One hundred tiles of a certain size are needed to pave a floor. If a tile, which measures 4 cm less on each side, will be used, 225 tiles will be needed. Find the size of the larger tile.
asked by Ivyl on August 2, 2011 
math
find the standard deviation for the given data. Round your answer to one more decimal place than original data. (9,7,13,24,32,45,47) I get 16.62041 but how do I round my answer to one or more decimal places? I am a little lost.
asked by Marie on November 19, 2009 
Algebra
A tugboat goes 160 miles up stream in 20 hours, return trip downstream takes 5 hours. Find speed of tugboat without the current and the speed of the current
asked by Ruth on March 6, 2013 
algebra
Find all rational zeros of the polynomial function P(x)=x^4 + 2 x^3  13 x^2 + 4 x  30. Enter the rational zeros in a comma separated list. If there are none, enter "none". 3 1 2 13 4 30 3 15 6 30 1 5 2 10 0 so (x+3)(x^35x^2+2x10 so 5 1 5 2
asked by kim on June 23, 2015 
Calculus
Assume that a demand equation is given by q=9000100p. Find the marginal revenue for the given production levels. a. 500 Units the marginal revenue at 500 units is
asked by Duane on November 1, 2014 
physics
as light passes from air to water vi/vr=4/3 find the angle of incidence of a ray of light if the angle or refration is 25 degrees 40 minutes (i is the angle of incidence and r is the angle of refraction)
asked by merri on January 13, 2013 
algebra
The angle of elevation from the tip of the shadow to the top of the tree is 36°. Find the distance from the top of the tree to the tip of the shadow. Round the answer to the nearest tenth.
asked by Bob on March 30, 2015 
calculus
A force of 10 pounds is applied to a wagon, directed at an angle of 30∘30∘. Find the component of this force pulling the wagon straight up, and the component pulling it horizontally along the ground.
asked by andre on August 14, 2016 
STATISTICS
Consider a binomial random variable where the number of trials is 12 and the probability of success on each trial is 0.25. Find the mean and standard deviation of this random variable. I have a mean of 4 and a standard deviation of 2.25 is this correct
asked by John on June 10, 2010 
Math,algebra
ann is 20 years older than her daughter faye. three years from now she will be six times as old as her daughter. find their present ages. This is my work: ( i'm not sure if it's correct ) Now 3 yrs from now Ann A A+3 Faye 6A 6A+3 7a+21 = 6A+3 6A 6A
asked by Ellofrmdaodersyde on February 15, 2016 
math
there are 30 marbles in a bag; 4 blue, 10 red,6 white, 10 yellow. You randomly draw5 marbles without replacement. Find the percent of drawing 2 red marbles and at least 2 white marbles.
asked by em on May 23, 2014 
math
A LAMP POST IS 10 FEET TALL AND CAST A SHADOW. THE DISTANCE FROM THE TOP OF THE LAMP POST TO THE TIP OF THE SHADOW IS 20 FEET. FIND THE ANGLE OF THE ELEVATION.
asked by BRANDI on August 12, 2014 
Business
The number of square meters in a square rooms floor area exceed the number of meters in the rooms perimeter by 60.Find the sidelength of the room.
asked by Jane on April 18, 2016 
history
For the quote "Remember the Maine" I went on a lot of websites and most of the websites said that "remember the Maine" was said by Americans. I can't seem to find what the meaning of the quote was. Did people say it when they wanted to go to war with
asked by Amy~ on August 28, 2010 
Math
The area of a rectangular garden is 110 square meters. The width is 6 meters loner than onehalf of the length. Find the length and the width using area=lengthxwidth
asked by Amber on April 30, 2013 
Math
Under ideal conditions, a population of rabbits has an exponential growth rate of 11.8% per day. Consider an initial population of 300 rabbits. Find the exponential growth function.
asked by Sarah on December 6, 2016 
Basic Caluculus
f(x)=2x^3x^2+1 [1,4]=interval Using the limit process, (once with right endpts, and the other with left entdpts.) find the area under the curve and above the xaxis on the given interval i got the area to be 107.5 for right endpts. (not sure if its right)
asked by Munni on May 29, 2011 
Math radical form
Find the distance of the line segment whose endpoints are (5,7) and (2,3) in simplest radical form. sqrt [(73)^2 + (5 (2))^2] = sqrt [16 + 49] = sqrt 65 That is the simplest form I can think of. sqrt means "square root of"
asked by sheka on August 11, 2007 
Math
A walkway is formed by four semi circles. The diameter of the inner semi circles is 14 feet. The width between the outer and inner semicircles is 2 feet. Find the area of the walkway. Use 3.14 as an approximation for pi.
asked by Eiyannah on June 9, 2015 
math
In an election among three contestant P,Q and R. P gets 120% more votes than Q. P beats R by 350000 votes. Q beats R by 5% of the total votes. Find the total number of votes polled (in lakhs) How to do easy way
asked by vipul on June 27, 2016 
Physics
An 85 kg jogger is heading due east at a speed of 1.7 m/s. A 55 kg jogger is heading 40° north of east at a speed of 3.4 m/s. Find the magnitude and direction of the sum of momenta of the two joggers.
asked by Will on April 1, 2008 
Calculus
The vertical position of an object is modeled by the function h(t)=16t^2 +5t+7, where h is measured in feet and t is measured in seconds. Find the object's initial velocity (that is, the velocity at t=0). Is it 5 feet per second?
asked by Kayla on March 26, 2014 
Math
A box contains 3 red marbles, 6 blue marbles, and 1 white marble. The marble are selected at random, one at a time, and are not replaced. Find the probability. P(blue and red) Please help me
asked by Lisa on February 2, 2012 
Stat
Of 84 adults selected randomly from one town, 62 have health insurance. Find a 90% confidence interval for the true proportion of all adults in the town who have health insurance. Please help mr solve.
asked by Billy on October 1, 2014 
algebra
The formula for the area of a trapezoid is A = h(B + b) 2 . The area of the trapezoid truss in the illustration is 72 square feet. Find the height of the truss shown below if the shorter base is the same as the height.
asked by f on March 21, 2014 
geometry
for that some problem: A board that is 12 feet long must be cut into 2 pieces that have lengths in a ratio of 3 to 2. Find the lengths of the two pieces. arn't you solving two parts because the board was cut in two?
asked by shannon on February 27, 2011 
Algebra
An object is dropped from a bridge. Find the distance the object has fallen when its speed reaches 132 ft/s. Use the equation v = 64d , where v is the speed in feet per second and d is the distance in feet.
asked by Irma on July 6, 2016 
Pre calc
Thanks in advance for any help. I need help with this whole problem. The distance s(t) between an object and its starting point is given by the antiderivative of the velocity function v(t). Find the distance between the object and its starting point after
asked by Peter on May 14, 2008 
Maths
A and B are two balloons at the same height and 1000 metre apart. O is a ground observation position. Angle AOX is 45 degree 15' and angle BOX is 10 degree and 30'. Find the height of the balloons.
asked by Shane on April 29, 2013 
Algebra
From a group of 6 men and 4 women, a committee of 3 is to be selected at random. Find P(at least 2 women). It might be a little out of order but this is what I got. C(10,2) (10*9*8*7*6*5*4*3*2*1)/(8*7*6*5*4*3*2*1*2*1) =45 C(6,2) (6*5*4*3*2*1)/(2*1) =360
asked by Jon on March 5, 2008 
math
a basketball hoop is 120 inches above the court. a player is 62 inches tall. find the approximate distance between th top of the player's head and the basketball hoop.
asked by shron on December 10, 2012 
same type of binomial theorem question
Question: Find the first 3 terms in the expansion, in ascending powers of x, of (2 + x)^6. Hence, obtain the coefficient of x^2 in the expansion of (2 + x  x^2)^6 I know the first part of the question, and the first 3 terms are (64 + 192x + 240x^2 + ...)
asked by nicholas on August 4, 2009 
algebra
a tugboat goes 160 miles upstream in 20 hours. The return trip downstream takes 10 hours. Find the speed of the tugboat without a current and the speed of the current.
asked by Math Girl on June 10, 2012 
Math
Can someone tell me how to start to solve this A bag contains 4 white, 3 blue, and 5 red marbles. 1. Find the probability of choosing a red marble, then a white marble if the marbles are replaced. A. 1/12 B. 5/36 C. 5/6 D. 5/12
asked by Katie on February 27, 2019 
college alg
Find (a) the equation of a line that is parallel to the given line and includes the given point, and (b) the equation of a line that is perpendicular to the given line through the given point. Write both answers in slopeintercept form. y = 4x + 2, (5, 4)
asked by sunny on January 4, 2012 
algebra
The value of a certain twodigit number is eight times he sum of its digits. if the digits of the number are reversed the result is 45 less than the original number. find the original number. **please show both equations and work... thanks =)
asked by Bri on February 28, 2011 
math
bob has a container with a capacity of 12 quarts. he wants to express this capacity in gallons. write a proportion to find the number of gallons of water bob's container can hold.
asked by pavleen on February 10, 2011 
Algebra 2
The red spinner has six equal sectors labeled with numbers 1 through 6. The blue spinner has four equal sectors labeled with letters A, B, C, and D. Find the probability of spinning the two spinners and getting a 5 with a B?
asked by Megan on February 28, 2012 
Mensuration
A sheet of paper measures 30cm by 20cm. A strip 4cm wide is cut from it all around. Find the area of the remaining sheet and also the area of the strip cut out.
asked by Sunil on February 24, 2016
Pages
 1
 2
 3
 4
 5
 6
 7
 8
 9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
 100
 101
 102
 103
 104
 105
 106
 107
 108
 109
 110
 111
 112
 113
 114
 115
 116
 117
 118
 119
 120
 121
 122
 123
 124
 125
 126
 127
 128
 129
 130
 131
 132
 133
 134
 135
 136
 137
 138
 139
 140
 141
 142
 143
 144
 145
 146
 147
 148
 149
 150
 151
 152
 153
 154
 155
 156
 157
 158
 159
 160
 161
 162
 163
 164
 165
 166
 167
 168
 169
 170
 171
 172
 173
 174
 175
 176
 177
 178
 179
 180
 181
 182
 183
 184
 185
 186
 187
 188
 189
 190
 191
 192
 193
 194
 195
 196
 197
 198
 199
 200
 201
 202
 203
 204
 205
 206
 207
 208
 209
 210
 211
 212
 213
 214
 215
 216
 217
 218
 219
 220
 221
 222
 223
 224
 225
 226
 227
 228
 229
 230
 231
 232
 233
 234
 235
 236
 237
 238
 239
 240
 241
 242
 243
 244
 245
 246
 247
 248
 249
 250
 251
 252
 253
 254
 255
 256
 257
 258
 259
 260
 261
 262
 263
 264
 265
 266
 267
 268
 269
 270
 271
 272
 273
 274
 275
 276
 277
 278
 279
 280
 281
 282
 283
 284
 285
 286
 287
 288
 289
 290
 291
 292
 293
 294
 295
 296
 297
 298
 299
 300
 301
 302
 303
 304
 305
 306
 307
 308
 309
 310
 311
 312
 313
 314
 315
 316
 317
 318
 319
 320
 321
 322
 323
 324
 325
 326
 327
 328
 329
 330
 331
 332
 333
 334
 335
 336
 337
 338
 339
 340
 341
 342
 343
 344
 345
 346
 347
 348
 349
 350
 351
 352
 353
 354
 355
 356
 357
 358
 359
 360
 361
 362
 363
 364
 365
 366
 367
 368
 369
 370
 371
 372
 373
 374
 375
 376
 377
 378
 379
 380
 381
 382
 383
 384
 385
 386
 387
 388
 389
 390
 391
 392
 393
 394
 395
 396
 397
 398
 399
 400
 401
 402
 403
 404
 405
 406
 407
 408
 409
 410
 411
 412
 413
 414
 415
 416
 417
 418
 419
 420
 421
 422
 423
 424
 425
 426
 427
 428
 429
 430
 431
 432
 433
 434
 435
 436
 437
 438
 439
 440
 441
 442
 443
 444
 445
 446
 447
 448
 449
 450
 451
 452
 453
 454
 455
 456
 457
 458
 459
 460
 461
 462
 463
 464
 465
 466
 467
 468
 469
 470
 471
 472
 473
 474
 475
 476
 477
 478
 479
 480
 481
 482
 483
 484
 485
 486
 487
 488
 489
 490
 491
 492
 493
 494
 495
 496
 497
 498
 499
 500
 501
 502
 503
 504
 505
 506
 507
 508
 509
 510
 511
 512
 513
 514
 515
 516
 517
 518
 519
 520
 521
 522
 523
 524
 525
 526
 527
 528
 529
 530
 531
 532
 533
 534
 535
 536
 537
 538
 539
 540
 541
 542
 543
 544
 545
 546
 547
 548
 549
 550
 551
 552
 553
 554
 555
 556
 557
 558
 559
 560
 561
 562
 563
 564
 565
 566
 567
 568
 569
 570
 571
 572
 573
 574
 575
 576
 577
 578
 579
 580
 581
 582
 583
 584
 585
 586
 587
 588
 589
 590
 591
 592
 593
 594
 595
 596
 597
 598
 599
 600
 601
 602
 603
 604
 605
 606
 607
 608
 609
 610
 611
 612
 613
 614
 615
 616
 617
 618
 619
 620
 621
 622
 623
 624
 625
 626
 627
 628
 629
 630
 631
 632
 633
 634
 635
 636
 637
 638
 639
 640
 641
 642
 643
 644
 645
 646
 647
 648
 649
 650
 651
 652
 653
 654
 655
 656
 657
 658
 659
 660
 661
 662
 663
 664
 665
 666
 667
 668
 669
 670
 671
 672
 673
 674
 675
 676
 677
 678
 679
 680
 681
 682
 683
 684
 685
 686
 687
 688
 689
 690
 691
 692
 693
 694
 695
 696
 697
 698
 699
 700
 701
 702
 703
 704
 705
 706
 707
 708
 709
 710
 711
 712
 713
 714
 715
 716
 717
 718
 719
 720
 721
 722
 723
 724
 725
 726
 727
 728
 729
 730
 731
 732
 733
 734
 735
 736
 737
 738
 739
 740
 741
 742
 743
 744
 745
 746
 747
 748
 749
 750
 751
 752
 753
 754
 755
 756
 757
 758
 759
 760
 761
 762
 763
 764
 765
 766
 767
 768
 769
 770
 771
 772
 773
 774
 775
 776
 777
 778
 779
 780
 781
 782
 783
 784
 785
 786
 787
 788
 789
 790
 791
 792
 793
 794
 795
 796
 797
 798
 799
 800
 801
 802
 803
 804
 805
 806
 807
 808
 809
 810
 811
 812
 813
 814
 815
 816
 817
 818
 819
 820
 821
 822
 823
 824
 825
 826
 827
 828
 829
 830
 831
 832
 833
 834
 835
 836
 837
 838
 839
 840
 841
 842
 843
 844
 845
 846
 847
 848
 849
 850
 851
 852
 853
 854
 855
 856
 857
 858
 859
 860
 861
 862
 863
 864
 865
 866
 867
 868
 869
 870
 871
 872
 873
 874
 875
 876
 877
 878
 879
 880
 881
 882
 883
 884
 885
 886
 887
 888
 889
 890
 891
 892
 893
 894
 895
 896
 897
 898
 899
 900
 901
 902
 903
 904
 905
 906
 907
 908
 909
 910
 911
 912
 913
 914
 915
 916
 917
 918
 919
 920
 921
 922
 923
 924
 925