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Drawing a counter from 2 bags 2020-05-21
From Sephy:
Question 4: Two bags, 1 and 2, each contain equal size counters.
Bag 1 contains a pink counter, yellow counter and white counter. Bag 2 contains counters labelled 1, 4, 5 and 7.
A counter is drawn at random from bag 1 and a counter is drawn at random from bag 2.
If the counter from bag 1 is pink, the number on the counter from bag 2 is increased by 1
If the counter from bag 1 is yellow, the number on the counter from bag 2 is decreased by 5
If the counter from bag 1 is white, the number is halved.
Find the probability of scoring a number below 3

Answered by Penny Nom.
An angle i a triangle 2020-05-16
From Ogunjobi:
Two goal post are 8m apart a footballer is 34 m from one post and 38m from the other within what angle must he kick the ball if he is to score
Answered by Penny Nom.
The flight of a football 2020-05-06
From Michael:
Football is thrown from a 10-yard line. It reaches its highest height of 20 yards. It lands on the 50-yard line after 2 seconds. What is the equation of the parabola that models this throw? I really need help as I've been on this for the longest amount of time.
Answered by Penny Nom.
7 spheres on a hexagonal tray 2019-01-14
From herm:
what is the length of each side of a hexagonal tray, with the height of each side 0.75 inch, to hold seven spheres, each with a diameter of 3.00 inches? The spheres are placed such that each side of the hexagon is touched by one sphere at its midpoint (and the seventh sphere is place in the center of the "ring" of the other six spheres.
Answered by Harley Weston.
Throwing a football 2018-04-26
From Abby:
Daring Danny's threw a football at an angle of 40 degrees to the horizontal. The football hit the ground at 36 feet. Danny is 5 feet 1 inch tall. Find the initial velocity

I have been trying to figure this problem out for forever! Please help! I am really confused because I don't know time either and you are supposed to find that as well as velocity.

Answered by Penny Nom.
A footballer angle 2018-02-14
From Kim:
Two goal posts are 8m apart. A footballer is 34m from one post and 38m from the other. Within what angle must he kick the ball if he is to score a goal.
Answered by Penny Nom.
Baseball Cards 2017-04-20
From Raquel:
A minor league baseball team gave away baseball cards to each person entering the stadium. One group receives 28 baseball cards. A second group received 68 baseball card. If each person entering the stadium receive the same number of cards, what was the greatest possible number of baseball cards that each person could have received?
Answered by Penny Nom.
An open ball is an open set? 2016-06-23
From Aqeel:
Theorem: The open ball is an open set?
Answered by Harley Weston.
A rotating schedule for a softball team 2016-03-25
From Caroline:
I couldn't find a similar question, hopefully there isn't one!

I have a softball team of 18 people (7 girls and 11 boys), but am limiting each game to 13 players (6 girls and 7 boys). The season is 10 games long. How do I create a rotating schedule which allows members to play evenly? I tried separating the boys and girls to create rotation for each but I got confused. Some are unable to attend all games but for the simplicity of a rotation schedule can you please help?

Answered by Robert Dawson and Victoria West.
Golf for 6 - 2 three balls 2016-02-01
From Andy:
We are shortly having a golf holiday in Phoenix. There are 6 people playing 6 rounds, so we will play in 2 three balls. Is there a combination of pairings that ensures everyone plays with each other the same number of times. Many thanks for your help ! Andy
Answered by Victoria West.
The sweep angle of a video camera 2015-11-25
From Franc:
a television camera is 30ft from the sideline of a basketball court 94 ft long. The camera is located 7 ft from the mid court. through what angle must it sweep in order to cover all action on the court?
Answered by Penny Nom.
An 8 Team Basketball League Schedule 2015-10-28
From Janice:
We have an eight team league that play at four time slots each week. It's a seven week season. How do we schedule so that each teams plays each other at least once?
Answered by Victoria West.
The flight of a ping pong ball 2015-10-13
From Abigail:

Wondering if there is a way to figure out the quadratic equation of half of a parabola?
Doing an assignment about finding quadratic equations for separate bounces of a ping pong ball, but the first bounce is incomplete (as the ball has presumably been dropped, hit the ground and then went on to make a complete bounce).
Please see attachment for references to the diagram that I am using.

Not sure whether I would have to look at it from a different perspective.



Answered by Harley Weston.
20 golfers playing four rounds 2015-08-17
From Paul:
I have a party of 20 golfers playing four rounds in fourballs. I realise that everyone will have 7 players that they do not play with, however I want to ensure that no one plays with the same person twice and that the Captain plays with the 12 players of his choice.
Answered by Victoria West.
A fantasy football league 2015-06-11
From Jason:
Hello. We have a fantasy football league with 14 teams. The season is 13 weeks long and we would like to figure out a way to have two divisions of seven teams each with each team playing their inter-division opponents twice. Is there a way to set this up? I cannot seem to find a way to do it. Thanks!
Answered by Victoria West.
Team selection 2015-04-13
From Peter:
I manage a football team with a list of 28 players.
Only 24 can play each game.
The season is 16 games.
How do I fairly select 24 players each week.

Answered by Robert Dawson.
8 golfers playing in 2x2 balls in 5 games 2015-03-18
From Brian:
We are 8 golfers who will be playing in 2x2 balls in 5 games. is there a formula to minimize the chances of playing with a partner or opponent too often please ?
Answered by Victoria West.
A tennis ball in a triangular prism 2014-10-06
From Anna:
Hi, I need to find the the base and the height of a triangular prism, but I only know the diameter of a tennis ball that fits exactly in the triangular container.. The diameter for the ball is 8.50cm. Can you help me find the formula? Thank you!
Answered by Penny Nom.
6 inches of dirt in a baseball field 2014-06-01
From Mary:
The baseball field is 20,000 Square feet, 6 inched deep I need to know how many cubic yards of dirt this will generate.
Answered by Penny Nom.
A ball in a box 2014-02-09
From kenneth:
I have 2 questions.What is the radius of the largest ball that will fit into a box that has the inside dimensions of 6feet by 8 feet by 10feet. and the second question is how many cubic feet of concrete will you need to complete a patio that is 20 feet long by 15 feet wide by 5 inches in hight.
Answered by Penny Nom.
Watching a bouncing ball through a window 2014-01-15
From Bob:
A ball falls from the roof, at a height of 10m. After each impact on the ground it bounces back up to 4/5 of its previous height. How many times will the ball appear in front of a rectangular window whose bottom edge is at a height of 5m, and whose top edge at a height of 6m?
Answered by Penny Nom.
Schedule for a 4 team basketball league 2013-12-08
From Sommer:
I need a schedule for my kids basketball league. There are 4 teams. We will play every Saturday for 4 weeks with 4 games per Saturday. Week 5 will be the playoffs where 1st will play 4th and 2nd will play 3rd. Week 6 will be winners of week 5. Please help!!
Answered by Victoria West.
If the earth was made of a ball of string 2013-09-18
From Tammy:
My 9 year old son asked me a question and I have no idea how to work it out! Please can you help?

If the earth was made of a ball of string and you unravelled the string how long would it be? Assuming the string is 5mm thick.

Answered by Penny Nom.
Covering a styrofoam ball with fabric 2013-09-11
From Alice:
I am trying to create a pattern in order to cover a styrofoam ball with fabric. The pattern needs to be done in such a way as to have only a center seam, rather than several vertical lines as in slicing a melon.
Answered by Chris Fisher.
Fantasy football league 2013-06-18
From Chris:
Hello, I am the commissioner of a fantasy football league. In this week, we play all 17 weeks of the season. It's a 12 team league, and we play each team twice. To do that, we have 5 "double header" weeks, which means you play 2 different teams. I am struggling to come up with a schedule to make this work. Does anyone have a solution?
Answered by Victoria West.
What is the probability that the sixth draw will be a red ball? 2012-11-23
From Patty:
The probability of drawing a red ball out of a bag containing one red ball and one black ball is 1/2. An experiment is conducted where these two balls are placed in a bag before drawing a ball out. A ball is drawn 5 times from the bag containing the two balls. Each of the first five times the red ball was drawn out. what is the probability that the sixth draw will be a red ball?
Answered by Penny Nom.
Three tennis balls 2012-05-17
From eiman:
Three tennis balls are placed inside a container . the tennis balls are tangent to the top, bottom,and sides of the container . find the volume of air inside the container surrounding the tennis balls if the diameter of the tennis balls is 6 inches
Answered by Chris Fisher.
Golf: 8 players over 4 days in 4-balls 2012-05-03
From JimB:
I cannot seem to get this to work. Previous answers cover 2-balls, but we are 4-balls.

What we really want is for each player to play with each other, at least once and no more than twice.
Ideally, each would also play equally in the first and the second 4-ball of the day.

Answered by Victoria West.
Parametric equations 2 2012-02-25
From Kathy:
If the angle at time 0 is not 45 degrees how can you find the initial velocity? Ball thrown from height of 7 feet. Caught by receiver at height of 4 feet after traveling 90 feet down the field. Find initial velocity. You had a similar problem answered but the angle was 45 degrees so the cos and sin were equal and the equations were simpler to work with. Thank you!
Answered by Harley Weston.
What is the altitude of the balloon? 2011-12-04
From C:
Chelcy and Jorgeare 2.32 miles apart. The observe a hot air balloon directly overhead between them Chelcy's angle of elevation is 28 degrees. Jorge's Angle of elevation is 37 degrees. What is the altitude of the balloon?
Answered by Penny Nom.
A mythical soccer ball 2011-10-27
From Joel:
We've been working on this problem diligently and can't seem to come up with the answer book's answer. We think it may be wrong, yet want to check it with an expert. Here goes. The school's new soccer balls are covered with 64 regular hexagonal panels. Each hexagon measures 2 inches between opposite corners and 1.5 inches between opposite sides. What is the total surface area of the soccer ball?
Answered by Robert Dawson and Lorraine Dame.
A spherical ball in a conical wine glass 2011-10-26
From Jules:
A heavy spherical ball is lowered carefully into a full conical wine glass whose depth is h and whose generating angle (between the axis and a generator) is w. Show that the greatest overflow occurs when the radius of the ball is (h*sin(w))/(sin(w)+cos(2w)).
Answered by Claude Tardif.
Throwing a football 2011-02-08
From Janet:
a football is thrown into the air from 2 meters high. After 1 second it is 6.9 meters high. After another second it is 2 meters high. How high is it after 1.02 seconds and .05 seconds? when will it reach 5.136 meters? I am not sure how to extract the numbers I need and what equations to use them in?
Answered by Stephen La Rocque.
A player runs from second base to third base 2011-01-30
From Marie:
A baseball diamond is a square with side 90 feet in length. A player runs from second base to third base at a rate of 18 ft/sec. At what rate is the area of the trapezoidal region, formed by line segments A, B, C, and D changing when D is 22.5
Distance A is the players distance from first base when running from 2nd to third. Distance D is his distance from 3rd base. Distance C is the distance from 3rd to 3rd to Home. Distance B is the distance from Home to First. I have found dA/dt in a previous problem.

Answered by Penny Nom.
A television camera at a basketball court 2010-12-06
From ryan:
Can you just please give me an idea on how the diagram would look like. I'm really confused.

A television camera is 30 ft. from the sideline of a basketball court 94 ft long. The camera is located 7 ft from the midcourt. Through what angle must it sweep in order to cover all action on the court?

Answered by Penny Nom.
Will the ball clear the tree? 2010-11-14
From MK:
Sam hits a golf ball with a five-iron a distance of 120m horizontally. A tree 45m high and 35m in front of Sam is directly in the path of the ball. Will the ball clear the tree if the ball makes a parabolic curve and has a maximum height or 80m?
Answered by Brennan Yaremko.
How far must the pitcher travel to get to the ball? 2010-11-04
From ken:
A baseball player bunts a ball down the first base line. It rolls 35ft at an angle of 26 degrees with the first base path. The pitchers mound is 60.5 ft from the plate. How far must he travel to get to the ball.
Answered by Penny Nom.
There are 12 balls and one balls weight is different than the others 2010-08-12
From david:
if there was 12 balls and one balls weight is different than the other and use a balance 3 times is there a possible way to find which weigh different
Answered by Robert Dawson.
Packing spheres in a given region 2010-01-27
Answered by Robert Dawson.
The 3-ball lottery 2009-12-09
From Lee:
A friend and I are trying to calculate the odds of choosing the winning numbers in the 3-ball lottery (3-digits 0-9). We realize that there are 720 Permutations and 120 possible Combinations of said lottery, but we're having trouble figuring how to determine the "odds" or probability of winning (1) when order matters, and (2) when it doesn't. Please help!
Answered by Penny Nom.
A baseball diamond 2009-11-18
From maelee:
the official distance between home plate and second base in baseball diamond is 120ft. Find the area of the official ball diamond & the distance between the bases.
Answered by Robert Dawson, Chris Fisher and Penny Nom.
A drawing of a baseball diamond 2009-11-09
From Beth:
My husband has a drawn diagram on a piece of paper of a baseball diamond. He knows that on the paper 1 1/16" (1.6875") = 90 actual feet. How do we calculate how many feet 5 7/8" on the paper would be?
Answered by Penny Nom.
A football schedule 2009-08-14
From Bill:
I am having trouble with a football schedule that has two divisions of five teams each, 1-5 and 6-10. 1-5 will play against each other in the first 4 weeks and also the the last 4 weeks with teams 6-10 completing the middle of the schedule. The schedule is 13 weeks. Thank you for your time
Answered by Chris Fisher and Victoria West.
A 6 team social softball league 2009-05-02
From Don:
Hi We have a 6 team social softball league with only two fields. Each team plays two games each Saturday. We have three time slots 10:00, 12:00 and 2:00 We play for 11 Saturdays and than have a 2 weekend playoff. All teams prefer double headers vs the split at 10:00and 2:00. How do we schedule as balanced a schedule as possible and minmize the splits ? Thanks Don
Answered by Laura Morrison and Victoria West.
The volume of water in a cone 2009-03-17
From Freddie:
A ball of diameter 20cm rests in a conical container whose angle with the slant height and the vertical axis is 25degrees. if water is poured into the container just enough to touch the bottom of the ball, find the quantity of water in the container.
Answered by Penny Nom.
How many ball bearings can you make from a cone? 2009-03-14
From Vatsal:
there is a sum in my maths book which states the following: how many ball bearings of diameter 2.5 cm. can you get by melting a solid metalic cone of radi. 20cm and a Hight of 5 meters? how do i do this please tell me even the minute things like cancellatoins and where to use = , ; or any such thing because Im a bit weak in maths
Answered by Harley Weston.
The amount of concrete in a football stand 2009-01-30
From jacques:
A football stand 150 yd long has 20 tiers of seats; each tier has a rise of 2ft and tread of 3ft.Its construction of reinforced concrete with a cross section as shown. Find the amount of the material used in its construction.
Answered by Penny Nom.
A football field covered in garbage 2008-10-17
From AMie:
a small city produces 500,000 cubic ft of garbage per week. If all of this garbage were stacked neatly (in a nice vertical pile) on a 100-yard by 60-yard football field, how high would the pile be (in feet)?
Answered by Penny Nom.
Balls and cubes in an urn 2008-09-09
From Dave:
In an urn, there are 80 objects of two kinds: cubes (C) and balls (B). An object can be either red (R) or green (G). Note that all the four combinations are possible and that the number of cubes is not necessarily equal to the number of balls. Similarly, the number of red objects is not necessarily equal to the number of green objects. Someone tells us that in the urn there are 20 red cubes, 50 balls, and 30 red objects. An object is randomly selected from the urn.
(a). What is the probability that a green ball is selected?
(b). If we know that a cube has been selected, what is the probability that it's red?
(c). If we know that a red object has been selected, what is the probability that it's a cube?

Answered by Harley Weston.
The path of a baseball 2008-06-04
From Tom:
How high would a batter have to hit a ball to clear the stadium roof in right field if the distance to the right field fence is 320 feet from home plate? Is this solvable?
Answered by Janice Cotcher.
Parametric equations 2008-03-05
From kumi:
I have made a picture of a football pass 45 degrees with 30yds and height of 7ft and 4ft. But I am just stuck there. I have stared at the worksheet for soo long. I have no idea how to solve this, and I don't even know where this is going (I don't understand how parametric equations work). Can you help me with this problem?

1.The quarterback of a football team releases a pass at a height, h, of 7ft above the playing field, and the football is caught by a reciever at a height of 4ft, 30yds directly downfield. The pass is released at an angle of 45 degrees with the horizontal with an initial velocity of vo. The parametric equations for the position of the football at time t are given, in general, by x(t)=(vo cosθ)t and y=h+(vo sinθ)t-16t^2.

a. find the initial velocity of the football when it is released
b. write the specific set of parametric equations for the path of the football
c.use a graphing calculator to graph the path of the football and approximate its maximum height
d. find the time the reciever has to position himself after the quarterback releases the football

Answered by Harley Weston.
Ball bearings in an oil can 2007-12-03
From Lisa:
One hundred ball bearings with radius 5 mm are dropped into a cylindrical can, which is half full of oil. The height of the cylinder is 20 cm and the radius is 8 cm. By how much does the level of the oil rise?
Answered by Stephen La Rocque.
The volume of a soccer ball 2007-11-25
From Ria:
A student of me is working on a paper about soccer and math/physics. He wants to calculate the volume of the ball, which is composed of 5- and 6-sided pyramids. We are looking after a formula to express the volume of these pyramids in function of the radius of the ball (and if possible how we can derive this formula). Afterwards we'll try to calculate the difference with the volume of a sphere with radius r.
Answered by Stephen La Rocque.
A wiffleball field 2007-10-31
From Svitlana:
The Adam's family has set up a wiffleball field in their backyard. The bases are arranged like a typical baseball diamond, where the distance between consecutive bases is the same. First base is opposite of third base, and second base is opposite of home plate. The distance between consecutive bases is 50 feet. Now, the pitcher stands 25 feet from home plate and lies on the line between home plate and second base. How far is the pitcher from first base? Round your answer down to the nearest inch.
Answered by Penny Nom.
Angle of depression to a football 2007-08-15
From Tosin:
The angle of depression to a football from the top of building 10m high is 17 degrees. Find the distance of the ball from the foot of the building.
Answered by Stephen La Rocque.
A football stand 2007-07-19
From jean:
a football stand 150 yd. long has 20 tiers of seats; each has a rise of 2 ft. and tread of 3 ft. it constructed of reinforced concrete with a cross section of 36*54. find the amount of material used in its construction.
Answered by Harley Weston.
Projectile motion equations 2007-06-12
From Dillon:
Ron throws a ball straight up with an initial speed of 60 feet per second from a height of 5 feet. Find parametric equations that describe the motion of the ball as a function of time. How long is the ball in the air? When is the ball at its maximum height? What is the maximum height of the ball?
Answered by Stephen La Rocque.
Kicking a field goal 2007-03-13
From san:
A football player attempts a field goal by kicking the football. The ball follows the path modelled by the equation h= -4.9^2+10t+3, where h is the height of the ball above the ground in metres, and t is the time since the ball was kicked in seconds. *the ball must clear the uprights for the field goal to count. The uprights are approximately 5 m high. How long does the ball stay above 5 m in height?
Answered by Penny Nom.
As many player combinations as possible 2007-01-18
From Ken:
I coach a 5th grade basketball team with 12 players. I'd like to come up with a way to get as many player combinations as possible with two teams of 6 so that the makeup of the teams is different each time. An example would be: Players 1-6 on one team and players 7-12 on the other. Then I could have 1,3,5,7,9,11 on one team and the evens on the other. Then 1,2,6,7,9,10 on one team and the rest on the other. Can you help set something like this up?
Answered by Chris Fisher.
A melting snowball 2006-11-06
From Jay:
A snowball melts at a rate proportional to its surface area. Show that its radius shrinks at a constant rate. If it melts to 8/27 of its original volume in 20 minutes, how long will it take to melt completely? Please I need your help.
Answered by Stephen La Rocque.
The radius of a soccor ball 2006-05-05
From Jacqui:
A soccer ball is made up of hexagons and pentagons with the same side lengths. A manufacturer wants to produce a ball of certain diameter. The questions that follows is what side length for the polygons will produce a ball of certain diameter.
Answered by Chris Fisher.
Volume of a tennis ball can 2006-04-16
From Jon:
Tennis balls are generally packaged in circular cylinders that hold 3 balls each. The diameter of a tennis ball is 6.5 cm. Find the volume of a can of tennis balls.
Answered by Stephen La Rocque.
Balls in a cylinder 2006-03-03
From Roxanne:
If a cylindrical can holds three balls with no room to spare, explain how to find the volume of the air that surrounds the balls in the can. Yet the balls have a diameter of six inches
Answered by Stephen La Rocque.
Twelve golf balls 2005-12-28
From Todd:
You have 12 golf balls and 11 of them are the exact same weight, but one of them is either a little heavier or a little lighter. You only have three attempts to weigh the balls. How can you determine which ball weighs more/less than the rest?
Answered by Penny Nom.
Skeeball 2005-12-21
From Jenny:
Kira and Dajuan decided to have a Skeeball contest. They each played one game to see who would get the highest score. A description of their contest follows:
Answered by Denis Hanson.
I want to place four sticks equal distance apart into a tennis ball. 2005-12-13
From Bev:
I want to place four sticks equal distance apart into a 3 inch tennis ball. The circumference of the ball is 9 inches. Where should I place the sticks and how many inches apart.
Answered by Chris Fisher.
What shape do I say a football is? 2005-11-14
From Peter:
I am a 43 year old man. I am no longer in school, I have a bachelors degree. I like to tell stories about sports in ways to make people think about the amount of time they devote to the sports. For example, while attending a church in Chicago on the north side, I would pass by Wrigley field. I began to call it the church of the flying orb or sphere. Now if I want to tell a similar story about football (not soccer), what shape do I say a football is?
Answered by Chris Fisher.
My fantasy football league 2005-08-16
From Jim:
I have to make a schedule for my fantasy football league. There are 10 teams in the league and we play a 13 week season. The challenge is we want to play each team only once during the first 10 weeks. This way no team will play another team twice without having played each team at least once. Is this possible?
Answered by Penny Nom.
The volume of a sphere 2004-11-30
From Lyndsay:
twenty cubic metres of air are pumped into a spherical hot air balloon with each given diameter: 1.0m; 2.0m; 3.0m; 4.0m; 5.0m;6.0m
a)calculate the new diameter, new suface area, and new volume of each balloon.

Answered by Penny Nom.
Tennis balls and probability 2004-11-01
From Jeremy:
I have a hopper of tennis balls that contains 25 new tennis balls and 10 old tennis balls. In the hopper the tennis balls are mixed up randomly. If i take one ball out of the hopper and hit it and then put it back and then take another ball out of the hopper and hit it and put it back, what is the probability that i hit two new tennis balls? Also a tennis ball becomes old after being hit just once.
Answered by Penny Nom.
The combined force of two vectors 2004-10-30
From Brian:
Two teams are playing push ball with a large 8 foot diameter ball. One team exerts a force represented by the vector a = 2i + -5j, and the other team exerts a force represented by the vector b = -8i-3j.

1.Determine the direction of movement of the ball if the i axis is due east.

2.Determine the combined force magnitude.

Answered by Harley Weston.
Forty balls are placed in a bag 2004-06-19
From Sheila:
Forty balls numbered 1-10 are placed in a bag and four are drawn at random. What is the probability that the first ball drawn is between 1-10 (inclusive) the second is between 11-20, the third is between 21-30 and the last is between 31-40?
Answered by Penny Nom.
Related rates and baseball 2004-04-26
From Bethany:
A baseball diamond is the shape of a square with sides 90 feet long. A player running from second to third base at a speed of 28 feet/ second is 30 feet from second base. At what rate is the player's distance from home plate changing?
Answered by Penny Nom.
Baseball games 2004-03-14
From Fabian:
Let's say I have 12 different Baseball games. There is one of only 2 possible outcomes for each of the 12 games. How would I fugure out how many combinations there are for the 12 games and for 11,10, and so fourth.
Answered by Penny Nom.
Selecting balls from a golf bag 2004-02-21
From A student:
There are 5 white and 5 yellow balls in a golf bag. Two are selected randomly, and simultaneously. What is the probability that the first one or the second one will be white?
Answered by Penny Nom.
Twelve acres 2004-01-13
From Heather:
I am looking at buying a property that includes 12 Acres of land and I am trying to visualize what this size is equivalent to. I have searched your site and figured out how many square feet it is but I was hoping that you could apply 12 Acres to something tangible, like a football field!
Answered by Penny Nom.
A snowball melts 2003-12-11
From Adam:
A spherical snowball has diameter 10cm and density 0.75g/cm3. It is placed in a cylindrical can with diameer 12cm. After the snow melts it turns to water with density 1.0g/cm3. What will be the depth of the water in the can (to 1 decimal place)?
Answered by Penny Nom.
The cross-section of a football field 2003-05-25
From Francis:
Have you ever walked on a football field covered with artificial turf? If so, you probably noticed that the field is not flat. The profile of the surface is arched and highest in the centre, permitting rainwater to drain away quickly.

height from base to highest point- 45.75 centimetres distance of the field- 50 metres

a) The diagram shows the profile of an actual field, viewed from the end of the field. Assuming that the cross-section is a parabola, find the algebraic model that describes this shape.

b) Use your equation to determine the distance from the sidelines where the field surface is 20 cm above the base line.

Answered by Harley Weston.
How many hits? 2003-04-06
From Jack:

My name is Jack. I'm a uncle. Student is in the 5th grade email is above.

If a baseball player at sping training had a good season with the following:

one seventh of his hits were doubles.
12.5% of his hits were home runs.
But didn't have any triples.
How many hits did he have?

Can you give me an explanation of you solved the problem.

Answered by Penny Nom.
Distributing r identical balls into n distinct boxes 2003-03-16
From Diana:
How many ways to distribute r identical balls into n distinct boxes with exactly m boxes empty?
Answered by Penny Nom.
A bouncing ball 2002-12-14
From Eman:

Q : When a childís ball is dropped from a height h metres on to a hard, flat floor, it rebounds to a height of 3/5h metres. The ball is dropped initially from a height of 1.2m.

  1. Find the maximum height to which the ball rises after two bounces.
  2. Find the total distance that the ball has traveled when it hits the floor for the tenth time.
  3. Assuming that the ball continues to bounce in the same way indefinitely, find the total distance that the ball travels.

Answered by Penny Nom.
Jimmy's hits 2002-10-27
From Patty:
One seventh of Jimmy's hits were doubles
12.5% of his hits were homeruns
Jimmy had 82 singles
He did not have any triples

How many hits did Jimmy have? (Be sure to include the equation that represents the number of hits)

Answered by Penny Nom.
Baseball, basketball and football 2002-10-08
From Debbie:
The school newspaper is interviewing 6th grade students to see what sports they follow regularly on TV. Of the 70 students interviewed; 40 enjoyed basketball; 40 enjoyed baseball; 40 enjoyed football; 20 enjoyed basketball and football; 22 enjoyed baseball and basketball; 27 enjoyed football and baseball; and 12 enjoyed all three sports. How many students out of the 70 interviewed didn't follow any one of the three sports?
Answered by Leeanne Boehm, Penny Nom and Walter Whiteley.
A schedule for a fantasy football league 2002-09-01
From Steve:
i am in a ten(10) team league, split evenly into two five team divisions. we play a thirteen(13) game schedule and would like to play each team in your own division twice, and each team in the other division once. according to my rudimentary mathematics that equals 13 games. a good schedule should look somthing like this: team 1-5 = division 1 team 6-10 = division 2 team 1 should play teams 2-5 twice and teams 6-10 once.
Answered by Claude Tardif.
Designing a ballot 2002-04-26
From Kelley:
I want to design a ballot for four elections. Actually all the candidate races are on 1 ballot. I need to know how many different ballot styles would be needed for all of the candidates to be in each rotation an equal number of times.

For example:

  • A,B,C & D are running for mayor

  • E,F,G & H are running for congress

  • I,J & K are running for senate

  • L,M & N are running for governor

They are all on the same ballot. But in each race their name (for instance A) has to be in the #1 rotation, #2 rotation, #3 rotation, and #4 rotation for his race on this ballot an equal number of times as B,C and D.

The same goes for the other candidates for their perspective races.

How many total ballot styles will there be?

Answered by Penny Nom.
Baseball and sit ups 2002-01-31
From A student:
A baseball team won 8 more games than it lost. If it played 56 games, how many games did it win?

On the first day of practice, Paul did 3 sit ups. On the second day he did 5, and on the the third day he did 8, and on the fourth day he did 12. If this pattern continued, how many sit-ups did ihe do on the sixth day of practice?

Answered by Penny Nom.
Manufactures golf balls 2001-11-06
From Kevin:
A company manufactures golf balls. Golf balls are each numbered consecutively 0 to 4, and then the numbering starts over with zero again. Every 12th golf ball is yellow. Every 8th golf ball is tested for defects. The company produces 120,000 golf balls in an eight-hour shift.

A. How many yellow golf balls are tested for defects during the day? Explain your reasoning.

B. How many of these yellow balls that are tested are imprinted with the numeral 2? Explain your reasoning.

Answered by Penny Nom.
The best of 7 2001-09-08
From Michelle:
Professional basketball, hockey, and baseball championships are decided on the best 4 out of 7 games. The first team to win four games wins the championship. In how many possible ways could the team win the championship series after winning the first game?

Game   1    2    3    4    5     6     7         
Result W    L    L    W    W     W 

Answered by Leeanne Boehm.
Buckets of golf balls 2001-02-08
From A student:
A bucket containing 40 golf balls weighs 135 ounces. The same bucket with 20 golf balls weighs 75 ounces. What is the weight of the bucket?
Answered by Claude Tardif.
The path of a cannonball 2001-01-15
From A student:
Artillerymen on a hillside are trying to hit a target behind a mountain on the other side of a river. Their cannon is at (x, y) = (3, 250) where x is in kilometers and y is in meters. The target is at (x, y) = (-2, 50). In order to avoid hitting the mountain on the other side of the river, the projectile from the cannon must go through the point (x, y) = (-1, 410).

Write the equation for the problem.

Answered by Penny Nom.
Lobbing a tennis ball 2000-10-31
From Alex:
If a tennis ball is lobbed into the air with an initial upward velocity of 12 meters per second, its velocity and height will be functions of time in flight described by the following rules:

V=12-9.8T and H=1+12T-4.9T 2

Find the maximum height of the tennis ball and the time it takes to reach that height.

Answered by Penny Nom.
The perimeter of a football field 2000-10-18
From Paige:
The width of a football field is 67ft greater than the length. The perimeter is 480ft What is the width and length?
Answered by Penny Nom.
Play ball 2000-02-03
From Jessie:
Here's a calc question that is probably a lot easier than I am making it. If you have a legendary "baseball problem" for the related rates section of Calc I, and you are given that the runner is running from 2nd to 3rd base at a given rate, and the umpire is standing at home plate, and you are given the distance between the bases on the field, how do you find the rate of change of the angle between the third base line (from the point of the umpire) and the runner? Here is a sample prob: Runner is moving from 2nd to 3rd base at a rate of 24 feet per second. Distance between the bases is 90 feet. What is the rate of change for the angle (theta, as described previously) when the runner is 30 feet from 3rd base?
Answered by Harley Weston.
.400 in Baseball 1999-12-15
From Nieve Nielson:
I have several questions to ask about the probability of getting a .400 in baseball:
  1. What is the probability of a baseball player hitting a .400 in one game, considering that the hitter is up to bat four times?

  2. What is the probability of a baseball player hitting a .400 in a season, considering that there are 100 games in a season? With the first two questions in mind:

  3. Considering that baseball has been around for about 100 years, about how many people should hit .400 inthat time?

Answered by Chris Fisher.
Selecting some players 1999-11-20
From Korbin Brown:
Roger Craig, during his term as team manager of the San Francisco Giants, received a strange communication from the team general manager, Al Rosen. Mr. Rosen told him to select 25 players according to this formula: 1/2 of the team had to be outfielders and infielders 1/4 of the team had to be starting pitchers 1/6 of the team had to be relief pitchers 1/8 of the team had to be catchers Roger was a bit confused by Al's request, yet complied anyway. How did he do it?
Answered by Claude Tardif.
Cannonballs 1999-01-27
From Roger King:
How many cannonballs can be stacked in a triangular pyramid?
Answered by Penny Nom.



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