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psbhowmick answered: 529 problems
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sets-and-operations/627583: QUESTION TIME!~
in a class of 40 students, 17 have ridden an airplane 28 have ridden a boat 10 have ridden a train 12 have ridden both airplane and a boat 3 have ridden a train only 4 have ridden an airplane only
some students in the class have not ridden any of the modes of transportation. QUESTION: how many students have taken all three transportation?
1 solutions
Answer 395001 by psbhowmick(529)   on 2012-07-11 11:48:58 (Show Source):
You can put this solution on YOUR website!Let the no. of students who have ridden airplane be A, the no. of students who have ridden boat be B and that who have ridden train be C.
Further, let the no. of students who have ridden only airplane be A', the no. of students who have ridden only boat be B' and that who have ridden only train be C'.
If the total number of students be N then we have
N = A' + B' + C' + A∩B + B∩C + C∩A + A∩B∩C ________ (1)
Also, we know
A' = A - A∩B - C∩A ________ (2)
B' = B - A∩B - B∩C ________ (3)
C' = C - B∩C - C∩A ________ (4)
Substituting in the equation (1) we have
N = A + B + C - A∩B - B∩C - C∩A + A∩B∩C __________ (5)
Now let us list all the values that we have:
N = 40, A = 17, B = 28, C = 10, A∩B = 12, C' = 3, A' = 4
Substituting all these values into equation (5)
40 = 17 + 28 + 10 - 12 - (B∩C + C∩A) + A∩B∩C
40 = 17 + 28 + 10 - 12 - (C - C') + A∩B∩C [Using equation (4)]
40 = 17 + 28 + 10 - 12 - (10 - 3) + A∩B∩C
A∩B∩C = 4
Answer: The no. of students who have ridden all modes of transportation is 4.
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Permutations/627330: How many committes of 4 can be formed from 20 Republicans and 15 Democrats if at least 1 Republican and at least 1 Democrat must be on the committee?
1 solutions
Answer 394882 by psbhowmick(529) on 2012-07-10 14:45:01 (Show Source):
You can put this solution on YOUR website!Combinations possible in the committee
a) 1 Republican + 3 Democrats: 20C1 x 15C3 = 20 x (13x14x15)/(2x3) = 9100
b) 2 Republican + 2 Democrats: 20C2 x 15C2 = (19x20)/2 x (14x15)/2 = 19950
c) 3 Republican + 1 Democrats: 20C3 x 15C1 = (18x19x20)/(2x3) x 15 = 17100
Total number of such committees possible is: a + b + c = 46150.
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Volume/627292: Hi, How many layers of balls 22cm diameter i can fit in 6 feet square base pyramid. I know how to calculate number of balls in each layer i just need to calculate number of layers.
1 solutions
Answer 394840 by psbhowmick(529) on 2012-07-10 13:06:47 (Show Source):
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Equations/627061: Need help solving a word problem with drawing a diagram and a table.
Olimpiada Ivanova, a world-record holding race-walker, is on one end of a 6-mile track. John Doe, an average walker, is on the other end of the track. The two start walking towards each other and meet in 1/2 hour. If Olimpiada's average speed exceeds John's by 6 mph, find the speed of both walkers.
represent your unknown: ?
S=Speed for both walkers
J+6=Olympiada's average speed
draw diagram:
fill out a table:
solve equation:
check:
1 solutions
Answer 394640 by psbhowmick(529) on 2012-07-09 16:11:39 (Show Source):
You can put this solution on YOUR website!Solve it like this. The way you were proceeding is incorrect as the average speed of both are NOT the same.
Let the average speed of Olimpiada be x mph.
Then, Joe's average speed is (x-6) mph.
Hence, the distance covered by Olimpiada in 0.5 hr = x/2 miles, and
the distance covered by John in 0.5 hr = (x-6)/2 miles.
Each were at the extreme end of the 6 mile long track and they meet each other in 0.5 hr.
The sum of the distance travelled by them when they met each other is 6 miles.
Thus, Olimpiada's average speed is 9 mph whereas John's average speed is 3 mph.
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Quadratic-relations-and-conic-sections/626969: Suppose you are an event coordinator for a large performance theater. One of the hottest new Broadway musicals has started to tour and your city is the first stop on the tour. You need to supply information about projected ticket sales to the box office manager. The box office manager uses this information to anticipate staffing needs until the tickets sell out. You provide the manager with a quadratic equation that models the expected number of ticket sales for each day x. ( is the day tickets go on sale).
- 0.4x2 + 13x + 14
a. Does the graph of this equation open up or down? How did you determine this?
down because the coefficient of the highest power term is negative.
b. Describe what happens to the tickets sales as time passes.
Number of ticket sales goes down to zero
c. Use the quadratic equation to determine the last day that tickets will be sold.
Note. Write your answer in terms of the number of days after ticket sales begin.
d. Will tickets peak or be at a low during the middle of the sale? How do you know?
Peak; the parabola has a maximum point.
e. After how many days will the peak or low occur?
30th day
f. How many tickets will be sold on the day when the peak or low occurs?
g. What is the point of the vertex? How does this number relate to your answers in parts e. and f?
h. How many solutions are there to the equation? - 0.4x2 + 13x + 14. How do you know?
2 because it is a quadratic.
i. What do the solutions represent? Is there a solution that does not make sense? If so, in what ways does the solution not make sense?
1 solutions
Answer 394601 by psbhowmick(529) on 2012-07-09 14:06:00 (Show Source):
You can put this solution on YOUR website!This is a very long question I will now answer only the first part.
a. The equation of the parabola is  .
Reorganizing the equation
As the coefficient of  is negative so the parabola is facing downwards.
You can verify this from the graph below.
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Matrices-and-determiminant/626890: Find the given element of the matrix product C = AB.
A=
[3,1,-4,0]
[2,-5,0,4]
[-4,5,4,1]
B=
[5,-4,2]
[5,5,0]
[-3,0,3]
[0,-1,2]
C23=
1 solutions
Answer 394555 by psbhowmick(529) on 2012-07-09 08:51:20 (Show Source):
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Linear-equations/626955: Graph a line that passes through the point (–5, 2) and has a slope of (–3/4). What is the ordered pair of a second point you could use to graph the line?
1 solutions
Answer 394544 by psbhowmick(529) on 2012-07-09 08:23:52 (Show Source):
You can put this solution on YOUR website!The equation of the line is  i.e.  .
For x = 3, y = -4. Hence another ordered pair through which this straight line passes is (3, -4).
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Angles/626941: the measure of an angle is 30 degree more than twice the measure of its supplement. Find the measures of the angles.
1 solutions
Answer 394539 by psbhowmick(529) on 2012-07-09 08:10:31 (Show Source):
You can put this solution on YOUR website!Let the angle be X degree.
Then its supplement is (180-X) degree.
Given that, Angle - 2 x Supplement = 30.
X - 2(180 - X) = 30
X - 360 + 2X = 30
3X = 30 + 360 = 390
X = 390/3 = 130
Hence, the angles are 130 and 50 degrees.
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Probability-and-statistics/626952: What is the probability of rolling a 2, 4 or 8 on a single roll of 2 die?
What is the probability of not rolling any of the numbers above on a single roll.
Hint: ( Use compliment rule).
1 solutions
Answer 394535 by psbhowmick(529) on 2012-07-09 08:00:31 (Show Source):
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Rectangles/626939: 1. )Find the length of the diagonal of a rectangle whose sides are 24 cm and 35 cm.
2.) Solve for the area of a square whose diagonal is 16 √2 cm long.
3. What is the area of a right triangle if the hypotenuse is 35 cm and the shorter leg is 21 cm.
1 solutions
Answer 394529 by psbhowmick(529) on 2012-07-09 07:40:31 (Show Source):
You can put this solution on YOUR website!1)  
2) Diagonal of the square of side  is  .
If the diagonal of the square is  then  .
Hence, area of the square is   .
3) Use Pythagoras theorem again, the longer side is 28 cm.
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Angles/626942: Find the measure of x given the information in the diagram.
two angles equal 8, and the degree is 102
1 solutions
Answer 394527 by psbhowmick(529) on 2012-07-09 07:34:04 (Show Source):
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Volume/626944: A cylindrical carton has a base of 160 square feet. If the carton is 16 feet tall, what is the volume of the carton in cubic feet?
1 solutions
Answer 394526 by psbhowmick(529) on 2012-07-09 07:32:26 (Show Source):
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Volume/626935: how much liquid will fit into a container thatis 320 cubic yards capacity ?
1 solutions
Answer 394520 by psbhowmick(529) on 2012-07-09 07:06:18 (Show Source):
You can put this solution on YOUR website!Liquid takes the shape and volume of the container into which it is poured. If the capacity of the container is 320 cubic yards then that much volume of liquid can be poured into it at the most.
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Graphs/626937: (8,16) (4,0) (0,-16)
WITH THESE POINTS WHAT WOULD THE EQUATION BE FOR Y?
1 solutions
Answer 394517 by psbhowmick(529) on 2012-07-09 06:58:31 (Show Source):
You can put this solution on YOUR website!This is a straight line. Observe that the slope is constant (equal to 4). First try to write the equation for the straight line yourself, if you can't then I will help.
Cheers!!!
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Numbers_Word_Problems/626933: Find three consecutive even integers whose sum is 38 more than four times the largest integer.
1 solutions
Answer 394515 by psbhowmick(529) on 2012-07-09 06:35:17 (Show Source):
You can put this solution on YOUR website!Let the consecutive even integers be: (2n-2), 2n and (2n+2).
Their sum = 
The largest integer = 
By problem i.e. Sum - 4 x Largest Integer = 38
Thus, the three consecutive integers are: -48, -46 and -44
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Polynomials-and-rational-expressions/626899: Given:
How many total zeros does the function have?
Possible real zeros? Possible negative zeros?
1 solutions
Answer 394514 by psbhowmick(529) on 2012-07-09 06:23:12 (Show Source):
You can put this solution on YOUR website!Every polynomial in one variable of degree n, n > 0, has exactly n real or complex zeros.
Total zeroes = total no. of roots = degree of the polynomial = highest index = 5
Since the coefficients of the polynomial are real so is there has to be complex roots, that will occur in pairs - at max there can be two pairs of complex and conjugate roots. Hence, there is at least one real root.
To find max no. of negative roots, express f(x) as f(-x).
The no. of sign changes from the term with highest degree of x to that with lowest degree of x is 4. Thus max. possible no. of negative roots is 4.
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t e s t/626932: ``Carpenters A and B can complete a piece of furniture if they work together for 4 days .They can also finish the work if A works 2 days and B works 6 days.How does it take each of them to finish the furniture alone?
1 solutions
Answer 394513 by psbhowmick(529) on 2012-07-09 06:01:31 (Show Source):
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