Question to Draw Box Plot for a Collection of Data

Topic : Box Plot

Question : In a survey of the cafeteria food at Metropiolis Middle School, 50 students were asked to rate how well they liked the lunches on a scale of 1 to 10, with 1 being the lowest rating and 10 being the highest rating. The box plot was made from the collected data.
What percent of the students in the sample rated the cafeteria food between 5.75 and 9

Solution :








First Quartile = Q1 = 5.75
That is 25% of students lie between 3 and 5.75
Second Quartile = Q2 = 6.5
That is 50% of students lie between 3 and 6.5
Third Quartile = Q3 = 8
That is 75% of the students lie between 3 and 8
100% of students lie between 3 and 9
So the % of students who lie between 5.75 and 9 = 100% - 25% = 75%
and Answer is 75%

Question on Finding the area of a Field

Topic : Area of Rectangle

Question : A farmer wants to use 1000 meters of fencing to enclose 3 sides of a rectangular field. What dimensions should be used to maximize the area of the field, and what is the maximum area of the field?

Solution :

Equation of Circle Passing Through Point (-1,-9)

Topic : Equation of Circle

Question : Write the Standard from of the equation of the circle that passes through the given point (-1,-9) and whose center is the origin.

Solution :
The Standard equation of the circle with center at origin (0,0) is x² + y² = r²
r being its radius as x² + y² = r² passes through (-1,-9) we have
(-1)² + (-9)² = r²
or
r² = 1 + 81 = 82
So the required circle is x² + y² = 82

Problem on Simultaneous Equation

Topic : Simultaneous Equation

Question : Solve and find the value of x and z
x + z = 22
x +6z = 50

Solution :
x + z = 22---------------(1)
x +6z = 50--------------(2)

Subtracting second equation from first equation
we get, -5z = -28
divide both sides by -5
So z = 5.6

Substitute the value of z in equation (1)
x+5.6 = 22
x=22-5.6
x= 16.4

So the value of x = 16.4 and z = 5.6

Problem on Square Roots

Topic : Square Roots

Question : Solve:
(x – 2)^2 = 4

Solution :
Taking square roots on both the sides, we get
(x – 2) = ± rad(4)
Case (i)
x – 2 = 2
Add 2 on both the sides of the equation
x – 2 + 2 = 2 + 2
x = 4
Case (ii)
x – 2 = -2
Add 2 on both the sides of the equation
x – 2 + 2 = -2 + 2
x = 0
The solutions are x = 0, 4

Question on Calculating the Value of a Property

Topic : Value of a Property

Question : John left 1/3 of his property to his son, ¼ to his daughter and remaining to his wife. If the wife’s share was $40,000. Find the total value of his property.
Solution : Let Total value of property = $ Y
Son’s share = Y x 1/3 = $ Y/3 (1/3 of the property)
Daughter’s share = Yx1/4 =$ Y/4 (1/4 of the property)
Property left for son and daughter = Y/3 + Y/4
= (4Y+3Y)/ 12 (by LCM)
= 7Y/12
Hence Remaining part of property = Y – 7Y/12 (Subtracting son’s & daughter’s
Share from total property)
= (12Y-7Y)/12
= 5Y/12
This remaining was given to wife. According to given information
Wife’s share = $40,000
5Y/12 = 40,000
Y = 40000 x 12/5 = $ 96000
Hence Total value of property= $96000

A Question From Probability

Topic : Probability Word Problem

Question : In transmitting dot and dash signals, a communication system changes ¼ of the dots to dashes and 1/3 of the dashes to dots. If 40% of the signals transmitted are dots and 60% are dashes, what is the probability that a dot received was actually a transmitted dot?

Solution :
[a]Dot Signals transmitted = 40%
[b]Dash signals transmitted = 60%
Let A be the event of receiving a dot.
And B the event of a transmitted dot received as dot.
So the required probability P(BA). = P(A and B)/P(A).
P(A) = 3/4 X 0.40 + 1/3 X 0.60 = 0.30 + 0.20 = 0.50
P(A and B) = 3/4 X 0.40 = 0.30
So the required Probability = P(BA) = 0.30/0.50 = 3/5.