Solved Word Problem on Standard Deviation

Topic : Standard Deviation

Question : The average amount customers at a certain grocery store spend yearly is $636.55. Assume the variable is normally distributed. If the standard deviation is $89.46, find the probability that a randomly selected customer spends between $550.67 and $836.94.

Solution :

A Simple Integration Problem

Topic : Integration

Problem : Integrate x Cos x dx

Solution :

Order of Differential Equation with Example

Topic : Differential Equation
Question : State the Order of Differential Equation with Example.
Solution :
The order of the heighest order derivative occuring in a differential equation is called Order of the Differential Equation.
Example :
1) dy/dx +Cos x = 0
2) d²y/dx² = e^x

Question to Solve for x

Topic : Relation with identities

Question : Solve the expression
(x-1)/(4 + 2x) greater than or equal to (2x-1)/(3 +2)

Solution :
(x-1)/(4 + 2x) greater than or equal to (2x-1)/(3 +2)
(x-1+8x)/4 greater than or equal to (2x-1+6)/3
(9x-1) / 4 greater than or equal to (2x+5)/3
27x-3 greater than or equal to 8x +20
27x-8x greater than or equal to 20+3
19x greater than or equal to 23
x greater than or equal to 23/19

Question on Slope Intercept Form

Topic : Slope Intercept Form

Question : Find the slope of 4x+3y = 6.

Solution :
Slope intercept form of an equation is y = mx +b,
Where ‘m’ is the slope and ‘b’ is the y intercept.
To find the slope of the given equation, it should be in the standard form...
Implies 3y = -4x+6
Dividing by 3 on both sides we get:
3y = -4x + 6
3 3 3
.. y = -4x/3 + 2.
Comparing the above equation with standard form
Slope m = -4/3 and b = 2.

Problem to Solve Simultaneous Equation

Topic : Simultaneous Equation

Question : Solve for x and y,
8x - 3cy = 9c
12x - 7cy = - 39c

Solution :
8x - 3cy = 9c------- (1)
12x - 7cy = - 39c----(2)
Multiply equation (1) by 3 and (2) by 2
24x - 9cy = 27c
24x -14cy = -78c
-------------------
00 + 5cy = +105c (divide both sides by 5c)
So y = 21

Substituting the Value of y in equation (1)
8x - 3c(21) = 9c
8x-63c = 9c (adding +63c on both sides)
8x = 72c
x = 9c