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3) Solve the area bounded by the curve y = 4x-x and the lines x = -2 and y = 4.
2) Find the area bounded by the curve x = y² + 2y and the line x = 3.
1) Find the area bounded by the curve y-9-x and the x axis.
a) Horizontal Strip
b) Vertical Strip
The following table gives the recorded grades for 10 students on a midterm test and the final examination in a statistics course.
Student
Midterm Test
Final Examination
1
84
73
2
98
63
3
91
87
4
72
66
5
86
78
6
93
78
7
80
91
8
9
92
88
10
87
77
a. Calculate the rank correlation coefficient.
b. Test the hypothesis @ .05 level of significance.
Consider the R^2 - R function f defined by f(x,y) = (x^2 +y)/y.
Determine each of the following limits,if it exists.
a) lim (x,y) -> (0,0) f(x,y),where C1 is the curve y=x
b) lim (x,y) -> (0,0) f(x,y),Where C2 is the curve y=2x
c) lim (x,y) -> (0,0) f(x,y),Where C3 is the curve y=x^2
d) lim (x,y) -> (0,0) f(x,y)
Consider the R^2 - R function defined by f(x,y) = 3x + 2y.
Prove from first principles that lim (x,y) -> (1,-1) f(x,y) = 1
Use resolution to show the hypotheses “Allen is a bad
boy or Hillary is a good girl” and “Allen is a good boy or
David is happy” imply the conclusion “Hillary is a good
girl or David is happy.”
There is a bag filled with 5 blue and 4 red marbles.
A marble is taken at random from the bag, the colour is noted and then it is replaced.
Another marble is taken at random.
What is the probability of getting 2 reds?
The mean lifetime of the light bulbs produced by Volta Corporation is 1705 hours with a population standard deviation of 150 hours. The CEO of the company claims that a new production process has led to an increase in the mean lifetimes of the light bulbs. If Jeremy tested 130 bulbs made from the new production process and found that their mean lifetime is 1650 hours, test the hypothesis that the mean is not equal to 1705 hours using the level of significance of 0.10.
On average, an insurance company receives 6 claims between 14:00 and 16:00 on a particular day. What is the probability that the company receives exactly 17 claims between 08:00 and 16:00?
