9367 14, 24, 31, 43
Posted: Fri Oct 17, 2008 8:48 pm
So I just took the 9367 today and had questions on 4 problems.
14. At a 15 percent annual inflation rate, the value of the dollar would decrease by approximately one-half every 5 years. At this inflation rate, in approximately how many years would the dollar be worth 1/1,000,000 of its present value?
A) 25
B) 50
C) 75
D) 100
E) 125
Answer (D)
So, I put D down when taking this but the way I got the answer was a little less then desired. I approximated log_2(100) ~ 20 which took me awhile. I was wondering how you guys did this. I remember there being a function to tell you this answer but I forget the exact expression.
24. If A and B are events in proabability space such that 0 < P(A) = P(B) = P(A Intersect B) < 1, which of the following CANNOT be true?
A) A and B are independent.
B) A is a proper subset of B.
C) A != B
D) A intersect B = A union B
E) P(A)P(B) < P(A Intersect B)
Answer (A)
I got this wrong, I have never taken a class dealing with proabability spaces so I may just not have enough tools at my disposale. But if anyone could explain this to me I would appreciate it.
31. If
f(x) =
Root( 1 - x^2) for 0</= x </=1
x-1 for 1 < x </= 2
then the Integral from 0 to 2 of f(x) dx is?
A) pi/2
B) Root(2)/2
C) 1/2 + pi/4
D) 1/2 + pi/2
E) Undefined
So, I started by spliting the integral from 0 to 1 and then 1 to 2. My problem is that I was unsure how to integrate Root(1-x^2) I used integration by parts with little to no help.
43. Let n be an integer greater than 1. Which of the following conditions guarantee that the equation x^n = Sum from i=0 to n-1 of a_i x^i has at least one root int he interval (0,1)?
I. a_0 > 0 and Sum i=0 to n-1 of a_i < 1
II. a_0 > 0 and Sum i=0 to n-1 of a_i > 1
III. a_0 < 0 and Sum i=0 to n-1 of a_i > 1
A) None
B) I Only
C) II Only
D) III Only
E) I and III
Answer (E)
So, I was sure that this problem had to do with the two expressions
Sum of the roots = (-1)^n * -a_(n-1)
Product of the roots = a_0
But I'm unsure how their conditions imply the root is between 0 and 1.
14. At a 15 percent annual inflation rate, the value of the dollar would decrease by approximately one-half every 5 years. At this inflation rate, in approximately how many years would the dollar be worth 1/1,000,000 of its present value?
A) 25
B) 50
C) 75
D) 100
E) 125
Answer (D)
So, I put D down when taking this but the way I got the answer was a little less then desired. I approximated log_2(100) ~ 20 which took me awhile. I was wondering how you guys did this. I remember there being a function to tell you this answer but I forget the exact expression.
24. If A and B are events in proabability space such that 0 < P(A) = P(B) = P(A Intersect B) < 1, which of the following CANNOT be true?
A) A and B are independent.
B) A is a proper subset of B.
C) A != B
D) A intersect B = A union B
E) P(A)P(B) < P(A Intersect B)
Answer (A)
I got this wrong, I have never taken a class dealing with proabability spaces so I may just not have enough tools at my disposale. But if anyone could explain this to me I would appreciate it.
31. If
f(x) =
Root( 1 - x^2) for 0</= x </=1
x-1 for 1 < x </= 2
then the Integral from 0 to 2 of f(x) dx is?
A) pi/2
B) Root(2)/2
C) 1/2 + pi/4
D) 1/2 + pi/2
E) Undefined
So, I started by spliting the integral from 0 to 1 and then 1 to 2. My problem is that I was unsure how to integrate Root(1-x^2) I used integration by parts with little to no help.
43. Let n be an integer greater than 1. Which of the following conditions guarantee that the equation x^n = Sum from i=0 to n-1 of a_i x^i has at least one root int he interval (0,1)?
I. a_0 > 0 and Sum i=0 to n-1 of a_i < 1
II. a_0 > 0 and Sum i=0 to n-1 of a_i > 1
III. a_0 < 0 and Sum i=0 to n-1 of a_i > 1
A) None
B) I Only
C) II Only
D) III Only
E) I and III
Answer (E)
So, I was sure that this problem had to do with the two expressions
Sum of the roots = (-1)^n * -a_(n-1)
Product of the roots = a_0
But I'm unsure how their conditions imply the root is between 0 and 1.