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MATH 495
Problem Set 2
1.
Fifty middle school students were given an
assignment to complete. The graph to the
right shows the frequency distribution of the
number of days it took to complete the
assignment. What is the mean number of
days it took a student to complete the
assignment?
2.
Find the equations of the lines that pass through the point (1,3) and are tangent to the circle with
equation 𝑥 2 + 𝑦 2 = 2.
3.
If tan x 
4.
The circle in the figure to the right is centered at the origin and has
radius 3. How many points with integral coordinates lie inside or
on the boundary of the circular region?
2
3
and   x 
, then find the exact value for cos x .
3
2
-3
3
5.
A continuous random variable X has mean 60.0 and standard deviation 8. What value does the random
variable 2.5 standard deviations above the mean have?
6.
In a league that has 6 teams, every team plays every of the other team twice in a season. What is the total
number of games played in a season?
7.
8.
If f x  4 x , g x   x 2  1 and hx   1x , for what values of x is h f g x  
A rabbit is hopping around in a fenced-off flat
rectangular field with dimensions as shown to the
right. If the position of the rabbit is uniformly
random throughout the field, what is the
probability it is 10 feet or more away from the
fence at any given time?
1
?
4
40 ft.
50 ft.
9.
 x
 x
If A is a 22 matrix and A    3   for all real x and y, then find A.
 y
 y
10.
11.
What is printed out in STEP 4 when the
program to the right is executed?
STEP 1:
X = 100, Y = 10
STEP 2:
If ((X > 100) or (X < 20))
then X ← (X + 1)
else X ← (X - 1)
STEP 3:
If ((X > Y) and (Y < 10))
then X ← (X + Y)
else X ← (X - Y)
STEP 4:
Print the value of X
In the circle to the right with center O, what is the
degree measure of ∡𝐴𝐵𝐶 ?
A
O
34°
B
C
12.
In the figure to the right, ABC is a right
triangle with right angle at B. BD is
perpendicular to AC . If CD  9 and AD  3 ,
then find the exact value of BC  AB  BD .
A
D
B
C
13.
14.
15.
if n  1
 1
A sequence is defined recursively by a n  
. Find a closed form representation of the
a n1  n if n  1
sequence.
If f x   x 5  7 x 3  6 x 2  2 x  17 , for how many values of x is the derivative of f x  equal to zero?
A glass window is composed of a rectangle that is h feet
long by d feet wide and a semicircle with diameter d, as
shown in the figure to the right. If the area of the
1
semicircular region is of the total area of the window,
3
what is the ratio of h to d?
d
h