Probability Distributions
Trignomometry
Functions
Vectors (A)
Vectors (B)
100
A random variable X has the probability distribution function P(x) described in the table. Find P(X>3).
P(X>3) = 0.05
100
What do the parameters a, b, c, and d effect in the general sine or cosine function: f(x)=a sin(b(x-c))+d ?
A is the amplitude
B effects period
C is horizontal shift
D is vertical shift
100
Determine whether each relation listed below is a function:
a. Function
b. Not a function
c. Function
d. Not a function
e. Function
f. Function
100
Find the vector vec(AB) with points A(-1, 4) and B(3,-1) .
vec(AB)= ((4),(-5))
100
Consider the vectors veca=((2),(-3)) ,. Let 2veca+vecb+vecc=0 , where 0 is the zero vector. Find vecc .
-5i+2j
200
In a game, the numbers from 1 to 20 are written on tickets and placed in a bag. Players draw out a number at random. They win $3 if the number is even, $6 if the number is square and $9 if the number is square and even. How much should be charged to play the game so that it is fair?
$2.40
200
Find the area of the triangle shown:
A = 38.7 cm2
200
Given f(x)=2x+1 and g(x)=3-4x , find both (f@g)(x) and (g@f)(x)
(f@g)(x)=7-8x
(g@f)(x)=-8x-1
200
What are the vectors i, j, and k?
The unit vectors in the x, y and z directions.
200
Find the magnitude of 3i+5j . Then find the unit vector in the same direction.
Magnitude: 5
Unit Vector: frac{3}{5}i+frac{4}{5}j
300
Alison walks to school every day. The time she takes to walk to school is modeled by the normal distribution with a mean of 36 minutes and standard deviation of 3.12 minutes. If the probability that Alison walks longer than M minutes is 0.015, find the value of M in minutes and seconds.
42 minutes, 46 seconds
300
Find the measure of angle C in the triangle shown.
C = 41.6º
300
Given f(x)=6x-5 and g(x)=x^2+x , find (g@f)(-1)
(g@f)(-1)=110
300
Find the magnitude of vector -2i+3j
sqrt13
300
Find a vector in the same direction as 3i+4j with a magnitude of 13.
frac{39}{5}i+frac{52}{5}j
400
A manufacturer finds that 18% of the items produced from its assembly lines are defective. During a floor inspection the manufacturer randomly selects 10 items with replacement. Find the probability that the manufacturer finds at least two defective items
0.561
400
Write a function that this graph represents.
f(x)=3sin(frac{π}{2}(x-0.5))+1
400
Write down the equations of the vertical asymptotes, horizontal asymptotes, and the domain and range of the function g(x)=frac{6}{x-2}+4
Vertical Asymptote: x=2
Horizontal Asymptote: y=4
Domain: xne2
Range: yne4
400
Find a vector parallel to 2i+3j with a magnitude of 26.
4sqrt13i+6sqrt13j
400
The point D is such that vec(CD)=((-4),(5),(p)) , where p>0. Given that abs(vec(CD))=sqrt(50) , find the value of p.
p = 3
500
The random variable X is normally distributed with mean 8. Given that P(X > 7) = 0.69146, find the value of the standard deviation of X.
2
500
Ben is a fisherman with a boat in Rhyl harbor. This is part of a graph of the depth of the water at the mouth of the harbor. 
Create a cosine function to model this data, and then calculate the depth of the water at 9:30 am.
h(t)= 3cos(frac{π}{6}(t-4))+5
h(9.5)=2.10 m
500
Is f(x)=frac{3x-8}{x-3}, xne3 a self-inverse function?
Yes
500
Find the magnitude of vec(CD) given the points C(3, -4, 1) and D(-1, 0, 2) .
sqrt33
500
Let vec(AB)=((6),(-2),(3)) , and vec(AC)=((-2),(-3),(2)) .
a. Find vec(BC)
b. Find a unit vector in the direction of vec(AB)
vec(BC)=((-8),(-1),(-1))
Unit Vector: ((frac{6}{7}), (frac{-2}{7}),(frac{3}{7}))