Probability and Counting
A 4 character passcode has to have 2 letters followed by 2 digits with repeats allowed. How many possible passcodes are there?
67600
What is the amplitude of the following function?
y=3sin(2x)+4
3
Evaluate the following:
sin(frac(5pi)(3))
frac(-sqrt(3))(2)
What type of graph will this equation make?
frac((x+2)^2)(4)+frac((y-3)^2)(9)=1
Ellipse
Write the explicit formula for the sequence:
12, 9, 6, …
a_n=12-3(n-1)
How many 6 letter words can we create with the letters in SUMMER?
360
What is the period of the following function?
y=-3sin(frac(x)(2))-5
4π
Solve on the interval [0,2π).
cos(x)=-frac(1)(2)
frac(2pi)(3)
frac(4pi)(3)
Where are the major vertices of this graph?
frac((x+2)^2)(4)+frac((y-3)^2)(9)=1
(-2,6) and (-2,0)
Write the explicit equation for the sequence:
10, 15, 22.5, …
a_n=10(1.5)^(n-1)
There are 20 students running for student council positions. How many different ways can we select president, vice president, and secretary?
6840
What is the period of the following function?
y=4tan(2x)+7
π/2
Finish the identity:
frac(cos(x))(sin(x))=
cot(x)
Where are the focus points of this graph?
frac((x+2)^2)(4)+frac((y-3)^2)(9)=1
(-2,3+sqrt(5))
(-2,3-sqrt(5))
Find the sum:
22.5 + 15 + 10 + …
67.5
When rolling two dice, what is P(rolling a 5 and rolling an even)?
1/6 =0.167
Where is the smallest, positive (non-zero) asymptote of this function?
y=tan(2x)-1
x= π/4
Finish the identity:
sin^2(x)+cos^2(x)=
1
What are the slopes of the asymptotes?
frac((x+2)^2)(4)-frac((y-3)^2)(9)=1
3/2 and -3/2
Find the sum:
12+9+6+… for 11 terms
-33
40% of people in Utah have gone skiing/snowboarding. 30% of people in Utah have gone mountain biking. 25% have gone both skiing/snowboarding AND biking. What is the probability of finding someone who has never been skiing/snowboarding nor mounting biking?
55%
A Ferris wheel has a diameter of 30 feet. The center of the wheel is 35 feet above ground. The wheel rotates once every 90 seconds. If a passenger starts at the bottom, what is the equation for the passengers height over time?
y=-15cos(frac(pi)(45))+35
Finish the identity:
sin(2x)=
2sin(x)cos(x)
Where are the focus points of this graph?
frac((x+2)^2)(4)-frac((y-3)^2)(9)=1
(-2+sqrt(13),3)
(-2-sqrt(13),3)
Find the sum:
2, 6, 18, … for 8 terms
6560