Number and Algebra
The first 4 terms of an Arithmetic Sequence is:
4, 7, 10, and 13
Find the 100th Term
301
Find the equation for the perpendicular bisector between points (0,2) and (3,4).
y=(-2/3)x+4
A sphere's volume is roughly 8,580cm3.
What is the radius of the sphere?
12.7cm
At a school, 70% of students play a sport and 20%of the students are involved in band. 18% of the students do neither activity.
Find the probability that a random student plays a sport and is involved in band.
8%
Differentiate the function:
f(x)=x4+2x3-4x2+7x-2
f'(x)=4x3+6x2-8x+7
Write this Number in terms of cm in Scientific Notation:
158.2 Km
1.582x107 cm
Find the vertex for the function: h(t)=-2t2+20t+8
If this function modeled a ball being thrown, what does the vertex and positive x intercept represent?
(5,58)
The highest Point.
When the ball hit the ground.
A pizza with 8 slices and a diameter of 12 inches has one slice missing. The angle of the missing slice's sector is 45o.
What is the area of the remaining pizza?
99.0 in2
The following table shows how many hours a certain number of students spend exercising each week:
Time Excersising #of Students
2hours 5
3hours 1
4hours 4
5hours 3
6hours 7
Find the standard deviation.
1.56
Consider the function f(x)=x2
Find the equation of the tangent to f(x) when x=2
y=4x-4
Slove for x in terms of e2 when:
2 ln x = ln 9 + 4
x=3e2
A bird watcher modeled the migration of birds using the function P(t)=1350+400(1.25)-t where (P) represents Population and (t) represents time.
Calculate when the bird population will decrease below 1400.
9.32 days
A right cone has a square base and a hight of 5cm.
Given that the volume of the cone is 26cm2, find the slant hight of the cone.
6.37cm
The following table shows the probability of a weighted tetrahedral die rolling on each given value:
Roll: 1 2 3 4
P(X=x) k2 7k+2 -2k 3k2
Find the value of k.
(-1/4)
What is f'(x) if for the function f(x)=x2 - (k/x)
2x - (k/x2)
A geometric sequences common ratio (r) is 2
The sum of the first 5 terms in the sequence is 31.
What is the 1st term in the sequence?
1
The height of a single point on a spoked wheel is modeled by the function h(t)=10cos(2๐t) where h is height inches and t is time in seconds.
How long does it take a single spoke of the wheel to make a full rotation? How far has the outside edge of the spoke traveled?
1 second
20pi or 62.8 inches
The lenghts of two sides of Triangle ABC are: AB=6 and AC=8, and the cosA=(5/6)
What is the area of the triangle?
13.3 units2
A and B are events such that P(A) = 0.5, P(B) = 0.4 and P(AUB) = 0.6
Find P(A|B)
.75
A curve passing through the following points:
(0,2) (2,5) (4,7) (6,3) (8,3) (10,10)
Estimate the under the curve between x=0 and x=10 using the trapezoidal rule.
10f(x)dxโ(2โ0)25+2+(4โ2)27+5+(6โ4)23+7+(8โ6)23+3+(10โ8)210+3=48.
I take out a $100,000 30 year loan to buy a home. The bank gives ma an intrest rate of 6% compunded annually. What is my monthly payment?
$599.55
A quadratic function has a vertex of (-2,10) and an x intercept of (2,0).
What is the other x intercept?
(-6,0)
Solve: sin(2x) + cos(2x) - 1 + cos(x) - sin(x) = 0 |for all solutions between 0 and 2pi.
7pi/6
11pi/6
pi/4
5pi/4
A teacher is drawing popsicle sticks to decide the order that the students will present their projects. There are 12 girls and 7 boys in the class. What is the probability that the teacher will first pull two boys followed by 1 girl?
12.4%
A curve passing through the following points:
(0,2) (2,5) (4,7) (6,3) (8,3) (10,10)
Given that the curve is a cubic function, find the area under the curve betwen the x axis and x=0 through 10.
48.2