Trigonometry
Sin theta is = ?/hypotenuse
Opposite
f(x)=2x+5
find f(3)
find x when f(x)=11
find f(3) ans:11
find x when f(x)=11 ans:3
A fair coin is flipped twice. What is the probability that it lands on heads at least once?
3/4
is 67 degrees an acute angle?
yes
A boat travels 10 km east, then 10 km north. What is the bearing of the boat's final position from the starting point?
Since the boat travels equal distances east and north, the angle is 45°45°. The bearing is 045°045°.
What do you say to remember trig ratios?
A. Soh Cah Toa (soka kah tuah trig on that thang also accepted)
g(x)=x2-4x+3
find the roots of the function
find the axis of symmetry and the vertex of the parabola.
find the roots of the function ans:x=1,x=3
find the axis of symmetry and the vertex of the parabola. ans:vert=(2,-1)
A bag contains 5 red, 4 blue, and 3 green marbles. If you randomly draw one marble, replace it, and then draw another, what is the probability that both marbles are blue?
1/9
All sides of a triangle add up to？
180
A ship sails from point A on a bearing of 090° for 5 km, then changes course to 180° for 5 km. What is the ship's final bearing from point A?
The ship's final position forms a right triangle. The bearing from point A to the final position is 135°.
A ladder leans against a vertical wall. The ladder is 10 meters long and makes an angle of 60 degrees with the ground. How high up the wall does the ladder reach? Calculate the height to the nearest tenth of a meter.
≈8.7 meters
h(x)=5*2x
find h(3)
solve for x when h(x) = 40
find h(3) ans:40
solve for x when h(x) = 40 ans:x=3
A pair of fair, standard dice are rolled. What is the probability the sum of the dice is 5?
1/9
A sphere of radius 19m has what volume? (keep pi as it is)
25.333∏ m3
Vector a=2i+3j and vector b=4i-j. Find a+b.
a+b=6i+2j
Q. area of triangle with 20cm side and 30cm side with 30 degree angle in between
A. 150 cm^2
f(x)=(2x+3)/(x-1)
Determine the domain of f(x)
Identify any vertical and horizontal asymptotes of f(x)
Determine the domain of f(x) ans: x!=1
Identify any vertical and horizontal asymptotes of f(x)
ans:y=2
In a room of 30 people, what is the probability that at least one person was born in January?
N/A
Volume is proportional to (Surface area)?
what is ?
3/2
A plane flies from point P to Q on a bearing of 060° for 60 km, and then to R on a bearing of 150° for 40 km. What is the plane's total displacement from point P?
about 72.12KM
In triangle ABC, side AB is 13cm long, side AC is 15cm long, and angle A is unknown. The triangle has an area of 72cm2.
a) Find the measure of angle A in degrees, rounded to the nearest whole number.
b) Once you've found angle A, determine the length of side BC.
A = about 48
11.46cm
f(x)=3sqrt(x-2)+4
find f-1(x)
determine the domain and range for both f(x) and f-1(x)
find f-1(x)
ans:((x-4)/3)2+2
determine the domain and range for both f(x) and f-1(x)
domain f(x)= x>=2 f-1x=any real
range f(x)>=4 f-1x>=2
“ The Birthday Problem” (famous)(modified) In a roomful of 10 people, what is the probability that at least two people have the same birthday? Assume birthdays are uniformly distributed and there is not leap year complication. (Hint: what is the probabilty that they all have different birthdays?
0.117
A circle has a center of O and a radius of 10 centimeters. From point P outside the circle, a tangent is drawn that touches the circle at point T. The distance from point P to the center O is 26 centimeters. What is the length of the tangent PT? Find the length using the given measurements, expressed in centimeters.
24cm
A plane flies from point P to Q on a bearing of 030° for 40 km, and then to R on a bearing of 120° for 30 km. What is the plane's displacement from P?
50.31 KM