What is the distance in space between the points with coordinates (-3, 6, 7) and (2, -1, 4)?
9.11
100
In the xy- plane, what is the area of a triangle whose vertices are (√2, 0), (2, √10) and (5,0)?
5.67
100
sin²t + cos²t = ?
1 :)
100
A coin is tossed three times. Find the probability that head and tail show alternately.
¼
Set of possible outcomes = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}
Set of favorable outcomes = {HTH, THT}
so 2/8=1/4
100
What is 1 X 0 + 24?
24 :)
200
If the functions f and g are defined as f(x) = x^2 – 2 and g(x) = 2x + 1, what is f[g(x)]?
4x^2 + 4x - 1
200
The diameter and height of a right circular cylinder are equal. If the volume of the cylinder is 2, what is the height of the cylinder?
1.37
200
Find all positive values of t less than 180°that satisfy the equation 2 sin² t – cos t – 2 = 0.
90 and 120 degrees
200
If y = 3^x, than 3^(x+2) = ?
9y
200
What is one of the most common ways to memorize the units of pi?
number of letters of each successive word corresponds to a digit of pi
exp: 3.14159 ~ "Wow! I made a great discovery"
300
At a party, everyone shook hands with everybody else. There were 66 handshakes. How many people were at the party?
12
300
A pentagonal pyramid has the following properties:
Base Area = 32.7 cm2
Perimeter = 21.8 cm
Height = 4 cm
Side Length = 5 cm.
All side faces are the same.
What is its total surface area?
87.2 cm2
300
What is the half angle identity for sin?
Square root of (1-cosx)/2
300
Tickets for a show cost $3 or $5. If 50 tickets were sold for a total of $230, how many tickets were sold for $3?
10
300
What US states begin with the letter W? Name all of them.
Washington (WA)
West Virginia (WV)
Wisconsin (WI)
Wyoming (WY)
400
In January 1990 the world’s population was 5.3 billion. Assuming a growth rate of 2 percent per year, the world’s population, in billions, for t years after 1990 can be modeled by the equation P = 5.3(1.02)^t . According to the model, what is the population growth from January 1995 to January 1996?
117,000,000
400
Given triangle ABC, where line segment AC is perpendicular to line segment BC, AD = DB, and DC = BC. If BC = 1, what is the length of line segment AB?
√(4 + 2√2)
400
Stream gradient
The Colorado river drops from 3200 feet at Lake Mead to 900 feet elevation at Lee's Ferry, a river distance of 270 miles. What is the gradient in degrees?
0.11 degrees
400
For what value of a in the equation ax^2 – 6x + 9 = 0 are the roots of the equation equal?
1
400
What scientist—remembered for his triangle, his theorem, and his wager—died at the tender age of 39?
Pascal
500
If a man buys several articles for n cents per dozen and his selling price is n/9 cents per
article, what is his profit, in cents, on each article?
n/36
500
One side of a given triangle is 18 in. Inside the triangle a line segment is drawn parallel
to this side cutting off a triangle whose area is two-thirds that of the given triangle. Find
the length of this segment in inches.
6√6
500
The angle of repose is the steepest angle at which dry, unconsolidated sediment is stable. You create a conical pile of sand that is as steep as you can make it. The pile is 11 cm high and has a radius of 16 cm. What is the angle of repose of this sand?
Hint: It is a cone shape
34.5 degrees
500
Find the solution set of the inequality |x + 3| < 5.
x < 2
x > -8
500
What is the golden ratio that creates aesthetically pleasing designs and art works such as Leonardo da Vinci’s Mona Lisa and found in nature (such as pine cones)?