Algebra
Identify the imaginary part of the following complex number:
1−3i
-3
If ∠A measures (40−10x)∘, which of the following is equivalent to the measure of the supplement of ∠A ?
(10x + 140)
The position s of a particle at time t is given by s(t) = 3t^2 − 2t. What is the particle's velocity at time t = 3
16
Calculate the standard deviation of the following data set:
3, 7, 2, 9, 8, and 10
2.986
Simplify the following expression:
3 x 8 / 9 of 6 - 2 / 3 x (5 - 2) x 2 + 18 / 3 of 3
- 1 5/9
Solve for x:
4/3 x - 5/6 = 6
3 5/8
The measure of the supplement of angle A is 40 degrees larger than twice the measure of the complement of angle A. What is the sum, in degrees, of the measures of the supplement and complement of angle A?
190
Find the velocity function if the position function is given as: s(t)= 3t^2 + 3t + 1
v(t) = 6t + 3
Which of the following best describes a data set with a correlation coefficient equal to zero?
Random
The ratio of two numbers A and B is 5 : 8. If 5 is added to each of A and B, then the ratio becomes 2 : 3. The difference in A and B is:
15
Solve for x: x^2 − 144 = 0
x = 12, -12
One-half of the measure of the supplement of angle ABC is equal to the twice the measure of angle ABC. What is the measure, in degrees, of the complement of angle ABC?
54
A weight hanging from a spring is stretched down 3 units beyond its rest position and released at time t=0 to bob up and down. Its position at any later time t is
s= 3cos (t)
What is its velocity at time t?
−3sin (t)
There are four different colored marbles in a jar—red, blue, white, and black—calculate how many outcomes are possible if a person picks two of the marbles if the order in which the marbles are picked matters.
12
Fourteen people can work in 18 days. After 5 days of work, 6 workers left, and joined back on the last day of the work. In how many days did the work get completed?
27
Solve for x:
x (x−2) = x^2 − 8
4
A student creates a challenge for his friend. He first draws a square, the adds the line for each of the 2 diagonals. Finally, he asks his friend to draw the circle that has the most intersections possible.
How many intersections will this circle have?
12
Find the velocity at t=2 if the acceleration function is: a(t)=1
2
Type I errors occur when a researcher incorrectly __________ the ___________ hypothesis; therefore, they erroneously accept the __________ hypothesis.
rejects. . . null. . . alternative
The population of a city is 8000. If the number of males increases by 8% and that of females by 12% then the population will become 8680. Find the number of females in the city.
1000
Solve the system of equations.
4x + y = 16
2x + 3y = 18
(3, 4)
A man at the top of a lighthouse is watching birds through a telescope. He spots a pelican 5 miles due north of the lighthouse. The pelican flies due west for 12 miles before resting on a buoy. What is the distance, in miles, from the pelican's current resting spot to the lighthouse?
13
If during the first 15 seconds of its flight the displacement of a spacecraft is given by the equation 21.25x + x2 feet, what is its velocity at 10 seconds, given that its initial velocity is 0?
1.25 * 212.5 * log(2) + 20 feet/second
What is the probability of drawing an ace from a standard deck of fifty-two cards?
7.69%
The marked price of an article is Rs. 240. A shopkeeper sells it by allowing 18% discount on it's marked price and still gains 23%. What is the cost price (in Rs.) of the article?
160