Algebra
(log(base e+1) (1728))/(log(base e+1) (12))
The perimeter of the two congruent sides of an isosceles triangle with a base of 10 inches and a height of 12 inches is:
What is 36 in?
A die is rolled twice. Let A equal the probability that the first roll is even. Let B equal the probability that the sum of both rolls is 7. Calculate P(A | B).
What is 0.5?
The sum of the series:
(From n = 0 to infinity) The sum of:
6(0.25)n
What is 8?
Agnes writes the following four statements on a blank piece of paper.
At least one of these statements is true.
At least two of these statements are true.
At least two of these statements are false.
At least one of these statements is false.
Each statement is either true or false. Agnes wrote __ false statements on the paper.
What is 1?
Simplify:
(2x3-5x2-8x+15)/(x-3)
What is 2x2+x-5 ?
A circle with a center at the point (4,3) and a radius of r is drawn. A line tangent to the circle at the point (0,6) is also drawn. The slope of the line tangent to the circle at (0,6) is:
What is 4/3 ?
A fair die is rolled three times. The probability that at least one roll is a 6 is:
What is 91/216 ?
Solve the indefinite integral of:
(t+5)(cos(t/4))
What is 4(t+5)sin(t/4)+16cos(t/4) +C?
The value of:
(√(16√(81)))/(√(81√(16)))
What is 2/3 ?
If f(x) = (x-3)/(x+7), the value of the inverse function is:
What is f-1(x) = (-7x-3)/(x-1) ?
The circle is represented by the function x2-3x+y2-5y= 40.5, the length of the radius is:
What is 7 units?
The average score on an English essay is 67 points. A certain student obtains a score of 41, with a z-score of 2.37. 95% of data points in this set fall between these two numbers (round to nearest whole number):
What are 45 and 89?
Find the volume of the solid with the given cross section, y = √(𝑥) and 𝑦 =x/3 cross sections perpendicular to the 𝑦-axis are rectangles whose height is 6.
What is 27 units cubed?
A group of 7 friends all shake hands with each other. The number of unique handshakes that take place.
What is 21?
The product of the following matrices:
1 2 3
4 5 6
7 8
9 10
11 12
What is:
58 64
139 154
A circle has a center of (-2,3). Line p is tangent to the circle at (2,6). Which of the following points land on the line p?
A. (5,3)
B. (-9,0)
C. (-1,8)
D. (6,1)
E. (5,2)
What is E?
The slope of the population regression line relating circumference and weight for male sambras is 4.5kg/cm. A biologist conducted a test with the following hypotheses:
H0: β = 4.5
Ha: β =/= 4.5
If the test statistic is calculated to be 3.408, find the p-value (use a graphing calculator).
Set up, but do not solve, the equation for the total area outside the polar curve 𝑟 = 5 cos 2𝜃 and inside the polar curve 𝑟 = 5
What is:
A = 25(pi) - 0.5 (integral from 0 to 2(pi) with respect to 𝜃)[(5cos(2𝜃))2]
The sequence 1, x, y, z is arithmetic. The sequence 1, p, q, z is geometric. Both sequences are strictly increasing and contain only integers, and z is as small as possible. The value of
x + y + z + p + q
What is 149?
(x = 22, y = 43, z = 64, p = 4, q = 16)
The produce of the two matrices:
2 7 9
6 7 3
1 0 1
9 1 1
1 2
3 4
5 6
What is:
68 86
42 58
6 8
17 28
The statement and the proof are provided below provided below:
In a parallelogram MNOP, ray MO bisects angle PMN and ray OM bisects angle PON. Prove triangle PMO is congruent to triangle NMO
Proof:
1. Ray MO bisects angle PMN
2. Angle PMO is congruent to angle NMO
3. Line segment MO is congruent to line segment MO
4. Ray OM bisects angle PON
5. Angle POM is congruent to angle NOM
6. Triangle PMO is congruent to triangle NMO
Give the postulates, theorems, or reasons behind each statement of the proof provided.
What is:
1.Given
2.Definition of Angle Bisector
3.Reflexive Property Congruence
4.Given
5.Definition of Angle Bisector
6.ASA postulate
The following are the SAT score results for two groups of students.
Juniors: 133 students, mean = 1274, SD = 142
Seniors: 139 students, mean = 1208, SD = 239
Using a two-sample t-test, calculate the t-statistic for the difference in means between Seniors and Juniors, and determine whether this difference is statistically significant at the 95% confidence level.
What is:
T-statistic: ~2.78. The calculated t-statistic is 2.78; thus, we reject the null hypothesis and conclude that the difference in means between Juniors and Seniors is statistically significant.
The common interior of the polar graphs r = 2sin𝜃 and r = 2cos𝜃
What is (pi)/2 -1 ?
Patrick started walking at a constant speed along a straight road from his school to the park. One hour after Patrick left, Tanya started running at a constant speed of 2 miles per hour faster than Patrick walked, following the same straight road from the school to the park. One hour after Tanya left, José started bicycling at a constant speed of 7 miles per hour faster than Tanya ran, following the same straight road from the school to the park. All three people arrived at the park at the same time. The distance from the school to the park is m/n miles, where m and n are relatively prime positive integers. Find m+n.