Exercises L3: Probability Theory
... 6. A car driver has caused an accident and has to take an alcohol test. Research has shown that 75% of the persons who had (too much) alcohol shows a positive test result. However, 2% of the persons who did not drink also show a positive test result. Assume that in case of accidents 5% of the car dr ...
... 6. A car driver has caused an accident and has to take an alcohol test. Research has shown that 75% of the persons who had (too much) alcohol shows a positive test result. However, 2% of the persons who did not drink also show a positive test result. Assume that in case of accidents 5% of the car dr ...
Programming Exam 1
... Problem. Write a program Intersects.java that reads in a sequence of circles from standard input, plots them using standard drawing, computes the circle that intersects with the most other circles, plots that circle in red, and prints to standard output the circle and the number of circles that it ...
... Problem. Write a program Intersects.java that reads in a sequence of circles from standard input, plots them using standard drawing, computes the circle that intersects with the most other circles, plots that circle in red, and prints to standard output the circle and the number of circles that it ...
Continued fraction expansion of the square-root operator
... Continued fractions first appeared in the works of the Indian mathematician Aryabhata in the 6th century. He used them to solve linear equations. They re-emerged in Europe in the 15th and 16th centuries and Fibonacci attempted to define them in a general way. The term "continued fraction" first appe ...
... Continued fractions first appeared in the works of the Indian mathematician Aryabhata in the 6th century. He used them to solve linear equations. They re-emerged in Europe in the 15th and 16th centuries and Fibonacci attempted to define them in a general way. The term "continued fraction" first appe ...
Section 6: Solving Right Triangles
... Of course, we could have instead used the Pythagorean theorem to find c = ...
... Of course, we could have instead used the Pythagorean theorem to find c = ...
Area
... factor-a number that can be multiplied to get another number. 1, 3, 5, and 15 are factors of 15. multiple-a counting number of a certain number multiples of 15 are 15, 30, 45, 60… prime-a number that has only 2 factors, 1 and itself. ...
... factor-a number that can be multiplied to get another number. 1, 3, 5, and 15 are factors of 15. multiple-a counting number of a certain number multiples of 15 are 15, 30, 45, 60… prime-a number that has only 2 factors, 1 and itself. ...
QUESTIONS AND SOLUTIONS
... Be sure to circle the appropriate choice on the answer sheet! Solution. If (a, b, c) is a primitive pythagorean triple, then one of a, b must be even. We will relabel so b is the even one (so possibly a > b). Then (a, b, c) is a primitive p. triple if and only if a = m2 − n2 , b = 2mn, c = m2 + n2 f ...
... Be sure to circle the appropriate choice on the answer sheet! Solution. If (a, b, c) is a primitive pythagorean triple, then one of a, b must be even. We will relabel so b is the even one (so possibly a > b). Then (a, b, c) is a primitive p. triple if and only if a = m2 − n2 , b = 2mn, c = m2 + n2 f ...
Chapter 3 Section 3.1
... NOT significant. They are placeholders. By writing the measurements in scientific notation, you can eliminate such placeholding zeros. Each of these measurements has only two significant figures: 0.0071 meter = 7.1 x 10-3 meter ...
... NOT significant. They are placeholders. By writing the measurements in scientific notation, you can eliminate such placeholding zeros. Each of these measurements has only two significant figures: 0.0071 meter = 7.1 x 10-3 meter ...
2015 Junior Solutions
... Solutions and investigations These solutions augment the printed solutions that we send to schools. For convenience, the solutions sent to schools are confined to two sides of A4 paper and therefore in many cases are rather short. The solutions given here have been extended. In some cases we give al ...
... Solutions and investigations These solutions augment the printed solutions that we send to schools. For convenience, the solutions sent to schools are confined to two sides of A4 paper and therefore in many cases are rather short. The solutions given here have been extended. In some cases we give al ...
GEOMETRY CP FINAL REVIEW
... 23) The sum of the measures of the exterior angles of any convex polygon is 24) The measure of each exterior angle of a regular 15-sided polygon is 25) If mA 3x 3 , mB 2x 8 , and mC 2x 1 , find the numerical measures of each angle of ABC . ...
... 23) The sum of the measures of the exterior angles of any convex polygon is 24) The measure of each exterior angle of a regular 15-sided polygon is 25) If mA 3x 3 , mB 2x 8 , and mC 2x 1 , find the numerical measures of each angle of ABC . ...
Chapter 1, Section 9
... d ( x2 x1 )2 ( y2 y1 ) 2 To compute the distance between two points, find the square of the difference between the x-coordinates plus the square of the difference between the y-coordinates. The principal square root of this sum is the distance. ...
... d ( x2 x1 )2 ( y2 y1 ) 2 To compute the distance between two points, find the square of the difference between the x-coordinates plus the square of the difference between the y-coordinates. The principal square root of this sum is the distance. ...
6.2 - Unit Circle and the six trigonometric functions
... For an angle in standard position, let P = (x, y) be the point on the terminal side of is also on the circle x 2 y 2 r 2 we get the following trigonometric functions: ...
... For an angle in standard position, let P = (x, y) be the point on the terminal side of is also on the circle x 2 y 2 r 2 we get the following trigonometric functions: ...
Approximations of π
Approximations for the mathematical constant pi (π) in the history of mathematics reached an accuracy within 0.04% of the true value before the beginning of the Common Era (Archimedes). In Chinese mathematics, this was improved to approximations correct to what corresponds to about seven decimal digits by the 5th century.Further progress was made only from the 15th century (Jamshīd al-Kāshī), and early modern mathematicians reached an accuracy of 35 digits by the 18th century (Ludolph van Ceulen), and 126 digits by the 19th century (Jurij Vega), surpassing the accuracy required for any conceivable application outside of pure mathematics.The record of manual approximation of π is held by William Shanks, who calculated 527 digits correctly in the years preceding 1873. Since the mid 20th century, approximation of π has been the task of electronic digital computers; the current record (as of May 2015) is at 13.3 trillion digits, calculated in October 2014.