Concept explainers
Videos
To enter the program and run it for several times for large values of D like
Explanation of Solution
Given:
Break a stick into three pieces to get the probability that you can join the pieces end-to-end to form a triangle. If the sum of the length of any two pieces is less than or equal to that of the third, a triangle can’t be form. This is known as Triangle Inequality. By an experiment your class can estimate the probability that three pieces of broken stick will form a triangle.
Calculation:
Let D, N, I, X, Y, R, S and T variables used in program. Where D stands for number of sticks you have to break, N stands for first end of stick that is 0, I stands for variable of for loop assign from 1 to D, X and Y are stand for the length of points distance from initial point that is 0, R assigned as X, S assigned as Y − R and T assigned for 1 − R − S. Consider the program below
Program:
'Print this statement "SIMULATION-BREAKING STICKS TO MAKE TRIANGLES" on output screen.
10 PRINT "SIMULATION-BREAKING STICKS TO MAKE TRIANGLES"
'PRINT use to create blank line.
20 PRINT
30 PRINT "HOW MANY STICKS DO YOU WANT TO BREAK”;
40 INPUT D
50 LET N=0
60 FOR I=1 to D
70 LET X=RND(1)
80 LET Y=RND(1)
90 IF X>=Y THEN 70
100 LET R=X
110 LET S=Y.R
120 LET T=1.R.S
130 IF R+S<=THEN 170
140 IF S+T<=R THEN 170
150 IF R+T<=S THEN 170
160 LET N=N+1
170 NEXT I
180 LET P =N/D
190 PRINT
200 PRINT “THE EXPERIMENTAL PROBABILITY THAT”
210 PRINT “A BROKEN STICK CAN FORM A TRIANGLE IS”, P
220 END
Sample Output:
SIMULATION-BREAKING STICKS TO MAKE TRIANGLES
HOW MANY STICKS DO YOU WANT TO BREAK ?100
THE EXPERIMENTAL PROBABILITY THAT
A BROKEN STICKS CAN FORM A TRIANGLE IS 0.28
Output Explanation:
SIMULATION-BREAKING STICKS TO MAKE TRIANGLES
Enter number of sticks as 100 which you want to break that is value of variable D
HOW MANY STICKS DO YOU WANT TO BREAK ?100
THE EXPERIMENTAL PROBABILITY THAT
Than you get experimental probability is equal to 0.28
A BROKEN STICKS CAN FORM A TRIANGLE IS 0.28
The probability is less than
SIMULATION-BREAKING STICKS TO MAKE TRIANGLES
HOW MANY STICKS DO YOU WANT TO BREAK ?400
THE EXPERIMENTAL PROBABILITY THAT
A BROKEN STICKS CAN FORM A TRIANGLE IS 0.2275
Output Explanation:
SIMULATION-BREAKING STICKS TO MAKE TRIANGLES
Enter number of sticks as 400 which you want to break that is value of variable D
HOW MANY STICKS DO YOU WANT TO BREAK ?400
THE EXPERIMENTAL PROBABILITY THAT
Than you get experimental probability is equal to 0.2275
A BROKEN STICKS CAN FORM A TRIANGLE IS 0.2275
The probability is less than
SIMULATION-BREAKING STICKS TO MAKE TRIANGLES
HOW MANY STICKS DO YOU WANT TO BREAK ?800
THE EXPERIMENTAL PROBABILITY THAT
A BROKEN STICKS CAN FORM A TRIANGLE IS 0.26375
Output Explanation:
SIMULATION-BREAKING STICKS TO MAKE TRIANGLES
Enter number of sticks as 800 which you want to break that is value of variable D
HOW MANY STICKS DO YOU WANT TO BREAK ?800
THE EXPERIMENTAL PROBABILITY THAT
Than you get experimental probability is equal to 0.26375
A BROKEN STICKS CAN FORM A TRIANGLE IS 0.26375
The probability is less than
Chapter 6 Solutions
McDougal Littell Jurgensen Geometry: Student Edition Geometry
Additional Math Textbook Solutions
Pre-Algebra Student Edition
Elementary Statistics (13th Edition)
Thinking Mathematically (6th Edition)
Calculus: Early Transcendentals (2nd Edition)
Precalculus
University Calculus: Early Transcendentals (4th Edition)
- Please help me answer this question!. Please handwrite it. I don't require AI answers. Thanks for your time!.arrow_forward1 What is the area of triangle ABC? 12 60° 60° A D B A 6√√3 square units B 18√3 square units 36√3 square units D 72√3 square unitsarrow_forwardPar quel quadrilatère est-elle représentée sur ce besoin en perspective cavalièrearrow_forward
- -10 M 10 y 5 P -5 R 5 -5 Ο 10 N -10 Οarrow_forwardDescribe enlargement on map gridarrow_forward◆ Switch To Light Mode HOMEWORK: 18, 19, 24, 27, 29 ***Please refer to the HOMEWORK sheet from Thursday, 9/14, for the problems ****Please text or email me if you have any questions 18. Figure 5-35 is a map of downtown Royalton, showing the Royalton River running through the downtown area and the three islands (A, B, and C) connected to each other and both banks by eight bridges. The Down- town Athletic Club wants to design the route for a marathon through the downtown area. Draw a graph that models the layout of Royalton. FIGURE 5-35 North Royalton Royalton River South Royption 19. A night watchman must walk the streets of the Green Hills subdivision shown in Fig. 5-36. The night watch- man needs to walk only once along each block. Draw a graph that models this situation.arrow_forward
- Solve this question and check if my answer provided is correctarrow_forwardProof: LN⎯⎯⎯⎯⎯LN¯ divides quadrilateral KLMN into two triangles. The sum of the angle measures in each triangle is ˚, so the sum of the angle measures for both triangles is ˚. So, m∠K+m∠L+m∠M+m∠N=m∠K+m∠L+m∠M+m∠N=˚. Because ∠K≅∠M∠K≅∠M and ∠N≅∠L, m∠K=m∠M∠N≅∠L, m∠K=m∠M and m∠N=m∠Lm∠N=m∠L by the definition of congruence. By the Substitution Property of Equality, m∠K+m∠L+m∠K+m∠L=m∠K+m∠L+m∠K+m∠L=°,°, so (m∠K)+ m∠K+ (m∠L)= m∠L= ˚. Dividing each side by gives m∠K+m∠L=m∠K+m∠L= °.°. The consecutive angles are supplementary, so KN⎯⎯⎯⎯⎯⎯∥LM⎯⎯⎯⎯⎯⎯KN¯∥LM¯ by the Converse of the Consecutive Interior Angles Theorem. Likewise, (m∠K)+m∠K+ (m∠N)=m∠N= ˚, or m∠K+m∠N=m∠K+m∠N= ˚. So these consecutive angles are supplementary and KL⎯⎯⎯⎯⎯∥NM⎯⎯⎯⎯⎯⎯KL¯∥NM¯ by the Converse of the Consecutive Interior Angles Theorem. Opposite sides are parallel, so quadrilateral KLMN is a parallelogram.arrow_forwardQuadrilateral BCDE is similar to quadrilateral FGHI. Find the measure of side FG. Round your answer to the nearest tenth if necessary. BCDEFGHI2737.55arrow_forward
- An angle measures 70.6° more than the measure of its supplementary angle. What is the measure of each angle?arrow_forwardName: Date: Per: Unit 7: Geometry Homework 4: Parallel Lines & Transversals **This is a 2-page document! ** Directions: Classify each angle pair and indicate whether they are congruent or supplementary. 1 1.23 and 25 2. 24 and 28 3. 22 and 25 4. 22 and 28 5. 21 and 27 6. 22 and 26 Directions: Find each angle measure. 7. Given: wvm25-149 m21- 8. Given: mn: m1=74 mz2- m22- m.23- m23- mz4= V mz4= m25= m26- m26= m27- m27 m28- m48= 9. Given: a || b: m28 125 m2- 10. Given: xy: m22-22 m21- = mz2- m43- m3- mZA m24-> m. 5- m25- m26- m.26=> m2]=> m27= m28- 11. Given: rm2-29: m15-65 m2=> m29-> m3- m. 10- mc4= m25= m212- m.46- m213- mat- m214- m28- & Gina when (N) Things ALICE 2017arrow_forwardMatch each statement to the set of shapes that best describes them. 1. Similar triangles by SSS 2. Similar triangles by SAS 3. Similar triangles by AA 4. The triangles are not similar > U E 35° 89° S F 89° J 35° 94° G 52° 90° E K 52° Iarrow_forward
Elementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,
Elementary Geometry for College StudentsGeometryISBN:9781285195698Author:Daniel C. Alexander, Geralyn M. KoeberleinPublisher:Cengage Learning