There are three trails to the top of the mountian. in how many different ways can a person hike up and down the mountain if a)she wants to take the same trail both ways? b)she can, but need not, take the same trail both ways c)she does not want to take the same trail both ways?

There are three trails to the top of the mountian. in how many different ways can a person hike up and down the mountain if a)she wants to take the same trail both ways? b)she can, but need not, take the same trail both ways c)she does not want to take the same trail both ways?

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter4: Quadrilaterals

Section4.2: The Parallelogram And Kite

Problem 5E: A carpenter lays out boards of lengths 8 ft, 8 ft, 4 ft, and 4 ft by placing them end to end. a If...

See similar textbooks

Related questions

Q: that Sup antl Shaw SA thut inf

Q: In a convex, regular 16-gon. .how many diagonals can be drawn from one vertex? ..how many triangles…

A: Polygon property

Q: The tax on clothing in Stat A is 15%, and the tax on food is 10% . What is the price difference…

A: The price of a sweater after tax is added is $15+$15×15100=$(15+225100) =$(15+2.25)=$17.25 The…

Q: There are three places P, Q and R such that 3 roads connect P and Q and 4 roads connects Q and R. In…

A: Hi there! Thanks for posting the question. Since there are two different questions, we have solved…

Q: How many distinct triangles can be constructed if m∠A = 30, side a = √34 and side b = 12

A: It is given that, ∠A=30° sides are a=34 and b=12 So, we have to…

Q: 2. If AC = 32, h = 19 and C = 41°, find ZABD.

Q: If circles are inscribed inside the six triangles into which a triangle ABC is divided by its…

Q: If the height requirements are changed to exciude only the tallest 50% of men and the snortest 5% of…

A: As given, Men's heights are normally distributed. With a mean of 68.3 and a standard deviation of…

Q: 4. In a convex 16-gon: a. How many diagonals can be drawn from 1 vertex? b. How many triangles are…

A: We can solve this problem by observing the pattern by taking some polygons with smaller number of…

Q: In AUVW, UW is extended through point W to point X, (7x + 10)°, m/WUV = (2x + 20)°, and mZVWX =…

Q: Prove if a,b > 0 then : a+b>1, to aª + bª 1 > 8

Q: S. Gives 4. Prove mADC-ABC D.

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: In a convex 22-gon, how many diagonals can be drawn from one vertex? In a convex 22-gon, how many…

A: 209 diagonals So, a polygon with 22 sides has 209 diagonals. The sum of the exterior angles…

Q: Is it true that if AB(line segment)≅PQ(line segment)then AB=PQ? Why, or why not? Is it true that…

A: Is it true that if AB(line segment)≅PQ(line segment)then AB=PQ? Why, or why not? Is it true that if…

Q: siven: ALMN; mLL > m2N rove: MN > TM

A: We have to prove that one side is greater than other side in given triangle.

Q: triangle MNP is formed by arranging three squares. Which statement must be true for triangle MNP…

Q: 3.3. Let a, BEC. Prove that la + B2 + la – B|2 2(la|? + |B|?), and deduce that |a + Va? – B2|+ |la –…

Q: Determine whether the following statement is true or false, and explain why.

A: The difference property of logarithms is ln xy=ln x-ln y. This is written for natural logarithms but…

Q: The ASA congruency axiom states that two triangles are congruent if: A. two angles and the contained…

A: Given, The ASA congruency axiom states that two triangles are congruent :

Q: 9.- Del gráfico, hallar "BC" 20 45° 53°

Q: How many ways can the five points of a five-pointed crown bepainted if three colors of paint are…

Q: Given: AABC with A(1,6), B(5,4), C(5, –2) Prove: The circumcenter of AABC is E( 1, 1 )

A: This question is related to triangle.

Q: A pyramid is going to be built with the following number of bricks. Three thousand eight hundred…

A: number oh bricks need for each flood decreases in arithmetic progression the sequence is…

Q: Solve the houndauy valu prwblen du avith Condihas 2. ulo,) = ull, ) =o and

Q: (a) In(ax), (b) In(x* + 1), (c) æ In a, (d) æ", (e) In(e" + 1), (f) exp(e" +1), (8) In +1

A: We have to differentiate the given functions.

Q: If MZTSV= 38°, MLUSW= 40°, and mZTSW=61° find mZUSV.

Q: 1. If BCDE is congruent to OPQR, then DE is congruent to (2 points)

A: Each side is congruent to corresponding side.

Q: If a quadrilateral has four right angles as well as two diagonals that are congruent, then the…

Q: Assuming the roles of president and secretary cannot be filled by the same person, how many ways are…

A: When Tyler is chosen as president, we have 3 choices for the post of secretary. So there are 3 such…

Q: 1:Calculate the measure of one interior angle of a regular 30-gon. 2: if the measure of interior…

A: Sum of all interior angles of regular polygon is = (n-2)180°

Q: In the figure,GHF is congruent to EHD. Which statement is true by CPCTC?

A: Given that in figure DEFG, ∆GHF and ∆EHD are congruent.

Q: The five leaves shown are all congruent,but one differs from the others. Whichone is different and…

A: Given that all are congruent. We shall number the leaves as follows.

Q: If m straight cuts are to be made right across a huge circular pizza (with no three cuts…

A: 1. There are m straight cuts. 2. The pizza is divided into 121 parts, not necessarily equal. 3.…

Q: Given: 24 = Prove: 25 = 26 9, atements Reasons Gro en 25 26 5

Q: how many diffrent seating arrangements are possible for king arthur and his 12 knights around their…

A: The number of ways, n items can be arranged around a circular table is equal to (n-1)! . The formula…

Q: If a, b, c are in A.P., then prove that ao +C), b(c +a), c(a + b) ab are also in A.P. bc са

A: arithmatic sequence prove , a, b,c are in A.P then prove

Q: 7. An overnight express company must include five cities on its re ferent routes are possible,…

A: Since order matters for this example, then permutations should be used.

Q: Prove the following is a Pythagorean Triple: (16, 30, 34)

Q: When three squares are joined at their vertices to form a rght triangle, the combined area of the…

A: answer of given question is in step 2

Q: In ANOP, NP is extended through point P to point Q, mZNOP= (3x + 8)°, MZPNO = (2x + 9)°, and mZOPQ =…

A: To find the value of x

Q: In AOPQ, m O = 44° and mZP = 51°. Which statement about the sides of AOPQ must be true?

Q: If all three perpendicular bisectors are drawn in the triangle below, where will they intersect? O…

A: The point at which all three perpendicular bisector of sides of a triangle meet is called…

Q: 4. If mZROS = 57° and ZROT = 165° , what is MZPOT. R. 57°

Q: Choose 1 answer: In quadrilateral ABCD, if AB = DC and ADE BC, then AB || DC and AD BC. In…

A: If the opposite sides of the quadrilateral are congruent then, it is a parallelogram, The given…

Q: B. THERE ARE 23 MEMBERS N THE FITNESo auB AW HOW barEenNG BOARD Of iCECTORS? MAM WAYS B IT PossiBLE…

A: Given Data: The total number of members in the club is: n=23 (A) The number of people selected for…

Q: 3, can the re inder be 5? Explain.

Q: The ASA congruency axiom states that two triangles are congruent if: A. two angles and the contained…

Q: ssume ZA is opposite side a, ZB is opposite side b, and ZOC is opposite side c.

A: Explanation and solutions is given below....

Q: From a pack of standard cards numbered from 1 to 20, a card is drawn at hobilitu that the card drawn…

A: We have given that, Pack of standard cards numbered from 1 to 20 then the sample space (s) is, s =…

Concept explainers

Counting Principles

In statistics, the counting principle can be said to be the concept in which the quantity of an item is determined. There can be a single item, or a group of items, or items that are related to each other. In every possible set of items, the quantity of the possible item groups or their sorting measures can be determined with counting principles.

Question

There are three trails to the top of the mountian. in how many different ways can a person hike up and down the mountain if

a)she wants to take the same trail both ways?

b)she can, but need not, take the same trail both ways

c)she does not want to take the same trail both ways?

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step by step

Solved in 4 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Fundamental Counting Principle$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.

Similar questions

With ABDCBE and A-D-E-C, does it necessarily Follow that AEB and CDB are congruent?
In Exercises 41 to 50, use deduction to state a conclusion, if possible. All mathematics teachers have a strange sense of humor. Alex is a mathematics teacher. Conclusion?
In Exercises 41 to 50, use deduction to state a conclusion, if possible. If you study hard and hire a tutor, then you will make an A in this course. You make an A in this course. Conclusion?
In Exercises 25 to 32, name the type of reasoning if any used. While judging a science fair project, Mr. Cange finds that each of the first 5 projects is outstanding and concludes that all 10 will be outstanding.
A carpenter lays out boards of lengths 8 ft, 8 ft, 4 ft, and 4 ft by placing them end to end. a If these are joined at the ends to form a quadrilateral that has the 8-ft pieces connected in over, what type of quadrilateral is formed? b If these are joined at the ends to form a quadrilateral that has the 4-ft and 8-ft pieces alternating, what type of quadrilateral is formed?
In Exercise 11 and 12, provide the missing statements and reasons. Given: 12;34 s 2 and 3 are complementary Prove: s 1 and 4 are complementary PROOF Statements Reasons 1. 13 and 34 1. ? 2. ? and ? 2. If two s are , then their measures are equal. 3. s 2 and 3 are complementary 3. ? 4. ? 4. The sum of the measures of complementary s is 90 5. m1+m4=90 5. ? 6. ? 6. If the sum of the measures of two angles is 90, then the angles are complementary
In Exercises 41 to 50, use deduction to state a conclusion, if possible. If a student is enrolled in a literature course, then he or she will work very hard. Bram Spiegel digs ditches by hand six days a week. Conclusion?
In O,OY=5 and XZ=6. If XWWY, find WZ.
In Exercises 7 10, state the property or definition that justifies the conclusion the then clause. Given that m3+m4=180, then s3 and 4 are supplementary.