1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
dedylja [7]
3 years ago
14

(a) Suppose you have 9 gold coins that look identical, but you also know one (and only one) of them is counterfeit. The counterf

eit coin weighs slightly less than the others. You also have access to a balance scale to compare the weight of two sets of coins — i.e., it can tell you whether one set of coins is heavier, lighter, or equal in weight to another (and no other information). However, your access to this scale is very limited. Can you find the counterfeit coin using just two weighings? Prove your answer.
(b) Now consider a generalization of the same scenario described above. You now have 3^n coins, n ≥ 1, only one of which is counterfeit. You wish to find the counterfeit coin with just n weighings. Can you do it? Prove your answer
Mathematics
1 answer:
alisha [4.7K]3 years ago
8 0

Answer:

Step-by-step explanation:

You can split the coins into 3 groups, each of them has 3 coins. Weigh group 1 vs group 2, if one is lighter, that group has the fake coin. If both groups weigh the same, then group 3 has the fake coin.

Continue to split the group that has the fake coin into 3 groups, each group has 1 coin. Now apply the same procedure and we can identify the fake coin.

Total of scale usage is 2

b) if you have 3^n coins then you can apply the same approach and find the fake coin with just n steps. By splitting up to 3 groups each step, after each step you should be able to narrow down your suspected coin by 3 times.

Step 1: you narrow down to group of \frac{3^n}{3} = 3^{n-1} coins

Step 2: you narrow down to group of \frac{3^{n-1}}{3} = 3^{n-2} coins

Step 3: you narrow down to group of \frac{3^{n-2}}{3} = 3^{n-3} coins

...

Step n: Step 1: you narrow down to group of 3^{n-n} = 3^0 = 1coin

You might be interested in
A model car is 8 inches long and 5.2
Sphinxa [80]
Use proportions here - 8/5.2 = 96/width of actual car. using cross multiplication, 5.2*96 = 8x. this gives you 499.2 = 8x. divide both sides by eight to get x=62.4. the width of the actual car is 62.4 inches.
7 0
2 years ago
I really need help fast
xenn [34]

Answer:

Tom jogged farther.

Step-by-step explanation:

2 1/2 + 3 1/8 = 5 5/8   5 6/8 would be equalt to 5 3/4 but since it isn't 5 3/4 is farther.    

Tom jogged 1/8 farther.

6 0
3 years ago
What is the area of this figure
anastassius [24]

Answer:

185

Step-by-step explanation:

sorry. had to do something but im bsck :)

5 0
3 years ago
Read 2 more answers
A 234 inch board is cut into two pieces. One piece is five times the length of the order. Find the length of the shorter piece.
hammer [34]

Answer:

39 inches

Step-by-step explanation:

5x+x=234

6x=234

234/6=39

x=39 inches

7 0
2 years ago
Pls do 2 3 4 a and b
kirza4 [7]

Answer:

2.a)11.355 b)0.94625

3. divide 6 by 4

4. 0.8kg, 800g

Step-by-step explanation:

To convert one measurement to another you need to set it up so that the old measurement gets cancelled out when you multiply the conversion ratio.

2a)  \frac{3 gallons}{1} *\frac{3.785 milliliters}{1 gallon}=11.355 milliliters the gallons on top and bottom get cancelled out leaving you with the measurement that you want

2b) \frac{1quart}{1} *\frac{1 gallon}{4 quarts} *\frac{3.785 milliliters}{1 gallon} = 0.94625 milliliters

3) \frac{x}{y} \frac{6 quarts}{1} *\frac{1 gallon}{4 quarts} = 1.5 gallons

4) \frac{28 ounces}{1} *\frac{1 kilogram}{35 ounces} = 0.8 kilograms

\frac{0.8 kilograms}{1} *\frac{1000 grams}{1 kilogram} = 800 grams

7 0
3 years ago
Other questions:
  • The perimeter of a quadrilateral is 38 yards. If three of the sides measure 5.8 yards, 7 yards, and 11.2 yards, what is the leng
    9·1 answer
  • Ali Yahoo had $24 to spend on se ven pencils. After buying them she had $10. How much did each pencil cost?
    9·2 answers
  • Solve 1/3 x = -4/5????
    15·2 answers
  • I have no clue how to do this............
    8·2 answers
  • Which system is equivalent to StartLayout Enlarged left-brace 1st Row 5 x squared + 6 y squared = 50 2nd row 7 x squared + 2 y s
    6·2 answers
  • Determine if the given pair of lines is parallel, perpendicular or neither.
    10·1 answer
  • Write a multiplication equation that describes the picture of the half pants below use fraction below
    10·1 answer
  • Samantha was driving down a road and after 4 hours she had traveled 70 miles. At this speed, how many hours would it take Samant
    13·1 answer
  • PLEASE HELP QUESTION IN PICTURE
    6·1 answer
  • 3. There are 9 tables in the cafeteria. Each table has the same number of chairs. If there is a tota of 171 chairs, how many cha
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!