There is always at least one consecutive value of n for which Marvin has a successful approach.
By induction, we can demonstrate that the game must conclude after a maximum of n(n+1)/2 turns for the first half of the issue, Here Induction Means a method for demonstrating that a statement P(n) is true for every natural number n, and that the infinitely numerous examples P(0), P(1), P(2), P(3), etc. all hold, is mathematical induction. Informal analogies, such a ladder or a falling domino, are used to explain this technique .
Base case: If there is just one bowl, Marvin can get rid of it in one turn, ending the game after one.
Step one of induction: Assume that there are k bowls and that the game terminates after no more than k(k+1)/2 turns. When there are k+1 bowls, we shall demonstrate that the game terminates after at most (k+1)(k+2)/2 turns. The number of bowls lowers by one if Marvin takes a marble out of one, and the game must terminate after no more than k(k+1)/2 turns through induction hypothesis
When Marvin transfers a marble from bowl A to bowl B, where bowl A contains at least one marble and bowl B contains an equal number of marbles, bowl A loses one marble and bowl B gains one marble. The number of bowls stays the same because bowl B has at least as many marbles as bowl A. As a result, the game must still terminate after k(k+1)/2 turns at the latest.
In any scenario, the game ends after at most k(k+1)/2 turns, thus when there are k+1 bowls, the game must end after at most (k+1)(k+2)/2 turns. For the second component of the issue, we can demonstrate that for every positive integer k, there exists a n such that Marvin can devise a plan to extend the n-bowl game for at least kn turns.
Let's say Marvin wants the n-bowl match to go at least kn turns. He can accomplish this by ensuring that each bowl always contains at least k marbles. Marvin can start by putting k marbles in the first bowl, k-1 marbles in the second bowl, and so forth, down to 1 marble in the nth bowl, to accomplish this.
For the second component of the issue, we can demonstrate that for every positive integer k, there exists a n such that Marvin can devise a plan to extend the n-bowl game for at least kn turns.
Let's say Marvin wants the n-bowl match to go at least kn turns. He can accomplish this by ensuring that each bowl always contains at least k marbles. Marvin can start by putting k marbles in the first bowl, k-1 marbles in the second bowl, and so forth, down to 1 marble in the nth bowl, to accomplish this.
Marvin can select a bowl containing at least k marbles on each turn and transfer one marble to a bowl containing fewer than k marbles .Marvin can transfer one marble from the first bowl to the second bowl, for instance, if there are k+1 marbles in the first bowl and k marbles in the second bowl. This guarantees that there are at least k marbles in each bowl. The game will go for at least kn turns because Marvin can take at least one turn every bowl.
For the third component of the issue, we can demonstrate that there is always at least one value of n for which Marvin has a successful strategy.
Assume that n is a positive integer. We shall demonstrate that either Marvin or Marisa has a winning strategy for the game of n bowls or the game of (n+1) bowls.
If Marvin has a winning strategy for the N-bowl game, he can use that method to win the N-bowl game.
If Marisa has a winning strategy for the n-bowl game and Marvin does not, then Marisa does as well. In this scenario, Marvin can use Marisa's successful approach to the n-bowl game as his own successful approach to the (n+1)-bowl game.
To learn more about induction at: brainly.com/question/8419798
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pls pls pls help me giving brainlist
Answer:
The first one is a similie
second is a metaphor
Step-by-step explanation:
like ice means like a hatred glare
the hug is a a good thing thats
happens on a bad dat
Answer:
simile
the referee was angry
metaphor
they have a lot of love for each other
Step-by-step explanation:
please mark me branliest
Two students spent the same amount of
money on their lunches and got the same
number of toppings. One bought a steak
burger and paid $3.80 plus $0.40 for each
topping. The other bought a hamburger
and paid $3.20 plus $0.60 for each
topping. How many toppings did each
student get?
0.60-0.40=0.20
3.80-3.20=0.60
0.60 divided by 0.20=3
Hence, each student got 3 toppings each.
hope it helps:))
In which step did John first make a mistake?
look at photos
Answer:
John did not make a mistake
Step-by-step explanation:
he did everything correct
NO LINKS FOR THE LAST TIME JUST HELP ANSWER THE QUESTION WITH A B C OR D WILL GIVE BRAINLIEST!!
Answer: letter b
Step-by-step explanation:
Please solve the question in the picture below.
Answer:
a
Step-by-step explanation:
because y=mx+b m =slope and b is the y intercept
Answer:
A. is the right answer
slope is 1.5 and y intercept is -2
Find an expression in its simplest form for the perimeter of this shape
Answer:
(18p + 18)
Explanation:
the perimeter of the shape is the sum of all its sides. we are given the individual lengths of all the sides except for the horizontal one at the bottom and the vertical one between (2p + 5) and (3p + 4), but they can easily be calculated using the other values.
the horizontal length at the bottom is the sum of (2p + 5) and (3p + 4), or (5p + 9).
the vertical length is the difference between 4p and 2p, which is 2p.
now, we can add all of these values together:
4p + (2p + 5) + 2p + (3p + 4) + 2p + (5p + 9)
= 4p + 2p + 2p + 3p + 2p + 5p + 5 + 4 + 9
= 18p + 18
i hope this helps! :D
The temperature of a hot steak starts at 140f and decreases at 5f per minute what will the temperature of this steak after a certain number of minutes
Answer:
T(m) = (140 - 5m)
Step-by-step explanation:
Given that :
Initial temperature, a = 140 F
Rate of decrease = 5 F per minute
Given a certain Number of minutes, m
Temperature, T after m minutes ;
Using the formula :
Final temperature = Initial temperature - 5*number of minutes)
T(m) = (140 - 5m)
Given that ; m = 10
T(10) = 140 - 5(10)
T(10) = 140 - 50
T(10) = 90 F
List three integers that are between -22 and -10
PLEASE HELP ASAP
Answer:
-21, -20, -19, --18, -17, -16, -15, -14, -13, -12, -11
Step-by-step explanation:
There is no step by step explanation.
Draw a line through the point (2, 2) with a slope of 1. Draw a line through the point (1,−1) with a slope of 1.
Answer:
should look like this
Step-by-step explanation:
equations are y=x and y = -x if needed
The equation of the lines are y = x and y = x - 2
A linear equation is given by:
y = mx + b;
where y, x are variables, m is the slope of the line and b is the y intercept
The equation of a line passing through the point (2, 2) with a slope of 1 is:
[tex]y-y_1=m(x-x_1)\\\\y-2=1(x-2)\\\\y = x[/tex]
The equation of a line passing through the point (1, -1) with a slope of 1 is:
[tex]y-y_1=m(x-x_1)\\\\y-(-1)=1(x-1)\\\\y = x-2[/tex]
Therefore both lines have equation of y = x and y = x - 2. The graphs of the lines are attached.
Find out more at: https://brainly.com/question/1391192
3 − 1 = 5 + 10 = −5 1/2 Check whether the given value of is a solution to the equation. Justify your answer.
Answer:
[tex]x = -5\frac{1}{2}[/tex] is the solution
Step-by-step explanation:
Given
[tex]3x - 1 = 5x + 10[/tex] --- Correct expression
[tex]x = -5\frac{1}{2}[/tex]
Required
Determine if the given solution is correct
To do this, we simply solve for x in the given equation.
So, we have:
[tex]3x - 1 = 5x + 10[/tex]
Collect like terms
[tex]3x - 5x = 1 + 10[/tex]
[tex]-2x = 11[/tex]
Divide both sides by -2
[tex]\frac{-2x}{-2} = \frac{11}{-2}[/tex]
[tex]x = -\frac{11}{2}[/tex]
[tex]x = -5\frac{1}{2}[/tex]
The company Apple is worth approximately 8×10^9 dollars. The company Jackson Avenue Coffee is worth approximately 2×10^5 dollars. How many times bigger is Apple's worth than Jackson Coffee's worth?
Answer:
35
Step-by-step explanation:
answers r
268
201
151
67
67in³
Answer:
we have
volume of sphere =4/3 πr³=1/3×π×4³=67.02=67in³ is your answer.
Newton's law of gravitation state that the force F of attraction between two bodies varies jointly as their masses M1 and M2 and inversely as the square of the distance between them. Two bodies whose centers are 500mi apart attract each other with a force of 15lb.What will be the force of attraction if their masses were tripled and the distance between their centers doubled?
Please help no link as answers
Step-by-step explanation:
You can imagine this figure as a rectangle and cube
If you want volume of this irregular figure than you have to do it like this:
V(figure)= V(rectangle)+ V(cube)
V(figure)= a*b*c+ a³
V(figure)= 4*3*(I don't see dimension on the left)+ 3³
V(figure)=12*(I don't see dimension on the left)+ 27
And only you have to to do is to set this dimension which I can't see.
What is the measure of ABC?
I am not absolutely sure but it should be 310
Find the area of the semicircle
Answer:
25.13 m
Step-by-step explanation:
pi r²÷2
pi 4²÷2=25.13
PLS HELP!!!
Find x M 13 P х 18° R .02 40 42.07 4.22
just add them up EZZZZZZZZZZZ
24 is what percent of 400?
Answer:
The answer is 6%
Answer:
6%
Step-by-step explanation:
tell me if I’m wrong lol
How to solve systems of inequalities
Answer:
Determine whether an ordered pair is a solution of a system of linear inequalities.
Solve a system of linear inequalities by graphing
Solve applications of systems of inequalities
You can use desmos
Step-by-step explanation:
Graph x>2 on a number line.
Solve the inequality 2a<5a+12.
Determine whether the ordered pair \left(3,\frac{1}{2}\right) is a solution to the system \left\{\begin{array}{c}x+2y=4\hfill \\ y=6x\hfill \end{array}.
Determine Whether an Ordered Pair is a Solution of a System of Linear Inequalities
The definition of a system of linear inequalities is very similar to the definition of a system of linear equations.
System of Linear Inequalities
Two or more linear inequalities grouped together form a system of linear inequalities.
A system of linear inequalities looks like a system of linear equations, but it has inequalities instead of equations. A system of two linear inequalities is shown below.
\left\{\begin{array}{c}x+4y\ge 10\hfill \\ 3x-2y<12\hfill \end{array}
To solve a system of linear inequalities, we will find values of the variables that are solutions to both inequalities. We solve the system by using the graphs of each inequality and show the solution as a graph. We will find the region on the plane that contains all ordered pairs \left(x,y\right) that make both inequalities true.
Solutions of a System of Linear Inequalities
Solutions of a system of linear inequalities are the values of the variables that make all the inequalities true.
The solution of a system of linear inequalities is shown as a shaded region in the x-y coordinate system that includes all the points whose ordered pairs make the inequalities true.
To determine if an ordered pair is a solution to a system of two inequalities, we substitute the values of the variables into each inequality. If the ordered pair makes both inequalities true, it is a solution to the system. s
Solve for x.
please help real quick
Answer:
(7/2, 0)
Step-by-step explanation:
Answer:
x=11
Step-by-step explanation:
6x-21=45
6x=66
x=11
which of the following is a exponential function ?
Three friends were helping to push a car. If all three are pushing equally hard and the net force is 600N, how hard is each one pushing the car?
Answer:
One person is pushing the car in the net force of 200N
Step-by-step explanation:
600 divided by 3 (600 N in total, and 3 person pushing.)
Solve 8y - 9 = -3y + 2
Answer:
y=1
Step-by-step explanation:
8y-9=-3y+2
-2
8y-11=-3y
-8y
-11=-11y/-11
Answer:
y=1
Step-by-step explanation:
8y+3y=2+9
11y/11=11/11
y=1
Find the perimeter of this complex figure
Answer:
38
Step-by-step explanation:
9 + 10 + 2 + 6 + (9 - 2) + (10 - 6) = 38
Which equation does this model represent
Answer:
G.
Step-by-step explanation:
5 + (-9) = -4.
. .
. .....
In triangle ABC, B = 120°, a = 10, c = 18
Find angle C
choices
A. 40°
B. 50°
C. 45°
D. 20°
Answer:
kk
Step-by-step explanation:
Jayden went to the shop and bought and orange juice for $150 and a bun for $90 . He told the shopkeeper he didnt want any coins below $10.00 nor did he want any one hundred dollar notes.
Jaydens Change included?
Answer:
give 300 and get back 60?
Step-by-step explanation:
find m the in this screenshot
Answer:
[tex]x + x + 4 + 3x - 9 =90 \\ 5x = 95 \\ x = 19 \\ \\ gjh = 19 + 4 = 23[/tex]
Which of the following circumstances describes a proportional relationship?
Water flows from a hose into an empty 10 gallon bucket at a rate of 2 gallons per minute.
plumber is paid $50 per hour plus a $75 service charge.
The cost of renting a car is $45 for the first day and $20 per day for each additional day.
A student has $100 in a savings account and saves $5 per month for the next twelve months.
bStep-by-step explanation:
Is 9.90 greater than or lesser than 9.9
Answer:
it is equal too.
Step-by-step explanation:
Answer:
it is equal to
Step-by-step explanation: