A huge Ping-Pong tournament is held in Beijing with 65,536 participants at the start of the tournament. Each round of
the tournament eliminates half the participants.
a.
If p(r) represents the number of participants remaining after r rounds of play, write a formula to model the
number of participants remaining.
Answers
Answer:
[tex]P(r)=65536(\frac{1}{2})^{r}[/tex]
Step-by-step explanation:
Since the total number of participants in the tournament is 65,536 people, and the exponential decay is [tex]\frac{1}{2}[/tex], using [tex]P(r)[/tex] as the representative of the number of people after [tex]r[/tex] rounds, the formula to represent the model would be [tex]P(r)=65536(\frac{1}{2})^{r}[/tex].
Answer:
[tex]p_r = 65\ 536 \div 2^r = 65\ 536 \div 2^-^r = 2^{16-r}; r\ \in \{0,1,2,3...16\}[/tex]
Step-by-step explanation:
Pet peeve of mine: let's call it [tex]p_r[/tex] (read p sub r)since it's a representation over the natural numbers and not over [tex]\mathbb{R}[/tex].
Old man yelling at clouds moment gone, we know that the number of people gets halved every time so
At round 0, we do not halve, so [tex]p_0 = 65\ 536\div 1[/tex]
At round 1, we halve once, so [tex]p_1 = 65\ 536\div 2[/tex]
At round 2, we halve twice, so [tex]p_2 = 65\ 536\div 4 = 65\ 536\div 2^2[/tex]
At round 3, we halve three times, so [tex]p_3 = 65\ 536\div 8 = 65\ 536\div 2^3[/tex]
...
At round k, we halved k times, so [tex]p_k = 65\ 536 \div 2^k[/tex]
...
At round 16 we [tex]2^1^6 =65\ 536[/tex] so we have a winner.
That allows us to write a formula. I personally find the last one to be the neater, but any of the three is formally correct.
[tex]p_r = 65\ 536 \div 2^r = 65\ 536 \div 2^-^r = 2^{16-r}; r\ \in \{0,1,2,3...16\}[/tex]
Related Questions
HELP PLEASE. Check picture. I have tried but cannot seem to get it.
Answers
Answer:
[tex]884^{-7}[/tex]
Step-by-step explanation:
Start by simplifying the denominator of the fraction. When multiplying exponents of the same base, you can add the exponents. This is also known as the product rule.
[tex]a^x\cdot a^y=a^{x+y}[/tex]
["a" is the base, and "x" and "y" are the exponents]
Using this we find...
[tex]884^{58}\cdot884^{46}=884^{58+46}=884^{104}[/tex]
When dividing exponents of the same base, you can subtract the exponents. This is also knows as the quotient rule.
[tex]a^x\div a^y=a^{x-y}[/tex]
Using this we find...
[tex]\frac{884^{97}}{884^{104}}=884^{97-104}=884^{-7}[/tex]
Answer:
[tex]884^{-7[/tex]
Step-by-step explanation:
≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡
Before we begin solving, let's review a few rules of exponents.
If an exponent is multiplying with another exponent and their bases are the same, you can simply add the exponents.If an exponent is dividing with another exponent and their bases are the same, you can simply subtract the exponents.≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡
⇒ [tex]\dfrac{884^{97} }{884^{58} \times 884^{46} }[/tex]⇒ [tex]\dfrac{884^{97} }{884^{58 + 46}}[/tex] [#1]⇒ [tex]\dfrac{884^{97} }{884^{104}}[/tex]⇒ [tex]884^{97 - 104[/tex] [#2]⇒ [tex]\boxed{884^{-7}}[/tex]≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡
Solve each inequality.
X+5 < 6
Pls help
Answers
Answer:
x<1
Step-by-step explanation:
You would just subtract 5 from both sides of the equation. The sign does not flip because you are not multiplying or dividing any negative number across the sign. So simply x+5 (-5) < 6 (-5). On the left side the 5 would cancel out. on the other side 6-5 is equal to 1.
Answer: x<1
Answer: x < 1
Step-by-step explanation: x + 5 < 6
Subtract 5 from both sides,
x < 1
I just need 13⅗% as a decimal please thanks
Answers
the answer to 13 3/5% as a decimal
0.136
What is the rule and how do you find n? 100 points and brainliest to answer!
Answers
Answer:
n = 6
Step-by-step explanation:
Let's convert the x and y values into (x,y) form.
(x, y) ⇒ (3, 5), (4, 7), (n, 11), (8, 15)
Now, let's find the rule in slope intercept form. To find the equation in slope intercept form, pick any two points. Then find the slope of the line.
⇒ (3, 5) and (4, 7)
Now, find the slope using the slope formula.
[tex]\dfrac{y_{2} - y_1}{x_2 - x_1} = \text{Slope}[/tex]
[tex]\rightarrow \dfrac{7 - 5}{4 - 3} = \text{Slope}[/tex]
[tex]\rightarrow \dfrac{2}{1} = 2 =\text{Slope}[/tex]
Now, let's use point slope form to find the equation in slope intercept form.
[tex]y - 5 = 2(x - 3)[/tex]
[tex]\rightarrow y - 5 = 2x - 6[/tex]
[tex]\rightarrow y = 2x - 1 \ \ \ \ \ (\text{Rule})[/tex]
Now, substitute the value of y into the equation.
[tex]11 = 2x - 1[/tex]
[tex]\rightarrow 12 = 2x[/tex]
[tex]\rightarrow \boxed{x = n = 6}[/tex]
Take two points find equation
(3,5)(4,7)Slope:-
m=7-5/4-3=2Equation in point slope form
y-5=2(x-3)y=2x-6+5y=2x-1Now put n
11=2n-12n=12n=6The ratio of red candy to green candy in a bag is 3 to 4
If there were 36 pieces of green candy in the bag, how many pieces of candy in the bag were red?
Answers
Answer:
27
Step-by-step explanation:
we know that 4 multiplied with something is 36
=> 4x = 36
=> x = 36/4
=> x = 9
so we have to multiply 3 with 9
=> 3*9 = 27
What is the most common amount of hours students spent studying? (2 points)
A line plot with the title, time students spent studying, and the line is measured in hours. The horizontal line goes from one third to three. In between, there are seven tick marks labeled as two thirds, one, one and one third, one and two thirds, two, two and one third, two and two thirds. The tick mark one third has two xs, the tick mark two thirds has one x, the tick mark one has four xs, the tick mark one and one third has three xs, the tick mark one and two thirds has three xs, the tick mark two has five xs, the tick mark two and one third has three xs, the tick mark two and two thirds has two xs, and the tick mark three has two xs.
a
1 hour
b
one and one third hours
c
2 hours
d
3 hours
Answers
Joe drove 567 miles in 9 hours.
At the same rate, how many miles would he drive in 5 hours
Answers
Answer:
answer down below
Step-by-step explanation:
it would be 315
Answer:
13 hours
Step-by-step explanation:
567/9=63
she drives 63mph
it will take her 13 hours to drive
20 = (-10) = (-20) +10
1) Is the equation up there true or false?
2) Support your decision below.
Help quick
Answers
Answer:
No, 20 ≠ -10
Step-by-step explanation:
20 = (-10) = (-20)+10
20≠-10=-20+10
20≠-10=-10
Two numbers have a sum of 1,212 and a difference of 518. What are the two numbers?
Answers
Answer:
347 and 865
Step-by-step explanation:
Let the two number be x and y
Therefore, from the given information:
x + y = 1212
x - y = 518
Rewrite both equations to make x the subject:
x = 1212 - y
x = 518 + y
Equate equations and solve for y:
1212 - y = 518 + y
694 = 2y
y = 347
Substitute found value of y into one of the equations and solve for x:
x = 518 + 347
x = 865
Therefore, the two numbers are 347 and 865
André paid a $65 annual fee to register with a car rental company. The company charges $8.50 for each hour a car is rented. What is the rate of change of the function that represents André's cost for renting a car over the course of a year?
A. $8.50 per hour
B. $65 per year
C. $73.50 per hour
D. $73.50 per year
Answers
Answer:
I dont know if this is the right answer, but my best guess is that it is A.
Step-by-step explanation:
The rate of change of the function that represents André's cost for renting a car over the course of a year $8.50 per hour.
What is the rate of change?
The rate of change is the cost by which the cost of renting the car increases by. The cost of renting the car increases by $8.50 per hour.
The annual fee can be described as the fixed cost of renting the car per year.
To learn more about fixed cost, please check: https://brainly.com/question/25879561
Find M angle B.
Round to the nearest degree.
Answers
Answer: 41
Step-by-step explanation:
Which equation represents the data in the table?
Answers
Answer:
c
Step-by-step explanation:
It all adds up. Ex; 2*2=4 4-3=1
and continues through the rest of the table
The circumference of a circle is 43.96 yards. What is the circle's radius?
Answers
Answer:
Step-by-step explanation:
Radius = circumference / 2π
= 43.96 / 2π
= 7.00 yards to the nearest hundredth.
Help me, please! It's all in the question...!
Answers
Answer:
the answer is the first one
Step-by-step explanation:
because
Answer
c hope it helps
Answer the questions in the image.
Answers
#1
Radius=9/2=4.5inArea:-
πr²4.5^2π20.25πin^263.58in^2#2
Side=a=4inArea:-
a²4²16in^2#3
Area of the white part=Area of circle-Area of square
63.585-1647.585in^2#4
Probability
16/63.5850.252#5
Probability
47.58/63.5850.75Answer:
1. 63.62 in².
2. 16 in².
3. 47.62 in².
4. 0.25 .
5. 0.74 .
Step-by-step explanation:
1.
Solution,
Given,
Diameter = 9 inch.
Now,
Area = πr²
Diameter = r²
Then,
Area = 1/4 πd²
= 1/4 π9²
= 63.62 in².
2.
Solution,
Given,
Length of a Side = 4 inch.
Now,
Area = L²
= 4²
= 16 in².
3.
Solution,
Given,
Area of the Circle = 63.62 in².
Area of the Square = 16 in².
Now,
Area of The White Part of the Circle = Area of Circle - Area of Square
= 63.62 in² - 16 in².
= 47.62 in².
4.
Solution,
Given,
Area of the Square = 16 in².
Area of the Circle = 63.62 in².
Now,
The probability of landing in the Square = Square Area / Circle Area
= 16 / 63.62
= 0.25 .
5.
Solution,
Given,
White Part of the Circle = 47.62 in².
Area of the Circle = 63.62 in².
Now,
The probability of landing in the white Part = White Area / Circle Area.
= 47.62 / 63.62
= 0.74 .
You decide to put $2,000 in a savings account to save for a $3,000 down payment on a new car. If the account has an interest rate of 4% per year and is compounded monthly,
how long does it take until you have $3.000 without depositing any additional funds?
Answers
Answer:
12.5 years = 216 months
Step-by-step explanation:
4% of 2000= $80
1000/80=12.5
It will take 12.5 years to make $1000 on its own without adding additonal funds.
I am so confused. Help.
Answers
[tex]\large\sf\underline{ANSWER:}[/tex]
√3
x is the length of the third side
x²+1² = 2² { Pythagorean Theorem}
x²+1 = 4 {Simplify}
x²=3 {Subtract 1 from each side}
x=√3 {Take the square root of each side}
The Length of the third side is √3
#[tex]\large\sf\underline{CarryOnLearning}[/tex]
help please? with a working out would be nice
Answers
Answer:
280 cups total.
Step-by-step explanation:
Tricky. The explanation and answers are on attached images.
The value 3pie/16 is a solution for the equation 2cos^2(4x)-1=0 true or false
Answers
Answer:
This is true
Step-by-step explanation:
The Hire Purchase priceola microwave
a deposit of $600 and equal monthly
installmentsof$4s. Howmany installmen,
Answers
Answer:
150
Step-by-step explanation:
$600/$4 =150
=150 installments
factor 1/2 out of 1/2x + 9/2
Answers
Answer:
Equation would be x + 9/2.Step-by-step explanation:
Factoring out means taking out a Number, or an unknown quantity.
So, Factor out 1/2:
New equation with old step by step:
Step 1:
Remove 1/2 from 1/2x + 9/2Step 2:
Equation should be: x + 9/2.New equation:
x + 9/2Given the function g(x)=√x+4, which of the following values cannot be the domain of g?
A. X=1
B. X=2
C. X=12
D. X=-5
Answers
Answer:
D. x = -5
Step-by-step explanation:
The square root function is only defined for non-negative arguments. For the function ...
[tex]g(x)=\sqrt{x+4}[/tex]
this means we must have ...
x +4 ≥ 0
x ≥ -4 . . . . . . subtract 4 from both sides
All of the numbers on your answer choice list are more than -4 except -5.
x = -5 is not in the domain of g(x)
please no guessing (WILL GIVE BRAINILIST)
STATISTICS
Answers
Answer:
#2 mean is 90.3846154 and range is 40
#3 mean 91.9230769 and range is 20
(you might have mixed the second and third graph up)
Step-by-step explanation:
Please guys help me , i need help with this math work im not doing so good un math
Answers
Answer: If you need help on both here are both answers.... Answer 1- f(x)=6.50x+48.00 because Let
x ----> the number of adult tickets
f(x) ----> amount of money collected
To find the amount collected multiply the number of adult tickets by the cost and multiply the number of student tickets by the cost, and then sum the two quantities
The linear equation that represents this problem is
f(x)=6.50x+4.00(12)
f(x)=6.50x+48.00
and for Answer 2- Is 4
Farm workers plant 980 beans in 35 rows. How many beans do they plant in one row
Answers
Can someone help me with math I need help I will attempt to give y’all help too!
Answers
Answer:
48%
Step-by-step explanation:
there are 250 cars in total 50+70 is 120 (the red or blue cars)
so there are 120 "yes" out of 250 total of 120 divided by 250 equal 0.48 or 48%
Karen has just baked 17 cookies. She wants to put them in paper bags in groups of 6. How many groups of 6can she make ? How many cookies will she have remaining ?
Answers
Answer:
She can make 2 groups of six, with five cookies remaining
Step-by-step explanation:
First, divide 17 by 6 to get 2 5/6. The whole number is the number of groups she can make, and the fraction is how many are left over. She can make two groups, with five left over.
Hopefully this helps - let me know if you have any questions!
Answer:
2 groups with 5 left over.
Step-by-step explanation:
to solve, take 17 and divide it by 2. since we only have 17 cookies, we round down no matter what. to get the left over, multiply 2 by 6, then subtract by 17.
please mark as brainlest.
Lisa is checking out at the bookstore. Each book (b) costs $1.50 and she has a $5 off coupon she can use. She wants to spend $25 or less in the bookstore. How many books can Lisa buy?
Answers
Answer:
20
Step-by-step explanation:
Given:
Lisa is checking out at the bookstore.
Each book (b) costs $1.50 and she has a $5 off coupon she can use.
She wants to spend $25 or less in the bookstore.
Solve:
Since there is a $5 off coupon..
$1.5b - $5.00<=$25.00
$1.5b<= $30.00
$1.5b/1.5 = $30.00/1.5
b=20
Lisa can buy 20 book.
~lenvy~
Find x 20 and 15 geometric mean
Answers
Answer: 17.320508075689
Step-by-step explanation:
Find the value of x.
A. 53°
B. 72°
C. 39°
D. 48°
Answers
Answer: 53
Step-by-step explanation: