Answer: Option B. exponential decay
Solution:
If initially the number of competitors is n
If the number of round is "r" and the number of competitors after "r" rounds is N(r)
1) After the first round (r=1), the number of competitors is:
N(r)=N(1) = n * 50% = n * 50/100 →N(r)=N(1)=n*0.5=n*0.5^1
2) After the second round (r=2), the number of competitors is:
N(r)=N(2) = N(1) * 50% = (0.5 n)*(50/100)=(0.5n)*(0.5)→N(r)=N(2)=n*0.5^2
3) After the third round (r=3), the number of competitors is:
N(r)=N(3)=N(2)*50%=(n*0.5^2)*(50/100)=(n*0.5^2)*(0.5)→N(r)=N(3)=n*0.5^3
Then:
For r=1→N(r)=N(1)=n*0.5^1
For r=2→N(r)=N(2)=n*0.5^2
For r=3→N(r)=N(3)=n*0.5^3
In general: N(r)=n*0.5^r
This is an exponential function because the independent variable "r" is in the exponent, and because the number of competitors (funcion N(r) )decrease with the number of rounds the type of relationship most appropiately models this situation is an exponential decay
The reduction by 50% of competitors each round in a chess tournament is modeled by an exponential decay relationship, not a linear decrease, as it depends on the current number of competitors.
The chess tournament with the number of competitors decreasing by 50% each round is best modeled by a exponential decay relationship. This is because with each round, the number of competitors is halved, which is a rate that depends on the current number of competitors. (A) linear decrease would imply a constant decrease irrespective of the current number of competitors, which is not the case here.
Exponential relationships can be represented by mathematical functions where the rate of change is proportional to the current value. In contrast to exponential growth, where the quantity increases at a rate proportional to its current value, exponential decay describes a situation where the quantity is reduced by a certain factor over equal successive periods.
Select a number for ⬜️ that will make a true comparison mark all that apply
lady. 703,209◽️
A. 702,309 B.703,029
C.703,209. D.703,290
E.730,029. F.730,209
The valid options that can fill the blank ⬜️ and make the comparison true for "lady. 703,209⬜️" are B (703,029), C (703,209), and F (730,209).
To determine which number can fill the blank ⬜️ and make the comparison true for "lady. 703,209⬜️," we need to look at the place values of each digit in the numbers provided. The comparison should be such that the digit in ⬜️ is greater than or equal to the corresponding digit in 703,209. Let's analyze the options:
A. 702,309: The digit in the hundreds place (⬜️) is smaller than in 703,209, so this option is not correct.
B. 703,029: The digit in the thousands place (⬜️) is the same as in 703,209, so this option could be correct.
C. 703,209: This is the same as the original number and satisfies the comparison, so it is a valid choice.
D. 703,290: The digit in the tens of thousands place (⬜️) is larger than in 703,209, so this option is not correct.
E. 730,029: The digit in the hundreds place (⬜️) is larger than in 703,209, but the other digits do not match, so this option is not correct.
F. 730,209: The digit in the hundreds place (⬜️) is larger than in 703,209, and the other digits match, so this option is also a valid choice.
The valid options are B (703,029), C (703,209), and F (730,209) as they satisfy the comparison.
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The sum of a number and five more than the number is 17. What is the number?
Answer should be six. Hope this helps :)
6 is the number of which sum of a number and five more than the number is 17.
What is a numerical expression?A numerical expression is in the form of numbers with their arithmetic operations the numbers can be variables and constants. We can form numerical expressions from statements, and from real-life situations also.
Assuming the number to be 'n' and the given statement the sum of a number and five more than the number is 17can be numerically expressed as,
n + (n + 5) = 17.
2n + 5 = 17.
2n = 12.
n = 6.
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The area of a rectangle is 48 square feet, If the perimeter is 32 feet, find the length and width of the rectangle
the length totals out to 12ft and the width totals out to 4ft.
To find the length and width of the rectangle, set up a system of equations using the given information. Solve for one variable in terms of the other using the equation for the area. Substitute the value of one variable into the equation for the perimeter. Solve the resulting quadratic equation to find the possible values for the width. Choose the appropriate positive value for width and find the corresponding length using the equation for the area.
Explanation:To find the length and width of the rectangle, we need to set up a system of equations using the given information. Let's represent the length as 'l' and the width as 'w'. We know that the area of a rectangle is given by the formula A = lw, and the perimeter is given by the formula P = 2(l + w).
Given that the area is 48 square feet and the perimeter is 32 feet, we can set up the following equations:
A = lw = 48P = 2(l + w) = 32From equation (1), we can solve for one variable in terms of the other. Let's solve for 'l':
l = 48/w
Now, substitute this value for 'l' in equation (2):
32 = 2(48/w + w)
Simplifying further:
16 = 48/w + w
Multiply both sides of the equation by 'w' to eliminate the fraction:
16w = 48 + w^2
Rearrange the equation:
w^2 + 16w - 48 = 0
Factoring the quadratic equation, we get:
(w + 8)(w - 6) = 0
Therefore, the possible values for 'w' are -8 and 6. Since width cannot be negative, we discard the -8 and conclude that the width is 6 feet.
To find the length, substitute the width value of 6 into equation (1):
l = 48/6 = 8 feet
Therefore, the length of the rectangle is 8 feet and the width is 6 feet.
how do you decide whick of two numbers is greater when both numbers are positive,both numbers ate negative, and one number is positive and one number is negative
Final answer:
To compare two numbers, understand that positive numbers are greater than negative ones, among positives or negatives, larger numerical values determine greatness, and among two negatives, those closer to zero are greater.
Explanation:
Comparing two numbers to decide which is greater involves understanding their signs and values. Here's how you can determine this:
If both numbers are positive, the one with the higher numerical value is greater. For example, between 3 and 5, 5 is greater because 3 < 5.If both numbers are negative, the one with the lower absolute value is greater because it is closer to zero. For example, between -4 and -2, -2 is greater because -4 < -2.If one number is positive and the other is negative, the positive number is always greater than the negative one. This is because positive numbers are always to the right of negative numbers on the number line, indicating they are greater.Remember, the key to comparing numbers is understanding the role of positive and negative signs and the numerical value of the numbers.
Solve 3a+4b=1-2c/d for c.
(Can you please show all your steps?)
Hello!
To solve for c, we will need to use SADMEP. SADMEP is strictly used to solve algebraic equations. It is an acronym for subtraction, addition, division, multiplication, exponents, and parentheses. There are some cases in which we need to divide or multiply before subtracting/adding terms, like in this problem. Our main goal is to isolate c.
3a + 4b = (1 - 2c)/d (multiply both sides by d)
d(3a + 4b) = 1 - 2c (subtract 1 from both sides)
d(3a + 4b) - 1 = 2c (divide both sides by 2)
d(3a + 4b)/2 - 1/2 = c
We can simplify still this equation.
(3ad + 4bd)2 - 1/2 = c (distribute d)
3ad/2 + 4bd/2 - 1/2 = c (divide 3ad and 4bd by 2)
3ad/2 + 2bd - 1/2 = c (simplify)
Therefore, c is equal to 3ad/2 + 2bd - 1/2.
Final answer:
c = -d(3a + 4b - 1)/2
Explanation:
To solve for c in the equation 3a+4b=1-2c/d, rearrange the terms to isolate c, multiply both sides by d to eliminate the fraction, and then divide by -2.
To solve 3a+4b=1-2c/d for c, we will isolate the variable c by following these algebraic steps:
First, we need to move all the terms involving c to one side of the equation. The equation should look like this:3a + 4b - 1 = -2c/dNext, multiply both sides by d to get rid of the fraction:d(3a + 4b - 1) = -2cFinally, divide both sides by -2 to solve for c:c = -d(3a + 4b - 1) / 2This is how we derive the expression for c in terms of a, b, and d.
(CO 4) Forty-nine percent of US teens have heard of a fax machine. You randomly select 12 US teens. Find the probability that the number of these selected teens that have heard of a fax machine is exactly six (first answer listed below). Find the probability that the number is more than 8 (second answer listed below).
Forty-nine percent of US teens have heard of a fax machine, then the probability that the teen has heard of a tax machine is p=0.49 and the probability that the tenn hasn't heard of a tax machine is q=1-p=1-0.49=0.51.
Use binomial distribution.
The probability that among 12 randomly selected teens exactly 6 have heard of a fax machine is
[tex]Pr(X=6)=C_{12}^6p^6q^{12-6}=\dfrac{12!}{6!(12-6)!}(0.49)^6(0.51)^6=\\\\\dfrac{6!\cdot 7\cdot 8\cdot 9\cdot 10\cdot 11\cdot 12}{6!\cdot 2\cdot 3\cdot 4\cdot 5\cdot 6}(0.49\cdot 0.51)^6=924\cdot (0.2499)^6\approx 0.22505.[/tex]
The probability that among 12 randomly selected teens more than 8 have heard of a fax machine is
[tex]Pr(X>8)=C_{12}^9p^9q^{12-9}+C_{12}^{10}p^{10}q^{12-10}+C_{12}^{11}p^{11}q^{12-11}+C_{12}^{12}p^{12}q^{12-12}=\\\\\dfrac{12!}{9!(12-9)!}(0.49)^9(0.51)^3+\dfrac{12!}{10!(12-10)!}(0.49)^{10}(0.51)^2+\dfrac{12!}{11!(12-11)!}(0.49)^{11}(0.51)^1+\dfrac{12!}{12!(12-12)!}(0.49)^{12}(0.51)^0=220\cdot (0.49)^9(0.51)^3+66\cdot (0.49)^{10}(0.51)^2+12(0.49)^{11}(0.51)^1+(0.49)^{12}\approx 0.0638.[/tex]
Solve for t.
−5t≥70
Help Please
A. is this answer to this question.
The value of inequality is t ≤ -14 which means t will have all value less then and equals to -14 In number line.
What is number line ?
Number line is virtual representation of numbers along with coordinates axis with number equally spaced with equal number of interval.
Here the given inequality is :
−5t ≥ 70
Now, to solve for t we divide both side by -5 :
−5t/-5 ≥ 70/-5
t ≤ -14
It should be noted that negative -5 reverse the inequality sign.
Therefore, the value of inequality is t ≤ -14 which means t will have all value less then and equals to -14 In number line.
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What is the prime factorization of 40? 2x3(4th power). 2(2nd power)x10. 2(third power)x5. 3(third power)x5.
40|2
20|2
10|2
5|5
1
[tex]40=2^3\cdot5[/tex]
Dario bakes a lasagna containing 2/3 pound of parmesan cheese, 5/4 pounds of ricotta cheese, and 4/3 pounds of mozzarella cheese. Dario cuts the lasagna into several equal slices, each containing exactly 1/4 pound of cheeses (of all types totalled). How many slices are there?
Dario could make 9 slices of lasagna with the provided amount of cheese, as each slice contains 1/4 pound of cheese and he has a total of roughly 2.33 pounds of cheese.
Explanation:To answer this question, we first need to calculate the total weight of the cheese used in the lasagna. This consists of 2/3 pound of parmesan cheese, 5/4 pounds of ricotta cheese, and 4/3 pounds of mozzarella cheese. To total these up, we convert them into fractions with a common denominator. Doing this, we find that, in total, 28/12 or approximately 2.33 pounds of cheese are used. As each slice of lasagna contains 1/4 pound of cheese, we can determine the total number of slices by dividing the total weight of the cheese by the weight of the cheese in each slice. This gives us: 2.33 ÷ 0.25 = 9.32. As we can't have a fractional number of slices, we round down to get 9 slices, which would be the amount of lasagna slices Dario could make with the provided amount of cheese.
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what is 0.79 as a percent
it is 79% hoped i helped
A rectangle has a perimeter of 144 inches. The width of the rectangle is 12 inches less than the length. What is the width, in inches, of the rectangle?
Answer:
30 inches
Step-by-step explanation:
width = 1/4 ( 144 - 2 * 12 )
The width of the rectangle is 30 inches.
What is the perimeter?The perimeter is defined as the sum of all the sides of the figure. For a rectangle, the perimeter will be defined as the sum of all the sides of the rectangle.
Given that a rectangle has a perimeter of 144 inches. The width of the rectangle is 12 inches less than the length.
Lenght = L
Width = L - 12
The perimeter is calculated by the formula below:-
P = 144 inches
2 ( L + W ) = 144
2 ( L + L - 12 ) = 144
4L - 24 = 144
4L = 168
L = 42 inches
The width will be calculated as:-
W = L - 12
W = 42 - 12
W = 30 inches
Therefore, the width of the rectangle is 30 inches.
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Windless Surfing Company’s marketing manager observes that if the price of designer windsocks is $40, then on average 70 windsocks are sold per month. Experience has shown that if the price is raised from $40, then for every $1 increase in price, two fewer windsocks are sold each month.
Answer:
The answer is x ≤ 50.
Step-by-step explanation:
As, A -70 = -2 (P -40)
A = -2P + 80 + 70
A = -2P + 150
Y = -2x + 150.
When y = 0,
Putting in the values
-2x = -150
x = 75.
-2x + 150 ≥ 50
-2x ≥ -100
x ≤ 50.
What is the equivalent fraction for 40/100
The equivalent fraction for 40/100 is 2/5.
Explanation:To find the equivalent fraction for 40/100, we can simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 20. When we divide 40 by 20, we get 2, and when we divide 100 by 20, we get 5. So, the equivalent fraction for 40/100 is 2/5.
The equivalent fraction for 40/100 is 2/5, which is obtained by dividing both the numerator and the denominator by their greatest common divisor, 20. In decimal form, 40/100 is 0.40, and as a percentage, it is 40%.
Explanation:To find the equivalent fraction for 40/100, we look for a common factor that both the numerator (40) and the denominator (100) share. In this case, the number 20 is a common factor of both. Dividing the numerator and the denominator by 20, we reduce 40/100 to its simplest form:
40 ÷ 20 = 2
100 ÷ 20 = 5
Therefore, the equivalent fraction for 40/100 is 2/5.
Additionally, converting a fraction to a decimal involves dividing the numerator by the denominator, so 40/100 converted to a decimal is 0.40.
To convert this decimal to a percentage, we multiply by 100, yielding 40%.
-1(2x +3) -2(2x-1) simplified
- 6x - 1
distribute parenthesis and collect like terms
- 2x - 3 - 4x + 2
= (- 2x - 4x) + (-3 + 2) = - 6x - 1
write an expression to represent the perimeter of:
"Perimeter" is the distance all the way around the drawing. If the drawing has sides, then the perimeter is the SUM of the lengths of all the sides. It's exactly the distance an ant would have to walk along the line, to get all the way around to where he started from.
To get the perimeter of the triangle, you have to add up the lengths of the three sides.
(2a - 3) + (2a) + (3a + 1) =
2a - 3 + 2a + 3a + 1 .
Add up all the 'a's: 2a + 2a + 3a = 7a
Add up all the just plain numbers: -3 + 1 = -2
Write them together, as a binomial: 7a - 2
THAT's your expression for the perimeter.
The perimeter of a shape is the distance around it. For a rectangle, the perimeter can be represented by the expression '2(length + width)', which can also be written as '2(L + W)' when L is the length and W is the width.
Explanation:Perimeter refers to the distance around a two-dimensional shape. Since the shape isn't specified in the question, let's assume a rectangle for our example. The perimeter of a rectangle is given by the formula '2(length + width)'. This means, you add the length and width of the rectangle together, and then multiply by 2. If we let L represent the length and W represent the width, then our expression for the perimeter of a rectangle would be '2(L + W)'.
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In a recent year a baseball team paid two times as much to their ace pitcher as they paid to their shortstop. If they paid $21 million for the two salaries, what did they pay each player?
The ace pitcher was paid $14 million and the shortstop was paid $7 million.
Explanation:In order to solve this problem, we can set up a system of equations. Let's say the salary of the ace pitcher is x million dollars and the salary of the shortstop is y million dollars. We are given that the ace pitcher was paid twice as much as the shortstop, so we can set up the equation x = 2y.
We also know that the total salaries paid were $21 million, so we can set up the equation
x + y = 21.
Using the first equation, we can substitute 2y for x in the second equation to get 2y + y = 21, which simplifies to 3y = 21. Dividing both sides by 3, we find that y = 7 million.
Substituting this value back into the first equation, we find that x = 2(7) = 14 million.
Therefore, the ace pitcher was paid $14 million and the shortstop was paid $7 million.
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Determine the domain of the function h(x)=9x/x(x^2-49)
Final answer:
The domain of the function h(x)=9x/x(x²-49) is all real numbers except for x = 0, x = -7, and x = 7, where the function is undefined due to division by zero. There are no additional nondifferentiable points within the domain, as the nondifferentiable points coincide with the excluded values.
Explanation:
To determine the domain of the function h(x)=9x/x(x^2-49), we need to identify all values of x for which the function is defined. Since this is a rational function, the function will be undefined where the denominator is zero. Thus, we set up the equation x(x² - 49) = 0 and solve for x.
First, factor the quadratic expression: x(x + 7)(x - 7) = 0. The solutions of this equation are x = 0, x = -7, and x = 7, which are the points where the function will be undefined.
Therefore, the domain of the function h(x) is all real numbers x except for x = 0, x = -7, and x = 7. These are the excluded values from the domain because they make the denominator equal to zero, which would result in division by zero.
Nondifferentiable Points
Aside from the excluded values, there may also be nondifferentiable points within the domain where the derivative does not exist or is not continuous. However, since all nondifferentiable points in this case coincide with the excluded values (the points where the denominator is zero), there will be no additional nondifferentiable points within the domain of the function.
Lakshmi donates 20% percent of her income to charity.
What fraction of her income does Lakshmi donate to charity?
Just put 20 over 100 and simplify. The answer is 1/5.
The fraction of Lakshmi's income that is donated to charity is [tex]\frac{1}{5}[/tex].
Given the following data:
Percentage of donation = 20%To find what fraction of Lakshmi's income is donated to charity:
In this exercise, you're required to determine the fraction of Lakshmi's income that is being donated to charity.
Hence, we would express the given percentage as a fraction.
[tex]Percent = \frac{20}{100}[/tex]
Next, we would simplify the fraction by dividing by 20:
[tex]Fraction = \frac{1}{5}[/tex]
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Complete the ratio table below to show ratios equivalent to 4:18.
A jet ski rental company charges a $100 rental fee, plus $20 per hour. Write and dole an equation to determine how many hours you can rent the jet ski for it if you have a budget of $175.
Solve the word problem
3 hours because if u have 175 dollers and u spend 100 so now u have 75. 75 -20 is 55. then 55 - 20 is 35. then 35 - 20 is 15 so then you have 15 dollers to spare. so 3
You can represent this problem as a linear equation 100 + 20x = 175. Solving for x gives you 3.75, hence with $175, you can rent the jet ski for 3.75 hours.
Explanation:To solve this problem, you need to set up a linear equation. Let's represent the number of hours of the jet ski rental as x. The jet ski rental company charges a $100 rental fee plus $20 per hour, so we can write this as a equation: 100 + 20x = 175.
Next, we need to solve for x. First, subtract 100 from each side of the equation, you obtain 20x = 75. Then, divide each side by 20 to solve for x. You'll find that x = 3.75. Therefore, with $175, you can rent the jet ski for 3.75 hours.
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What is the value of k?
Answer:
k=2
Step-by-step explanation:
We have got a right triangle LNO with sides = m,4 and 8
By Pythagorean theorem
m^2=4^2 +8^2
Or m^2 = 80 ... i
IN triangle NOM, 4^2 +k^2 = l^2
i.e. 16+k^2 = l^2... i
In triangle LNM, m^2+l^2 = (8+k)^2
Substitute for m^2 as 80,
i.e. 80+l^2 = 64+k^2 +16k ... iii
From i, l^2 = 16+k^2
Substitute in iii
80+16+k^2 = 64+k^2 +16k
16k = 32 or k =2
eight is greater than or equal to the sum of a number and 3
an $1000 investment is made in a trust fund that pays 12% compounded monthly. how long will it take the investment to double?
Plz anyone help I don't understand this
Simplify: (–6) • (7) – (6) • (–2)
You must perform a subtraction between the result of two multiplications. In fact, since multiplications have a higher priority than subtraction, you must perform them first. Also, remember that a positive times a negative is a negative.
So, you must perform the operations in this order:
[tex] [-6\cdot 7]-[6\cdot(-2)] = [-42]-[-12] = -42+12 = -30 [/tex]
In the past two weeks, Sue earned $513 at her part-time job. She worked a total of 54 hours. About how much did Sue earn per hour?
I think the answer you're looking for is $9.50.
513 / 54 = 9.5
Sue made $9.50 an hour.
What main challenges did early colonists at Jamestown face? Select all that apply.
A) disease
B) lack of land
C) religious conflict
D) low food supply
Fernando bought 8 pints of milk. how many fluid ounces of milk Fernando buy?
128 fluid ounces of milk
1 pint equals to 16 ounces.
(16 x 8) = 128 ounces. :)
an art teacher has one and a half pounds of red clay and 3/4 pounds of the yellow clay the teacher mixes the red play and yellow clay together each student in the class needs one eight pounds of the clay mixture to finish the assigned art project for the class how many students can get enough clay to finish the project
the teacher has 2 1/4 pounds of clay so none of the students have enough
Which numbers are greater then 4.16
theres no option...so really any number going up frome 4.16= 104/25 as a fraction
evaluate each expression for the given values of the variables 5X + 2Y^2-Y^3; x = 2 and y=4
what are they wanting me to reflect?
We are given the expression:
[tex]5x+2y^{2}-y^{3}[/tex]
Now we have to determine the value of this expression at x=2 and y=4.
So let us plug the values of x and y in the expression:
[tex]5(2)+2(4)^{2}-(4)^{3}[/tex]
[tex]=10+32-64[/tex]
=-22
So on plugging x=2 and y=4 in the given expression we get the value as -22
Answer : [tex]5x+2y^{2}-y^{3}[/tex]=-22