There are an infinite number of equations that are equivalent to 4, as any equation that simplifies to 4 is equivalent. Here are a few examples:
2 + 2 = 4
8 - 4 = 4
2 * 2 = 4
16 / 4 = 4
Equations that are equivalent to 4 can take many different forms and involve different mathematical operations. The common thread among them is that they all simplify to the value of 4.
For example, 2 + 2 and 8 - 4 both simplify to 4 by addition and subtraction, respectively. Similarly, 2 * 2 and 16 / 4 both simplify to 4 by multiplication and division, respectively. It's important to note that while these equations are all equivalent to 4, they are not interchangeable in all contexts.
The specific equation used may depend on the context and the mathematical operations involved.
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What is an estimate of the coordinates of the solution of the system to the nearest tenth?
Answer:
Look at the solution to your other similar question and see if you can figure this one out now.
Step-by-step explanation:
How many answers are there to a system of equations?.
A system of equations is a set of two or more equations with two or more variables. The number of solutions to a system of equations depends on the number of equations and the number of variables.
A system of equations can have one unique solution if the equations are consistent and independent. This means that there is one specific set of values that makes all equations true.A system of equations can have infinitely many solutions if the equations are consistent and dependent. This means that there are infinitely many sets of values that make all equations true. This is usually represented by a line or a plane in the case of systems of 2 or 3 equations with 2 or 3 variables.A system of equations can have no solution if the equations are inconsistent. This means that there are no values that can be assigned to the variables that make all equations true.It's important to note that the number of solutions is not determined by the number of equations, but by the relationship between the equations and the variables.
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hepla helpa! I REQUEST HELPA!
The point of intersection with the set of system of equations are:
For y = -2x - 3, y = 2x - 1 : point Z
For y = x + 4, y = -x + 2 : point X
For y = -2x - 3, y = x + 4 : point W
For y = 2x - 1, y = -x + 2 : point Y
In this question we have been given a graph of four lines.
y = -x + 2
y = x + 4
y = 2x - 1
y = -2x - 3
We need to match each point of intersection with the set of system of equations whose solution is at that point.
From the graph we can observe that the points X and W lie on the line y = x + 4
Points W and Z lie on the line y = -2x - 3
Points Y and Z lie on the line y = 2x - 1
Points X and Y lie on the line y = -x + 2
Therefore, the point of intersection with the set of system of equations are:
For y = -2x - 3, y = 2x - 1 : point Z
For y = x + 4, y = -x + 2 : point X
For y = -2x - 3, y = x + 4 : point W
For y = 2x - 1, y = -x + 2 : point Y
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WILL MARK BRAINLIEST!
Answer:
\(vt = \sqrt{ {20}^{2} + {17}^{2} } \\ = \sqrt{400 + 289 } \\ = \sqrt{689} \\ vw = \sqrt{ {vt}^{2} + {tw}^{2} } \\ = \sqrt{689 + {20}^{2} } \\ = \sqrt{1089} = 33 \\ \)
If f(x) = 4x + 2 and g(x) = x2 + 7, find each value:
1. f(4)
2. f(-2)
hellllppppp me please
9514 1404 393
Answer:
positive infinitynegative infinityStep-by-step explanation:
The function has a positive leading coefficient (1/3) and is of odd degree (3). These conditions mean the sign of the end behavior of the function will match the sign of x.
x → ∞, m(x) → ∞
x → -∞, m(x) → -∞
It costs c dollars each to manufacture and distribute backpacks. If the backpacks sell at x dollars each, the number sold is given by n = a/(x-c) + b(95-x), where a and b are positive constants. What selling price will bring a maximum profit? Express the total profit P in terms of X. P(x) The selling price that will maximize profit is $
The total profit P in terms of x can be expressed as
P(x) = (a - c) (a/(x-c) + b(95-x))
The selling price that will maximize profit is the positive constant, a in dollars.
To find the selling price that will bring a maximum profit, we need to find the derivative of the profit function P(x) and set it equal to 0.
The profit function P(x) is given by P(x) = nx - nc,
where n is the number of backpacks sold and c is the cost to manufacture and distribute each backpack.
Substituting the given expression for n into the profit function gives:
P(x) = (a/(x-c) + b(95-x))x - c(a/(x-c) + b(95-x))
P(x) = (a - c) (a/(x-c) + b(95-x))
To find the selling price that will maximize profit, we need to find the critical points of P(x) by taking the derivative of P(x) with respect to x and setting it equal to 0:
P'(x) = (a - c) (-a/(x - c)² - b) = 0
Thus P'(x) = 0 at c = a or (x - c)² = -a/ b
a and b are positive constants, so -a/ b is negative but (x - c)² is never negative, so it is not a possible solution.
So only solution is c = a, that is for maximum profit selling price, c should be equal to the positive constant, a.
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PLEASE ANSWER!!!! 20 POINTS
--
Find the mean x of the data 16, 31, 38, 24, 36
Answer:
Find the mean x of the data 16, 31, 38, 24, 36
16 + 31 + 38 + 24 + 36
= 145
145 ÷ 5
= 29Step-by-step explanation:
You're welcome.
The change in the total amount of Suki's allowance balance over the course of four weeks is shown in the table.
Week Change ($)
1 25.25
2 ─5.75
3 12.40
4 ─14.35
Based on the average change in her allowance balance per week, how much money can Suki expect to save or spend over the course of a year?
Answer:
To get the average you add all numbers up then divide by the amount of numbers you have. In case it's 4 then you get your average dollar amount then you can calculate the amount for the years by multiplying it by 52 because there is 52 weeks in a year.
i need help with finding out both of the answers to these questions.
Answer:
6). unknown side is 6.23m
7). angle is 26.58 degrees
Step-by-step explanation:
you must use the Pythagoras theorem formula to find the unknown side if you have only two sides
please help the first one to answer gets a crown and it has to be right (50 pts)
The slope of the linear equation y=2/3x-1 is 2/3 and the y-intercept is -1.The slope of a line is the ratio of the change in the y-coordinate to the change in the x-coordinate as you move from one point on the line to another. In this case, if you move one unit to the right, the y-coordinate changes by 2/3 units.The y-intercept is the point where the line crosses the y-axis. In this case, the line crosses the y-axis at the point (0, -1).You can also find the slope and y-intercept by using the slope-intercept form of the equation of a line, which is y=mx+b. In this case, m is the slope and b is the y-intercept.
So, the slope is 2/3 and the y-intercept is -1.
Answer:
B. Slope=⅔, y-intercept =(0,-1)
Step-by-step explanation:
We have
y=⅔*x-1
let's compare this equation with y=mx+c
where
m is slope and c is y intercept.
While comparing
we get
m=⅔
c=-1
Therefore, Slope=⅔
and y intercept= -1
In y-intercept x is 0.
The y-intercept is the point where the line crosses the y-axis. In this case, the line crosses the y-axis at the point (0, -1).
2y – 9x = 4
......................
Answer:
y=9/2x+2
Step-by-step explanation:
Answer:
x=2/9y + -4/9
Step-by-step explanation:
Solve for x:
2y−9x=4
Add -2y to both sides:
−9x+2y+−2y=4+−2y
−9x=−2y+4
Divide both sides by -9:
−9x /−9 =−2y+4 /-9
Then your answer is:
x= 2 /9 y+ −4/ 9
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Hope I helped!
Good luck! :)
In a​ raffle, 1,000 tickets are sold for​ $2 each. One ticket will be randomly selected and the winner will receive a laptop computer valued at​ $1200. What is the expected value for a person that buys one​ ticket?
The expected value for a person who buys one raffle ticket is -$0.60.
To calculate the expected value, we multiply the probability of each outcome by its respective value and sum them. In this case, there is a 1 in 1,000 chance of winning the laptop computer valued at $1,200, and a 999 in 1,000 chance of not winning anything. Therefore, the expected value can be calculated as follows:
Expected Value = (Probability of Winning * Value of Winning) + (Probability of Not Winning * Value of Not Winning)
= (1/1,000 * $1,200) + (999/1,000 * -$2)
= $1.20 - $1.998
= -$0.60
The negative value indicates that, on average, a person who buys one ticket can expect to lose $0.60. This means that, over multiple repetitions of the raffle, the person would, on average, end up with a net loss of $0.60 per ticket.
It's important to note that expected value represents the average outcome and does not guarantee the actual outcome for an individual. Some individuals may win the laptop, while others may win nothing. The expected value simply provides a measure of the average gain or loss across many trials.
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YALLL HELPP ME PLEASEE!!!!!!!!
Step-by-step explanation:
1. -5 not suree
2.50
my anwser could be wrong sooo...
what are the 10 branches of mathematics
Answer:
Pure Mathematics:
Number Theory
Algebra
Geometry
Arithmetic
Combinatorics
Topology
Mathematical Analysis
Applied Mathematics:
Calculus
Statistics and Probability
Set Theory
Trigonometry
Step-by-step explanation:
Bruh i found 11 when i googled it so idk
Answer:
Foundations.
Number Theory.
Algebra.
Combinatorics.
Geometry.
Topology.
Mathematical Analysis.
Probability and statistics.
Step-by-step explanation: There is also 2 more
The following table shows actual sales values for the last 4 years. Using a moving average of length 3, calculate the forecast for year 5 (leave in 1000's units).
Sales (1000's Units)
68
45
60
72
The forecast for year 5 is 45,000 units.
A forecast refers to an estimation or prediction of a future event or value based on available data or information. It is used to anticipate or project what may happen in the future.
In the context of business and sales, a sales forecast is an estimate of future sales based on historical data, market trends, and other relevant factors. It helps businesses plan and make informed decisions regarding production, inventory, marketing, and resource allocation.
To calculate the forecast for year 5 using a moving average of length 3, we need to take the average of the sales values for the previous 3 years. Here's how you can do it:
Sales (1000's Units)
Year 1: 68
Year 2: 45
Year 3: 60
Year 4: 72
Step 1: Calculate the moving average for years 2 to 4:
Moving Average Year 2 = (68 + 45 + 60) / 3 = 57.67 (approximately)
Moving Average Year 3 = (45 + 60 + 72) / 3 = 59
Moving Average Year 4 = (60 + 72 + forecast) / 3
Step 2: Rearrange the formula to solve for the forecast:
Forecast = (3 * Moving Average Year 4) - 132
Step 3: Substitute the values and calculate the forecast:
Forecast = (3 * 59) - 132
Forecast = 177 - 132
Forecast = 45 (in 1000's units)
Therefore, the forecast for year 5 is 45,000 units.
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Integrating sums of functions
Answer:
(a) -12
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityCalculus
Integrals
Integration Rule [Reverse Power Rule]: \(\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C\)
Integration Property [Swapping Limits]: \(\displaystyle \int\limits^b_a {f(x)} \, dx = -\int\limits^a_b {f(x)} \, dx\)
Integration Property [Multiplied Constant]: \(\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx\)
Integration Property [Addition/Subtraction]: \(\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx\)
Integration Property [Splitting Integral]: \(\displaystyle \int\limits^c_a {f(x)} \, dx = \int\limits^b_a {f(x)} \, dx + \int\limits^c_b {f(x)} \, dx\)
Integration Rule [Fundamental Theorem of Calculus 1]: \(\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)\)
Step-by-step explanation:
Step 1: Define
\(\displaystyle \int\limits^6_4 {f(x)} \, dx = 5\)
\(\displaystyle \int\limits^4_{10} {f(x)} \, dx = 8\)
\(\displaystyle \int\limits^{10}_6 {[4f(x) + 10]} \, dx\)
Step 2: Solve Pt. 1
[Integral] Rewrite [Integration Property - Addition]: \(\displaystyle \int\limits^{10}_6 {[4f(x) + 10]} \, dx = \int\limits^{10}_6 {4f(x)} \, dx + \int\limits^{10}_6 {10} \, dx\)[Integral] Rewrite [Integration Property - Multiplied Constant]: \(\displaystyle \int\limits^{10}_6 {[4f(x) + 10]} \, dx = 4\int\limits^{10}_6 {f(x)} \, dx + 10\int\limits^{10}_6 {} \, dx\)Step 3: Redefine
Manipulate the given integral values.
[Integrals] Combine [Integration Property - Splitting Integral]: \(\displaystyle \int\limits^6_4 {f(x)} \, dx + \int\limits^4_{10} {f(x)} \, dx = \int\limits^6_{10} {f(x)} \, dx\)[Integral] Rewrite: \(\displaystyle \int\limits^6_{10} {f(x)} \, dx = \int\limits^6_4 {f(x)} \, dx + \int\limits^4_{10} {f(x)} \, dx\)[Integral] Substitute in integrals: \(\displaystyle \int\limits^6_{10} {f(x)} \, dx = 5 + 8\)[Integral] Add: \(\displaystyle \int\limits^6_{10} {f(x)} \, dx = 13\)[Integral] Rewrite [Integration Property - Swapping Limits]: \(\displaystyle -\int\limits^{10}_6 {f(x)} \, dx = 13\)[Integral] [Division Property of Equality] Isolate integral: \(\displaystyle \int\limits^{10}_6 {f(x)} \, dx = -13\)Step 4: Solve Pt. 2
[Integral] Substitute in integral: \(\displaystyle \int\limits^{10}_6 {[4f(x) + 10]} \, dx = 4(-13) + 10\int\limits^{10}_6 {} \, dx\)[Integral] Integrate [Integration Rule - Reverse Power Rule]: \(\displaystyle \int\limits^{10}_6 {[4f(x) + 10]} \, dx = 4(-13) + 10(x) \bigg| \limits^{10}_6\)[Integral] Evaluate [Integration Rule - FTC 1]: \(\displaystyle \int\limits^{10}_6 {[4f(x) + 10]} \, dx = 4(-13) + 10(10 - 6)\)[Integral] (Parenthesis) Subtract: \(\displaystyle \int\limits^{10}_6 {[4f(x) + 10]} \, dx = 4(-13) + 10(4)\)[Integral] Multiply: \(\displaystyle \int\limits^{10}_6 {[4f(x) + 10]} \, dx = -52 + 40\)[Integral] Add: \(\displaystyle \int\limits^{10}_6 {[4f(x) + 10]} \, dx = -12\)Topic: AP Calculus AB/BC
Unit: Integration
Book: College Calculus 10e
How would you graph y =- 3x 7?.
Any algebraic expression can be represented graphically. The given problem can be solved as shown in the image attached.
A polynomial in one variable is also an algebraic expression. It can be written in the form aˣn. Here, n is a non-negative integer and a is a real number. The a is also called the coefficient of the term.
The given problem also consists of a polynomial in one variable. It can be solved as such.
We have been told that = y = -3x+7
We need to graph this. For this, we plot at least two values for x and y -
x = 0 and y = 7
x = 1 and y = 4
We plot both these coordinates on the graph which has been attached below.
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Arafa has collected data on the relationship between physical attractiveness and judgments of personality characteristics. In order to determine if the results obtained from the sample are representative of the population, Arafa will need to employ ________ statistics.
Answer:
Inferential
Step-by-step explanation:
The process of drawing inferences about a population on the basis of information contained in a sample taken from the population is called Statistical Inferences.
In the given question the inferences have to be drawn from the sample which is representative of the population.
So the best answer is inferential statistics.
Kasey needs 1.5 cups of milk and 4 cups of sugar to make 12 muffins. She plans to make 36 muffins . How many fl oz of sugar does she need
Answer:
12 cups of milk
Step-by-step explanation:
36/12= 3
4 x 3= 12
So the Answer is 12 cups of milk
A rectangular shaped living room bas dimensions of 32 feet by 18 feet. What is the length of the diagonal? Round your answer to the nearest tenth, if necessary.
Answer:
D = 36.7 feet
Step-by-step explanation:
Diagonal of a Rectangle
Given a rectangle of width W and length L, its diagonal can be calculated as the hypotenuse of a triangle of legs W and L as follows:
\(D=\sqrt{W^2+L^2}\)
The dimensions of the living room are 32 feet by 18 feet, thus the diagonal is:
\(D=\sqrt{32^2+18^2}\)
\(D=\sqrt{1024+324}=\sqrt{1348}\)
D = 36.7 feet
Find the common difference of the arithmetic sequence 13, 9, 5,
Answer:
4
Step-by-step explanation:
Mark me as brainlist ez
Answer:
-4
Step-by-step explanation:
13, 9, 5, 1, -3, -7, .......
brewer, a graduate student, would like to determine how often college students are going to local restaurants to eat lunch instead of eating on campus. which method should be used to gather data? case study
For performing this analysis Brewer can use a method such as a survey for gathering the data.
Brewer would like to determine how often college students are going to local restaurants to eat lunch instead of eating on campus. He will require a large amount of data to determine this.
This data that he requires can be gathered using the method of survey, and a conclusion can be drawn from the data with the help of statistical analysis and probability analysis.
Surveys can be conducted by email or in an online survey form and can include both open-ended and closed-ended questions to gather both quantitative and qualitative data on the subject.
In this case, the survey can also be conducted by using orthodox methods of gathering data, such as observing people who are going to eat at local restaurants and on campus, although this is not the most ideal method.
Surveys allow the researcher to reach a large number of participants and gather data efficiently and effectively.
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The best way for her to find this data reliably is by using survey's
She can go around campus and survey the other students, and eventually get enough data to find an answer to her question (I also took the test and this answer was right)
have a good day :)
answer quickly. thank you
A candy manufacturer is marketing a gift box containing four cream-filled nuggets and five pieces of fudge. The manufacturing process for each candyis designed so that the mean weight of a cream-filled nugget is 3 ounces with a standard deviation of 0.2 ounces and the mean weight of a piece of fudge is 4 ounces with a standard deviation of 0.3 ounces. The boxes have a mean weight of 3 ounces with a standard deviation of 0.1 ounces. If three gift boxes are selected at random, what is the probability that at least one box will weigh less than 34 ounces?
The probability that at least one box in a selection of three candy gift boxes will weigh less than 34 ounces needs to be found.
To calculate the probability, the weight of a box can be considered as the sum of the weights of the individual candies in the box. The weights of the individual candies are normally distributed with known means and standard deviations.
Using the properties of normal distributions, the weights of the boxes can be modeled as normally distributed with a mean of 27 ounces (9 candies x 3 ounces per candy) and a standard deviation of 0.374 ounces (sqrt(4*(0.2^2)+5*(0.3^2)+0.1^2)). Then, the probability of at least one box weighing less than 34 ounces can be calculated using the normal distribution function.
The calculated probability is 0.0569, or approximately 5.69%. Thus, there is a 5.69% chance that at least one of the three selected candy gift boxes will weigh less than 34 ounces.
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The probability that at least one box will weigh less than 34 ounces is approximately 0.117.
To solve this problem, we can use the Central Limit Theorem to approximate the distribution of the total weight of three gift boxes. The mean weight of one gift box is 3*(4)+5*(3) = 27 ounces, and the standard deviation is sqrt((4*(0.2)^2 + 5*(0.3)^2)) = 0.69 ounces.
The probability that one gift box weighs less than 34 ounces is given by the standard normal distribution, which we can find using a z-score of (34-27)/0.69 = 10.14.
The probability that all three boxes weigh at least 34 ounces is (1-0.117)^3 = 0.770, so the probability that at least one box weighs less than 34 ounces is approximately 1 - 0.770 = 0.117.
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I need this ASAP. I WILL MARK BRAINLIEST AND GIVE 50 POINTS!!
PLEASE I need this quick
Answer:
there were 8 adults and 7 students
Step-by-step explanation:
7.25(8) + 5.5(7) = 96.5
the numbers in the parenthesis stand for the number of people
have a great day :D
Step-by-step explanation:
The Answer Is
8 Adults And 7 Students
4. In the graph below, what is the line of reflection for triangle XYZ and triangle X'Y'Z"? (1 point)
the x-axis
Othe y-axis
Ox=2
Oy=2
In the graph given, the line of reflection for the triangle XYZ and triangle X'Y'Z' is x=2.
Given, the coordinates of the triangle XYZ are:
X = (4,5)
Y = (6,3)
Z = (3,2)
and the coordinates of the triangle X'Y'Z' are:
X' = (0,5)
Y' = (-2,3)
Z' = (1,2)
for image of the triangle XYZ to get reflected and become X'Y'Z',
reflection of axis takes place.
But the images are not identical and symmetrical, so the reflection is not about y axis.
we check for x=2
hence reflection of axis when x=a is :
P(x,y) →x'(2a-x , y)
therefore use the above formula and check the coordinates of the reflected image.
X(4,5) when x=2X(4,5) → X'(2(2)-4 , 5)
x(4,5) → X'(0,5)
Y(6,3) when x=2Y(6,3) → Y'(2(2)-6 , 3)
Y(6,3) → Y'(-2,3)
Z(3,2) when x=2Z(3,2) → Z'(2(2)-3 , 2)
Z(3,2) → Z'(1,2)
hence x=2 is the reflection of triangle XYZ and X'Y'Z'.
Therefore we get the requires answer.
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10. The y-intercept uses which letter?
M
Z
B
Y
Answer:
if it were an equation it would be y = mx + b and B would be the y intercept and mx is slope.
Step-by-step explanation:
Hey there!
The y-intercept is
b
Remember Slope-Intercept form, where
m is the slope
b is the y-intercept
I hope you find my answer helpful.
Good luck!
Have a great day!
~Stars~
Answer all or none! Ty!
Consider the following sequence 1,4, 16, 64, 256, ... Find the term number of 1048576
The 6th term of the sequence is 1048576.
Consider the sequence of numbers: 1, 4, 16, 64, 256, 1024, 4096, 16384, 65536, 262144, 1048576.
The sequence starts at 1 and continues by squaring the previous term.
Thus the pattern is given by:
\(\[{a_n} = {a_{n - 1}}^2\]\)
To find the term number of 1048576, we need to find n such that:
\(\[{a_n} = 1048576\]\)
Therefore, we have:
\(\[{a_6} = {a_5}^2\)
= \({1024^2}\)
= \(1048576\]\)
So the term number of 1048576 is 6.
We can conclude that the 6th term of the sequence is 1048576.
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Consider the following sequence 1,4,16,64,256,.... 1048576 is the 20th term of the sequence.
To find the term number of 1048576, we need to determine the pattern in the sequence and use it to find the answer.
We can observe that each term is equal to the previous term multiplied by 4.
Therefore, we can find any term in the sequence by raising 4 to the power of its term number.
That is, the nth term of the sequence is given by \(4^{(n-1)\).
Using this formula, we can find the term number of 1048576 by equating it to the nth term of the sequence and solving for \(n.4^{(n-1)} = 1048576\)
Dividing both sides by 4,
we get:\(4^{(n-1)/4} = 1048576/44^{(n-2)\)
= 262144
Dividing both sides by 4,
we get: \(4^{(n-2) / 4} = 262144/4 4^{(n-3)\)
= 65536
Dividing both sides by 4, we get:4^(n-4) = 4096
Dividing both sides by 4,
we get:\(4^{(n-5)\) = 256
Dividing both sides by 4, we get:\(4^{(n-6)\) = 16
Dividing both sides by 4, we get:\(4^{(n-7)\) = 1
Therefore, 1048576 is the 20th term of the sequence.
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