Answer:
(x - 8)^2 + (y + 10)^2 = 169
Step-by-step explanation:
you need to do completing the square
x^2 + y^2 -16x + 20y - 5 = 0
(x)^2 - 2(8)(x) + (y)^2 + 2(10)(y) - 5 = 0
(x)^2 + 2(-8)(x) + (-8)^2 - (-8)^2 + (y)^2 + 2(10)(y) + (10)^2 - (10)^2 - 5 = 0
[(x)^2 + 2(-8)(x) + (-8)^2] + [(y)^2 + 2(10)(y) + (10)^2] - (10)^2 - (-8)^2 - 5 = 0
### (a)^2 + 2(a)(b) + (b)^2 = (a + b)^2 ###
(x - 8)^2 + (y + 10)^2 -100 - 64 - 5 = 0
(x - 8)^2 + (y + 10)^2 -169 = 0
(x - 8)^2 + (y + 10)^2 = 169
Before a basketball game, a referee noticed the ball had been deflated. She dropped it from 6 feet and measured the first bounce at 36 inches and the second bounce at 18 inches.
a) write an exponential equation to model the height of the ball.
b)How high was the ball on the fifth bounce?
Therefore , the solution of the given problem of equation comes out to be the ball is 2.25 inches tall after the fifth bounce.
What is an equation?In order to demonstrate consistency between two opposing statements, variable words are frequently used in sophisticated algorithms. Equations are academic phrases that are used to demonstrate the equality of different academic figures. Consider expression the details as y + 7 offers. In this case, elevating produces b + 7 when partnered with building y + 7.
Here,
a)
We are aware that the ball was dropped from a height of 6 feet, or 72 inches, and that it bounced twice, the first time for 36 inches and the second time for 18 inches. We can thus write:
=> a = 72 (the initial height)
=> B = (height of previous bounce minus height of each subsequent bounce) = 18/36 = 1/2
As a result, the following exponential equation can be used to predict the ball's height:
=> y = 72*(1/2)ˣ
b) We enter x = 5 into the equation we derived in part a) to determine the height of the ball on the fifth bounce:
=> y = 72*(1/2)⁵
=> y = 72*(1/32)
=> 2.25 inches for y.
As a result, the ball is 2.25 inches tall after the fifth bounce.
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Arthur has decided to start saving for a new computer. His money is currently in a piggy bank at home, modeled by the function s(x) - 85. He was told that he could do the laundry for the house and his allowance would be a(x) = 10(x - 1), where x is measured in weeks. Explain to Arthur how he can create a function that combines the two, and describe any simplification that can be done.
The simplification of the function is r(x)=10x - 95.
We are given that;
s(x) = -85 and a(x) = 10(x - 1)
Now,
To create a function that combines them, you can substitute these expressions into the formula above:
r(x) = s(x) + a(x) r(x) = (-85) + 10(x - 1)
You can simplify this function by distributing the 10 and combining the constants:
r(x) = -85 + 10x - 10 r(x) = 10x - 95
Therefore, the function will be r(x)=10x - 95.
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How to write Two times the sum of y and 5 is 24
Then solve
Answer:
Step-by-step explanation:
2(y+5)=24
6. Stewart is making fruit punch for
his birthday party. He is filling a
240-ounce bowl with cans of apple
juice and pineapple juice. Each
can of apple juice holds 10 ounces,
while each can of pineapple juice
holds 18 ounces.
Write an inequality in standard
form representing the maximum
number of cans of apple juice, a,
and cans of pineapple juice, p,
Stewart can use.
The inequality in standard form that will represent the maximum number of cans of apple juice and cans of pineapple juice Stewart can use would be = 240ounce = 10a + 18p.
How to determine the inequality in standard form?The total quantity of fruit punch that would be used for the birthday = 240 ounce.
The quantity of juice each can holds for apple juice,a, = 10 ounces.
The quantity of juice each can hold for pineapple juice,p,= 18 ounces.
Therefore the best expression in standard form would be = 240ounce = 10a + 18p.
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Ned has 55 marbles in his collection. He has twice as many white marbles as red marbles. He has five more blue marbles than white marbles. How many white marbles does Ned have?
Answer:
Ned has 20 white marbles.
Step-by-step explanation:
Let's call the number of red marbles "r".
We know that Ned has twice as many white marbles as red marbles, so the number of white marbles would be 2r.
We also know that he has five more blue marbles than white marbles, so the number of blue marbles would be 2r + 5.
The total number of marbles in Ned's collection is 55, so:
r + 2r + (2r + 5) = 55
Simplifying this equation, we get:
5r + 5 = 55
Subtracting 5 from both sides:
5r = 50
Dividing by 5:
r = 10
So Ned has 10 red marbles.
We can use this to find the number of white marbles:
2r = 2(10) = 20
So Ned has 20 white marbles.
SOMEONE, PLEASE HELP! ASAP, WILL GIVE 30 POINTS!
Using the equations given, only equation 2 has a proportional relationship.
What is a proportional and non-proportional relationship?Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other.
The difference between proportional and non-proportional linear relationships is that, although both have constant rates of change the proportional relationship has constant output to input ratios, and the non-proportional relationship does not.
In this problem, to determine the proportional relationship, we can also check for both values of x and y.
1. y = -0.75x + 5
When x = 1
y = -0.75(1) + 5
y = 4.25
when x = 2
y = -0.75(2) + 5
y = 3.5
The relationship is not proportional since as one variable increase, the other decreases.
2. y = 4x - 1
When x = 1
y = 4(1) - 1
y = 4 - 1
y = 3
when x = 2
y = 4(2) - 1
y = 8 - 1
y = 7
This relationship is proportional since the variables increases or decreases with one another.
3. y = (3/4)x
When x = 1
y = (3/4)(1)
y = 3/4
when x = 2
y = (3/4)(2)
y = 2/3
This relationship is not proportional
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Drag the tiles to the correct boxes to complete the pairs.
Match the accounting terms to their relevant action by the company or the investors.
high free cash flow
low free cash flow
capital expenditure
company buying assets like machinery or a plant
investors think about selling the shares of the company
investors will hold on to their shares as the company is sure to pay dividends
comoany try to reduce this to increase profits.
Reset
Next
operating activities
The accounting terms when matched with their relevant actions would be;
high free cash flow - investors will hold on to their shares as the company is sure to pay dividendslow free cash flow - investors think about selling the shares of the companycapital expenditure - company buying assets like machinery or a plantoperating activities - company trying to reduce capital expenditure to increase profits What do some accounting terms lead to ?A company's free cash flow is an indicator of its ability to cover expenses and invest in future growth opportunities. A high level of free cash flow suggests that the business is doing well financially, while a low amount indicates that the opposite is true.
In order to generate income or save money over time, companies will make capital expenditures. However, if investors deem a company to be underperforming or unlikely to provide returns on investment, they may choose to sell their shares as a preventative measure against further financial losses.
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Compute the area of the following triangle. (Express answer in cm^2)
b= 20in
h= 4in
A= ? Cm^2
Answer:
A = 40 cm^2
Step-by-step explanation:
The area of a triangle is given by
A = 1/2 bh where b is the base and h is the height
A = 1/2 ( 20) (4)
A = 40 cm^2
Answer:
40in²
Step-by-step explanation:
The formula to find the area of a triangle is:
[tex]\sf Area = \frac{1}{2}*Base*Height[/tex]
Accordingly, let us solve it now.
[tex]\sf \frac{1}{2}*Base*Height\\\\\sf \frac{1}{2}*20*4\\\\40\:in^2[/tex]
Find the volume of the cylinder. Use π = 3.14.
(If answered correctly with an explanation giving brainlyest)
A. 321.54 ft3
B. 10,048 ft3
C. 8,038.4 ft3
D. 100.48 ft3
The volume of the cylinder is 8,038.4 ft3
How to calculate the volume of the cylinder?The height(H) is 10ft
The diameter is 32 ft
The formula for calculating the volume of a cylinder is
πr²h
Radius= 32/2
= 16
Volume= 3.14 × 16² × 10
= 3.14 × 256 × 10
= 8,038.4
Hence the volume of the cylinder is 8,038.4 ft3
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How can you describe its content and style in Words of the Devil, by Parau na te Varua ino, that was painted in 1892. ??
Answer:
Words of the Devil, by Parau na te Varua ino, is a painting that was created in 1892 in French Polynesia. The painting depicts a scene from Tahitian mythology, in which the goddess Hina is visited by the devil, who is represented as a horned figure with a large, forked tongue. The painting is rich in detail and vivid color, with the figures depicted in bright, bold colors that stand out against the darker background.
The style of the painting is characteristic of the Tahitian art of the time, which was heavily influenced by the traditional Polynesian art forms of carving, tattooing, and tapa cloth decoration. The figures in the painting are depicted in a stylized, almost abstract way, with exaggerated features and bold, sweeping lines. The use of bright colors and bold brushstrokes gives the painting a dynamic, almost chaotic energy that reflects the intense emotions of the scene.
Overall, Words of the Devil is a powerful and striking work of art that captures the mythology and cultural traditions of French Polynesia in the late 19th century.
help please
The half-life of Radium-226 is 1590 years. If a sample contains 500 mg, how many mg will remain after 1000 years? -----------
after 1000 years, there will be approximately 218.7 mg of Radium-226 remaining in the sample. use formula for radioactive decay to solve
what is radioactive decay ?
Radioactive decay is the process by which an unstable atomic nucleus loses energy by emitting radiation, such as alpha particles, beta particles, and gamma rays. The decay occurs in order to achieve a more stable configuration of the nucleus.
In the given question,
The formula for radioactive decay is:
N(t) = N0 * (1/2)ᵃ⁾ᵇ
where:
N(t) is the amount of radioactive material at time t
N0 is the initial amount of radioactive material
t is the time elapsed since the initial measurement
T is the half-life of the radioactive material
We can use this formula to solve the problem as follows:
N0 = 500 mg (the initial amount)
T = 1590 years (the half-life)
t = 1000 years (the time elapsed)
N(t) = 500 * (1/2)¹⁰⁰⁰⁾ ¹⁵⁹⁰
N(t) = 500 * 0.4374
N(t) = 218.7 mg
Therefore, after 1000 years, there will be approximately 218.7 mg of Radium-226 remaining in the sample.
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Please help with these two equations and show work as well, thank you!
13.) The simplified polynomials that can represent the area and perimeter of the large rectangle =40x + 5x² and
12X + 16 respectively.
14.)The simplified polynomials that can represent the area and perimeter of the large rectangle =21+10x + x² and 20+4x respectively.
How to determine the simplified polynomials that can be used to represent the given shape?To determine the simplified polynomials, the formula for the area and perimeter of the rectangule should be used. That is:
Area of rectangle = length×width
where;
length = 5x
width = 8+X
Area = 5x * 8+X
= 40x + 5x²
Perimeter of rectangle = 2(length+width)
= 2(5x + 8+X)
= 10x + 16 + 2x
= 12X + 16
For question 14.)
Area of rectangle = length× width
where;
length = 7+X
width = 3+X
Area = 7+X × 3+X
= 21+7x+3x +x²
= 21+10x + x²
Perimeter = 2(length+width)
= 2(7+X+3 + X)
= 2(10+2x)
= 20+4x
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Suppose that the readings on the thermometers are normally distributed with a mean of 0∘ and a standard deviation of 1.00∘C.
If 12% of the thermometers are rejected because they have readings that are too high, but all other thermometers are acceptable, find the reading that separates the rejected thermometers from the others.
The reading that separates the rejected thermometers from the others is given as follows:
1.175 ºC.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution of the data-set, depending if the obtained z-score is positive(above the mean) or negative(below the mean).The z-score table is used to obtain the p-value of the z-score, and it represents the percentile of the measure X in the distribution.The mean and the standard deviation for this problem are given as follows:
[tex]\mu = 0, \sigma = 1[/tex]
The 12% higher of temperatures are rejected, hence the 88th percentile is the value of interest, which is X when Z = 1.175.
Hence:
1.175 = X/1
X = 1.175 ºC.
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3 problems for 1 final answer. fairly easy 8th grade math.
When we evaluate the given expression, A/5 + √(B - C), the result obtained is 9 (option B)
How do i determine the value of A/5 + √(B - C)?
First, we shall determine the value of A. Details below:
A = Product of roots in x² - 11x + 30Value of A =?Quadratic equation is expressed as:
x² - (sum of root)x + product of root
Comparing the above with x² - 11x + 30, we have
x² - 11x + 30 = x² - (sumof root)x + product of root
Product of roots = 30
Thus,
A = 30
Next, we shall determine the value of B. details below:
f(x) = x² + 5Value of B = f(2) =?f(x) = x² + 5
f(2) = 2² + 5
f(2) = 9
Thus,
B = 9
Next, we shall determine the value of C. Details below:
(x² - 2x - 24) / (x + 4)Value of C = Remainder =?Let
x + 4 = 0
Thus,
x = -4
Substitute the value of x into x² - 2x - 24 to obtain the remainder as shown below:
Remainder = x² - 2x - 24
Remainder = (-4)² - 2(-4) - 24
Remainder = 0
Thus,
C = 0
Finally, we shall determine value of A/5 + √(B - C). Details below:
A = 30B = 9C = 0Value of A/5 + √(B - C) =?A/5 + √(B - C) = 30/5 + √(9 - 0)
A/5 + √(B - C) = 6 + √(9
A/5 + √(B - C) = 6 + 3
A/5 + √(B - C) = 9
Thus, the value of A/5 + √(B - C) is 9 (option B)
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For her geography project, Karen built a clay model of a
volcano in the shape of a cone. Her model has a diameter
of 12 inches and a height of 8 inches. Find the volume of
clay in her model to the nearest tenth. Use 3.14 for pi
Answer:
301.4 in^3
Step-by-step explanation:
Divide 12 by 2 to get the radius
12/2=6
Square 6 and multiply by 3.14 according to the area of a circle formula πr^2.
6^2=36 36*3.14=113.04
We now have the area of the base.
Multiply it by the height and divide by three to follow the formula for the volume of a cone, 1/3bh.
113.04*8=904.32. 904.32/3= 301.44, or 301.4 after rounding.
a) Find the value of 8 1/3 b) Find the value of 8 2/3 c) Find the value of 16 3/4
Answer:
a) 27. b) 27.3333 c) 40.75
SOMEONE, PLEASE HELP!
Determine any horizontal or slant asymptotes of the rational function: f(X)= 3x^2-x/2x^2-1
The horizontal asymptote is y = 3/2, and the slant asymptote is y = x/2.
How to express the asymptoteWe need to compare the degrees of the numerator and denominator.
The degree of the numerator is 2, and the degree of the denominator is also 2. Therefore, the horizontal asymptote is given by the ratio of the leading coefficients, which is 3/2. The horizontal asymptote is y = 3/2
Furthermore, f(x) = 3/2 + x/(2x² - 1)
This expression shows that the function has a slant asymptote given by the line: y = x/2
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You deposit $3000 each year into an account earning 7% interest compounded annually. How much will you have in the account in 30 years?
The amount you will have in the account in 30 years is $22836.77
How much will you have in the account in 30 years?From the question, we have the following parameters that can be used in our computation:
You deposit $3000 each year 7% interest compounded annually.Using the above as a guide, we have the following:
Amount = P * (1 + r)^t
Where
P = Principal = 3000
r = Rate = 7%
t = time = 30
Substitute the known values in the above equation, so, we have the following representation
Amount = 3000 * (1 + 7%)^30
Evaluate
Amount = 22836.77
Hence, the amount is 22836.77
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If polygon A is a parallelogram, and polygon B is a rectangle, which of the
B
following is true?
X
35°
W
Polygon A
35 Z
A
90°
90%
PolygonB
90°
90
C. Polygon A and B are parallelograms so neither can be
circumscribed by a circle.
D
A. Polygon B represents the only parallelogram that a circle can
circumscribe because opposite angles are supplementary.
B. Both polygon A and B are quadrilaterals, therefore a circle can
circumscribe either one.
D. Polygon A can be circumscribed by a circle because opposite
sides must be supplementary.
Answer:
The answer is A
Step-by-step explanation:
Trust me
ces
Which sequence below would best model the
following description?
A newly planted tree releases 250 pounds of
oxygen over the period of its first year. The amount
of oxygen released by the tree grows at a rate of
12% per year, but the tree cannot generate more
than 6000 pounds of oxygen per year.
The correct sequence to model the given scenario is (b) f(n) = 1.12f(n-1)(1- f(n-1/6000)), and we can use this formula to calculate the oxygen released by the tree in each year, option (b) is correct.
The amount of oxygen released by the tree increases at a rate of 12% per year, which is represented by the factor 1.12f(n-1).
However, the tree cannot generate more than 6000 pounds of oxygen per year, which is represented by the limiting factor:
(1- f(n-1/6000)).
To understand this better, let's calculate the oxygen released by the tree in the second year using the formula
f(n) = 1.12f(n-1)(1- f(n-1/6000)).
f(2) = 1.12f(1)(1- f(1)/6000)
= 1.12(250)(1- 250/6000)
= 295.67 pounds of oxygen
Hence, option (b) is correct.
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The correct question is:
Which sequence below would best model the following description? A newly planted tree releases 250 pounds of oxygen over the period of its first year. The amount of oxygen released by the tree grows at a rate of 12% per year, but the tree cannot generate more than 6000 pounds of oxygen per year.
a. f(n) = 1.12f(n-1)(1+ f(n-1/6000)
b. f(n) = 1.12f(n-1)(1- f(n-1/6000)
c. f(n) = 1.12f(n-1) {6000/f(n-1)}
d. f(n) = 1.12f(n-1)(f(n-1) -6000)
Find the slope of the line represented
by the data below.
x 2 4 6 8
-3 39
3
9 15
y|-3
Simplify completely.
Slope = [?
Hint: The slope of a line is the
Change in y
Change in x
A mathematics teacher wanted to see the correlation between test
scores and homework. The homework grade (x) and test grade (y) are
given in the accompanying table. Write the linear regression equation
that represents this set of data, rounding all coefficients to the nearest
hundredth. Using this equation, find the projected test grade, to the
nearest integer, for a student with a homework grade of 61.
Homework Grade (x) 72 53 90 77 82 74 78 74 83Test Grade (y)
75 39 81 70 83 78 75 70 85
Answer:
54
Step-by-step explanation:
You want the approximate test grade of a student with a homework grade of 61, using a linear regression equation for the given homework and test scores.
RegressionThe linear regression equation can be found using any of a number of calculators, apps, or spreadsheets. The attachment shows the equation is approximately ...
y ≈ 1.22x -20.01
For a homework score of 61, the expected test grade is ...
y = 1.22(61) -20.01
y ≈ 54
The student's projected test grade is 54.
__
Additional comment
If the regression coefficients are used to their full precision, the projected test score is about 54.6, which rounds to 55.
<95141404393>
A sample of 500 high schools in a state results in an average number of students per grade level of 178.6 students, with a margin of error of ±45.2. If there are 3250 high schools in the state, what is the estimated number of students per grade level?
between
and
students
The estimated number of students per grade level in the state is between 66,700 and 112,800 students, with an estimated total of 580,450 students.
The anticipated number of students in line with grade level within the state is between:
(178.6 - 45.2) x 500 = 66,700 students
and
(178.6 + 45.2) x 500 = 112,800 students.
This is the range of values that we can be 95% confident includes the actual average number of students according to grade degree within the state, based on the sample of 500 high schools and the margin of mistakes of ±45.2.
To estimate the whole number of students according to grade level in the state, we can multiply the anticipated average with the aid of the total number of high schools:
3250 x 178.6 = 580,450 students
Consequently, the estimated number of students per grade level in the state is between 66,700 and 112,800 students, with an estimated total of 580,450 students.
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A research institute poll asked respondents if they felt vulnerable to identity theft. In the poll, n=918 and x=592 who said "yes." Use a 90% confidence level.
The values received after utilizing confidence interval are (0.614, 0.674)
Poll = n = 918
X = 592
Calculating the value of p -
p = x/n
= 592/918
= 0.644
The mean of an estimate plus and minus the range of that estimate constitutes a confidence interval. inside a specific degree of confidence, this is the range of values that anticipates the estimate to fall inside if the test is repeated.
Using the formula of confidence interval -
[tex]CI = p + z\sqrt{} p ( 1-p/n)[/tex]
Substituting the values -
[tex]CI = 0.644 + 1.645 \sqrt{} ( 0.644 ( 1 - 0.644) / 918)[/tex]
= 0.644 ± 0.030
Thus, the interval values are -
= 0.644 + 0.030 = 0.674
= 0.644 - 0.030 = 0.614
With 90% certainty that this range represents the true percentage of the population who feel vulnerable to identity theft.
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Find the area of the regular polygons and degree of central angle when given either the apothem or side length.
The length of the apothem is 10. 99cm
How to determine the valuesTo determine the apothem of a polygon, we have to use the formula;
a = s/2 tan (180/n)
Such that the parameters are;
a is the length of the apothem.s is the side length of the polygonn is the number of sides of the polygonNow, substitute the values, we have;
a = 8/2tan(180/9)
divide the values
a = 8/2tan 20
Find the values
a = 8/0. 7279
Divide the values
a = 10. 99cm
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A scale drawing of a square has a sidle length of 9 inches. The drawing has a scale of 1 in. : 7 mi. Find the actual permitted and area of the square
Answer: To find the actual perimeter and area of the square, we need to use the scale given in the problem, which is 1 inch on the drawing represents 7 miles in real life.
The side length of the square on the drawing is 9 inches, so in real life, the side length would be:
9 inches x 7 miles/inch = 63 miles
Therefore, the actual perimeter of the square would be:
4 x 63 miles = 252 miles
To find the actual area of the square, we can use the formula:
area = side length x side length
In this case, the side length is 63 miles, so:
area = 63 miles x 63 miles = 3,969 square miles
So the actual perimeter of the square is 252 miles, and the actual area of the square is 3,969 square miles.
Step-by-step explanation: can i get brainliest :D
Solve 4x-8 + 4 = 16.
The solutions are x =
and x =
BEYHODNA
MIGRANTA
www
www
wer
Answer:
x = 5
Step-by-step explanation:
To solve the equation 4x-8 + 4 = 16, we first combine the constants on the left-hand side:
4x-8+4 = 16
4x-4 = 16
Next, we add 4 to both sides to isolate the variable on one side:
4x-4+4 = 16+4
4x = 20
Finally, we divide both sides by 4 to solve for x:
4x/4 = 20/4
x = 5
Therefore, the solution to the equation 4x-8 + 4 = 16 is x = 5.
Please help discrete math question.
The number of ways you can tile your walkway if you choose single tiles and double tiles is 3,992,781,803 ways.
How to find the number of ways ?To tile a 1x20 walkway using red, blue, and yellow single tiles (1x1) and green and white double tiles (1x2), we can consider the number of ways to combine the single and double tiles to fill the entire 1x20 space.
The exact number of ways to tile the 1x20 walkway using red, blue, and yellow single tiles and green and white double tiles:
= 3^20 + 3^18 x 2 + 3^16 x 4 + 3^14 x 8 + 3^12 x 16 + 3^10 x 32 + 3^8 x 64 + 3^6 x 128 + 3^4 x 256 + 3^2 x 512 + 1, 024
= 3486784401 + 258280326 + 172186884 + 38263752 + 8503056 + 1889568 + 419904 + 93456 + 20736 + 4608 + 1024
= 3,992,781,803 ways
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what is the volume of the rectangular prism with a length of 11 meters, width of 26, and height of 38 meters?