A(11) counts partitions of 11 into parts congruent to ±1 mod 6 is A(11) = 2 and B(11) counts partitions of 11 into distinct parts congruent to ±1 mod 3 is B(11) = 2. C(11) counts partitions of 11 into parts differing by at least 3 and multiples of 3 differing by at least 6 is C(11) = 1.
A(11) counts the number of partitions of 11 into parts congruent to ±1 mod 6. One such partition is 11, which is already congruent to ±1 mod 6. Another partition is 7+1+1+1+1, which consists of four parts that are congruent to 1 mod 6 and one part that is congruent to -1 mod 6. Therefore, A(11) = 2.
B(11) counts the number of partitions of 11 into distinct parts congruent to ±1 mod 3. One such partition is 11, which is already congruent to ±1 mod 3. Another partition is 7+3+1, which consists of three distinct parts that are congruent to 1 mod 3. Therefore, B(11) = 2.
C(11) counts the number of partitions of 11 into parts that differ by at least 3, with the added condition that any parts that are multiples of 3 must differ by at least 6. One such partition is 11, which is the only way to partition 11 into parts that differ by at least 3. Therefore, C(11) = 1.
Therefore, the partitions of 11 counted by A(11), B(11), and C(11) are:
A(11): 11, 7+1+1+1+1
B(11): 11, 7+3+1
C(11): 11
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if the area of a rectangle is represented by 25x^3y^6 and its width is represented by 10xy, express the length of the rectangle in terms of x and y
The length of the rectangle in terms of x and y, given that its area is represented by 25x³y⁶ and its width is represented by 10xy is 2.5x²y⁵.
The area of a figure is the total space enclosed in two dimensions within its boundary.
The area of a rectangle is given as, area = length*width.
In the question, we are given that the area of a rectangle is represented by 25x³y⁶ and its width is represented by 10xy, and are asked to express the length of this rectangle in terms of x and y.
We know that the area of a rectangle is given as, area = length*width.
Substituting the known values in the equation, we get:
25x³y⁶ = length*10xy.
Rearranging this equation, we get:
length = 25x³y⁶/10xy = (5x²y⁵)/2 = 2.5x²y⁵.
Thus, the length of the rectangle in terms of x and y, given that its area is represented by 25x³y⁶ and its width is represented by 10xy is 2.5x²y⁵.
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When I flip a coin, the outcome can be either heads or tails; it is uncertain. However, in a large number of flips, the distribution of heads and tails is very regular. We say that flipping a coin is Group of answer choices predictable. deterministic. none of the above. random.
If the distribution of heads and tails of a fair coin is very regular in a large number of flips, then flipping a fair coin is: D. random.
What is a fair coin?A fair coin can be defined as an idealized type of coin that has an equal probability of revealing both heads and tails when randomly flipped or tossed by anybody.
This ultimately implies that, the outcome of flipping a fair coin is generally going to produce only one of two results and these include the following:
HeadTailIn this context, we can infer and logically conclude that if the distribution of heads and tails of a fair coin is very regular in a large number of flips, then flipping a fair coin is considered as being random.
In conclusion, it is important to note that a fair coin is considered as being random when the distribution of heads and tails of a fair coin is very regular in a large number of flips.
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In the following table, the age (in years) of the respondents is given as the x value, and the earnings (in thousands of dollars) of the respondents are given as the y value. Use Excel to find the best fit linear regression equation in thousands of dollars. Round the slope and intercept to three decimal places.
The required equation based on the information given is y =0.433x + 24.493
How to illustrate the information?It should be noted that one can simply copy and paste the data set into excel sheet
Then, use intercept and the slope formula to find slope and intercept. We will have
slope = SLOPE(y values, x values)
= 0.433
intercept = INTERCEPT(y values, x values)
= 24.493
Therefore, the required equation is y =0.433x + 24.493
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Several different roadways are in the same region as the railroad.
Part A: A highway's path can be found using the equation 2x+3y=21. Use the graphs of the functions to determine the number of intersections there will be between the railroad and the
highway, and explain completely. (5 points)
Part B: A turnpike's route is determined by the equation y=x2 Prove algebraically how many intersections there will be between the railroad and the turnpike, showing all necessary
work. (5 points)
There are 0 intersections between the railroad and the highway and there are 2 intersections between the railroad and the turnpike
The number of intersections there will be between the railroad and the highwayFrom the graph, we have the following points on the railroad
(x, y) = (3, 3) and (0, 5)
The slope is calculated as:
m = (y2 - y1)/(x2 - x1)
This gives
m = (5 -3)/(0 - 3)
Evaluate
m = -2/3
The equation is then calculated as:
y = mx + b
This gives
y = -2/3x + b
Substitute (0, 5)
5 = -2/3 * 0 + b
This gives
b = 5
Substitute b = 5 in y = -2/3x + b
y = -2/3x + 5
Multiply through by 3
3y = -2x + 15
Rewrite as:
2x + 3y = 15
The equation of the highway's path is
2x+3y=21
So, we have:
2x+3y=21
2x + 3y = 15
Subtract the equations
2x - 2x + 3y - 3y = 21 - 15
Evaluate
0 = 6
The above equation is false because 0 and 6 are not equal.
This means that the system of equations have no solution
Hence, there are 0 intersections between the railroad and the highway.
How many intersections there will be between the railroad and the turnpike?Here, we have
y = x^2 and 2x + 3y = 15
Substitute y = x^2 in 2x + 3y = 15
2x + 3x^2 = 15
Rewrite as:
3x^2 + 2x - 15 = 0
Calculate the discriminant using
d =b^2 - 4ac
This gives
d = 2^2 - 4 * 3 * -15
Evaluate
d = 184
The discriminant d is greater than 0.
This means that the equation has 2 real solutions
Hence, there are 2 intersections between the railroad and the turnpike
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Anyone know?? I’d appreciate it.
[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Here we go ~
[tex]\qquad \sf \dashrightarrow \: (1.6 \times 10 {}^{5} ) \sdot(2 .3 \times {10}^{1} )[/tex]
[tex]\qquad \sf \dashrightarrow \: (1.6 \times 2.3) \sdot(10 {}^{5} \times 10 {}^{1} )[/tex]
[tex]\qquad \sf \dashrightarrow \: 3.68 \times 10 {}^{6} [/tex]
What percentage of its total accounts receivable does grainger feel are uncollectible at december 31, 2016?
Using percentage of its total accounts the $50,000 is the amount to be uncollectible. The amount of $50,000 will be reported as an allowance for uncollectible accounts for the Year 2 on December 31 in the balance sheet.
According to the question,
Under the approach of the balance sheet, the ending balance of the allowance for the uncollectible accounts is the percentage (%) of the ending balance of the accounts receivable.
The amount of uncollectible accounts should reflect the aggregate needed ending balance of the allowance which amounts to $50,000.
Hence, using percentage of its total accounts the $50,000 is the amount to be uncollectible.
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I dentist the slope and a point on the line
Answer:
2/3 (0,-3) is one possible answer.
Step-by-step explanation:
y -1 = 2/3(x-6) We want to get this into the slope intercept form of a line. We want it to be in the form y = mx + b. Let's clear the fraction first by multiplying the whole equation through by 3.
3(y - 1) = 3[2/3(x - 6)]
3y -3 = 2(x -6)
3y - 3 = 2x -12
3y = 2x - 9 Now divide all the way through by 3 to get
y = 2/3x - 3
y = mx + b. The m part is the slope. In this equation the slope is 2/3
There are in infinite amount of points on a line. I do not know if they give you a picture or if you are just to create your own. I am going to create a point that have x = 0. I get to pick the point. I could pick any number. 0 is just usually really easy. So, if I substitute 0 for x I will get:
y = 2/3(0) - 3
y = 1 so my point is (0,-3)
Now that I think about it, I do not think that I would start out clearing the fraction even though it works. I think that I would do it like this"
y - 1 = 2/3(x - 6) Distribute the 2/3 through (x - 4) to get
y-1 = 2/3x -4 I can make -6 a fraction by putting it over 1. Now we have 2/3(-6/1) multiply across to get -12/3. A positive times a negative is a negative. -12 divided by 3 is -4.
y - 1 = 2/3x -4 now add 1 to both sides.
y = 2/3x -3
Giving away brainly for help ASAP
Answer:
[tex]g(f(x))=25x^2-15x-7[/tex]
domain: (-∞,∞)
Step-by-step explanation:
g of f means plug the function f(x) in to x in the function g(x)
[tex]g(f(x))=5(5x^2-3x-2)+3\\g(f(x))=25x^2-15x-10+3\\g(f(x))=25x^2-15x-7[/tex]
since this is a parabola with no interval, the domain (the graph on the x-axis from left to right) is all real numbers or (-∞,∞)
arrange the steps in the correct order to express cos3x in terms of cosx
The correct order to express cos3x in terms of cosx is; As shown in steps 1 to 9 below.
How to simplify Trigonometric Identities?The steps to simplify the trigonometric identities cos 3x in terms of cos x are as follows;
Step 1; cos x = cos(2x + x)
Step 2; cos(2x) cosx - sin(2x) sinx
Step 3; 1 - 2sin^2x(cosx) -(2sinxcosx)sinx
Step 4; cosx - 2sin²x cosx - 2sin²x cosx
Step 5; cosx - 4sin²x cosx
Step 6; cosx( 1 - 4sin²x)
Step 7; cosx{1 - 4(1 - cos²x)}
Step 8; cosx{-3 + 4cos²x}
Step 9; 4cos³x - 3cosx
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The average amount of money held by each child in a group of 5 is $0.50. If one of the children loses a quarter, what is the new average of money held by each child
Answer:
$0.45.
Step-by-step explanation:
Total amount of money held by all 5 children
= 5 * 0.50 = $2.50.
After 0.25 is lost the total = $2.25.
So the new average = 2.25 / 5
= $0.45.
Which of the following is a characteristic of the circumcenter of a triangle? A. It is the center of the circle that can be inscribed in a given triangle. B. It is equidistant from all three sides of the triangle. C. It is equidistant from all the vertices in the triangle. D. It is the intersection of all three angle bisectors of the triangle.
2. Is x² + 4√x a polynomial ? Justify your answer.
Answer:
No it isn't
As the variable "x" has root in it which means it isn't a whole number and for a expression to be a polynomial the variable must be whole no.
Hope it helps you!
Answer:
yes
Step-by-step explanation:
A polynomial is an algebraic expression of two or more terms
[tex]x^{2} +4\sqrt{x}[/tex] It is an algebraic expression of two terms, It is more common to label it binomial, but it is also a polynomial.
Hope this helps
[tex]Y-intercept = -4 Slope = 1/4[/tex]
Please help i need this
Answer:
Step-by-step explanation:
Answer:
Refer to the attached image!!
Hope it helps!
What is the 32nd term of an arithmetic sequence with a first term of 7 and a common difference of 4?
Select one:
a. 119
b. 123
c. 127
d. 131
Answer:
a₃₂ = 131
Step-by-step explanation:
the nth term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
here a₁ = 7 and d = 4 , then
a₃₂ = 7 + (31 × 4) = 7 + 124 = 131
Help me please help me fast
The value of [tex]f^{-1}(49)[/tex] is 4
Inverse of a function
The given function is:
[tex]f(x)=(x+3)^2[/tex]
Let f(x) be represented by y
[tex]y=(x+3)^2[/tex]
Make x the subject of the formula
[tex]\sqrt{y} =x+3[/tex]
Subtract 3 from both sides
[tex]x=\sqrt{y} -3[/tex]
Replace x by [tex]f^{-1}(x)[/tex] and let y be replaced by x
[tex]f^{-1}(x)=\sqrt{x} -3[/tex]
Substitute x = 49 into the inverse function
[tex]f^{-1}(x)=\sqrt{49} -3\\\\f^{-1}(x)=7-3\\\\f^{-1}(x)=4[/tex]
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Determine the volume of a cube with a side length of 5 1/3 in.
Answer:
151 19/27 in^3
Step-by-step explanation:
volume of cube is (side length)^3
(5 1/3)^3 = (16/3)^3 = 4096/27 = 151 19/27
Zara is preparing a juice blend.In her recipe, the amount of water is twice the amount of strawberry juice, and amount of lemon juice is 1/5 the amount of strawberry juice. What is the ratio of the lemon water?
The ratio of the lemon water is 10:1
How to determine the ratioFrom the information, we have that;
The ratio of water to strawberry juice is 2 : 1
That of strawberry juice to lemon juice is 5: 1
The, we have that of water to lemon juice to be 10: 1 when compared
Hence, the ratio of the lemon water is 10: 1
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A group of friends is on a rafting trip. They plan to travel 5 miles downstream and then 5 miles back upstream. They need to finish their rafting trip in 6 hours to allow enough time to get back to their hotel. The group knows that the river is moving at a rate of 2 miles per hour.
Answer:
I don't understand what the question is what do you need to find?
The lengths of two sides of a triangle are shown below:
Side 1: 3x² - 2x - 1
Side 2: 9x + 2x² - 3
The perimeter of the triangle is 5x³+4x2 - x - 3.
Part A: What is the total length of the two sides, 1 and 2, of the triangle? (4 points)
Part B: What is the length of the third side of the triangle? (4 points)
Part C: Do the answers for Part A and Part B show that the polynomials are closed under
addition and subtraction? Justify your answer. (2 points)
(10 points)
Part A
[tex]3x^2 -2x-1+9x+2x^2 -3=\boxed{5x^2 + 7x-4}[/tex]
Part B
[tex](5x^3 +4x^2 - x-3)-(5x^2 + 7x-4)=\boxed{5x^3 - x^2 - 8x+1}[/tex]
Part C
No, because although they provide examples for specific polynomials being closed under addition and subtraction, there is a loss of generality.
pls answer fast , pls
Answer:
x is 14
1st is 14
2nd is 20
Step-by-step explanation:
4/7 (x ) = (34 - x )(2/5)
4x/7 + 2x/5 = 34 x 2/5 = 68/5
34x/35 = 68/5
x = 14
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The number of visitors to the homepage of an online magazine can be modeled by the equation y = 1100.74x − 1976.47, where x = 5 represents the year 2005 and y represent the total number of visitors.
FIRST ONE GETS BRAINLIEST OR 5 STARS
The number of visitors to the homepage of an online magazine in the year 2005 is 3527
What is an equation?An equation is an expression that shows the relationship between two or more number and variables.
Let y represent the total number of visitors x years since 2000. Hence:
y = 1100.74x - 1976.47
In the year 2005 (x = 5):
y = 1100.74(5) - 1976.47 = 3527.23
The number of visitors to the homepage of an online magazine in the year 2005 is 3527
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Which term describes the red curve in the figure below?
• A. Parabola
O B. Circle
• C. Hyperbola
O D. Ellipse
Answer:
the red curve is a hyperbola
Write the log equation as an exponential equation. You do not need to solve for x.
Answer:
x² - 5x + 17 = [tex](2x)^{3x}[/tex]
Step-by-step explanation:
using the rule of logarithms
[tex]log_{b}[/tex] x = n ⇒ x = [tex]b^{n}[/tex]
given
[tex]log_{2x}[/tex] (x² - 5x + 17) = 3x , then
x² - 5x + 17 = [tex](2x)^{3x}[/tex]
A magazine provided results from a poll of 1000 adults who were asked to identify their favorite pie. Among the 1000 ​respondents, 14​% chose chocolate​ pie, and the margin of error was given as +3 percentage points. What values do ​, ​, ​n, E, and p​ represent? If the confidence level is ​%, what is the value of ​?
The completion of the tabs are:
The value of [tex]\bar p[/tex] is the sample proportion.The value of [tex]\bar q[/tex] is found by evaluating [tex]1-\=p[/tex]The value of n is the sample size.The value of E is the margin of error.The value of p is the population proportion. α = 0.05.What is the margin of error.?You may calculate how many percentage points your findings will deviate from the actual population figure by using something called a margin of error.
In conclusion
The worth of p^ is the fraction of the sample.The worth of p^ is discovered by assessingThe sample size is given by the number n.The margin of error is expressed as E's value.The population percentage is represented by the value of p. α = 0.05.In conclusion,
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A firework is launched from the ground at a speed of 160 feet per second. It’s height after t seconds is given by the polynomial -16t^2+160t. What is the height of the firework after 4 seconds?
What is the end behavior of the graph
Answer:
as x is approaching positive infinity, y approaches positive infinity
as x is approaching negative infinity, y is approaching negative infinity
How many different 2-digit numbers are there with the following property: it is evan and its digits are distinct?
By counting all the even 2-digit numbers between 10 and 100, there are 41 even and distinct digits.
What is an even number?An even number can be defined as a type of number which is divisible by two (2) without any remainder.
How to determine this 2-digit number?Since this 2-digit numbers are even and its digits are distinct, we can infer and logically deduce the following points:
They are between 10 and 100.They are not repeated.They must contain two digits only.By counting all the even 2-digit numbers between 10 and 100, there are 41 even and distinct digits.
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Question 5(Multiple Choice Worth 1 points)
(02.01 LC)
Which of the following tables represents a function?
its the first one
a system can only be a function if there is only one value of y for each value of x. there cannot be two or more values of y for one single value of x in a function.
?? math-domain and range
Answer:
Domain: All real numbers (infinite) Range: [tex]y \leq -4[/tex]
Step-by-step explanation:
For the domain, the x-axis will continue to be used for the parabola, because the parabola can go on forever and can use an x- value on the x-axis. For the range, the largest number the parabola will go up to is -4. Therefore, if that is the highest point/ where the vertex is, the highest point on the y-axis is -4, resulting in the answer y can be equal to or less than -4 (y [tex]\leq[/tex] -4), since the parabola will continue to go down with the reflection over the x-axis.
Mario's car cost $15,999. Each year the car's value decreases by $1,550. This relationship is described by the equation V = 15,999 − 1,550t, when V is the value of the car and t is the age of the car in years. What is the value of his car after 5 years?
The value of Mario's car after 5 years is $8,249.
What is the value of the car after 5 years?Deprecation is when the value of an asset declines with the passage of time as a result of wear and tear.
V = 15,999 − 1,550t
V = 15,999 − 1,550(5)
V = 15,999 - 7,750
V =$8,249
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