Answer:
[tex]\boxed{x^4+4x^3y+6x^2y^2+4xy^3+y^4\\}[/tex]
Step-by-step explanation:
Pascal’s triangle defines the coefficients which appear in binomial expansions. That means the nth row of Pascal’s triangle comprises the coefficients of the expanded expression of the polynomial (a + b)ⁿ
To create Pascal's triangle for any n in (a + b)ⁿ ,
To build the triangle, start with "1" at the top, then continue placing numbers below it in a triangular pattern.Here is Pascal's triangle for the first 5 rows. The first row is row 0
Row #
0 1
1 1 1
2 1 2 1
3 1 3 3 1
4 1 4 6 4 1
[tex]\textrm{ Here row 0 represents $(a + b)^0$ }[/tex] = [tex]\boxed{\textbf{1}}[/tex]
[tex]\textrm{Row 1 corresponds to $(a + b)^1$} =[/tex] [tex]\boxed{1}\;a + \boxed{1}\;b[/tex]
[tex]\textrm{Row 2 corresponds to $(a + b)^2$} = \boxed{1}\;a^2 + \boxed{2} \;ab +\boxed{1}\;b^2[/tex]
[tex]\textrm{Row 3 corresponds to $(a + b)^3$} = \boxed{1}\;a^3 + \boxed{3}\;a^2b + \boxed{3}\;ab^2 + \boxed{1}\;b^3[/tex]
[tex]\textrm{Row 4 corresponds to $(a + b)^4$} = \boxed{1}\;b^4 + \boxed{4} \;a^3b +\boxed{6}\;a^2b^2 + \boxed{4} \;ab^3 + \boxed{1} \;b^4[/tex]
For the specific problem, (4x + 3y)³ use coefficients of row 3 and use 4x instead of a and 3y instead of b
[tex]\mbox{\normal(4x + 3y)^3= \boxed{1}\;(4x)^3 + \boxed{3}\;(4x)^2(3y) + \boxed{3}\;4x(3y)^2 + \boxed{1}\;(3y)^3}[/tex]
[tex]= \boxed{x^4+4x^3y+6x^2y^2+4xy^3+y^4\\} \;\;\; \textrm{ANSWER}[/tex]
Step-by-step explanation:
l don't know how to solve
it
Solve for x ∼
[tex]\color{purple} \large\frak{3x + 5 = 3(x - 5)}[/tex]
[tex] \\ \\ \\ \\ \\ \\ \\ \\ [/tex]
Ty
————————————————————————
[tex]3x+5=3(x-5)[/tex]
Distribute numbers outside of parentheses:
[tex]3x+5=(3)(x)+(3)(-5)[/tex]
[tex]3x+5=3x-15[/tex]
Subtract 3x from both sides:
[tex]3x+5-3x=3x-15-3x[/tex]
[tex]5=-15[/tex]
Subtract 5 from both sides:
[tex]5-5=-15-5[/tex]
[tex]0=-20[/tex]
[tex]\fbox{No solution}[/tex]
a 32-bit signed number expressed in hexadecimal? enter a hexadecimal number with eight digits and the leading 0x, e.g., 0x12345678.
A 32-bit signed number expressed in the hexadecimal number is 0xFFFFFFFB.
For negative number is represented by 2's complement. It is 1's complement +1.
0000-> Hex digit 0
0001-> Hex digit 1
0010-> Hex digit 2
0011-> Hex digit 3
0100-> Hex digit 4
0101-> Hex digit 5
0110-> Hex digit 6
0111-> Hex digit 7
1000-> Hex digit 8
1001-> Hex digit 9
1010-> Hex digit A
1011-> Hex digit B
1100-> Hex digit C
1101-> Hex digit D
1110-> Hex digit E
1111-> Hex digit F
Hexadecimal is a numbering system with base 16. It can be used to represent large numbers with fewer digits. In this system there are 16 symbols or possible digit values from 0 to 9, followed by six alphabetic characters -- A, B, C, D, E and F.32-bit number is 00000000000000000000000000000101. Its 1's complement is 11111111111111111111111111111010
2's complement is 11111111111111111111111111111010+1 =11111111111111111111111111111011
for hexadecimal, we group 4 binary bits
11111111111111111111111111111010= 1111 1111 1111 1111 1111 1111 1111 1010
hexadecimal value of 1111 is F
hexadecimal value of 1111 is F
hexadecimal value of 1111 is F
hexadecimal value of 1111 is F
hexadecimal value of 1111 is F
hexadecimal value of 1111 is F
hexadecimal value of 1111 is F
hexadecimal value of 1011 is B
Therefore, the hexadecimal number is 0xFFFFFFFB.
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A circle with radius 1-inch rolls without slipping along the sides of a right triangle whose side lengths are 3 inches, 4 inches, and 5 inches as shown. When the circle gets to a vertex, it continues to rotate around the vertex. The circle stars and ends at the middle of the 5 inch side. The center of the circle travels a total distance of [tex]M+N\pi[/tex]
in one complete circuit. Find [tex]M+N[/tex] in simplest form
The total distance covered by the circle is 15.14 inches.
What is a triangle?A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.
Given, A circle with a radius of 1 inch rolls without slipping along the sides of a right triangle.
We know the distance around the triangle is the perimeter of the triangle.
The perimeter of the triangle is the sum of the lengths of all the sides.
Here, 'M' is the perimeter and 'N' is the number of complete rotations.
Therefore,
M + Nπ.
= (3 + 4 + 5) + 1(3.14).
= 12 + 3.14.
= 15.14 inches.
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what is an irreflexive closure
Irreflexive closure is the creation of a new binary relation by adding irreflexivity property, meaning no element is related to itself.
What is binary ?
A binary number is a number expressed in the base-2 numeral system or binary numeral system, a method of mathematical expression which uses only two symbols: typically "0" and "1".
An irreflexive closure is a mathematical concept that refers to the creation of a new binary relation from a given binary relation by adding the property of irreflexivity. A binary relation is irreflexive if it does not relate any element to itself. The irreflexive closure of a binary relation is the smallest irreflexive relation that contains it.
In other words, the irreflexive closure of a binary relation is a modified version of the original relation where no element is related to itself. The process of finding the irreflexive closure involves removing all self-referential relationships and adding new relationships to preserve the original relationships between elements.
Irreflexive closure is the creation of a new binary relation by adding irreflexivity property, meaning no element is related to itself.
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The speed of a boat in still water is 15Km/hr. It needs four more hours to travel 63 Km against the current river than it needs to travel down the river. Determine the speed of the current of the river.
Answer:
The speed of the current of the river is 6 km/hr--------------------------------
Let the speed of the current be x.
The speed with current is 15 + x and the speed against current is 15 - x.
The time difference to travel the distance of 63 km is 4 hours:
63/(15 - x) - 63/(15 + x) = 463(15 + x - 15 + x) = 4(15 + x)(15 - x)63*(2x) = 4(225 - x²)63x = 450 - 2x²2x² + 63x - 450 = 0x = (-63 + √(63² + 2*4*450))/4 (negative root is discarded)x = (-63 + 87)/4x = 6Write an expression that is equivalent to -4(3x - 7)=?
Answer:
-12x + 28
Step-by-step explanation:
To do this question we have to expand the brackets and collect like terms
1) Expand brackets
-4 (3x - 7)-4 × 3x = -12x-4 × -7 = 28-12x + 282) Collect like terms
There are no like terms in the final answer so it must still be the sameTOP TIP:
Be careful with the operations for example if we were to say that -4 × -7 = -28 our answer would be wrong!
The rules for the operations is that if a - and a + are multiplied the answer will always be -.
If the operations are a - and - the answer will always be +
What is the samole variance for the data given:
5,10,7,12,0,20,15,22,8,2
The Samole variance for the given data is 0.
What is the variance of the data?The variance is mean squared difference between each data point and the center of the distribution measured by the mean.
The given data is 5,10,7,12,0,20,15,22,8,2.
We know that, Variance = [tex]\frac{\sum( {\bar x-x} )}{Number of observations }[/tex]
Here, [tex]\bar x[/tex] = (5+10+7+12+0+20+15+22+8+2)/10
= 101/10
= 10.1
Now, variance = [(10.1-5)+(10.1-10)+(10.1-7)+(10.1-12)+(10.1-0)+(10.1-20)+(10.1-15)+(10.1-22)+(10.1-8)+(10.1-2)]/10
= 0/10
= 0
Therefore, the Samole variance for the given data is 0.
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Solve the equation7(x+4)=-21. X=
Answer: x = -7
Step-by-step explanation:
7(x + 4) = -21
x + 4 = -3
x = -7
Answer:
-7 because -7 + 4 is -3 and 7 x -3 is -21
Step-by-step explanation:
A ballet school wants to buy new slippers for students in a class. They collected the sizes and displayed them in a line plot. A horizontal number line starting at 3.5 with tick marks every 0.5 units up to 8. The following values are labeled: the value of 3.5 has one dot, the value of 4 has two dots, the value of 5 has one dot, the value of 6.5 has one dot, the value of 7 has one dot, the value of 7.5 has two dots and the value of 8 has one dot. The image is titled Ballet Shoe Sizes. What is the range, and what does it mean in terms of this data set? The range is 3.5, and it means that it is the value that occurs the most. The range is 4.0, and it means that the data varies by a value of 4.0. The range is 3.5, and it means that it is the value that is the smallest. The range is 4.5, and it means that the data varies by a value of 4.5.
The range is 4.5, and it means that the data varies by a value of 4.5.
What is the data set?
A data set is an ordered collection of data. As we know, a collection of information obtained through observations, measurements, study, or analysis is referred to as data. It could include information such as facts, numbers, figures, names, or even basic descriptions of objects.
The range is the difference between the largest and smallest values in a data set.
In this case, the largest value is 8 and the smallest value is 3.5, so the range is 8 - 3.5 = 4.5.
This means that the ballet shoe sizes in this class vary by 4.5, with the largest size being 8 and the smallest size being 3.5.
Hence, The range is 4.5, and it means that the data varies by a value of 4.5.
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Please help fast!
The first two terms of an infinite geometric series are 4 and 3. Which of these could be used to find the sum of the series?
The formula for the sum of the infinite series is; Sn= 4/1 - 3/4. Option D
What is infinite geometric series?
An infinite geometric series is a series of numbers in which each term is a constant multiple of the previous term. The sum of an infinite geometric series can be found if the absolute value of the common ratio is less than 1.
The formula for the sum of the infinite geometric series can be found to be;
Sn = a/1 - r
r = common ratio
a = first term
Sn = Sum of the terms
Sn = 4/1 - 3/4
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Please help me
Show work
For the system of equations x - 2y = 4 and y = 4 - x, the solution is (4, 0) Trevor is correct. So Option B is correct
What is an Equation ?An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.
For example, 3x+2y=0.
Types of equation
1. Linear Equation
2. Quadratic Equation
3. Cubic Equation
Given that,
the system of equations,
x - 2y = 4
And y = 4 - x,
x - 2y = 4
-x - y = -4 (multiply the equation by -1)
-3y = 0
y = 0
x - 0 = 4
x = 4
Hence, the solution of system is (4, 0)
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What number is halfway between -38.7 and -38.71?
Answer:
the answer to this question is -77.41
What is the depth of recursion in the binary search?
arr = {2, 6, 10, 99, 898) and key = 898
a. 3
b. 5
c. 2
d. 4
If the arr = {2, 6, 10, 99, 898) and key = 898 , then the depth of recursion in the binary search is (c) 2 .
The Depth of Recursion in Binary Search refers to the number of recursive calls required to find the target element in the array.
In the Binary Search, the array is repeatedly divided in half until , we find the target element or conclude that it is not present in the array.
The target element (Key) is = 898 and the array is {2, 6, 10, 99, 898} .
The initial array is divided into two parts: {2, 6, 10, 99} and {898} ;
Since 898 is larger than 99, we only need to consider the right half of the array: that is {898}.
The next step is to compare the target element (Key) = (898) with the middle element which is {898} .
and Since they both are equal, we have found the target element.
Therefore , the depth of recursion in this binary search is (c) 2.
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Give an exact condition for when a rational number p, q E Z,q 0 has a a terminating base 60 representation. Prove your assertions. (b) What about base n?
A rational number p/q has a terminating base 60 representation if q is a factor of 60. This can be proven by noting that q is a factor of p if and only if the remainder of p divided by q is 0. For any base n, q must be a factor of n in order for p/q to have a terminating base n representation.
A rational number p/q has a terminating base 60 representation if q is a factor of 60. This can be proven by noting that q is a factor of p if and only if the remainder of p divided by q is 0. This can be seen by noting that if q is a factor of p, then p can be written as a multiple of q, or p = kq, where k is an integer. Thus, p/q = k, and the remainder of p divided by q must be 0. If q is not a factor of p, then the remainder of p divided by q will not be 0. Thus, for a rational number p/q to have a terminating base 60 representation, q must be a factor of 60. To determine if q is a factor of n for any base n, we must again consider the remainder of p divided by q. If the remainder of p divided by q is 0, then q is a factor of n, and the rational number p/q will have a terminating base n representation. If, however, the remainder of p divided by q is not 0, then q is not a factor of n and the rational number p/q will not have a terminating base n representation.
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A political candidate is told by his polling organization that a 90% confidence interval for the true proportion of voters who support his candidacy is 0.45 to 0.53. Which of the following claims is justified?
a. A political reporter claims that 90% of registered voters favor this candidate.
c. A political reporter claims that at least 53% of registered voters favor this candidate.
d. A political reporter claims that the majority of registered voters favor this candidate.
e. A political reporter claims that at least 45% of registered voters favor this candidate.
Need the answer here
Therefore , the solution of the given problem of mean comes out to be on total he gets $2.00 from the bags.
What is mean?A dataset's mean is the sum of all values divided by the total number of values, often known as the arithmetic mean (as opposed to the geometric mean). Often referred to as the "mean," this is the most often used measure of central tendency. Simply dividing the dataset's total number of values by the sum of all of those values yields this result. Both raw data and data that have been combined into frequency tables can be used for calculations.
Here,
Given :
A ,B , C , D , E, F .
The game is played by choosing 2 bags.
Each of five of bags holds $1.00 and one of the bags total $10.00 .
So, there are 5/6 th bags are average is $1.00 .
Thus , on average if they choose 2 bags is $1.00 each .
on total he gets $2.00 from the bags.
only 1/6th bag he will get $10.00
Therefore , the solution of the given problem of mean comes out to be on total he gets $2.00 from the bags.
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chandler is building a wooden birdhouse for his mom. he finds a plank in the garage to use for the base. when he realizes it's too long, chandler cuts 3 inches off the plank. now it's the correct length of 8.25 inches.which equation can you use to find the length p of the plank before chandler cuts it?
The equation p = 8.25 + 3 inches can be used for finding the length p of the plank before chandler cuts it.
Addition is one of the four fundamental mathematical operations, the others being subtraction, multiplication, and division. When two whole numbers are added together, the total quantity or sum of those values is obtained.
In mathematics, addition is the process of joining two or more integers. The numbers being added are known as addends, and the result or final response obtained after the procedure is known as the total.
From the given data,
The length of the plank cut by the chandler =3 inches
The correct length = 8.25 inches.
So, for finding the value of the length p of the plank before the chandler cuts, we will add the value of the correct length and the length of the plank cut by the chandler.
So, the value of p will be: 8.25+3 = 11.25 inches.
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should the researcher use the rows or the columns of the field as blocks? justify your answer.
Yes, the researcher use the rows or the columns of the field as blocks.
When conducting research, it is important to think about which structure to use as the basis for your work.
In particular, when dealing with a matrix, the question arises of whether the researcher should use the rows or columns as blocks.
Both have their own advantages and drawbacks, which should be taken into consideration before making a decision.
However, it can be challenging to discover similarities between data points within the same row.
Additionally, the matrix structure can become distorted, as the data points no longer form a neat square or rectangle.
Ultimately, which approach the researcher should take depends on the type of research being conducted and the goals of the project.
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Which of the following graphs is decreasing when x > 3?
-2
-2
2
W.
24
-24
Y.
-2
-2
4+
121
-2
X.
у
++
24
2
Z.
2
X
X
The graph that is decreasing when x > 3 is Graph y .
How to find the graph ?With graph W, when x > 3, the graph is still increasing as shown by the arrow going up . With graph x , when the graph gets to the point where x > 3, it will keep increasing as well .
For graph Y, the graph rises all the way up to x = 3 and then from there, begins to decrease. This means that for all points where x > 3, the graph would be decreasing.
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a different poll of households had a sample mean of children and a sample standard deviation of children. what is the -statistic? type as:
The number of the degrees of freedom for the data given below is 14.
Given that ,
According to data from the US Census Bureau, there are 1.86 children on average in each American home. In a specific city, 15 households were polled.
To find : The degree of the freedom ?
The mean number of children in an
American House hold is 1.86
Polls of 15 households were conducted in a city.
So, No . of households sampled
D = 15
Degrees of freedom of = n- 1
= 15 - 1
=14
Therefore, the degree of the freedom is 14.
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The United States Census Bureau determined that the mean number of children in an American household is 1.86. Polls of 15 households were conducted in a certain city. What is the number of degrees of freedom?
A line segment is translated 3 units down and 1 unit to the left. One of the endpoints after the translation is (5, 8). What was this point before the translation?
The endpoint before the translation was (6, 11).
What was this point before the translation?A translation of 3 units down and 1 unit to the left, applied to a general point (x, y), gives:
(x - 1, y - 3)
We know that after we apply this to a point, we get the endpoint of the segment (5, 8)
Then we can write the equation:
(x - 1, y - 3) = (5, 8)
Then we can write:
x - 1 = 5 -----> x = 5 + 1 = 6
y - 3 = 8 -----> y = 8 + 3 = 11
The point before the translation is (6, 11).
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plssss anyone helppp mee plsss
Answer:
Distance = ✓2
Midpoint = (-4, 10)
Step-by-step explanation:
a.) (-3,8) and (-5,12)
These coordinates are (x,y)
Let's subtract the X's
-5-(-3) = -2
And for the Y's
12-8 = 4
Next, you would add these together
-2+4 = 2
Last step is squaring rooting this number
✓2, you can either find the actual square root by calculator or leave it as ✓2. This would be your distance.
Finding the midpoint is like the average. Right in the middle. So you would do the same with these.
To find X you'll add them then divide by 2 since there are 2 x coordinates
-3+-5 = -8
Divided by 2 = -4
Same with Y
8+12 = 20
Divided by 2 = 10
Now we can say the midpoint is (-4, 10)
Solve the equation: 2x + x + (x + 20) = 180
What is the value of x?
35, 40, 50, or 90
Answer:
x=40
Step-by-step explanation:
Please explain the best you can. And please don’t answer if you don’t know how to do it. :)
Answer:
10
Step-by-step explanation:
whole circle area = π r² = π*7² =49π
60 = 1/6 of the circle
so 49π/6 is the slice area
then minus the triangle area
triangle area =1/2*6* height
height² =6²-3² =36-9 = 27
so height = 5.2
triangle area =1/2*6* 5.2 =15.6
so the sliver = 49π/6 -15.6 =10
what is the time complexity of uttkonen’s algorithm?(1 point) a) o (log n!) b) o (n!) c) o (n2) d) o (n log n)
The time complexity of uttkonen’s algorithm is option(a) that is
O (n log n)
The time complexity is the number of operations an algorithm performs to complete its task (considering that each operation takes the same amount of time). The algorithm that performs the task in the smallest number of operations is considered the most efficient one in terms of the time complexity.
O(log N) is a common runtime complexity. Examples include binary searches, finding the smallest or largest value in a binary search tree, and certain divide and conquer algorithms. If an algorithm is dividing the elements being considered by 2 each iteration, then it likely has a runtime complexity of O(log N)
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HELP ME PLSS!?!?
In the mall you receive a coupon for $5 off of a pair of jeans when you arrive at the store you find that all jeans are 25% off
.let x represent the original cost of the jeans
.the function f(x)=x-5 represents the cost of the jeans if you use the coupon
.the function g(x)=0.25x represents the cost of the jeans if you apply the store discount of 25% first
You find a pair of jeans for $36. How much would you pay for it using h(x)? How much would you pay using j(x)? Explain which function composition will give you the better discount?
Answer:
The function h(x) represents the cost of the jeans if you first use the coupon and then apply the store discount. The function h(x) can be computed using the composition of functions f(x) and g(x). The function j(x) represents the cost of the jeans if you first apply the store discount and then use the coupon. The function j(x) can be computed using the composition of functions g(x) and f(x).
If you use the composition h(x), you will pay $27 for the jeans. If you use the composition j(x), you will pay $30 for the jeans. Therefore, the composition h(x) will give you a better discount since it is cheaper.
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at his school's spring carnival, javier is in charge of the balloon-launcher contest. in this contest, each team builds a catapult to launch water balloons at a target. javier gives a bucket of 12 water balloons to each team in the contest. in all, he gives out 48 water balloons.which equation can you use to find the number of teams t in the contest?
The equation which represents the number of the team 't' participated in the water balloon contest is equal to 12t = 48 and number of teams are 4.
Let us consider 't' represents the number of teams participated in the water balloon contest.
Total number of water balloons given by Javier to each team is equal to 12
Total number water balloons distributed by the Javier is equal to 48.
The equation which represents the number of the team in the water balloon contest is given by :
12t = 48
Number of teams participated in contest are:
⇒ t = 48 / 12
⇒ t = 4
Therefore, the equation represents the number of teams in the balloon contest is equal to 12t = 48 and number of teams are 4.
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calculate -8000 * 41 with long division
The solution to the expression is -328000
How to evaluate the expressionFrom the question, we have the following parameters that can be used in our computation:
calculate -8000 * 41 in long division
The above expression is a product expression
This means that it cannot be evaluated using long division
When the expression is evaluated. we have
-8000 * 41 = -328000
Hence, the solution is -41000
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HELP ME ASP !!!!!!!!!!!!!!!!!!!!
(a) Determine the y coordinate of the center of the circle
(b) The radius of the circle is 7 units. What is the value of b in the equation?
a. The y coordinate of the center of the circle is -1.
b. The value of b in the equation is 44 units.
The solution has been obtained using circles.
What is a circle?
A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point.
a. We are given the equation as
x² + y² - 4 x + 2 y = b
On solving the equation, we get
x² - 4 x + 4 + y² + 2 y + 1 = b + 4 + 1
This can be written as
( x - 2 )² + ( y + 1 )² = b + 5 ...(1)
So, the y - coordinate of the center of the circle is - 1.
b. We know that equation of circle is
( x - a )² + ( y - c)² = r²
On comparing this with (1), we get
b + 5 = r²
b + 5 = 7²
b + 5 = 49
b = 49 - 5
b = 44
Hence, the value of b is 44 units.
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