The coefficient of x^11 in the binomial expansion of (x - 3)^12 is -36.
What is binomial expansion?
The binomial theorem in basic algebra explains how a binomial's powers can be expanded algebraically.
Exponents of x and y added together always equal n. The binomial coefficients that are equally spaced from the start and end are equal, i.e., nC0 = nCn, nC1 = nCn-1, nC2 = nCn-2, etc.
Consider, the given expression (x - 3)^12
We have to find the coefficient of x^11 in the expansion of (x - 3)^12.
Applying the binomial theorem,
(a + b)^n = Σ(i = 0 to n) nCi a^(n- i)b^i
Here a = x, b = -3.
⇒ (x - 3)^12 = Σ(i = 0 to 12) 12Ci x^(12 - i)(-3)^i
[tex](x -3)^1^2 = x^ 1^2-36^1^1+59x^1^0 - 5940x^9 + 40095x^8 - 192456x^7+ 673596x^6 - 1732104x^5 + 3267695x^4-4330260x^3 + 3897234x^2- 2125764x+531441[/tex]
Hence, the coefficient of x^11 in the binomial expansion of (x - 3)^12 is -36.
To know more about binomial expansion, click on the link
https://brainly.com/question/13602562
#SPJ1
Is y 3x 1 a direct variation?
The expression y-3x-1 is not a direct variation as it does not satisfy the criteria.
What is direct variation?It is a mathematical relationship between two variables shown by the form of an equation that says one variable is equal to the other variables that is multiplied by a factor.
Such as y =4x is an equation which express the direct variation between x and y as y is equal to four times of x
How can we identify the direct variation?The formula for direct variation is given by the equation y = kx.
x and y are variables, k is the constant or factor.
Suppose we examine a number of linear equations and check the ratio of the variables such as x and y ratio. If we find a constant ratio, then it is termed as direct variation.
In the given expression, y-3x-1 that could not satisfy the criteria of direct variation because there is a constant -1 in the expression. And while writing in an equation form, we get y-3x-1 =0
we never get constant ratio from x and y variables.
hence, this is not a direct variation.
To learn more about direct variation visit:
https://brainly.com/question/13977805
#SPJ4
whats 2+2+2+4+4+2+4 and writting form
2+2+2+4+4+2+4 = 20 and It's written in the addition form.
What is addition ?
One of the four fundamental mathematical operations, along with addition, subtraction, multiplication, and division, is addition. This operator is used to combine two or more objects or numbers.
Given, 2+2+2+4+4+2+4
The result can be found by applying addition,
So, 2+2+2+4+4+2+4 = 20
We can also find the sum of the above numbers by applying multiplication,
We've, 2+2+2+4+4+2+4
We will rearrange it in such a way that all the same numbers come together,
So, 2+2+2+2+4+4+4
Now, we can see that the number 2 is occurring 4 times and the number 4 is occurring 3 times,
So, It can be written as,
(2 × 4) + (4 × 3)
= 8 + 12
= 20.
Hence, We get the same answer in both the cases.
Learn more about Addition from the given link :
https://brainly.com/question/24536701
#SPJ1
What is 1/2 of a square?
One-half squared is one-fourth. In other words , 1/ 4 is the square is 1/2 .
What does Squaring mean?In mathematics, a square is the result of multiplying a number by itself. The verb "to square" is used to denote this operation. Squaring is the same as raising to the power 2, and is denoted by a superscript 2; for instance, the square of 3 may be written as 32, which is the number 9.
Squaring a number is simply multiplying the value by itself. When you take the square root of a number, you are figuring out what number had to be squared to get the original value.
The square of a number (let x) is given by the formula x².
According to the Question ,
Square of 1/2 is given by = (1/2)²
Since , the square of a number (let x) is given by the formula x².
(1/2)²
= 1/(2)²
= 1/ 4
= 0.25
Hence, One-half squared is one-fourth. In other words , 1/ 4 is the square is 1/2 .
Learn more about Square at:
https://brainly.com/question/27307830
#SPJ4
What's the relationship between the volume of the pyramid inscribed in a cube and the volume of the cube?
The relationship between the volume of the pyramid inscribed in a cube and the volume of the cube can be determined by comparing both. The volume of cube is three times the volume of the pyramid inscribed in the cube.
Let us say the cube is of side a. Then for a pyramid inscribed in the cube the base is the surface of the cube with dimensions a×a and is of height a.
Volume of a cube of side a is a³.
Vc = a³
Volume of a pyramid of base l×b and height h is given by
V = l×b×h/3
Therefore in this case volume of pyramid is
Vp = (a×a×a)/3
Vp = a³/3
Thus Vp = Vc/3, or we can say Vc = 3Vp.
To know more on volume of pyramid
https://brainly.com/question/17615619
#SPJ4
What is 3/4 in lowest terms as a fraction?
3/4 is the lowest form of the given fraction.
What is lowest form of fraction?if the highest common factor of numerator and denominator if equals to 1. then that fraction can't be reduced further and is said to be in the lowest form.
so suppose we are having any fraction of the form [tex]\frac{a}{b}[/tex]
the lowest form of the given fraction is given by [tex]\frac{x}{y}[/tex]
where x = [tex]\frac{a}{gcd(a,b)}[/tex] , y = [tex]\frac{b}{gcd(a,b)}[/tex]
where gcd is greatest common divisor of a , b
we are given fraction = 3/4
=> a = 3 and b = 4
gcd(3,4) = 1
so x = 3/(gcd(3,4)) = 3
y= 4/(gcd(3,4)) = 4
so the lowest form of 3/4 = [tex]\frac{x}{y}[/tex]
and x=3 and y=4
and hence lowest form = 3/4
To know more about lowest form click on below link:
https://brainly.com/question/28515437#
#SPJ4
Does 6 only have 2 factors?
Answer:
no
Step-by-step explanation:
the factors of 6 are
1, 2, 3, 6
that is 6 has 4 factors
If a€R then multiplicative inverse of a is ?
Answer:
[tex]\frac{1}{a}[/tex]
Step-by-step explanation:
the product of a number and its multiplicative inverse = 1 , then
a × [tex]\frac{1}{a}[/tex] = 1
multiplicative inverse of a is then [tex]\frac{1}{a}[/tex]
Sean can walk 2 1/4 miles in 2/3 hour.
At this rate, how far can he walk in 1 hour?
Answer:
3.375 or 3 3/8
Step-by-step explanation:
divide 2 1/4 to get 1 1/8 or 1.125 then multiply by 3 to get 3.375 or 3 3/8
What is the elevation of point a? point a has an elevation that is greater than 3350 feet. Point a has an elevation that is less than 3350 feet. Point a has an elevation of 3350 feet.
The elevation of point A is greater than 3350 feet.
The lines of equal elevation are known as contour lines. In relation to the mean sea level, it reflects the height of any specific site. The crucial elements on a topographic map are those that never cross each other.
Locations A and B are shown on the provided topographic map. By reading the contour and the contour interval, which is shown to be 50 feet, it is clear that Location A is higher up than Location B.
Location A is at a higher contour line, with respect to the contour 3250 feet, mentioned on the left side of location A.
Thus, the height of location A is slightly more than 3350 feet above the mean sea level.
(Refer to the image attached for the topographic map)
To know more about elevation points visit: brainly.com/question/29008290
#SPJ4
Context lines are those lines that have the same elevation. It reflects the height of any particular site in relation to the average sea level. A topographic map's most important features are those that never cross one another.
The topographic map is displayed with the locations A and B. It is evident that Location A is higher up than Location B by reading the contour and the contour interval, which is indicated to be 50 feet.
In comparison to the contour line of 3250 feet listed on the left side of location A, position A is at a higher contour line.
As a result, position A is higher above the norm by about 3350 feet.
Why are rigid transformations important?
Rigid body motion is a change that preserves space's geometric characteristics. It is a distance-preserving map or isometric since Euclidean qualities may be described in terms of distance.
What is rigid transformations?The separation between each pair of the geometric object's points is preserved during a rigorous change of the object. In other words, a rigid transformation maintains the object's size and shape. For instance, the rigid transformation of a triangle retains the angles and lengths of the triangle. Imagine a stiff shape distortion, similar to a cardboard shape. The form remains the same after being pushed left and right, rotated, and flipped. When the mold was created using putty, the opposite was true. The thing can then be twisted and stretched. These conversions, nevertheless, are not exact. Stretching a form alters the distances between each pair of its points.
To know more about rigid transformations visit:
https://brainly.com/question/29175049
#SPJ4
What is the median of the following numbers 8 1 2 6 1 4?
The median for the next batch of observations is 2.
What is median?The median is the value in the middle of a data set, which indicates that 50% of the data points have a value less than or equal to the median, and 50% have a value greater than or equal to the median. The median is the number in the middle of a set of numbers. The median represents the 50th percentile of the set of numbers. In other words, the median is the value in the center of a set of numbers where half are less than the median and half are more than the median.
Here,
given set of observation,
=1,1,2,4,6,8
n=6
median=6/2
=3rd term
=2
The median for following set of observation is 2.
To know more about median,
https://brainly.com/question/29156884
#SPJ4
The graph represents a quadratic function. Write an equation of the function in standard form.
The equation for the quadratic function in standard form is 4x² - 16x - 9
Writing Quadratic equationFrom the question, we are to write an equation for the quadratic function in standard form.
From the given quadratic graph,
The roots of the function are -0.5 and 4.5.
That is,
x = -0.5 and x = 4.5
That is,
x = -1/2 and x = 9/2
Therefore,
2x = -1 and 2x = 9
The factors of the quadratic function are (2x + 1) and (2x - 9)
Thus,
We can write that
(2x + 1)(2x - 9) = 0
4x² - 18x + 2x - 9 = 0
Simplify
4x² - 16x - 9 = 0
Hence, the equation is f(x) = 4x² - 16x - 9
Learn more on Writing quadratic equation here: brainly.com/question/23991455
#SPJ1
What are the 3 arguments for the range function?
The Python range() method needs three arguments to work: start value, stop value, and step value. after increasing the values by the step value's stated amount.
what are range ?For a specific data collection, the statistical range is the range of values between the highest and lowest values. The difference between the highest and lowest observation can also be used to illustrate the range. Subtracting the highest number from the lowest yields the sample interval. The sample range is a crucial indicator of variability for variables that are continuous.
here ,
The series of integers returned starts with this integer, startNumber (optional).
stopNumber: This number is the last in the series of integers returned by range().
the stepValue (optional): An integer value indicating how much each successive integer differs from the previous one.
To know more about range visit :-
https://brainly.com/question/28135761
#SPJ4
Haruki took a total of 12 quizzes over the courses or 2 weeks. After a school vacation, he took 18 quizzes over the span of 3 weeks. How many quizzes does Haruki take per week?
Answer:6 quizzes over 1 week
Step-by-step explanation: because if u add 6 + 6+ 6 that 18 so ya
A recipe for cinnamon rolls calls for 3 cups of flour for every 1/2 cup of water. Using the same recipe, how much water will you need for 5 cups of flour?
Answer: 3/10 cup of water
Step-by-step explanation:
Take 3 divided by 5 = 0.6
So, we know to get from 3 to 5 we need to times 0.6
So, we take 1/2 times 0.6
1/2 = 0.5
0.5 times 0.6 = 0.3 cup of water
0.3 = 3/10
So, the answer is 3/10 cup of water
3x+2=5x-6 i need the answer for x
Answer:
x=4
Step-by-step explanation:
3x+2=5x-6
3x+2-2=5x-6-2
3x=5x-8
3x-5x=5x-8-5x
-2x=-8
divide by -8 by -2
x= 4
What is the standard deviation of 2 4 6 and 8?
The calculated value of standard deviation for the given data set is 2.236.
What is standard deviation?Standard deviation is the measure of dispersion of the observed values relative to the mean value. It indicates how far each value is apart from mean value.
How to calculate the standard deviation of the given data set?we have data list 2 4 6 8
the list is denoted by X and X² is the square of the data set
X X²
2 4
4 16
6 36
8 64
we add all the data, and the result is ∑X = 20
similarly, we add all the squared value, and the result is ∑X² = 120
Standard deviation is calculated by using the formula below
SD = √[∑X²/N - (∑X/N)²]
here, N denotes the amount of data set
hence, N= 4
SD = √[120/4 - (20/4)²] = 2.236
hence, standard deviation is 2.236
To know more about standard deviation visit:
https://brainly.com/question/12402189
#SPJ4
Why is the square of i 1?
Let x=(i+1)^2. So the square of given expression will be x= 2i.
What is meant by square?A square in mathematics is produced by multiplying a number by itself. To describe this operation, the term "to square" is employed. For example, the square of 3 may be expressed as 3^2, which is the number 9, since squaring is the same as raising to the power 2. Squaring is indicated by a superscript 2.
How do you find square?We'll examine the square of any number, which we'll refer to as "n." The square of the digit "n" is represented by the symbol "n^2," and it can be determined by multiplying n by n.
(i+1)^2= i^2+1+2i
= -1+1 +2i
=2i.
To learn more about square visit the link:
https://brainly.com/question/27307830
#SPJ4
In what circumstances would an employee not qualify for SSP?
If the employee received maximum SSP in 28 weeks, then he or she is not qualified.
Here we have to identify the reason for the rejection of SSP for the employee.
In order to find the reason, we must know that is meant by SSP.
The term SSP refers a tool used to coordinate the supply and distribution of ad inventory to and from advertisers
Based on the definition, we have identified that if the employees does not qualify for SSP if they have received the maximum amount of SSP in last 28 weeks are getting Statutory Maternity Pay or Maternity Allowance then there are special rules for pregnant women and new mothers who do not get these payments.
To know more about Allowance here.
https://brainly.com/question/28831354
#SPJ4
HELP MEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE PLEASEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEHELP MEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE PLEASEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEHELP MEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE PLEASEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEHELP MEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE PLEASEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEHELP MEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE PLEASEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
Answer:
adult ticket $16
child ticket $12
Step-by-step explanation:
let x = price of adult tix
y = price of child tix
1) 3x + 4y = $96
2) 2x + 3y = $68
Subtract equation 2 from equation 1 to get:
3) x + y = 28
x = 28 - y (now substitute this into equation 1)
3(28-y) + 4y = 96
84 - 3y + 4y = 96
y = 96 - 84 = 12 (price of child tickets)
Now that you know the value of y, plug it into equation 3:
x + 12 = 28
x = 28 - 12 = 16 (price of adult tickets)
How do you know if it's a function or Nonfunction?
A function is a relationship between a set of possible inputs and outputs, where each input is associated with exactly one output.
A non-function is a relation between a set of inputs and a set of possible outputs where there is at least one input with more than one output.
The vertical line test can be used to ascertain whether a relation is a function. If you can draw a vertical line through the graph of the relationship and it intersects the graph at more than one point, then the relation is a non-function. If the vertical line intersects the graph at only one point, then the relation is a function.
Another way to determine if a relation is a function is to look at the equation defining the relation. If the equation does not contain any x's in the denominator, then the relation is a function. If the equation contains x's in the denominator, then the relation is a non-function.
For example, consider the relation defined by the equation y = x^2. This relation is a function because there are no x's in the denominator.
On the other hand, consider the relation defined by the equation y = 1/x. This relation is a non-function because the equation contains an x in the denominator.
To learn more about function, refer:-
https://brainly.com/question/5975436
#SPJ4
What is the sum of 5/14+24 1/2 ?
Enter your answer as a mixed number in simplest form by filling in the boxes.
Answer:
24 6/7
Step-by-step explanation:
5/14+24 1/2
24 1/2 = 49/2
5/14 + 49/2
The common factor is 14
5/ 14 + 343 / 14 = 348 /14 = 174 / 7
174/ 7 = 24 6/7
Step-by-step explanation:
1. Convert the mixed number 24 1/2 to an improper fraction by multiplying the whole number (24) by the denominator of the fraction (2) and adding the numerator (1). This gives us an improper fraction of 49/2.
2. Find a common denominator for the fractions 5/14 and 49/2. The least common multiple of 14 and 2 is 14, so we can rewrite the fractions as 7/7 and 49/14, respectively.
3. Add the numerators and keep the denominator the same: 7/7 + 49/14 = (7+49)/7 = 56/7
4. Simplify the fraction 56/7 by dividing both the numerator and the denominator by their greatest common factor, which is 7. This gives us a simplified fraction of 8/1, or 8.
5. The sum of 5/14+24 1/2 is equal to 8.
There are 2 squares and 4 triangles. What is the simplest ratio of squares to triangles?
Answer:
squares : triangles
1:2 or 1/2
Step-by-step explanation:
⭐What is a ratio?
A ratio is a comparison of two units.In this problem, the two units are squares and triangles.⭐ How can we write a ratio?
You can write a ratio as a fraction (e.g. 2/2)You can write a ratio with a colon (e.g. 2:2)For this problem, we can write the ratio of squares to triangles as:
[tex]\frac{2}{4}[/tex], or [tex]2:4[/tex].
But, we can further simplify this ratio.
To simplify the ratio, divide the numerator and denominator or both sides of the colon by the number they are both divisible by.
2 is divisible by 2, and 4 is divisible by 2:
[tex]\frac{2}{4}[/tex]
[tex]\frac{2 /2}{4/2}[/tex]
Simplified is: [tex]\frac{1}{4}[/tex]
[tex]2:4[/tex]
[tex]\frac{2}{2} : \frac{4}{2}[/tex]
Simplified is: [tex]1:4[/tex]
The temperature of magnesium must be at least 650 degrees for the metal to melt. a sample of magnesium is currently 255 degrees. the temperature of the magnesium is increased by 10 degrees every minute. which inequality shows the number of minutes (m) needed to raise the temperature to the melting point?
a. m > 39.5
b. m ≥ 39.5
c. m > 87.5
d. m ≥ 87.5
It will take at least 39.5 minutes to raise the temperature of the magnesium sample to its melting point.
B. m ≥ 39.5
Formula:
[tex]m ≥ (650 - 255)/10[/tex]
We can use the formula [tex]m ≥ (650 - 255)/10[/tex] to solve for the number of minutes (m) needed to raise the temperature of the magnesium from 255 degrees to the melting point of 650 degrees.
First, we subtract the initial temperature of 255 degrees from the melting point of 650 degrees. This gives us 395.
Then, we divide 395 by 10, which is the number of degrees the temperature is increasing every minute. This gives us the result of 39.5 minutes.
Therefore, the answer is m ≥ 39.5, which means that it will take at least 39.5 minutes to raise the temperature of the magnesium to the melting point.
Learn more about Temperature here :
brainly.com/question/29768169
#SPJ4
What is degree 3 equation called?
Answer:
An equation with a degree of 3 is called a cubic function.
Step-by-step explanation:
Functions are named by their degree.
Examples:
[tex]y = ax^2 + bx + c[/tex] is named a quadratic function because it has a degree of 2.
Similarly, [tex]y = ax^3 + bx^2 +cx + d[/tex] is named a cubic function because it has a degree of 3.
How do you tell if a system has no solution or infinitely many?
When a system has no solution it is called inconsistent equation
When a system has infinitely many solution it is called consistent and dependent equations
How to tell if a system is are inconsistent equationsA system is considered to be inconsistent if there is no solution. There is no solution because the line graphs are parallel and not intersecting.
x + 5y = 4 and x + 5y = −2
subtracting gives
0 = -6 no solution
this is an instance
How to tell if a system is consistent and dependent equationsA consistent system is dependent if there are an endless number of possible solutions. The two equations represent the same line when you graph them. An instance of the situation is
3x + y = 4
−6x − 2y = −8
subtracting gives
9x + 3y = 12 - none eliminates, meaning infinite many solutions
Learn more on simultaneous equation here:
https://brainly.com/question/29729655
#SPJ1
What is meant by preimage?
The preimage of a value z by the function f are all the values for which the function f(x)=z.
What is preimage?
The preimage of a value z by the function f are all the values for which the function f(x)=z.
According to the given question:
As a simple example, consider the function f(x) = √x . The preimage of 5 is 25; for ℕ(the set of natural numbers) it is the set of all perfect squares in ℕ
PREIMAGES OF SET: The pre Given a function f:A→B , and D⊆B , the preimage D of under f is defined as
f−1(D)={x∈A∣f(x)∈D}.(5.4.5)
Hence, f−1(D) is the set of elements in the domain whose images are in C . The symbol f−1(D) is also pronounced as “ f inverse of D .”
The preimage of a value z by the function f are all the values for which the function f(x)=z.
To know more about preimage, check out:
https://brainly.com/question/29054921
#SPJ4
How do you solve parallel and perpendicular lines with equations?
The equations allow us to compare the slopes of two lines to determine if they are parallel. The lines are parallel if the slopes are the same and the y-intercepts are different. The lines are not parallel if the slopes differ.
Perpendicular lines do meet, but parallel lines do not. They meet at a straight angle, or 90 degrees.Different perpendicular lines have different slopes. There is a distinct difference in the slopes of perpendicular lines.
One line's slope is equal to the other line's slope's negative reciprocal. A number's reciprocal and its product equal one. If m 1 and m 2 are negative reciprocals of one another, then multiplying them together will result in the number 1.
As with parallel lines, we can determine whether two lines are perpendicular by comparing their slopes. The slope of each line below is the negative reciprocal of the other so the lines are perpendicular.
To know more about slope of line refer to:
brainly.com/question/19131126
#SPJ4
The slope of one line is equal to the negative reciprocal of the slope of the other line. The product and reciprocal of a number are both one. The outcome of multiplying m 1 and m 2 together if they are the negative reciprocals of one another is 1.
Similar to parallel lines, we can compare the slopes of two lines to determine if they are perpendicular. Each of the lines below has a slope that is the negative reciprocal of the other, making them perpendicular.
Values for relation g are given in the table. Which ordered pair would be found in the inverse of g?.
The ordered pair found in inverse of g is ( 1 , 4 ) .
Given :
Relation :
A function is a relation which describes that there should be only one output for each input (or) we can say that a special kind of relation (a set of ordered pairs), which follows a rule .
Values for relation g are given in the table:
X Y = g( X )
5 -3
4 1
3 -2
2 0
then the table for g inverse will be:
X Y = g^-1 ( x )
-3 5
1 4
-2 3
0 2
Hence, the ordered pair found in inverse of g is ( 1 , 4 )
Learn more about the relation here:
https://brainly.com/question/6241820
#SPJ4
Full question :
Values for relation g are given in the table. Which ordered pair would be found in the inverse of g?.
X Y = g( X )
5 -3
4 1
3 -2
2 0
If EG = 19 and FG = 12, then EF
Answer:
EF = 7
Step-by-step explanation:
Take EG - FG = EF
19 - 12 = 7
So, the answer is EF = 7