Answer:
125, 216, 343, 512
Step-by-step explanation:
The next number in the sequence 1, 8, 27, 64 is 125.
This sequence follows the pattern of starting with the number 1, then finding the cube of each subsequent integer (the cube of a number is found by multiplying the number by itself twice, so the cube of 2 is 222=8). Therefore, the next number in the sequence would be 555=125.
What are the types of sum?.
The types of sum are following :
Sum of single digit numbersSum of double digit numbersSimilarly, sum of n numbersSum of numbers is defined as the total which is result of adding numbers. Now, we have to discuss about types of sum. It is represented by plus sign (+) and summation, sigma symbol.
Type 1 : Sum of one-digit numbers : We can get the sum of 2, single-digit numbers such as 1, 2, 3, 4, 5, 6, 7, 8, 9 with different combinations. For example: 3 + 15 = 18.
Type 2 : Sum of two-digits numbers : first add the one's place digits if result is greater than 9 then transfer carry digit. After that add the ten's place digits with carry digit. For example, 35 + 56 = 91
Sum of n natural numbers : The summation formulas are used to calculate the sum of the sequence. To write the sum of more terms, say n numbers of a sequence {aₙ}, we use the summation formula instead of writing the whole sum, i.e., a₁ + a₂ + ------+ aₙ = ∑ aᵢ ; 1≤ i ≤ n. There are various types of sequences such as arithmetic sequence, geometric sequence, etc and hence there are various types of summation formulas of different sequences.
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Find the 10th term for 5-,20,-80,320
The 10th term of the sequence is -131072.
What is a geometric sequence?
A geometric sequence is a sequence of numbers such that the quotient between any two consecutive terms is a constant called the common ratio.
This sequence appears to be a geometric sequence with a common ratio of -4.
To find the nth term of a geometric sequence, we can use the formula:
[tex]a_n = a_1 * r^{n-1}[/tex]
where a_n is the nth term, a_1 is the first term, r is the common ratio, and n is the position of the term in the sequence.
So, in this case:
[tex]a_10 = 5 * (-4)^(10-1) = 5 * (-4)^9 = 5 * -262144 = -131072[/tex]
Therefore, the 10th term of the sequence is -131072.
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PLEASEE HELP ME ILL GIVE U BRAINLIST
A triangle has vertices located at coordinates (-2, 4), (-2,-4), and (1, 0)
What are the coordinates of the centroid of this triangle?
The centroid is the object's focal point. The centroid of a triangle is the location where the three medians of the triangle intersect.
What is centroid of triangle?The centroid is the object's focal point. The centroid of a triangle is the location where the three medians of the triangle intersect. The junction of all three medians is another definition for it. The median is a line that connects the middle of a side to the triangle's opposite vertex. The centroid of the triangle can then be determined by averaging the x and y coordinates of each of the three vertices. Thus, G(x, Y) = ((x1 + x2 + x3)/3, (y1 + y2 + y3)/3 is a mathematical expression for the centroid formula.The triangle's centroid is the point at where its three medians cross. These characteristics apply to it: Always in the center of the triangle is where the centroid. The segment that connects the vertex to the opposite side's midpoint has the centroid at a distance from the vertex of two thirds of that segment.To learn more about centroid of triangle refer to:
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The notation "f(x)" (f of x) is another way of representing y-values in a function question 1 options: true false
The given statement " the notation "f(x)" is another way of representing y-values in a function" is true because f (x) and y are the same things.
The notation f(x), read as "f of x", indicates a function named f. It reflects that 'y is a function of x'. The letter 'x' refers to the input value or independent variable. While the letter 'y' is replaced by f(x) and it refers to the output value or dependent variable.
The notation 'f (x)' is exactly the same as that of 'y'. Even on graphs, y-axis can be labelled with 'f (x)'.
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how do you solve for the midsegment of a trapezoid with only the coordinates given?
The midsegment of a trapezoid with only the coordinates given can be determine by following steps 1,2 and 3 below
How to solve for the midsegment of a trapezoid with only the coordinates given?The midsegment of a trapezoid is a line segment that connects the midpoints of the two parallel sides of the trapezoid.
To solve for the midsegment of a trapezoid with only the coordinates given, you can use the following steps:
1. Find the coordinates of the midpoints of the two parallel sides of the trapezoid. To do this, you need the coordinates of the four vertices of the trapezoid. For example, if the trapezoid has vertices A(x1, y1), B(x2, y2), C(x3, y3), and D(x4, y4), the midpoints of the two parallel sides are:
Midpoint of AB: ((x1 + x2)/2, (y1 + y2)/2)
Midpoint of CD: ((x3 + x4)/2, (y3 + y4)/2)
2. Use the coordinates of the two midpoints found in step 1 to find the equation of the line that contains the midsegment. The slope of the midsegment is the average of the slopes of the two parallel sides of the trapezoid.
The equation of the line can be written in slope-intercept form (y = mx + b) or point-slope form (y - y1 = m(x - x1))
3. Once you have the equation of the line you can use it to find the y-intercept b and the slope m.
For example:
Trapezoid with coordinates A(2,3), B(4,4) , C(7,5) and D(5,6)
Midpoint of AB: (3,3.5)
Midpoint of CD: (6,5.5)
Slope of AB = (y2-y1)/(x2-x1) = (4-3)/(4-2) = 1/2
Slope of CD = (y4-y3)/(x4-x3) = (6-5)/(5-7) = -1/2
Midsegment slope = (1/2 + (-1/2))/2 = 0
The equation of the midsegment line is y = 0x+b
by using the point (3,3.5)
we can find the value of b = 3.5
Thus, the equation of midsegment is y = 0x + 3.5
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Last week, Nico bought 11 shirts and hats for total of $194. Today, Nico bought shirts and hats for total of $120. Assuming neither item has changed price, what is the cost of a shirt dollars?
Answer:
2 dollers
Step-by-step explanation:
120$ +194$ divided by C square is e square so in conclution the sum will eventually be 4$ and 4$÷2= 2$
How do you find the value of x in a logarithmic function?.
To find the value of x in a logarithmic function, you need to use the definition of logarithms, which states that log_b x is the power to which b must be raised to produce x.
In other words, if f(x) = log_b x, then b^(f(x)) = x. To find x, you simply need to raise b to the power of f(x), using the inverse of the logarithmic function, which is the exponential function. This can be done using a calculator or by using logarithmic rules and properties to simplify the expression and solve for x. It's important to remember that logarithmic functions are only defined for positive values of x and that the base b must be positive and not equal to 1.
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How do you convert a mixed fraction to an improper fraction Class 4?.
To transform a mixed fraction into an improper fraction, first, we multiply the denominator of the proper fraction by the whole number attached to it, and then we add the numerator.
An improper fraction is a kind of fraction in which the numerator will be greater than or equal to the denominator.
Let's take an example to understand the process completely.
For example, 3(1/2) is a mixed fraction. Convert it into an improper fraction.
Step 1: Multiply the denominator with the whole number of the fraction, i.e. Multiply 2 with 3 in the given example, 3(1/2).
2 × 3 = 6
Step 2: Add the numerator of the Fraction to the answer from step 1. i.e., Add 1 + 6
= 7.
Step 3: Keep the Denominator the same, i.e. 2.
Step 4: The Improper fraction obtained is: 7/2.
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3)
Oranges cost $0.36 per pound. Write an equation to represent the total cost, C, of pounds, p of oranges.
Then p + $0.36 is an equation to represent the total cost, C, of pounds, p of oranges.
The overall cost calculation formula?The formula for average total cost is created by dividing the sum of all production costs by the sum of all payments in money. The total-cost formula is a simple and user-friendly process that works by dividing the total production cost by the quantity of goods produced.
Together, fixed and variable costs make up the overall cost. The total cost, for instance, would be $35 if a company had a fixed cost per unit of $30 and a variable cost per unit of $5 that increased as output increased.
Then p + $0.36 is an equation to represent the total cost, C, of pounds, p of oranges.
p + $0.36
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A contractor can spend at most $250 a day on operating costs and payroll. It costs $45 each day to operate the forklift and $60 a day for each crew member. Write an inequality to represent the contractor's budget for the day.
60x + 45 ≥ 250
60x + 45 ≤ 250
60 − 45x ≥ 250
60 − 45x ≤ 250
Every math class is made up of 18 twelve graders and 4 eleventh graders. The twelve grades averaged a 83, on the midterm exam, and the eleventh graders averaged a 79 on the midterm exam. What was the average grade on the midterm exam for the entire class? Round to the nearest whole number.
The average midterm exam grade for the entire class is 82.
What is average?The middle value in a set of numbers is the average, which is calculated by dividing the total of all the values by the number of values.
Here given that,
Math class contains 18 twelve graders.
Also contains 4 eleventh graders
Total number of students = 18 + 4 = 22
Total marks of students in the twelve grade = 18 x 83 = 1494
Total marks of students in the eleventh grade = 4 x 79 = 316
Total marks = 1494 + 316 = 1810
Therefore to find the average grade of midterm exam is :
1810 / 22 = 82.2
Therefore the average grade on the midterm exam for the entire class is 82.
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i need the answers please help! i will give brainliest, but please give a small explanation of why your answer is correct :)
The required (A) maximum height of the ball is 60 yards, (b) the height of the Brad cannot be justified and (C) the horizontal distance the ball traveled is 300 yards.
What are functions?Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
Here,
Draw the function of the ball on the coordinate plane, as shown.
From the figure, the maximum height of the golf ball is given as 60 yards while the maximum horizontal distance is 300 yards.
Thus, the required (A) maximum height of the ball is 60 yards, (b) the height of the Brad cannot be justified and (C) the horizontal distance the ball traveled is 300 yards.
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HELP MEEEEEE PLEASEEEEE
5 4/12 is what in improper fraction
Answer:
[tex]\frac{16}{3}[/tex]
Step-by-step explanation:
Multiply the whole number by the denominator
5 × 12 = 60
Add the answer from Step 1 to the numerator
60 + 4 = 64
Write the answer from Step 2 over the denominator
64/12
Simplify the fraction :
Find the greatest common factor of 64 and 12
GCF of 64 and 12 = 4
64 ÷ 4 = 16
______
12 ÷ 4 = 3
The mixed number 5 4/12 converted to an improper fraction is, therefore :
16/3
Answer:
16/3
Step-by-step explanation:
Multiply the whole number by the denominator=5x12
=60.
2. Add the product to the numerator
=60+4
=64.
3. Answer = 64/12.
4. Simplify the answer by using the
greatest common factor of 64 and
12, which is 4.
=64÷4
12÷4
=16
3
The improper fraction for 5 4/12 is 16/3.
if[ tex]x-\frac{1}{x} =1[/tex] then what is [tex]\frac{x}{x^{2}+3x-1 } =\frac{1}{4}[/tex]
The value of the equation is x² - x - 1 = 0
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
x - ( 1/x ) = 1 be equation (1)
On simplifying the equation , we get
( x² - 1 ) / x = 1
Multiply by x on both sides of the equation , we get
x² - 1 = x
Subtracting x on both sides of the equation , we get
x² - x - 1 = 0
Now , given that ( x / ( x² + 3x - 1 ) ) = 1/4
On simplifying the equation , we get
Cross multiplying the equation , we get
4x = ( x² + 3x - 1 )
Subtracting 4x on both sides of the equation , we get
x² - x - 1 = 0
Hence , the equation is x² - x - 1 = 0
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what is the intermediate step in the form of (x+a)=b for x^2+5x+11=13x
To find the intermediate step in the form of (x+a)=b for the equation x^2+5x+11=13x, we need to first move all the terms to one side of the equation.
x^2+5x+11 = 13x
x^2 - 8x + 11 = 0
To solve this equation, we can factor it.
x^2 - 8x + 11 = 0
(x-11)(x-1) = 0
So, we have two solutions for x: x = 11 and x = 1
To find the intermediate step in the form of (x+a)=b, we can write each solution as (x+a)=b
x = 11, so (x+(-11)) = 11
x = 1, so (x+(-1)) = 1
So, the intermediate step in the form of (x+a)=b for the equation x^2+5x+11=13x is:
(x-11) = 11 and (x-1) = 1
How do you graph the inverse of a linear graph?.
The inverse of a linear graph can be graphed by x and y coordinates.
When a function is stated in the form which is y = mx + b, where m and b are real integers and m is not equal to 0, the function is said to be linear. The variables in this equation are x and y, while the coefficients are m and b. A linear graph is the graph of a linear function, where a linear function has a straight line as its graph; its slope is m and its y-intercept is (0,b). The inverse of a linear graph can be thus created as -
Firstly, all the points on the original graph should have their x and y coordinates switched.Second, there should be reflecting the new points on the y = x line.Thus, the inverse function's graph will be a line that crosses the line y = x and reflects it on the original graph.Read more about the linear graphs on:
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what 5 1/3 minus 3 2/3 and 8 4/7 minus 7 5/7 is? And if possible try simplifying the answers. But at least show a step by step explanation.
The answers to each part is -
(5 1/3) - (3 2/3) = 5/3(8 4/7) - (7 5/7) = 6/7What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is to find -
(5 1/3) - (3 2/3) (8 4/7) - (7 5/7) ( 1 ) -We can write the expression as -
{x} = [tex]5\frac{1}{3} - 3\frac{2}{3}[/tex]
{x} = 16/3 - 11/3
{x} = 5/3
( 2 ) -We can write the expression as -
{x} = [tex]8\frac{4}{7} - 7\frac{5}{7}[/tex]
{x} = 60/7 - 54/7
{x} = 6/7
Therefore, the answers to each part is -
(5 1/3) - (3 2/3) = 5/3(8 4/7) - (7 5/7) = 6/7To solve more questions on algebraic expressions, visit the link below -
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How many different 5-digit PIN codes are there that only include the digits 6, 2, 5, 4, 8 and 7?
Answer:
First, there are NO 5-digit pin codes that include the digits 7, 2, 4, 6, 9, and 3. But, there are 720 pin codes that include 5 out of the 6 digits.
Step-by-step explanation:
what is the perimeter of a sector of a circle of radius 6cm with a sector angle of 35°?
Sector perimeter equals 2 radius plus arc length. The formula for calculating arc length is: arc length = l = (/360) 2 r. As a result, the sector's perimeter is equal to 2 Radius plus ((/360) 2r).
What does a sector's and a segment's perimeter mean?The perimeter of a form is its entire outer circumference. Using what we know about determining the length of an arc, we can get the perimeter of a sector. The intersection of two radii and an arc creates a sector. We must sum these values in order to determine the perimeter. Arc length plus two is the perimeter.
How do you calculate a circle's sector area?Sector area is easily calculated by multiplying the central angle by the radius squared and dividing by two: Sector Area is equal to r2 / 2.
When the sector angle = 360° , curved length of the arc = 2πR
Hence when the central angle = 80 degree, the curved length = (80/360x(2πR)
= 1.3963 R = 1.3963 * 6 = 8.3776 cm.
Hence the perimeter = R + R + 8.3776 = 20.3776 cm
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Divide the following: Please show your work. (Lots of points.)
Answer:
-27
10x +8.
Step-by-step explanation:
x² - 9 ÷ x² - 4x - 5
=x²+5x+4 x² - 2x - 15
x² - 9 × x² - 2x - 15
=x² +5x +4 x² - 4x - 5
-9 × 3
=5x. 4. 2
-27.
=10x + 8 .
The mass of a cube, M (kg), is proportional to the cube of the length of its edge,
L (m).
The mass of the cube is 40 kg when the length of its edge is 35 cm.
Work out M (to 2 DP) when L = 0.6 m
Thank you
Answer:
We are given that the mass of a cube, M, is proportional to the cube of the length of its edge, L. This means that we can write the relationship between M and L as:
M = kL^3
where k is the proportionality constant.
We are also given that when the length of the cube's edge is 35 cm, the mass of the cube is 40 kg. So we can use this information to find the value of the proportionality constant k.
35 cm = 0.35 m (converting cm to m)
Now we can substitute the given values into the equation and find k:
40 = k(0.35)^3
k = 40 / (0.35)^3
Now that we have the value of k, we can use it to find the mass of the cube when the length of its edge is 0.6 m.
M = kL^3
M = 40 / (0.35)^3 * (0.6)^3
M = 40 / (0.35)^3 * (0.216)
M = 40 / (0.003375) * (0.216)
M = 40 / 0.00726 * 0.216
M = 40 / 0.015856
M = 2511.53 kg (to 2 decimal places)
So the mass of the cube when the length of its edge is 0.6m is 2511.53kg
The answer would be M = 204.6 kg
The mass of the cube, M, is given by the equation M = kL^3, where k is the proportionality constant.
Given that M = 40 kg when L = 0.35 m, we can find k by substituting these values into the equation:
40 = k(0.35)^3
k = 40 / (0.35)^3
= 40 / 0.0421875
= 947.125
To find M when L = 0.6 m, we can substitute this value of L into the equation:
M = 947.125 * (0.6)^3
= 947.125 * 0.216
= 204.6
The given information is that M is proportional to the cube of L. This means that the mass of the cube is directly proportional to the cube of the length of its edge. The proportionality constant k is found by using the given values of M and L, and then using that constant value we can find the mass when we know the length of the edge.
We have found the mass of the cube when the length of its edge is 0.6m is 204.6 kg by using the proportionality constant and equation we have derived from the given information.
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Pat has a fever. His temperature is 99.3 degrees F.
If the conversion to Celsius is C=5/9 (F-32), what is the most accurate measurement of Pat's temperature in degrees Celsius?
Answer: the most accurate measurement of Pat's temperature in degrees Celsius is 37.3 degrees.
Step-by-step explanation:
The conversion from Fahrenheit to Celsius is C = 5/9 (F-32).
First, we substitute Pat's temperature of 99.3 degrees Fahrenheit into the equation:
C = 5/9 (99.3-32)
C = 5/9 * 67.3
C = 37.3 degrees Celsius
So the most accurate measurement of Pat's temperature in degrees Celsius is 37.3 degrees.
Answer:
37.4 degrees
Step-by-step explanation:
C = 5/9 (F-32)
F = 99.3 so plug F into the equation
C = 5/9 (99.3 - 32)
C = 5/9 (67.3)
5/9 in a calculator = .555 repeating
.555 x 67.3 = 37.35
Rounded = 37.4 degrees
A giraffe is 18 feet tall and casts a shadow of 12 feet. Corry casts a shadow of 4 feet. How tall is Corry? Use similar triangles to find the missing information.
What is an example of Avogadro's number?.
According to the definition of Avogadro's number , the correct statement is (d) Avogadro’s number is 6.02×10²³ , which equals the number of items in one mole.
The Avogadro number or Avogadro constant is the number of units present in one mole of any substance is .
The Avogadro number is equal to 6.022140857 × 10²³ .
The Avogadro number creates a bridge between the macroscopic world and microscopic world by relating the amount of substance to number of particles.
Therefore , the correct statement is (d) .
The given question is incomplete , the complete question is
What is the correct statement about Avogadro's number ?
(a) Avogadro’s number is 8.31, which equals the number of items in one mole.
(b) Avogadro’s number is 1.60×10¹⁹ , which equals the number of items in one mole.
(c) Avogadro’s number is 1.38×10²³, which equals the number of items in one mole.
(d) Avogadro’s number is 6.02×10²³ , which equals the number of items in one mole.
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The row reduction algorithm applies only to augmented matrices for a linear system. True or False?
The assertion is untrue. Regardless of whether a matrix is considered to be an augmented matrix for a linear system, the procedure can be applied to any matrix.
What is linear system?A system of linear equations is a collection of two or more equations with the same variables. Here, one may state that first-order linear equations are those in which the variable's greatest power is 1.One variable, two variables, or three variables can all be present in a linear equation. Therefore, if the output of the system caused by the weighted sum of the inputs equals the weighted sum of outputs, we may conclude that the system is linear. Examples of linear systems include filter circuits, communication channels, etc. Simply said, a system of linear equations is a collection of two or more linear equations. An equation system with two variables (x and y) has a graph that is two lines in the plane.To learn more about linear system, refer to:
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16% of what number is 2? Pls reply quick I. Need help
Answer:
12.5
Step-by-step explanation:
What is set Give 2 example?.
A Set is a collection of well-defined entities or elements.
A capital alphabetic symbol represents a set, and the number of elements in the finite set is represented as the cardinal number of a set in a curly bracket {…}. For example, set A is a collection of all the natural numbers, such as A = {1, 2, 3, 4, 5, 6, 7, 8,…..∞}.
Sets can be represented in three forms:
Roster Form: Set of even numbers less than 8 = {2, 4, 6}
Statement Form: A = {Set of Odd numbers less than 9}
Set Builder Form: A = {x: x = 2n, n ∈ N and 1 ≤ n ≤ 4}
Examples of sets are,
(a) Set of first 8 multiples of 7
Suppose the set of first 8 multiples of 7 is A
Set A = {7, 14, 21, 28, 35, 42, 49, 56}.
As there are 8 elements in the set, cardinal number n(A) = 8
(b) Set B = {a, e, i, o, u, j, k}
Set B = {a, e, i, o, u, j, k}. This set contains 7 elements,
Thus, the cardinal number of set B, n(B) = 7.
(c) Set C = {x | x are even numbers between 10 and 20}
Set C = {12, 14, 16, 18}. These numbers create the elements of set C.
Thus, the cardinal number of set C, n(C) = 4.
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Roman and Sienna are comparing the number of pages they’ve each read over the Winter Break. Roman said he read 40% of his book, which has a total of 200 pages. Sienna’s book has a total of 400 pages, and she read 1/5 of it. Who do you predict has read more pages of their book? Explain your reasoning.
Roman and Sienna read equal number of the pages of the book.
What is comparison?Comparison or comparing is the act of evaluating two or more things by determining the relevant, comparable characteristics of each thing, and then determining which characteristics of each are similar to the other, which are different, and to what degree.
Given that, Roman and Sienna are comparing the number of pages they’ve each read over the Winter Break. Roman said he read 40% of his book, which has a total of 200 pages. Sienna’s book has a total of 400 pages, and she read 1/5 of it.
Book read by Roman = 40% of 200
= 40 / 100 x 200
= 80 pages
Book read by Sienna = 1/5 of 400
= 400 x 1/5
= 400/5
= 80 pages
Since, both of them read equal number of pages.
Hence, Roman and Sienna read equal number of the pages of the book.
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Aume a multiple-choice quetion on an online quiz ha 9 anwer choice in if, which ar hown in random order to each tudent. In how many way can thi quetion be diplayed
So, the question can be displayed in 362880 ways.
A multiple-choice question on an online quiz has 9 answer choices, which are shown in random order to each student. The number of ways the question can be displayed is determined by the number of permutations of the 9 answer choices. In this case, the question can be displayed in 9! (9 factorial) different ways.
9! is the shorthand notation for 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1. Factorial notation is used to indicate the product of all integers from 1 to a given number. In this case, 9! means that the product of all integers from 1 to 9 is calculated.
The reason why it is 9! and not 9^9 is because, when arranging the 9 items in different ways, order matters. So, in the first slot, we have 9 options to choose from, in the second slot, we have 8 options left to choose from, in the third slot we have 7 options left and so on.
Therefore, the question can be displayed in 362880 ways.
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The abbreviation 9! stands for 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1. To represent the sum of all integers from 1 to a specified number, the factororial notation is used. 9! in this context denotes the computation of the product of all numbers from 1 to 9.
Because order counts when arranging the 9 items in various ways, the answer is 9! rather than 99. Therefore, we have nine options to choose from in the first spot, eight options are still available in the second slot, seven options are still available in the third slot, and so on.
