Answer:
See below
Step-by-step explanation:
Permutation is to select an object then arrange it and it cares about the orders while Combination is about only selecting an object without caring the orders.
Permutation can be expressed in math as:
[tex]\displaystyle{_n P _r = \dfrac{n!}{(n-r)!} \ \ \ (n \geq r) }[/tex]
where n is a number of total object and r is a number of selected object to arrange. Hence. n cannot be less than r.
Now let's see an example of permutation, suppose we have letter A, B and C. I'd like to know how many ways these words can be arranged:
Since there are 3 letters total and 3 selected letters to arrange then:
[tex]\displaystyle{_3 P _3 = \dfrac{3!}{(3-3)!}}\\\\\displaystyle{_3 P _3 = \dfrac{3 \times 2 \times 1}{0!}}\\\\\displaystyle{_3 P _3 = \dfrac{6}{1}}\\\\\displaystyle{_3 P _3 = 6}[/tex]
Therefore, there are 6 ways to arrange the letters - we can also demonstrate visually:
ABC - 1
ACB - 2
BAC - 3
BCA - 4
CAB - 5
CBA - 6
Notice that if you do visually, you'll get the same answer as the calculation of permutation!
----
Combination can be expressed mathematically as:
[tex]\displaystyle{_n C _r = \dfrac{n!}{(n-r)!r!} = \dfrac{_n P _r}{r!} \ \ \ (n \geq r) }[/tex]
The difference between permutation and combination is that you only find how many ways you can select object in combination. Therefore, no arrange and doesn't care about order, just ways to select.
Suppose we have same 3 letters: A, B and C. I want to find how many ways I can select these 3 letters:
Since there are 3 letters total and 3 selected letters:
[tex]\displaystyle{_3 C _3 = \dfrac{3!}{(3-3)!3!}}\\\\\displaystyle{_3 C _3 = \dfrac{3!}{0!3!}}\\\\\displaystyle{_3 C _3 = \dfrac{3!}{3!}}\\\\\displaystyle{_3 C _3 = 1}[/tex]
Hence, there is only one way to select 3 letters. This makes sense because if you have 3 letters then you can only select 3 letters only one way.
Permutations and combinations have many practical applications in various fields such as statistics, Probability theory, and computer science.
Permutations and combinations are two concepts in mathematics that deal with counting and arranging elements in a set.
Permutations refer to the number of ways in which a set of objects can be arranged or ordered. In other words, permutations involve counting the number of possible ways in which a group of objects can be arranged in a particular order. For example, if we have three objects A, B, and C, the possible permutations would be ABC, ACB, BAC, BCA, CAB, and CBA. The formula for permutations is nPr = n! / (n - r)!, where n is the total number of objects and r is the number of objects being arranged.
Combinations, on the other hand, refer to the number of ways in which a subset of objects can be selected from a larger set, without regard to the order in which they are selected. In other words, combinations involve counting the number of possible subsets that can be formed from a larger set. For example, if we have three objects A, B, and C, the possible combinations would be AB, AC, and BC. The formula for combinations is nCr = n! / (r! * (n - r)!), where n is the total number of objects and r is the number of objects being selected.
The key difference between permutations and combinations is that permutations involve ordering objects, while combinations do not. Another important distinction is that in permutations, each arrangement is considered distinct, whereas in combinations, different arrangements that contain the same objects are considered identical.
Permutations and combinations have many practical applications in various fields such as statistics, probability theory, and computer science. For example, they are commonly used in solving problems related to probability, combinations of locks, and permutations of passwords. Understanding these concepts is essential in order to effectively analyze and solve problems in these fields.
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What is a dilation What does it mean to dilate by a factor of 2?
To expand or contract, we say something has "dilated. Every point's coordinates in the initial triangle are multiplied by the scale factor if it is 2, which multiplies each point's coordinates by 2.
What exactly does the term "dilate by a factor" mean?Factor of scale (Dilation) Scale Factor (Dilation) The scale factor specifies how much larger or smaller the image will be in a dilation of a mathematical entity (compared to the original object). An expansion takes place when the scale factor's absolute value is higher than one.To expand or contract, we say something has "dilated." For instance, the y-axis will contract by a factor of 2 when x is replaced with x/0.5=x/(1/2)=2x. When A is negative, we first flip the y-axis and then enlarge by a factor of |A|.Every point's coordinates in the initial triangle are multiplied by the scale factor if it is 2, which multiplies each point's coordinates by 2.To learn more about dilated refer to:
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What is the formula to find centre?
The general equation to find centre of a circle is ( x - h )^2 + ( y - k )^2 = r^2, where ( h, k ) is the center and r is the radius.
Centre of the CircleThe location of a moving point on a plane such that its separation from a stationary point on the plane remains constant or fixed is described as a circle. The centre of the circle is the name given to the fixed point
A circle's centre and radius make up its 2D shape. Knowing the circle's centre and radius allows us to draw any circle. The number of radii that a circle can have is unlimited. The intersection of all the radii constitutes the centre of a circle. It is also known as the centre of the circle's diameter.
Center of Circle FormulaThe general equation of a circle is another name for the centre of circle formula. If the radius is r, the center's coordinates are (h,k), and any point on the circle is (x,y), the centre of the circle formula is as follows:
(x - h)2 + (y - k)2 = r2
2 = r2
Also known as center of the circle equation. we'll use this formula to determine a circle's equation or centre.
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Hello. I have an inverse function question that I cannot figure out. Please help!!
Answer: simplify the answer
Step-by-step explanation:
12aª²b²+ llab-5 with the solutions
Answer:
5127658756789587;'70
Which of the following refers to an angle whose measures is between 90degrees and 180 degrees?A. Acute Angle C. Obtuse AngleB. Right Angle D. Straight Angle
C. Obtuse Angle refers to an angle whose measure is between 90 degrees and 180 degrees.
An acute angle measure less than 90 degrees, a right angle is exactly 90 degrees and a straight angle is 180 degrees.
What is the Sin(B)? need help! Thanks
The diameter of a child's bicycle wheel is 12 inches. Approximately how many revolutions of the wheel will it take to travel 1,200 meters? Use 3.14 for π and round to the nearest whole number. (1 meter ≈ 39.3701 inches)
It will take 1274 revolutions to cover 1200 meters
What is the area and circumference of a circle?
The circumference (or) perimeter of a circle = 2πr units. The area of a circle = πr2 square units. Where r is the radius of the circle. The circumference of the circle or the perimeter of the circle is the measurement of the boundary of the circle. Whereas the area of the circle defines the region occupied by the circle.
Given here: The diameter of a child's bicycle wheel is 12 inches.
The diameter of the wheel is 12 inches=0.30 m
∴ circumference=3.14 ×0.3
=0.942
Therefore the number of revolutions are = 1200/0.942
= 1274
Hence, It will take 1274 revolutions
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Answer:
its 1254 revolutions
Step-by-step explanation:
you multiply 39.3701 by 1200 which gives 47,244.12 and you multiply 12 by 3.14 and that gives 37.68 so you then divide 47,244.12 by 37.68 which will give you a very long decimal including 1253 which becomes rounded to 1254
Answer: D. 1254 revolutions
What is the exponential value?
The exponential value of a number is equivalent to the number which is multiplied by itself a particular set of times.
When we represent a number in the exponential form then we can say that its power has been raised by an exponent. The exponential form is an easier way of representing repeated multiplication involving base and exponents.
The number which is multiplied by itself is called the base and the number of times it is to be multiplied is the exponent.
For example, If we have to write the exponential form of a×a×a×a×a, we can write it as a base and the number of a's as the power that is
a×a×a×a×a = a⁵
Where
a is the base
5 is the power of a
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What is the value of (−127) − 62 − (−15)?
−174
−50
−204
−80
Answer:
(-127)-62-(-15)
Open the bracket
-127-62+15
Bodmas rule(addition first)
-127-47=-174
Paula is 10 less than thrice Kaye's age. Two years from now, Paula's age is twice Kaye's present age. How old is Kaye now?
( Please show solution )
Answer: Kaye is 4 years old
Step-by-step explanation:
Paula is 10 less than thrice of Kaye's age. two years from now, Paula's age is twice Kaye's present age. how old is Kaye now? Let Kaye's age now be x years Paula is 10 less than thrice of Kaye's age =3x-10 TWO YEARS LATER Paula,s age = (3x-10)+2 = 3x-8 3x-8 =x 2x=8 x=4 Kaya,s age = 4 years
Out of a cla of 24 tudent, 7/14 of the total tudent were
choen for drill, 4/16 of the total tudent were choen for variou race, 1/6 of the total
took part in gymnatic. The ret of them did not attend the Sport Day. I) How many tudent did not attend the Sport Day?
2 students did not attend the Sports Day.
In mathematics, a fraction is used to denote a portion or component of the total. It stands for the proportionate pieces of the whole. The numerator and denominator are the two components that make up a fraction.
Given that,
Total number of students in a class = 24
Total number of students chosen for drills = 7/14 = 7/14 *24 = 12
Total number of students chosen for various races = 4/16 = 4/16 *24 = 6
Total number of students chosen for gymnastics= 1/6= 1/6* 24 = 4
Thus, the Total number of students participating in sports day = 12+6+4 = 22
Hence, the Total number of students that did not attend sports day= 24 - 22 = 2
Therefore, 2 students did not attend the Sports Day
Correct question: Out of a class of 24 students, 7/14 of the total students were chosen for drills, 4/16 of the total students were chosen for various races, and 1/6 of the total took part in gymnastics. The rest of them did not attend the Sports Day.
i) How many students did not attend the Sports Day?
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Word Problems Involving Real Numbers (Rational Numbers)
Solve for the following. Show your solution.
1. Paul spent 3
1/2
hours doing her assignment. Lorence did his assignment for
1 and 2/3 times as many hours as Paul did. How many hours did Lorence spend doing
3
his assignment?
2.
How many thirds are there in six-fifths?
3.
Hanna donated 2/5
of her monthly allowance to the landslide survivors. If her
monthly allowance is 500 aed, how much did she donate?
i will give brainliest if you answers fast
You are not going out of the same time for the same thing
Step-by-step explanation:
Uhgvhddfd dtcgxgstdd fhfgyfeywc
Gjufchhjjjjujch
The perimeter of a rectangle is 108 ft. If the length is 24 ft more than the width, find the dimensions of the rectangle. 
The dimensions of the rectangle will be -
x {length} = 39 ft
y {width} = 15 ft
What is the area of a rectangle?The area of a rectangle is -
Area = Length x Breadth
A = L x B
Given is the perimeter of a rectangle is 108 ft. Also the length is 24 ft more than the width.
We can write the length is equivalent to -
x {length} = y {width} + 24
The perimeter will be -
2(x + y) = 108
x + y = 54
y + 24 + y = 54
2y = 30
y {width} = 15 ft
Then, we can write the length as -
x {length} = 15 + 24 = 39
x {length} = 39 ft
Therefore, the dimensions of the rectangle will be -
x {length} = 39 ft
y {width} = 15 ft
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Find the olution of the quadratic equation 3x2−x8=03x 2 −x8=03, x, quared, minu, x, plu, 8, equal, 0
The solution of the given quadratic equation is x = 1/3 or -3.
The given quadratic equation is 3x^2 + 8x - 3 = 0.
Multiplying the coefficient of the first term and the last term, we get:
3 x 3 = 9
Factors of 9 are:
1 and 9
3 and 3
We choose 1 and 9 as these factors, when subtracted give us the middle term.
Hence, we can write 3x^2 + 9x - x - 3 = 0
3x (x+3) -1 (x+3) = 0
(3x -1) (x+3) = 0
x = 1/3 or -3
The question is incomplete, the complete question is:
Find the solution of the quadratic equation 3x^2 + 8x - 3 = 0.
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factorise x^2-2x-48.
Answer: (x+6) (x-8)
Step-by-step explanation:
x^2-2x-48
x^2+6x-8x-48
x*(x+6) -8(x-6)
(x+6) (x-8)
Why must the base of a logarithm be a positive real number not equal to 1?
The base of a logarithm must be a positive real number and not equal to 1 because logarithms are defined as the inverse operation of exponentiation. The base must be a positive real number to be able to raise it to the power of the argument and not equal to 1 to get a meaningful result.
The base of a logarithm represents the number that is being raised to a certain power to produce the argument of the logarithm. If the base of a logarithm is not a positive real number, it is not possible to perform this inverse operation.
For example, if the base of a logarithm is 0, it would mean that the argument of the logarithm is being raised to the power of 0, which is always 1. Therefore, the logarithm would be 0 for any argument, which does not provide any useful information.
The base of a logarithm must be a positive real number and not equal to 1 because it is not possible to raise 1 to any power to produce any value other than 1. Therefore, a logarithm with base 1 is not a meaningful concept.
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pls send the correct answer answer
they're similar because the triangles are having the same set of angles
Find the length of side xx in simplest radical form with a rational denominator.
Answer:
x = √22
Step-by-step explanation:
This is a right triangle.
In right triangles the sum of square value of legs is equal to the square value of hypotenuse:
Since this is also an isosceles triangle, both legs are √11.[tex]( { \sqrt{11}) }^{2} + ( \sqrt{11} {)}^{2} = {x}^{2} [/tex]
The second power of √11 = 11[tex]11 + 11 = {x}^{2} [/tex]
Find the root of both sides√22 = x
What is the radius of a globe that has a volume of 904.78 in.³?
Since the globe is in a shape of a sphere, the radius of the globe with a given volume of 904.78 in.³ is equal to 6 in .
What is a sphere?The sphere is a three-dimensional form that is sometimes referred to as a circle's second cousin. A sphere is a solid form that is circular, without borders. Examples of spherical shapes include a playing ball, a balloon, and even light bulbs.
What is the formula for calculating the volume of a sphere?The formula for calculating the volume of a sphere is given by,
Volume of a sphere (V) = [tex]\frac{4}{3} \pi r^{3}[/tex] .
Where [tex]\pi[/tex] = 3.14 and r is the radius of the sphere.
Given information in the question,
volume of a sphere(V) = 904.78 in.³
Radius (r) = ?
To find the radius of the sphere, using the formula for volume of sphere,
Volume of a sphere (V) = [tex]\frac{4}{3} \pi r^{3}[/tex] .
or, 904.78 = [tex]\frac{4}{3} \pi r^{3}[/tex]
Therefore, r = 6 in.
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There are 30 students in a class. Today, 26 students are present. Choose an equation to show how many students are absent.
Responses
26+a=30, a=4; 4 students are absent.
26 plus A is equal to 30, , A is equal to 4, ; , 4 students are absent.,
26+30=a, a=56; 56 students are absent.
26 plus 30 is equal to A, , A is equal to 56, ; , 56 students are absent.,
a−26=30, a=56; 56 students are absent.
A minus 26 is equal to 30, A is equal to 56; 56 students are absent.
26−a=30, a=4; 4 students are absent.
The equation that represents the number of absent students is:
30 - 26 = a
so a = 4, there are 4 absent students.
Which equation shows how many students are absent?We know that there are 30 students in a given class, and particularly, today there are 26 students present.
We want to find an equation that gives the number of students absent, and that would be equal to the difference between the total number of students (30) and the number of present students (26)
Then we will get the equation:
30 - 26 = a
Solving that we get:
30 - 26 = a
4 = a
There are 4 absent students.
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In kite ABCD, BE = –x + 6 and ED = 0.5x. Determine the value of x in the kite shown.
Answer: X=4
Step-by-step explanation:
.5x=-x+6
1.5x=6
x=4
reflection across x = 4
F(3,-5), C(3,-4), P(5,-4)
Given:
Points F(3,-5), C(3,-4), P(5,-4)The triangle FCP is reflected across the line x = 4.
See the attached with both FCP and F'C'P' triangles shown.
The x-coordinates are 1 unit apart from the x = 4 line, hence the new coordinates are 2 units less or greater than the original one and the y-coordinates remain as is.
Reflected points:
F(3, -5) → F'(5, - 5)C(3, - 4) → C'(5, - 4)P(5, - 4) → P'(3, - 4)Answer:
F' = (5, -5)
C' = (5, -4)
P' = (3, -4)
Step-by-step explanation:
When an object is reflected over a vertical line, the x-value changes but the y-value does not change.
To reflect points across x = 4, determine the distance of the x-value of each of the points to the line of reflection by subtracting 4 from the x-values:
F: 3 - 4 = -1C: 3 - 4 = -1P: 5 - 4 = 1Point F is located 1 unit to the left of the line of reflection. Therefore, the reflection of this point is 1 unit to the right of the line of reflection. So the reflection of point F is 2 units to the right of point F:
F' = (3+2, -5) = (5, -5)As point C has the same x-value as point F, the x-value of its reflection in the line of reflection will be the same as point F:
C' = (3+2, -4) = (5, -4)Finally, point P is located 1 unit to the right of the line of reflection. Therefore, the reflection of this point is 1 unit to the left of the line of reflection. So the reflection of point P is 2 units to the left of point P:
P' = (5-2, -4) = (3, -4)Josiah's monthly bank statement showed the following deposits and withdrawals: $94.57, -−$87.78, -−$16.36, -−$64.92, $10.73 If Josiah's balance in the account was $62.72 at the beginning of the month, what was the account balance at the end of the month?
The account balance at the end of the month is $-1.04.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Josiah's monthly bank statement showed the following deposits and withdrawals: $94.57, -−$87.78, -−$16.36, -−$64.92, $10.73 If Josiah's balance in the account was $62.72 at the beginning of the month.
The balance after the end of the withdrawal and deposits will be,
Account balance = $62.72 + $94.57−$87.78−$16.36−$64.92 + $10.73
Account balance = $-1.04
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Ann has 5,634 beads and wants to place the same number of beads in each of 9 storage boxes. Which of the following will help determine if 5,634 is divisible by 9?
A. 5,634 is an odd number and divisible by 3, so 5,634 is divisible by 9.
B. 5,634 is an even number, so 5,634 is not divisible by 9.
C. 5 + 6 + 3 + 4 = 18 and 18 is divisible by 9, so 5,634 is divisible by 9.
D. 34 is not divisible by 9, so 5,634 is not divisible by 9.
PLEASE HELP!!!
The option C, 5 + 6 + 3 + 4 = 18 and 18 is divisible by 9, so 5,634 is divisible by 9 helps to determine that 5,634 is divisible by 9.
What are Divisibility Rules?Divisibility rules are certain rules for each number to check whether a number is divisible by a certain number or not.
Here Ann has 5,634 number of beads.
She wants to place the beads in 9 storage boxes such that each box contains same number of beads.
For that, we have to divide 5634 by 9.
Check the divisibility of 5634 in 9.
Divisibility rule of 9 is that if the sum of the digits of a number is divisible by 9, then the given number itself is divisible by 9.
5 + 6 + 3 + 4 = 18
18 is divisible by 9.
So 5634 is divisible by 9.
Hence 5634 is divisible by 9 because of option C.
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If BD=7x -10, BC = 4x-29,and CD=5x-9 , find each value
Since x is 1 and BD=7x -10, BC = 4x-29, and CD=5x-9, the values of BD, BC, and CD are 4 and 21, respectively.
what is number line ?An introduction to mathematics tool is the number line, which is a visual depiction of real numbers. It is a representation of an intensity line. Each precise figure is taken to symbolize a point on the real number, and each precise figure is taken to indicate a point. On a number line, distances between increments are equal. A train's values can only be answered in the way that is specified by those numbers. The question that coincides with the number will define how it is used. B: Speak your mind.
given
BD = BC + CD
7x - 10 = 4x-29 + 5x-9
x = 2
Since x is 1 and BD=7x -10, BC = 4x-29, and CD=5x-9, the values of BD, BC, and CD are 4 and 21, respectively.
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What is the y-intercept of the graph?
Answer:
The y-intercept is the vertical line (population of butterflies)
Marques is going to invest in an account paying an interest rate of 2% compounded daily. How much would Marques need to invest, to the nearest dollar, for the value of the account to reach $28,000 in 6 years?
Answer:
$24833.83
Step-by-step explanation:
the equation for interest is A=P(1+r/n)^nt
plugging the numbers you have in, 28000=P(1+ .02/365)^ 365(6)
then you get 28000=P(1.000054795)^2190
then divide 28000 by (1.000054795)^2190 to get P alone
P=24833.82779
rounded to the nearest dollar would be $24833.83
Order the numbers from least to greatest: 0.82, 0.8, 0.83 repeating.
Answer: 0.83,0.82,0.8
Are 0. 5 - 3(-2x - 1/3 4 8x) and -1. 5(12x 7) equivalent expreion? Show your work
0.5( -3)(-2x - 1/3+ 4 + 8x) and -1.5(12x -7) expressions are not equivalent
given that
first expression = 0.5( -3)(-2x - 1/3+ 4 + 8x) and
second expression =-1.5(12x -7)
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.
now we need to solve the first expression
0.5 (-3)(-2x - 1/3+ 4 + 8x)
= 0.5 (-3)(-1/3 + 4 + 6x)
= -1.5(6x + 11/3)
first expression is not equivalent to second expression
0.5( -3)(-2x - 1/3+ 4 + 8x) ≠ 1.5(12x -7)
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Please answer this and explain it
The above computation is called a Long Division Method of carrying out Mathematical Division.
What is the explanation of the above Long Division Solution?The original question form above requires that the student divides 896 by 29. When using the long division method, 896 is called the Dividend while 29 is the Divisor.
30 is the Quotient while 26 is the remainder. Thus, 896 divided by 29 will yield 30 with a remainder of 26.
The way it works is:
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