The empty shelf can be filled in 120 ways
The total number of books is
[tex]n = 10[/tex]
The number of books to move is:
[tex]r = 3[/tex]
To fill the empty shelf with three books, we make use of the following combination formula
[tex]^{n}C_r = \frac{n!}{(n - r)!r!}[/tex]
So, we have:
[tex]^{10}C_3 = \frac{10!}{(10 - 3)!3!}[/tex]
Evaluate the expression
[tex]^{10}C_3 = \frac{10!}{7!3!}[/tex]
Expand
[tex]^{10}C_3 = \frac{10 \times 9 \times 8 \times 7!}{7! \times 3\times 2 \times 1}[/tex]
Cancel out the common factors
[tex]^{10}C_3 = \frac{10 \times 9 \times 8}{3\times 2 \times 1}[/tex]
Evaluate the products
[tex]^{10}C_3 = \frac{720}{6}[/tex]
Divide
[tex]^{10}C_3 = 120[/tex]
Hence, the empty shelf can be filled in 120 ways
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What is AAS similarity theorem?
How do you read X sets?
The elements in sets are separated by commas so they can be read easily.
Define set builder notation.Instead of describing the constituents of a set, a set-builder notation describes them. The elements are listed, for instance, in the set {5, 6, 7, 8, 9}. We interpret the collection of all x such that x is a counting number between 4 and 10 as the collection of all x.
Define set.In mathematics, a set is a logically arranged group of items that can be represented in either set-builder or roster form. Sets are typically denoted by curly brackets {}; for instance, A = {1, 2, 3, 4} is a set.
The sequence of elements (separated by commas) between the curly braces " and "in mathematics form an unordered group of elements known as a set. For instance, the domesticated animals {cat, cow, dog} , the odd numbers {1, 3, 5, 7, 9} and the alphabets {a, b, c, d, e} are all sets. So they can be read or interpreted easily.
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I almost thought that this had no solutions, but I'm not sure, could anyone help me on this? I would deeply appreciate it!
Consider the equation 2x = 3x. Does this equation have one solution, no solution, or infinite solutions? Explain your reasoning
Answer:
one solution because when you isolate the x terms:
2x-3x=0 and you combine like terms
-x=0
and divide by negitive one because -x is (-1)(x)
you get x=0
Step-by-step explanation:
Answer:
One solution
Step-by-step explanation:
It appears this problem has no solution, buttt let's look closer.
2x and 3x are like terms, meaning they can be added and subtracted because they both have x!
So let's combine these like terms and see what we get...
2x = 3x
0 = 3x -2x
0 = 1x
x = 0 / 1
x = 0
The only solution is 0! No other number is possible.
A sunflower is 3 inches tall after 1 week, 5 inches after 2 weeks, and 7 inches after 3 weeks. What is the recursive rule and explicit rule of this sequence?
Answer: f(x)= 2x+ 1
Step-by-step explanation:
Let's set up an equation
f(x)=mx+b
We know it's 3 inches tall and grows 2 inches weekly.
Our equation is
f(x)= 2x + 1
Now let's test the week is 1
f(1) = 2(1) +1
f(1) = 3
Let test the week is 2
f(2) = 2(2)+1
f(2) = 5
So we know this equation work
what is the sign of f on -5/2 < x < 4
Answer:
f is negative
Use a recursive function for the geometric sequence 2, −6, 18, −54, ... to represent the 9th term.
a. f(9)=f(8)•(-3)
b. f(9)=f(1)•(-3)^8
c. f(9)=f(1)+3(8)
d. f(9)=f(8)+3(8)
The geometric sequence 2, −6, 18, −54, ... to represent the 9th term is
d. f(9)=f(8)+3(8)
A geometric sequence is a sequence of numbers in which each term after the first is found by multiplying the previous one by a fixed, non-zero number, called the common ratio. In the given sequence, the common ratio is -3, so the nth term of the sequence can be found by multiplying the previous term by -3.
Using the recursive formula for a geometric sequence, the nth term can be found by multiplying the first term, f(1), by the common ratio raised to the (n-1) power, or f(n) = f(1)•(-3)^(n-1). In the given sequence, f(1) is 2, so the 9th term can be found by multiplying 2 by -3 raised to the 8th power, or f(9)=f(1)•(-3)^8.
Alternatively, the nth term can also be found by multiplying the previous term, f(n-1), by the common ratio, or f(n) = f(n-1)•(-3). Since the 8th term in the given sequence is -54, the 9th term can be found by multiplying -54 by -3, or f(9)=f(8)•(-3).
Therefore, the 9th term in the given sequence is -486 and the correct answer is d. f(9)=f(8)+3(8).
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6 less than a number in algebraic expression
Answer:
Step-by-step explanation: Let x represent the number in the algebraic expression, then 6 less means the following:
x-6
The whales' star cornerback is paid $1 million and is guaranteed a 19% pay raise for the next three years. What will his salary be three years from now?.
The income of whales star after 3 years and getting 19% rise every year will be $1685159 .
Given, The whales' star cornerback is paid $1 million and is guaranteed a 19% pay raise for the next three years .
To get the salary of whale star after 3 years of increment with 19%.
Salary = $1 million
Salary after 1st increment = $1 million + $1 million of 19%
Salary after 1st increment = $1190000
Salary after 2nd increment = $1190000 + $1190000 of 19%
Salary after 2nd increment = $1416100
Salary after 3rd increment = $1416100 + $1416100 of 19%
Salary after 3rd increment = $1685159
Final salary after 3 years will be $1685159.
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How do you find the inverse of a 2x2 matrix on a calculator?
We find the inverse of a 2x2 matrix on a calculator using formula
A⁻¹ = Adjoint of A / determinant of A
Where, adjoint of A = [ d -b]
[-c a]
and, determinant of A = 1/ ad - bc
What is inverse of a 2X2 matrix?A real number's inverse is a number that, when multiplied by the inputted number, yields the multiplicative identity, which is 1, or 1. A matrix's inverse, represented by A⁻¹ in matrices, is a matrix that, when multiplied by A, yields the identity matrix I, or A.A⁻¹ = A⁻¹.A = I
The formula (adj A)/(det A) can be used to determine the inverse of a matrix A, where "adj A" stands for "adjoint of A" and "det A" for "determinant of A".
Let A is a 2x2 matrix such that, A = [a b]
[c d]
then, A⁻¹ = Adjoint of A / determinant of A
Where, adjoint of A = [ d -b]
[-c a]
and, determinant of A = 1/ ad - bc
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please help me with this question it is urgent
Answer:
4 1/3, 4.337, 35/8, 4.44
Step-by-step explanation:
4.337, 4 1/3, 35/8, 4.44
4 1/3 = 13/3 = 4.333
35/8 = 4.375
So, the order from least to greatest is: 4 1/3, 4.337, 35/8, 4.44
Answer:
4 1/3, 4.337, 35/8, 4.44
Step-by-step explanation:
"order from least to greatest" means put the smallest first and each next one bigger and the biggest one last.
Change everything to decimals to compare.
A fraction bar is just a division symbol.
1/3 means 1÷3 which is .33333...
4 1/3 = 4.33333...
35/8 means 35÷8
= 4.375
Smallest is 4.333...
So 4 1/3 goes first.
Then 4.337 and next 35/8 (bc 4.375)
Last is biggest 4.44 so it goes last.
In order from least to geatest is:
4 1/3, 4.337, 35/8, 4.44
1: The drama department sold a total of 360 tickets to there Friday and Saturday night shows. They Sold three times as many tickets for Saturday's show than for Fridays show.
A: Write a system of equations to represent this scenario
B: How many tickets were sold for Friday, and Saturday? Is there more than one solution?
C: Graph the system of equations on a coordinate plane. Label the axes.
D: Justify algebraically that your solution is correct.
(A) Given question can be represented in the system of linear equations as x + y = 360,
y =3x
(B) 90 tickets were sold on Friday and 270 tickets were sold on Saturday.
There will be only one solution to this question.
(C) We have drawn the graph for the solution.
(D) We have justified our answers by using the substitution method.
What is a linear equation in two variables?
An equation is said to be a linear equation in two variables if it is written in the form of ax + by + c=0, where a, b & c are real numbers and the coefficients of x and y, i.e a and b respectively, are not equal to zero.
Let x number of tickets sold on Friday and y number of tickets sold on Saturday.
By using the given condition,
x + y = 360 ----------(I)
y =3x -------(II)
Put y = 3x in equation (I), we get
x + 3x = 360
4x = 360
x = 90
Now put x = 90 in equation (I), and we get
90 + y = 360
y = 270
Hence, 90 tickets were sold on Friday and 270 tickets were sold on Saturday.
There will be only one solution to this question.
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According to the rational root theorem, the following are potential roots of f(x) = 6x4 + 5x3 – 33x2 – 12x + 20. negative five-halves, –2, 1, ten-thirds which is an actual root of f(x)?
As per the rational root theorem, the actual root of the polynomial is - 5/2
The term polynomial refers the algebraic expression in which the exponents of all variables should be a whole number
Here we have given that f(x) = 6x⁴ + 5x³ – 33x² – 12x + 20. and we need to find which is an actual root of f(x).
In order to find the root for the polynomial we have to apply each value as the replacement of x in the polynomial.
And then we have to find in which one makes the polynomial result as zero.
First we have to take the value of x as -5/2, then the polynomial equation be like,
Here we have to substitute x=-5/2, then we get
=> f(-5/2) = 6(-5/2)⁴ + 5(-5/2)³ - 33(-5/2)² - 12(-5/2) + 20
=> f(-5/2) = 6(625/16)-5(125/8)-33(25/4)+30+20
when we simplify this one then we get,
=> f(-5/2)=(1,875-625-1,650+400)/8
=> f(-5/2)=0/8
Here we know that if we zero by any number we get the result as zero.
Therefore, f(-5/2)=0 then x=-5/2 is a root of f(x)
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Answer:
its A
Step-by-step explanation:
Just took the test
How do you find the largest and smallest number in an unsorted integer array Python?
There are 3 methods to find the largest and smallest number in an
unsorted integer array Python.
How do you find the largest and smallest number in an unsorted integer array Python?Method 1 : Using Iteration.Method 2 : Using Sort() function.Method 3 : Using max() and min() functionMethod 1:
Take a variable say mini to store the smallest element of the array and maxi to store the largest element.Set mini = arr[0] and maxi = arr[0]Check if(arr[i]<mini) then set mini = arr[i]Also check if(arr[i]>maxi) then set maxi = arr[i]After complete iteration print mini and maxi.Method 2:
Sort the array using inbuilt sort()functionSmallest element is at index 0 and largest is at index -1So, print(arr[0])And, print(arr[-1])Method 3:
Using inbuilt function min(arr) , it return smallest element of the array.Similarly max(arr) return the largest element of the array.There are 3 methods to find the largest and smallest number in an
unsorted integer array Python.
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Which inequality repreent the compound in equality x i greater than 3 and x i le than 5
The compound inequality x > 3 or x < 5 is 4 , that set of all real numbers.
What is inequality ?
If an inequality has no real solution, this means that there are no numbers that can be substituted into the inequality to make the statement true. If an inequality has all real numbers as the solution, this means that every real number can be substituted into the inequality to make a true statement.
Have given,
x > 3 and x < 5
Since this compound inequality is an or statement , it includes all of the integral numbers in each of the solutions, which in this case is all the numbers on the number line .
The region of the line greater than 3 and less than 5 that number is 4.
Hence,
The compound inequality x > 3 or x < 5 is 4 , that set of all real numbers .
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Have given,
x > 3 and x < 5
Since this compound inequality is an or statement , it includes all of the integral numbers in each of the solutions, which in this case is all the numbers on the number line .
The region of the line greater than 3 and less than 5 that number is 4.
The compound inequality x > 3 or x < 5 is 4 , that set of all real numbers.
How do you write 308 in expanded form?
(-3,4) (6,0),(-3,4),(-8,-2) a function
There is no input mapped into two or more outputs in the given relation:
(-3,4) (6,0),(-3,4),(-8,-2)
Thus, the relation is a function.
Is the relation a function or not?A relation maps elements of a set (inputs, usually defined by the variable x) into elements of another set (outputs, usually defined by the variable y).
So, for example, the coordinate pair (x, y) means that a relation is mapping the input x into the output y.
A relation is also a function if there is no input being mapped into two or more outputs.
For the case of the given relation:
(-3,4) (6,0),(-3,4),(-8,-2)
The mappings are:
-3 → 4 (this one appears twice)
6 → 0
-8 → -2
So no input is mapped into two or more outputs, then the relation is a function.
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Question : A good practice when using credit cards is to routinely
A: take advantage of major sales.
B: use one credit card to pay debt on another credit card.
C: pay the complete balance each month.
D: accept all pre-approved credit card offers.
Answer: C: pay the complete balance each month
Calculate the perimeter of the irregular shape please show ur work Bc I have too
Answer:
34 cm
Step-by-step explanation:
the gap in the middle is 2 cm because 9 - ( 4 + 3 ) = 2
4 + 2 + 2 + 3 + 3 + 6 + 9 + 5 = 34
Help with special right triangles rounding
Answer:
9.8 units-----------------------------------
Hypotenuse of an isosceles triangle is √2 times the leg:
x = √12 × √2 = √24 = 4√6 ≈ 9.8 units (rounded to the nearest tenths)Find the greatest common factor. ab4c7, a7b4c
We know that,
Greatest common factor= the greatest common factor is the greatest factor that divides both numbers.
According to question.
Given data,
Factor of a= a
Factor of b=b× b× b× b
Factor of c=c× c× c× c× c× c× c
Therefore,
Factor of a=a× a× a× a× a ×a ×a
Factor of b4=b ×b ×b× b
Factor of c=c
Greatest common factor=ab4c
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The longest ladder on the fire truck reaches 95 feet. A building has 20 stories, and each story is 18 feet high. what is the highest story that the ladder can reach?
(A) 5th story
(B) 6th story
(C) 10th story
(D) 18th story
(Somebody please help me answer this question I rlly need help with this!)
Answer:
Rounding down to the nearest whole number, we get 5 stories. The correct answer is, therefore (A) the 5th story.
Step-by-step explanation:
To solve this problem, we need to find the number of stories the ladder can reach by dividing the length of the ladder by the height of each story.
The longest ladder on the fire truck reaches 95 feet, and each story is 18 feet high, so the highest story that the ladder can reach is:
95 feet / 18 feet/story = <<95/18=5.28>>5.28 stories
10. A new bank customer with $3,000
a money market account. The
wants to open
simple interest rate of 1.1%.
bank is offering a
a. How much interest will the customer earn in
20 years?
b. What will be the account balance after
20 years?
Answer:
a. $660
b. $3660
Step-by-step explanation:
a. 1.1% = 1 years
22% = 20 years
22% = 0.22
Take 3000 times 0.22 = $660
So, they will earn $660 interest in 20 years
b. $3000 + $660 = $3660
$3660 is their account balance after 20 years
Is 990 divisible by 3 yes or no?
Yes it is divisible by 3. A number is fully divisible by three if its digit sum is also divisible by three, according to the rule of divisibility for three.
what is divisibility test?The divisibility rule is a concise and practical approach to check, often by looking at the integer's digits, whether a given integer is divisible by a given set divisor without actually executing division. Without actually doing the division procedure, you may quickly discover if a given number can be divided by a defined divisor using the divisibility test. When dividing two numbers exactly, the quotient must be an integer and the remainder must be zero.
add all number
9+9+0 = 18
and 18/3 = 6
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What is integration in simple words?
Regional economic integration has facilitated trade among neighbors while allowing nations to concentrate on issues pertinent to their stage of development. Four forms of regional economic integration are possible. Zone of unrestricted trade. The most basic form of economic cooperation is this one.
Worldwide integration of the markets. global integration of the economy. On the financial markets, the effects of globalization are being assessed. More than ever, people, companies, and sectors are linked. This facilitates linkages, which encourages specialization, innovation, and economic expansion.
These accords have made it possible for nations to trade successfully with one another today by removing trade and financial restrictions. actions taken to lower prices for consumers in the member countries of the bloc when tariffs are decreased
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What is the factor of 2x³ 3x² 17x 30?
Therefore, the solution to this problem is (x - 2)(x + 3) are the factors of p(x) (2x - 5).
Examine the equation.An equation is a mathematical statement that is created by connecting two expressions using the equivalent sign. An example of an equation is 2x - 5 = 15. By resolving this equation, we may ascertain that the variable x has a value of 5.
Here,
Given, the polynomial in this case is 2x3 - 3x2 - 17x + 30.
It is necessary to factor the polynomial.
Let p(x) equal 2x3, 3x2, 17x, and 30.
P(xconstant )'s term is 30.
Factors of 30 are equal to 1, 2, 3, 5, 6, 10, 15, and 30.
Consider x = 2.
Replace x = 2 in p. (x),
2(2)³ - 3(2)² - 17(2) + 30 =p(2)
=> 2(8) - 34 - 3(4) + 30
= >16 - 16
= 0
So, x - 2 is a factor of 2x³ - 3x² - 17x + 30.
Now splitting the x² and x terms,
2x³ - 4x² + x² - 2x - 15x + 30= 2x³ - 3x² - 17x + 30
=> x(x - 2) - 15(x - 2) + 2x²(x - 2)
= > (x - 2) * (2x² + x - 15)
factoring 2[tex]x^{2}[/tex] + x - 15
= 2[tex]x^{2}[/tex] + 6x - 5x - 15
= - 5(x + 3) + 2x(x + 3)
= (x + 3)(2x - 5)
Therefore, the solution to this problem is (x - 2)(x + 3) are the factors of p(x) (2x - 5).
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How do you represent three consecutive odd integers?
You represent three consecutive odd integers with x, x + 2 and x + 4
How to determine the representation of odd integersFrom the question, we have the following parameters that can be used in our computation:
Three consecutive odd integers
As a general rule
Odd integers are integers that cannot be divided by 2
Consecutive odd integers have a difference of 2
This means that the three consecutive odd integers are
x, x + 2 and x + 4
Where the least of the integers is x
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1)No regime de juros composto, encontre as taxas trimestral e anual equivalentes à taxa de 1,05% ao mês
2)Calcule a taxa de juros compostos equivalente a uma taxa efetiva de 1% ao mês, nos períodos a seguir:
a)ao semestre;
b)ao ano.
alguém pode me ajudar a entender como fazer esses tipos de exercícios? estive tentando aprender a um tempo mas não to conseguindo e o livro não ajuda muito.
Answer:
Para encontrar a taxa trimestral equivalente à taxa de 1,05% ao mês, basta dividir a taxa mensal por 3, pois um trimestre é composto por 3 meses. Portanto, a taxa trimestral equivalente à taxa de 1,05% ao mês é de 1,05% / 3 = 0,35%.
Para encontrar a taxa anual equivalente à taxa de 1,05% ao mês, basta multiplicar a taxa mensal por 12, pois um ano é composto por 12 meses. Portanto, a taxa anual equivalente à taxa de 1,05% ao mês é de 1,05% x 12 = 12,6%.
2)a) Para calcular a taxa de juros compostos equivalente a uma taxa efetiva de 1% ao mês ao semestre, basta multiplicar a taxa mensal por 6, pois um semestre é composto por 6 meses. Portanto, a taxa de juros compostos equivalente a uma taxa efetiva de 1% ao mês ao semestre é de 1% x 6 = 6%.
b) Para calcular a taxa de juros compostos equivalente a uma taxa efetiva de 1% ao mês ao ano, basta multiplicar a taxa mensal por 12, pois um ano é composto por 12 meses. Portanto, a taxa de juros compostos equivalente a uma taxa efetiva de 1% ao mês ao ano é de 1% x 12 = 12%.
What is the example of linear inequality in two variables?
4x + 8y ≤ -24 is the example of linear inequality in two variables.
What is a linear inequality equation?Linear equations are one-degree equations. It is a straight-line equation. A linear equation with parameters a and b equal to zero has the conventional form ax + by + c = 0.
The graph of a two-variable inequality is the set of points that describe all solutions to the inequality. The coordinate plane is split in half by a boundary line created by a linear inequality, with one-half representing the solutions to the inequality.
It's a line with a shaded side on one side to show which xy pairings are the inequality's solutions.
For example -
Let us take a equation, 4x + 8y ≤ -24
Now, solve the above equation in the form of slope-intercept.
4x + 8y ≤ -24
or, 8y ≤ - 4x - 24
or, y ≤ -(1/2)x - 3
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What are the 3 parameters used in a for loop in Python?
Range with three parameters: start, end, step.
Now, According to the question:
What are the 3 loops in Python?
The three types of loop control statements are:
break statement.continue statement.pass statement.What are the three parameters in range in Python?
The range() function in Python works by taking three inputs as parameters which are start_value, stop_value, and step value. The range() function returns an immutable sequence of numbers starting from the start_value, and increments the values by the value given in the step_value, and stops at the stop_value.
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Solve the systems of equations.
Answer: x=2, y=-8
Step-by-step explanation: there are a couple of different methods you can use, my favourite is substitution
to do this, find a value of x or y from one equation and plug it into the other. let's use x in this case
so we have 13x-6y=22 and x=y+6
for the x value of the first equation, plug in x=y+6 from the second equation to get:
13(y+6)-6y=22
then you solve for y,
13y+78-6y=22
7y=-56
y=-8
then to solve for x, plug in your y value to either of the first 2 equations. lets use x=y+6
so you'd have x=(-8)+6 to give you x=2
hope this helps!