The total number of unique positions of n identical rooks on an n by n chessboard such that exactly one pair of rooks can attack each other is (n - 1)^2 * (n - 1)! or (n - 1) * (n - 1)! * (n - 1).
To find the number of unique positions of n identical rooks on an n by n chessboard such that exactly one pair of rooks can attack each other, we need to consider the number of empty rows and columns.
First, let's consider the number of empty rows. Since exactly one pair of rooks can attack each other, we know that there can be at most one rook in each row. This means that there are n rows with at most one rook each, leaving (n - 1) empty rows.
Next, let's consider the number of empty columns. Again, since exactly one pair of rooks can attack each other, there can be at most one rook in each column. This means that there are n columns with at most one rook each, leaving (n - 1) empty columns.
Now, we can use combinations to find the number of ways to choose one row and one column for the pair of rooks that can attack each other. There are (n - 1) options for the row and (n - 1) options for the column, giving us a total of (n - 1) * (n - 1) = (n - 1)^2 possible combinations.
Finally, we need to multiply this by the number of ways to place the remaining rooks in the empty rows and columns. Since each rook can be placed in any of the empty rows or columns, there are (n - 1)! ways to arrange the remaining rooks.
Therefore, the total number of unique positions of n identical rooks on an n by n chessboard such that exactly one pair of rooks can attack each other is (n - 1)^2 * (n - 1)! or (n - 1) * (n - 1)! * (n - 1).
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I need help on this
Answer:
(1,0)
Step-by-step explanation:
Subtract the x's and y's from eachother than divide this by two. Add this number onto the lowest of the x and ys and you get the midpoint. The same as fining the middle of two numbers but you are dealing with 2 pairs of numbers
Last year, Michael opened an investment account with $5400. At the end of the year, the amount in the account had decreased by 23.5%. How much is this
decrease in dollars? How much money was in his account at the end of last year
can someone help me with these three? I just need to find the unit rates for all, I’ll mark as brainliest!!
Answer:
6. 7.5/1
7. 2.4/1
8. 40/1
Step-by-step explanation:
All you have to do is divide the 2 numbers to find the unit rate.
Answer:
6: 7.5 pizzas per Classroom
7: 2.4 Liters per test
8: 40 Points per Game
Alek gives 18 flowers to each person at his office, There are 42 people at his office. How many flowers does alek give away?
Answer:
he gives away 756 flowers
Step-by-step explanation:
18*42=756
A measure of how much space something takes up ?
Answer:
Volume
Step-by-step explanation:
Mass is measured using a scale. Volume is the amount of space matter takes up. Volume can be measured by multiplying the length, width, and height of an object, or by using a measuring cup and seeing how the measurement of water changes in a cup. Density is the amount of matter an object has in a certain space.
Answer:
VOLUME
Step-by-step explanation:
În desen este reprezentat trapezul
ABCD și O punctul de intersecție a di-
agonalelor AC și BD. Completați case-
ta, astfel încât să obțineți o propoziţie
adevărată:
Dacă aria triunghiului DOA este egală
cu 20 cm², atunci aria triunghiului COB
este egală cu
Answer:
ab hyppotenusejabqianahqiwnna. jajabanqk
HELPPP ME PLEASEEE!!!!
What is the slope of the line shown?
A. slope = 3
B. slope = 1/2
C. slope = 2
D. slope = -3
Answer:
The answer is B - 1/2.
Step-by-step explanation:
Rise over run tells you the slope. You take two points (in this it's (0,-3) and (6,0)) and you see how many units it takes to be on the same y line as the other point. Then you do the same for the x line. You divide the rise (y line) by the run (x line) and that's your slope.
That's not an answer for me
Answer:
so you need a answer or a question
Answer:
child anywaysssss
Step-by-step explanation:
yfgxgx
in integers how to know if minus (-) 1 upon 2 is greater or minus (-) 1 is greater???
Answer:
1/2 is 0.5 so -1/2=-0.5
-0.5 is greater than -1
use a number line
Step-by-step explanation:
By looking at the number line we can easily tell which integers are greater (larger) than a certain number and which are less (smaller) than the number. When two numbers are located on a number line, the number to the right is larger than the number to the left. –1 is less than –1/2 because it is to the left of –1/2.
(Please heart the answer if you find it helpful, it's a motivation for me to help more people)
What is the surface area?
5 mm
4 mm
5 mm
6 mm
7 mm
square millimeters
Answer:
Base of 5mm, Height of 6mm, Width of 7mm214mm^2
Base of 4mm, Height of 4mm, Width of 10mm192mm^2
Base of 5mm, Height of 6mm, Width of 7mm214mm^2
Base of 6mm, Height of 3mm, Width of 2mm72mm^2
7mmLittle over 1/4 Inch0.27559 Inches
The total surface area is 124 square millimeters.
What the surface area of a rotating prism?To find the surface area of any kind of prism we use the general formula. The total surface area of a prism is the sum of lateral surface area and area of two flat bases.
The total surface area of a Prism = (2 × Base Area) + (Base perimeter × Length).
Here, area of base is Area=2(Base×Height)
= 2(6×4)
= 12 square millimeters
Now, Base perimeter × Length= (5+5+6)×7
= 16×7
= 112 square millimeters
Total area = 12+112
= 124 square millimeters
Therefore, the total surface area is 124 square millimeters.
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BRAINLIEST to wherever gets this correct
Answer:
[tex]300\pi[/tex] cubic feet
Step-by-step explanation:
Let r be the radius of cone and h be the height of cone.
Radius of cylinder=r
Height of cylinder=h
Volume of cone=[tex]100\pi ft^3[/tex]
We have to find the volume of cylinder.
We know that
Volume of cone=[tex]\frac{1}{3}\pi r^2 h[/tex]
[tex]100\pi=\frac{1}{3}\pi r^2 h[/tex]
[tex]r^2 h=300[/tex]
Volume of cylinder=[tex]\pi r^2 h[/tex]
Using the formula
Volume of cylinder=[tex]\pi (300)=300\pi ft^3[/tex]
Hence, the volume of cylinder=[tex]300\pi[/tex] cubic feet
What is the vertex form of 3x^2+6x+10
Answer:
3x2+6x−10
y=3x2+6x−10
Rewrite the equation in vertex form.
y=3(x+1)2−13
Use the vertex form, y=a(x-h)2+k, to determine the values of a h, and k.a=3h=−1k=−13 (h,k).(−1,13)
Step-by-step explanation:
-6x-7-4x-2 How can I solve this?
Use PEMDAS
Parentheses first
Exponents next
Multiplication then
Division in the same step
Addition then
Subtraction
The correct answer is 10x-9
HELPPP PLEASEEEEEEE I NEED HELP
Answer:
Part A: -3x^8 + 2x^5 + 4x^3
Part B: 8
Part C: 3
Part D: -3x^8
Part E: -3
Step-by-step explanation:
A. Standard polynomial is :
[tex] - 3 {x}^{8} + 2 {x}^{5} + 4 {x}^{3} [/tex]
B. Degree of the polynomial is : 8
C. Number of terms are : 3
D. Leading term of the polynomial is:
[tex]-3 {x}^{8} [/tex]
E. Leading co effecient of the polynomial is: -3
Write your own algebraic expression with atleast four terms that can simplify to 12x+4 (PLEASE HELP ASAP)
Answer:
4(2x + 1) + 4x = 8x + 4 + 4x = 12x + 4
Select the correct answer. Which equation describes the line graphed above? A. y=-4x-5 B. y=-1/5x-4 C. y=-5x-4 D. y=-4x-1/5
Answer:
Option B
Step-by-step explanation:
Answer: B.
Step-by-step explanation: Plato
How do you simplify 14.938 - 14.93 ?
Please help
Answer:
0.008
Step-by-step explanation:
To know the steps pls look at the pic above
PLEASE HELP I WILL MARK BRAINLIEST
name 2 rights of someone accused of a crime that you observe in the pic above.
A. right to a trial and lawyer
B. right to a lawyer and providing evidence
C. Trial with a judge and witness
D. Right to take notes and provide evidence for defence
Answer:
it is b the right to evidence lawyer.
Answer:
B. right to lawyer and providing evidence
Step-by-step explanation:
12x + 15y = 9
−12x − 18y = −6
HELP JUST SOLVE IT
Answer:
x = 2, y = -1
Step-by-step explanation:
To solve a pair of equations using substitution, first solve one of the equations for one of the variables. Then substitute the result for that variable in the other equation.
12x+15y=9,−12x−18y=−6
Choose one of the equations and solve it for x by isolating x on the left hand side of the equal sign.
12x+15y=9
Subtract 15y from both sides of the equation.
12x=−15y+9
Divide both sides by 12.
x= 1/12 (−15y+9)
Multiply 1/12 times −15y+9.
x = -5/4y+3/4
Substitute -5y+3/4 for x in te other equation, -12x - 18y = -6
-12 ( -5/4y+3/4) -18y = -6
Multiply −12 times -5y +3/4
15y−9−18y=−6
Add 15y to −18y.
−3y−9=−6
Add 9 to both sides of the equation.
−3y=3
Divide both sides by −3.
y=−1
Substitute −1 for y in x= -5/4y+3/4. Because the resulting equation contains only one variable, you can solve for x directly.
x= -5/4(-1)+3/4
Multiply -5/4 times -1.
x = 5+3/4
Add 3/4 to 5/4 by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.
x=2
The system is solved.
A baker needs 4 3⁄4 cups of flour. If she uses a 1 1⁄2 cup measuring scoop, how many scoops of flour must the baker use to have at least 4 3⁄4 cups?(must be a whole number)
Answer:
If you did it three times it would be 4 1/2. If you wanted to make it at least 4 3/4 then you would need to do 1 1/2 4 times.
Step-by-step explanation:
PLSSSS HELP IM BEGGING YOU PLSSSS
7. What is the area of the trapezoid shown? 4 cm 10 cm 8 cm W 10 cm
Answer:
88 ... .... . ... . . . ... ............... ....
HELP QUICK whats the domain and range of g(x)=√x-3+5
Answer:
check it..
Step-by-step explanation:
domain and range...
So like I need help on this,
Choose the graph that represents the figure and classify it. Then find the area.
D(-1, -1), E(-1, 3), F(2, 4), G(2, -3)
Answer:
Trapezoid with the area 16.5 unit²Step-by-step explanation:
Plotted the given points to find out the figure is trapezoid.
Area formula for trapezoid:
A = 1/2(b₁ + b₂)hThe length of the bases:
b₁ = DE = 3 - (-1) = 4b₂ = FG = 4 - (-3) = 7h is the horizontal distance between the bases:
h = 2 - (-1) = 3The area is:
A = 1/2(4 + 7)(3) = 16.5 unit²On Monday, Florencia's hair was h centimeters long. She got a haircut on Tuesday, so her hair was only 75% percent of the length it was on Monday.
Which expressions could represent how many centimeters long Florencia's hair was after the haircut?
(The Question says to pick 2 answers out of the multiple choice options so here you go)
A. h (1-0.75)
B.(1- 75/100) h
C. 3/4 h
D. 0.75 h
E. 1/4 h
Answer:
D
Step-by-step explanation:
75/100 = .75 x the Monday length (h)
Given a sphere with a radius of 2 cm find its volume to the nearest whole number.
A 17 cm
B.3cm
C. 33 cm
D. 3 cm
write an expression for the perimeter of the triangle shown below 2.3x + 14 2x -0.2x + 15
Answer:
4.1x + 29
Step-by-step explanation:
So the perimeter would be the sum of all of the sides, so:
[tex]2.3x + 14 + 2x - 0.2x + 15\\= 4.1x + 29[/tex]
Answer: 4.5x+ 29 which is 3, so 3 is correct.
Step-by-step explanation:
P = a+b+c
First do the ordered pairs ( add the numbers with the x to the end, then add the other numbers with no x's)
One morning, the thermometer read -14 fahrenheit. By noon, the temperature had risen 12 degrees. What was the temperature at noon?
Answer:
-2 degrees
Step-by-step explanation:
-14 + 12 = -2
Solve for x. Round your answer to the nearest tenth.
9.2
X
16.5
Answer:
152
Step-by-step explanation: