Solution:
This problem is a permutation because the order matters here. This means that choosing A as King, B as Knight, C as Bishop and D as Rook results in a different arrangement from B as King, A as Knight, D as Bishop and C as Rook. We would count them both because in the first case A is King, but in the second case A is Knight.
Therefore, the possible number of ways are given below:
[tex]19P4=\frac{19!}{(19-4)!} =\frac{19 \times 18 \times 17 \times 16 \times 15!}{15!} =19 \times 18 \times 17 \times 16 =93024[/tex]
Hence there will be 93024 ways 19 members of a chess club fill the offices of King, Knight, Bishop, and Rook.
There are 19 members in the chess club, and they can fill the offices of King, Knight, Bishop, and Rook in 38760 ways.
In how many ways can the 19 members of a chess club fill the offices of King, Knight, Bishop, and Rook.
To determine the number of ways to fill the offices, we use the concept of permutations. Since each office must be filled by a different member, the number of ways is calculated as 19P4 = 19! / (19-4)! = 38760 ways.
Michelle bought 72 pounds of cocoa powder for her backery everyday she used the same amount of cocoa powder to make bakery items after 10 days Michelle was left with 20.2 pounds of cocoa powder on avarage how many cocoa powder did Michelle used each day
Round 3.282828... To the nearest thousandth
BRAINLIEST!!PLEASE HELP ME!
If the patterns continued indefinitely, what letter would be in the 40th position? A, b, c, a, b, c
The sequence of 3 letters "a,b,c" is repeating.
[tex]40=3\cdot13+\boxed{1}[/tex]
So it will be the letter at the 1st position, which is a.
Multiply. ?2 3/5 ? 5/6 ? Express your answer in simplest form.
The area of a square is 36 square yards. How long is each side of the square?
The formula for area of a square is A=s^2
Taking the square root of each side
sqrt(A) =s
sqrt(36)=s
6yds =s
The length of each side of the square is 6 yards.
Coach Kunal stacks all of the tennis balls in a square pyramid.
The number of tennis balls, P(n), in n layers of the square pyramid is given by P(n) = P(n – 1) + n^2.
Which could not be the number of tennis balls Coach Kunal has?
A. 30
B. 9
C. 5
D. 14
Answer:
The correct option is: B. 9
Step-by-step explanation:
The number of tennis balls, [tex]P(n)[/tex] , in [tex]n[/tex] layers of the square pyramid is given by: [tex]P(n)=P(n-1)+n^2[/tex]
As the stack of the tennis balls is in shape of a square pyramid, that means in the top layer, there will be one ball. So, [tex]P(1)= 1[/tex]
Now, if [tex]n=2,[/tex] then [tex]P(2)= P(2-1)+(2)^2 = P(1)+4=1+4=5[/tex]
If [tex]n=3,[/tex] then [tex]P(3)=P(3-1)+(3)^2=P(2)+9=5+9=14[/tex]
If [tex]n=4,[/tex] then [tex]P(4)=P(4-1)+(4)^2 = P(3)+16=14+16=30[/tex]
That means, the number of tennis balls from the top layer will be: 1, 5, 14, 30, .......
So, the number of tennis balls that Coach Kunal could not have is 9.
the correct answer is b.9
Ima parking lot of 240 read and blue cars, the ratio of red cars to blue cars is 3:5 how many red cars are in the parking lot
Paula has 6 video games. Myles has 1 more video game than paula. Which could you use to find how many video games in all.
Paula = 6 video games
Myles = 1 video game + Paula(6 video games)
P + M = Total video games
M = 1 + P
P = 6
P + M = 6 + 1 = 7
Final answer:
To find the total number of video games Paula and Myles have, add Paula's 6 games to Myles's 7 games (since he has one more than Paula), which equals 13 games.
Explanation:
To find out how many video games Paula and Myles have in total, we can use a simple addition equation based on the information given. Paula has 6 video games, and Myles has 1 more video game than Paula. Therefore, we can express the number of video games Myles has as 6 games + 1 game, which equals 7 games.
Next, we add the total number of games Paula has to the total number of games Myles has:
Paula's video games: 6 games
Myles's video games: 7 games
Total video games: 6 games + 7 games = 13 games
By adding the two amounts together, we can find the total number of video games they have combined.
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!
Factor x^2 + 2x - 15.
A) (x - 5)(x + 3)
B) (x - 5)(x - 3)
C) (x + 5)(x + 3)
D) (x + 5)(x - 3)
[tex]x^2 + 2x - 15=\\\\x^2-3x+5x-15=\\\\x(x-3)+5(x-3)=\\\\(x+5)(x-3) \Rightarrow \text{D}[/tex]
Which phrase represents the algebraic expression 1/4d+7? the product of one-fourth and a number, plus seven the product of seven and a number the product of one-fourth and seven, plus a number the product of seven and one-fourth
Answer:
The answer is A
Step-by-step explanation:
(the product of one-fourth and a number plus seven)
An expression is defined as a set of numbers, variables, and mathematical operations. The correct option is D, the product of one-fourth and a number plus seven.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
2x + 3 is an example of a variable mathematical expression. Every variable must have a coefficient, which is a number multiplied by the variable. The coefficient of x in the formula 2x + 3 is the number 2, and it signifies 2 times x plus 3.
The given algebraic expression 1/4d+7 can be represented as a phrase as the product of one-fourth and a number plus seven.
Hence, the phrase that represents the algebraic expression 1/4d+7 is the product of one-fourth and a number plus seven.
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Rodrigo traveled at an average speed of 55 miles per hour for 5 hours to get from one national park to the next on his vacation l.What is the distane between the national parks
Answer: 275 Miles
Step-by-step explanation: 55 x 5 = 275
Answer:
275 Miles
Step-by-step explanation:
55 mph * 5hours= 275 Miles
Hank's pickup can travel 72 miles on 4 gallons of gas. How many gallons will Hank's pickup need to travel 54 miles?
Answer:
Hank's pickup need 3 gallons of gas to travel 54 miles.
Explanation:
Hank's pickup can travel 72 miles on 4 gallons of gas
Miles travel by Hank's pickup with 1 gallon of gas = 72/4 = 18 miles.
We need to find gallons of gas required for Hank's pickup to travel 54 miles.
Gallons of gas required = Miles need to travel/ Miles travel with 1 gallon of gas
= 54/18 = 3 gallons of gas.
So Hank's pickup need 3 gallons of gas to travel 54 miles.
Marta hopes to have a test average of at least 90 by the end of the marking period. Her grades on the first four tests have been 86, 84, 97 and 89. What is the lowest grade she can receive on her fifth and final test and still have a test average of 90 or higher?
Answer:
Marta need to score at least 94 to receive an average of 90 or higher considering all five tests.
Explanation:
Marks received by Marta in four tests = 86, 84, 97 and 89
Let mark received in fifth test be x
We have average of five test is more than or equal to 90
So we have
[tex]\frac{86+84+97+89+x}{5} \geq 90\\ \\ 86+84+97+89+x\geq 450\\ \\ x\geq 94[/tex]
So Marta need to score at least 94 to receive an average of 90 or higher considering all five tests.
The lowest grade she can receive on her fifth and final test to achieve an average of 90 or higher is 94.
Explanation:Marta hopes to have a test average of at least 90 by the end of the marking period. Her grades on the first four tests have been 86, 84, 97 and 89. To find the lowest grade she can receive on her fifth and final test to achieve an average of 90 or higher, we can use the formula:
Average = (Sum of all grades) / Total number of grades
Let x be the lowest grade she can receive on her fifth test. We can set up the equation:
(86 + 84 + 97 + 89 + x) / 5 = 90
Now we can solve for x:
86 + 84 + 97 + 89 + x = 90 * 5
356 + x = 450
x = 450 - 356
x = 94
Therefore, the lowest grade Marta can receive on her fifth and final test and still have a test average of 90 or higher is 94.
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The local high school hosted a hockey tournament. Tickets were sold before the tournament and at the door. When reviewing the ticket sales, the director of the tournament realized that there were 80 more tickets purchased before the tournament than at the door. A total of 820 tickets were sold. Which statements about ticket sales are true? Check all that apply.
The first thing we must do for this case is to define variables: x: number of tickets sold before the tournament. y: number of tickets sold at the door. The system of equations that adapts to this situation is given by: x + y = 820 x-y = 80 Answer: The correct options are: option 2 option 3 option 5
Answer:
The correct options are:
option 2
option 3
option 5
Step-by-step explanation:
Elena’s bus runs every 20 minutes. If she arrives at her bus stop at a random time, what is the probability that she will have to wait at least 5 minutes for the bus if it is running on schedule
Answer:
P = 15/20 = 3/4
Step-by-step explanation:
20 minutes - 5 minutes = 15 minutes.
The probability of waiting at least 5 minutes = 15/20 = 3/4 = 75%
which expression is equivalent to 14 times 14
The Answer Is 196
Hope It Helps Mark Me The Brainlyest
Answer:
it should be c 14 to the power 2
Step-by-step explanation:
If someone who worked 24 hours received 232 in pay what is his hourly wage
Answer:
[tex]9.67[/tex] per hour
Step-by-step explanation:
Rate per hour can be calculated by sing following equation,
Rate per hour = Total amount paid / Total number of hours worked
By substituting values to the above equation we can get the rate per hour,
Rate per hour = [tex]\frac{232}{24}[/tex] per hour
= [tex]9.67[/tex] per hour
48x^2 +44x=60 which of the following could be used to find the solution to the equation above? Select all that apply
To solve the quadratic equation 48x^2 + 44x = 60, one can rearrange it to the standard form, use the quadratic formula, attempt factoring if it is factorable, or multiply by a common factor to simplify. The most common method is the quadratic formula which provides a systematic way to find the solutions.
Explanation:To solve the equation 48x^2 + 44x = 60, we can use several methods that are commonly used to solve quadratic equations. First, we need to rearrange the equation into the standard quadratic form, which is ax^2 + bx + c = 0. By subtracting 60 from both sides of the equation, we get 48x^2 + 44x - 60 = 0.
One way to solve for x is by using the quadratic formula, which is x = (-b ± √(b^2 - 4ac))/(2a), where a, b, and c are coefficients from the quadratic equation ax^2 + bx + c = 0. In this situation, a = 48, b = 44, and c = -60. By plugging these values into the quadratic formula, we can find the two possible solutions for x.
Alternatively, we can try to factor the quadratic if it can be expressed as a product of two binomials. In some cases, like when the quadratic is a perfect square or can be easily factored, this is a simpler solution. However, if factoring is complicated or not apparent, the quadratic formula can always be used as a reliable method.
Additionally, if the equation has coefficients that are not integers or are difficult to work with, we can multiply both sides by a common factor to simplify the equation into a more manageable form with integer coefficients, after which we can proceed to use the quadratic formula or factor the quadratic, if possible.
The correct expression to find solutions is [tex]\(4(4x + 3)(3x - 5)\)[/tex], as it correctly factors the given quadratic equation.
To find the solutions to the given quadratic equation [tex]\(48x^2 + 44x = 60\)[/tex], we can use factoring. The equation needs to be rearranged to set it equal to zero:
[tex]\[48x^2 + 44x - 60 = 0\][/tex]
Now, we can factor the quadratic expression. The correct factorization is:
[tex]\[4(4x + 3)(3x - 5)\][/tex]
To verify this, distribute the factors:
[tex]\[4(4x + 3)(3x - 5) = 48x^2 + 36x - 60x - 45\][/tex]
Combine like terms:
[tex]\[48x^2 - 24x - 45\][/tex]
This matches the original quadratic expression, confirming the correct factorization.
Therefore, the correct expression that could be used to find the solutions to the given equation is [tex]\(4(4x + 3)(3x - 5)\)[/tex].
Complete Question:
Use properties to rewrite the given equation. Which equations have the same solution as 3/5x +2/3 + x = 1/2– 1/5x? Check all that apply.
a. 8/5x+2/3=1/2-1/5x
b. 18x + 20 + 30x = 15 – 6x
c. 18x + 20 + x = 15 – 6x
d. 24x + 30x = –5
e. 12x + 30x = –5
Answer:
Only options a ,b,d have the same solution as [tex]\frac{3}{5}x +\frac{2}{3}+x=\frac{1}{2}-\frac{1}{5}x[/tex]
Step-by-step explanation:
Given:
An equation: [tex]\frac{3}{5}x +\frac{2}{3}+x=\frac{1}{2}-\frac{1}{5}x[/tex] ....[1]
Like terms states that contain the same variables raised to the same power.
Combine like terms on left hand side in equation [1] we get,
[tex]\frac{3}{5}x+x +\frac{2}{3}=\frac{1}{2}-\frac{1}{5}x[/tex]
[tex]\frac{8}{5}x +\frac{2}{3}=\frac{1}{2}-\frac{1}{5}x[/tex]
we get option (a) as the same solution.
Using LCM(Least Common ) to change each fraction to make their denominators the same as the least common denominator
Taking LCM both sides in Equation (1) ,
[tex]\frac{3}{5}x +\frac{2}{3}+x=\frac{1}{2}-\frac{1}{5}x[/tex]
As LCM(3,5)=15 and LCM(2,5)=10 we have,
[tex]\frac{9x+10+15x}{15}= \frac{5-2x}{10}[/tex]
On simplifying we get,
[tex]10(9x+10+15x)= 15(5-2x)[/tex]=
Dividing both sides by 5 we get,
[tex]\frac{10(9x+10+15x)}{5} =\frac{15(5-2x)}{5}[/tex]
On simplify:
[tex]2(9x+10+15x)=3(5-2x)[/tex]
∴ [tex]18x+20+30x=15-6x[/tex]
which is same solution as given in option (b).
Now,
Use Additive Property of Equality states that allows one to add the same quantity to both sides of an equation.
Further, using the above property add 6x both sides in [tex]18x+20+30x=15-6x[/tex] we get,
[tex]18x+20+30x+6x=15-6x+6x[/tex]
On simplifying we get,
[tex]18x+20+30x+6x=15[/tex]
Subtract 20 from both the sides we get,
[tex]18x+20+30x+6x-20=15-20[/tex]
Simplify:
[tex]18x+30x+6x=-5[/tex]
or, [tex]24x+30x=-5[/tex] which is same solution as given in option(d)
But, options c and e equation doesn't have same solution as [tex]\frac{3}{5}x +\frac{2}{3}+x=\frac{1}{2}-\frac{1}{5}x[/tex]
If jamel does 2 sets of 25 push ups if he does this 10 times each month how many push ups does he do each month write and equation to show your work
In six seconds,a total of 3 waves crash onto the shore of the beach .The distance between each wave crest on the water is 8 meters.Find the wavelength
In six seconds,a total of 3 waves crash onto the shore of the beach .
The distance between each wave crest on the water is 8 meters.
Wave length is the length between two wave crests that is the distance between two wave crests.
We know distance between each wave crest is 8 meters
Total of 3 wave crests, the distance between first and second wave crest is 8 meters
the distance between second and third wave crest is 8 meters
So wave length = 8+8 = 16 meters
A store employes 11 women and 12 men. What percentage of employes are men?
2.53 is then answer .... im pretty sure
Please Help!
The product of a number minus ten and nine equals fifty when decreased by seven. Which equation represents the sentence?
A) 7(x - 10) - 9 = 50
B) 7(10 - x) - 9 = 50
C) 9(x - 10) - 7 = 50
D) 9(10 - x) - 7 = 50
This question i know. It is C
For this one, the best way to answer is to use the question and it will guide us to the answer.
First, you can eliminate two choices:
the problem states that a number minus ten and nine
so you can eliminate B and D because it is 10 minus a number. In math, you can be picky and take the question exactly.
Then, look at the last part, "when decreased by seven." So now look between A and C and see which one is decreasing by 7. Based on that C would be your answer
C) 9(x-10) -7 = 50
Hope this helps!
Help, 50 points , and brainliest
This diagram shows a pre-image △ABC , and its image, △A′′B′′C′′ , after a series of transformations.
Select from the drop-down menus to correctly complete the statements.
△ABC is___ ( reflected across the y axis , reflected across the line y=x ,or rotated 90 degrees counterclockwise about the origin )
to become △A′B′C′ . Then △A′B′C′ is ___(reflected across the x axix, translated 4 units down , or rotated 180 degrees about the origin )to become △A′′B′′C′′ . Because the transformations are_____ (both rigid or not both rigid) , the pre-image and image are _______(congruent or not congruent ) .
Step 1: reflected across the line y=x
Step 2: reflected across the x axix
Since all 3 shapes are still the same size and shape:
Because the transformations are both rigid , the pre-image and image are congruent
Eve had 24 stamps each valued at $24.75. What is the total value of her stamps?
To calculate the total value of Eve's stamps, multiply the number of stamps (24) by the value of each stamp ($24.75), resulting in a total value of $594.00.
The question involves calculating the total value of stamps using multiplication. Eve has 24 stamps, each valued at $24.75. To find the total value, we multiply the number of stamps by the value of each stamp.
Here is the calculation:
Number of stamps: 24Value per stamp: $24.75Total value = 24 stamps * $24.75 per stamp = $594.00Therefore, the total value of Eve's stamps is $594.00.
help asap please help
[tex]-\dfrac{2}{3}\left(2x-\dfrac{1}{2}\right)\leq\dfrac{1}{5}x-1\ \ \ \ \text{use distributive property}\\\\-\dfrac{4}{3}x+\dfrac{1}{3}\leq\dfrac{1}{5}x-1\ \ \ \ \ |\cdot15\\\\-5(4x)+5\leq3x-15\\\\-20x+5\leq3x-15\ \ \ \ \ |-5\\\\-20x\leq3x-20\ \ \ \ |-3x\\\\-23x\leq-20\ \ \ \text{change the signs} \\\\23x\geq20\ \ \ \ \ \ |:23\\\\\boxed{x\geq\dfrac{20}{23}}\to x\in\left[\dfrac{20}{23},\ \infty\right)[/tex]
Solve the equation. –3x + 9 = –3(2x + 3) + 3(x – 4) + 1 How many solutions does this equation have? one solution two solutions infinitely many solutions no solution
-3x+9 = -3(2x+3) + 3(x-4)+1
distribute
-3x+9 =-6x-9+3x-12+1
add like terms
-3x+9= -3x-20
add 3x to each side
9 = -20
there are no solutions because 9 does not equal -20
Answer:
Step-by-step explanation:
Simplify this: 2/3 x 150
If 2 pizzas cost $16.22, how much will 6 pizzas cost as a unit rate
Answer:
$48.66
Step-by-step explanation: