Level C
On the football team, there are 6 players who can throw or catch the football; they are called
skilled players. The skilled players are the quarterback, halfback, fullback, flanker, split end and tight end. If Alex, Bobby, Chris, Dee, El, Frances, Gab, and Hil all can play any skilled position, how
many different squads can be created using the players listed? Show your solution.
Answers
There are \(2,520\) different squads that can be created using the \(8\) players listed.
What is the concept of permutations?To determine the total number of different squads that can be created using the players listed, we need to use the concept of permutations. A permutation is an arrangement of objects in a specific order.
In this case, we need to find the number of permutations of 8 players taken 6 at a time, as there are 6 skilled positions to be filled.
The formula for permutations of n objects taken r at a time is given by:
\(P(n, r) = n! / (n - r)!\)
where n! denotes the factorial of n, which is the product of all positive integers up to and including n. For example, \(5! = 5 \times 4 \times 3 \times 2 \times 1 = 120\) .
So, for this problem, we have:
n = 8 (total number of players)
r = 6 (number of skilled positions)
\(P(8, 6) = 8! / (8 - 6)! = 8! / 2! = 8 \times 7 \times 6 \times 5 \times 4 \times 3 / 2 \times 1 = 2,520\)
Therefore, there are \(2,520\) different squads that can be created using the \(8\) players listed.
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Related Questions
Which triangle is a translation of triangle P? On a coordinate plane, triangle P is shifted 5 units to the right and 7 units up to form triangle C. triangle A triangle B triangle C triangle D Mark this and return
Answers
Answer: Triangle C.
Step-by-Step Explanation:
To solve this problem, we need to understand what it means for a triangle to be a translation of another triangle. A translation for a triangle means that it is the same shape and size as the original triangle, but it has shifted (or moved) a specific number of units either up, down, left, or right.
In this problem, we have Triangle P, which has been shifted 5 units to the right and 7 units up to form Triangle C. To determine which triangle is a translation of Triangle P, we can look at the coordinates of the different triangles.
Triangle A: (1, 4), (3, 7), (5, 6)
Triangle B: (2, 3), (4, 6), (6, 5)
Triangle C: (6, 11), (8, 14), (10, 13)
Triangle D: (3, 5), (5, 8), (7, 7)
If we compare the coordinates of each triangle with those of Triangle P, we can see that Triangle C, with coordinates (6, 11), (8, 14) and (10, 13), is the translation of Triangle P because all of the coordinates of Triangle P have been shifted 5 units to the right, and 7 units up. Therefore, the answer is Triangle C.
Evaluate the expression 2m + 9p - 11 when m = 3 and p = 4.
a
31
b
78
c
41
d
107
Answers
Answer: A: 31
Step-by-step explanation:
2m+9p-11
(plug in m=3, p=4)
2(3)+ 9(4)-11
6+36-11
42-11
31
How many square feet of outdoor carpet will we need for this hole?
Answers
The number of square feet needed to cover the hole is 44ft²
How many square feet of outdoor carpet will we need for this hole?To find this, we need to find the area of the green region and subtract the little square that it has inside.
Remember that for a rectangle, the area is the product between the dimensions, then the area of the green region is:
A = 12ft*4ft = 48ft²
The little square has an area:
a = 2ft*2ft = 4ft²
Then the area needed is:
area = 48ft² - 4ft² = 44ft²
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Line k is represented by the equation y = 2x + 2. Write
an equation of a line that is perpendicular to line k that also passes through the point (-2, 9)?
Answers
Step-by-step explanation:
so, we calculate the perpendicular slope, and then we start with the point-slope form (since we were given a specific point of the line), and transform into the regular slope-intercept form.
the slope in
y = 2x + 2
is the factor of x : 2 or 2/1
the perpendicular slope is turning this upside down and flips the sign : -1/2
the point- slope form is
y - y1 = a(x - x1)
"a" being the slope, (x1, y1) being the point.
y - 9 = -1/2(x - -2)
y - 9 = (-1/2)x - 1
y = (-1/2)x + 8
NO LINKS!! URGENT HELP PLEASE!!!
Determine if the sequence is arithmetic. If it is, find the common difference, the 52nd term, and the explicit formula.
34. -11, -7, -3, 1, . . .
Given the explicit formula for an arithmetic sequence find the common difference and the 52nd term.
35. a_n = -30 - 4n
Answers
Answer:
#34. aₙ = 4n - 15; a₅₂ = 193#35. a₅₂ = -238; d = - 4-----------------
Question 34Find the differences in the sequence -11, -7, -3, 1, ...
1 - (-3) = 4,-3 - (-7) = 4,-7 - (-11) = 4The difference is common, so the sequence is an AP.
The nth term is:
\(a_n=a_1+(n-1)d\)\(a_n=-11+(n-1)*4=-11+4n-4=4n-15\)Find the 52nd term:
\(a_{52}=4*52-15=208-15=193\)Question 35Find the 52nd term using the given formula:
\(a_{52}=-30-4*52=-30-208=-238\)Find the previous term:
\(a_{51}=-30-4*51=-30-204=-234\)Find the common difference:
\(d=a_{52}-a_{51}=-238-(-234)=-4\)Answer:
\(\begin{aligned}\textsf{34)} \quad d&=4\\a_n&=4n-15\\a_{52}&=193\end{aligned}\)
\(\begin{aligned}\textsf{35)} \quad d&=-4\\a_{52}&=-238\end{aligned}\)
Step-by-step explanation:
Question 34An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant.
Given sequence:
-11, -7, -3, 1, ...To determine if the given sequence is arithmetic, calculate the differences between consecutive terms.
\(a_4-a_3=1-(-3)=4\)
\(a_3-a_2=-3-(-7)=4\)
\(a_2-a_1=-7-(-11)=4\)
As the differences are constant, the sequence is arithmetic, with common difference, d = 4.
The explicit formula for an arithmetic sequence is:
\(\boxed{a_n=a+(n-1)d}\)
where:
a is the first term of the sequence.n is the position of the termd is the common difference between consecutive terms.To find the explicit formula for the given sequence, substitute a = -11 and d = 4 into the formula:
\(\begin{aligned}a_n&=-11+(n-1)4\\&=-11+4n-4\\&=4n-15\end{aligned}\)
To find the 52nd term, simply substitute n = 52 into the formula:
\(\begin{aligned}a_{52}&=4(52)-15\\&=208-15\\&=193\end{aligned}\)
Therefore, the 52nd term is a₅₂ = 193.
\(\hrulefill\)
Question 35Given explicit formula for an arithmetic sequence:
\(a_n=-30-4n\)
To find the common difference, we need to compare it with the explicit formula for the nth term:
\(\begin{aligned}a_n&=a+(n-1)d\\&=a+dn-d\\&=a-d+dn\end{aligned}\)
The coefficient of the n-term is -4, therefore, the common difference is d = -4.
To find the 52nd term, simply substitute n = 52 into the formula:
\(\begin{aligned}a_{52}&=-30-4(52)\\&=-30-208\\&=-238\end{aligned}\)
Therefore, the 52nd term is a₅₂ = -238.
Can someone please answer this question? Someone answered and they deleted their answer, so I need someone else to help me!
Please do not delete your answer, steal the points, or send links, I really need some help!
Answers
Check the picture below.
now, notice the triangles made, 3 right triangles with legs of 5 and 4 each.
looking at quadrilateral (1), from the leg 5 units long, we have a line with a run of -1 and a rise of 3, from the leg 4 units long, we have a line with a run of 4 and a rise of -1.
Now, quadrilaterals (2) and (4) display the same lengths and rise and runs, which means they're all congruent, quadrilateral (3) has no equal.
so 1 ≅ 2 and 1 ≅ 4.
Match the vocabulary word with its definition
Answers
Karla sells Valentine's Day teddy bears (x ) and flowers (Y) . it's teddy bear cost $5 and flowers are $8 . she sold a total of $214 and 35 items in all . how many teddy bears and flowers does Karla sell?
Answers
Answer:
Explanation:
Let x represents the number of teddy bears and y represents the number of flowers that Karia sells. If each teddy bear costs $5 and each flower costs $8 and she sold a total of 35 items for $214, we can express the above statements mathematically as per below;
\(\begin{gathered} 5x+8y=214 \\ x+y=35 \end{gathered}\)So let's go ahead and solve the above equations simultaneously to find x and y.
To find x, we'll make y the subject of the formula in the 2nd equation;
\(y=35-x\)So let's substitute y = 35 - x into the 1st equation and solve for x;
\(undefined\)Which is the largest ratio?
5/36, 2:9, 3 to 18, 1:3
Answers
The largest ratio, among the following ratios: 5/36, 2:9, 3 to 18, 1:3 is 1:3.
How the largest ratio is determined:The ratio refers to the relative size of one quantity compared to another.
The ratio, which is the quotient of two quantities or values, can be expressed as a decimal, percentage, or fraction. We can also express the ratio in its standard form (:).
Given Sum of Equivalent
Ratio Ratios Ratios
5/36 36 13.89% or 0.1389
2:9 11 18.18% or 0.1818
3 to 18 21 14.28% or 0.14.28
1:3 4 25% or 0.25
Thus, we can conclude that 1:3 is the largest ratio amont the others.
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Help plz? I don’t know what to write
Answers
Answer:
1. C
2. B
3. A
4. D
Step-by-step explanation:
Which number does not
belong to the pattern below? Explain.
5,470, 547, 54.7, 0.547
Answers
Jim ate two slices of pizza, which is 25% of the pizza. How many slices were in the whole pizza?Sonya buys a baseball jersey for her brother on sale for 20% off. If the price she paid was $6 lower than the regular price, what was the original price of the jersey
Answers
There were 8 slices in the whole pizza.
How many slices were in the whole pizza if Jim ate two slices?An equation means the formula that expresses the equality of two expressions by connecting them with the equals sign =. Let us assume the number of slices in the whole pizza is "x".
Since Jim ate two slices which is 25% of the pizza, we will set up the equation:
2 = 0.25x
To solve for "x":
2 / 0.25 = x
x = 8.
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Find the Values of X and Y in the diagram. PLZ HELP
Answers
Answer: x is 47, y is 75
Step-by-step explanation:
Which set of shapes could you use to form a net for a
rectangular pyramid?
4 triangles, 1 rectangle
3 triangles, 2 rectangles
1 triangle, 4 rectangles
5 rectangles
Answers
Answer:
A
Step-by-step explanation:
I did the assignment :>
Answer:
A) 4 triangles, 1 rectangle
Step-by-step explanation:
is correct, just did it :)
Are 4x, 4y, and 4xy like terms?
Answers
Explanation:
In algebra, like terms are terms that have the same combination of variables raised to the same powers. Let's determine whether 4x, 4y, and 4xy are like terms.
The term 4x consists of the variable x raised to the power of 1, while the term 4y contains the variable y raised to the power of 1. Thus, both 4x and 4y have the same combination of variables raised to the same power. Therefore, they can be considered like terms. On the other hand, the term 4xy consists of both the variables x and y, each raised to the power of 1.
Although it includes both x and y, the arrangement of the variables is different from the previous terms. This means that 4xy is not a like term to either 4x or 4y. In conclusion, among the given terms, 4x and 4y are like terms, while 4xy is not. It is important to identify like terms in algebra to simplify expressions and combine similar terms for easier calculations.
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f(x) = 5 - 2x and g(x)= x^2+ 7x, find each value.
g(3)
f(m)
f(1) + g(2)
f(11)
Answers
Answer:
Step-by-step explanation:
f(x) = 5 - 2x and g(x)= x^2+ 7x, find each value.
g(3)
f(m)
f(1) + g(2)
f(11)
10,000 times 100,00 help please
Answers
Answer:1,000,000
Step-by-step explanation:THERE U GO :)
What equation represents this graph?
Answers
Strawberries cost $3.00 per pound. For each question, explain or show your
reasoning.
a.
How many pounds of strawberries can you buy for $1.00?
b.
How many pounds of strawberries can you buy for $11.00?
I need help
Answers
Step-by-step explanation:
1. its either 0 or 1/4 cause cause each pound is $3 and he had less then that.
2. 3 cause its either u count by 3 till u get to 11 or below it
The answers to both subparts using mathematical operations are shown:
(A) Strawberries at $1.00: 0.33 pounds(B) Strawberries for $11.00: 3.67 poundsWhat are mathematical operations?A mathematical function known as an operation converts zero or more input values into a precisely defined output value. The quantity of operands affects the operation's arity.The order of operations is a rule that outlines the proper steps to take when analyzing a mathematical equation. We can recall the PEMDAS steps in the following order: parentheses, exponents, multiplication, and division (from Left to right), addition, and subtraction (from left to right).(A) Strawberries at $1.00:
1/30.33 poundsStrawberries at $1.00: 0.33 pounds
(B) Strawberries for $11.00:
11/33.67Strawberries at $11.00: 3.67 pounds
Therefore, the answer to both subparts using mathematical operations are shown:
(A) Strawberries at $1.00: 0.33 pounds(B) Strawberries for $11.00: 3.67 poundsKnow more about mathematical operations here:
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3 pounds because strawberries cost $3.00 per pound.What is cost? A cost is the worth of money that has been expended to produce something or provide a service and is therefore no longer available for use in production, research, retail, and accounting. In the case of an acquisition cost, the money spent on the acquisition is considered the cost.What connection exists between price and quality?Regardless matter whether the relationship is positive [higher costs are linked with higher quality] or negative [higher quality is associated with lower costs], the majority of research have concluded that the relationship between cost and quality is minimal to moderate.Given: Cost of Strawberries per pound = $3. 00a. How many pounds of strawberries can you buy for $1.00?Answer: 0 because the cost of per pound strawberries is $3.00So, he can not but any pound at $1.00but he can but 1/4 pound as the cost given b. How many pounds of strawberries can you buy for $11.00?Therefore, 3 pounds because strawberries cost $3.00 per pound.To learn more about : cost calculationRef: https://brainly.com/question/17215284#SPJ2
A bag contains 6 red, 5 white and 4 black balls. Two balls are drawn. Find the probability that one of them is red
Pls answer!!!!
Answers
Answer:
The probability of drawing one red ball out of a bag containing 6 red, 5 white and 4 black balls is equal to the number of favorable events (picking 1 red ball) divided by the total number of possible outcomes (picking 1 ball out of a pool of 15). Therefore, the probability of drawing one red ball from this bag is 6/15, or 2/5.
Chloe bought 5 sets of books. She donated 9 of her books to her school. She has 26 books left. How many books were in each set? please help
Answers
Answer:
7 books in each set.
Step-by-step explanation:
If you add the nine books that she donated (9) to the number of books that are left over (26) you would have 35. And since their are 5 sets you would divide 35 by 5 and get 7.
HELP! A paper airplane is thrown from the top of a treehouse. The paper airplane flies 16 feet through the air and lands in a sandbox that is 9 feet from the base of the tree that the treehouse is in.
What is the angle of depression that the paper airplane is flying down at?
Explain your process
Answers
The angle of depression that the paper airplane is flying down at 55. 78 degrees
How to determine the valueNote that the different trigonometric identities in mathematics are;
sinetangentcotangentsecantcosecantcosineThese identities also have their ratios are;
sin θ = opposite/hypotenuse
cos θ = adjacent//hypotenuse
tan θ = opposite/adjacent
From the information given, we have;
Using the cosine identity
Adjacent = 9 feet
Hypotenuse = 16 feet
Substitute the values
cos θ = 9/ 16
divide the values
cos θ = 0. 5625
θ = 55. 78 degrees
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Answer:
55.8° (nearest tenth)
Step-by-step explanation:
The angle of depression is the angle between the horizontal line of sight at the top of the treehouse and line of sight to the sandbox (the flight path of the paper airplane). (See attached diagram).
To find the angle of depression, we can use the cosine trigonometric ratio. The cosine of an angle is equal to the ratio of the length of the side adjacent the angle to the length of the hypotenuse.
\(\boxed{\begin{minipage}{9 cm}\underline{Cosine trigonometric ratio} \\\\$\sf \cos(\theta)=\dfrac{A}{H}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}\)
In this case, the length of the side adjacent the angle of depression is equal to the distance between the base of the tree and the sandbox, so A = 9 ft. The hypotenuse is the distance the airplane flies through the air, so H = 16 ft.
Substitute these values into the cosine ratio and solve for θ:
\(\cos (\theta)=\dfrac{9}{16}\)
\(\theta=\cos^{-1}\left(\dfrac{9}{16}\right)\)
\(\theta=55.7711336...^{\circ}\)
\(\theta=55.8^{\circ}\; \sf (nearest \; tenth)\)
Therefore, the angle of depression that the paper airplane is flying down at is 55.8° (nearest tenth).
14Y - 7y = 35. solve for y
Answers
Answer:
y = 5
Step-by-step explanation:
\(14y-7y=35\\7y=35\\y=5\)
14 minus 7 is 7
7Y is equal to 35
divide both sides by 7 is equal to 5
A person cycles from their home to a library which is 8 kilometers away. It takes them 20 minutes to reach the library. They stay there for 30 minutes to read, and then
walk to their friend's home which is 4 kilometers from the library and reach there in 20 minutes. Which graph best represents this situation?
Answers
Answer:
The third option
Step-by-step explanation:
What is the volume of a rectangular prism if the length is 21 feet width is nine and height is seven that's not nice what is the volume of a rectangular prism if the length is 21 feet width is nine and height is 7 feet
Answers
The volume of the prism is 1323 feet³ (cubic feet).
Step-by-step explanation:1. Annotate the values.Length= 21 feet.
Width= 9 feet.
Height= 7 feet.
2. Find a formula.The formula to calculate the volume of rectangular prisms is the following:
\(\sf V_{RP} =l*w*h\); where "l" is the length; "w" is the width, and "h" is the height of the prism.
Check the attached image to see where these values are measured from.
3. Calculate.Substitute the variables in the formula by the values on step 1.
\(\sf V_{RP} =l*w*h=(21\ feet)*(9\ feet)*(7\ feet)=\boxed{\sf1323\ feet}.\)
The volume of the prism is 1323 feet³ (cubic feet).
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Answer:
The volume of the rectangular prism is 1323 cubic feet.
Step-by-step explanation:
Step 1: Write down the formula for the volume of a rectangular prism:
\(\qquad\Large\boxed{\rm{\:\:\:V = l \times w \times h\:\:\:}}\)
Step 2: Substitute the given values for the length, width, and height:
\(\qquad\Large\rm{V = 21\: ft \times 9\: ft \times 7\: ft}\)
Step 3: Multiply the numbers together:
\(\qquad\Large\rm\implies{V = 1323\: ft^3}\)
Step 4: Write the final answer with the appropriate units:
The volume of the rectangular prism is 1323 cubic feet.
\(\blue{\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}\)
Calculate the difference and enter below. 3-9
Answers
Answer:
-6 is your answer
Step-by-step explanation:
I hope that's right
help i nedeed to pass the quizzzzzzzzzzzzzzz
Answers
The area of the figure is 108cm²
How to determine the value of the areaThe formula for calculating the area of a triangle is expressed as;
Area = 1/2 base × height
Substitute the values, we have;
Area = 1/2 ×8×3 = 12 cm²
The formula for calculating the area of a rectangle is expressed as;
Area = length × width
substitute the values, we have;
Area = 8 × 10
Area = 80 cm²
The formula for area of a trapezoid is expressed as;
Area = a + b/2 h
Substitute the values
Area = 4 + 4/2 (4)
Area = 16cm²
Total area = 16 + 12 + 80 = 108cm²
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If f(x)=x² – 4x, what is the value of 2f(a-1)?
Answers
The correct value of 2f(a-1) is 2a^2 - 12a + 10.
To find the value of 2f(a-1), we need to substitute (a-1) into the function f(x) and then multiply the result by 2.
Given: f(x) = x^2 - 4x
Substituting (a-1) into the function:
f(a-1) = (a-1)^2 - 4(a-1)
Expanding and simplifying:
f(a-1) = (a^2 - 2a + 1) - (4a - 4)
f(a-1) = a^2 - 2a + 1 - 4a + 4
f(a-1) = a^2 - 6a + 5
Now, we multiply the result by 2:
2f(a-1) = 2(a^2 - 6a + 5)
Expanding:
2f(a-1) = 2a^2 - 12a + 10
Therefore, the value of 2f(a-1) is 2a^2 - 12a + 10.
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Composition of functions Find g (f(x)) for the following problems
Answers
1.
\(f(x)=-3x\qquad g(x)=5x-6\\\\g(f(x))=5(-3x)-6=\boxed{-15x-6}\)
2.
\(f(x)=x-6\qquad g(x)=x^2+6x-2\\\\g(f(x))=(x-6)^2+6(x-6)-2=x^2-12x+36+6x-36-2=\\\\=\boxed{x^2-6x-2}\)
3.
\(f(x)=4x+3\qquad g(x)=2x^2-x+1\\\\g(f(x))=2(4x+3)^2-(4x+3)+1=2(16x^2+24x+9)-4x-3+1=\\\\=32x^2+48x+18-4x-3+1=\boxed{32x^2+44x+16}\)
4.
\(f(x)=2x^2\qquad g(x)=8x^2+3x\\\\g(f(x))=8(2x^2)^2+3(2x^2)=8\cdot4x^4+6x^2=\boxed{32x^4+6x^2}\)
How can I get the number 10 , by only using 1,6 and 7 
Answers
Answer:
7 + 1 + 1 + 1 = 10
Step-by-step explanation:
This question is not very clear as to what is required, or any possible limitations. One possible solution is listed below, hope it does help.
Using the numbers 1, 6, and 7, you can get the number 10 through the following equation:
7 + 1 + 1 + 1 = 10
By adding 7 with three instances of 1, you obtain 10.