Suppose that 21 people are competing in an Olympic event, where first place earns Gold, second place earns Silver, and third place earns Bronze. How many different possible outcomes are there for this Olympic event
Answers
Answer:
Step-by-step explanation:
This is a combination problem. Combination has to do with selection
Total people competing in the event = 21people
Prizes to be won = 3(Gold, silver and bronze)
Using the formula
nCr = n!/(n-r)!r!
21C3 = 21!/(21-3)!3!
21C3 = 21!/18!3!
21C3 = 21×20×19×18!/18!3!
21C3 = 21×20×19/3!
21C3 = 21×20×19/6
21C3 = 1330
Hence 1330 possible outcome are there for the event.
Related Questions
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Note: Figure is not drawn to scale.
If a = 5m, b = 8 m, c = 8 m, and d = 2 m, what is the perimeter of the swimming pool?
OA.
21 m
OB.
32 m
29 m
34 m
OC.
OD.
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Answers
After considering the given data we conclude that the perimeter of the given swimming pool is 23 meters which is Option A.
The perimeter of a rectangle is evaluated by adding up all its sides. For the given case, we possess a rectangle with sides
a = 5m,
b = 8m,
c = 8m and
d = 2m.
Perimeter regarding the swimming pool is evaluated as
a + b + c + d
= 5m + 8m + 8m + 2m
= 23 meters
Hence the option regarding the question which satisfy the perimeter is Option A.
Perimeter the counted measurement regarding the distance around the outside of a two-dimensional shape. In this system the length of the outline or boundary of any two-dimensional geometric shape is defined as perimeter .
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The complete question is
If a = 5m, b = 8 m, c = 8 m, and d = 2 m, what is the perimeter of the swimming pool?
A.23 m
B. 32 m
C.29 m
D.34 m
Round 258,177 to the nearest hundred thousand.
Answers
Answer:
It's 300,000
Step-by-step explanation:
if you round (25)0,000 off you get 300000, so you don't have to worry about the other digits too much
Hexagon DEFGHI is translated on the coordinate plane below to create hexagon D′E′F′G′H′I′: Hexagon DEFGHI and Hexagon D prime E prime F prime G prime H prime I prime on the coordinate plane with ordered pairs at D 2, 5, at E 5, 5, at F 6, 3, at G 5, 1, at H 2, 1, at I 1, 3, at D prime negative 6, negative 2, at E prime negative 3, negative 2, at F prime negative 2, negative 4, at G prime negative 3, negative 6, at H prime negative 6, negative 6, at I prime negative 7, negative 4
Answers
Answer: To find the image of a figure under a translation, you need to apply the same translation to every point in the figure.
In this case, the image of hexagon DEFGHI is hexagon D′E′F′G′H′I′. To find the image of each point, you can apply the translation that maps point D to point D′.
For example, to find the image of point E under the translation, you can apply the same translation that maps point D to point D′:
Point D is located at (2, 5).
Point D′ is located at (-6, -2).
The translation that maps point D to point D′ is a translation 6 units to the left and 2 units down.
To find the image of point E under this translation, you can apply the same translation to point E:
Point E is located at (5, 5).
The image of point E is located at (5 - 6, 5 - 2) = (-1, 3).
You can follow the same process to find the images of the other points under the translation.
Alternatively, you can use the coordinates of point D and point D′ to find the translation vector that describes the translation. The translation vector is a displacement that describes the change in position of a point under the translation.
In this case, the translation vector is given by the displacement from point D to point D′:
Point D is located at (2, 5).
Point D′ is located at (-6, -2).
The translation vector is given by the displacement (-6 - 2, -2 - 5) = (-8, -7).
To find the image of any point under the translation, you can add the translation vector to the coordinates of the point. For example, to find the image of point E under the translation, you can add the translation vector to the coordinates of point E:
Point E is located at (5, 5).
The translation vector is (-8, -7).
The image of point E is located at (5 - 8, 5 - 7) = (-3, -2).
You can follow the same process to find the images of the other points under the translation.
Step-by-step explanation:
please I need help with this
Answers
A. The following are sets A and B:
A = {2, 3, 5, 7, 11}
B = {1, 2, 3, 4, 6, 12}
C. Elements not in A or A' = ∅
B. The Venn diagram is attached
How to solve sets?A universal set is a set which consists of all elements related to the given sets. It is denoted by U.
A. Set A:
A = {2, 3, 5, 7, 11}
Set B:
B = {1, 2, 3, 4, 6, 12}
U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
A' = {1, 4, 6, 8, 9, 10, 12}
C. Elements not in A or A' = ∅
Complement of set A is refers to a set that contains the elements present in the universal set but not in set A.
Hence, the Venn diagram of sets A, B and U has been attached.
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Where does the line through A(−3, 1, 0) and B(−1, 5, 6) intersect the plane 2x + y − z + 2 = 0? Justify all your steps
Answers
Answer:
(0, 7, 9)
Step-by-step explanation:
The direction vector (a, b, c) is given by B - A
(a, b, c) = (−1, 5, 6) - (-3, 1, 0) = (2, 4, 6)
(a, b, c) = (2, 4, 6)
Let us use point A as \((x_o,y_o,z_o)\), therefore (-3, 1, 0) = \((x_o,y_o,z_o)\)
\(x=x_o+at\\\\x=-3+2t\\\\y=y_o+bt\\\\y=1+4t\\\\z=z_o+ct\\\\z=0+6t\)
Substituting the value of x, y and z into the plane equation:
2x + y − z + 2 = 0
2(-3+2t) + (1 + 4t) - (6t) + 2 = 0
-6 + 4t + 1 + 4t - 6t + 2 = 0
2t -3 = 0
2t = 3
\(\x=-3+2t\\\\x=-3+2(3/2)=0\\\\y=1+4t\\\\y=1+4(3/2)=7\\\\z=0+6t\\\\z=6(3/2)=9\\\\x=0,y=7,z=9\\\\(0,7,9)\)
t = 3/2
Answer:
Step-by-step explanation:
a square flower garden has an area of 1024 Square calculate its perimeterwhat is the area of a square whose perimeter is 84 metre
Answers
Answer:
The perimeter of a square is 128, the area when perimeter 84 is 441
Step-by-step explanation:
When the length of a square arm is l,
the area of a square is A = l^2.
So in your case, A = \sqrt{1024} = l^2
So l is simply, l = 32.
The perimeter of a square is, P = 4.l = 32*4 = 128
Again when the perimeter is, P = 84
l = 84/4 = 21
So then the area is, A = 21^2 = 441
(4x-10) x (3x²)
Find the area of the rectangle
Answers
If the length of the rectangle be (3x+2) units and width (4x+10)units then the area of the rectangle be \($x=-\frac{2}{3}, x=-\frac{5}{2}$$\).
How to find the area of rectangle?The region enclosed by an object's shape is referred to as the area. The area of the shape is the area that the figure or any other two-dimensional geometric shape occupies in a plane.
A rectangle's sides determine its area. In essence, the length and breadth of the rectangle multiplied together gives the area of the rectangle.
Let the length of the rectangle be (3x + 2) units and width of the rectangle be (4x + 10)units.
Area of rectangle = length × breadth
= (3x +2) × (4x +10)
simplifying the above equation, we get
= (3x) × (4x +10) + 2(4x +10)
= 12x² + 30x +8x +20
12x² + 38x + 20 = 0
simplifying the above equation, we get
By using quadratic equation, then
\($x_{1,2}=\frac{-38 \pm \sqrt{38^2-4 \cdot 12 \cdot 20}}{2 \cdot 12}$$\)
simplifying the above equation, we get
\($$\begin{gathered}x_{1,2}=\frac{-38 \pm 22}{2 \cdot 12}\end{gathered}$$\)
Separate the solutions, we get
\($$\begin{aligned}& x_1=\frac{-38+22}{2 \cdot 12}, x_2=\frac{-38-22}{2 \cdot 12} \\& x=\frac{-38+22}{2 \cdot 12}:-\frac{2}{3} \\& x=\frac{-38-22}{2 \cdot 12}:-\frac{5}{2}\end{aligned}$$\)
The solutions to the quadratic equation are:
\($x=-\frac{2}{3}, x=-\frac{5}{2}$$\)
The complete question is:
Find the area of rectangle with length (3x+2) units and width (4x+10)units.
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How many miles does he run in one year
Answers
Answer Key:
1. Since the question says Mr. Smith runs 2.7 miles every day of the week, you will need to multiply it with 365, the days of the year. The total answer you would get D. 985.5 miles.
| I just want to help you with #2 anyway
what is the average (mean) value of 3t^3-t^2
Answers
To calculate the average (mean) value of a function, you need to find the area under the curve of the function, divide it by the interval over which the function is defined, and then find the value of the function at the midpoint of the interval.
In this case, the function is 3t³ - t² and we need to find an interval to calculate the average (mean) value. A common interval used for this calculation is from 0 to 1.
The area under the curve of the function from 0 to 1 can be found by integrating the function from 0 to 1. However, to keep it simple, we can also use the definite integral of the function from 0 to 1, which is:
∫ (3t³ - t²) dt = 3t⁴/4 - t³/3 | from 0 to 1
= (3/4) - (1/3) = 1/4
So, the average (mean) value of the function 3t³ - t² over the interval 0 to 1 is: 1/4 ÷ 1 = 1/4
And the value of the function at the midpoint of the interval, which is 0.5, is: 3(0.5) ³ - (0.5) ² = 3/8 - 1/4 = -1/32
So, the average (mean) value of the function 3t³ - t² over the interval 0 to 1 is -1/32.
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How does Mathematics differ from language to language across the world
Answers
The answer is explained below.
In order to be considered a language, a system of communication must have vocabulary, grammar, syntax, and people who use and understand it. Mathematics meets this definition of a language. Linguists who don't consider math a language cite its use as a written rather than spoken form of communication.
Mathematics is pure language - the language of science. It is unique among languages in its ability to provide precise expression for every thought or concept that can be formulated in its terms. In a spoken language, there exist words, like "happiness", that defy definition.
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The length of a rectangular field is represented by the expression 14x-3x^2+2y . The width of the field is represented by the expression 5x-7x^2+7y . How much greater is the length of the field than the width?
Answers
The length of the field is greater than the width by the expression \((14x - 3x^2 + 2y) - (5x - 7x^2 + 7y).\)
1. The length of the field is represented by the expression \(14x - 3x^2 + 2y.\)
2. The width of the field is represented by the expression \(5x - 7x^2 + 7y\).
3. To find the difference between the length and width, we subtract the width from the length: (\(14x - 3x^2 + 2y) - (5x - 7x^2 + 7y\)).
4. Simplifying the expression, we remove the parentheses: \(14x - 3x^2 + 2y - 5x + 7x^2 - 7y.\)
5. Combining like terms, we group the \(x^2\) terms together and the x terms together: \(-3x^2 + 7x^2 + 14x - 5x + 2y - 7y.\)
6. Simplifying further, we add the coefficients of like terms:\((7x^2 - 3x^2) + (14x - 5x) + (2y - 7y).\)
7. The simplified expression becomes: \(4x^2 + 9x - 5y.\)
8. Therefore, the length of the field is greater than the width by the expression \(4x^2 + 9x - 5y.\)
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Tell whether -2 is a solution of the inequality n-5<8
Answers
Answer:
-2 is a solution
Step-by-step explanation:
-2-5<8
-7<8
Answer:
-2 is a solution.
Step-by-step explanation:
negative 2 minus 5 is less than 8
negative 7 is less than 8
Which of these expressions below is less than 345? Select all that apply.
A) 342.35 + 4.19
B) 256.79 + 98.11
C) 356.09 -10.45
D) 419.56 - 75.68
E) 199.75 +143.712
Answers
Answer:
D and E
Step-by-step explanation: Math
Answer:
d and e
Step-by-step explanation:
419.56-75.68=343.88
199.75+143.712=343.462
Please see screenshot
Answers
The graph of the feasible region is attached
How to determine the graph of the feasible regionFrom the question, we have the following parameters that can be used in our computation:
\(\left\{ \begin{array}{lr} y + 7x \ge 10 \\ 8y + 2x \ge 20 \\ y + x \ge 4 \\ y + x\le 10 \\ x \ge 0 \\ y \ge 0\end{array}\)
To plot the graph of the feasible region, we plot each inequality in the domain x ≥ 0 and y ≥ 0
Using the above as a guide, the graph is attached
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the area of the rectangular city park is 25/24 square miles. the length of the park is 5/9 mile. what is the width,in mils, of the park
Answers
Answer:
A rectangle's area is Length * Width [Let x = rectangle's width] A rectangle's area is Length * Width [Let x = rectangle's width] (25/54 square miles) = (5/9 miles)*(x miles) A rectangle's area is Length * Width [Let x = rectangle's width] (25/54 square miles) = (5/9 miles)*(x miles) A rectangle's area is Length * Width [Let x = rectangle's width] (25/54 square miles) = (5/9 miles)*(x miles) 25/54 = (5/9)x A rectangle's area is Length * Width [Let x = rectangle's width] (25/54 square miles) = (5/9 miles)*(x miles) 25/54 = (5/9)x (25/54)*(9/5) = x [multiply both sides by (9/5) A rectangle's area is Length * Width [Let x = rectangle's width] (25/54 square miles) = (5/9 miles)*(x miles) 25/54 = (5/9)x (25/54)*(9/5) = x [multiply both sides by (9/5) 5/6 = x [cancel out] A rectangle's area is Length * Width [Let x = rectangle's width] (25/54 square miles) = (5/9 miles)*(x miles) 25/54 = (5/9)x (25/54)*(9/5) = x [multiply both sides by (9/5) 5/6 = x [cancel out] A rectangle's area is Length * Width [Let x = rectangle's width] (25/54 square miles) = (5/9 miles)*(x miles) 25/54 = (5/9)x (25/54)*(9/5) = x [multiply both sides by (9/5) 5/6 = x [cancel out] The width is 5/6 miles A rectangle's area is Length * Width [Let x = rectangle's width] (25/54 square miles) = (5/9 miles)*(x miles) 25/54 = (5/9)x (25/54)*(9/5) = x [multiply both sides by (9/5) 5/6 = x [cancel out] The width is 5/6 miles Just to check: (5/9)*(5/6) = 25/54a bus traveled 60 km of north of its terminal. From this point, it traveled km east. How far is the bus from the terminal?
Answers
maybe 61km from northeast
19.
A box contains only quarters and dimes. If there were 10% more quarters, the total
value of the money in the box would increase by 7.5%. What is the ratio of the number of quarters to the
number of dimes in the box? Express your answer as a common fraction.
Answers
Answer:
The ratio of the number of quarters to the number of dimes in the box is 9:10
Step-by-step explanation:
Please help! And whoever responds first will get marked best!!Which container of milk would you buy? 1/2 gallon for $2.29 or 1 gallon for $3.99?
Explain why.
Answers
Answer:
1 gallon 3.99
reason
2 1/2 gallon= 4.58
one 1 gallon = 3.99
better deal if you get the one gallon
3. Show that 5424 9813 2720 0085 is an invalid MASTERCARD credit card number.
Answers
Answer:
Step-by-step explanation:
To check whether the given credit card number is valid or not, we need to apply the Luhn algorithm or the mod-10 algorithm. The Luhn algorithm works by adding up all the digits in the credit card number and checking if the sum is divisible by 10 or not. If it is, then the credit card number is considered valid, otherwise, it is invalid.
Let's apply the Luhn algorithm to the given credit card number:
Step 1: Starting from the rightmost digit, double every second digit
| 5 | 4 | 2 | 4 | 9 | 8 | 1 | 3 | 2 | 7 | 2 | 0 | 0 | 0 | 8 | 5 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| | 8 | | 8 | | 16| | 6 | | 14| | 0 | | 0 | | 10|
Step 2: If the doubled value is greater than 9, add the digits of the result
| 5 | 4 | 2 | 4 | 9 | 8 | 1 | 3 | 2 | 7 | 2 | 0 | 0 | 0 | 8 | 5 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| | 8 | | 8 | | 7 | | 6 | | 5 | | 0 | | 0 | | 1 |
Step 3: Add up all the digits in the credit card number, including the check digit
5 + 4 + 2 + 4 + 9 + 8 + 1 + 3 + 2 + 7 + 2 + 0 + 0 + 0 + 8 + 5 + 1 = 61
Step 4: If the sum is divisible by 10, then the credit card number is valid, otherwise, it is invalid.
61 is not divisible by 10, therefore the given credit card number is invalid.
Hence, it can be concluded that 5424 9813 2720 0085 is an invalid MASTERCARD credit card number.
Select the correct name in the table.
A teacher arranged some pencils on her desk as shown below and asked her students what concept the pencils demonstrated.
Allie said the pencils are an example of perpendicular lines.
Caryl said the pencils are an example of perpendicular segments.
Frank said the pencils are an example of parallel lines.
Hector said the pencils are an example of parallel segments.
Morgan said the pencils are an example of lines that are neither parallel nor perpendicular.
Terrence said the pencils are an example of segments that are neither parallel nor perpendicular.
Which student answered correctly?
Allie Caryl Frank
Hector Morgan Terrence
Answers
The person that is correct among the students is Frank who said the pencils are an example of parallel lines.
What are parallel lines?Parallel lines are lines that can never meet. These are lines that run a direction that is quite opposite to each other as we can see from the image. It is clear that the lines as shown are not able to meet at any point even if they are extended.
Thus, the person that is correct among the students is Frank who said the pencils are an example of parallel lines.
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anwser it pls aaaaaaaassaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa
Answers
Answer:
Step-by-step explanation:
Volume = Bh
Turn the shape so the trapezoid is on the bottom/base
h=18 for overall shape
B = area of base, trapezoid
B = 1/2 (b₁ + b₂) h
b₁ = 11
b₂ = 25
h = 24 for trapezoid
B = 1/2 (11 + 25)(24)
B = 432
V = Bh
V = (432)(18)
V= 7776 in³
Mabel bought b bags of beans. There are 15 beans in each bag. Write an expression that shows how many beans Mabel bought.
Answers
Answer:
y= x+15
Step-by-step explanation:
I think that will be your equation
A quadratic function g(x) passes through the points (-8, 33), (2, 1), and (8, 1).
Answers
By applying the features of polynomials, the quadratic function g(x) = (1/5) · x² - 2 · x + 21/5 passes through the points (x₁, y₁) = (-8, 33), (x₂, y₂) = (2, 1) and (x₃, y₃) = (8, 1).
How to derive a quadratic function that passes through three points
Polynomials are algebraic expressions of the form \(\sum \limits_{i=0}^{n} c_{i}\cdot x^{i}\), where \(c_{i}\) is the i-th coefficient of the polynomial and n is the grade of the polynomial. In addition, we know that polynomials have n + 1 coefficients.
In the case of quadratic functions, the grade is 2 and the function have three coefficients. Hence, we need three distinct points to determine all the coefficients of a quadratic function.
(x₁, y₁) = (-8, 33)
64 · a - 8 · b + c = 33 (1)
(x₂, y₂) = (2, 1)
4 · a + 2 · b + c = 1 (2)
(x₃, y₃) = (8, 1)
64 · a + 8 · b + c = 1 (3)
Then, we find the solution of this system of linear equations:
a = 1/5, b = -2, c = 21/5
By applying the features of polynomials, the quadratic function g(x) = (1/5) · x² - 2 · x + 21/5 passes through the points (x₁, y₁) = (-8, 33), (x₂, y₂) = (2, 1) and (x₃, y₃) = (8, 1).
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If s(x)= 2 -x^2 and f(x)=3x, which value is equivalent to (s°f)(-7)
Answers
What percent of the front page is taken up by the
prom story, including the prom photograph?
A. 20%
B. 22%
C. 25%
D. 45%
E. 60%
Answers
The percent of the front page taken up by the prom story is 20%
Calculating the percent of the front page taken up by the prom storyFrom the question, we have the following parameters that can be used in our computation:
The front page
From the front page, we have
Area front page = 5 * 4
Area front page = 20
Also, we have
Prom = 2 * 2
Prom = 4
So, we have
Percentage = 4/20 * 100%
Evaluate
Percentage = 20%
Hence, the percent of the front page taken up by the prom story is 20%
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i am confused on finding the answer i have tried a few times and i do not understand
Answers
Answer:
Volume = 7.912
Step-by-step explanation:
V = πr²h
V = 3.14 × 3/4 × 3/4 × 6 3/4 ( π = 22/7 or 3.14 )
V = 3.14 × 9/16 ×18/4
V = 3.14 × 0.56 × 4.5
V = 7.912
THIS IS FOR 25 POINTS
There is a pair of parallel sides in the following shape.
12
2
13
7
What is the area of the shape? __
Answers
Answer:
54
Step-by-step explanation:
two ways:
1. find the area of the trapesium
1/2(sum of parallel sides)x height
= 1/2(7+2)×12
1/2(9x12)
1/2(108)
= 54
Or
you can divide the figure into 2 parts, rectangle and triangle,
so you find the area of triangle(1/2basexheight) and then the area of rectangle (length x width)
and then add the two areas. it should also give you same answer.
let me know if it makes sense
find the area of each polygon I DONT GET IT SO PLZ HELP SOMEONE
Answers
Answer:
Step-by-step explanation:
Count each sides :)
Answer:
DONT DOWNLOAD THE DOC IT GIVES YOU A VIRUS WHERE U TYPE IN ALL CAPS
Step-by-step explanation:
Which is a correct two-column proof?
Given: ∠h and ∠c are supplementary.
Prove: j || l
Answers
Answer:
Third option is the correct answer.
Step-by-step explanation:
Third option is the correct answer.
LOOK BELOW PLEASE AM MARKING BAINLIST PLEASE GUYS
Answers
Answer:
C) 10
Step-by-step explanation:
hope it helps youuuuuu
Answer:
i got c) 10
Step-by-step explanation:
(11^2-9^2)*(1/2)^2
(121-81)
40*(1/2)^2
40*0.25
10
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