A movie theater offers two containers which container is the better value use 3.14 as an approximation for pi 
Answers
Answer:
cylinder
Step-by-step explanation:
You want to know which of two popcorn containers is a better value:
cone: diameter 12 cm, height 19 cm, cost $6.75cylinder: diameter 8 cm, height 15 cm, cost $6.25VolumeThe volume formulas for the two shapes are ...
V = 1/3πr²h . . . . . cone
V = r²h . . . . . . . . . cylinder
RatioFor r = d/2, the ratio of these two volumes is ...
[tex]\dfrac{V_{con}}{V_{cyl}}=\dfrac{\dfrac{1}{3}\pi\left(\dfrac{d_{con}}{2}\right)^2h_{con}}{\pi\left(\dfrac{d_{cyl}}{2}\right)^2h_{cyl}}=\dfrac{d_{con}^2\cdot h_{con}}{3\cdot d_{cyl}^2\cdot h_{cyl}}=\dfrac{12^2\cdot19}{3\cdot 8^2\cdot 15}=\dfrac{2736}{2880}=0.95[/tex]
The cone has less volume and costs more, so the cylindrical container is the better value.
Related Questions
PLEASE HELP (WILL GIVE BRAINLIEST
Answers
Answer:
6.7 = π(r^2)(33.5/12)
r = .874
75/(2 × .874) = 42.9 = 42 barrels
6.7 = (3.14)(r^2)(33.5/12)
r = .874
75/(2 × .874) = 42.9 = 42 barrels
A student argues that y=x/9 does not represent a proportional relationship between x and y because we need to multiply one variable by the same constant to get the other one and not divide it by a constant. Do you agree or disagree with this student? Explain why.
Answers
The student's argument that y=x/9 does not represent a proportional relationship between x and y is false because there is constant factor which shows the proportional relationship.
A proportional relationship exists between two variables if they are related by a constant factor, meaning that multiplying one variable by a constant results in the other variable. However, this constant can also be obtained by dividing one variable by the other, as in the case of y=x/9.
To see why, we can rearrange the equation to x=9y, which shows that x is proportional to y with a constant factor of 9. Multiplying y by 9 results in x, just as dividing x by 9 results in y. Therefore, the relationship between x and y is still proportional, regardless of whether we multiply or divide to obtain the constant factor.
In general, we can say that a relationship between two variables is proportional if it can be written in the form y=kx, where k is a constant. It does not matter whether we use multiplication or division to express this constant, as long as it is the same for all values of x and y.
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Medication with strength 125 mg/5 mL has been ordered at 5 mg/kg. The patient weighs 134 lb. How much should be administered? (If less than 1, round to the nearest hundredth; otherwise, round to the nearest tenth.)
Answers
Rounding to the closest hundredth, the final result is 12.16 mL, which is the amount of the drug that should be administered.
The patient's weight must first be converted from pounds to kilograms.
1 lb = 0.453592 kg
Therefore, 134 lb = 60.78 kg
The dose must then be determined depending on the patient's weight:
60.78 kg times 5 mg/kg equals 303.9 mg.
Now that we know the medication's concentration, we need to determine how much to deliver.
25 mg/mL x 125 mg/5 mL
The dosage for 303.9 mg is as follows:
303.9 mg x 25 mg/mL = 12.16 mL
The final result, rounded to the closest hundredth, is 12.16 mL.
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a robotic vacum cleanervacumsonehotelroomin 3/10 hour. at this rate, how many rooms of the same size will it vaccum in 3 hours
Answers
The number of rooms of the same size it willl vaccum in 3 hours is 10
How many rooms of the same size will it vaccum in 3 hoursFrom the question, we have the following parameters that can be used in our computation:
Unit rate = 3/10 hour per room
Time = 3 hours
using the above as a guide, we have the following:
Number of rooms = Time/Unit rate
Substitute the known values in the above equation, so, we have the following representation
Number of rooms = 3/(3/10)
Evaluate the quotient
Number of rooms = 10
Hence, the number of rooms is 10
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Differentiate y = x^3 ln 2x/e^x Sin x
Answers
Differentiating y = x^3 ln 2x/e^x Sin x is: y' = x^2 [(3 ln 2x/e^x Sin x + 3/x) - 2 ln 2x/e^x Sin x cos x + cos x].
What is Differentiation?Differentiate y can be find using the product and chain rule.
Using the chain rule
v'(x) = [1/(2x/e^x)] * (2e^x - e^x*2x) / (2x/e^x)^2
v'(x) = [e^x(2-e^x)] / (2x)^2
Using the product rule
y' = 3x^2 ln(2x/e^x) sin(x) + x^3 [e^x(2-e^x)] / (2x)^2 sin(x) + x^3 ln(2x/e^x) cos(x)
Simplifying
y' = 3x^2 ln(2x/e^x) sin(x) + (x/2) [2-e^x] sin(x) + x^3 ln(2x/e^x) cos(x)
So,
derivative of y is:
y' = 3x^2 ln(2x/e^x) sin(x) + (x/2) [2-e^x] sin(x) + x^3 ln(2x/e^x) cos(x)
Therefore the differentiate of y is 3x^2 ln(2x/e^x) sin(x) + (x/2) [2-e^x] sin(x) + x^3 ln(2x/e^x) cos(x).
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I called at 11:45 pm been on the phone for 1 hour 24 minutes what time did that person hang up
Answers
11:45 pm + 1 hour 24 minutes = 1:09 am
Answer:
If you called at 11:45 pm and were on the phone for 1 hour 24 minutes, the call would have ended at 1:09 am.
The circle with center O shown above has a 34° inscribed angle and a 42° central angle. What is the measure of minor arc ABC?
Answers
The measures of the three intercepted arcs from least to greatest are;
AC < BC < AB
We have,
We are given that
Angle ACB = 63 degrees
Arc BC is 118 degrees.
Now, from the Triangle angle sum theorem, we know that the sum of all interior angles of any triangle is always equal to 180 degrees.
Thus, the sum of the interior angles of the inscribed triangle given to us id also 180 degrees.
Now, since Angle ACB = 63 degrees
Then Arc AB = 63 * 2 = 126
Arc AC = 360 - (Arc BC + Arc AB)
We are given BC = 118 degrees
Thus;
Arc AC = 360 - (118 + 126)
Arc AC = 116°
Thus, the least arc angle is Arc AC while the greatest is Arc AB
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complete question:
Triangle ABC is inscribed in a circle centered at point O.
The figure shows triangle ABC is inscribed in a circle centered at point O and has an angle ACB is 63 degrees and arc BC is 118 degrees.
Order the measures of the three intercepted arcs from least to greatest.
log3 55=x
Use the base of formula to solve for x in logaritm experssion
Answers
The change of base formula log 55 / log 3. The base we use to solve via change of base formula is Base 10. The value of x = 55.
The logarithmic expression given is
log₃ 55 = x
To solve for x using the change of base formula, we can use the formula
logₐ b = log c / log a
where a, b, and c are positive real numbers and a ≠ 1.
Using this formula, we can rewrite the given expression as
log x / log 3 = log 55 / log 3
We can simplify this expression by canceling out log 3 on both sides
log x = log 55
Now, we can use the definition of logarithms, which states that if log a b = c, then [tex]a^c[/tex] = b. Using this definition, we get
x = 55
Therefore, the solution is x = 55, rounded to the nearest hundredth of a decimal.
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Using the above supply/demand graph, what is the price at the point of equilibrium
Answers
The price at the point of equilibrium is 105
What is the price at the point of equilibrium?From the question, we have the following parameters that can be used in our computation:
The supply/demand graph
The price at the point of equilibrium is the price where the lines/curves of the supply and the demand functions intersect
Using the above and the graph as a guide, we have the following:
Price = 105 when demand = supply
Hence, the price at the point of equilibrium is 105
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Question
Using the above supply/demand graph, what is the price at the point of equilibrium? a. 105 b. 100 c. 95 d. 80
Can someone please help me with this, it’s super confusing and I can’t find help anywhere
Answers
Answer:
Step-by-step explanation:
ask ur teacher
Given g(x)=x²-6x-16, which statement is true?
The zeros are -8 and 2, because the factors of gare (x+8) and (x-2).
The zeros are -8 and -2, because the factors of g are (x + 8) and(x+2).
The zeros are -2 and 8, because the factors of gare (x+2) and (x-
8).
The zeros are 2 and 8, because the factors of gare (x-2) and (x-
8).
Answers
Since g(x) = x² - 6x - 16, a statement which is true include the following: C. The zeros are -2 and 8, because the factors of g are (x+2) and (x-
8).
What is the general form of a quadratic function?In Mathematics and Geometry, the general form of a quadratic function can be modeled and represented by using the following quadratic equation;
y = ax² + bx + c
Where:
a and b represents the coefficients of the first and second term in the quadratic function.c represents the constant term.Next, we would solve the quadratic function by using the factorization method as follows;
g(x) = x² - 6x - 16
0 = x² - 6x - 16
0 = x² - 8x + 2x - 16
0 = x(x - 8) + 2(x - 8)
(x - 8)(x + 2)
x = 8 or x = -2.
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A cone has a volume of 200pi cubic centimeters and a height of 24 cm.
What is the radius of the base of the cone in centimeters?
Answers
Answer:
been wondering that my self
Step-by-step explanation:
that's why they asked
Answer:
5cm
Step-by-step explanation:
To find the radius of the base of the cone, we need to use the formula for the volume of a cone, which is V=31πr2h
, where V is the volume, r is the radius, and h is the height1
We are given the volume and the height, so we can plug them into the formula and solve for r:
200π=31πr2(24)
Simplify and isolate r:
r2=8π200π
r2=25
r=25
r=5
Therefore, the radius of the base of the cone is 5 cm.
60 POINTS ANSWER FOR BRAINLIST AND HEARTS
Answers
Answer:
a. The given equation is (y - 3)^2 -10 = 71. To determine the number and type of solutions, we need to use the discriminant, which is given by b^2 - 4ac, where a, b, and c are the coefficients of the quadratic equation in standard form (ax^2 + bx + c = 0). In this case, the equation can be rewritten as (y - 3)^2 = 81, which is in the form of (y - k)^2 = r^2, where k = 3 and r = 9. Therefore, the equation can be written as (y - k)^2 - r^2 = 0, which is a quadratic equation with a = 1, b = -6, and c = -72. The discriminant is then b^2 - 4ac = (-6)^2 - 4(1)(-72) = 300. Since the discriminant is positive, there are two real solutions.
b. To solve the equation (y - 3)^2 -10 = 71, we first add 10 to both sides to get (y - 3)^2 = 81. Then, we take the square root of both sides to get y - 3 = ±9. Adding 3 to both sides, we get y = 3 ± 9, which gives us two solutions: y = 12 and y = -6.
Therefore, the equation (y - 3)^2 -10 = 71 has two real solutions, which are y = 12 and y = -6.
Step-by-step explanation:
Answer: type: real number of solutions:2 y=12,-6
Step-by-step explanation:
see images for explanations
Highschool geometry please answer questions 8-10 in the attachment added
Answers
The Hullian learning model asserts that the probability p of mastering a task after t learning trials is approximated by p (t) = 1 - e -kt where k is a constant that depends on the task to be learned. Suppose that a new dance is taught to an aerobics class. For this particular dance, the constant k = 0.28.
a. What is the probability of mastering the dance's steps in 1 trial? 2 trials? 5 trials? 11 trials? 16 trials? 20 trials?
Find the rate of change, p'(t).
Sketch a graph of the function.
Answers
Answer:
Step-by-step explanation:
a. Using the formula p(t) = 1 - e^(-kt), where k = 0.28:
Probability of mastering the dance's steps in 1 trial: p(1) = 1 - e^(-0.28*1) ≈ 0.243
Probability of mastering the dance's steps in 2 trials: p(2) = 1 - e^(-0.28*2) ≈ 0.446
Probability of mastering the dance's steps in 5 trials: p(5) = 1 - e^(-0.28*5) ≈ 0.846
Probability of mastering the dance's steps in 11 trials: p(11) = 1 - e^(-0.28*11) ≈ 0.981
Probability of mastering the dance's steps in 16 trials: p(16) = 1 - e^(-0.28*16) ≈ 0.997
Probability of mastering the dance's steps in 20 trials: p(20) = 1 - e^(-0.28*20) ≈ 0.999
b. The rate of change, p'(t), can be found by taking the derivative of the function p(t):
p'(t) = k * e^(-kt)
c. Here's a graph of the function p(t):
I apologize for the technical issue, but the graph doesnt load, so here's a description of the graph:
The graph of p(t) should be an increasing curve that starts at 0 and approaches 1 asymptotically. As t increases, the rate of change of p(t) decreases, which means that the curve becomes flatter and approaches the horizontal asymptote of y=1. The curve is concave down, meaning that its rate of change is decreasing. At t=0, the rate of change is k, which is the steepest point of the curve.
_______________________
graph of p(t) = 1 - e^(-0.28*t)
The x-axis represents the number of learning trials, and the y-axis represents the probability of mastering the dance's steps. As the number of trials increases, the probability of mastering the steps approaches 1 (or 100%).
18+(d+3)(d-3)(4)
How do I distribute?
Answers
Answer:
Step-by-step explanation:
To distribute the expression 18+(d+3)(d-3)(4), you can use the distributive property of multiplication, which states that a(b+c) = ab + ac.
Here's how you can apply the distributive property to the expression:
First, simplify the expression inside the parentheses by using the difference of squares formula: (d+3)(d-3) = d^2 - 3d + 3d -9
(d+3)(d-3) = d^2 - 9
So now the expression becomes:
18 + (d^2 - 9)(4)
Next, use the distributive property to multiply 4 by each term inside the parentheses:
18 + 4d^2 - 36
Simplify by combining like terms:
4d^2 - 18
So the final result is 4d^2 - 18
Martina vence a Jelena en 2 juegos de un total de 3 en el tenis. ¿Cuál es la probabilidad de que Jelena gane un set de de tenis 6 juegos a 4?
Pista: ¿Cuál es el score que tendría que haber después de 9 juegos?
Answers
0.034141137 o sobre 17/500
Solve the following for θ, in radians, where 0≤θ<2π.
3cos2(θ)+6cos(θ)−4=0
Answers
Answer:
0 ≤ < 2
Step-by-step explanation:
Answer:1.02 5.27 are correct
Step-by-step explanation:We can solve this quadratic equation in cos(θ) by using the substitution u = cos(θ):
3u^2 + 6u - 4 = 0
Now we can use the quadratic formula to solve for u:
u = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = 3, b = 6, and c = -4. Substituting these values, we get:
u = (-6 ± sqrt(6^2 - 4(3)(-4))) / 2(3)
u = (-6 ± sqrt(84)) / 6
u = (-3 ± sqrt(21)) / 3
Therefore, either:
Two functions are shown in the table below. Function 1 2 3 4 5 6 f(x) = −x2 + 4x + 12 g(x) = x + 2 Complete the table on your own paper, then select the value that is a solution to f(x) = g(x). (2 points) Group of answer choices x = 2 x = 3 x = 5 x = 6
Answers
f(x) = g(x)
-x^2 + 4x + 12 = x + 2
-x^2 + 3x + 10 = 0
Now we can solve for x using the quadratic formula:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
x = (-3 ± sqrt(3^2 - 4(-1)(10))) / 2(-1)
x = (-3 ± sqrt(49)) / -2
x = (-3 + 7) / -2 or x = (-3 - 7) / -2
x = -2 or x = 5
Therefore, the value that is a solution to f(x) = g(x) is x = 5.
Gate posts are parallel and m<4 =47, what is m<1
Answers
The value of angle 1 given the value of angle 4 as 47° will be 133°
How to explain parallel linesParallel lines are two lines on a two-dimensional plane that, no matter how far they are extended, never collide. They always keep the same gap between them.
Parallel lines have the same slope, which means they have the same angle of inclination or steepness. In other words, they rise and fall at the same pace along their length.
The value will be:
= 180° - 47°
= 133°
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.54 oz of premium walnuts costs $12.95. what is cost per ounce
Answers
The cost per ounce of the premium walnut is $0. 23
What is proportion?To determine the value of the cost, we need to note that proportion is simply described as the comparison of numbers such that they are made equal to another.
From the information given, we have that;
54 ounces of premium walnuts costs $12.95
This is represented as;
54 ounces = $12. 95
Then 1 = x
cross multiply the values, we get;
x = $12.95/54
Divide the values, we get;
x = $0. 23
Hence, the value is $0. 23 per premium walnut
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In this figure, FE←→
is parallel to AD¯¯¯¯¯
, and m∠A
= 158°. What is m∠FCA? m∠FCA
= °
Answers
Note that where the above conditions are given, m∠FCA is also = 158°. This is due to the principle of alternate angles.
What are alternate angles?A pair of angles that are created by a transversal intersecting two parallel lines, known as alternate angles, have key properties which contribute to their importance in geometry.
They take place on opposite sides of the transversal and have equal magnitudes.
These concepts aid in understanding vertical angles and parallel lines within geometrical systems.
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Answer: ur correct answer is 158
Step-by-step explanation: not doing this to tke points!!
The letters of "EAGLES" should be evenly spaced across a 63 inch wide banner, with no margins. Each letter is 8 inches wide. How many inches (x) should exist between each pair of letter?
Answers
Answer:
To evenly space the letters of "EAGLES" across a 63 inch wide banner with no margins, you would need to divide the remaining space between each letter of the word equally. With five letters total and each letter being 8 inches wide, the total width occupied by the letters is 40 inches. Therefore, the remaining space is 23 inches (63-40=23). To find out how many inches should exist between each pair of letter, you would divide the remaining space by the number of gaps between the letters, which is 4 (one less than the total number of letters in the word).
23 inches ÷ 4 gaps = 5.75 inches between each pair of letters.
Step-by-step explanation:
[tex]\frac{v-2}{2v^2+10v} + \frac{1}{2v+10}=\frac{1}{2}[/tex]
Show all steps
Answers
The value of variable 'v' in the expression ( v - 2 ) / (2v² + 10v ) + 1 / ( 2v + 10 ) = 1 / 2 is equal to -4.
The expression is equal to,
( v - 2 ) / (2v² + 10v ) + 1 / ( 2v + 10 ) = 1 / 2
Simplify the expression we have,
⇒ ( v - 2 ) / 2v ( v + 5 ) + 1 / 2( v+ 5 ) = 1 / 2
Take the least common multiple of the denominator we have,
⇒ [( v - 2 ) + 2 ] / 2v( v+ 5 ) = 1 / 2
⇒ v / 2v( v+ 5 ) = 1 / 2
Multiply both the sides of the expression by 2 we get,
⇒ 1 / 2( v+ 5 ) = 1 / 2
⇒ 1 /( v + 5 ) = 1
Cross multiply the expression we get,
⇒ v + 5 = 1
Subtract 5 from the both the sides of the equation we get,
⇒ v = -4
Therefore , the value of v in the given expression is equal to -4.
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The number of bacteria in a certain population increases according to a continuous exponential growth model, with a growth rate parameter of 8.5% per hour. How many hours does it take for the size of the sample to double?
Answers
N(t) = N₀e^(rt)
where:
N(t) is the size of the population at time t
N₀ is the initial size of the population
r is the growth rate
t is time
To find the time it takes for the population to double, we need to solve for t in the equation:
2N₀ = N₀e^(rt)
Dividing both sides by N₀, we get:
2 = e^(rt)
Taking the natural logarithm of both sides, we get:
ln(2) = rt
Solving for t, we get:
t = ln(2)/r
The growth rate is given as 8.5% per hour, which is equivalent to 0.085 per hour. Substituting this into the formula, we get:
t = ln(2)/0.085
t ≈ 8.14
Therefore, it takes approximately 8.14 hours for the size of the population to double.
Ethan correctly answers 80% of the total questions on his history test. He correctly answers 32 questions.
Answers
Answer: There are 40 questions on Ethan's test.
Step-by-step explanation: To find what 32 is 80% of, you must first convert 80% to a decimal (.8).
Next, divide 32 by .8.
[tex]32/.8 = 40[/tex]
What is the answer to the question?
Answers
The solid that is produced rotating the triangle about the line m is given as follows:
A cylinder with height of 2 units.
What are the radius and the diameter of a cylinder?The cylinder has a circular base, hence we must start there, then we consider that;
The radius of a circle represents the distance between the center of the circle and a point on the circumference of the circle.The diameter of the circle is the distance between two points on the circumference of the circle that pass through the center. Hence, the diameter’s length is twice the radius length.Rotating the line, the features of the cylinder generated are given as follows:
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Find the average of the numbers: 16 and 17
Answers
Add up the two numbers and divide by how many values given
16+17/2=16.5
Answer:
16.5
Step-by-Step Explanation:
16.5 would be the average because it is right between 16 and 17. hope that helps :)
Help on calculus please
Answers
The expression for the area under the graph of f(x) = √x as a limit of Riemann sums is A = lim [n -> ∞ ] Ax [f(x₁) + f(x₂) + ... + f(xₙ)]
For a continuous function f(x), the area A of the region S that lies under the graph of the function can be expressed as the limit of the sum of the areas of approximating rectangles. Each rectangle has a width of Ax, where A is the interval over which we want to find the area and x is a point within that interval. The height of each rectangle is f(x).
Using this definition, we can find an expression for the area under the graph of f(x) = √x, where 1 ≤ x ≤ 13. We start by dividing the interval [1, 13] into n subintervals, each of width Ax = (13-1)/n = 12/n. We can label the endpoints of the subintervals as x₁, x₂, ..., xₙ+1, where x₁ = 1 and xₙ+1 = 13.
Next, we approximate the area under the curve using n rectangles. The height of the ith rectangle is f(xi), where xi is any point in the ith subinterval. The width of each rectangle is Ax, so the area of the ith rectangle is f(xi) Ax. The total area of the rectangles is then the sum of the areas of each rectangle:
f(x₁) Ax + f(x₂) Ax + ... + f(xₙ) Ax
We can simplify this expression by factoring out the common factor of Ax:
Ax [f(x₁) + f(x₂) + ... + f(xₙ)]
Taking the limit as n approaches infinity, we obtain:
A = lim [n -> ∞] Ax [f(x₁) + f(x₂) + ... + f(xₙ)]
To evaluate the limit, we need to find a formula for the sum of f(xi) for i = 1 to n.
This is a sum of square roots, which can be approximated using numerical methods or evaluated exactly using calculus techniques such as the definite integral.
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Answer:
[tex]\displaystyle \lim_{n \to \infty}\sum^n_{i=1}\left(\dfrac{12}{n}\right)\sqrt[7]{1+\dfrac{12i}{n}}[/tex]
Step-by-step explanation:
The Riemann sum is a method by which we can approximate the area under a curve using a series of rectangles.
Definite Integral Notation (Reimann Sum)The area under the curve of f(x) on the interval [a, b] is represented by:
[tex]\boxed{\begin{minipage}{6cm}$\displaystyle \int^b_af(x)\; \text{d}x=\lim_{n \to \infty}\sum^n_{i=1}f(x_i) \cdot \Delta x$\\\\\\where $\Delta x=\dfrac{b-a}{n}$ and $x_i=a+\Delta x \cdot i&\\\end{minipage}}[/tex]
Δx is the width of each rectangle.
[tex]f(x_i)[/tex] is the height of each rectangle.
[tex]x_i[/tex] is the right endpoint of each rectangle.
Therefore:
[tex]\begin{aligned}\displaystyle \int^b_af(x)\; \text{d}x&=\lim_{n \to \infty}\sum^n_{i=1}f(x_i) \cdot \Delta x\\\\&=\lim_{n \to \infty}\sum^n_{i=1}f\left(a+\left(\dfrac{b-a}{n}\right)i\right) \cdot \left(\dfrac{b-a}{n}\right)\end{aligned}[/tex]
The given interval is [1, 13]. Therefore, a = 1 and b = 13:
[tex]\implies \Delta x=\dfrac{13-1}{n}=\dfrac{12}{n}[/tex]
As f(x) = ⁷√x then:
[tex]\implies f(x_i)=f(a+i \Delta x)=\sqrt[7]{a+\Delta x \cdot i}=\sqrt[7]{1+\dfrac{12i}{n}}[/tex]
Substituting into the summation formula:
[tex]\begin{aligned}\displaystyle \int^{13}_1 \sqrt[7]{x}\; \text{d}x&=\lim_{n \to \infty}\sum^n_{i=1}\sqrt[7]{1+\left(\dfrac{13-1}{n}\right)i} \cdot \left(\dfrac{13-1}{n}\right)\\\\&=\lim_{n \to \infty}\sum^n_{i=1}\left(\dfrac{12}{n}\right)\sqrt[7]{1+\dfrac{12i}{n}}\\\\\end{aligned}[/tex]
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in a race in which 9 contestants are entered in how many ways can first second and third place be awarded
Answers
Answer: 504 different ways.
Step-by-step explanation:
This situation uses a permutation. We will use the given formula and simplify to solve. n is equal to the number of contestants and r is 3 since we are selecting and first-, second-, and third-place winner.
Given:
[tex]\displaystyle P = \frac{n!}{(n-r)!}[/tex]
Substitute values:
[tex]\displaystyle P = \frac{9!}{(9-3)!}[/tex]
Subtract:
[tex]\displaystyle P = \frac{9!}{6!}[/tex]
Multiply:
[tex]\displaystyle P = \frac{9*8*7*6*5*4*3*2*1}{6*5*4*3*2*1}[/tex]
Simplify using the knowledge that something divided by itself is 1:
P = 9 * 8 * 7
Multiply:
P = 504
We can also think of it as 9 different people could win 1st, 8 different people could win 2nd, and 7 different people could win 3rd. 9 * 8 * 7 = 504. However, the steps above show why this works with the formula as well.