please help:)
(stat & reasoning subject)
Two hundred runners enter a race. In how many ways can they finish first, second, third and fourth?
Answers
The number of ways the two hundred runners can finish in the first, second, third, and fourth positions of the race is 312,872,200.
To calculate this, we need to use the concept of permutations, as the order of the runners matters in this scenario.
For the first position, any of the 200 runners can finish first. Therefore, there are 200 possibilities for the first position.
For the second position, once the first-place runner is determined, there are 199 remaining runners who can finish second. Therefore, there are 199 possibilities for the second position.
Similarly, for the third position, once the first and second-place runners are determined, there are 198 remaining runners who can finish third. Thus, there are 198 possibilities for the third position.
Lastly, for the fourth position, once the first, second, and third-place runners are determined, there are 197 remaining runners who can finish fourth. Hence, there are 197 possibilities for the fourth position.
To find the total number of ways the runners can finish in the top four positions, we multiply the number of possibilities for each position:
Total number of ways = 200 * 199 * 198 * 197 = 312,872,200.
Therefore, there are 312,872,200 ways in which the two hundred runners can finish in the first, second, third, and fourth positions of the race.
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Related Questions
Given:
Prove:
Three lines AD, CF, and BE are intersecting each other at the midpoint O
Complete the proof.
It is given that
and
. By the
,
. Therefore,
. By the
,
, and by the
,
. After application of the
,
.
Answers
∠CFA ≅ ∠EDA (By Transitive Property of Congruence).
Given:
Three lines AD, CF, and BE are intersecting each other at the midpoint O.
To prove:
∠CFA ≅ ∠EDA
Proof:
Given that AD, CF, and BE intersect at the midpoint O.
By definition of a midpoint, OA ≅ OD, OB ≅ OE.
OA = OD and OB = OE.
Triangle OAD ≅ Triangle OBE (By Side-Side-Side congruence).
∠OAD ≅ ∠OBE (By Corresponding Parts of Congruent Triangles are Congruent).
∠CFA and ∠EDA are vertical angles.
∠OAD ≅ ∠CFA and ∠OBE ≅ ∠EDA (By Vertical Angles are Congruent).
Therefore, ∠CFA ≅ ∠EDA (By Transitive Property of Congruence).
Hence, it is proven that ∠CFA ≅ ∠EDA.
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a football stadium has 100,000 seats. in a game with full capacity people with the following ticket and associated cost attended the game: determine the number of people that attended the game in each cost cate- gory if the total revenue was $4,897,000, there were 11,000 more alumni than faculty, the number of public plus alumni together was 10 times the number of veterans, the number of faculty plus alumni together was the
Answers
The number of people that attended the game in each cost category is Faculty: 7,000,Alumni: 18,000,Public: 18,000,Veterans: 4,000
To determine the number of people that attended the game in each cost category, to consider the given information and set up a system of equations to solve for the unknowns. Let's break down the problem step by step.
Let's denote the number of people in each cost category as follows:
Faculty: F
Alumni: A
Public: P
Veterans: V
The number of alumni is 11,000 more than the faculty, so we have the equation:
A = F + 11,000
The number of public plus alumni together was 10 times the number of veterans, so the equation:
P + A = 10V
The number of faculty plus alumni together was the same as the number of veterans, so we have the equation:
F + A = V
The total number of people attending the game is the sum of the people in each category, so the equation:
F + A + P + V = 100,000
Now, use these equations to solve for the unknowns.
First, substitute equation 1 into equations 2 and 3:
P + (F + 11,000) = 10V
F + (F + 11,000) = V
Simplify these equations:
P + F + 11,000 = 10V
2F + 11,000 = V
Next, substitute these equations into equation 4:
F + (F + 11,000) + P + (2F + 11,000) = 100,000
Simplify and combine like terms:
4F + 22,000 + P = 100,000
Subtract 22,000 from both sides:
4F + P = 78,000
Now a system of two equations:
P + F + 11,000 = 10V
4F + P = 78,000
solve this system of equations to find the values of F, P, and V.
By solving the system,
F = 7,000
P = 18,000
V = 4,000
Finally, substitute these values back into equation 1 to find the value of A:
A = F + 11,000 = 7,000 + 11,000 = 18,000
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(Help please:)!)
What is the perimeter of A"B"C"D"? Explain how you found the perimeter.
Answers
Answer:
26.3
Step-by-step explanation:
Perimeter is found by adding up all the sides.
8+6+6+6.3
18.3+8 =26.3
Answer:
26.3
Step-by-step explanation:
First, you find the perimeter of the original image, 6+6+6.3+8 = 26.3
Because the shape is only rotated, they are equal which means all 3 shapes have the same perimeter.
The bearing of Measham from Tamworth is 052°
Calculate the bearing of Tamworth from Measham.
Answers
Answer:
232°
Step-by-step explanation:
1. 180-52=128
2. 360-128=232
first you subtract 52 from 180 bc you have to get the angle not included for calculating the whole bearing bc the starting point is the north line. so everything before the north line is not valid bc when you're calculating an angle like this you go from lef to to right, clockwise. in every calculation of bearings you go clockwise. next you just subtract the product you got from 360 and that's it.
hope it didn't sound too complicated.
Solve this problem , please
Answers
Answer:
1. 20.724 or 6.6π
2.3.14 or π
3. 15.7 or 5π
4. 9.42 or 3π
5. 25.12 or 8π
6. 18.84 or 6π
Step-by-step explanation:
just ask :)
PLEASE NEED HELP PROPOTION AND PERCENTS !!!WILL GIVE BEST RATE
Answers
Answer:
80
Step-by-step explanation:
40 is 100
32 is x
100*32/40=80
Answer:
125 percent
hope it help
Hey CAN SOME ONE PLEASEEE HELPP ME
Answers
Answer:
\(y=11*3^x\)
Here is the graph showing this function.
Answer:
\(\sf y = 11(3)^x\)
given points: ( 0, 11) , (2,99)
solve for 1st
\(\sf y = ab^x\)
\(\sf 11 = ab^0\)
since we know \(\sf b^0 = 1\)
\(\sf 11 =a\)
solve for 2nd
\(\sf y = ab^x\)
\(\sf 99 = ab^2\)
\(\sf \dfrac{99}{b^2} = a\)
solve simultaneously:
\(\sf 11 = \sf \dfrac{99}{b^2}\)
\(\sf 11 b^2= \sf 99}\)
\(\sf b^2= 9\)
\(\sf b = 3\)
Therefore equation: \(\sf y = 11(3)^x\)
What is the relative minimum of the function?
Answers
Answer: all the points x, in the domain of the function, such that it is the smallest value for some neighborhood
Step-by-step explanation:
Jorge needs to reflect a figure across the line y = negative 4. Which statements are correct regarding steps he could take to complete the reflection? Check all that apply.
Answers
The correct statements regarding the steps Jorge could take to complete the reflection are:
1) Jorge should graph in the vertical line with values of -4 for the line of reflection.
2) Jorge could count how far each pre-image point is from the line of reflection along the perpendicular from the point to the line of reflection.
3) Jorge could count how far each vertex of the figure is from the y-axis and count the same distance on the other side.
4) Jorge will not move any point that lies on the line of reflection.
5) Jorge could check his work by seeing if each segment joining a pre-image point with its image has the midpoint on the line of reflection.
6) Jorge could check his work by making sure that the image has the same orientation as the original.
To complete the reflection of a figure across the line y = -4, Jorge can take the following steps:
1) Jorge should graph the vertical line y = -4 as the line of reflection. This line represents the axis of reflection, and all points on this line will remain fixed in their positions after the reflection.
2) Jorge could count how far each pre-image point is from the line of reflection along the perpendicular from the point to the line of reflection. This will help him determine the distance and direction each point should move to reflect across the line.
3) Jorge could count how far each vertex of the figure is from the y-axis and count the same distance on the other side. Since the line of reflection is y = -4, which is parallel to the y-axis, he can use the distance from the vertex to the y-axis as a guide to placing the reflected point on the other side of the line.
4) Jorge will not move any point that lies on the line of reflection. Points on the line of reflection will remain fixed in their positions as they are symmetric to themselves across the line.
5) Jorge could check his work by seeing if each segment joining a pre-image point with its image has the midpoint on the line of reflection. In a reflection, the midpoint of each line segment connecting a point and its reflection will lie on the line of reflection. Checking this property helps ensure the accuracy of the reflection.
6) Jorge could check his work by making sure that the image has the same orientation as the original. The orientation refers to the arrangement or direction of the figure's components (e.g., angles, lengths, shapes). If the image retains the same orientation as the original, it indicates a correct reflection.
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Question
Jorge needs to reflect a figure across the line y = negative 4. Which statements are correct regarding steps he could take to complete the reflection? Check all that apply.
1) Jorge should graph in the vertical line with values of –4 for the line of reflection.
2) Jorge could count how far each pre-image point is from the line of reflection along the perpendicular from the point to the line of reflection.
3) Jorge could count how far each vertex of the figure is from the y-axis and count the same distance on the other side.
4) Jorge will not move any point that lies on the line of reflection.
5) Jorge could check his work by seeing if each segment joining a pre-image point with its image has the midpoint on the line of reflection.
6) Jorge could check his work by making sure that the image has the same orientation as the original.
GAAHHHHHHHHHHHHHH THis Homework hard THOSE 3 Over is bugging me
Answers
Answer:
8. X=33º
9. X=120º
10. X= 161º
Step-by-step explanation:
For all of the 3 questions, the sum of the interior angles is equal to the exterior angle.
Hope this helps! Have a great day!
An insurance company offers two policy options. A motorcycle owner can
choose an annual premium of $500 with a $600 deductible or an annual
premium of $900 with a $100 deductible. Suppose that the probability that a
motorcycle will be damaged in a given year is 20% and that if the motorcycle
is damaged, the cost of repairs will be about $800. Which option has the least
expected cost for the motorcycle owner? What is the expected cost?
Answers
Expected cost = $180 + $720 = $900.
The second option is the better choice for the motorcycle owner in terms of expected cost.
To determine which policy option has the least expected cost, we need to calculate the expected cost of each option and compare them.
Let's first consider the option with a $500 premium and a $600 deductible. If the motorcycle is damaged, the cost of repairs will be $800, but the owner will have to pay the $600 deductible. So, the expected cost of this policy is:
Expected cost = (probability of damage) x (cost of repairs + deductible) + (probability of no damage) x (annual premium)
Expected cost = (0.2) x ($800 + $600) + (0.8) x ($500)
Expected cost = $560 + $400 = $960
Now, let's consider the option with a $900 premium and a $100 deductible. If the motorcycle is damaged, the owner will only have to pay the $100 deductible, but the annual premium is higher. So, the expected cost of this policy is:
Expected cost = (probability of damage) x (cost of repairs + deductible) + (probability of no damage) x (annual premium)
Expected cost = (0.2) x ($800 + $100) + (0.8) x ($900)
Expected cost = $180 + $720 = $900
Comparing the expected costs, we see that the second option with the $900 premium and $100 deductible has the least expected cost of $900.
Therefore, the second option is the better choice for the motorcycle owner in terms of expected cost.
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What is the value of x if p(x)=-48. Please use this function: 3/4 x
Answers
u need to do 111111155151515151515151515151
Jeff bought 15 granola bars for $30. How much does it cost per granola bar? $
Answers
Answer:
Each granola bar costs $2
Step-by-step explanation:
per granola bar= $30/15=$2
Answer:
$2?
Step-by-step explanation:
PLEASE I NEED HELP WITH THIS
Answers
Answer:
a 2x² because all the others are just x... we actually just learned this
which list shows the numbers 2/3, 9/11 and 7/9 arranged from least to greatest
Answers
Answer:
2/3; 7/9; 9/11
Step-by-step explanation:
You have to divide them and you will get a decimal that is how you put them in numerical order
1. If cosA=21/29, what is the perimeter of the triangle?
2. If sinA=10/26, what is the perimeter of the triangle?
3. If tanA=15/8, what is the perimeter of the triangle?
4. If cosA-12/37, what is the perimeter of the triangle?
5. If tanA-12/16, what is the perimeter of the triangle?
Answers
Answer:
Step-by-step explanation:
For each one, solve for the missing side, x, then add all sides together to get the perimeter, P.
1) x = √(29² - 21²) = 20
P = 21+29+20 = 70
2) x = √(12² - 10²) = 6.63
P = 10+26+6.63 = 42.63
3) x = √(8² + 15²) = 17
P = 8+15+17 = 40
4) x = √(37² - 12²) = 35
P = 12+35+37 = 84
5) x = √(12² + 16²) = 20
P = 12+16+20 = 48
find the axis of symmetry using the formula
x=-b/2a
1. f(x)=-9x^2+1
2. f(x)=-2x^2+8x-9
3. f(x)=4x^2+24x+131
Answers
The axis of symmetry are:
1. x=0 2. x = 2 3. x = -3
What is a quadratic equation?
A quadratic equation is a second-order polynomial equation with a single variable such as x, where ax²+bx+c=0. with a ≠ 0 . Given that it is a second-order polynomial equation, the algebraic fundamental theorem ensures that it has at least one solution. Real or complicated solutions are both possible.
Standard form of quadratic function:
f(x)= ax² + bx + c
1. f(x)= -9x²+1 :
a = -9 , b=0
x= (-0)/2a = 0
2. a= -2 , b =8
x = (-8)/(2*-2) = -8/-4 = 2
3. a=4, b=24
x= -24/8 = -3
So, the axis of symmetry are:
1. x=0 2. x = 2 3. x = -3
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Paula bought a ski jacket on sale for $8 less than half its original price. She paid $84 for the jacket. What was the original price?
Answers
The original price of the ski jacket is $184.
What is price?
The sum of money paid or the amount of compensation offered by one party to another in exchange for goods or services is known as a price. The cost of production can take on different names depending on the circumstance. If the item is a "good" in a commercial transaction, the cost of the item will probably be referred to as its "price".
Given:
Paula bought a ski jacket on sale for $8 less than half its original price.
She paid $84 for the jacket.
We have to find the original price of the ski jacket.
Let
The original price = x
The amount she bought it = x/2 - 8
She paid $84 for the jacket
Therefore,
84 = x/2 - 8
Add 8 on both sides,
84 + 8 = x/2 - 8 + 8
92 = x/2
x = 184
Hence, the original price of the ski jacket is $184.
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A function model a linear relationhip between the balance in Leah' bank account and the number of month ince he began her new job. Currently, Leah' bank balance i $750, and it ha been increaing at a rate of $100 per month ince he began her new job 6 month ago. What i the initial value of the bank balance function, in dollar?
Answers
Using the linear rate data provided and using simple unitary method, The answer is $150.
What do you mean by linear relationship?A straight-line link between two variables is referred to statistically as a linear relationship (or linear association).
What do you mean by data?In mathematics, data is a collection of facts and figures that can take any shape, whether it be numerical or not. You can calculate numerical data, which is always gathered in number form and includes things like student test results, employee salaries, football team member heights, etc.
Total balance after 6 months = $750
Rate = $100 per month
Time = 6 months
Balance deposited at the rate in 6 months = 100 * 6
=$600
Initial Balance = $750 - $600
=$150
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question number 20 to 22
Answers
Answer:
20) Rectangular prism, Rectangle base
21) Triangular Prism, Triangle base
22) Pyramid, Triangle base
Step-by-step explanation:
Look at the picture
Find the missing length of the triangle. 7.2 feet, 9.6 feet, and c
Answers
By using pythagorean theorem, the length of the missing side is 12 feet.
What is the Pythagorean theorem?
Pythagoras' theorem is a fundamental principle in geometry that relates to the three sides of a right-angled triangle. It states that:
"In a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides."
In mathematical terms, if a, b, and c are the lengths of the sides of a right-angled triangle, where c is the hypotenuse, then the theorem can be written as:
\(c^2 = a^2 + b^2\)
We can use the Pythagorean theorem to determine the length of the missing side if we know that the given sides form a right triangle.
In this case, we have two sides of the triangle given: 7.2 feet and 9.6 feet. Let's assume that c is the length of the hypotenuse.
If the triangle is a right triangle, then we can use the Pythagorean theorem to solve for c:
\(c^2 = 7.2^2 + 9.6^2\)
\(c^2 = 51.84 + 92.16\)
\(c^2 = 144\)
\(c = \sqrt{144}\)
c = 12 feet
Therefore, if the triangle is a right triangle, then the length of the missing side is 12 feet.
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At Bernard's Hats, there are 19 baseball caps and 6 other hats. What percentage of the hats are baseball caps?
Write your answer using a percent sign (%).
Answers
Answer:
76%
Step-by-step explanation:
At Bernard's Hats, there are 19 baseball caps and 6 other hats. What percentage of the hats are baseball caps?
total hats = 19 + 6
total hats = 25
baseball caps are: 19/25
19/25 = 0.76
0.76 = 76%
1/3(6x-5)-x = 1/3-2(x+1)
Value of X
Answers
Answer:
x=0
Step-by-step explanation:
do you need work? I did it in my head
Answer:
x=5/24
Step-by-step explanation:
2x-\frac{5}{2}=-2x-\frac{5}{3} Then add 5/2 to both sides 2x-\frac{5}{2}+\frac{5}{2}=-2x-\frac{5}{3}+\frac{5}{2} simplify 2x=-2x+\frac{5}{6} add 2x to both sides 2x+2x=-2x+\frac{5}{6}+2x simplify 4x=\frac{5}{6} divide both sides by 4 \frac{4x}{4}=\frac{\frac{5}{6}}{4} simplify then u get x=5/24
Find the missing length indicated. Round to the nearest hundredth (two decimal places), if needed.
Answers
84/x = x/16
because if it is can solve it for you!
how to find the equation of a quadratic function given 3 points
Answers
1. Write the general form of a quadratic function: y = ax^2 + bx + c
2. Plug in the coordinates of the first point to get an equation: y1 = a(x1)^2 + b(x1) + c
3. Plug in the coordinates of the second point to get another equation: y2 = a(x2)^2 + b(x2) + c
4. Plug in the coordinates of the third point to get a third equation: y3 = a(x3)^2 + b(x3) + c
5. Use a system of equations to solve for a, b, and c. You can do this by either substitution or elimination.
Once you have solved for a, b, and c, you can plug them back into the general form of the quadratic function to get the equation.
YALL I NEED HELP MY DUMBSELF FORGETS TO DO THESE STUFF SMH
CAN U ALSO EXPLAIN HOW U GOT THE ANSWER PLZ THXX
I need to find the area
Answers
=1/2 x 7 x 3
= 21/2
=10.5
Can someone please help me with this question. If you do, you’ll be rewarded with brainliest and extra points!
Answers
Answer: NO/MN = QR/PQ
Answer:
\(\frac{NO}{MN}\) = \(\frac{QR}{FQ}\)
Step-by-step explanation:
∠ 0 ≅ ∠ R and ∠ M ≅∠ F
thus Δ NOM ≅ ∠ QRF ( by the AA postulate )
the ratios of corresponding sides are in proportion, so
\(\frac{NO}{MN}\) = \(\frac{QR}{FQ}\)
you run at a pace of 2 miles every min.Your friend runs at a pace of 3 miles every 24 min. Are you and your friend runnning at the same pace if not who is running faster
Answers
You: 2/1
Your friend: 3/24= 1/8
You are running faster because you are 16 times faster
The value of investments in the stock market change daily. Suppose you buy a stock for $1,000. It increases in value by 4.5% and then falls 4.5%. What is the new value
Answers
After the stock's value increases by 4.5% and then falls by the same percentage, the new value would be approximately $997.975.
Let's calculate the new value of the stock after the increase and decrease.
Starting with $1,000, a 4.5% increase in value would be calculated as (4.5/100) * 1000 = $45. This brings the value up to $1,045.
Next, a 4.5% decrease in value would be calculated as (4.5/100) * 1045 = $47.025. This amount is subtracted from the increased value of $1,045.
Subtracting $47.025 from $1,045 gives us $997.975, which is slightly less than $1,000.
Therefore, after the stock's value increases by 4.5% and then falls by the same percentage, the new value would be approximately $997.975. It's important to note that this calculation assumes a simple percentage increase and decrease without considering other factors that can affect stock market fluctuations.
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3. How is the circumference of a circle related to the length of its diameter?
Answers
Step-by-step explanation:
.The circumference is the distance around the circle. The circumference is equal to two times pi times the radius (C = 2*pi*r). Because the diameter is equal to two times the radius, the circumference is equal to the diameter times pi (C = D*pi), where pi is about 3.14… The diameter of a circle is 2 units.