Question 1
Part a) 9 Athletes are running the 200M event. How many ways can the first three finishers be awarded medals? Show your work using the Permutation or Combination formula for full credit.




Part b) You have 10 photos to arrange in an art gallery, where there are 5 spaces to place them. How many ways can they be arranged? Show your work using the Permutation or Combination formula for full credit.





Part c) Write an original word problem of your own creation that uses a combination and the numbers 8 and 4. Also state the solution. You may not use a pizza-themed scenario.

Answers

Answer 1

Using the permutation and the combination formula, we have that:

a) The first three finishers can be awarded medals in 504 ways.

b) They can be arranged in 252 ways.

c) In how many ways can 4 students form a team from a set of 8.

If the order is important, the permutation formula is used.If the order is not important, the combination formula is used.

Combination formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

Permutation formula:

The number of possible permutations of x elements from a set of n elements is given by:

[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]

Item a:

Order is important, as the finishers are ranked, hence:

[tex]P_{(9,3)} = \frac{9!}{6!} = 504[/tex]

The first three finishers can be awarded medals in 504 ways.

Item b:

The order is not important, hence:

[tex]C_{10,5} = \frac{10!}{5!5!} = 252[/tex]

They can be arranged in 252 ways.

Item c:

Situation in which the order is not important, hence, for example, in how many ways can 4 students form a team from a set of 8.

For more on permutation/combination, you can take a look at https://brainly.com/question/25247153


Related Questions

Graph the solution to this system of linear inequalities, and describe the meaning of the intersection of all 3 inequalities. HELP ASAP PLEASE!!!​

Answers

Answer:

Step-by-step explanation:

Coordinates ( x, y ) from "red area" satisfy all three inequality.

Find the slope of a line parallel to each given line.
y = x - 1

Answers

Answer:

1

Step-by-step explanation:

First, you should put the equation in slope intercept form (y = mx + b), where m is the slope.  A parallel line will have the same slope so if 1x is your slope for the first equation, 1 should also be the slope for the 2nd equation

a derpartment store sell 152 pair of jeans for 29 each. which is the best estimate of the total sales for the jeans

Answers

Answer:

44 dollars

Step-by-step explanation:

Since we need to find the total sales, we do 152 * .29, but we are estimating, therefore, instead we can do 150 * .29, which is 43.5. Rounding up we get 44, thus 44 is our answer

The shape on the left is transformed on the right.Which of the statements describes the transformation.​

Answers

Answer:

yall werid

Step-by-step explanation:

100
O () = 97 +18
or()- +2
x= +
OF (x) = 97 +2
F(x) = -27 + -
10

Answers

Answer:

9x+2

Step-by-step explanation:

the inverse of the function is the opposite. 1/9 becomes 9 and negative 2 becomes positive 2

Answer:

first option

Step-by-step explanation:

let y = f(x) and rearrange making x the subject

y = [tex]\frac{1}{9}[/tex] x - 2 ( add 2 to both sides )

y + 2 = [tex]\frac{1}{9}[/tex] x ( multiply through by 9 to clear the fraction )

9y + 18 = x

change y back into terms of x with x = [tex]f^{-1}[/tex] (x) , then

[tex]f^{-1}[/tex] (x) = 9x + 18

An old coin is sold for $2 and its value increases by 8% each year after it is sold. What is the value of the coin, in dollars, in 10 years

Answers

Principal=P=$2Rate of interest=8%=RTime=T=10years

Interest be I

[tex]\\ \sf\Rrightarrow I=\dfrac{PRT}{100}[/tex]

[tex]\\ \sf\Rrightarrow I=\dfrac{2(8)(10)}{100}[/tex]

[tex]\\ \sf\Rrightarrow I=\dfrac{280}{100}[/tex]

[tex]\\ \sf\Rrightarrow I=2.8\$[/tex]

Now

Value of coin after 10years =2+2.8=4.8$

Select all equations that represent this question:

Priya is stacking building blocks to make a tower. She takes a break when the tower is 2 1/2 feet tall, which is 5/8 of the hight of the tower she wants ti build. How tall is the tower when finished?

Answers

Answer:

4 feet tall

Step-by-step explanation:

First find the unit rate of how close she is to being completed / the height of the tower

2.5/5 =.5

Next, multiply .5x8 = 4 feet fall when she is done

Help me with this one please​

Answers

for me, it’s easiest when i distribute the negative sign if i need to and then reorder to put the like terms together. and then solve.
(also sorry if it’s a little confusing with all the parentheses, i use them because it helps me organize everything)


21. (4x-9y) + (6x+10) + (8y-4)
= 4x + 6x - 9y + 8y + 10 - 4
= 10x - y + 6
—> D

22. (6x+9y-15) + (2x-9y+8)
= 6x + 2x + 9y - 9y - 15 + 8 (the 9y - 9y = 0, so you can leave it out of the final equation)
= 8x - 7
—> D

23. (9x^2-8x+3) - (5x^2-6x+4)
= 9x^2 - 8x + 3 - 5x^2 -(-6x) - 4
= 9x^2 - 5x^2 - 8x + 6x + 3 - 4 (remember that two - signs next to each other make a + sign)
= 4x^2 - 2x - 1
—> A

24. (9x^3-7x+8) - (5x^2+7x-10)
= 9x^3 - 7x + 8 - 5x^2 - 7x -(-10)
= 9x^3 - 5x^2 - 7x - 7x + 8 + 10
= 9x^3 - 5x^2 - 14x + 18
—> D

25. (6x+14y) - ((7x+5y) + (x-8y))
= (6x+14y) - (7x + x + 5y - 8y)
= (6x+14y) - (8x-3y)
= 6x + 14y - 8x -(-3y)
= 6x - 8x + 14y + 3y
= -2x + 17y
—> B

Here is a balanced Hanger. Each triangle weighs 2.5 pounds, each circle weighs 3 pounds, and x represents the weight of each square. Select all equations that represent the hanger

Answers

Answer:

4x+2.5+2.5+3+3=2x+2.5+3+3+3 AND 4x+5+6=2x+2.5+6

Step-by-step explanation:

if you have 55 bad kids in classroom and 25 good kids how many bad have solve the equation

Answers

Answer:

none of them bc they're all bad kids

Step-by-step explanation:

How I can answer this question, NO LINKS, if you answer correctly I will give u brainliest!

Answers

Answer:

B,D,E

Step-by-step explanation:

GIVING BRAINLIEST. please help.


Answers

OK ILL HELP

Its the first option


Mario sells men's and women's shoes in his shoe store. He is considering selling children's
shoes. He randomly selected 120 customers to participate in a survey. The survey results are
shown below.
• 42 customers said they would shop for children's shoes
• 78 customers said they would not shop for children's shoes
Mario has an average of 440 customers per month. Based on the survey results, which
value is the best estimate of the number of customers that would shop for children's shoes
during an average month?
А
120
B
154
C
220
D
286

Answers

Answer:

154

Step-by-step explanation:

42 is 35% of 120, and 78 is 65% of 120. Thus 35% of 440 is 154 people who would shop for shoes.

Please like and thank, hope this helps.

The number of customers that would shop for children's shoes during an average month is 154.

Number of randomly selected customers = 120

Number of customers willing to shop for children's shoes = 42

42 is what percentage of 120?

As we know that percentage is the value per hundred.

So, (42/120) *100 = 35%

So, 42 is 35% of 120.

This means that 35% of customers are willing to shop for children's shoes.

Average customers per month = 440

35% of 440 = (35*440)*100

35% of 440 =154

So, the number of customers that would shop for children's shoes

during an average month =154.

Therefore, the number of customers that would shop for children's shoes during an average month is 154.

To get more about the percentage visit:

https://brainly.com/question/24304697

Kim's scores in the diving competition were 7.2, 6.975, 8.0, and 6.96. What is her total score?

Answers

29.135
Explanation
Hope this helps!

What is the simplified expression for 6^4.6^3 over 6^5
6^1
6^2
6^3
6^7

Answers

Answer:

6^2

Step-by-step explanation:

Question:-To simplify the given expression

Expression:-[tex] \frac{ {6}^{4} . {6}^{3} }{ {6}^{5} } [/tex]Solution:-

[tex] = \frac{ {6}^{4} . {6}^{3} }{ {6}^{5} } [/tex]

[As we know, a^x . a^y = a^(x+y)]

[tex] = \frac{ {6}^{(4 + 3)} }{ {6}^{5} } [/tex]

[On Simplification]

[tex] = \frac{ {6}^{7} }{ {6}^{5} } [/tex]

[As we know, a^x / a^y = a^(x-y)]

[tex] = {6}^{(7 - 5)} [/tex]

[On Simplification]

[tex] = {6}^{2} (ans)[/tex]

PlEASE HELP URGENT!!!!!!!!!

Answers

The answer is -3, i had a test with the same question

Tria had one each of five different-shaped number solids having 4, 6, 8, 12, and 20 sides. She rolled two at a time and found probabilities for the sum of the numbers that came up. She recorded the probabilities in the first column of the table. When it came time to fill in the second column, she had forgotten which number solids she had used. Figure out which number solids she must have used and explain your thinking. The first one has been done.
She found out that the probability of 4 is lesser than 5, which combinations did she use?

Answers

Answer:The probability of a 3 is 2/80 or 1/40

The probability of a 4 is less than the probability of a 5

Step-by-step explanation:

How do I find the function of a graph given?

Answers

Answer:

Explanation

Step-by-step explanation:

Well, to find a function of a given graph, you would need m, its slope, and b, its y-intercept. After you've done that, place the function in the format of f(x) or y = mx + b.

Find the slope using the formula y2-y1/x2-x1 or rise/run

Find the y-intercept by looking for the point that touched with the y-axis.

Carson rides his bike for 30 mins each day he rides a total of 12 miles every 3 days how many days will it take to ride a total of 80 miles

Answers

Answer:

20 days

Step-by-step explanation:

If he rides 12 miles every 3 days, then he rides 4 miles in one day. Divide 80 / 4 and you get 20 days.

question 5. Write an equation of the line that passes through the points (-2, -6) and (4, 6).
Answer in slope-intercept form

Answers

Answer:

y=2x-2

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(6-(-6))/(4-(-2))

m=(6+6)/(4+2)

m=12/6

m=2

y-y1=m(x-x1)

y-(-6)=2(x-(-2))

y+6=2(x+2)

y=2x+4-6

y=2x-2

Note that the slope-intercept form is y=mx+b where m=slope and b=y-intercept.

A dress originally priced at 8080 dollars was put on sale for 25\%% off. If 10\% tax was added to the sale price, then the total selling price (in dollars) of the dress was

Answers

Answer: If the dress orginially priced at 8080 dollars and put for 25 percent, that means that you have to move the decimal point to the left twice which will result as 0.25 and 10 percent tax ends up as 0.10. Multiply the two and the product, you have to add to the 8080!

Step-by-step explanation:

Which correlation coefficient best matches the graph?

Answers

Answer:

Which graph?

Step-by-step explanation:

Answer:

where is the graph

Step-by-step explanation:

umm i dont know how to answer


Which of the following is NOT a solution to the
inequality |-3x + 3) > 6?
A. -4
B. -3
C. -2
D. 3
E. 4.

Answers

Answer:

B

Step-by-step explanation:


520
38°
220°
X = degrees

Answers

by taking complete angle

52+38+220+x=360

310+x=360

x=360-310

x=50

I NEED HELP PLEASE! Thank you

Answers

Answer:

A

Step-by-step explanation:

21 -6×3

-6×3=-18

21-18

=3

Josephina lives on a farm with 3 sheep, 2 goats, 11 chickens, and 5 cows. She is going to randomly select an animal to take to the stock show. What is the probability of randomly selecting a cow or a goat

Answers

Answer:

7/21 or 1/3

Step-by-step explanation:

Adding all the animals together, we get 21. Then we add just the cows and the goats and get 7. Then we do 7/21 = 1/3 simplified

ab? that goes through points (0,2)
Write an exponential function in the form y
and (4, 1250).

Answers

Answer:

  y = 2·5^x

Step-by-step explanation:

Using the given points, we can solve for 'a' and 'b'.

  y = ab^x

  2 = ab^0 = a . . . . . substitute (0, 2) for (x, y)

__

  1250 = 2·b^4 . . . . substitute for 'a' and (4, 1250) for (x, y)

  625 = b^4 . . . . divide by 2

  5 = b . . . . . . . take the 4th root

The function is ...

  y = 2·5^x

____

Additional comment

There are two real and two imaginary 4th roots of 625. Only the positive real root is useful as the base in an exponential function like this.

The assessed value of a certain house is Rs.15 000. If the the relevant council institutions charges 5℅ of the value of the house as rates,calculate the rates that have to paid for year.

Answers

Answer:

15000×5/100=100/100x

150×5=x

750=x

Assessed value that you have to pay for a year is Rs.750.00

Step-by-step explanation:

Have a great day!

In two or three sentences, summarize what the essay suggests could help women succeed in

business. How does the summary help you identify Sandberg's message, audience, and

purpose?

Answers

The essay suggests women first need to end with internal barriers to succeed in business and this will later destroy external barriers. This helps identify the author's main message, audience, and purpose because it shows the main idea of the essay.

Lean In is an essay by Sheryl Sandberg about gender inequality and the way this inequality has prevented women from being successful and represented in specific areas including government and business.

About business, Sandberg suggests women are quite limited if compared to men due to sexism, sexual harassment, and even internal barriers women create. To stop this situation the author proposes women need to destroy internal barriers such as:

Believing they should do most of the housework and childcare-Believing they cannot be as successful as other women.Holding themselves due to unequal conditions.

Moreover, this idea helps identify other elements of the text by stating the main purpose.

Main message: Women need to destroy mental and internal barriers.Audience: Women.Purpose: To inspire women to end inequality.

Note: This question is incomplete because the text it refers to it is not given; here is the information about the text.

"Lean In: Women, work, and the will to lead" by Sheryl Sandberg.

Learn more about sexism in: https://brainly.com/question/6022376

solve the equation 1 = u over 2

Answers

Answer:

u = 2, as we multiply both sides by the denominator (2).

Other Questions
A serving of food that has 10% to 19% of a nutrient based on a 2,000-calorie diet is considered to have __________.A.low nutritional valueB.good nutritional valueC.average nutritional valueD.excellent nutritional valueA serving of food that has 10% to 19% of a nutrient based on a 2,000-calorie diet is considered to have __________.A.low nutritional valueB.good nutritional valueC.average nutritional valueD.excellent nutritional value Which coordinate grid shows Point A at (0.50, 1.25)? Coordinate grid shown from negative 2 to positive 2 on the x-axis and negative 2 to positive 2 on the y-axis in increments of 1 over 4. Only the whole numbers are labeled. A point A is shown at the intersection of 5 grid lines to the left of the y-axis and 2 grid lines above the x-axis. Coordinate grid shown from negative 2 to positive 2 on the x-axis and negative 2 to positive 2 on the y-axis in increments of 1 over 4. Only the whole numbers are labeled. A point A is shown at the intersection of 5 grid lines to the right of the y-axis and 2 grid lines below the x-axis. Coordinate grid shown from negative 2 to positive 2 on the x-axis and negative 2 to positive 2 on the y-axis in increments of 1 over 4. Only the whole numbers are labeled. A point A is shown at the intersection of 2 grid lines to the left of the y-axis and 5 grid lines above the x-axis. Coordinate grid shown from negative 2 to positive 2 on the x-axis and negative 2 to positive 2 on the y-axis in increments of 1 over 4. Only the whole numbers are labeled. A point A is shown at the intersection of 2 grid lines to the right of the y-axis and 5 grid lines below the x-axis. Who did the ram caught in the thicket (Genesis 22:13) represent? which statement best expresses the reason why the southern states decided to secede from the union after the election of 1860? 2. How many different hands of 3 cards hands be chosen from a deck of 52 cards? Ann and Betty shared a sum of money in the ratio 2:3 respectively. Ann Received $120. What was Bettys share? A cable is 40 decimeters long how long is the cable in meters and be sure to include the correct unit Read the excerpt from Good Country People. Mrs. Hopewell liked to tell people...how she had happened to hire the Freemans in the first place and how they were a godsend to her and how she had had them four years. The reason for her keeping them so long was that they were...good country people ...Before the Freemans she had averaged one tenant family a year...Mrs. Hopewell, who had divorced her husband long ago, needed someone to walk over the fields with her; and when Joy had to be impressed for these services, her remarks were usually so ugly and her face so glum... that Mrs. Hopewell would say, If you cant come pleasantly, I dont want you at all, to which the girl, standing square and rigid-shouldered with her neck thrust slightly forward, would reply, If you want me, here I amLIKE I AM. Based on the excerpt, what inferences can be made about the storys setting? Ella ensea y t y tus amigos (52.) __________ en las sillas. Yo (53.) ________ con unos amigo y t (54.)________ al lado de la puerta.Finish the sentence! ram said " why did you help me?" into indirect In the context of the poem, how has America changed over time?Consider the poem's references to Rosa Parks refusing to leave her seat, the murder of Emmett Till and Brown vs Board of Education, and contrast this with the current climate and race relations within America today. How have things changed? In what way have circumstances changed for the better, remained the same or even grown worse?Rosa ParksBY NIKKI GIOVANNIThis is for the Pullman Porters who organized when people saidthey couldn't. And carried the Pittsburgh Courier and the ChicagoDefender to the Black Americans in the South so they wouldknow they were not alone. This is for the Pullman Porters whohelped Thurgood Marshall go south and come back north to fightthe fight that resulted in Brown v. Board of Education becauseeven though Kansas is west and even though Topeka is the birth-place of Gwendolyn Brooks, who wrote the powerful "TheChicago Defender Sends a Man to Little Rock," it was thePullman Porters who whispered to the traveling men boththe Blues Men and the "Race" Men so that they both wouldknow what was going on. This is for the Pullman Porters whosmiled as if they were happy and laughed like they were tickledwhen some folks were around and who silently rejoiced in 1954when the Supreme Court announced its 90 decision that "sepa-rate is inherently unequal." This is for the Pullman Porters whosmiled and welcomed a fourteen-year-old boy onto their train in1955. They noticed his slight limp that he tried to disguise with adoo-wop walk; they noticed his stutter and probably understoodwhy his mother wanted him out of Chicago during the summerwhen school was out. Fourteen-year-old Black boys with limpsand stutters are apt to try to prove themselves in dangerous wayswhen mothers aren't around to look after them. So this is for thePullman Porters who looked over that fourteen-year-old whilethe train rolled the reverse of the Blues Highway from Chicago toSt. Louis to Memphis to Mississippi. This is for the men who kepthim safe; and if Emmett Till had been able to stay on a train allsummer he would have maybe grown a bit of a paunch, certainlylost his hair, probably have worn bifocals and bounced his grand-children on his knee telling them about his summer riding therails. But he had to get off the train. And ended up in Money,Mississippi. And was horribly, brutally, inexcusably, and unac-ceptably murdered. This is for the Pullman Porters who, when thesheriff was trying to get the body secretly buried, got Emmett'sbody on the northbound train, got his body home to Chicago,where his mother said: I want the world to see what they didto my boy. And this is for all the mothers who cried. And this isfor all the people who said Never Again. And this is about RosaParks whose feet were not so tired, it had been, after all, an ordi-nary day, until the bus driver gave her the opportunity to makehistory. This is about Mrs. Rosa Parks from Tuskegee, Alabama,who was also the field secretary of the NAACP. This is about themoment Rosa Parks shouldered her cross, put her worldly goodsaside, was willing to sacrifice her life, so that that young man inMoney, Mississippi, who had been so well protected by thePullman Porters, would not have died in vain. When Mrs. Parkssaid "NO" a passionate movement was begun. No longer wouldthere be a reliance on the law; there was a higher law. When Mrs.Parks brought that light of hers to expose the evil of the system,the sun came and rested on her shoulders bringing the heat andthe light of truth. Others would follow Mrs. Parks. Four youngmen in Greensboro, North Carolina, would also say No. Greatvoices would be raised singing the praises of God and exhortingus "to forgive those who trespass against us." But it was thePullman Porters who safely got Emmett to his granduncle and itwas Mrs. Rosa Parks who could not stand that death. And in notbeing able to stand it. She sat back down. sin(3x)+sin(x)=0 solve for x As a result of the belief in Manifest Destiny in the mid-1800s, westward expansion increased dramatically. Slowed significantly. Neither increased nor decreased. First decreased, then increased. Someone please help i forgot how to do math aaaaaaaaaa Use the claim to answer the question. Claim: Schools should improve the nutritional value of lunches served at school. Which source would provide the most relevant information for someone conducting research before writing a persuasive essay supporting this claim? Can somebody please help me with this true or false algebra 1 question?A relation that pairs each input with exactly one output is a function.True or False The interior angle of a regular polygon IS 180.find the value if its exterior regular polygon which set of integers is in the correct order, from Least to greatest? A. |-8|, 4, -3, 0,1.B. 0, 1, -3, 4, |-8|.C. -3, 0, 1, 4, |-8|.D. |-8|, -3, 0, 1, 4. Write 2^100 as a power with the following base of 32. Please help and quickly please and 20 points with brainelest Thank you