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



10 0breros construyen un complejo 336 días, ¿cuantos días les tomaría hacer el mismo complejo a 15 obreros?

Answers

Usando proporciones, se encuentra que 15 obreros hacerían el mismo complejo en 24 días.

Esta pregunta se resuelve por proporciones, usando una regla de tres. Cuanto mayor lo número de obreros, menor el tiempo, o sea, las medidas son inversamente proporcionales, lo que implica que la multiplicación es en línea.10 obreros toman 336 dias. ¿Cual el tiempo necessário para 15 obreros?

La regla de três es:

10 obreros - 336 días

15 obreros - x días

Aplicando multiplicación en línea:

[tex]15x = 336(10)[/tex]

[tex]x = \frac{336(10)}{15}[/tex]

[tex]x = 24[/tex]

15 obreros hacerían el mismo complejo en 24 días.

Para obtener más información sobre las proporciones, puedes visitar a https://brainly.com/question/24615636

If tanx = 0.75, what is the value of cosx + sinx ?

Answers

cosine (x) = 4 over 5
cos
(
x
)
=
4
5
Explanation:
First you must apply sohcahtoa
it means
sine = opposite side over hypotenuse
sine = opposite/hypotenuse
cosine = adjacent side over hypotenuse
cosine = adjacent/hypotenuse
tangent = opposite side over adjacent side
tangent = opposite/adjacent
then
solve the unknown by applying the Right Triangle Theorem.
draw a right triangle.
label the parts where
a
is the opposite side
b
is the adjacent side
c is the hypotenuse
Solve the unknown. The hypotenuse using
a
2
+
b
2
=
c
2

since the given
tan
x
=
3
4

it means
tan = opposite/adjacent
a
= opposite side =
3

b
= adjacent side =
4

c
= hypotenuse = ??
a
2
+
b
2
=
c
2

substitute the value
(
3
)
2
+
(
4
)
2
=
c
2

9
+
16
=
c
2

25
=
c
2

get the square root of
25

it is equal to
5

therefore
c
=
5

c
= hypotenuse =
5

cos
= adjacent/hypotenuse
cos
(
x
)
=
4
over
5

cos
(
x
)
=
4
5

Answer:

theta is eq to 36.86 value is. 0.5998+0.8=1.399

Some nuts cost $22/kg. How much would 150 g cost?

Answers

Answer:

$3.30

Step-by-step explanation:

1 kg = 1000 g

therefore, 150 g = 0.15 kg

multiply the cost by the amount

22 x 0.15 = 3.3, or $3.30

I giv Brainliest


Please select the best answer from the choices provided

A
B
C
D

Answers

Answer:

c

Step-by-step explanation:

Answer:

The best answer is option C.

Step-by-step explanation:

Option A is a linear function, Option D is translating the non-linear function 4 units up but nowhere right or left, and I don't know about Option B...

Add. Use models if needed. (-3x - 7) + (4x + 7)

Answers

-3x-7+4x+7

Negative -7 and positive 7 will give you 0.

So we're left with x. Therefore, the answer is x.

(-3x-7)+(4x+7) = -3x-7+4x+7 = -3x+4x = x

6m+7n+5m−3n simpified

Answers

Answer:

11m + 4n

Step-by-step explanation:

when two numbers with the same variable are added together or subtracted the result is just the numbers added or subtracted. So you can add 6m and 5m to get 11m. and you can subtract 3n from 7n to get 4n

11m + 4n

Which expression has a sum of 1 2/21

A. 3/7 + 2/3
B. 4/7 + 1/3
C. 5/7 + 2/3
D. 6/7 + 1/3

Answers

Answer:

A. is the answer

Step-by-step explanation:

the LCM of 7 and 3 is 21.

When added it would be 9+14 =23

23/21= 1 2/21

can someone pls help i need your help

Answers

12 miles
hope this is helpful!

Answer:

12 miles

Step-by-step explanation:

You would have to divide $26.40 by $2.20 which equals 12 so she traveled 12 miles.

In two or more complete sentences, describe the transformation(s) that take place on the parent function, f(x) = log(x), to achieve the graph of g(x) = log(-2x-4) + 1.

Answers

Using translation concepts, it is found that the parent function was:

Reflected over the x-axis.Horizontally compressed by a factor of 2.Shifted right 4 units.Shifted up 1 unit.

The parent function is:

[tex]f(x) = \log{x}[/tex]

The first transformation is:

[tex]\log{x} \rightarrow \log{-x}[/tex]

Which means that it was reflected over the x-axis.

Then, [tex]\log{-x} \rightarrow \log{-2x}[/tex], which means that it was horizontally compressed by a factor of 2.

Then, [tex]\log{-2x} \rightarrow \log{-2x - 4}[/tex], which means that it was shifted right 4 units.

Finally, 1 was added to the function, which means that it was shifted up 1 unit.

To learn more about translation concepts, you can take a look at https://brainly.com/question/4521517

All the numbers round to 7 except


6.61

7.89

6.58

7.37

Answers

7.89 rounds off to 8
7.89 because it’s closer to 8.00, not 7.00

anybody help please hm​

Answers

The answer is b, 20^247.

the heights of two cylinders are in the ratio of 5:3 and their volume are in the ratio 20:27. then the ratio of their radius is...... ?

plz its urgent

Answers

Answer:

The ratio of their radius is [tex]2:3[/tex]

Step-by-step explanation:

Volume of cylinder is [tex]\pi r^2h[/tex], where r is radius and h is height

We have

The heights of two cylinders are in the ratio of [tex]5:3[/tex]

[tex]\frac{h_1}{h_2} =\frac{5}{3}[/tex]

The volume are in the ratio [tex]20:27[/tex]

[tex]\frac{V_1}{V_2} =\frac{20}{27}\\\\\frac{\pi r_1^2h_1}{\pi r_2^2h_2} =\frac{20}{27}\\\\\frac{ r_1^2}{ r_2^2}\times \frac{3}{5} =\frac{20}{27}\\\\\frac{ r_1^2}{ r_2^2} =\frac{4}{9}\\\\\frac{ r_1}{ r_2} =\frac{2}{3}[/tex]

The ratio of their radius is [tex]2:3[/tex]

Answer:

2 : 3

Step-by-step explanation:

Let,

Radius of cylinder 1 = R

Radius of cylinder 2 = r

Now,

We know that

Volume of cylinder = πr²h

=> πR²h/πr²h' = 20/27

=> R² × 5/r² × 3 = 20/27

=> R²/r² = 20/27 × 3/5

=> R²/r² = 4/9

=> R/r = √(4/9)

=> R/r = 2/3

=> R : r = 2 : 3

Assigned seating forever! Ms. Clore has 28 desks in
her classroom. She numbers the desks from 1 to 28.
On the first day of class, Ms. Clore places identical
slips of paper numbered 1 to 28 in a hat. Each of the
28 students in her statistics class draws a slip from the
hat upon entering the classroom to determine his or
her assigned seat. How many possible seating assign-
ments are there?

Answers

Using the arrangement formula, it is found that there are [tex]28! = 3.05 \times 10^{29}[/tex] possible seating arrangements.

The number of possible arrangements of n elements is given by the arrangement formula, as follows:

[tex]A_n = n![/tex]

It is used when n elements are arranged in n positions.

In this problem, 28 students are arranged on 28 desks, hence [tex]n = 28[/tex], and:

[tex]A_{28} = 28! = 3.05 \times 10^{29}[/tex]

Hence, there are [tex]28! = 3.05 \times 10^{29}[/tex] possible seating arrangements.

You can learn more about the arrangement formula at https://brainly.com/question/24648661

15 POINTS HELP PLZ

Which expression is equal to f(x) - g(x)?

Answers

Answer:

B) x^3-x^2-8x-2

Step-by-step explanation:

Expand the equation of g(x) to standard form

f(x) = x^3-4x+2

g(x) = x^2-4x+4

Subtract like terms in the equation and solve for the answer.

f(x) - g(x) = x^3-x^2-4x-4x+2-4

x^3-x^2-8x-2

How many real solutions are there for the quadratic equation below?

0=2x^2-3x+7

A) 0

B) 1

C) 2

D) infinite

Answers

Answer:

2 solutions

Step-by-step explanation:

2 solutions

3/4 - i[tex]\sqrt{47}[/tex]/4

3/4 + i[tex]\sqrt{47}[/tex]/4

15)
Solve for X
X\42=6
A)
7
B)
252
C)
260
D)
332

Answers

Answer:

b)252 is the answer

Step-by-step explanation:

x\42=6

x=6*42

x=252

4/9 + 9/18. Please help me as soon as possible, it's due today.

Answers

Answer:

[tex]\frac{17}{18}[/tex]

Step-by-step explanation:

To solve 4/9 + 9/18 just find the common denominator which is 18.

to get 4/9 to get the denominator of 18 you multiply the denominator by 2:

9 x 2 = 18, what you do to the bottom you do to the top (Multiply the numerator by 2 also) so, 4 x 2 = 8.

Now, add the numerator and keep the denominator the same. 8 + 9 = 17.

8/18 + 9/18 = 17/18

Can someone please help?

Answers

Answer:

Well a midpoint makes the cutter segment or Line in exactly in half. So the two lines cutted are equal. In this case t is the midpoint. PT and TQ are equal. So you have two expressions, make then equal to each other since they are congruent.

6x+4=8x-8

12=2x

x=6

Now PT is 6x+4

So we subsitute x for 6 since x=6

6*6+4

40

PT is 40

у
42) Which equation best represents the line of best fit for this
scatter plot?
A. y = 4x - 4
B.y= 4x-2
C. y = x-4
D. y=x-2

Answers

What grade are u in?

(BRAINLIEST TO THE PERSON WHO HELPS ME WITH THESE THREE QUESTIONS)
Cheryl writes 7 fewer posts than Kevin on a social media site.
Answer the questions to write an algebraic expression. Then evaluate the expression for the given value.
1. Choose a variable to represent the number of posts Kevin writes. Explain why you chose this variable.

2. Which operation (addition, subtraction, multiplication, or division) applies to this situation? Justify your choice.
3. Use your variable and the operation you identified to write an expression for the number of posts Cheryl wrote.

Answers

Answer:

Cheryl's posts + 7 posts =Kevin Posts

K-C=7 or C+7+K I use them because C is Cheryl and K is Kevin

Operation=subtraction or addition because it could be K-C=7 or C+7+K

Cheryl wrote K-7=C posts

Answer:

Cheryl writes 7 fewer posts than Kevin on a social media site.

Answer the questions to write an algebraic expression. Then evaluate the expression for the given value.

1. Choose a variable to represent the number of posts Kevin writes. Explain why you chose this variable. (2 points)

The expression will be P for "of posts Kevin writes." 

2. Which operation (addition, subtraction, multiplication, or division) applies to this situation? Justify your choice. (2 points)

 The operation I will use is subtraction so P-7.

3. Use your variable and the operation you identified to write an expression for the number of posts Cheryl wrote. (3 points)

Subtraction would be the operation and my expression would be ( P-7 ) which would also be ( 21 - 7 )

The perimeter of an equilateral triangle is 14.4 cm. Find out the length of the side of that triangle in decimal fraction.​

Answers

Answer:

4.8 cm

Step-by-step explanation:

Given,

Perimeter of an equilateral triangle = 14.4 cm

As we know,

Perimeter of an equilateral triangle = 3 × sides (s) = 3s

Therefore,

By the problem,

=> 3s = 14.4 cm

[On dividing both sides with 3]

[tex] = > \frac{3s}{3} = \frac{14.4}{3} [/tex]

[On Simplification]

=> s = 4.8 cm

Hence,

The required side of the given equilateral triangle is 4.8cm(Ans)

someone please help me

Answers

Answer:

m = 5

Step-by-step explanation:

Since the triangles are similar in the way shown, then

6/10 = 3/m

6m = 10 × 3

m = 5

Please help! I need answers

Answers

Hill family's sprinkler was on for 25 hours, while Moore family's sprinkler was on for 35 hours

Represent the time the Hill family and the Moore family use the sprinkler with H and M.

So, the total time is:

[tex]H + M = 60[/tex]

And the rate is:

[tex]25H + 20M = 1325[/tex]

Make H the subject in [tex]H + M = 60[/tex]

[tex]H= 60 - M[/tex]

Substitute 60 - M for H in [tex]25H + 20M = 1325[/tex]

[tex]25(60 - M) + 20M = 1325[/tex]

Open brackets

[tex]1500 - 25M + 20M = 1325[/tex]

Collect like terms

[tex]- 25M + 20M = 1325 - 1500[/tex]

[tex]- 5M = -175[/tex]

Divide both sides by -5

[tex]M = 35[/tex]

Recall that:

[tex]H= 60 - M[/tex]

So, we have:

[tex]H = 60 - 35[/tex]

[tex]H = 25[/tex]

Hence, Hill family's sprinkler was on for 25 hours, while Moore family's sprinkler was on for 35 hours

Read more about system of equations at:

https://brainly.com/question/14323743

A 6am one morning the temperature was -14 degrees by noon it rose 8 degrees and then rose another 2 degrees by 3pm. By 6pm the temperature had dropped 5 degrees. What was the temperature at 6pm

Answers

Answer:

-9 degrees

Step-by-step explanation:

-14 + 8 = -6

-6 + 2 = -4

-4 - 5 = -9

The temperature at 6pm dropped down to .

What is a mathematical function, equation and expression?               function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.

Given is that at 6am one morning the temperature was -14 degrees by noon it rose 8 degrees and then rose another 2 degrees by 3pm. By 6pm the temperature had dropped 5 degrees

We can write -

T{6 AM} = - 14°

T{12 PM} = 8°

T{3 PM} = (8 + 2)° = 10°

T{6 PM} = 10° - 5° =

Therefore, the temperature at 6pm dropped down to .

To solve more questions on functions, expressions and polynomials, visit the link below -

brainly.com/question/17421223

#SPJ5

On Saturday Keisha ran 3.218 kilometers. on Su nday she ran 2.87 kilometers. How much further did she run on Saturday than on Sunday

Answers

Answer:

0.808 you find the difference between the two numbers

1
D
Question 1
Adding the complex numbers 7 - 6i and —3 + 8i is equivalent to the operation
(7 – 6) + (-3+8) i.

Answers

Yes, this identity is true. Those two operations are equivalent.

Edin has £300 in his savings account. His bank offers him a fixed 5% simple interest rate per annum, for a period of 3 years.

Answers

£45

300 x 0.05 = 15

15 x 3 = 45

Is 1 a real or an imaginary number?

Answers

Real number, 1 is a real number
1 is a real number for me and my sister

a total materials variance is analyzed in terms of

Answers

Entry field with correct answer
price and quantity variances.
quantity and quality variances.
buy and sell variances.
tight and loose variances.
price and quantity variances.

Write 2^100 as a power with the following base of 32.

Answers

Answer:

your answer is 30

Step-by-step explanation:

I have completed the test

Other Questions
A children's story that includes talking animals uses which type of figurativelanguage?A. ParadoxB. PersonificationC. ApostropheD. Hyperbole Fill out the 8 questions thanks! In justice Roberts opinion what serves as the ultimate guarantee of a fair trial? what is the solution 3x-1/4 = -5/11(3x-1)11 = -5(4)33x-11 = -20 +11 = +1133x = - 933x/33 = -9/33x = -3/11 find the midpoint of CD with C(-4,5) and D(-1,-4). The circle graph below represents the opinions of 100 students about their favorite sports. Each student chose exactly one of these four options: Basketball, Hockey, Football, and Other. The following statements are true about the graph: The number of students who chose Basketball is three times the number of students who chose Other. Ten more students chose Football than chose Hockey. The percent of students who chose Basketball plus the percent of students who chose Football equal 65.What percent of the students chose Basketball? solve pls brainliestA. Explain what Co-Vid is. B. How is it affecting the community? Why are these variants (Omicron) so dangerous? Find the equation of the line shown.1098765432NO1 2 3 4 5 6 7 8 9 10 given the function f(x)=3x-5, for which value in the domain does f(x)=-38? Hi guys, can someone tells me the three main effects that the Islamic revolution brought to women in Iran? Verbal communication skills are impacted by which factors? Plsssss help me this needs to be done ASAPPP state one way of monitoring the activity of the heart other than measuring pulse Qui est grand 0 ou -2,5 throughout most of human history, families had many children because Help me plz A)12.7B)13.3C)12.4 Find the 44th term in the followingarithmetic sequence :2, 3, 4, 5, ...Hint: Write a formula to help you.1st term + common difference(desired term - 1) M Which word best completes this sentence?Wireine Wohnung mieten.