Suppose we want to choose 3 objects, without replacement, from the 4 objects pencil, eraser, desk, and chair.


(a) How many ways can this be done, if the order of the choices is relevant?


?


(b) How many ways can this be done, if the order of the choices is not relevant?

Answers

Answer 1

Answer:24 , 4

Step-by-step explanation:

Given

There are 4 objects

(a)When the order is relevant

We use permutation to get the no of ways, that is

Choosing 3 objects out of 4

[tex]^4P_3=\dfrac{4!}{(4-3)!}=\dfrac{4!}{1!}\\^4P_3=24[/tex]

(b) When the order is not important, the same thing can be done in

[tex]^4C_3\ \text{ways}\\\\\Rightarrow \dfrac{4!}{1!3!}=4\ \text{ways}[/tex]


Related Questions

If the radius of a circle is 8 inches, what is the area. Use the formula shown below, and round the answer to the nearest hundredth, please.

A = π r² π ≈ 3.14

Answers

A≈201.06in²

A=πr2=π·82≈201.06193in²

Answer:

A=πr2=π·82≈201.06193

this is your answer.

201.1 — estimated.

Have a great day!!

I NEED HELP PLEASE !

Answers

Answer:

x = 4, -2 1/2

Step-by-step explanation:

factors:

(2x + 5) (x - 4)

set each factor equal to zero:

2x + 5 = 0

2x = -5

x = -5/2

x - 4 = 0

x = 4

If you can create 1 item in 3/4 hr how many can you create in 8 hrs

Answers

Answer:

10.6, or 10 entire items

Step-by-step explanation:

Answer:

[tex]\frac{32}{3}[/tex] items

Step-by-step explanation:

Please see the attached image.

I hope this helps!

Four laps around the track is equal to one mile. It takes Taylor 8 minutes to run 3 laps.
How many minutes would it take Taylor to run 6 miles?
A. 16 minutes
B. 36 minutes
C. 48 minutes
D. 64 minutes

Answers

Answer:

D

Step-by-step explanation:

8x60=480

480÷3=160

160x4=640

640 is 10 Minutes 40 Seconds

6 Miles is 24 Laps

640x6=3840

3840÷60=64

The Answer Will be 64 Minutes.

Let a and b be rational numbers.

Answers

Answer:

Ok, let me guess... 4 and 5

Step-by-step explanation:

x/12-5>-2 please help

Answers

Answer:

The inequality for x is x > 36

(In interval notation form it is (36, ∞)

Step-by-step explanation:

Multiply to remove the fraction, then set equal to zero and solve.

Hope this helped you!

Please consider giving brainliest!

Dont forget to give a rating and leave a thanks.

which expression is equivalent to 3 to the power of 9

Answers

Answer:

3^9

Step-by-step explanation:

Also 3 to the power of 9 is 19,683

Hope This Helps :b

Answer:

What he said which is the answer I just want to get more points

-2c^2 -9c -2 = -3c^2

its very important, please help asap

Answers

The answer is to your question is 89

Which Equation Is equivalent To Log2y =x+7

Answers

Answer:

the second one

Step-by-step explanation:

A unicycle wheel has a diameter of 30 inches. How many inches will the unicycle travel in 5 revolutions? Use π = 3.14 and round your answer to the nearest hundredth of an inch.

Answers

Answer:

471.3inches

Step-by-step explanation:

Given data

Diameter= 30in

Radius= D/2= 30/2= 15in

The circumference is the same as the distance covered in one revolution

C= 2πr

Hence the distance  covered in 5 revolutions is

C= 2*5*πr

Substitute

C=10*3.142*15

C= 471.3inches

Evaluate: 2-^4=
A.1/16
B.1/8
c. -8
D.-16

Answers

Answer:

A. 1/16

Step-by-step explanation:

[tex] {2}^{ - 4} = \frac{1}{ {2}^{4} } = \frac{1}{16} \\ [/tex]

2 Doctors is _______________% of 25 Doctors what is it.

Answers

Answer:

8%

Step-by-step explanation:

if you divide 2 by 25, you would get 0.08, which is equal to 8%

Answer:

8%

Step-by-step explanation:

Compare |-2/5| and |-3/8|

Answers

Answer:

2/5 and 3/8

2/5 is greater than 3/8

Step-by-step explanation:

Those parallel lines mean absolute value which means no signs no positive nor negative.

The americans with disabilities act sets a maximium angle for a wheelchair ramp entering a business at 4.76 degrees. Determine the horizontal distance needed to occomidate a ramp that goes up to a door.

Answers

Answer:

d = 48.03 feet

Step-by-step explanation:

Given that,

The maximum angle for a wheelchair ramp entering a business at 4.76 degrees.

We need to find the horizontal distance needed to accomidate a ramp that goes up to a door 4 feet of the ground.

We can solve it using trigonometry.

[tex]\tan\theta=\dfrac{h}{d}[/tex]

Where

h is height

d is the angle of elevation

[tex]d=\dfrac{h}{\tan\theta}\\\\d=\dfrac{4}{\tan(4.76)}\\\\d=48.03\ ft[/tex]

So, the horizontal distance is equal to 48.03 feet.

4(5-2x)+3=7 step by step pls

Answers

Answer: x = 2

The step by step is attached to this answer, hope it helped!

show dis and i will mark you correcr

Answers

Answer:

A and D

Step-by-step explanation:

The area of the combined rectangle is:

t(5 + 4) = 5t + 4t = 9t

Incorrect choices are:

A. 4*5*tD. t + 5 + 4

Answer:

Solution :-

Second option is correct because t is the breadth and 5 and 4 are length. So, Option B is correct 5t + 4t

On adding both we get 9t. Option C is correct

We may also take t as common and may be written as

t(5 + 4)

Correct option are B,C,E

[tex] \\ [/tex]

In the diagram to the right, a right circular cone has a diameter of 8 inches and a height of 12 inches.What is the volume of the cone to the nearest cubic inch? A. 201 in3 B. 481 in3 C. 603 in3 D. 804 in3

Answers

Answer:

(A) 201

Step by step explanation :

Volume of a cone is approximately equal to [tex]\boldsymbol{201}[/tex] inches.

So, option A. is correct.

Volume of cone

A cone is a three-dimensional geometric object with a smooth trans-ition from a flat base to the ap-ex or vertex.

Radius of a cone is half of the diameter.

Radius of a cone [tex](r)=\frac{8}{2}[/tex]

                                 [tex]=4[/tex] inches

Height of a cone [tex](h)=12[/tex] inches

Volume of a cone [tex]=\frac{1}{3}\pi r^2 h[/tex]

                              [tex]=\frac{1}{3}(\frac{22}{7} ) (4)^2 (12)[/tex]

                              [tex]\approx 201[/tex] inches

So, volume of a cone is approximately equal to [tex]\boldsymbol{201}[/tex] inches.

So, option A. is correct.

Find out more information about cone here:

https://brainly.com/question/2920315?referrer=searchResults

Triangle ABC is graphed on a coordinate plane with vertices at A (-3,7), B (9,-8), and
C(-5, -6). If triangle ABC is dilated by a scale factor of m with the origin as the center
of dilation to create triangle A'B'C', what will be the coordinates of the dilated vertex
B?

Answers

Answer:

Step-by-step explanation:

Given that h varies inversely with respect to g, and that h= -24 when g= 3, write an
equation that describes the relationship between h and g. Then find h when g=-1,

Answers

Answer:

h = 72

Step-by-step explanation:

Given that h varies inversely with g then the equation relating them is

h = [tex]\frac{k}{g}[/tex] ← k is the constant of variation

To find k use the condition h = - 24 when g = 3 , then

- 24 = [tex]\frac{k}{3}[/tex] ( multiply both sides by 3 )

- 72 = k

h = - [tex]\frac{72}{g}[/tex] ← equation of variation

When g = - 1 , then

h = - [tex]\frac{72}{-1}[/tex] = 72

Consider the equation: X^2+16x-2=11 1) Rewrite the equation by completing the square

Answers

Answer:

[tex](x+8)^{2}[/tex] =77

x= -8 +/- [tex]\sqrt\\ 77[/tex]

From Khan Academy

1/6-9/8 as a fraction in simplest form

Answers

Hopes this helps:

Answer: -23/24

Rewrite 3log(4) in the form log(c)

Answers

Step-by-step explanation:

this is the answer of this question

Answer:

log(64)

Step-by-step explanation:

3 log (4) = log (4^3) = log (64)

Hope this helps!

Find the surface area of the regular hexagonal prism.

Answers

Answer:

I think the surface is

Step-by-step explanation:

3.5

The point C(-2, -4) is rotated 270° clockwise around the origin. What are the coordinates of the resulting point, C′?

Answers

Answer:

(2,4)

Step-by-step explanation:

The functions f(x) = 2x2 + 2 and g(x) = 2x+1 + 2 are graphed on the coordinate plane as shown.
32
24
16
8+000
0
1
2
For what values of x is g(x) > f(x)?
O A 0 < x < 2 and x > 4
OB. 2 C. X > 4
OD. X > 2

Answers

Answer:

Step-by-step explanation:

Given the functions f(x) = 2x^2 + 2 and g(x) = 2^x+1 + 2

If g(x) > f(x)

2^(x+1) + 2  > 2x^2 + 2

2^x*2 + 2 >2x^2 + 2

2^x*2 >2x^2

2^x > x^2

2^x - x^2 > 0

g(x) > f(x) over the interval 0 < x < 2 and x > 4.

What is a function?

A function is an expression that shows the relationship between two or more numbers and variables.

Given the function:

f(x) = 2x² + 2 and g(x) = 2ˣ ⁺ ¹ + 2

From the graph:

We can see that g(x) > f(x) over the interval 0 < x < 2 and x > 4.

Find out more on function at: https://brainly.com/question/25638609

Examine the sequence of integers below.
−16, −10, −4, 2, 8, 14
Which algebraic expression represents the nth integer in this sequence?
A.
6n − 16

B.
−6n − 10

C.
−6n + 2

D.
6n − 22

Answers

Answer: D

6n-22

Step-by-step explanation:

10 = g - 19. Please help!!!

Answers

Answer: g = 29

10 = g - 19

add 19 to both sides:

29 = g

flip if u want

g = 29

hope this helped :)

What is i^34?
A. -1
B. -i
C. 1
D. 1

Answers

Answer:

A.-1 all you had to do was look up the answer

Step-by-step explanation:

The answer to the question is A.

Gary goes to the grocery store to buy hot dogs and hamburgers for a cookout. He buys a total of 8 packages for a total of $28.52. A package of hot dogs costs $2.29 and a package of hamburgers costs $5.69.

Answers

Answer:

3 hamburger packs

5 hot dog packs

Step-by-step explanation:

The system of equations that corresponds to the situation is:

1. x + y = 8

2. 2.29x + 5.69y = 28.52

Let's use variables to represent the unknowns in the problem.

Let:

x = number of packages of hot dogs purchased

y = number of packages of hamburgers purchased

We are given the following information:

1. Gary buys a total of 8 packages: x + y = 8

2. The total cost of the packages is $28.52: 2.29x + 5.69y = 28.52

So, the system of equations that corresponds to the situation is:

1. x + y = 8

2. 2.29x + 5.69y = 28.52

To know more about equations:

https://brainly.com/question/10724260

#SPJ2

Complete question is:

Write a system of equations that corresponds to the situation. Do not solve. Gary goes to the grocery store to buy hot dogs and hamburgers for a cookout. He buys a total of 8 packages for a total of $28.52. A package of hot dogs costs$2.29 and a package of hamburgers costs $5.69.

(This is for my Algebra ll project all you need to do is answer this question) How many siblings do you have?

Answers

Answer:

I have two Sisters

Step-by-step explanation:

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