Alicia has 7 paintings she wants to hang side by side on her wall.
2. If Alicia only wants to display 4 of the paintings, in how many ways can she choose the paintings she wishes to display? Show your work.
3. In how many ways can Alicia arrange 4 out of the 7 paintings? Show your work.

Answers

Answer 1

The question is an illustration of permutation and combinations.

The number of ways she can choose 4 out of the 7 paintings is 35The number of ways she can arrange 4 out of the 7 paintings is 840

The given parameters are:

[tex]\mathbf{n = 7}[/tex]

[tex]\mathbf{r = 4}[/tex]

(a) Choose 4 of 7 paintings

Choosing 4 of 7 paintings implies combination.

So, we have:

[tex]\mathbf{^nC_r = \frac{n!}{(n - r)!r!}}[/tex]

Substitute values for n and r

[tex]\mathbf{^7C_4 = \frac{7!}{(7 - 4)!4!}}[/tex]

[tex]\mathbf{^7C_4 = \frac{7!}{3!4!}}[/tex]

Expand

[tex]\mathbf{^7C_4 = \frac{7 \times 6 \times 5 \times 4!}{3 \times 2 \times 1 \times 4 !}}[/tex]

[tex]\mathbf{^7C_4 = 35}[/tex]

Hence, the number of ways she can choose 4 out of the 7 paintings is 35

(b) Arrange 4 of 7 paintings

Arranging 4 of 7 paintings implies permutation.

So, we have:

[tex]\mathbf{^nP_r = \frac{n!}{(n - r)!}}[/tex]

Substitute values for n and r

[tex]\mathbf{^7P_4 = \frac{7!}{(7 - 4)!}}[/tex]

[tex]\mathbf{^7P_4 = \frac{7!}{3!}}[/tex]

Expand

[tex]\mathbf{^7P_4 = \frac{7 \times 6 \times 5 \times 4 \times 3!}{3!}}[/tex]

[tex]\mathbf{^7P_4 = 840}[/tex]

Hence, the number of ways she can arrange 4 out of the 7 paintings is 840

Read more about permutation and combinations at:

https://brainly.com/question/15301090


Related Questions

guys pls help me!!!!!!

Answers

Answer:

x= 55

y=125

Step-by-step explanation:

y = 180 - 55

hope it's correct

What is the number 18 written in a+bi form

Answers

Answer:

Step-by-step explanation:To see that

i

18

=

1

note that

i

1

=

1

i

0

=

1

i

1

=

1

1

i

2

=

1

1

=

1

i

18

=

(

i

2

)

9

=

(

1

)

9

=

1

The number 18 in the form of complex numbers will be written as 18 + 0i.

What are complex numbers?

Every complex number may be represented in the form a + bi, where a and b are real numbers. A complex number is an element of a number system that extends the real numbers with a specific element labeled I sometimes known as the imaginary unit, and satisfies the equation i² = 1.

The given number is 18. The number in the form of a complex number can be written as:-

Complex number =  a + bi

Complex number =  18 + 0i

Therefore, the number 18 in the form of complex numbers will be written as 18 + 0i.

To know more about complex numbers follow

https://brainly.com/question/2801231

#SPJ2

can someone please help me with this

Answers

Answer:

Perimeter = 18m

Area = 18m²

Step-by-step explanation:

On a rectangle, opposite sides have equal lengths. This means to find the perimeter you would do (3 × 2) + (6 × 2) which is 6 + 12 = 18

The perimeter is 18m

To find the area, you would do length × width. The length is 6 and the width is 3 so 6 × 3 is 18

The area is 18m²

Hope this helps!

ISOSCELES


EQUILATERAL


SCALENE

Answers

Answer:

scalene because all the angles are different in an isosceles triangle 2 angles are the same

Answer:

Scalene triangle

Step-by-step explanation:

the answer is the scalene triangle

Winter fills 2/5 of a water bottle in 1/4

of a minute. How many bottles can

Winter fill in 1 minute?

Answers

Answer:

1.6 (decimal), 1 6/10 (proper), and 8/5 (improper)

Step-by-step explanation:

If it’s 2/5 in 1/4 and to get one while you need four 1/4 you need to multiply to get how much it can fill in that 4/4. To do this multiply 2/5 by 4 which is 1.6 (decimal) and 1 6/10 fractional. Or if you want it improper, 8/5

Ryan has 15 meters of stereo wire He used 7/8 of the wire to hook his new speakers. How much wire did he use?​

Answers

Answer:

13.125 meters

Step-by-step explanation:

7/8 times 15

write the equation
it passes through (0,-2) and is perpendicular to the graph of y=5x+7

Answers

Step-by-step explanation:

the line passes through (0,-2) and perpendicular to the graph of y=5x+7.

solution :

the slope = -1/5

the equation :

y+2 = -1/5 (x-0)

y = -1/5x - 2

Describe the translation of the point to its image. (-2,-3) to (-2,4)

Answers

Up 8 Units, Hope this helps :)

The diagram below represent the rate of making copies on a copy machine. Which table represent this rate?

Answers

Answer:

its B

Step-by-step explanation:

Which number equals (34)−2?

Answers

Answer:

32

Step-by-step explanation:

PLEASE HELP WILL MARK BRAINLIEST NO FAKE ANSWERS OR WILL BE REPORTED
Evaluate the expression IN EXPONENTIAL FORM

Answers

Answer:

-10 × -10= 100

dkfofjdnrjf

need a well explained ans ...
● no spams needed

Answers

5. We need to subtract 20% from the selling price of 18 000 as that will give his cost price

20/100 X 18 000 = 3600

18 000 - 3600

= 14 400.



7) 20 527,5 Rs

[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]

Question : 1

Cost price of the T.V. is :

[tex]₹ \: 15000[/tex]Question : 2

The scooter cost him :

[tex]₹ \: 21000[/tex]

The solution is in attachment ~

[tex]\sf x-5=16[/tex]

Answers

Answer:

x=21

Step-by-step explanation:

[tex]x-5=16[/tex]

[tex]x-5+5=16+5[/tex] (Add 5 to bth sides)

[tex]x=21[/tex]

Which equation represents a line which is parallel to the y-axis?

Answers

Answer:

x= 3

Step-by-step explanation:

I hope this helps but if there are options lmk

Answer:x= -2

Step-by-step explanation:

Use synthetic division to find the result when 4x^3+3x^2– 8x – 7 is divided by x+1.

Answers

Answers:

4x^2 - x - 7

what is 26 divide 7,124

Answers

Answer:

1/274

Step-by-step explanation:

Solution 1: Use a fraction simplifier calculator :)

Solution 2: divide by 2 first, then test to find 13, and your there.

Answer: There are two answers ( just for explanation ) 1. 0.0036496350364964    2. 274

Step-by-step explanation:

1. If we do 26 divided by 7124 answer is = 0.0036496350364964  ( check the pic-div1, div2, div3 )

2. If we do 7124 divided by 26 answer is = 274 (check pics-div4, div5)

Find the area and perimeter of
the parallelogram:
17ft
12ft
15ft

Answers

Answer:

Hi there!

Here is your answer...

The Area of the Parallelogram is:

[tex]204ft^{2}[/tex]

The Perimeter of the Parallelogram is:

[tex]64ft[/tex]

Step-by-step explanation:

To find the Area of a Parallelogram you must first identify the Base and Height. In this instance the Base would be the top and bottom which we know are 17ft in length. The Height would be the dotted line that we know it 12ft tall. The next step would be to Multiply the Base by the Height. That would give us 204. After we add the correct units we have [tex]204ft^{2}[/tex].

To find the Perimeter we would simply add together all side lengths. We know that the top and bottom are equal to 17ft and the left and right are equal to 15 feet. This gives us 17+17+15+15. Which would equal 64, add the units and it becomes [tex]64ft[/tex].

Area=base x height

Perimeter = base + base + angle +angle

(angle is the side length.)

Show that (√7+i√3/√7-i√3 + √7-i√3/√7+i√3) is real​

Answers

Answer:

Step-by-step explanation:

Step-by-step explanation:

[tex]\large\underline{\sf{Solution-}}[/tex]

Consider,

[tex]\rm \longmapsto\:\dfrac{ \sqrt{7} + i \sqrt{3} }{ \sqrt{7} - i \sqrt{3}} + \dfrac{ \sqrt{7} - i \sqrt{3} }{ \sqrt{7} + i \sqrt{3} } [/tex]

On taking LCM, we get

[tex]\rm \:  =  \: \dfrac{ {( \sqrt{7} + i \sqrt{3})}^{2} + {( \sqrt{7} - i \sqrt{3})}^{2} }{( \sqrt{7} + i \sqrt{3})( \sqrt{7} - i \sqrt{3})} [/tex]

We know,

[tex] \purple{\rm \longmapsto\:\boxed{\tt{ {(x + y)}^{2} + {(x - y)}^{2} = 2( {x}^{2} + {y}^{2})}}} \\ [/tex]

and

[tex] \purple{\rm \longmapsto\:\boxed{\tt{ (x + y)(x - y) = {x}^{2} - {y}^{2} \: }}} \\ [/tex]

So, using these Identities, we get

[tex]\rm \:  =  \: \dfrac{2\bigg[ {( \sqrt{7})}^{2} + {(i \sqrt{3}) }^{2} \bigg]}{ {( \sqrt{7}) }^{2} - {(i \sqrt{3})}^{2} } [/tex]

[tex]\rm \:  =  \: \dfrac{2(7 + 3 {i}^{2})}{7 - {3i}^{2} } [/tex]

We know,

[tex] \purple{\rm \longmapsto\:\boxed{\tt{ {i}^{2} = - 1}}} \\ [/tex]

So, using this, we get

[tex]\rm \:  =  \: \dfrac{2(7 - 3)}{7 + 3} [/tex]

[tex]\rm \:  =  \: \dfrac{2 \times 4}{10} [/tex]

[tex]\rm \:  =  \: \dfrac{4}{5} [/tex]

Hence,

[tex] \red{\rm\implies \:\boxed{\sf{ \dfrac{ \sqrt{7} + i \sqrt{3} }{ \sqrt{7} - i \sqrt{3}} + \dfrac{ \sqrt{7} - i \sqrt{3} }{ \sqrt{7} + i \sqrt{3} } \: is \: purely \: real}}}[/tex]

Write the equation parallel to y=−1/4x (meaning with a slope of −1/4) but passing through the point (−12,1).

Answers

Answer: y=1/4x+4

Step-by-step explanation:

Parallel means the new equation will have the same slope.

y= 1/4x+b

We don't know the b value yet but we can plug in coordinates to solve. We can use the one provided since it has to be a value of this equation.

1= 1/4(-12)+b

1= -3+b

b= 4

y=1/4x+4

Which point is the vertex?
C
B
A
None of the above

Answers

The answer is B because its where the two lines intersect or cross each other

HELP PLSSS THIS IS HARD SOMEONEEE

Answers

Answer:

correct option is f(x,y) -----> ( -y,x) option 1.

Answer:

correct option is f(x,y) -----> ( -y,x) option 1.

Step-by-step explanation:

Can someone help me with this?​

Answers

Answer:

they are correct

Step-by-step explanation:

Answer:

317m

Step-by-step explanation:

I am not sure its the perimeter (p) you need because thats what i understood.

p=2(109.7)+2(48.8)=317m

please help me, thank you! :)

Answers

Answer:

x=-4

Step-by-step explanation:

2(x+6)=4

2x+12=4

2x=4-12

2x=-8

x=-4

Answer:

x = -4

Step-by-step explanation:

First distribute 2 among everything in the parentheses. So now you'll have 2x + 12 = 4

Next subtract 12 on both sides to get -8.

Lastly divide 2 on both sides to get x = -4

Hope this helps :)

Identify the parallel lines.

Answers

Answer:

lines m and n

Step-by-step explanation:

Uhh parallel lines are basically lines that have the same slope.

There are only three lines, lines m, n, and t

It can't be t because it's traversing lines m and n

so it has to be lines m and n

Hope that helps, let me know if you have any further questions

at sunrise,the temperature outside was 5 below zero . by noon the temperature dropped 27. what was the temprature at noon

Answers

Answer:

-32

Step-by-step explanation:

hope this helps you with the question

A bank fee increased by 200% from $7.20. What is the charge for the new bank fee

Answers

Hello!

Answer:

21.6

Steps:

7.20 increase 200% =

7.20 × (1 + 200%) = 7.20 × (1 + 2) = 21.6

Simplify (3x^2y^3)^3

Answers

Answer:

27 x^( 6 )y^( 9)

Step-by-step explanation:

Find the value of f(5) for the function f(m) = 1 - 4(m/2) *

Answers

Answer:

f(m) = -9

Step-by-step explanation:

We replace m with 5 in the function.

f(m) = 1 - 4(m/2) becomes f(5) = 1 - 4(5/2)

then we solve the numbers in the parenthesis first

= 1 - 4 (5/2)

= 1 - 4 (2.5)

= 1 - 10

= -9

137.8×3.5 with explanation

Answers

Answer:

482.3

Step-by-step explanation:

because 137.8 times 3.5 is

482.3

137.8x3.5 is 482.3 because 137.8 3.5s is 482.3

A polynomial function of degree 4 with real coefficients could have -3, 1+i, 1-i, and -3,7i as its zeros. true or false

Answers

Using complex numbers concepts, it is found that the statement is false.

When a complex number is a root of a polynomial function, it's conjugate also has to be.

A complex number has the format [tex]a + bi[/tex], and it's conjugate is [tex]a - bi[/tex].

In this problem:

Real root -3.Complex-conjugate roots 1 + i and 1 - i.Complex root -3 + 7i.

The conjugate of -3 + 7i also has to be a root, which would make the polynomial of the 5th degree, as it would have 5 roots, thus, the statement is false.

A similar problem is given at https://brainly.com/question/24450834

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