The inverse of Fx) is a function.
True or False

The question is an illustration of permutation and combinations.

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

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Answer:

5.25 miles.

Step-by-step explanation:

1) Rosa spends 10 minutes in 3/4=0.75 miles, then

2) Rosa can spend 70 in 0.75*7=5.25 miles.

Answer:

5.3 miles

Step-by-step explanation:

3miles/40min =x miles/70min

cross multiply the fractions

3*70 = 40*x

210=40x

divide by 40 on both sides

210/40 = 5.25

Sorry for the wait.....

Hope this helps and Happy Halloween!!!!

The effective rate for a payday loan is 3.21%.

The amount that the lender charges the borrower over and beyond the principal amount is referred to as the interest rate. A person who deposits money in a bank or other financial institution also earns additional income in terms of the recipient, known as interest, taking into account the time value of money.

Given:

Amount Financial = 430

Financial Charge= 53.29

Term of loan= 14 days

So, the effective rate will be

= (53.29/430 ) x 365

= 45.2345

and, =45.2345/14

= 3.21

Hence, the effective rate is 3.21%.

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Answer:

x = 11 ; y =13

Step-by-step explanation:

3x - 2 y = 7    -------------(I)

        y = x + 2  -----------(II)

Substitute y = x + 2 in equation (I)

3x - 2(x + 2) = 7

3x - 2*x + 2*(-2) = 7

3x - 2x - 4 = 7

      x - 4 = 7

           x = 7 + 4

x = 11

Plugin x = 11 in equation(II)

y = 11 + 2

y = 13

Answer:

x =-26

Step-by-step explanation:

-15x = 390

Divide each side by -15

-15x/-15 = 390/-15

x =-26

Answer:

X = -26

Step-by-step explanation:

Divide both sides by -15.

390/-15 = -26

X is equal to -26.

Step-by-step explanation:

8 + b/2 = 6

8 more than the quotient of is 6

a number and 2

Answer:

A=6 cm, D=4.5cm and E=80 cm

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

3 x 5 =15 + 3 = 18. so 18 over 5 divided by 2 over 5. you flip the 2nd fraction and multiply. the 5s cancel. 18 ÷2 = 9

Answer:

- 5198/11

Step-by-step explanation:

Answer: 2

Step-by-step explanation:

Perimeter is all the sides added up together so a square has 4 sides. 8/4= 2

(about) 6.6 or 6 2/3

Answer:

see explanation

Step-by-step explanation:

The perimeter is the sum of the sides of the figures

(1)

The figure has 5 congruent sides , then perimeter P

P = 5 ([tex]\frac{2}{5}[/tex] x + 1) ← multiply each term in the parenthesis by 5

  = 2x + 5

(2)

There are 4 congruent sides of ([tex]\frac{5}{2}[/tex] x - y) and 8 of y , then

P = 4([tex]\frac{5}{2}[/tex] x - y) + 8y ← distribute parenthesis by 4

  = 10x - 4y + 8y ← collect like terms

  = 10x + 4y

(3)

P = 2([tex]\frac{2a-b}{2}[/tex] ) + 2([tex]\frac{3b}{2}[/tex] ) + 2a ← distribute parenthesis

  = 2a - b + 3b + 2a ← collect like terms

  = 4a + 2b

Answer:

C=22

Step-by-step explanation:

8+9+10+11+x divided by 5 gives 12

38+x divide by five gives 12

12×5=60

38+x=60

x=22

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Answer:

p = 18

Step-by-step explanation:

4(p-7) = 44

The operations in order are to distribute first, 4p - 28 = 44

Isolate the variable, 4p = 72

and divide for the answer, p = 18

P stands for pictures, the number of pictures that can be saved to your photo stream at once is 18.

Answer:

y = x + 2

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 2, 1) and (x₂, y₂ ) = (- 1, 2) ← 2 points on the line

m = [tex]\frac{2-1}{-1-(-2)}[/tex] = [tex]\frac{1}{-1+2}[/tex] = [tex]\frac{1}{1}[/tex] = 1

The line crosses the y- axis at (0, 2 ) ⇒ c = 2

y = x + 2 ← equation of line

Answer:

A is 30 inches

b is Yes

c

Step-by-step explanation:

Answer:

One solution

Step-by-step explanation:

3x+x+2=8x-4x+2

Combine like terms.

4x+2=4x+2

Solve for x

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

2=2

This equation has one solution because 2 only equals 2 and will not equal any other number.

Answer:

7.5×10^-3

Step-by-step explanation:

[tex] \frac{ 0.027}{64000} = \frac{2.7 \times{10}^{ - 2} }{6.4 \times {10}^{4} } [/tex]

due to the law of indices :

[tex] = 4.21875 \times 10 ^{ - 7} [/tex]

don't forget

(0.027/64000)⅓

so :

[tex] ({4.21875 \times {10}^{ - 7} })^{ \frac{1}{3} } [/tex]

i.e third root of the answer above

[tex] = 7.5 \times {10}^{ - 3} [/tex]

Answer:

$6.69

Step-by-step explanation:

Since we know the total cost of 5 pairs of gloves, all we have to do to find the unit price is divide the total cost by how many gloves were are being sold:

33.45 / 5 = 6.69

Therefore, one pair of gloves costs $6.69

Hope this helps :)

Step-by-step explanation:

5(3x+2)-2(4x-1)

15x+10-8x+2

7x+12

Answer:

ummm?

Step-by-step explanation:

Answer:

Something

Step-by-step explanation:

I have no idea what u just asked

Answer: To do so, reflect it on the Y axis and then move it 4 times.

Step-by-step explanation:

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: uoᴉʇnlos ɹnoʎ sᴉ ǝɹǝɥ

Answer:

the answer is the 3rd one.

Step-by-step explanation:

Answer:

a(0,-8)

Step-by-step explanation:

4x0=0

0--8= 8