19 POINTS evaluate the expression 2n, if n = 4
ANWSER:
o 8
o 6
o 24
o 2

Answer:74613

Step-by-step explanation:

n!/r!(n-r)!

22!/6!(22-6)!

=74613

Answer:

a) |z+w|² cannot be uniquely determined from the information provided.

b) |zw|² = [|z| × |w|]² = (4×2)² = 64.

c) |z+w|² cannot be uniquely determined from the information provided.

d) |z/w|² = [|z|/|w|]² = (4/2)² = 4

Step-by-step explanation:

z & w are complex numbers with magnitudes

|z| = 4

|w| = 2

We are the told to find

|z + w|²

|zw|²

|z - w|²

|z/w|²

Let the complex numbers be

z = x + iy

w = a + ib

|z| = √(x² + y²) = 4

|w| = √(a² + b²) = 2

|z|² = x² + y² = 16

|w|² = a² + b² = 4

z+w = (x + iy) + (a + ib) = (x + a) + i(y + b)

|z+w|² = (x + a)² + (y + b)² = x² + 2ax + a² + y² + 2by + b²

= (a² + b²) + (x² + y²) + 2ax + 2by

= |w|² + |z|² + 2ax + 2by

= 4 + 16 + 2ax + 2by

= 20 + 2(ax + by)

This cannot be determined from the information provided.

zw = (x + iy)(a + ib) = ax + i(bx + ay) - by

= (ax - by) + i(bx + ay)

|zw|² = a²x² + b²y² - 2abxy + b²x² + a²y² + 2abxy

= a²x² + b²y² + b²x² + a²y²

= a²(x² + y²) + b²(x² + y²)

= (a² + b²)(x² + y²)

= |w|² × |z|²

= 4×16

= 64

c) z-w = (x + iy) - (a + ib) = (x - a) + i(y - b)

|z-w|² = (x - a)² + (y - b)²

= x² - 2ax + a² + y² - 2by + b²

= (a² + b²) + (x² + y²) - 2ax - 2by

= |w|² + |z|² - 2ax - 2by

= 4 + 16 - 2ax - 2by

= 20 + 2(ax + by)

This cannot be determined from the information provided.

d) z/w = (x + iy)/(a + ib)

Rationalizing by multiplying numerator and denominator by (a - ib)

(z/w)= [(x + iy)(a - ib)/(a + ib)/(a - ib)]

= [ax - by + i(ay - bx)]/(a² + b²)

|z/w|² = [(ax + by)² + (ay - bx)²]/(a² + b²)²

= [a²x² + b²y² + 2abxy + b²x² + a²y² - 2abxy]/(a⁴ + b⁴ + 2a²b²)

= [a²x² + b²y² + b²x² + a²y²]/[(a² + b²)² - 2a²b² + 2a²b²]

= [(a² + b²)(x² + y²)]/[(a² + b²)²]

= [(x² + y²)/(a² + b²)]

= |z|²/|w|²

= (4/2)²

= 4

Hope this Helps!!!

Answer:

133

Step-by-step explanation:

Answer is 133

[tex]answer \\ = 133 \\ please \: see \: the \: attached \: picture \: for \: full \: solution \\ hope \: it \: helps[/tex]

Answer: (b - 4)(b - 3); b = 4 and 3

Step-by-step explanation:

ima assume these are exponents since you didnt care to correctly write the equation.

What two numbers multiply to equal 12, but add to equal -7? That's -4 and -3

So the factored form of this trinomial is (b - 4)(b - 3) = 0. Make each of these expressions equal to 0 in order to get your answer.

Answer:

P = 10a +2b+12

Step-by-step explanation:

P = 2 (l+w) for a rectangle

P = 2 ( 4a+b + a+6)

Combine like terms

P = 2(5a+b+6)

Distribute

P = 10a +2b+12

Answer:

Given below

Hope it helps

Step-by-step explanation:

Perimeter= 2(l+b)

= 2(4a+b+a+6)

= 2(5a+b+6)

= 10a+2b+12 cm^2

Answer: yes

Step-by-step explanation:

They are both equal to 4/5

Answer:

45 minutes

Step-by-step explanation:

75% is the same as [tex]\frac{3}{4}[/tex]. This means that we can multiply 60 by  [tex]\frac{3}{4}[/tex] to find 75% of 60.

[tex]60*\frac{3}{4} \\\\\frac{180}{4} \\\\\frac{90}{2}\\\\45[/tex]

Answer:

45 minutes

Step-by-step explanation:

Of means multiply

75% * 60

Change to a decimal

.75 * 60

45

45 minutes

Answer:

3 the patten is the previous subtracted about decrease by 3

Step-by-step explanation: the pattern decrease the number subtracted by 3 so it starts with 15 and goes to 12 then to 9 so the last one would be six and 9 - 6 = 3

Answer:

The side lengths of triangle ABC are 6, 6.67 and 5.33

Step-by-step explanation:

In this question, we are interested in calculating the lengths of triangle ABC

ED: AC = 3:4

4.5:AC = 3:4

4.5/AC = 3/4

3AC = 4 * 4.5

3AC = 18

AC = 18/3 = 6

EB:AB = 3:4

5/AB = 3/4

3AB = 4 * 5

3AB = 20

AB = 20/3 = 6.67

DB:CB = 3/4

4/CB = 3/4

3CB = 4 * 4

CB = 16/3 = 5.33

Answer:

x=6

Step-by-step explanation:

You can reach this answer by doing

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

If you do this equation you will get 6 as your answer.

Hope this helps :)

Answer:

4224

Step-by-step explanation:

Here, we want to calculate the sum of the first 44 digits

Term a which is first digit is 10

common difference which is difference of terms = 14-10 = 18-14 = 4

Now the nth term of an arithmetic sequence is

a + (n-1)d

44th term means n = 44

10 + (44-1)4

10 + 43(4)

10 + 172 = 182

To find the sum, we use the formula

Sn = n/2[a + L]

where a is the first term and L is the 44th term

Sn = 44/2 (10 + 182)

Sn = 22(192)

Sn = 4,224

Answer:

b) 68%

The percentage of the parts will have lengths between 3.8 in. and 4.2 in

P( 3.8 ≤ x ≤ 4.2) = 0.6826 = 68 %

Step-by-step explanation:

Let 'X' be the normally distributed

mean 'μ'= 4 inches

standard deviation 'σ' = 0.2 inches

Case(i):-

when x₁ = 3.8 inches

[tex]Z_{1} = \frac{x_{1}-mean }{S.D} = \frac{3.8-4}{0.2} = -1[/tex]

Case(ii):-

when  x₂= 3.8 inches

[tex]Z_{2} = \frac{x_{2}-mean }{S.D} = \frac{4.2-4}{0.2} = 1[/tex]

The probability of the parts will have lengths between 3.8 in and 4.2 in

[tex]P( 3.8\leq x\leq 4.2) = P(-1\leq z\leq 1)[/tex]

                        = P(Z≤1) - P(Z≤-1)

                        =  0.5 +A(1) -(0.5-A(1)

                       = 2 A(1)

                       = 2×0.3413

                      = 0.6826

Conclusion:-

The percentage of the parts will have lengths between 3.8 in. and 4.2 in

P( 3.8 ≤ x ≤ 4.2) = 0.6826 = 68 %

Answer:

B

Step-by-step explanation:

E2020

Answer:

£216

Step-by-step explanation:

Total number of people:

Total payment:

Teacher earns in total per given week:

Answer:

It's B. (2x+5) (x+4)

Answer:

b

Step-by-step explanation:

2x²+13x+20

You can just try all the answers if you'd like and see which one equals 2x²+13x+20.

Using FOIL for all of them:

a. (2x-5)(x-4) = 2x²-8x-5x+20 = 2x²-13x+20

b. (2x+5)(x+4) = 2x²+8x+5x+20 = 2x²+13x+20

c. (2x+2)(x+10) = 2x²+20x+2x+20 = 2x²+22x+20

d. is obviously not correct since we already have an answer.

Our answer is b. (2x+5)(x+4)

Answer:

Step-by-step explanation:

i hope

the the answer is 2ab3(a4+3b3−7ab)

hope it helps.

sorry if it wrong

-Delilah

Answer:

y = 8(x-5)^2 -232

Step-by-step explanation:

Factor out the 8 to get

y = 8(x^2-10x-4)

y = 8(x-5)^2 -232

Answer:

y = 8 (x - 5)^2 - 232

Step-by-step explanation:

Dividing the whole equation by 8, we get:

y = 8 (x^2 - 10x - 4)

y = 8 (x - 5)^2 - 232

Hope this helps!

Answer:

143

Step-by-step explanation:

Since the values of x y and z are given

Substitute the value in the polynomial, so it'll become,

x+yz+xyz

= (3)+(-5)*(-7)+(3)*(-5)*(-7)

= 3+35+(3)*(-7)*(-5)

{Two negatives when multiplied becomes positive}

=3+35+3*35

= 3+35+105

=143

_________________________________

Solution,

30% of 400

= 30/100*400

=120

120 yellow water bottles were in the shipment.

Hope it helps

Good luck on your assignment

__________________________________

Answer:

81.64

Step-by-step explanation:

2(3.14)=6.28

6.28*13=81.64

Plug r into the equation provided...

c = 2(3.14)(13)

c = 81.64cm

Answer:

Option (D).

Step-by-step explanation:

In the figure attached,

An exponential function has been graphed with certain points marked on it.

To find the average rate of change for this function between the given interval we will use the formula,

Average rate of change = [tex]\frac{f(x_2)-f(x_1)}{y_2-y_1}[/tex]

where [tex]f(x_2)[/tex] = value of the function at x = 4

[tex]f(x_1)[/tex] = value of the function at x = 2

By substituting these values in the formula,

Average rate of change = [tex]\frac{16-4}{4-2}[/tex]

                                        = [tex]\frac{12}{2}[/tex]

                                        = 6

Therefore, Option D will be the answer.

Answer:

even = 1/2

prime = 1/2

multiple of 5 = 1/6

Step-by-step explanation:

probability is the chances of obtaining a certain result out of many attempts.

when rolling a die, the maximum number of results you can get is 6

Then, calculate how many times each of the occurrences appear(even, prime or multiples of 5)

Even = There are only 3 even numbers from 1 to 6

Prime: There are only 3 primes from 1 to 6

Multiples of 5 = There is only one multiple of 5.

Now you present each of this out of 6:

Even: 3/6 = 1/2

Prime: 3/6 = 1/2

Multiple of 5 = 1/6

This can also be presented as a decimal or percentage:

Even: 50% = 0.5

Prime: 50% = 0.5

Multiple of 5 = 16.67% = 0.16

Hope this helps.

Good Luck

Answer:

[tex]\dfrac{2s^3+136}{s}[/tex]

Step-by-step explanation:

Let the side length of the square base =s feet

Let the height of the box = h

Given that the volume of the box = [tex]34$ ft^3[/tex]

Volume of the box =[tex]s^2h[/tex]

Then:

[tex]s^2h=34$ ft^3\\$Divide both sides by s^2\\h=\dfrac{34}{s^2}[/tex]

Surface Area of a Rectangular Prism =2(lb+bh+lh)

Since we have a square base, l=b=s feet

Therefore:

Surface Area of our closed box[tex]= 2(s^2+sh+sh)[/tex]

[tex]S$urface Area= 2s^2+4sh\\Recall: h=\dfrac{34}{s^2}\\$Surface Area= 2s^2+4s\left(\dfrac{34}{s^2}\right)\\=2s^2+\dfrac{136}{s}\\$Surface Area in terms of length only=\dfrac{2s^3+136}{s}[/tex]

Answer:

the answer is 0.84

Step-by-step explanation:

assume the two numbers are on a number line and take the absolute value of their difference

Answer:

you are assuming that everyone in the class took the test. 33 people took the test but there could be more in the class but they were just not there for the test.

Answer:

first one and the second one.

Step-by-step explanation:

nothing ：)

Answer:

this is right

Answer:

see explanation

Step-by-step explanation:

This polynomial is irreducible, that is cannot be factored.

4x² + 25y² ← is a prime polynomial

Answer:

1, the polynomial itself

Step-by-step explanation:

This is a prime polynomial since the terms have no common factor. The only factors it has are 1 and 4x2+25y2 (the number itself)

===========================================================

Work Shown:

1/500 = 0.002 is the probability of winning $390

3/500 = 0.006 is the probability of winning $230

16/500 = 0.032 is the probability of winning $170

Multiply the probabilities with their respective winnings

0.002*390 = 0.78

0.006*230 = 1.38

0.032*170 = 5.44

Then add up those results

0.78+1.38+5.44 = 7.60

which is the expected value.

Side note: This game is not a fair game because mathematically a "fair game" is defined as such where the expected value is 0; ie, neither the player nor the dealer win and things break even.

Answer:

Step-by-step explanation:

[tex]2*(3+4x) *2 -5\\6+8x*2-5\\16x =-6-5\\16x = -11\\x = 11/16[/tex]