The conjugate of complex number z = 3 + 2i is

Answer :

Probability = 16/18

Reduce the fraction with 2

Probability = 8/9

Answer:

[tex]\implies\boxed{\red{\sf P( not \ having\ red\ hair)=\dfrac{ 8}{9}}}[/tex]

Step-by-step explanation:

Given :-

And we need to find the probability that a person picked at random from the room does not have red hair . So for that firstly let us find how many people do not have red hair.

According to Question :-

[tex]\implies n_{(red)}+ n_{(not\ red)}= 18 \\\\\implies 2 + n_{(not\ red)}= 18 \\\\\implies n_{(not\ red)}= 18 -2 =\boxed{\red{16}}[/tex]

Hence the probability is :-

[tex]\implies P( not \ having\ red\ hair)=\dfrac{ n_{(favourable\ outcomes)}}{n_{(possible\ outcomes)}} \\\\\implies P( not \ having\ red\ hair)=\dfrac{ 16}{18} \\\\\implies\boxed{P( not \ having\ red\ hair)=\dfrac{ 8}{9}}[/tex]

Hence the required probability is 8/9 .

Answer:

549 pumps

Step-by-step explanation:

We'll begin by calculating the radius of the larger ball. This can be obtained as follow:

Circumference (C) = 71

Pi (π) = 3.14

Radius (r) =?

C = 2πr

71 = 2 × 3.14 × r

71 = 6.28 × r

Divide both side by 6.28

r = 71 / 6.28

r = 11.3 in

Next, we shall determine the volume of the larger ball.

Since a ball is spherical in shape, we shall use the formula for calculating the volume of a sphere to obtain the volume of the ball. This can be obtained as follow:

Pi (π) = 3.14

Radius (r) = 11.3 in

Volume (V) =?

V = 4/3πr³

V = 4/3 × 3.14 × 11.3³

V = 4/3 × 3.14 × 1442.897

V = 6041 in³

Finally, we shall determine the number of pumps will it take to fill the large soccer ball. This can be obtained as follow:

11 in³ = 1 pump

Therefore,

6041 in³ = 6041 in³ × 1 pump / 11 in³

6041 in³ = 549 pumps

Thus, it will take approximately 549 pumps of air to fill the large soccer ball.

Answer:

By using the pythagorean property such that GJ^2+HJ^2 = GH^2

GJ = √(GH^2-HJ^2)

GJ √(11881-8281)

GJ = √ 3600

GJ = 60.00 (ANS)

Hope it helps

[tex]sin^{-1} (sin17^{0} )[/tex] = [tex]17^{0}[/tex]

The inverse sine function (also called arcsine) is the inverse of sine function. Since sine of an angle (sine function) is equal to ratio of opposite side and hypotenuse, thus sine inverse of same ratio will give the measure of the angle.

sin ([tex]sin^{-1}x[/tex]) = x, whenever x ∈ [-1, 1] and

sin ([tex]sin^{-1}x[/tex]) is NOT defined whenever x ∉ [-1, 1].

Given

[tex]sin^{-1} (sin17^{0} )[/tex]

Cancel out [tex]sin^{-1}[/tex] and sin

[tex]sin^{-1} (sin17^{0} )[/tex] = [tex]17^{0}[/tex]

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Answer:

34

Step-by-step explanation:

all sides of a triangle add up to 180

Answer:

(1.5,6)(15,33) slope=2

Step-by-step explanation:

Answer:

y-2x=3; A(1.5, 6) B(15,33) Slope = 2

Step-by-step explanation:

First thing, you add 2x on both sides and get y=2x+3. Since the equation y=mx+b states that m is the slope, the slope is 2.

2nd step is finding the missing coordinate for a. You plug in 6 as the y in the equation y=2x+3, and then get 2x+3=6. Now it is a simple algrebraic equation and you get x=3/2 or 1.5.

The final step is to solve for B. Using the equation y=2x+3, and substituting in x as 15, you get y=30+3 which equals 33.

I hope this gave you an in depth explanation on solving these problems!

Answer:

Given that a worker earns a 3% increase in her annual salary for each of 5 years, and they plan to continue working in their position for an additional N years, if they continue to earn a 3% increase in their annual salary, to determine what statement could describe the expression that can be used to calculate the total percent increase in their annual salary from the first year to the last year the following calculation should be performed:

1 + 0.03 (interest rate) ^ N (number of years) = final interest rate

1.03 ^ N = Final interest rate

Thus, for example, if it were invested for 5 years, the equation would operate as follows:

1.03 ^ 5 = X

1.16 = X

The total percent increase in their annual salary from the first year to the last year is [tex](1.03)^n[/tex].

A percentage is a way to describe a part of a whole. such as the fraction 1/4 can be described as 0.25 which is equal to 25%.

To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.

As it is given that the annual salary of the worker increases at a rate of 3%. therefore, the salary of the worker increases compounded at a rate of 3% annually. Therefore, the salary of the worker after n number of years can be written as,

[tex]A = P(1+\dfrac{r}{100})^n[/tex]

where A is the final salary of the worker, P is the initial salary of the worker, r is the rate at which the salary is increasing, and n is the number of years.

Substituting the values in the formula,

[tex]A = P(1+\dfrac{3}{100})^n\\\\A = P(1.03)^n[/tex]

Hence, the total percent increase in their annual salary from the first year to the last year is [tex](1.03)^n[/tex].

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Answer:

r = 2

Step-by-step explanation:

2(8r + 5) = 24 + 9r

16r + 10 = 24 + 9r

16r - 9r = 24 - 10

7r = 14

r = 2

Answer:

$172.75 is the amount Ahmed has

Answer:

f(x) = x

Step-by-step explanation:

example of points on line: (40,40), (45,45), (50,50)

x-values are the same as y-values which means the line is y=x

Answer:

9

Step-by-step explanation:

3² = 3 x 3 = 9

Answer:

3) 522

4) 468

Step-by-step explanation:

hello!

3) in the question, it says the cross section is a square, and the area of PQRS is 81.

for the square, we know that the length and height have to be the same, so if the area is 81, then we know the sides are both 9 because 9*9 is 81 and they're the same numbers multiplied. (same height and length)

with the information that all 4 sides of the square is 9 and the other side is labeled 10, we can figure out the rest.

both squares : 81+81=162

both 10 by 9 sides: 90+90=180

both 10 by 9 sides (top and bottom): 90+90=180

total surface area=162+180+180=522

4) for this problem, we can see that the triangle is a right triangle.

to solve the area of the triangle, we can do (9*12)/2=108/2=54.

there are two sides with triangles, so we double 54 (54*2=108)

9 by 10 side: 90

10 by 12 side: 120

now for the last slide, theres no information on the length. the formula for the diagonal is

a^2+b^2=c^2

which is

9^2+12^2=81+144=255=15^2

with this, the area of the rectangular side gives us 10*15 which is 150.

adding it together, we get

108+90+120+150=468.

hope this helps!

Answer:

did you find the answer

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Using the graph, we pick a convenient point: (20, 180)

This point means that for 20 hours of work, Vincent is paid 180 dollars. In fraction form, we can write 20hrs/180 dollars. If we simplify the fraction by dividing both the numerator and denominator by 20 we get 1/9 AKA 1hr/9 dollars. So in 1 hour, Vinnie is paid $9.00

Have a good rest of your day

Answer:

9/4 ÷ 7/2

9/4 × 2/7

9/14

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

The equivalent expression is ~

[tex] \boxed{ \frac{9}{14} }[/tex]

[tex] \huge \boxed{ \mathfrak{Explanation}}[/tex]

Answer:

(a) PR = 55.2 cm

(b) RT = 19.7 cm

(c) <RPT = [tex]20.8^{o}[/tex]

Step-by-step explanation:

(a) to determine the value of PR, apply the Pythagoras theorem to PQR.

PQ = 45, and SP = QR = 32. So that;

[tex]/hyp/^{2}[/tex] = [tex]/Adj 1/^{2}[/tex] + [tex]/Adj 2/^{2}[/tex]

[tex]/PR/^{2}[/tex] = [tex]45^{2}[/tex] + [tex]32^{2}[/tex]

          = 2025 + 1024

          = 3049

PR = [tex]\sqrt{3049}[/tex]

     = 55.218

PR = 55.2 cm

(b) To determine RT, apply the appropriate trigonometric function to QRT.

Let RT be represented by x, so that;

Sin [tex]38^{o}[/tex] = [tex]\frac{x}{32}[/tex]

x = 32 * Sin [tex]38^{o}[/tex]

  = 32 * 0.6157

x = 19.7024

RT = 19.7 cm

(c) To determine <RPT, let the angle be represented by θ.

Sin θ = [tex]\frac{opposite}{hypotenuse}[/tex]

        = [tex]\frac{RT}{PR}[/tex]

Sin θ = [tex]\frac{19.7024}{55.218}[/tex]

         = 0.3568

θ = [tex]Sin^{-1}[/tex] 0.35568

  = [tex]20.84^{o}[/tex]

Thus, <RPT = [tex]20.8^{o}[/tex]

Answer:

37

Step-by-step explanation:

You subtract 142-132 then add 14+13 and 14+13=27 & 142-132=10

Answer:

37 :)

Step-by-step explanation:

Well, the first step you do is you do 142-132 which is (10). The Next step is to do 14+13 which is (27). Now you have 10 and 27 which you now add to get you.. (37)!

Hope this helps! ^^

Answer:

72

Step-by-step explanation:

Answer:

it will take 3 yrs for the value of camera to reach $162.

Step-by-step explanation:

Pd = P(1-R/100)^T

162 = 384(1-25/100)^T

162/384 = (3/4)^T

27/64 = (3/4)^T

(3/4)^3 = (3/4)^T

T = 3

Answer:

this represents: exopnential decay, the rate of growth or decay is equal to: 0.25, value of the camera each year is: 0.75, it will take 3 years.

Step-by-step explanation:

Answer:

13.0

Step-by-step explanation:

sin(65°) × 14.3 would give u 12.9 then u round it to the 13

Answer:

It's the second answer down : Angle B, A and C

Step-by-step explanation:

The sequence from the smallest to the largest is angle B, angle A, angle C .

A triangle is a three-sided polygon that consists of three edges and three vertices.

Given AB= 22 units

BC=16 units

AC=12 units

The property of Triangle says, in a triangle, angle opposite to the greater side have greater angle.

That is angle opposite to the shorter side have shorter angle.

Therefore, we have

Therefore,

angle opposite to side AC is angle B,

angle opposite to side BC is angle A,

angle opposite to side AB is angle C,

Therefore, the sequence from the smallest to the largest is angle B, angle A, angle C .

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Answer:

B is correct

Step-by-step explanation:

Answer:

M > 3

Step-by-step explanation:

4M > 12

M > 3

Answer:

um... you can have M as 4. 4 x 4 =16

Answer:

sorry i dont know the answer

Step-by-step explanation:

Answer:

sorry Wala po akong answer ehhh sorry