Convert the polar representation of this complex number into its standard form: z=4(cos5pi/6 + i sin 5pi/6)

Step-by-step explanation:

For Slant Height (l)

(l)^2=(3)^2+(4)^2

Using Pythagoras Theroem,

(l)^2=9+16

(l)^2=25

l=5cm

For lateral surface area (pi*r*l)

pi*4*5

20pi cm^2

The lateral area of the cone in terms of π, given that the cone has a radius of 4 cm is 20π cm²

First, we shall obtain the slant height of the cone. This is shown below:

L² = r² + h²

L² = 4² + 3²

L² = 16 + 9

L² = 25

Take the square root of both side

L = √25

= 5 cm

Finally, we shall obtain the lateral area of the cone. This is shown below:

LA = πrL

= π × 4 × 5

= 20π cm²

Thus, the lateral area of the cone is 20π cm²

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Answer:

  about 626.1 ft

Step-by-step explanation:

The geometry of the problem can be modeled by a right triangle. The given angle is opposite the given side, and we are asked to find the hypotenuse. The relevant trig relation is ...

  Sin = Opposite/Hypotenuse

__

Solving for the hypotenuse, we get ...

  Hypotenuse = Opposite/Sin

  cable length = (balloon height)/sin(53°) = (500 ft)/0.79864

  cable length ≈ 626.1 ft

The expected score of each at bat if he earns 1 point for each hit that is not a home run and 5 points for each home run is 0.57

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words the probability is the number that shows the happening of the event.

Number of bats = 369

Number of hits = 127

Number of home runs = 21

The probability of a hit:

[tex]=\frac{127}{369}[/tex]   (includes home run)

The probability of home run:

[tex]=\frac{21}{369}[/tex]

The probability of hit run(without home run)

[tex]=\frac{127}{369}-\frac{21}{369}[/tex]

[tex]=\frac{106}{369}[/tex]

The probability of no hit:

[tex]=\frac{369-127}{369}[/tex]

[tex]=\frac{242}{369}[/tex]

For home run, the score will be 5 points.

If not, a home run score will be 1 points.

If Miguel does not get hit, score will be zero point.

Expected value of Miguel hit at each bat is (without home run):

For 5 hit:

[tex]=\frac{106}{369}[/tex]

For 21 home runs, the points will be 21×5 = 105  (5 points for each home run)

The expected value for this:

[tex]\frac{105}{369}[/tex]

Adding both expected hits, we get:

[tex]=\frac{106}{369}+\frac{105}{369}[/tex]

[tex]=\frac{211}{369}[/tex]

= 0.571 ≈ 0.57

Thus, the expected score of each at bat if he earns 1 point for each hit that is not a home run and 5 points for each home run is 0.57

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Answer:

0.57

Step-by-step explanation:

Answer:

I believe it is 6 but I'm not sure

Step-by-step explanation:

Sorry I am unsure

Step-by-step explanation:

the function for x≥—1 is x²—3

so f(3) = 3²—3=9—3=6

Answer:

12

Step-by-step explanation:

Answer:

3+3+6=12

Step-by-step explanation:

the sides are both3 and bottomed is 6

Answer:

18.9

Step-by-step explanation:

Answer:

x = 2-√13/3

Step-by-step explanation:

[tex]\text{Given that,}\\\\1-\cos A = \dfrac 12\implies \cos A = 1-\dfrac 12 = \dfrac 12\\\\\text{L.H.S}\\\\=\tan^2 A + 4 \sin^2 A\\\\=\dfrac{\sin^2 A}{\cos^2 A}+4(1-\cos^2 A)\\\\\\=\dfrac{1-\cos^2 A}{\cos^2 A} +4-4\cos^2 A\\\\\\=\dfrac{1-\left( \dfrac 12 \right)^2 }{\left(\dfrac 12 \right)^2 } +4 -4 \left( \dfrac 12 \right)^2\\\\\\=\dfrac{1- \dfrac 14}{\dfrac 14}+4-4\cdot \dfrac 14\\\\\\=\dfrac{\tfrac 34}{\tfrac 14}+4-1\\\\\\=\dfrac 34 \cdot 4 +3\\\\=3+3\\\\=6\\\\=\text{R.H.S}[/tex]

Answer:

$216

Step-by-step explanation:

Find how much Mary made per hour by dividing 144 by 8 to get 18. Then, multiply that number by 12 which $216

Answer:

$216

Step-by-step explanation:

First, find out what Mary makes every hour. To find this, we divide 144 by 8.

144/8 = $18

This means that Mary makes $18 per hour.

Now, we find out how much Mary would make if she worked for 12 hours:

x = # of hours worked

18n

18(12)

$216

Therefore, Mary would make $216 in 12 hours.

Hope this helps!

So first, lets caculate how much you get in one day

10x7= 70$

So, in one day you make 70$.

Since we make 70$ in one day, we need to find out if we worked all week.

70x7 = 490$

So in one week,we make $490.

~NatLikesAnime~

The expression that represents the volume of the prism is x²(x-2).

Given side of the base =[tex]x[/tex]

So, the area of the base =[tex]x^{2}[/tex]

Given the height of the prism = [tex]x-2[/tex]

The volume of the prism with base area A and height h is Ah.

So, the volume of the given prism with the base area [tex]x^{2}[/tex] and height [tex](x-2)[/tex] will be:

V= [tex]x^{2} *(x-2)[/tex]

V= [tex]x^{2} (x-2)[/tex]

Hence, the expression that represents the volume of the prism is x²(x-2).

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Answer:

its C trust me

Step-by-step explanation:

Answer:

Proportional relationships are relationships between two variables where their ratios are equivalent.

So if one of your answers have equivalent ratios, that is your answer

Check the picture below.

[tex]\textit{surface area of a cylinder}\\\\ SA=2\pi r(h+r)~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=3\\ h=10 \end{cases}\implies \begin{array}{llll} SA=2\pi (3)(10+3) \\\\\\ SA=6\pi (13)\implies SA=78\pi \\\\\\ SA\approx 245.04 \end{array}[/tex]

Answer:

[tex]78\, \pi[/tex].

Step-by-step explanation:

A cylinder of height [tex]h[/tex] and radius [tex]r[/tex] could be unrolled into:

The radius of each circle is the same as the radius of the cylinder, [tex]r[/tex].

The height of the rectangle is the same as the height of the cylinder, [tex]h[/tex].

The width of this rectangle would be [tex](2\, \pi\, r)[/tex], same as the circumferences of the two circles. The reason is that when this rectangle is rolled to build the cylinder, the top and bottom edges of the rectangle would wrap around the circumference of the two circles.

The area of each circle would be [tex]\pi\, r^{2}[/tex]. Note that there are two such circles, one at the top of the cylinder and one at the bottom.

With a height of [tex]h[/tex] and a width of [tex](2\, \pi\, r)[/tex], the area of the rectangle on the side would be [tex](2\, \pi\, r)\, h[/tex]. Add these areas up to find the total surface area of this cylinder:

[tex]\begin{aligned}& \text{(Surface Area of the Cylinder)} \\ =\; & (\text{Surface area of circle on the top}) \\ & + (\text{Surface area of circle at the bottom}) \\ & + (\text{Surface area of rectangle on the side}) \\ =\; & \pi\, r^{2} + \pi\, r^{2} + (2\, \pi\, r)\, h \\ =\; & 2\, \pi\, r^{2} + (2\, \pi\, r)\, h \end{aligned}[/tex].

For the cylinder in this question, [tex]h = 10[/tex] whereas [tex]r = 3[/tex]. The surface area of this cylinder would be:

[tex]\begin{aligned}& 2\, \pi\, r^{2} + (2\, \pi\, r) \, h \\ =\; & 2 \,\pi \times 3^{2} + (2\, \pi\times 3) \times 10 \\ =\; & 78\, \pi\end{aligned}[/tex].

Answer:

8 is 5/2, 9 is an undefined slope

Step-by-step explanation:

8 rise 5 and runs 2 and 9 is a vertical line so there is no slope meaning its undefined.

Answer:

it would mean that the anwser is positive

Step-by-step explanation:

Answer:

1) Y

2) Y

3) N

4) N

5) N

steps

1) How many bananas did Joe eat yesterday?

The word "many" tells you that its talking about variability.

2) What is the population of Austin, Texas?

The phrase "What is the population..." tells you that its talking about variability.

3) What kind of sandwiches does your class like?

Doesn't talk about variability.

4) What is the name of your teacher?

Doesn't talk about variability.

5) How much do televisions cost?

Doesn't talk about variability.

(YYNNN)

The direct variation of x to y implies that x and y increases at the same time, and the formula of x in terms of z is [tex]x = 4z^3[/tex]

The direct proportion of x to y is represented as:

[tex]x\ \alpha\ y^2[/tex]

As an equation, we have:

[tex]x\ =\ ky^2[/tex]

The direct proportion of y to z is represented as:

[tex]y\ \alpha\ z^3[/tex]

As an equation, we have:

[tex]y\ =\ kz^3[/tex]

Square both sides

[tex]y^2 = k^2z^3[/tex]

Substitute [tex]y^2 = k^2z^3[/tex] in [tex]x\ =\ ky^2[/tex]

[tex]x =k^3z^3[/tex]

When z = 2, x = 32.

So, we have:

[tex]32 =k^3 * 2^3[/tex]

Evaluate

[tex]32 =k^3 * 8[/tex]

Divide both sides by 8

[tex]k^3 =4[/tex]

Substitute [tex]k^3 =4[/tex] in [tex]x =k^3z^3[/tex]

[tex]x = 4z^3[/tex]

Hence, the formula of x in terms of z is [tex]x = 4z^3[/tex]

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It is Given that two lines segment, AC and BD bisect each other at C.

The missing statement is ∠ACB ≅ ∠ECD

Two triangles are said to be congruent if the length of the sides is equal, a measure of the angles are equal and they can be superimposed.

Given two lines segment, AC and BD bisect each other at C.

We have to prove that ΔACB ≅ ΔECD

In triangle ACB and ECD

AC=CE    (Given)

BC=CD   (Given)

so, as seen in options the angle ∠ACB ≅ ∠ECD due to vertically opposite angles

hence, the missing statement is ∠ACB ≅ ∠ECD

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Answer:

C.∠ACB ≅ ∠ECD

Step-by-step explanation:

Answer:
7

Step-by-step explanation:

because if you spinned it , it has a 1/5 chance, if we divide 35 by 5 we can see its 7 meaning she could exect a average of 7 spins.

Answer:

40%

Step-by-step explanation:

20+45=60

100-60=40

Answer:

ill say C too

Step-by-step explanation:

Answer:The answer is 400

I hope this helps have a great day!

Step-by-step explanation:

Answer:

-3

Step-by-step explanation:

10x=-33+3 isolate the variable

10x=-30 divide by 10

X=-3

x=-3

Hope it helps.

Do comment if you have any query.

Answer:

O C. x = 3, y = -6

Step-by-step explanation:

Take Equation 1 and equate to x.

Now, substitute in Equation 2.

Answer:

C)  x = 3, y = -6

Step-by-step explanation:

[tex]\textsf{Equation 1}:x-2y=15[/tex]

[tex]\textsf{Equation 2}:2x+4y=-18[/tex]

Rewrite Equation 1 to make x the subject:

[tex]\implies x=15+2y[/tex]

Substitute into Equation 2 and solve for y:

[tex]\implies 2(15+2y)+4y=-18[/tex]

[tex]\implies 30+4y+4y=-18[/tex]

[tex]\implies 8y=-48[/tex]

[tex]\implies y=-6[/tex]

Substitute found value of y into Equation 1 and solve for x:

[tex]\implies x-2(-6)=15[/tex]

[tex]\implies x+12=15[/tex]

[tex]\implies x=3[/tex]

Therefore, the solution to the system of equations is:

x = 3, y = -6

Answer:  

[tex]\mathrm{Slope = \dfrac{1}{2}}[/tex]

Step-by-step explanation:

To find the slope of a graph, we use the formula below:

[tex]\mathrm{m =\dfrac{y\x_{2}-y\x_{1}}{x\y_{2}-x\y_{1}}}[/tex]

m = slope

(x1, y1) = coordinates of first point in the line

(x2, y2) = coordinates of second point in the line

Step 1: Find any two points on the line

Lets choose: (0, 3) and (2, 4)

Step 2: Put these points into the slope formula

[tex]\mathrm{m =\dfrac{y\x_{2}-y\x_{1}}{x\y_{2}-x\y_{1}}}[/tex]

Step 3: Substitute points into formula

[tex]\mathrm{m =\dfrac{4-3}{2-0}}[/tex]

Step 4: Subtract 3 from 4 and 0 from 2

[tex]\mathrm{m =\dfrac{1}{2}}[/tex]

----------------------------------------------------------------------------------------------------------

Another way you could easily do this is:

Step 1:  Find two ponts on the line

For this problem, let's use (0, 3) and (2, 4)

Step 2: Then from the first point, how much do you need to go up and to the left or right to get to the second point

For this problem, we start on the on the point (0, 4) and go up by 1 and then to the right by 2

Step 3: Then you do rise over run to get the slope

The slope is rise over run:

Rise = 1

Run = 2

So, the slope is 1/2

________________________________________________________[tex]\mathrm{Answer:\dfrac{1}{2}}[/tex]                                                                                                                     ----------------------------------------------------------------------------------------------------------    

Answer:

g(x) = x² - 6

h(x) = x² + 3

   g(x) = h(x) + k

 x² - 6 = (x² + 3) + k

 x² - 6 = x² + 3 + k

- x²       - x²

     -6 = 3 + k

    - 3  - 3

     -9 = k

The value of k is -9.

Step-by-step explanation:

MathPapa.com

Answer:

106.6 minutes

Step-by-step explanation:

49.2/6 = 8.2

8.2x13 = 106.6

Answer:

the sum of 6 and a number g

Answer:

4800

Step-by-step explanation:

→ Find how 15yr periods there are in 45 years

45 ÷ 15 = 3

→ Substitute this value as x into the equation

75 × 4³ = 4800