find the area of the figure. use 3.14 for pi

Answer:

Sandra's speed was consistent and persistent she proved it by lining up the segments she placed on the graph and at what time as well.

Answer:

I can't see it...

Step-by-step explanation:

Can you ask me the question in the comments?

Answer:

Step-by-step explanation:

Complex numbers polar multiplication form:

\(\boxed{z_{1}z_{2}=r_{1}*r_{2}(Cos \ (\theta_{1}+ \theta_{2})+iSin \ (\theta_{1}+ \theta_{2})}\)

z₁ = 2 (Cos 60 + i Sin 60)    & z₂ = 8(Cos 150 + i Sin 150)

z₁z₂= 2*8 (Cos [60+150] + i Sin [60+150])

     = 16 (Cos 210 + i Sin 210)     Option C

2) Point A  :   3 - 5i   Option A

The x-axis represent real part and the y-axis represent imaginary part.

4) z = -5√3 -i 5

x = -5√3  & y = -5

\(r=\sqrt{x^{2}+y^{2}}\\\\ = \sqrt{(-5\sqrt{3})^{2}+(-5)^{2}}\\\\ = \sqrt{25*3 + 25}= \sqrt{75+25}\\\\ = \sqrt{100}\\\\r = 10\)

\(\theta = tan^{-1} \ \dfrac{y}{x}\\\\\\=tan^{-1} \ \dfrac{-5}{-5\sqrt{3}}\\\\\\= tan^{-1} \ \dfrac{1}{\sqrt{3}}\)

\(\sf \theta = 30^ \circ\)

Theta lies in third quadrant

Ф = 180 + 30

Ф = 210°

z = 10(Cos 210° + i sin 210°)

Answer:

See below for answers and explanations

Step-by-step explanation:

Problem 1

To multiply two complex numbers in polar form, we use the rule \(z_1z_2=r_1r_2[cos(\theta_1+\theta_2)+isin(\theta_1+\theta_2)]\), so:

\(z_1z_2=r_1r_2[cos(\theta_1+\theta_2)+isin(\theta_1+\theta_2)]\\z_1z_2=(2)(8)[cos(60^\circ+150^\circ)+isin(60^\circ+150^\circ)]\\z_1z_2=16(cos210^\circ+isin210^\circ)\)

This means that C is the correct answer

Problem 2

We treat a complex plane almost exactly like a Cartesian plane where the x-axis is the real axis and the y-axis is the imaginary axis. Hence, point A is located at (3,-5) if this were a Cartesian plane, but since it is a complex plane, it would be read as 3-5i, making A the correct answer

Problem 3

The first part of the problem is really just using the distance formula, treating the real and imaginary parts of the complex numbers as coordinate points:

\(\sqrt{(6-2)^2+(7-(-5))^2}\\\sqrt{(4)^2+(7+5)^2}\\\sqrt{16+(12)^2}\\\sqrt{16+144}\\\sqrt{160}\\4\sqrt{10}\)

The second part of the problem is simple enough, again, treating the real and imaginary parts of the complex numbers as coordinate points:

\(\bigr(\frac{2+6}{2},\frac{-5+7}{2}\bigr)=\bigr(\frac{8}{2},\frac{2}{2}\bigr)=(4,1)=4+i\)

Thus, A is the correct answer

Problem 4

Rectangular Form: \(z=a+bi\)

Polar/Trigonometric Form: \(z=r(cos\theta+isin\theta)\)

Conversion Rules: \(r=\sqrt{a^2+b^2}\\\theta=tan^{-1}(\frac{b}{a})\)

Calculations:

\(r=\sqrt{(-5\sqrt{3})^2+(-5)^2}\\r=\sqrt{75+25}\\r=\sqrt{100}\\r=10\)

\(\theta=tan^{-1}(\frac{-5}{-5\sqrt{3}})\\\theta=tan^{-1}(\frac{1}{\sqrt{3}})\\\theta=30^\circ\)

Because the complex number is located in Quadrant III, then the reference angle is \(30^\circ\) counterclockwise from the negative x-axis, which is equal to \(180^\circ+30^\circ=210^\circ\)

Thus, the complex number is trigonometric form is \(z=10(cos210^\circ+isin210^\circ)\), making C the correct answer

Problem 5

This is just a simple evaluation:

\(6\biggr(cos\frac{5\pi}{6}+isin\frac{5\pi}{6}\biggr)\\ \\6\biggr(-\frac{\sqrt{3}}{2}+\frac{1}{2}i\biggr)\\ \\-3\sqrt{3}+3i\)

Treating the real and imaginary parts of the complex number as coordinate points, we can see that the best point is Q.

Answer:

Step-by-step explanation:

search it up

Using the radius of the Ferris wheel and the angle between the two positions, the time spent on the ride when they're 28 meters above the ground is 12 minutes

The radius of the Ferris wheel is 30 / 2 = 15 meters.

The highest point on the Ferris wheel is 15 + 4 = 19 meters above the ground.

The time spent higher than 28 meters is the time spent between the 12 o'clock and 8 o'clock positions.

The angle between these two positions is 180 degrees.

The time spent at each position is 10 minutes / 360 degrees * 180 degrees = 6 minutes.

Therefore, the total time spent higher than 28 meters is 6 minutes * 2 = 12 minutes.

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We have the next comparations

-3 is greater than -7 --- -3>-7 -- correct

-9 is greater than 4 ---- -9>4 -- incorrect

-4 is greater than -6 --- -4>-6 -- correct

7 is greater than 5 --- 7>5 -- correct

ANSWER

-9>4

The distance between the points G and H is D = 8 units

Given data ,

Let the distance between 2 points be represented as D

Now , let the first point be G ( 0 , 8 )

Let the second point be H ( 8 , 8 )

Now , let the distance between G and H be D , where

D = √( ( x₂ – x₁ )² + ( y₂ – y₁ )²)

D = √ ( 0 - 8 )² + ( 8 - 8 )²

D = √64 units

D = 8 units

Hence , the distance is 8 units

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Therefore , the solution of the given problem of unitary method comes out to be the fence's true length is about 17.92 feet.

Use the tried-and-true fundamental method, the actual variables, and any relevant information gleaned from general and specific questions to complete expression the assignment. Customers may be given another chance to taste the products in response. If these adjustments don't happen, we'll lose out on significant advancements in our understanding of programmes.

Here,

We can utilise the idea of proportions to determine the fence's actual length based on the scale drawing.

Given:

24 feet are represented by 3.75 inches at the given scale.

Let's establish a ratio:

=>  24 feet x 3.75 inches = 2.8 inches

where x represents the fence's real length.

If we cross-multiply, we obtain:

=>  24 feet * 2.8 inches * 3.75 inches

If we simplify, we get:

=>  3.75x = 67.2

By multiplying both sides by 3.75, we obtain:

=>  x = 67.2 / 3.75

=> × ≈ 17.92 feet

Therefore, the fence's true length is about 17.92 feet.

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Answer:

Step-by-step explanation:

THIS IS THE COMPLETE QUESTION BELOW;

A florist currently makes a profit of $20 on each of her celebration bouquets and sells an average of 30 bouquets every week. She noticed that when she reduces the price such that she earns $1 less in profit from each bouquet, she then sells three more bouquets per week. The relationship between her weekly profit, P(x), after x one-dollar decreases is shown in the graph below.

CHECK THE ATTACHMENT FOR THE GRAPH

EXPLANATION;

FIRST QUESTION:

From the graph maximum profit is the value gotten where p(X) has maximum value, and the maximum value is observed at y- axis at P(X)to be 675.

Thefore, maximum profit the florist will earn from celebration bouquet is $675.

SECOND QUESTION:

Break even is the exact point that profit p(x) is observed as zero.

Checking the given g graph the point where there is zero value of p(X) is observed at x=20 and x= -10 but we can only pick the positive value which is x=20

Therefore, the florist will break even after 20 one- dollar decreases

THIRD QUESTION;

The interval of number of one dollar decreases can be observed at the point where we have the value of P(x) been more than zero, looking at the given graph, the P(x) has its value greater than zero at the interval 0 to 20.Therefore, it can be concluded that the interval of number of one dollar decreases for which the florist makes a profit from celebration bouquet is (0, 20)

Answer:

Step-by-step explanation:

Answer:
i = \(\sqrt{-1}\)
i^2 = -1

Step-by-step explanation:

I hope this helps you out :D

since i = square root of -1 when you square i (i^2) you get rid of the parenthesis.

Answer:

25 dollars is the ANSWER

Step-by-step explanation:

The possible numbers that Melody could have picked are -4 and 4.

The operation that prevents us from knowing with 100% certainty the number Melody had picked is multiplication which is implied by the phrase "double the number".

Given, Let x be the number Melody had chosen.

Thus, tripling the number will give 3x, and

squaring this will result to (3x)² which is equals to 9x².

Dividing the square of the number by 2 and subtracting 30 from its quotient will give 42:

9x²/2 ₋ 30 = 42

9x²/2 = 42 ₊ 30

9x²/2 = 72

9x² = 72 × 2

9x² = 144

x² = 144/9

x² = 16

x = ±√16

x = ±4

x = ₊4 or x = 4

hence melody could have picked ₊4 or ₋4 numbers.

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Step-by-step explanation:

1/4 in percentage

= 1/4 * 100%

= 25%

Answer:

4/4=100%

1/4=100÷4

   = 25%

keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

\(y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{3}{2}}x+4 \qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill\)

\(\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{3}{2}} ~\hfill \stackrel{reciprocal}{\cfrac{2}{3}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{2}{3}}}\)

so we're really looking for the equation of a line whose slope is -2/3 and that it passes through (-6 , 2)

\((\stackrel{x_1}{-6}~,~\stackrel{y_1}{2})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{2}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{2}=\stackrel{m}{- \cfrac{2}{3}}(x-\stackrel{x_1}{(-6)}) \implies y -2= -\cfrac{2}{3} (x +6) \\\\\\ y-2=-\cfrac{2}{3}x-4\implies {\Large \begin{array}{llll} y=-\cfrac{2}{3}x-2 \end{array}}\)

Answer:

y=4/7x

Step-by-step explanation:

perpendicular lines have opposite slopes. that means reciprocal and opposite sign.

The current weight of the truck is given as follows:

3496 kg.

The current weight of the truck is obtained applying the proportions in the context of the problem.

The initial weight of the truck is given as follows:

3796 kg.

The weight removed from the truck is given as follows:

6 x 50 = 300 kg.

Hence the current weight of the truck is given as follows:

3796 - 300 = 3496 kg.

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ANSWER 92°

REMEMBER! angles in a triangle add up to 180°

this means that:

(x) + (3x + 13) + (x - 8) = 180

5x + 5 = 180

5x = 175

therefore x = 35

now that we know x, we can apply this to work out the angle mentioned, the angle a:

A = 3(35) - 13

   = 92°

Answer:

A

Step-by-step explanation:

Answer: A6

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

4 in hundreds (400)

3 in ones (3)

2 in tenths (.2)

9 in hundredths (.09)

Answer:

(a) 0.0000245

(b) 0.000025

Step-by-step explanation:

The complete question is:

Suppose that a computer chip company has just shipped 10,000 computer chips to a computer company. Unfortunately, 50 of the chips are defective. (a) Compute the probability that two randomly selected chips are defective using conditional probability. (b) There are 50 defective chips out of 10,000 shipped. The probability that the first chip randomly selected is defective is  50 /10,000  = 0.005.  Compute the probability that two randomly selected chips are defective under the assumption of independent events.

Solution:

(a)

In this case we need to compute the conditional probability of selecting two defective chips, i.e. the selection of the second defective chip is dependent on the first defective chip.

The probability of selecting the first defective chip is:

\(P(1D)=\frac{50}{10000}=0.005\)

Now there are 9999 chips left and 49 defective chips among them.

The probability of selecting the second defective chip is:

\(P(2D)=\frac{49}{9999}=0.0049\)

Compute the probability that two randomly selected chips are defective using conditional probability as follows:

P (Two defective chips) \(=P(1D)\times P(2D)=0.005\times 0.0049=0.0000245\)

Thus, the answer is 0.0000245.

(b)

Compute the probability that two randomly selected chips are defective under the assumption of independent events as follows:

The above statement implies that the selection was done with replacement.

The probability is:

P (Two defective chips) \(=P(1D)\times P(2D)\)

                                      \(=\frac{50}{10000}\times \frac{50}{10000}\\\\=0.005\times 0.005\\\\=0.000025\)

Thus, the probability that two randomly selected chips are defective under the assumption of independent events is 0.000025.

Answer:

$6625

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Simple Interest Rate Formula: A = P(1 + rt)

Step-by-step explanation:

Step 1: Define

Identify variables

P = 5000

r = 6.5% = 0.065

t = 5

Step 2: Find Interest

Step-by-step explanation:

If (5) = 3

Then (10) = 6

Because 5 x 2 = 10 so 3 x 2 = 6

The inequality tha calculates the possible values of x is x < 2

From the question, we have the following parameters that can be used in our computation:

The figure

Where, we have

3x + 2 < 10

And, we have

2x + 6 < 10

Evaluate the expressions

So, we have

3x < 8 and 2x < 4

Evaluate

x < 8/3 and x < 2

Hence, the inequality tha calculates x is x < 2

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Answer:

The answer is 6.5 meters tall

Step-by-step explanation:

650 divided by 100

do your 2 loops to the left and you get 6.5

Answer:

C becausee I'm trying to help

Answer:

m<wzx = 71

Step-by-step explanation:

Assuming these are interior angles of a triangle.

The sum of all three interior angles of a triangle is always 180 degrees, therefore:

m<xyz + m<wxz + m<wzx = 180

Substitute our values:

58 + 51 + m<wzx = 180

m<wzx = 180 - 58 - 51

m<wzx = 71

Answer: 88.2

..........................

Answer:

184320 Cubic Cenimeters

Step-by-step explanation:

Answer:

Step-by-step explanation:

Well, since the length of a month can vary in the number of days, this answer can also vary.

For example, February is only 28 days long, while December is 31 days long.

That being said, the average length of all 12 months is 30.436875 days, so if Denny left to another country on June 20th, he would most likely be back   July 19th of July 20th.

I hope this helps!

The probability that you, Shirley, and Matthew are chosen is 0.0001

Probability:

Probability refers the measure of the likelihood of an event to occur.

The formula of Probability is

Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes

Given,

Suppose that your boss must choose three employees in your office to attend a conference in Jamaica. Because all 28 of you want to go, he decides that the only fair way is to draw names out of a hat.

Here we need to find the probability that you, Shirley, and Matthew are chosen.

Here we have assuming that the selection process is fair;

We know that, the total number of employees is 28

Therefore, the probability of selecting each employee is,

=> 1/28

So, the probability of selecting yourself, Shirley, and Matthew is calculated as,

=> 1/28 x 1/27 x 1/26

=> 1/19656

=> 0.00005

When we round off it into four decimal place then we get,

=> 0.0001

Therefore, the probability that you, Shirley, and Matthew are chosen 0.0001.

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