HELLPP DUE BY 1pm PACIFIC HELLPP ASAP

Answer:

- 4 + 4√3 i, where a = -4 & b = 4√3

Step-by-step explanation:

z = 8 cis(2π/3)

z = 8 [cos(2π/3) + i sin(2π/3) ]

z = 8 [cos(π - π/3) + i sin(π - π/3)]

z = 8 [ - cosπ/3 + i sin(π/3)]

z = 8[ - 1/2 + i √3/2 ]

z = - 4 + 4√3 i [in a + bi form]

Note that: cis x = cosx + i sinx

Answer:

[tex]a + bi = - 4 + 4 \sqrt{3} i[/tex]

Step-by-step explanation:

we are given [tex]\displaystyle cis(\dfrac{2\pi}{3})[/tex]

recall complex number trigonometric form:

[tex] \displaystyle \: r( \cos( \theta) + i \sin( \theta) )[/tex]

we are already given that [tex]\theta=\dfrac{2\pi}{3}[/tex]

recall complex number rectangular form

[tex] \displaystyle \: a + bi[/tex]

where [tex]\displaystyle a=r\cos(\theta)\: and\: b=r\sin(\theta)[/tex]

let's work with a:

substitute the value of [tex]\theta[/tex] and r

[tex] \displaystyle \: a = 8 \times \cos( \frac{2\pi}{ 3} ) [/tex]

recall unit circle

so [tex]\cos(\dfrac{2\pi}{3})[/tex] should be in Q:II

[tex] \displaystyle \: a = 8 \times - \frac{1}{2} [/tex]

simplify multiplication:

[tex] \displaystyle \: a = - 4[/tex]

let's work with b:

substitute the value of [tex]\theta[/tex] and r:

[tex] \displaystyle \: b = 8\sin( \frac{3\pi}{2} ) [/tex]

recall unit circle so [tex]\sin(\dfrac{3\pi}{2})[/tex] should be in Q:II

[tex] \displaystyle \: b = 8 \times \frac{ \sqrt{3} }{2} [/tex]

simplify:

[tex] \displaystyle \: b = 4 \sqrt{3} [/tex]

so

[tex] \displaystyle \: b i= 4 \sqrt{3} i[/tex]

hence,

[tex]a + bi = - 4 + 4 \sqrt{3} i[/tex]

Answer:c

Step-by-step explanation:cccccc

Answer:

x = 16

Step-by-step explanation:

If the figure is a parallelogram, the opposite sides are the same length

3x+20 = 5x-12

Subtract 3x from each side

3x+20 -3x = 5x-12-3x

20 = 2x-12

Add 12 to each side

20+12 = 2x-12+12

32 = 2x

Divide each side by 2

32/2 = 2x/2

16 =x

The number of years before the new car becomes $5700 is 11.4 years.

Depreciation is when the value of an asset declines with the passage of time.

Number of years = (In FV / PV) / r

(IN 5700 / 20,000) / 0.11 = 11.4 years

To learn more about depreciation, please check: https://brainly.com/question/25552427

#SPJ1

Answer:

30.5°

Step-by-step explanation:

Supplementary angles add up to 180°. You know one angle is 149.5°, so you can find the other angle.

Measure of its supplementary angle = 180° - 149.5°

                                                             = 30.5°

Answer:

x = 9

Step-by-step explanation:

[tex]a^{2} = c^{2} - b^{2}[/tex]

[tex]a^{2} = 15^{2} - 12^{2}[/tex]

[tex]a^{2} = 225 - 144[/tex]

[tex]a^{2} = 81[/tex]

[tex]\sqrt{a^2} = \sqrt{81}[/tex]

[tex]a = 9[/tex]

Answer:

Step-by-step explanation:

θ = 2π/9 radians

arc length = rθ = 8π/9 units

area of sector = πr²/9 = 16π/9 square units

Answer:

840cm² its 840cm²

answer:

a. scarf costs today = $6

b. scarf costs 3 days from now = $3

step-by-step explanation:

a. original price of scarf: $12

12 X 1/2 = 6

12 - 6 = 6

— scarf costs today = $6

b. 12 X 3/4 = 9

12 - 9 = 3

— scarf costs 3 days from now = $3

Answer:

a.

Step-by-step explanation:

the formula is y2-y1/ x2-x1, so it would be -14-19/ 0- (-4) which simplifies to -33/4

Answer:

12

13

89

Step-by-step explanation:

ez pz

Answer:

80-89

Step-by-step explanation:

When you put it in a stem- and - leaf plot, you'll see that 80-89 is the mode interval.

Answer:

80-89

Step-by-step explanation:

That is the range that most students got.

Answer:

total of 25 to clean.

did 10

has 15 left

Answer: 15

Step-by-step explanation:

Ran Needs to clean 17 cams... he already cleaned 10, so subtract 17-10... it would be 7

he finds 8 cams to clean... so we add 8+7... and it becomes 15...

brainliest appreciate

Answer: A=bh to find the area of parallelograms.

Step-by-step explanation:

Answer:

Well its basically 3 x 4 = 12, so for every lamb add four legs until you get to three

Step-by-step explanation:

Answer:

angle B is 27 degrees.

Step-by-step explanation:

Answer:

the total surface area of the prism is 245.67

Step-by-step explanation:

Given;

height of the triangular prism, h = 8

length of the triangular bases, = 7, 8, and 9

The total surface area of the prism is calculated as;

T.S.A = ph + 2B

Where;

p is the perimeter of the base

B is area of the base

P = 7 + 8 + 9 = 24

Area of the base can be calculated using Hero's formula;

[tex]S = \frac{7+8+9}{2} = 12\\\\Base \ area (B) = \sqrt{12(12-7)(12-8)(12-9)} = 26.833[/tex]

T.S.A = (24 x 8)   +  2 x 26.833

T.S.A = 192 +  53.666

T.S.A = 245.67

Therefore, the total surface area of the prism is 245.67

Answer:

a) 0.0618 = 6.18% probability that the sample will contain at least three defectives.

b) 0.076 = 7.6% probability that the sample will contain at least three defectives

Step-by-step explanation:

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

Normal probability distribution

Problems of normally distributed distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].

Sample of 20 items is selected from the machine.

This means that [tex]n = 20[/tex]

5% defectives

This means that [tex]p = 0.05[/tex]

(a) the normal approximation to the binomial

The mean is:

[tex]\mu = E(X) = np = 20*0.05 = 1[/tex]

The standard deviation is:

[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{20*0.05*0.95} = 0.9747[/tex]

The probability is, using continuity correction, [tex]P(X \geq 3 - 2.5) = P(X \geq 2.5)[/tex] , which is 1 subtracted by the pvalue of Z when X = 2.5. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{2.5 - 1}{0.9747}[/tex]

[tex]Z = 1.54[/tex]

[tex]Z = 1.54[/tex] has a pvalue of 0.9382

1 - 0.9382 = 0.0618

0.0618 = 6.18% probability that the sample will contain at least three defectives.

(b) the exact binomial tables

This is:

[tex]P(X \geq 3) = 1 - P(X < 3)[/tex]

In which

[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{20,0}.(0.05)^{0}.(0.95)^{20} = 0.358[/tex]

[tex]P(X = 1) = C_{20,1}.(0.05)^{1}.(0.95)^{19} = 0.377[/tex]

[tex]P(X = 2) = C_{20,2}.(0.05)^{2}.(0.95)^{18} = 0.189[/tex]

[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.358 + 0.377 + 0.189 = 0.924[/tex]

[tex]P(X \geq 3) = 1 - P(X < 3) = 1 - 0.924 = 0.076[/tex]

0.076 = 7.6% probability that the sample will contain at least three defectives

Answer:

20 minutes( 0.3333 hours) after they leave the station will they be 50 km apart, if the Two trains on opposite tracks leave the same station at the same time.

Step-by-step explanation:

One train travels at an average speed of 80 km/hr and the other travels at an average speed of 70 km/hr.

Answer: 7

Step-by-step explanation:

2x - 3 = x + 4

2x - x - 3 = 4           Mius x from the both side

       x - 3 = 4          

             x = 7          Add the 3 from both side

Answer:

$1000

Step-by-step explanation:

It would be $1000 in total of all the people attending the party. This is because, you need to multiply, 50 and 20! The answer will be 1000.

Answer:

1/3 divided by 4

Step-by-step explanation:

Because you start off with 1/3 and then you split it into 4, 1/12's and 4*1/12 is equal to 1/3

So the answer is 1/3 divided by 4

Answer:

add 6 to both sides and dividing both sides by 5.

Answer:

add 6 to both sides then divide both sides by 5

Step-by-step explanation: