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[tex]z1=\stackrel{a}{3}+\stackrel{b}{3}i~~ \begin{cases} r = \sqrt{a^2+b^2}\\ r = \sqrt{18}\\[-0.5em] \hrulefill\\ \theta =\tan^{-1}\left( \frac{b}{a} \right)\\ \theta =\frac{\pi }{4} \end{cases}~\hfill z1=\sqrt{18}\left[\cos\left( \frac{\pi }{4} \right) i\sin\left( \frac{\pi }{4} \right) \right] \\\\[-0.35em] ~\dotfill[/tex]

[tex]\cfrac{z1}{z2}\implies \cfrac{\sqrt{18}\left[\cos\left( \frac{\pi }{4} \right) i\sin\left( \frac{\pi }{4} \right) \right]} {7\left[\cos\left( \frac{5\pi }{9} \right) i\sin\left( \frac{5\pi }{9} \right) \right]} \\\\[-0.35em] ~\dotfill\\\\ \qquad \textit{division of two complex numbers} \\\\ \cfrac{r_1[\cos(\alpha)+i\sin(\alpha)]}{r_2[\cos(\beta)+i\sin(\beta)]}\implies \cfrac{r_1}{r_2}[\cos(\alpha - \beta)+i\sin(\alpha - \beta)] \\\\[-0.35em] ~\dotfill[/tex]

[tex]\cfrac{z1}{z2}\implies \cfrac{\sqrt{18}}{7}\left[\cos\left( \frac{\pi }{4}-\frac{5\pi }{9} \right)+i\sin\left( \frac{\pi }{4}-\frac{5\pi }{9} \right) \right] \\\\\\ \cfrac{\sqrt{18}}{7}\left[\cos\left( \frac{-11\pi }{36} \right) +i\sin\left( \frac{-11\pi }{36} \right) \right]\implies \cfrac{\sqrt{18}}{7}\left[\cos\left( \frac{83\pi }{36} \right) +i\sin\left( \frac{83\pi }{36} \right) \right] \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \cfrac{z1}{z2}\approx 0.348~~ + ~~0.496i~\hfill[/tex]

The value of z1/z2 is √18/ 7 (cos ( 11π/36 ) - isin ( 11π/36 )).

"A complex number is the sum of a real number and an imaginary number and it is of the form x + iy and is usually represented by z".

For the given situation,

z1= 3+3i and

z2= 7(cos(5π/9) + i sin (5π/9))

To divide the complex numbers, both should be in same form.

Convert z1 in polar form.

z is of the form x+iy, so, r=[tex]\sqrt{x^{2}+y^{2} }[/tex]

⇒[tex]r=\sqrt{3^{2}+3^{2} }[/tex]

⇒[tex]r=\sqrt{18}[/tex]

θ = [tex]tan^{-1}(\frac{b}{a} )[/tex]

⇒[tex]tan^{-1}(\frac{3}{3} )[/tex]

⇒[tex]tan^{-1}(1)[/tex]

⇒[tex]45[/tex]°

The polar form is of the form, z= r (cosθ + i sinθ),

⇒ z1 = [tex]\sqrt{18}[/tex] (cosπ/4 + isinπ/4)

The formula for dividing complex number is

z1/z2 = r1(cos θ1 + isin θ1) / r2(cos θ2 + isin θ2)

⇒ z1/z2 = r(cosθ + isinθ)

where, r = r1/r2 and θ = (θ1 - θ2)

z1/z2 = [tex]\sqrt{18}[/tex] (cos π/4 + isin π/4) / 7 (cos 5π/9 + isin 5π/9)

⇒ r = [tex]\sqrt{18}[/tex] / 7 and

θ = (π/4 - 5π/9 )

⇒ θ = (-11π/36)

cos(-θ) = cos θ

⇒cos( -11π/36 ) = cos ( 11π/36 )

sin(-θ) = -sin θ

⇒ sin ( -11π/36 ) = -sin ( 11π/36 )

Thus, z1/z2 = [tex]\sqrt{18}[/tex] / 7 (cos ( 11π/36 ) - isin ( 11π/36 ))

Hence we can conclude that the value of z1/z2 is

√18/ 7 (cos ( 11π/36 ) - isin ( 11π/36 )).

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Answer:

146 is the answer im positive

Answer:

Step-by-step explanation:

x=0

Answer:

8

Step-by-step explanation:

18×4 = 72

And 72 ÷ 9 = 8

So 9×8 would be 72

Answer:

2.72 inches

Step-by-step explanation:

1040/8.5=122.35

1 inch on the map = 122.35 miles actual distance

333/122.35=2.72

Answer:

C.24

Step-by-step explanation:

First multiply 8 by 24 this is so you know how much 24 adults would be. You will get 192 so next you need to subtract 192 from the total money 272 to get 80 and 80 should be how much all of the kids cost now to check and make sure there are 40 people divide 80 by 5 to get 16 which is the total number of kids no just add 16 and 24 together to get 40

Answer:

Priya

Step-by-step explanation:

Mai= 5:3 Priya=7:5

Mai= 15:15 Priya=21:15

The ratios above are blue:yellow so Priya's shade has more of a blue tint because it is 21:15 and Mai's is 15:15 so it is evenly spread.

Answer:

One Solution

Step-by-step explanation:

x + 3y = 3      

x - y = -3        

4y = 6           Subtract to solve by elimination.

y = [tex]\frac{3}{2}[/tex]              Divide by 4.

x - [tex]\frac{3}{2}[/tex]  = -3      Substitute [tex]\frac{3}{2}[/tex] for y in the original equation.

x = -[tex]\frac{3}{2}[/tex]            Add [tex]\frac{3}{2}[/tex].

Using the normal approximation to the binomial, it is found that there is a 0.9319 = 93.19% probability that fewer than 260 are women.

In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

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

In this problem:

The mean and the standard deviation for the approximation are given by:

[tex]\mu = np = 300(0.833) = 249.9[/tex]

[tex]\sigma = \sqrt{np(1 - p)} = \sqrt{300(0.833)(0.167)} = 6.46[/tex]

Using continuity correction, as the binomial distribution is discrete and the normal distribution is continuous, the probability that fewer than 260 are women is P(X < 260 - 0.5) = P(X < 259.5), which is the p-value of Z when X = 259.5, hence:

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

[tex]Z = \frac{259.5 - 249.9}{6.46}[/tex]

[tex]Z = 1.49[/tex]

[tex]Z = 1.49[/tex] has a p-value of 0.9319.

0.9319 = 93.19% probability that fewer than 260 are women.

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Answer:37

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given f(x)=40-1.25x, where x=pounds of birdseed and 40=her saved amount, and birdseed costs 1.25/lb.

f(3)=40-1.25(3)

f(3)40-3.75

f(3)=36.25

If she buys (3 pounds) of birdseed, she saves ($36.25).

f(18)=40-1.25(18)

f(18)=40-22.5

f(18)=17.5

If she buys (18 pounds) of birdseed, she saves ($17.5)

f(36)=40-1.25(36)

f(36)=40-45

f(36)=-5

If she buys (36 pounds) of birdseed, she will need an extra $5 to pay off her debt.

If she buys (36 pounds) of birdseed, she will need an extra $5 to pay off her debt.

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

Given function f(x)=40-1.25x,

where x=pounds of birdseed and 40 is her saved amount, and birdseed costs is 1.25/lb.

f(3)=40-1.25(3)

f(3)40-3.75

f(3)=36.25

If she buys (3 pounds) of birdseed, she saves ($36.25) then;

f(18)=40-1.25(18)

f(18)=40-22.5

f(18)=17.5

If she buys (18 pounds) of birdseed, she saves ($17.5) then;

f(36)=40-1.25(36)

f(36)=40-45

f(36)=-5

If she buys (36 pounds) of birdseed, she will need an extra $5 to pay off her debt.

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Answer: 99% sure its b

Step-by-step explanation:

Answer:

The nearest hundredth would be 3,817,500

Step-by-step explanation:

The hundreds place is the four and the five behind it rounds the number to a up to a 5

Answer:

$0.30 x b

$10.20

Step-by-step explanation:

The equation is

$0.30 x b

Since we know JoAnn uses 34 beads, we can replace b with 34

$0.30 x 34 = $10.20

Answer:

last one

Step-by-step explanation:

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

[tex]\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}\qquad \impliedby y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{1}{5}}x+7 \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope}{\cfrac{1}{5}}\qquad \qquad \qquad \stackrel{reciprocal}{\cfrac{5}{1}}\qquad \stackrel{negative~reciprocal}{-\cfrac{5}{1}\implies -5}}[/tex]

so then line K has a slope of -5 and pass through (-1, -3)

[tex](\stackrel{x_1}{-1}~,~\stackrel{y_1}{-3})\qquad \qquad slope=m=-5 \\\\\\ \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}{(-3)}=\stackrel{m}{-5}[x-\stackrel{x_1}{(-1)}] \\\\\\ y+3=-5(x+1)\implies y+3=-5x-5\implies y=-5x-8[/tex]

Answer:

a=0.62

b=7/9

c=10/9

Answer: 11

Step-by-step explanation:

9. The Sum of 9 terms is 513/64.

10. The sum of 15 terms is -1.

11. The sum of 6 terms is 364

12. The sum of 10 terms is -682.

We have,

Sn =a (1 - [tex]r^n[/tex] ) ÷ (1 – r)

9. 12, -6, 3, .....

Here, r=  -6/ 12= -1/2

So, S(9)

= 12 (1- [tex](-1/2)^9[/tex])/ (1 - (-1/2))

= 513/ 64

10.-1, +1, -.....

Here, r= 1/ (-1)= -1

So, S(15) = 1 (1- [tex](-1)^{15[/tex])/ (1 - (-1))

              = -1

11. 1, 3, .....

Here, r = 3/1 = 3

So, S(6) = 1 (1- [tex](3)^{6[/tex])/ (1 - 3)

              = 364

12. 2, -4, ...

Here, r= (-4)/ 2= -2

So, S(10) = -682

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The correct statement is Sara can afford to purchase the items because the final price of the items is $60.

The first step is to determine the total cost of the items Sara wants to buy. The total cost can be determined by adding the cost of the items together.

Total cost = $14.95 + $25.49 + $35.79 = $76.23

The second step is to determine the cost of the items after the discount.

Price of the items = total cost x (1 - discount)

= total cost x (1 - 1/4)

total cost x 3/4

$76.23 x 3/4 = $57.17

The third step is to determine the cost of the items after tax.

Cost = (1.05) x $57.17 =$60.03

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Answer:

Root:(-⅗,0)

vertical intercept:(0,5)

Step-by-step explanation:

in essence it's just asking on getting the equation of that line in more or less slope-intercept form, hmmm well, it's a line, so all we need is two points to get it, hmmm let's see let's use the starting point and terminal point, so we know it goes through the origin, (0,0) and also goes through (1, 0.7), let's change 0.7 to a fraction, so its 7/10, ok, let's use those two points from it.

[tex](\stackrel{x_1}{0}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{\frac{7}{10}}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{\frac{7}{10}}-\stackrel{y1}{0}}}{\underset{run} {\underset{x_2}{1}-\underset{x_1}{0}}}\implies \cfrac{~~ \frac{7}{10}~~}{1}\implies \cfrac{7}{10}[/tex]

[tex]\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}{0}=\stackrel{m}{\cfrac{7}{10}}(x-\stackrel{x_1}{0})\implies y = \cfrac{7}{10}x[/tex]

Answer:

The 95% confidence interval for the true mean score is [tex][73.539,76.461][/tex]

Step-by-step explanation:

Note that [tex]CI=\bar x\pm z\frac{s}{\sqrt{n}}[/tex] where [tex]\bar x[/tex] is the sample mean, [tex]z[/tex] is the upper critical value for the desired confidence level, [tex]s[/tex] is the sample standard deviation, and [tex]n[/tex] is the sample size.

Therefore, [tex]CI=75\pm 1.96\frac{5}{\sqrt{45}}\approx[73.539,76.461][/tex]

Answer:

infinite solutions...

Step-by-step explanation:

Is there more information to this problem? It can be pretty much anything.

N=3M

Nina can be 30 and Maryna 10, Nina can be 3 and Maryna 1, Nina can be 15 and Maryna 5...

Answer:

N - 4 = 3(M - 4). Simplified further, N - 4 = 3(M - 4)

Given,

Nina is N years old now and;

Maryna is M years old now

If four years ago, Nina was three times as old as Maryna was, then

Four years ago, Nina's age was N - 4

Four years ago, Maryna's age was M - 4

Given that Nina was three times as old as Maryna was four years ago, it means that

N - 4 = 3(M - 4)

To solve further

N = 3m - 12 + 4

N = 3M - 8

Step-by-step explanation:

Given that

log √x (x) + log c² (c)

⇛ log x^1/2 (x) + log c² (c)

We know that

log a^m (b^n) = m/n log a (b)

⇛ 1/2 log x (x) + 2 log c (c)

We know that

log a ( a) = 1

⇛ (1/2)(1) + 2(1)

⇛ (1/2)+2

⇛ (1+4)/2

⇛ 5/2

Answer:- log √x (x) + log c² (c) = 5/2

[(x) ,(c) , (a) represents the bases ]

Additional comment:

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simplify the following expression. log(x2) - log(x) A. log(x^2+x) B. log(x^3) C. log(x^2-x) D. log(x)....

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Answer:

negative

Step-by-step explanation:

Answer:

negative

Step-by-step explanation:

as it goes further right, it goes further down, so it is a negative slope

Answer:

10[tex]sin^{2} ([/tex]β[tex])[/tex]

Step-by-step explanation:

We can find this two ways, first by seeing in the step after it, cosines are canceled out. Since you already have 10[tex]sin^{2} ([/tex]β[tex])[/tex] on the next step, you can assume that (since only the cosines changed and the cosine next ot the blank was removed), the value is 10[tex]sin^{2} ([/tex]β[tex])[/tex].

You can also use double angle formulas from the previous step:

(sin(2β) = 2 sin(β) cos(β))and find that:

5 sin (2β) sin(β) = 5 * (2 sin(β) cos(β)) sin(β)) = (10 sin(β) sin(β)) cos(β) =

10[tex]sin^{2} ([/tex]β[tex])[/tex] cos(β)

But since cos(β) is already present, we can see that the answer is 10[tex]sin^{2} ([/tex]β[tex])[/tex]