You take out a loan for $ 1 , 000 at a simple interest rate of 10 % to be paid back in 12 monthly installments. What is the amount of the monthly payments?

Step-by-step explanation:

I need to use the fact that it has exactly one root to find the y part - do I use the quadratic formula on the last bit I have written?

I have x already and z = x+iy

3i and 3 are two complex numbers that fulfill this equation.

A complex number is a number of the form (a + bi), where [a] and [b] are real numbers and [i] is equal to [tex]\sqrt{-1}[/tex]. The general form of the complex number representation is (a + ib). In this, [a] is called real part and [ib] is called imaginary part.

We have -

zz* + 3iz = p + 9i

Assume the complex number to be -

z = a + ib

Then -

(a + ib)(a - ib) + 3i(a + ib) = p + 9i

a² + b² + 3ai + 3bi = p + 9i

(a² + b²) + i(3a + 3b) = p + 9i

So -

3(a + b) = 9

a + b = 3

(a² + b²) = p

Now -

Assume p = 9

Then -

a + b = 3

a² + b² = 9

we get two possible values -

(a, b) = (0, 3)

and

(a, b) = (3, 0)

It can be seen that the values of complex number depend upon the value of p. For p = 9, two complex numbers fulfill this equation -

0 + i3 = 3i

3 + i0 = 3

Therefore, 3i and 3 are two complex numbers that fulfill this equation.

To solve more questions on complex numbers, visit the link below-

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Answer:

51

Step-by-step explanation:

To find the mode of a data set, you must order the data set from least to greatest and find out which number appears the most. For example, I ordered the data set in this example, and found the out that 51 appeared the most.

Answer:

87 !

Step-by-step explanation:

Step-by-step explanation:

Don't you need a key for what K equals to solve this?

Answer:

5x6x6

Step-by-step explanation:

5x6x6=180

3x3x20=180

4x5x9=180

[tex]\sqrt[3]{180}[/tex]=5.65

Answer:

8 mm

Step-by-step explanation:

Answer attached....

Hope it helps :)

Answer:

a = 8mm is the answer

Step-by-step explanation:

a = ?

b = 6mm

c = 10mm

By using the Pythagoras theorem,

a² + b² = c²

a² + 6² = 10²

a² + 36 = 100

a² = 100 - 36

a² = 64

a = 8

∴ a = 8mm is the length of the missing leg

Answer:

Step-by-step explanation:

Answer:

D. Just follow the definition in the first line of the answer.

Step-by-step explanation:

Tan(A) = the opposite Side / Adjacent Sid

Tan(A) = 12/21

Tan(A) = 0.5714

Answer:

D. 0.5714

Step-by-step explanation:

I am a rizzly bear

Answer:

Ihe answer is 845 times

Step-by-step explanation:

Answer:

Cuboid's volume is l · w · h

for number one, (9 1/2)·6·(4 2/3), you get 266

there is also triangular prism, which is V = 1/2 b·h·l

which is (1/2 6.9)·8·18 which is 496.8

the surface area is just the area of all the shapes added together, i didn't see any lateral surface area on there, so im not gonna explain unless you want me to.

Answer:

12 Units

A total of 12 units have been traveled.

Answer:

400

Step-by-step explanation:

Answer:

the answer would be the second one

Answer:

Second choice

Step-by-step explanation:

18=2x9

9=3^2

X^7=(x)x^6)

root 18x^7

=3x^3root 2x

Answer:

add up to 90 degree

Step-by-step explanation:

Answer:

Since the calculated Z falls in the critical region therefore the null hypothesis is rejected and concluded that there is a difference between the views of these two populations.

Step-by-step explanation:

1) Formulate the hypotheses:

H0 : p1=p2

Ha: p1 ≠ p2

2) The significance level is chosen at ∝= 0.1  

3) The critical region is Z∝/2 ≥ ± 1.645

4) The test statistic under H0 is

Z = p1^- p2^/ √p^q^( 1/n1 + 1/n2)

p1^= proportion of of teenagers liking the new product.

p2^ = proportion of of parents of young children liking the new product.

p1^= 4/5

p2^= 1/5

p^= 5(0.8) + 5(0.2)/5+5= 4+1/10= 0.5

q^= 0.5

Thus

Z= p1^- p2^/ √p^q^( 1/n1 + 1/n2)

z= 0.8-0.2/√0.5*0.5( 1/5 + 1/5)

z= 0.6/ 0.316227

z= 1.897

5) Conclusion:

Since the calculated Z falls in the critical region therefore the null hypothesis is rejected and concluded that there is a difference between the views of these two populations.

Answer:

B

Step-by-step explanation:

Substitute the coordinates of the point into the left side of the equation and if the value obtained equals the right side then it is a solution.

A (- 4, 4 )

- 3(- 4) - 4 = 12 - 4 = 8 ≠ 6 ← not a solution

B (- 3, 3 )

- 3(- 3) - 3 = 9 - 3 = 6 ← this is a solution

The result is B

Answer:

Its 12.51

Step-by-step explanation:

Divide the ones column dividend by the divisor.

Multiply the divisor by the quotient in the right place column.

Subtract the product from the ones column.

then you get your answer! Hope this helps!

Answer:

The first one would be the top answer.

He can play less than 5 minutes before he loses a life.

Step-by-step explanation:

9514 1404 393

Answer:

  R(p) = -3500p^2 +48000p . . . revenue function

  $6.86 . . . price for maximum revenue

Step-by-step explanation:

The 2-point form of the equation for a line can be used to find the attendance function.

  y = (y2 -y1)/(x2 -x1)(x -x1) +y1

  y = (27000 -20000)/(6 -8)(x -8) +20000

  y = -3500(x -8) +20000

  y = 48000 -3500x . . . . y seats sold at price x

The per-game revenue is the product of price and quantity sold. In functional form, this is ...

  R(p) = p(48000-3500p)

  R(p) = -3500p^2 +48000p . . . per game revenue

__

Revenue is maximized when its derivative is zero.

  R'(p) = -7000p +48000

  p = 48/7 ≈ 6.86

A ticket price of $6.86 would maximize revenue.

Step-by-step explanation:

In the above right Angled triangle , we have ,

For finding hypontenuse use Pythagoras Theorem , we have ,

⇒ h² = p² + b²

⇒ h² = 9² + 12²

⇒ h² = 81 + 144

⇒ h² = 225

⇒ h = √225

⇒ h = ± 15

⇒ h = 15 [ Neglect -ve value ]

Therefore ,

Answer:

b = 30 yd is the answer.

Step-by-step explanation:

a = 40 yd

b = ?

c = 50 yd

According to the Pythagoras theorem,

a² + b² = c²

40² + b² = 50²

1600 + b² = 2500

b² = 2500 - 1600

b² = 900

b = 30 yd

∴ b = 30 yd is the length of the missing leg.

Answer:

3m

Step-by-step explanation:

3-dimensional space an object occupied

Answer:

1/5, 1/6, 1/7 is expressions not greater than 1/4

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

Answer:

120°

Shape Sides Each Angle

Hexagon    6              120°

Answer:

[tex]\alpha=0.11767[/tex]

[tex]\beta=0[/tex]

Step-by-step explanation:

From the question we are told that:

Population size size [tex]N=500[/tex]

Sample mean [tex]n=313[/tex]

Null hypothesis [tex]H_0:P=0.6[/tex]

Alternative hypothesis[tex]H_a:P>0.6[/tex]

Generally the equation for for P value is mathematically given by

[tex]P=\frac{n}{N}[/tex]

[tex]P=\frac{313}{500}[/tex]

[tex]P=0.6[/tex]

Generally the mean [tex]\=x[/tex] is mathematically given by

[tex]\=x=np\\\=x=500*0.6[/tex][tex]\=x=300[/tex]

Generally the standard deviation [tex]\sigma[/tex] is mathematically given by

[tex]\sigma=\sqrt{npq}[/tex]

[tex]\sigma=\sqrt{500*0.6*(1-0.6)}[/tex]

[tex]\sigma=10.95[/tex]

a)

Generally the probability of Type_I error [tex]P(X>313)[/tex] is mathematically given as

[tex]P(X>313)=P(\frac{x-\mu}{\sigma}>\frac{313-300}{10.95} )[/tex]

[tex]P(X>313)=P(z>1.187 )[/tex]

Therefore using z table

[tex]\alpha=0.11767[/tex]

b)

Null hypothesis [tex]H_0:P=0.75[/tex]

Alternative hypothesis[tex]H_a:P>0.75[/tex]

Generally the probability of Type_II error [tex]P(X<313)[/tex] is mathematically given as

[tex]P=0.75,n=500\\q=1-0.75\\q=0.25[/tex]

Generally the mean [tex]\=x'[/tex] is mathematically given by

[tex]\=x'=500*0.75[/tex]

[tex]\=x'=500*0.75[/tex]

[tex]\=x'=375[/tex]

Generally the standard deviation [tex]\sigma[/tex] is mathematically given by

[tex]\sigma=\sqrt{npq}[/tex]

[tex]\sigma=\sqrt{500*0.75*(1-0.75)}[/tex]

[tex]\sigma=9.68[/tex]

Therefore

[tex]P(X<313)=P(\frac{x-\mu}{\sigma}<\frac{313-375}{9.68} )[/tex]

[tex]P(X<313)=P(z<-6.405)[/tex]

Therefore from standard normal table

[tex]P(X<313)=0[/tex]

[tex]\beta=0[/tex]

Answer:

A, B, and C All have four sides, and they all have opposite sides that are equal. B and C have right angels. A has angels on opposite side that are the same

Step-by-step explanation: