Ralph chase plan to sell a piece of property for $160,000. He wants the money to be paid off in two ways- a short term note at 10% interest and a long term note at 7% interest. Find the amount of each note if the total annual interest paid is $13750.

Any complex number [tex]z[/tex] can be written in trigonometric form as

[tex]z = |z| e^{i\arg(z)} = |z| \left(\cos(\arg(z)) + i \sin(\arg(z))\right)[/tex]

where [tex]|z|[/tex] is the modulus of [tex]z[/tex] and [tex]\arg(z)[/tex] is its argument, i.e. the angle [tex]z[/tex] makes with the positive real axis in the complex plane.

We have

[tex]|z| = \sqrt{3^2 + \left(\sqrt3\right)^2} = \sqrt{12} = 2\sqrt3[/tex]

and

[tex]\arg(z) = \tan^{-1}\left(\dfrac{\sqrt3}3\right) = \tan^{-1}\left(\dfrac1{\sqrt3}\right) = \dfrac\pi6[/tex]

Then

[tex]3 + \sqrt3 \, i = \boxed{2\sqrt 3 \left(\cos\left(\dfrac\pi6\right) + i \sin\left(\dfrac\pi6\right)\right)}[/tex]

The probability that Rebecka selects a terrier and Aaron selects a retriever is 10/121

The distribution of the puppies is given as:

4 ​poodles, 5 ​terriers, and 2 retrievers

The probability of selecting a terrier is;

P(terrier) = 5/11

The probability of selecting a retriever is;

P(retriever) = 2/11

The required probability is

P = 5/11 * 2/11

Evaluate

P = 10/121

Hence, the probability that Rebecka selects a terrier and Aaron selects a retriever is 10/121

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The function represented by the table is therefore y = -x -2 which is linear in nature

Linear function are functions that have a leading degree of 1. using the coordinate points on the graph

(0, -2) and (1, -3)

Note that the function will be linear since the dependent and independent variables both have the same common difference.

Determine the slope

slope =  -3+2/1-0
slope = -1/1

slope = -1

For the intercept, it is -2 according to the coordinate (0, -2)

The function represented by the table is therefore y = -x -2 which is linear in nature

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The number of minutes Samantha needs to run on Friday to reach her goal is 45 minutes.

Average = (Monday + Tuesday + Wednesday + Thursday + Friday) / 5

40 = (45 + 30 + 55 + 25 + x) / 5

40 × 5 = 155 + x

200 = 155 + x

200 - 155 = x

45 = x

x = 45 minutes

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The amount Anneliese started with before her deductions is -$235.00.

Total amount spent = $58.00 + $35.00

= $93.00

Amount left in her account = $-142.00

Amount Anneliese started with = -$93.00 - $-142.00

= -$235.00

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The number of orders Michael, Rafael and Amanda served are 16.8, 33.6, and 41.6 servings

respectively.

x + 2x + (2x + 8) = 92

3x + 2x + 8 = 92

5x = 92 - 8

5x = 84

x = 84/5

x = 16.8 servings

Therefore,

Michael = x

= 16.8 servings

Rafael = 2x

= 2(16.8)

= 33.6 servings

Amanda = 2x + 8

= 33.6 + 8

= 41.6 servings

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Considering the given data-set, the quartiles are given as follows:

There is an even number of elements(26), hence the median is the mean of the 13th and 14th elements, the first half is the 12 elements from 1 to 12, and the second half is the 12 elements from 15 to 26.

The first quartile is the mean of the 6th and 7th elements, which are 67 and 68, hence:

Q1 = (67 + 68)/2 = 67.5.

The third quartile is the mean of the 6th and 7th elements of the second half, hence:

Q3 = (91 + 92)/2 = 91.5.

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Given that In 3 years, Dianna will be 4 times as old as she was 33 years ago, her present age is 45.

Given that, in 3 years, Dianna will be 4 times as old as she was 33 years ago.

Let x represent the age of Dianna presently.

Dianna's age in 3 years time will be: x + 3

Dianna's age 33 years ago is: x - 33

Since in 3 years, she will be 4 times as old as she was 33 years ago.

x + 3 = 4( x - 33 )

We solve for x

x + 3 = 4x - 132

3 + 132 = 4x - x

135 = 3x

x = 135/3

x = 45

Given that In 3 years, Dianna will be 4 times as old as she was 33 years ago, her present age is 45.

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Using translation concepts, the graph of [tex]y = 2 - \sqrt{x}[/tex] is described as follows:

On a coordinate plane, a curved line approaches the grid line at (3, 0.3), and ends at (0, 2).

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

Function [tex]y = 2 - \sqrt{x}[/tex], in blue in the graph, is the function [tex]y = \sqrt{x}[/tex], in red, reflected over the x-axis and shifted 2 units, as shown in the graph.

Hence the correct statement is:

On a coordinate plane, a curved line approaches the grid line at (3, 0.3), and ends at (0, 2).

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Answer:

D

Step-by-step explanation:

to determine the relationship between these two lines you have to find the slope.

=> if they have the same slope ,then they are parallel.

=> if they have negative inverse slope relative to each other ,then they are perpendicular.

=> if the slope for both equations is neither of the above cases ,then the two equations are neither parallel nor perpendicular.

so if we divide the first equation by 3 which is the commen factor for the whole equation and arrange it in the form y=mx +b it would give us y =5x +4. and since the two have the same slope which is 5 ,then we can conclude they are parallel lines.

The simplified expression of [tex]\frac{1}{a + 1} + \frac{1}{a - 1} - \frac{2a}{a^2 + 1} - \frac{4a}{a^4 + 1}[/tex] is [tex]\frac{8a}{a^8 - 1}[/tex]

The expression is given as:

[tex]\frac{1}{a + 1} + \frac{1}{a - 1} - \frac{2a}{a^2 + 1} - \frac{4a}{a^4 + 1}[/tex]

Add the first two terms

[tex]\frac{a - 1 + a + 1}{(a + 1)(a - 1)} - \frac{2a}{a^2 + 1} - \frac{4a}{a^4 + 1}[/tex]

Evaluate

[tex]\frac{2a}{a^2 - 1} - \frac{2a}{a^2 + 1} - \frac{4a}{a^4 + 1}[/tex]

Evaluate the first two terms

[tex]\frac{2a^3 + 2a - 2a^3 + 2a}{(a^2 - 1)(a^2 + 1)} - \frac{4a}{a^4 + 1}[/tex]

Evaluate

[tex]\frac{4a }{a^4 - 1} - \frac{4a}{a^4 + 1}[/tex]

Take the LCM

[tex]\frac{4a^5 + 4a - 4a^5 + 4a }{(a^4 - 1)(a^4 + 1)}[/tex]

Evaluate the like terms

[tex]\frac{8a}{a^8 - 1}[/tex]

Hence, the simplified expression is [tex]\frac{8a}{a^8 - 1}[/tex]

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The expanded form of the expression; (-a)^3 is; (-a)(-a)(-a).

It follows from the task content that the expanded form of the expression given is to be written.

On this note, the expression (-a)³ can simply be rewritten in it's expanded form as; (-a)(-a)(-a).

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Answer:

Step-by-step explanation:

2cm = 5m, so we know that the length is 5m

4cm = 2cm * 2, so the width is 5m * 2, which is 10m.

Now, we multiply them together.

5*10 = 50

The backyard area is 50 meters

Answer:

50m^2

Step-by-step explanation:

For the given systems we have:

1) Just swap the equations in system A.

2) Yes, the systems are equivalent.

Here we have the systems:

A:

-3x - 2y = 4

5x - 8y = -1

B:

5x - y = -1

-3x - 2y = 4

Notice that we have the same equations, just in a different order. So if we swap the first and second equations in system A, we get system B.

Are the systems equivalent?

Yes, because both systems are defined by the same equations.

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The measure of the interior angle at vertex C is D. 144.

Based on the information given, the angle will be calculated thus:

8x + 8x + 8x + 3x + 3x = (5 - 2) × 180

30x = 540

Divide both side by 30

30x/30 = 540/30

x = 18

Therefore, at vertex C, we have 8x. This will be:

= 8x

= 8 × 18

= 144

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The simplified expression of [tex]\sqrt{\frac{162x^9}{2x^{27}}}[/tex] is [tex]\frac{9}{x^9}[/tex]

The expression is given as:

[tex]\sqrt{\frac{162x^9}{2x^{27}}}[/tex]

Divide 162 and 2 by 2

[tex]\sqrt{\frac{81x^9}{x^{27}}}[/tex]

Take the square root of 81

[tex]9\sqrt{\frac{x^9}{x^{27}}}[/tex]

Apply the quotient rule of indices

[tex]9\sqrt{\frac{1}{x^{27-9}}}[/tex]

Evaluate the difference

[tex]9\sqrt{\frac{1}{x^{18}}}[/tex]

Take the square root of x^18

[tex]\frac{9}{x^9}[/tex]

Hence, the simplified expression of [tex]\sqrt{\frac{162x^9}{2x^{27}}}[/tex] is [tex]\frac{9}{x^9}[/tex]

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Answer:

4.375

Step-by-step explanation:

First add all the numbers together. [tex]3+2+0+1+9+12+3+5=35[/tex] Second, divide the number you just got by how many numbers there are. [tex]35/8=4.375[/tex] Therefore, the mean is 4.375.

Answer:

156 : 48

Step-by-step explanation:

Solution:

Since

169 : 52 = 156 : X

Then we know

52/169 = X/156

Multiplying both sides by 156 cancels on the right

156 × (52/169) = (X/156) × 156

156 × (52/169) = X

Then solving for X

X = 156 × (52/169)

X = 48

Therefore

169 : 52 = 156 : 48

Hello !

Look at the picture

Using proportions, it is found that the coordinate that is not marked is given by:

c. 3

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

There are 6 congruent segments between -2 and 10, hence the length of each segment is given by:

l = (10 - (-2))/6 = 2.

Then the points are: -2, 0, 2, 4, 6, 8, 10. 3 is not marked, hence option c is correct.

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Answer:

9 and 11  

Step-by-step explanation:

First number = x -2

Second number = x

  and   2x = 3(x-2)  - 5

            2x = 3x - 6 - 5

             x = 11

              first number = 11-2 = 9

Using the Empirical Rule, it is found that 49.85% of buyers paid between $150,000 and $154,800.

It states that, for a normally distributed random variable:

Considering the given mean and standard deviation, the interval between $150,000 and $154,800 corresponds to the interval between the mean and 3 standard deviations above the mean.

The normal distribution is symmetric(50% above the mean, 50% below), hence the percentage corresponding to this interval is:

P = 0.5 x 99.7% = 49.85%.

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the price that they should charge on the 2 year extended warranty is in order to break even is $10.

the price at which the company would breakeven is:

= percentage of product that will fail x replacement cost

solving gives:

= 4% x 250

= $10

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Answer:

If the x-6 is all under the sqrt, the last answer is right:

6<= x <= infinity

If only x is under the sqrt and - 6 is NOT under the sqrt, then:

0 <= x <= infinity is the correct answer.

Step-by-step explanation:

You can look at the equation and or graph to determine the domain of a function. The domain is all the x's that may go into the equation or all the x's on the graph of the function. Inside of a squareroot symbol the number inside there must be positive. While considering the equation, only x's that keep that inside positive can be used.

For sqrt(x-6), x has to be 6 or bigger.

For sqrt(x) - 6, x has to be 0 or bigger.

Answer:

We are 90% confident that the true mean lies between 8..6563 and     9.9437  

Step-by-step explanation:

The mean of your estimate plus and minus the range of that estimate constitutes a confidence interval. Within a specific level of confidence, this is the range of values you anticipate your estimate to fall within if you repeat the test. Confidence is another word for probability.

mean (x) = 9.3                        

standard deviation (s) = 2                        

sample size (n) = 28                        

T- Distribution:

degree of freedom = n - 1 = 28 - 1 = 27    

90% Confidence Interval ==> α = 0.1

critical value, t =  1.703 ( t-table)

standard error, SE = s/√n = 2 /√28 = 0.3780

margin of error, E = t × SE= 1.703 × 0.3780 = 0.6437

Confidence Interval: x ± E = 9.3 ± 0.6437

lower limit: x - E = 9.3 - 0.6437 = 8.6563    

upper limit: x + E = 9.3 + 0.6437 = 9.9437    

Confidence Interval: 8.6563 < µ < 9.9437

Z - Distribution:

Formula: Confidence Interval = x ± z (s/√n)

Sample Mean = s/√n = 2/√28 = 2/5.29 = 0.3781

z = 1.645 (from z - table)

From formula, z (s/√n): 0.3781 x 1.645 = 0.620 (rounded)

x ± 0.62

lower limit: x - 0.62 = 9.3 - 0.62 = 8.68  

upper limit: x + 0.62 = 9.3 + 0.62 = 9.92

Confidence Interval: 8.68 < µ < 9.92

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The volume of the pyramid with the given length, width and height is 165in³.

The volume of a right rectangular pyramid is expressed as;

V = ( L × W × H ) / 3

Given that;

We substitute into the equation above.

V = ( L × W × H ) / 3

V = ( 11in × 9in × 5in ) / 3

V = 495in³ / 3

V = 165in³

The volume of the pyramid with the given length, width and height is 165in³.

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