6. Which quadrant is the pre-image located in?
B
Quadrant III
Quadrant I
O Quadrant II
O Quadrant IV
9
A

The rectangular form of z1 is -4 + j3 and the polar form is 5∠153°. The rectangular form of z2 is 1 - j and the polar form is √2∠-45°. The other expressions have similar rectangular and polar forms.

The rectangular form of complex numbers is represented by two coordinates, one real, and one imaginary. The polar form of complex numbers is represented by the magnitude and angle of the number.

In the expression (a), z1 = -4 + j3; the rectangular form is -4 + j3, and the polar form is 5∠153°. In the expression (b), z2 = 1 - j; the rectangular form is 1 - j, and the polar form is √2∠-45°.

In the expression (c), z1 + z2 = -3 + 2j; the rectangular form is -3 + 2j, and the polar form is 2.82∠29.14°. In the expression (d), jz2 = j(1 - j); the rectangular form is j(1 - j) and the polar form is 1∠-135°.

In the expression (e), z1(-1) = 1/z1; the rectangular form is 1/z1, and the polar form is 0.25∠-33.7°. In the expression (f), z1/z2 = (-4+j3)/(1-j); the rectangular form is (-4+j3)/(1-j), and the polar form is 2.24∠-118.4°.

In the expression (g), ez2 = e(1 - j); the rectangular form is e(1 - j), and the polar form is 2.72∠-44.99°. In the expression (h), z1z1 = (-4+j3)(-4+j3); the rectangular form is (-4+j3)(-4+j3), and the polar form is 25∠306°.

In the expression (i), z1z2 = (-4+j3)(1-j); the rectangular form is (-4+j3)(1-j), and the polar form is 7∠-96.6°.

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The standard deviation for the cost is given as follows:

$12.

The total number of students is given as follows:

7 + 20 + 20 + 14 + 10 = 71.

Considering the midpoint of each interval, and dividing their absolute frequencies by 71, the discrete distribution modeling the situation is given as follows:

The expected value is given by the sum of each outcome multiplied by it's probability, hence:

E(X) = 15 x 0.0986 + 25 x 0.2817 + 35 x 0.2817 + 45 x 0.1972 + 55 x 0.1408

E(X) = 35.

The sum of the differences squared between each observation and the mean, multiplied by their respective probabilities, is given as follows:

V(X) = (15-35)² x 0.0986 + (25-35)² x 0.2817 + (35-35)² x 0.2817 + (45-35)² x 0.1972 + (55-35)² x 0.1408

V(X) = 143.65.

The standard deviation is obtained taking the square root of V(X), hence:

S(X) = sqrt(143.65)

S(X) = $12. (rounding).

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Answer:

m<1 = 119°

Step-by-step explanation:

The entire figure is an irregular hexagon, a 6-sided polygon.

The sum of the measures of the angles of a polygon with n sides is

(n - 2)180°

For a hexagon, n = 6.

(6 - 2)180° = 4(180°) = 720°

All angle measures of the polygon are known except for the measure of <1.

m<1 + (37° + 113°) + 90° + 147° + (80° + 44°) + 90° = 720°

m<1 + 601° = 720°

m<1 = 119°

The statement that is true about histograms graphs is: "Data is organized in equal intervals."

Academics are using graphs to logically chart or graphically depict events or quantities. A graph point is a common way to depict how different things interact. The non-linear storage structure known as a graph is made up of nodes, also referred to as vertices, and lines. Glue ought to be used to connect the edges, also known as nodes , respectively.  (4.5).

Here,

The statement "Data appears as bars that are all about the same height" is false.

A histogram is a graph that represents the distribution of numerical data by organizing it into "bins" or "intervals" and displaying the count or frequency of data points that fall within each interval. The height of each bar represents the frequency or count of data points in that interval. The bars may or may not touch depending on the data and the chosen intervals.

The statement that is true about histograms is: "Data is organized in equal intervals."

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Answer:

-3

Step-by-step explanation:

The slope of the line that passes through the points (-1, 4) and (1, -2) can be found using the formula:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are the coordinates of the two points. Substituting the values, we get:

m = (-2 - 4) / (1 - (-1))

m = -6 / 2

m = -3

So, the slope of the line is -3.

The only function that represents exponential decay is (A) f(x) = 2(1/3)ˣ.

What is exponential decay?

Exponential decay refers to a process in which a quantity decreases over time, with the rate of decrease becoming proportionally smaller as the quantity gets smaller.

Exponential decay occurs when a quantity decreases over time or space by a fixed percentage of the remaining amount per unit.

This is represented by an exponential function of the form [tex]f(x) = a \cdot b^x[/tex], where a is the initial value and b is the decay factor (a number between 0 and 1).

Among the given options, the only function that represents exponential decay is (A) f(x) = 2(1/3)ˣ.

To see why, note that as x increases, (1/3)ˣ gets smaller and smaller, approaching zero as x goes to infinity. This means that f(x) gets smaller and smaller over time or space, representing exponential decay.

Functions (B), (C), and (D) do not represent exponential decay because their exponential factors 3ˣ, -3ˣ, and 5/3ˣ are either greater than 1 or negative, meaning that the quantity being modeled increases over time or space instead of decreasing.

Hence,  the only function that represents exponential decay is (A) f(x) = 2(1/3)ˣ.

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Answer: The intersection of two submodules of an R-module is itself a submodule of the R-module. To show that the intersection of any nonempty collection of submodules of an R-module is a submodule, we can use induction.

Suppose we have a collection of submodules M1, M2, ..., Mn of an R-module R. We will prove that the intersection of this collection is a submodule of R.

Base case: n = 2.

In this case, M1 and M2 are submodules of R, and their intersection is also a submodule of R.

Inductive step: n = k + 1 (k > 1).

Suppose the intersection of any collection of k submodules of R is a submodule of R. Let M1, M2, ..., Mk, Mk+1 be a collection of k + 1 submodules of R.

Then, the intersection of M1, M2, ..., Mk is a submodule of R, and the intersection of this submodule and Mk+1 is also a submodule of R.

Therefore, by induction, the intersection of any nonempty collection of submodules of an R-module is a submodule.

Step-by-step explanation:

The triangle is congruent by the Angle side Angle property.

In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other. The meaning of congruency is that the two shapes are similar as well as equal in size.

The Angle side Angle Congruence Theorem (ASA) defines two triangles to be congruent to each other if the included two angles and one side of one are congruent to the included angle and corresponding two sides of the other triangle.

The three parameters that are congruent are:-

BV ≅ BV ( common side)

∠1 ≅ ∠2  ( Bisector)

∠3 ≅ ∠4  ( Bisector)

Hence, the two triangles are congruent with each other.

The question on geometry is attached with the answer below.

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On solving the provided question, we can say that the quadratic function [tex]f(x)=x^{2}+10x+24.[/tex] , so f(-2) = 8

Quantities and their variations, equations and related structures, shapes and their placements, and locations where they can be found are all included in the study of mathematics.

The relationship between a group of inputs, each of which has a related output, is referred to as a "function." A function is a relationship between inputs and outputs where each input produces a single, unique result. Every function has a domain and a codomain, often known as a scope. F is typically used to denote functions (x). An x is the input. Based on the following criteria, there are four primary categories of functions that are available: on functions, one-to-one functions, many-to-one functions, within functions, and on functions.

the quadratic function [tex]f(x)=x^{2}+10x+24.[/tex]

By substituting different values of x

For x = 0

if f(0) = 24

For x = 1

if f(1) = 35

For x = 2

if (2) = 48

For x = -2

so f(-2) = 8

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The one-digit integers that satisfy the inequality "k < 0" are:

-1, -2, -3

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

k < 0

A number line representation of the inequality "k < 0" is as follows:

-3 -2 -1 0 1 2 3

---------<----------

The inequality k < 0 represent all the numbers less than 0 on the number line.

This includes all negative one-digit integers, which are -1, -2, and -3.

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Answer:

132

Step-by-step explanation:

The pattern is adding 18 napkins, so Friday would be 114 napkins and Saturday would be 132

Answer:

60

Step-by-step explanation:

Because we are told the figure is a regular polygon, then it must be an equilateral triangle. This means all angles are equal (60 degrees each)

Answer:

284

Step-by-step explanation:

open up the triangle

so you get 3 sides for the length  13+10+13=36 * 5 2/3width =204

then add the 2 triangles surface

1/3 * 10base  * 12height * 2 =80

total 284

Information pertaining to the ownership of the business, such as changes in the number average of shares held by shareholders, dividend payments, and proceeds from stock issue, is included in the statement of changes in stockholder's equity.

Information about the ownership of the business and how it affects the financial statements of the business is captured in the statement of changes in stockholder's equity. This statement contains information on the number of shares issued and outstanding, ownership changes brought on by stock splits and dividends, issuance proceeds, and the impact of transactions involving treasury stock. As a result of net gains or losses and other adjustments, it also keeps track of changes in retained earnings. Because it gives a general picture of the company's equity and how it has changed over time, this statement is significant. It is also a helpful tool for investors since it enables them to assess the financial performance of the business and decide on their investments with knowledge.

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An expression for the given phrase is 5(r+s).

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.

The given phrase is 5 times as much as the sum of r and s.

Here, the sum of r and s is r+s

Now, 5 times as much as the sum of r and s is

5(r+s)

Therefore, an expression is 5(r+s).

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Answer:

d ≈ 5.1

Step-by-step explanation:

calculate the distance d using the distance formula

d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = L (3, 7 ) and (x₂, y₂ ) = M (- 2, 8 )

d = [tex]\sqrt{(-2-3)^2+(8-7)^2[/tex]

   = [tex]\sqrt{(-5)^2+1^2}[/tex]

   = [tex]\sqrt{25+1}[/tex]

    = [tex]\sqrt{26}[/tex]

    ≈ 5.1 ( to the nearest tenth )

Answer:-5 -5

Step-by-step explanation: Look at the middle of 6 and 4 the middles 5 so the other one is 5 to because is one the same position and how is on the 3 quart is negative so don't forget to add that:)

Therefore, the probability of selecting a defective battery followed by another defective battery is 1/145.

Calculating the likelihood that a statement is true or that a particular event will take place is the centre of probability theory, a branch of mathematics. Any number between 0 and 1, where 1 is usually used to range confidence as well as 0 is routinely used it to convey possibility, can be used to represent chance. A probability diagram shows the likelihood that a particular occurrence will occur.

Here,

The probability of selecting a defective battery on the first draw is 3/30, or 1/10, since there are 3 defective batteries out of 30 total.

Since one battery has already been drawn, there are now 29 batteries left in the box, and 2 defective batteries remaining.

The probability of selecting another defective battery on the second draw, without replacement, is 2/29.

To find the probability of both events happening (selecting a defective battery followed by another defective battery), we multiply the probabilities of each event:

P(defective battery and then another defective battery) = P(defective battery on first draw) × P(defective battery on second draw)

= (1/10) × (2/29)

= 2/290

= 1/145

Therefore, the probability of selecting a defective battery followed by another defective battery is 1/145.

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Number of outcomes are in R​,

⇒ n (R) = 8 / 19

And, Number of outcomes are not in R,

⇒ n (R') = 11 / 8

A combination is a technique to determines the number of possible arrangements in a collection of items where the order of the selection does not matter.

Given that;

You take a random token from a bag that contains 8 red, 7 green, and 4 blue tokens.

Hence, Number of outcomes are in R​,

⇒ ⁸ C ₁ / ¹⁹C₁

⇒ 8 / 19

⇒ n (R) = 8 / 19

And, Number of outcomes are not in R,

⇒ 1 - 8/19

⇒ 11 / 8

⇒ n (R') = 11 / 8

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Answer:

1st term(a)=0.25

2nd term(t2)=0.5

common difference (d)=0.25

nth term(tn)=a+(n-1)d

=0.25+(n-1)0.25

=0.25+0.25n-0.25

=0.25-0.25+0.25n

=0.25n

Answer: nth term of the geometric sequence = (n^-1)/2

Step-by-step explanation:  The nth term of a GP is Tn = arn^-1

where a is the first term 0.25  

r is the common ratio 0.5/0.25 or 1/0.5 or 2/1, which is 2

Therefore the nth term = 0.25 x 2 x n^-1

= 0.5n^-1

=(n^-1)/2

The value of y in  [tex]x^\frac{1}{2} - 3y^\frac{1}{4} + 2 = 0[/tex]  is y = 1.189 for the quadratic-like equation.

Any equation of the form  where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

The equation [tex]x^\frac{1}{2} - 3y^\frac{1}{4} + 2 = 0[/tex] is not a traditional quadratic equation, but it can be solved using numerical methods or by using a change of variables.

1) One possible method to solve the equation is to use the Newton-Raphson method, which is an iterative numerical method for finding the roots of a function. This method involves finding a first approximation for the root and then using that approximation to improve the estimate in each iteration until the root is found to a desired level of accuracy.

2) Another possible method is to change the variables to make the equation a traditional quadratic equation. For example, one could substitute  [tex]y\frac{1}{4} = x[/tex] and then solve for x. This would result in the equation [tex]x^{2} - 3x + 2 = 0[/tex], which can be solved using the quadratic formula.

Let us substitute [tex]y\frac{1}{4} = x[/tex]

Then we have x² - 3x + 2 = 0

On solving

⇒ x² -2x -  1x + 2

⇒ x² -2x -  1x + 2

⇒ x(x - 2) -1(x + 2)

⇒ (x - 2)(x - 1)

Thus, x = 1 and x = 2

Solving for y

[tex]y^{\frac{1}{4}} = 2[/tex]

y = [tex]\sqrt[4]{2}[/tex]

y = 1.189

[tex]1.189^{1/2} = 1.09[/tex]

Thus, the value of y in  [tex]x^\frac{1}{2} - 3y^\frac{1}{4} + 2 = 0[/tex]  is y = 1.189 for the quadratic-like equation.

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Answer:

2A=B

Step-by-step explanation:

use ratio of axis to solve the scale. verify to second axis.

x axis: 4 A to 8 B

set Ratio A/4 = B/8 and solve

2A = B or A = (1/2)B

verify to sefond axis.

y axis: 3A to 6 B

A/3 = B/6

2A = B or A = (1/2)B

Answer:

x = -3

y = -4

Step-by-step explanation:

Given system of equations:

[tex]\begin{cases}6x-y=-14\\2x-3y=6\end{cases}[/tex]

Multiply the second equation by -3:

[tex]\implies 2x(-3)-3y(-3)=6(-3)[/tex]

[tex]\implies -6x+9y=-18[/tex]

Add this to the first equation to eliminate the term in x:

[tex]\begin{array}{crcrcl}\vphantom{\dfrac12}& 6x & - & y & = & -14\\\vphantom{\dfrac12}+ & (-6x & + & 9y & = & -18)\\\cline{2-6}\vphantom{\dfrac12}&&&8y&=&-32\\\cline{2-6}\end{array}[/tex]

Solve the equation for y:

[tex]\implies 8y=-32[/tex]

[tex]\implies y=-4[/tex]

Substitute the found value of y into one of the original equations and solve for x:

[tex]\implies 2x-3(-4)=6[/tex]

[tex]\implies 2x+12=6[/tex]

[tex]\implies 2x=-6[/tex]

[tex]\implies x=-3[/tex]

Therefore, the solution to the given system of equations is (-3, -4).

Answer:

Step-by-step explanation:

The given equations to us are ,

In elimination method we eliminate any variable and then find the find the value of second unknown variable. Using that value we can find the value of 1st variable.

Multiply equation 1 by 3 ,

3(6x-y)=-14*3

18x - 3y = -42 ..... (3)

Now subtract equation 2 and 3 to eliminate y as,

2x - 3y - (18x -3y) = 6 -(-42)

2x -3y -18x +3y = 6+42

-16x = 48

x = 48/-16 = -48/16

x = -3

Substitute this value in equation 2 ,

2*(-3) -3y = 6

-6-3y =6

-3y =6+6

-3y = 12

y = -4

And we are done!

The positions are located at points A

In the given question Emily generated 10,000 random digits between 0 and 10 we have to find the approximate location of the median is in interval A/B/CV and the approximate location of the mean is in interval A/B/CV.

The mean can roughly be found in interval B, whereas the median can roughly be found in interval A.

How to find the median and mean's placement in a table

The mean

We can utilize the following inputs for our calculation as we got them from the question:

The histogram

We can observe from the histogram that it is a uniform histogram.

This indicates that the mean is in the middle.

So, we have

Mean = point A

The median

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

The histogram

We can observe from the histogram that it is a uniform histogram.

This indicates that the median is situated in the middle.

So, we have

Median = point A

Hence, the positions are located at points A

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The complete question is:

Emily generated 10,000 random digits between 0 and 10. Here are the results:

Frequency

1000

800

600

400

200

04

A B

0 1 2 3 4 5 6 7 8 9 10

Digit

The approximate location of the median is in interval A/B/C

The approximate location of the mean is in interval A/B/C

To save $10,000 over two years, you would need to deposit $20,407 per month in an account earning 4.7% interest (compounded monthly).

Divide the capital by the cost of borrowing, the length of time, and certain other considerations to arrive at simple interest. Simple return = principal + interest + hours is the commercial formula. This method allows it easiest to calculate interest. The most basic technique to figure the interest is as a portion of the outstanding amount. He will only pay his share of the 100% interest, for example, if he borrowed $100 from a partner and agrees to repay the loan th with 5% interest. $100 (0.05) = $5. When you keep borrowing, you must pay interest, and when you give it out, you must lend money.

given

Future Value = Current Value x (Present Value + Interest Rate) (Years/frequency of payments per year)

FV = (-15,000 x [1+8%]^

[4/1])

PV is adverse because you are redistributing funds.

FV = $20,407

Calculator for Finances: Enter PV of -15,000 as

Make 4 N.

Set 8 as I/Y CPT FV and 0 as PMT

$20,407

To save $10,000 over two years, you would need to deposit $20,407 per month in an account earning 4.7% interest (compounded monthly).

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For a distribution that is skewed right, the true statement is (c) mean> median

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

a distribution that is skewed right,

For a distribution that is skewed right, it means that there are more values on the right tail of the distribution and the tail extends further to the right than the left.

In this case, the mean is typically greater than the median.

Hence, the correct answer is "mean > median."

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The quadrilateral exists not a parallelogram.

The formula to calculate the distance between two points is equal to

[tex]$$d=\sqrt{(y 2-y 1)^2+(x 2-x 1)^2}$$[/tex]

We have Q(-10,-2), R(1,-1)

substitute the values in the above equation, we get

[tex]& d=\sqrt{(-1+2)^2+(1+10)^2} \\[/tex]

simplifying the equation, we get

[tex]& d=\sqrt{(1)^2+(11)^2} \\[/tex]

d = √122 units

Find the distance TS

the formula to calculate the distance between two points is equal to [tex]$d=\sqrt{(y 2-y 1)^2+(x 2-x 1)^2}$[/tex]

we have

T(-11, -8), S(1, -7)

substitute the values in the above equation, we get

[tex]$d=\sqrt{(-7+8)^2+(1+11)^2}$[/tex]

simplifying the equation, we get

[tex]$d=\sqrt{(1)^2+(12)^2}$[/tex]

d = √145 units

We know that the opposite sides of QR and TS exist.

The opposing sides of a parallelogram are congruent, but in this case, QR TS.

√122 units ≠ √145 units

Therefore, the quadrilateral exists not a parallelogram.

The complete question is:

Determine whether the quadrilateral is a parallelogram using the indicated method Q(-10,-2), R(1,-1), S(1,-7), T(-11,-8) (Distance Formula)

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The rate at which a particular animal grows is proportional to the difference between its adult height and current height. As the animal grows, the difference between the adult height and current height decreases. T

Therefore the rate of growth decreases. This is because, as the animal grows, it reaches a point where it cannot grow any taller and the rate of growth slows down. In other words, the rate of growth is proportional to the difference between the adult's height and current height. the rate of growth is also related to the age of the animal.

Younger animals tend to grow faster than older animals because their adult height is still far away, so the difference between their current height and adult height is greater.As the animal gets older and closer to its adult height, the rate of growth decreases.

furthermore, the rate of growth is also affected by the animal's diet and overall health. If the animal is malnourished or unhealthy, then its rate of growth will be slower than if it had a healthy diet and lifestyle. In conclusion, the rate of growth of  a particular animal is proportional to the difference between its adult height and current height

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The amount of the required down payment is $532000.

The amount of the mortgage is $2710260/

The monthly payment for principal and interest is  $7528.5

We know simple interest (SI) is given by SI = (p×r×t)/100, where

p = principle, r = rate in percentage, and t = time in years.

The amount of the required down payment would be 19% of $2800000 which is, = (19/100)×2800000.

= $532000.

Felix obtains a 30​-year mortgage with an interest rate of ​%6.5 which is,

= [(2800000 - 532000)×6.5×30]/100.

= 2268×30×6.5.

= $442260 he has to pay in 30 years in addition to the principal of (2800000 - 532000) = 2268000.

P = $2710260

Now, 30 years has 30×12 = 360 months.

Therefore, His monthly downpayment would be,

= (2710260/360).

= $7528.5

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Answer:

means that s = 10

Step-by-step explanation:

given P(s) = 60 and P(s) = 3s , then equating the right sides

3s = 60 ( divide both sides by 3 )

s = 10

an equilateral triangle with a perimeter of 60 has side length of 10