Find all cube roots of the complex number 64(cos (219°) + i sin (219°)). Leave answers in polar form
and show all work

Lisa would need to serve 12 customers to attain the projected income if Daisy calls in sick that day

What is linear function ?

A linear function is a mathematical function that can be represented by a straight line on a graph. It has the form of:

y = mx + b

where m is the slope of the line, which determines how steeply the line rises or falls, and b is the y-intercept, which is the point where the line crosses the y-axis.

According to the question:
If Daisy calls in sick, then Lisa will be the only stylist at the salon, and all customers will go to her. Let's use x to represent the number of Lisa's customers. Then the income generated by Lisa's customers can be represented by the equation:

18x = projected income

We can solve for x by dividing both sides of the equation by 18:

x = projected income / 18

Substituting the given projected income of $216, we get:

x = 216 / 18 = 12

Therefore, Lisa would need to serve 12 customers to attain the projected income if Daisy calls in sick that day.

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To check if the line drawn is diameter it should be intersected at centre and it must be equidistant from the centre of the circle.

A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle has rotational symmetry around the centre.

To determine if the line Neil drew is an actual diameter of the circle and not just a smaller chord, he can use the following method -

Extend the line on both sides to create two lines that intersect at a point outside the circle.

Use a compass to draw a circle with the same center as the original circle, and with a radius that is greater than half the length of the line Neil drew.

Check if the two lines intersect the circle at two points that are equidistant from the center of the circle.

If they do, then the line Neil drew is an actual diameter of the circle.

If they do not, then the line Neil drew is just a chord.

This method works because a diameter of a circle is the longest chord that passes through the center of the circle.

By extending the line Neil drew and creating two lines that intersect outside the circle, we can compare the distance from the center of the circle to each of the two intersection points with the radius of the circle we drew.

If the distances are equal, then the line Neil drew must be a diameter of the circle.

Therefore, the method to find the actual diameter is explained.

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You have a 4/12 probability.

Answer:

=(x+9)(x+5)

Step-by-step explanation:

The seller purchased the product at a cost of 7500 and sold it for 7950, which resulted in a gain of 6%. So, the cost price is 7500.

In business, it is essential to keep track of cost prices and profit margins to ensure profitability. If the selling price is 7950 and the gain is 6%, we can use the following formula to calculate the cost price:

Cost price = Selling price / (1 + Gain%)

Substituting the given values, we get:

Cost price = 7950 / (1 + 0.06)

Cost price = 7500

Therefore, the cost price of the product is 7500, the gain percentage is calculated based on the cost price and not the selling price.

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Answer:

$32.50

Step-by-step explanation:

20% * y = 6.5 =>

y =6.5 ÷ 20% =

6.5 ÷ (20 ÷ 100) =

(100 × 6.5) ÷ 20 =

650 ÷ 20 =

32.5

Percentage of 20% of what number = 6.5?

20% × ? = 6.5

20% of 32.5 = 6.5

The given statement "if we take a simple random sample from a normal distribution, the probability that the sample mean is equal to the population mean is 1 (i.e., 100%)" is false.

The probability that a sample mean is equal to the population mean is actually zero, since any given sample will differ slightly from the population mean due to sampling error. However, as the sample size increases, the sample mean is likely to be close to the population mean, and the probability of it being equal approaches 1 (i.e., 100%).

To explain further, the population mean is the mean of the entire population and is calculated by adding up all the values of the population and dividing them by the total number of individuals in the population. A sample mean, on the other hand, is the mean of a sample taken from the population and can be calculated by adding up the values of the sample and dividing them by the total number of individuals in the sample. Since the sample size is usually smaller than the population size, the sample mean is likely to be slightly different from the population mean due to sampling error.

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Answer: 40

Step-by-step explanation:

25/100 x ? = 10

multiply both sides by 100/25

x= 10 x 100/25

x=10

The pizza would be covered by approximately 100.48 centimeters of the pizza cutter if it is rotated exactly 4 times.

The circumference of a circle can be calculated using the formula:

circumference = π x diameter

where π is approximately equal to 3.14.

Given that the diameter of the pizza cutter is 8 centimeters, we can calculate its circumference as:

circumference = π x diameter

circumference = 3.14 x 8

circumference = 25.12 centimeters

If the pizza cutter is rotated exactly 4 times, it will cover a distance equal to 4 times its circumference:

distance covered = 4 x circumference

distance covered = 4 x 25.12

distance covered = 100.48 centimeters

Therefore, approximately 100.48 centimeters of the pizza would be covered by the pizza cutter if it is rotated exactly 4 times.

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Complete question

The image shows a circular pizza cutter that has a diameter of 8 centimeters. Approximately how many centimeters would the pizza cutter cover if it is rotated exactly 4 times

In the bridge, when the south has 13 points and 3 clubs and bids 1 club, the north responding with 3 clubs means that the North has a strong hand with six or more clubs.

In the game of bridge, bidding is a method of indicating the strength of a player's hand, which is the number of tricks that they believe they can win if they become the declarer. Every player has to declare their abilities based on the bid of the previous player when it is their turn to bid.

The bidding starts with the dealer and proceeds in a clockwise direction. The players can either make a bid or pass. The following are the four basic bids in Bridge:

When South has 13 points and 3 clubs, he makes a 1 Club bid. This bid can be interpreted as follows:

South has a strong hand with five or more clubs and 13 to 21 high card points. When South bids 1 Club, he implies that he has a balanced hand, which means that he has four cards in each suit, or an unbalanced hand, which means that he has a long suit, a singleton, or a void in some other suit.

When North responds with 3 Clubs, it means that he has a strong hand with six or more clubs. North has understood that South has five or more clubs and therefore responds with the number of clubs that he has in his hand to show that he is strong enough to support South's suit. Thus, North is trying to force South to become the declarer in clubs.

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Answer:

13 - The first option

11 - (x+1)

16 - first option

Step-by-step explanation:

The sampling method used in the study where the sample is chosen by separating all cars by size, and selecting 10 of each size grouping is known as stratified random sampling.

Stratified random sampling is a method of sampling that involves dividing the population into smaller sub-groups known as strata. In this method, each stratum is composed of elements that have similar characteristics.

The strata could be based on demographic characteristics such as age, sex, education, and so on. Once the strata have been created, the next step is to select a sample from each of the strata to make up the final sample. The selection is done randomly, and the number of elements selected from each stratum is proportional to the size of the stratum. This ensures that the sample is representative of the entire population in terms of the different characteristics of the population.

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In conclusion, the power series converges absolutely over an interval given by [tex]\left|x-7\right|>\frac{\left|a_n+1\right|}{\left|a_n\right|}\;\;\;\forall\;\;\;n\in\mathbb{N}\;\;\;\text{and}\;\;\;n>N, where N\in\mathbb{N}[/tex]is a natural number.

The interval over which the power series converges absolutely is given by [tex]\left|x-7\right|>\frac{\left|a_n+1\right|}{\left|a_n\right|}\;\;\;\forall\;\;\;n\in\mathbb{N}\;\;\;\text{and}\;\;\;n>N, where N\in\mathbb{N}[/tex] is a natural number.

In other words, for any given N, the series will converge absolutely over the interval \left|x-7\right|>\frac{\left|a_n+1\right|}{\left|a_n\right|}\;\;\;\forall\;\;\;n>N.

This means that the series will converge absolutely over a larger interval as N increases, since the terms \frac{\left|a_n+1\right|}{\left|a_n\right|} get closer to 1 for larger values of n.

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Answer:

The correct answer would be option (A).

Step-by-step explanation:

Answer: 5

Step-by-step explanation:

length = x

Width=x-2
Area=lw

15=(x)(x-2)

15=x^2-2x

0=x^2-2x-15

Quadratic formula:

X=-15

X=5

the length is 5 because the length can’t be negative

Answer:

[tex]2 \sqrt{61} \: in[/tex]

Step-by-step explanation:

Use the Pythagorean theorem (assume, that the length of hypotenuse is x):

[tex] {x}^{2} = {10}^{2} + {12}^{2} = 100 + 144 = 244[/tex]

[tex]x > 0[/tex]

[tex]x = \sqrt{244} = 2 \sqrt{61} [/tex]

Answer:

Step-by-step explanation:

To find out how many more hours Jason worked than Sheldon, we need to subtract the number of hours Sheldon worked from the number of hours Jason worked:

Jason's hours = 14/3

Sheldon's hours = 25/6

Jason's hours - Sheldon's hours = (14/3) - (25/6)

To subtract fractions, we need to have a common denominator, which in this case would be 6:

(14/3) - (25/6) = (28/6) - (25/6) = 3/6

Simplifying the result, we get:

3/6 = 1/2

Therefore, Jason worked 1/2 more hours than Sheldon.

Jason worked 1/3 more hours than Sheldon.

To find out how many more hours Jason worked than Sheldon, we need to subtract the number of hours Sheldon worked from the number of hours Jason worked.

Jason worked for 14/3 hours, which can be simplified to 4 and 2/3 hours. Sheldon worked for 25/6 hours, which can be simplified to 4 and 1/6 hours.

Subtracting the hours Sheldon worked from the hours Jason worked, we get: 4 and 2/3 - 4 and 1/6 = 2/3 - 1/6 = 1/3.

Therefore, Jason worked 1/3 more hours than Sheldon.

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The answer of the given question based on the supplementary angle is  the two angles are 58° degrees and 122° degrees.

An angle is a geometric figure that is formed by two rays or lines that share a common endpoint, called the vertex. The rays or lines are called  sides or arms of  angle. Angles are typically measured in the degrees or the radians.

The measure of an angle is determined by the amount of rotation needed to bring one of its sides into coincidence with the other side. A full rotation is 360° degrees, so an angle that is half of a full rotation is 180 degrees, an angle that is a quarter of a full rotation is 90° degrees, and so on.

Let's call the two angles "x" and "y". We know that they are supplementary, which means that their sum is 180° degrees:

x + y = 180

We also know that one angle (let's say "x") is two times the sum of the other angle (y) and 3:

x = 2(y + 3)

Now we can substitute the second equation into the first equation to eliminate "x":

(2(y + 3)) + y = 180

Simplifying the equation, we get:

3y + 6 = 180

Subtracting 6 from both sides, we get:

3y = 174

Dividing both sides by 3, we get:

y = 58

Now that we know "y", we can substitute it back into the equation for "x" to find its value:

x = 2(y + 3) = 2(58 + 3) = 122

Therefore, the two angles are 58° degrees and 122° degrees.

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The probability of hitting the black circle is closer to 0 and the probability of hitting the white portion of the target is closer to 1.

What is probability?

Probability refers to the numerical measure of the likelihood or possibility of a specific event taking place. It is a mathematical concept that involves calculating the ratio of the number of desired outcomes to the total number of possible outcomes. Probability ranges from 0 (representing an impossible event) to 1 (representing a certain event), with values in between indicating the degree of likelihood. Probability is widely used in various fields, including mathematics, statistics, science, engineering, finance, and social sciences, to make predictions, analyze data, and make decisions under uncertainty.

Explanation of the given questions :

Part A: The black circle has a radius of 1 unit and its center is the same as that of the square. Therefore, its diameter is 2 units, which is much smaller than the side length of the square, which is 11 units. This means that the area of the circle is much smaller than the area of the square.

Therefore, the probability of hitting the black circle is closer to 0.

Part B: The white portion of the target is the area of the square minus the area of the black circle. The area of the square is [tex]11 x 11 = 121[/tex] square units.

The area of the circle is [tex]\pi \times r^2 = \pi\times 1^2 = \pi[/tex] square units, which is approximately 3.14 square units. Therefore, the area of the white portion of the target is [tex]121 - 3.14 = 117.86[/tex] square units.

Since this is much larger than the area of the black circle, the probability of hitting the white portion of the target is closer to 1.

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Answer:

x:5,x:7

x^2-12x+35

x^2-12x=-35

x^2-12x+6^2=-35+36

(x+6)^2=1

insert a radical anywhere

x+6=1

x=1-6

x=-5. x=5

x=-1-6

x=-7. x=7

Therefore , the solution of the given problem of graphs comes out to be a = [P² * G * Ms / [tex](4\pi ^2* Mp)]^(1/3)[/tex]

Graphs are used by theoretical coordinate points physicists to analytically and graphically present assertions rather than values. Typically, a graph point shows the relationship between several distinct objects. A graph is a particular kind of pas de container construction composed of groups and lines. The borders, also known as the channels, should be joined with glue.

Here,

According to Kepler's third law, one can determine the connection between a planet's orbital period and its separation from a star by:

=> P² = (4π² / GM) * a³

where P denotes the orbit's duration in years, a denotes the semi-major axis in astronomical units (AU), G denotes gravity's constant, and M denotes the star's mass in solar masses.

If we rewrite this equation, we obtain:

=> a = [P² * G * Ms / [tex](4\pi ^2* Mp)]^(1/3)[/tex]

We can rewrite this equation as follows since our goal is to estimate the distance from the sun in AU based on the mass of the planet in relation to the sun:

=> a = [P² * G * Ms / [tex](4\pi ^2* Mp)]^(1/3)[/tex]

where Mp is the mass of the planet in relation to the sun and Ms is the mass of the sun.

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Only the final option, which is typical of a longitudinal study, calls for retesting the same set of individuals over a lengthy period of time.

It is a numerical value that runs from 0 to 1, with 0 denoting the impossibility of an event and 1 denoting its certainty. The probability of an event A is expressed mathematically as P(A), where P(A) is the number of possible ways that event A could happen divided by the total number of outcomes.

given

The final choice is the long-term study: "An intelligence test is given to a class of kindergarteners. During 30 years, they are retested every other year."

In a longitudinal study, a group of individuals are followed over a lengthy period of time, frequently years or even decades. A longitudinal study's goal is to look at how people change or grow over time and to pinpoint any potential contributing elements.

Only the final option, which is typical of a longitudinal study, calls for retesting the same set of individuals over a lengthy period of time.

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Odd coefficients of the polynomial are obtained by multiplying both odd integers.

Even coefficients of the polynomial are obtained by multiplying both even integers.

Even and odd coefficients of the polynomial are obtained by multiplying both odd integers.

Lets take two integer m and n,

If both 'm' and 'n' are odd integers, then the coefficients of the polynomial obtained by multiplying out will be odd.

If both 'm' and 'n' are even integers, then the coefficients of the polynomial obtained by multiplying out will be even.

If one of 'm' and 'n' is even and the other is odd, then the coefficients of the polynomial obtained by multiplying out will be even and odd.

There are no other cases.

The general form of the polynomial obtained by multiplying out a binomial is:

[tex](a+b)^n = nC_0a^n + nC_1a^{(n-1)}b + nC_2a^{(n-2)}b^2 + .....+ nC_n-1ab^{(n-1)} + nC_nb^n[/tex]

where [tex]nC_k[/tex] is a binomial coefficient.

In general, for a polynomial [tex](a+b)^n[/tex], the coefficient of the term of degree k is [tex]nC_k[/tex].

The binomial coefficients are defined as:  [tex]nC_k = n! / (k!\times(n-k)!)[/tex]

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The probability that Emme answers exactly 3 questions correctly is 0.1961.

Since each question has four answer choices and only one is correct, the probability of Emme randomly guessing the correct answer for each question is 1/4 = 0.25. Emme needs to answer exactly 3 out of the 9 questions correctly, so we use the binomial distribution with n = 9 and p = 0.25 to calculate the probability:

P(X = 3) = (9 choose 3) * (0.25)^3 * (0.75)^6

Using a calculator, we get:

P(X = 3) = 0.1961

Therefore, the probability that Emme answers exactly 3 questions correctly is 0.1961.

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On a control chart, Control limits separates common from assignable causes of variation option C.

Shewhart charts, after Walter A. Shewhart, are another name for control charts. It is a statistical process control tool that aids in tracking process advancements over time. For instance, hospital management decides to utilise a solution technique in order to shorten the time required to admit a patient.

The process flow diagram for how patients are admitted to the hospital is first created. The average amount of time it takes to admit a patient each day is then measured. Lastly, plot the process variables across time on a control chart.

This control chart's goals are to identify any "special" reasons of variation as well as to document any process improvements.

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The values of x is [tex]x < 39.5[/tex].

Given that the shopkeeper spends on rent and electricity is [tex]= 5x+14[/tex]

Spending of shopkeeper on rent [tex]= 3x-7[/tex]

So shopkeeper spends on electricity [tex]= (5x+14) - (3x-7) = 2x+21[/tex]

Given that amount the shopkeeper spends on electricity less than 100.

So suitable inequality,

[tex]2x+21 < 100[/tex]

[tex]2x < 100-21[/tex]

[tex]2x < 79[/tex]

[tex]x < 39.5[/tex]

All the values of [tex]x < 39.5[/tex].

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Step-by-step explanation:

[tex]volume = {x}^{3 \\} \\ so \: 1000000 = {x}^{3 \\} \\ x = \sqrt[3]{1000000} \\ x = 100[/tex]

Answer:

Let's denote the first term of the sequence as a, and the common difference between consecutive terms as d.

Then, we know that the fifth term is 5, so:

a + 4d = 5

Similarly, we know that the sixth term is 2.5, so:

a + 5d = 2.5

We can solve this system of equations by subtracting the first equation from the second:

(a + 5d) - (a + 4d) = 2.5 - 5

d = -2.5

Now, we can substitute this value of d into either equation to find the value of a:

a + 4d = 5

a + 4(-2.5) = 5

a - 10 = 5

a = 15

Therefore, the first term of the sequence is 15, and the common difference is -2.5. We can use this to find the value of the second term:

a + d = 15 + (-2.5) = 12.5

Therefore, the second term of the sequence is 12.5.

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The probability of red is 0.1724, given the following table.

The table provided is given in the form of a contingency table. It is used to display the relationship between two categorical variables or nominal data through frequency distribution. It is also referred to as a two-way frequency table.

The table has "Yes" and "No" categories in the rows and "Red" and "Blue" categories in the columns.

The probability of Red can be calculated using the formula;

P(Red) = (Frequency of Red) / (Total Frequency)

Using the values provided in the table

,P(Red) = 15/87P(Red) = 0.1724

Hence, the probability of red is 0.1724.

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The line-plot of the the given data 9 3/4, 10 1/2, 9 1/4, 10 1/4, 11, 10 1/4, 9 1/2 that displays the lengths of the books on the booom shelf is attached.

What is line plot?

A line plot is a type of graph that represents the kind of data representation. It is line plot or a line chart shows the data in a visual form or visual representation. The graph is plotted with help of straight lines and points or dots. The x-axis is represented by straight lines or the it is labelled about the data. The y-axis is represented by the dots or frequency of the data. It is generally used to represent the small data set. This graph uses symbols to show or represent the frequency of the observations.

The data represented here is 9 3/4, 10 1/2, 9 1/4, 10 1/4, 11, 10 1/4, 9 1/2

we can make the frequency table using the above values, after which it can be plotted on the line-plot graph.

1-9 1/4--1 dot

2-9 1/2--1 dot

3-9 1/2--1 dot

4-10 1/4-2 dots

5-10 1/2--1 dot

6-11--1 dot

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Attached is a line-plot of the given data showing the lengths of the books on the book shelf: 9 3/4, 10 1/2, 9 1/4, 10 1/4, 11, 10 1/4, and 9 1/2.

An example of a graph that shows this sort of data representation is a line plot. The data is presented visually in the form of a line plot or a line chart. With the aid of straight lines, points, or dots, the graph is drawn. Straight lines or labels that describe the data are used to depict the x-axis. The dots or frequency of the data are used to depict the y-axis. It often serves as a representation for a tiny group of data. The frequency of the observations is shown or represented by symbols on this graph.

9 3/4, 10 1/2, 9 1/4, 10 1/4, 11, 10 1/4, and 9 1/2 are the numbers shown.

Using the aforementioned variables, we can create the frequency table, which can then be plotted on the line-plot graph.

1-9 1/4--1 dot

2-9 1/2--1 dot

3-9 1/2--1 dot

4-10 1/4-2 dots

5-10 1/2--1 dot

6-11--1 dot

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Answer:

[tex]2 \sqrt{2(6 + \sqrt{3} )} [/tex]

Step-by-step explanation:

There's your answer.