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Answer:

The expression (8-i)/(2+i) in standard form is, 3 - 2i

Step-by-step explanation:

The expression is,

(8-i)/(2+i)

writing in standard form,

\((8-i)/(2+i)\\\)

Multiplying and dividing by 2+i,

\(((8-i)/(2+i))(2-i)/(2-i)\\(8-i)(2-i)/((2+i)(2-i))\\(16-8i-2i-1)/(4-2i+2i+1)\\(15-10i)/5\\5(3-2i)/5\\=3-2i\)

Hence we get, in standard form, 3 - 2i

The expression (8-i)/(2+i) in standard form a+bi is (15 - 10i) / (3 + 4i).

To write the expression (8-i)/(2+i) in standard form a+bi, we need to eliminate the imaginary denominator. We can do this by multiplying the numerator and denominator by the conjugate of the denominator.

The conjugate of 2+i is 2-i. So, we multiply the numerator and denominator by 2-i:

(8-i)/(2+i) * (2-i)/(2-i)

Using the distributive property, we can expand the numerator and denominator:

(8(2) + 8(-i) - i(2) - i(-i)) / (2(2) + 2(i) + i(2) + i(i))

Simplifying further:

(16 - 8i - 2i + i^2) / (4 + 2i + 2i + i^2)

Since i^2 is equal to -1, we can substitute -1 for i^2:

(16 - 8i - 2i + (-1)) / (4 + 2i + 2i + (-1))

Combining like terms:

(15 - 10i) / (3 + 4i)

Therefore, the expression (8-i)/(2+i) in standard form a+bi is (15 - 10i) / (3 + 4i).

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Using the bisection concept, we have that the measure of angle AXB is of 160º.

A bisection of an angle is the formation of a ray that divides the angle into two equal parts.

For this problem, we have that:

Hence the measure of angle AXB is of 160º.

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Step-by-step explanation:

parellogram

two opposite sides are equal

opposite angles add up to 180°

Since 3n² + 6n is both O(n² log n) and Ω(n² log n), we can conclude that it is indeed Θ(n² log n).

To prove that 3n² + 6n is in Θ(n² log n), we need to show both the upper and lower bounds.

First, we will prove the upper bound by showing that 3n² + 6n is O(n² log n). This means we need to find constants c and n₀ such that 3n²+ 6n ≤ c(n² log n) for all n ≥ n₀.

Let's simplify the expression 3n² + 6n:

3n² + 6n ≤ 3n² + 6n² (for n ≥ 1, since n is always positive)

            = 9n²

Now, we can set c = 9 and n₀ = 1. For all n ≥ 1:

3n² + 6n ≤ 9n² (which is the same as c(n²))

           ≤ 9n² log n

Therefore, we have shown that 3n² + 6n is O(n² log n), satisfying the upper bound.

Next, we will prove the lower bound by showing that 3n² + 6n is Ω(n² log n). This means we need to find constants c and n₀ such that 3n²+ 6n ≥ c(n² log n) for all n ≥ n₀.

Let's simplify the expression 3n² + 6n:

3n² + 6n ≥ 3n² (for n ≥ 1, since n is always positive)

            = 3n² log n

Now, we can set c = 3 and n₀ = 1. For all n ≥ 1:

3n² + 6n ≥ 3n² log n (which is the same as c(n² log n))

Therefore, we have shown that 3n² + 6n is Ω(n² log n), satisfying the lower bound.

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Answer:x=11.8

Step-by-step explanation:

Answer:

Cost of each pencil = $12.5

Cost of each eraser = $7.5

Step-by-step explanation:

Given:

Number of eraser bought = 3

Number of pencil bought = 2

Total amount paid = $47.50

Cost of one pencil and one eraser = $20

Find:

Each cost

Computation:

Let;

Cost of each eraser = e

Cost of each pencil = p

So,

e + p = 20

e = 20 - p .................................... eq1

3e + 2p = 47.50

3(20 - p) + 2p = 47.50

60 - 3p + 2p = 47.50

-p = -12.5

Cost of each pencil = $12.5

e = 20 - p

e = 20 - 12.5

e = 7.5

Cost of each eraser = $7.5

Answer:

reeee

Step-by-step explanation:

Answer:

the answer would be: -27bk

10 goes on top of the b

4 goes on top of the k

The probability of the event "~ (a ∩ d)", or the probability that either "a" OR "d" does not occur, is 3/5.

The symbol "∩" represents the intersection of two events.

For example, "a ∩ d" means the event where both "a" and "d" occur together.

The symbol "~" means "not" or "complement." So, "~ (a ∩ d)" means the event where "a ∩ d" does NOT occur, or in other words, where "a" OR "d" does not occur.

Now, onto the question.

We are given that p(a ∩ d) = 2/5, which means that the probability of both events "a" and "d" occurring together is 2/5.

We want to find the probability of the event "~ (a ∩ d)", or the probability that either "a" OR "d" does not occur.

To find this probability, we need to use some basic probability rules.

One of these rules is that the probability of an event happening (let's call it "E") is equal to 1 minus the probability of the complement of that event not happening (~E).

In other words, p(E) = 1 - p(~E).

So, if we apply this rule to the event "~ (a ∩ d)", we get:
p(~ (a ∩ d)) = 1 - p(a ∩ d)

Now we can substitute in the value we were given for p(a ∩ d):
p(~ (a ∩ d)) = 1 - 2/5

Simplifying this gives:
p(~ (a ∩ d)) = 3/5

Therefore, the probability of the event "~ (a ∩ d)", or the probability that either "a" OR "d" does not occur, is 3/5.

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Answer:

A: x=-1

Step-by-step explanation:

Answer:

There is a 47cm difference between the two....

So you just added 28cm to 19cm to get 47cm....

Because 19-(-28) is 19 + 28.

Hope this helps :D

Step-by-step explanation:

This figure begins with the sentence, “We substitute x equals 3 and y equals 2 into both equations.” The first equation reads 3 times x minus 7equals 7. Then, 3 times 3 minus 2 equals 7. Then 7 = 7 is true. The second equation reads x minus 2y equals 4. The n times 2 minus 2 times 2 = 4. Then negative 2 = 4 is false.

The ordered pair (3, 2) made one equation true, but it made the other equation false. Since it is not a solution to both equations, it is not a solution to this system.

Exercise  5.1.1

Determine whether the ordered pair is a solution to the system:  {x−y=−12x−y=−5

(−2,−1)

(−4,−3)

Answer

Exercise  5.1.2

Determine whether the ordered pair is a solution to the system:  {3x+y=0x+2y=−5

(1,−3)

(0,0)

Answer

Exercise  5.1.3

Determine whether the ordered pair is a solution to the system:  {x−3y=−8−3x−y=4

(2,−2)

(−2,2)

Answer

Solve a System of Linear Equations by Graphing

In this chapter we will use three methods to solve a system of linear equations. The first method we’ll use is graphing. The graph of a linear equation is a line. Each point on the line is a solution to the equation. For a system of two equations, we will graph two lines. Then we can see all the points that are solutions to each equation. And, by finding what the lines have in common, we’ll find the solution to the system.

Most linear equations in one variable have one solution, but we saw that some equations, called contradictions, have no solutions and for other equations, called identities, all numbers are solutions. Similarly, when we solve a system of two linear equations represented by a graph of two lines in the same plane, there are three possible cases, as shown in Figure  5.1.1 :

This figure shows three x y-coordinate planes. The first plane shows two lines which intersect at one point. Under the graph it says, “The lines intersect. Intersecting lines have one point in common. There is one solution to this system.” The second x y-coordinate plane shows two parallel lines. Under the graph it says, “The lines are parallel. Parallel lines have no points in common. There is no solution to this system.” The third x y-coordinate plane shows one line. Under the graph it says, “Both equations give the same line. Because we have just one line, there are infinitely many solutions.”

Figure  5.1.1

For the first example of solving a system of linear equations in this section and in the next two sections, we will solve the same system of two linear equations. But we’ll use a different method in each section. After seeing the third method, you’ll decide which method was the most convenient way to solve this system.

Exercise  5.1.4 : How to Solve a System of Linear Equations by Graphing

Solve the system by graphing:  {2x+y=7x−2y=6

Answer

Exercise  5.1.5

Solve each system by graphing:  {x−3y=−3x+y=5

Answer

Exercise  5.1.6

Solve each system by graphing:  {−x+y=13x+2y=12

Answer

The steps to use to solve a system of linear equations by graphing are shown below.

TO SOLVE A SYSTEM OF LINEAR EQUATIONS BY GRAPHING.

Graph the first equation.

Graph the second equation on the same rectangular coordinate system.

Determine whether the lines intersect, are parallel, or are the same line.

Identify the solution to the system.

If the lines intersect, identify the point of intersection. Check to make sure it is a solution to both equations. This is the solution to the system.

If the lines are parallel, the system has no solution.

If the lines are the same, the system has an infinite number of solutions.

Exercise  5.1.7

Solve the system by graphing:  {y=2x+1y=4x−1

Answer

Exercise  5.1.8

Solve the system by graphing:  {y=2x+2y=−x−4

Answer

Exercise  5.1.9

Solve the system by graphing:  {y=3x+3y=−x+7

Answer

Both equations in Exercise  5.1.7  were given in slope–intercept form. This made it easy for us to quickly graph the lines. In the next example, we’ll first re-write the equations into slope–intercept form.

Exercise  5.1.10

Solve the system by graphing:  {3x+y=−12x+y=0

Answer

Exercise  5.1.11

Solve each system by graphing:  {−x+y=12x+y=10

Answer

Exercise  5.1.12

Solve each system by graphing:  {2x+y=6x+y=1

Answer

Usually when equations are given in standard form, the most convenient way to graph them is by using the intercepts. We’ll do this in Exercise  5.1.13 .

Exercise  5.1.13

Sopt form.y=12x−3m=12,b=−3{y=12x−3x−2y=4 If we solve the second equation for y, we get x−2y=4x−2y=−x+4y=12x−2m=12,b=−2

The two lines have the same slope but different y-intercepts. They are parallel lines.

Figure  5.1.3  shows how to determine the number of solutions of a linear system by looking at the slopes and intercepts.

Answer:

25 pounds

Step-by-step explanation:

Answer:

I would say 25 pounds

Step-by-step explanation:

Working together, Shayna and Huong can clean an attic in 6.16 hours. Had she done it alone, it would have taken Huong 11 hours. Therefore, Shayna can clean the attic alone in 80 hours.

Let's denote the amount of work to be done by x units. The work done by Shayna in one hour is y.

Shayna and Huong work together for 6.16 hours, so in one hour they do 1/6.

16 of the work together.According to the problem:

x/6.16 = 1/6.16 units per hour

Therefore, the amount of work done by Huong in one hour is (x/11).

Now, we can express the amount of work done by Shayna and Huong in one hour as:

(x/11) + y = 1/6.16

To determine the value of y, we can solve the above equation. Solving the equation:

(x/11) + y = 1/6.16y = (1/6.16) - (x/11)y = (11-6.16x)/(11 × 6.16)

So the amount of work done by Shayna in one hour is y = (11-6.16x)/(11 × 6.16).

To find how long it would take Shayna to do it alone, we have to express the amount of work done by Shayna alone in one hour as x/h.

Using the unitary method we have:

x/h = yx/h = (11-6.16x)/(11 × 6.16)

hx = 11 × 6.16 - 6.16x

hx + 6.16x = 11 × 6.16

hx = (11 × 6.16)/0.84 = 80 hours

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The equation 7x² - 5x + 7y² + z² = 3 in the cylindrical coordinate system is 7r² - 5r cos θ + z² = 3.

In the cylindrical coordinate system, cylindrical dimensions are ordered triples that describe the location of a point.

The equation is given below.

7x² - 5x + 7y² + z² = 3

The conversion of the cartesian coordinate to the cylindrical coordinate system.

x = r cosθ

y = r sinθ

z = z

Then put these values in the equation. Then we have

\(\begin{aligned} 7(r \cos \theta)^2-5(r \cos \theta) + 7(r \sin \theta)^2 + z^2 &=3\\\\7r^2 \cos ^2\theta-5r \cos \theta + 7r^2 \sin ^2\theta + z^2 &=3\\\\7r^2 (\sin ^2\theta + \cos ^2\theta ) - 5r \cos \theta + z^2 &= 3\\\\7r^2 - 5r \cos \theta + z^2 &= 3 \end{aligned}\)

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Answer:

-15.6 or -15 3/5

Step-by-step explanation:

Answer:

m = -2/3

Step-by-step explanation:

m = slope

\( m = \frac{y2 - y1}{x2 - x1} \)

m = -3 -1/ 3 - (-3)

m= -4/ 6

m= -2/3

Answer:

14

Step-by-step explanation:

AB = 10+( 10/15 × 6)

= 10 + 4= 14

Answer:

85 ° is the answer to the question

Answer:

85 degrees

Step-by-step explanation:

Angles in a triangle add up to 180 in total so to solve it add the two angles you know so 18+77 which is 95 than you subtract it from 180 so 180 - 95 is 85

The labor-force participation rate was 154/ 234.9  

The rate of the entire working-age population that is actively seeking employment is defined as the "labor force participation rate." In simple words, it measures the size of the labor force, which consist of both the labor force that is employed and the labor force that is actively seeking employment.

The formula for the rate of Labour-force participation is given by

Labor Force Participation Rate = Labor Force / Total Civilian Non-Institutional Population

Where,

Labor Force = Total Employed Civilians + Total Unemployed civilians

Here we have,

The total adult population = 234. 9 million

The population of unemployment = 12.4 million

The population of employment = 141.6 million    

From the above formulas,

Labor Force = 141.6 million + 12.4 million = 154 million  

Labor Force Participation Rate =  154/ 234.9  

Therefore, The labor-force participation rate was 154/ 234.9  

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To find the new average height of the 10 trees, we need to take into account the additional height of the one tree. We can start by calculating the total height of all 10 trees before the growth, which would be 10 trees x 2.6 metres per tree = 26 metres in total. Then, we can add the height of the one tree that grew, which is 2.2 - 1.7 = 0.5 metres.

Therefore, the total height after growth is 26 + 0.5 = 26.5 metres. To find the new average height, we divide the total height by the number of trees, which is 26.5/10 = 2.65 metres. We are asked to give the answer to two decimal places, so we round it to 2.65. Therefore, the new average height of the 10 trees is 2.65 metres. The new average height of the 10 trees is 2.65 metres, given to two decimal places.

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Answer:

Hope it helps dear.Please let me know

Answer:

Step-by-step explanation:

3) Opposite sides of a parallelogram are parallel

4) Alternate interior angles theorem

5) Reflexive property

6) ASA

The ratios of (a) square kens to square meters (1 ken² / 1 m²) is 3.88

For given question,

We have been given the unit conversion.

A traditional unit of length in Japan is the ken

and 1 ken = 1.97 m

We need to find the the ratios of (a) square kens to square meters.

First we find the square of 1 ken.

⇒ 1 square kens = (1.97 m)²

⇒ 1 square kens = 1.97 × 1.97 m²

⇒ 1 square kens = 3.88 m²                  ..................(1)

And 1 square meters = 1 m²                 ................. (2)

Now we take the ratio of square kens to square meters.

From (1) and (2),

⇒ 1 ken² / 1 m² = 3.88 / 1

⇒ 1 ken² / 1 m² = 3.88

Therefore, the ratios of (a) square kens to square meters (1 ken² / 1 m²) is 3.88

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There is an outstanding bond from BP with a 15-year maturity, a $1,000 par value, a 6.9% coupon rate that is paid semi-annually, and a price of 98.17. As a result, the annual cost of debt for this bond is roughly 8.5 percent.

To calculate the cost of debt, we need to determine the yield to maturity (YTM) of the bond. The YTM is the rate of return an investor would earn by purchasing the bond and holding it until maturity. We can use the bond pricing formula to calculate the YTM.

The bond pricing formula is as follows:

\(\text{Bond Price} = \frac{{C \times (1 - (1 + r)^{-n})}}{{r}} + \frac{{M}}{{(1 + r)^n}}\)

Where:

C = Coupon payment

r = Yield to maturity (YTM)

n = Number of periods

M = Par value

Given information:

Coupon payment (C) = \(\$1,000 \times \frac{6.1\%}{2} = \$30.50\)

Par value (M) = $1,000

Bond price = $1,000 × 83.57% = $835.70

We know the bond has 15 years to maturity, and coupons are paid semiannually. So, the number of periods (n) is 15 years × 2 = 30.

Using the bond pricing formula, we can rearrange it to solve for the YTM:

\(Bond Price = \frac{{C \times (1 - (1 + r)^{-n})}}{{r}} + \frac{{M}}{{(1 + r)^n}}\)

Substituting the given values:

\($835.70 = \left(\frac{{\$30.50 \times (1 - (1 + r)^{-30})}}{{r}}\right) + \left(\frac{{\$1,000}}{{(1 + r)^{30}}}\right)\)

To find the YTM, we need to solve this equation either algebraically or using numerical methods like trial and error or using financial calculators/spreadsheets.

By using a financial calculator or spreadsheet, we find that the YTM is approximately 8.5%. Therefore, the cost of debt for this bond is approximately 8.5% per year.

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Complete question :

Problem 17 Intro BP has a bond outstanding with 15 years to maturity, a $1,000 par value, a coupon rate of 6.1%, with coupons paid semiannually, and a price of 83.57 (percent of par). | Attempt 1/10 for 10 pts. Part 1 What is the cost of debt? B+ decimals Submit

Answer:

102.14

Step-by-step explanation:

Answer:

The answer to your question is 102.14

Step-by-step explanation:

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Have a good day sir or, madam

The criterion used to obtain the ordinary least square (OLS) estimator is to minimize the sum of the squared differences between the observed values and the predicted values.

In OLS, the goal is to find the line that best fits the given data points. The estimator minimizes the sum of the squared residuals, which are the differences between the observed values and the predicted values. The squared residuals are used to ensure that both positive and negative differences contribute to the overall error measure.

The OLS estimator achieves this by calculating the coefficients of the linear regression model that minimize the sum of the squared residuals. It finds the intercept and slope of the line that minimizes the total squared distance between the data points and the regression line. This minimization process is based on the principle of least squares, which aims to find the best-fitting line by minimizing the overall error.

By minimizing the sum of the squared residuals, the OLS estimator provides a measure of how well the regression line represents the data points. It allows for the determination of the line's slope and intercept, which can be used for predicting values and understanding the relationship between the variables.

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