In the graph, z is a complex number represented as a vector from the origin. What is the product of z and its conjugate?

Final answer:

Miryam Williams' total pay is $3,237.50.

Explanation:

To calculate Miryam Williams' total pay, we first need to calculate her commission.

Her commission is 3.5% of her total sales, which is $92,500.

Commission = 3.5% × $92,500 = $3,237.50.

Next, we need to determine if Miryam's commission exceeds $5,000.

Since her commission is $3,237.50, it does not exceed $5,000. Therefore, she does not receive the $500 bonus.

Finally, to calculate her total pay, we sum her commission and the bonus (which is $0 in this case).

Total Pay = Commission + Bonus = $3,237.50 + $0 = $3,237.50.

There will be a second image that will be showing the answer

Answer:

x = -1

Step-by-step explanation:

[tex] x^2 + 2x + 5 = 4 [/tex]

Subtract the constant term.

[tex] x^2 + 2x = -1 [/tex]

Add half of the coefficient of the x-term to complete the square.

[tex] x^2 + 2x + 1 = -1 + 1 [/tex]

[tex] (x + 1)^2 = 0 [/tex]

[tex] x + 1 = 0 [/tex]

[tex] x = -1 [/tex]

Answer:

C - 2 2/9

Step-by-step explanation:

7 1 /2 x + 3 2/ 3 = −13

Subtract 3 2/3 from each side

7 1 /2 x + 3 2/ 3 - 3 2/3 = −13 - 3 2/3

7 1/2x = -16 2/3

Change each mixed number to an improper fraction

7 1/2 = (2*7 +1)/2 = 15/2

16 2/3 = (3*16+2)/3 = 50/3

15/2 x = -50/3

Multiply each side by 2/15 to isolate x

2/15 * 15/2 x = -50/3 * 2/15

x = -100/45

Simplify

x = -20/9

Change back to a mixed number

9 goes into 20 2 times with 2 left over

x = -2 2/9

Answer:

-1

Step-by-step explanation:

The midline is the average of the maximum and minum.

0.5 = (y + 2) / 2

1 = y + 2

y = -1

The minimum is at y=-1.

For the given problem the value of ymin is -1.

Suppose maximum is denoted by ymax and minimum is denoted by ymin ymid represents the mid.

By mid point theorem y

mid   = (ymax + ymin)/2

Given ymid  = 0.5

         ymax  = 2

          ymin  = y

substituing values 0.5 = (2+ y)/21 = 2+yy = -1

yminimum  = -1

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Answer: 15+X=27

Step-by-step explanation: 15+X=27 X Represents How Much More Is Added

Answer:

Here, the given expression is,

  ( By the cross multiplication ),

Since, an extraneous solution is a solution, which is emerged by solving the equation but it does not satisfying the equation,

But for x = -3, the equation  follows,

⇒ x = -3 is the non-extraneous,

⇒ The given equation has only one solution x = -3 which is non-extraneous.

Step-by-step explanation:

Answer:

x = -3 is not extraneous solution.

Step-by-step explanation:

[tex]\frac{6}{x-3} =\frac{3}{x}\\Cross\,\, Multiply\\6x =3(x-3)\\6x = 3x-9\\6x-3x=-9\\3x= -9\\x=-9/3\\x=-3[/tex]

An extraneous solution is the solution that is obtained by solving the question given but does not satisfy the original equation.

In our case x = -3

Putting value back to the original equation

[tex]\frac{6}{x-3} =\frac{3}{x}\\\frac{6}{-3-3} =\frac{3}{-3}\\\frac{6}{-6} =-1\\-1=-1[/tex]

Since our original equation is satisfied so,

x = -3 is not extraneous solution.

Answer:

The Correct answer is: 1/3

Step-by-step explanation:

x = 2, y = 3

(4x + 1) / 3y²

(4*2 + 1) / 3*3²

(8 + 1) / (3*9)

9 / 27

= 1/3

Answer:

The solution is (3,13) and (-1,-3). So none of the mentioned options is correct.

Step-by-step explanation:

Given that

[tex]y = 4x + 1  (i)[/tex]

[tex]y = x^2 + 2x -2 (ii)[/tex]

Now, by susbstituting the value of 'y' from equation i to equation ii, we get

[tex]4x+1=x^2 + 2x -2[/tex]

[tex]0=x^2 + 2x -2-4x-1[/tex]

[tex]0=x^2 + (2x -4x) +(-2-1)[/tex]

[tex]0=x^2 + (-2x) +(-3)[/tex]

[tex]0=x^2 -2x -3[/tex]

[tex]x^2 -2x -3 = 0 (iii)[/tex]

Now by factorization, equation iii can be written as

[tex]x^2 -3x +x -3 = 0[/tex]

[tex]x(x -3) + 1(x -3) = 0[/tex]

[tex](x -3)(x +1) = 0[/tex]

x = 3 and x = -1

By putting the values of x in equation i, we get

y = 4(3) + 1

y = 12 +1

y = 13

and

y = 4(-1) + 1

y = -4 +1

y = -3

Therefore, the solution is (3,13) and (-1,-3). So none of the mentioned options is correct.

Answer: Then you should pay her 4$ one hour

Step-by-step explanation:

Employees who earn increased commissions as their sales increase are paid a progressive commission. This method incentivizes employees to work harder to sell more, as their commission rate increases with sales volume.

Employees whose rate of commission increases as their sales increase are paid a progressive commission. With this method of remuneration, the more sales an employee makes, the higher their rate of commission becomes. This strategy is popular with both economists and the general public because it effectively incentivizes employees to work harder and achieve higher sales, leading to an increase in the overall performance of the business.

For example, a salesperson may earn a 10% commission on sales up to $10,000. However, any sales beyond that might attract a 15% commission rate, encouraging the employee to sell more. Such progressive commission schemes are common in sales-driven industries like real estate and retail.

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Answer:

4. 54- 8.5x>20

Step-by-step explanation:

Catherine only has $54, so she cannot spend more than that.

The canvas will cost at least $20, but we don't know how much exactly.

The tubes cost $8.50 each.

So, she starts with a total budget of $54, out of which she will buy paints (8.5x) and she wants to have at least $20 left for canvas.

So, we transpose those facts into the inequity:

54 - 8.5x > 20

Answer:

Opcion 4

[tex]54- 8.5x>20[/tex]

Step-by-step explanation:

We must identify the quantities.

Painting canvas

more than $ 20

Paint tubes (x):

$ 8.50 per tube = 8.50x

Available money:

$ 54

Then the expenses must not exceed $ 54, and the budget for the painting canvas must be greater than $ 20

The money after buying the paint tubes is:

[tex]54-8.50x[/tex]

We know that this amount must be greater than $ 20 because you need to buy the painting canvas. So  the inequality is:

[tex]54-8.50x> 20[/tex]

12%*14000*3

Which is 5040

Therefore, it will have to pay back $4050

J.T. will pay back a total of $18,480 altogether.

To calculate the total amount J.T. will pay back, we can use the formula for simple interest:

[tex]\[I = P \times r \times t\][/tex]

Where:

- (I) = Interest

- (P\) = Principal amount (the initial loan amount)

- (r) = Annual interest rate (in decimal form)

- (t) = Time (in years)

Given that J.T. borrows $14,000 at an annual interest rate of 12% for 3 years, we can plug these values into the formula:

[tex][I = 14000 \times 0.12 \times 3\][/tex]

[I = 5040]

So, the total interest J.T. will pay is $5,040.

To find the total amount J.T. will pay back, we add the interest to the principal:

[Total amount = Principal + Interest]

[Total amount = 14000 + 5040]

[Total amount = 18440]

Therefore, J.T. will pay back a total of $18,480 altogether.

In summary, by using the formula for simple interest, we determined the interest amount J.T. will pay over the 3-year period, and then added it to the principal amount to find the total repayment amount.

Complete question:

A bank offers a home improvement loan with simple interest at an annual rate of 12%. J.T. borrows an amount of $14,000 to pay back over 3 years. How much will he pay back altogether? Explain how you found the total amount.

Answer:

1.  mean

2. mode

3. range

4. measures of central tendency

5. outliers

6. median

good luck

Step-by-step explanation:

Answer:

Mean

Mode

Range

Measures of Central Tendency

Outliers

Median

Step-by-step explanation:

Just did the USTP got a 100%

Answer: x=5, y=15

Step-by-step explanation:

x= cost of a chair

y= cost of a table

The cost of each table and of each chair is x=5, y=15.

We have given that,

Five tables and eight chairs cost $115 three tables and five chairs cost $70.

Determine the cost of each table and of each chair.

A variable cost is a corporate expense that changes in proportion to how much a company produces or sells.

x= cost of a chair

y= cost of a table

Therefore, The cost of each table and of each chair is x=5, y=15.

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Final answer:

The conference rooms can accommodate approximately 34 attendees each, and the ballrooms can accommodate approximately 31 attendees each.

Explanation:

To find out how many attendees each room can accommodate, we need to divide the total number of attendees by the total number of rooms.

For the quarterly meeting, there are 2 conference rooms and 5 ballrooms, which can seat a total of 238 attendees. To find out how many attendees each room can accommodate, we divide 238 by 7 (2 + 5), which gives us approximately 34 attendees per room.

For the safety training event, there are 4 conference rooms and 5 ballrooms, which can seat a total of 286 attendees. Dividing 286 by 9 (4 + 5) gives us approximately 31 attendees per room.

To find the roots of the quadratic equation -10x^2 + 12x - 9 = 0, we can use the quadratic formula:
x = \frac{-b ± \sqrt{b^2 - 4ac}}{2a}
where
a is the coefficient of x^2, which is -10,
b is the coefficient of x, which is 12,
c is the constant term, which is -9.
First, let's identify the coefficients in our equation:
a = -10
b = 12
c = -9
Next, we will calculate the discriminant (Δ) using the formula:
Δ = b^2 - 4ac
Plug in the values of a, b, and c:
Δ = (12)^2 - 4*(-10)*(-9)
Δ = 144 - 4 * 10 * 9
Δ = 144 - 360
Δ = -216
Since the discriminant is negative, the quadratic equation has two complex roots. We will still use the quadratic formula to find them:
x = \frac{-b ± \sqrt{Δ}}{2a}
Substitute b, Δ, and a into the formula:
x = \frac{-12 ± \sqrt{-216}}{2 * (-10)}
Now, let's split the square root of the negative discriminant into real and imaginary parts:
√(-216) = √(216) * √(-1) = 14.697 * i
where i is the imaginary unit such that i^2 = -1. Substituting this into our quadratic formula gives:
x = \frac{-12 ± 14.697i}{-20}
Now, divide both the real and imaginary parts by -20:
x₁ = \frac{-12}{-20} + \frac{14.697i}{-20}
x₂ = \frac{-12}{-20} - \frac{14.697i}{-20}
Simplify those equations:
x₁ = \frac{12}{20} - \frac{14.697i}{20}
x₂ = \frac{12}{20} + \frac{14.697i}{20}
Further simplify by reducing the fractions:
x₁ = 0.6 - 0.73485i
x₂ = 0.6 + 0.73485i
Therefore, the roots of the quadratic equation -10x^2 + 12x - 9 = 0 are approximately x₁ = 0.6 - 0.73485i and x₂ = 0.6 + 0.73485i.

Using Pythagorean theorem, for the 8-feet wide picture window to pass through the 3-feet wide door, the door must be at least approximately 7.4 feet tall.

The picture window here is a rectangular sheet of glass. The longer side (8 feet) must fit through the door. The door is only 3 feet wide, which means that the 8-foot side of the window must be angled to pass through the door in vertical orientation.

To calculate the height of the door needed, consider the Pythagorean theorem which states that in a right triangle, the square of the hypotenuse (longest side) equals the sum of the squares of two sides (a2 + b2 = c2). Here 'a' is the width of the door (3 feet) and 'c' is the diagonal length of the window (8 feet). Solving for 'b' which represents the door's required height, we get:

b2 = c2 - a2

b2 = 82 - 32

b = sqrt(64 - 9) = sqrt(55)

Therefore, b is approximately 7.4 feet.

So the door must be at least 7.4 feet tall to pass the 8-feet picture window through it when angled vertically.

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The door needs to be approximately 21.3 feet tall for the glass to pass through.

To determine the height of the door, we need to consider that the glass is 8 feet wide. Since the door is only 3 feet wide, the glass needs to fit through a smaller opening. We can use similar triangles to find the height of the door. Let's set up a proportion:

8 / 3 = H / 8

Cross-multiplying, we get:

3H = 64

H = 64/3

Therefore, the door needs to be approximately 21.3 feet tall for the glass to pass through.

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Answer:

C) horizontal compression and reflection across the y-axis

Step-by-step explanation:

To quickly solve this problem, we can use a graphing tool or a calculator to plot the equation.

Please see the attached image below, to find more information about the graph

The original equation is:

f(x) = 2x

The new equation is:

f(-5x) = 2(-5x)

f(-5x) = -10*x

The answer is

C) horizontal compression and reflection across the y-axis

Answer:

Average mean salary [tex]=$26327.83[/tex]

Step-by-step explanation:

We have been given year and respective salaries in each year.

1960 $4,995

1970 $8,626

1980 $15,970

1990 $31,367

2000 $41,807

2010 $55,202

Now we nee do to determine the average mean salary for the six decades, 1960 – 2010.

So we just need to add all those six salaries and divide that sum by 6 to find the average mean salary.

Average mean salary [tex]=\frac{(4995+8626+15970+31367+41807+55202)}{6}[/tex]

Average mean salary [tex]=\frac{(157967)}{6}[/tex]

Average mean salary [tex]=26327.83333333[/tex]

Hence final answer is approx:

Average mean salary [tex]=$26327.83[/tex]

The answer would be 26327.83

Add up all the salaries and you will get $157,967

Then divide 157,967 by how many salaries there are which there’s 6

You will then get the answer 26327.83

Answer:

$24

Step-by-step explanation:

What you do is you just times 84 x 2/7 to get your answer.

84 x 2/7=$24 is your answer.

Answer:

$24

Step-by-step explanation:

To find out how much he spent on the shoes, take the amount of money he has and multiply by the fraction he spent on shoes

84 * 2/7

168/7

24

He spent 24 dollars on new shoes

Answer:

It would be Symmetric,

Uniform is when all of the lines are almost lined up perfectly with each other.

Symmetric is when the lines are in a mountain formation with both sides looking the same

Skewed it where one side will look very steep and the other side looks like a hill

Answer:

The answer is B. symmetric

Step-by-step explanation:

A symmetric distribution is one in which the two halves of the histogram appear as mirror-images of one another. So, this histogram is symmetric.

A "skewed left" or "skewed right" distribution is one in which the tail is on the left side or on the right side.

A uniform histogram has almost same height bars. This means that the data has approximately the same number of values in each group.

Answer:

Since we can see that angle L and angle C are supplementary angles, we have the following equation:

∠C + ∠L = 180°

Therefore to find the measurement of angle C, we need to subjact the measurement of angle C from 180°:

∠L = 180° - ∠C

Answer:Angle L and angle C are supplementary angles. The sum of supplementary angles is 180°. So, I can find the measurement of angle L by subtracting the measurement of angle C from 180°.

Step-by-step explanation:

Answer: 32 Quilts and you will have 11 squares left over

Step-by-step explanation:

Answer: [tex]x=2[/tex]

Step-by-step explanation:

The equation for inverse variation is:

[tex]x=\frac{k}{y}[/tex]

Where "k" is the constant of variation.

If you solve for for the constant "k", you get the form:

[tex]k=xy[/tex]

So, if [tex]xy=2[/tex] then [tex]k=2[/tex]

Knowing the value of "k", you can find the value of "x" when [tex]y=1[/tex], by substituting these values into the equation [tex]x=\frac{k}{y}[/tex].

Therefore, you get that the value of "x" when [tex]y=1[/tex] is:

[tex]x=\frac{2}{1}\\\\x=2[/tex]

Answer:

x=2

Step-by-step explanation:

Answer:

30

Step-by-step explanation:

If we get 40% off, we still have to pay 100-40% = 60%

Take the original price * the percent we have to pay

50 * 60%

Change to decimal form

50 *.6

30

We have to pay $30

Answer:

f(x) = (x + 4)² - 3

Step-by-step explanation:

The equation of a quadratic function in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Given

f(x) = x² + 8x + 13

To obtain f(x) in vertex form use the method of completing the square

add/ subtract (half the coefficient of the x- term)² to x² + 8x

f(x) = x² + 2(4)x + 16 - 16 + 13

f(x) = (x + 4)² - 3 ← in vertex form

Answer:

$4440

Step-by-step explanation:

From the question, the annual cost of the plan is $14800

The employer pays 70% 0f the cost.

⇒70/100 ×14800 =$10360

Remaining amount to pay=

14800-10360=$4440

Answer:

85°

Step-by-step explanation:

Since you know that the overall angle measure for the whole shape is 540°, you can subtract the known angles measures to find the right one.

540-90

450-90

360-115

245-160

85

Answer: 48

Step-by-step explanation: All you are doing is substituting x and y with the numbers it gives u then u just solve. 2 to the 4th power is 16. 4 to the 3rd power is 64 and then times .5 gives u 32. then u add and get 16+32=48

Answer:

Step-by-step explanation:

In a normal equation, y=mx+b, the constant of variation is the thing that "constantly" "varies" and in other words changes the same. This is the slope. In the equation, the slope is m.

-4y=8x

y=-2x

The constant of variation, aka slope, is -2

Answer:

[tex]\sqrt{85}[/tex]

Step-by-step explanation:

distance between the points given from the statement:

[tex]d=\sqrt{(x_{2}-x_{1})^{2}+( y_{2}-y_{1})^{2}} \\\\d=\sqrt{(-6-0)^{2}+(-3-4)^{2}}\\ \\d=\sqrt{36+49}\\\\d=\sqrt{85}[/tex]