Complex mathematical
A) [tex]$x+y=(1+2 \sqrt{3})+(1-\sqrt{3}) i$[/tex]
B) [tex]$y+z=(\sqrt{3}+1)-(2+\sqrt{3}) i$[/tex]
c) [tex]$y-z=(\sqrt{3}-1)-\sqrt{3} i$[/tex]
are the value of given algebraic expression.
What is Complex Number?The numbers which can be expressed in the form of [tex]$x+iy[/tex] where, [tex]$x, y$[/tex] are real numbers and 'i' is an imaginary number called "iota".
here [tex]$\mathrm{i}$[/tex] is iota whose value is: [tex]$\mathrm{i}=\sqrt{-1}[/tex]
Given .
[tex]$$\begin{aligned}& x=1+\sqrt{3}+2 i \\& y=\sqrt{3}-(1+\sqrt{3}) i \\& z=1-i\end{aligned}$$[/tex]
upon solving two complex number we solve coefficient of iota together and real number together.
A) to find [tex]$(x+y)$[/tex]
[tex]$$\begin{aligned}& x+y=(1+\sqrt{3}+2 i)+(\sqrt{3}-i-\sqrt{3} i) \\& x+y=(1+2 \sqrt{3})+(2-1-\sqrt{3}) i \\& x+y=(1+2 \sqrt{3})+(1-\sqrt{3}) i\end{aligned}[/tex]
B) [tex]$\mathbf{y}+\mathbf{z}$[/tex]
[tex]$$\begin{aligned}& y+z=(\sqrt{3}-i-\sqrt{3} i)+(1-i) \\& y+z=(\sqrt{3}+1)-(2+\sqrt{3}) i\end{aligned}[/tex]
c) [tex]$\mathbf{y}-\mathbf{z}$[/tex]
[tex]$$\begin{aligned}& y-z=(\sqrt{3}-i-\sqrt{3} i)-(1-i) \\& y-z=(\sqrt{3}-1)-\sqrt{3} i\end{aligned}[/tex]
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Which fraction is represented by the red portion of the picture?
A. 3/8
B. 2/3
C. 5/3
D. 3/5
E. 1/2
F. 3/2
NO LINKS PLEASE
Find the length of c to the nearest tenth using the Pythagorean theorem
Answer:
c = 10.6
Step-by-step explanation:
c² = a² + b²
c² = 7² + 8²
c² = 49 + 64
c² = 113
Take the square root of both sides
c = 10.6301458127
Rounded
c = 10.6
1. Can the following quadratic equation be solved by factoring?
x² - x-3=0
yes
no
Answer: No. This equation can't be solved by factoring
standard equation for hyperbola with vertices (-2, 1), (2, 1) and foci (-3, 1) (3,1)
Will give brainliest
Answer:y=(x+3)2−17
Step-by-step explanation: 3,11 5,15
Round 0.09305085 to the nearest hundredth
The following probability distributions of job satisfaction scores for a sample of information systems (IS) senior executives and middle managers range from a low of 1 (very dissatisfied) to a high of 5 (very satisfied).
Probability
Job Satisfaction Score IS Senior Executives IS Middle Managers
1 0.05 0.04
2 0.09 0.10
3 0.03 0.12
4 0.44 0.45
5 0.39 0.29
1. What is the expected value of the job satisfaction score for senior executives (to 2 decimals)?
2. What is the expected value of the job satisfaction score for middle managers (to 2 decimals)?
3. Compute the variance of job satisfaction scores for executives and middle managers (to 2 decimals).
4. Compute the standard deviation of job satisfaction scores for both probability distributions (to 2 decimals).
5. What comparison can you make about the job satisfaction of senior executives and middle managers?
Answer:
1.)E₁ = 4,03
2) E₂ = 3,85
3) σ₁² = 1,23
4)σ₂² = 1,14
5)σ₁ = 1,11
6)σ₂ = 1,07
5 ) Distribution of senior executive and Middle Manager look pretty similar , diference in median 0,18 and difference in standard deviation 0,04
Step-by-step explanation:
1.-Expected value of the job satisfaction score for senior executive
E₁, variance σ₁ and standard deviation σ₁ and expected value of the job satisfaction score for Middle Manager E₂ variance σ₂ and standard deviation σ₂
E(X) = ∑ ( xi *f(xi)
JSS IS senior executive IS Middle Managers
1 0,05 0,04
2 0,09 0,1
3 0,03 0,12
4 0,44 0,45
5 0,39 0,29
∑ xi*f(xi) = 1*0,05 + 2 *0,09 + 3*0,03 + 4 * 0,44 + 5 * 0,39
E₁ = 0,05 + 0,18 + 0,09 + 1,76 + 1,95
1.)E₁ = 4,03
2.) ∑ xi*f(xi)
E₂ = 1* 0,04 + 2 * 0,1 + 3*0,12 + 4*0,45 +5*0,29
E₂ = 0,04 + 0,2 + 0,36 + 1,8 + 1,45
E₂ = 3,85
2 ) E₂ = 3,85
3) Variance of job satisfaction scores for senior executives.
x² f(x) x²* f(x)
1 0,05 0,05
4 0,09 0,36
9 0,03 0,27
16 0,44 7,04
25 0,39 9,75
σ₁² = [ ∑ x²*f(x) ] - μ² ∑ x²*f(x) = 17,47
In this case μ = E μ² = ( 4,03)² = 16,24
For senior executives: σ₁² = 17,47 - 16,24 = 1,23
σ₁² = 1,23
And standard deviation σ₁ = 1,11
For Middle managers
x² f(x) x²* f(x)
1 0,04 0,04
4 0,1 0,4
9 0,12 1,08
16 0,45 7,2
25 0,29 7,25
∑ x²*f(x) = 15,97
σ₂² = 15,97 - (3,85)² = 15,97 - 14,82
σ₂² = 1,14
σ₂ = √1,14 = 1,07
5 ) Distribution of senior executive and Middle Manager look pretty similar , diference in median 0,18 and difference in standard deviation 0,04
Thomas counts the number of cars he sees in the parking lot of the school each hour of the day. He counted the following number of cars the first four hours of the day.
•12 cars the first hour
•24 cars the second hour
•36 cars the third hour
•48 cars the fourth hour
What is true of the function Thomas wrote that represents the number of cars as a function of the number of hours, h? Select all that apply.
If a city that currently has a population of 1000 triples in size every 8 years, what will the population be in 24 years? Is the population growth modeled by a linear function or an exponential function?
Step-by-step explanation:
I'm pretty sure it's 19200? or maybe im writing is wrong
Answer:
After 24 years population of the city will be 27000.
exponential function.
Step-by-step explanation:
in picture
Simplify the following rational expression. Be sure to state the condition.
The simplified form of the rational expression (x²+5x+6)/(3x+6) is (x+3)/2.
And we used factorization to find the simplified form.
What is factorization?Factorization is a process to simplify the expression by finding the factors of that expression.
And to find the same expression from factors, you have to reverse the process.
Given:
The rational expression,
(x²+5x+6)/(3x+6).
Simplifying,
the expression using factorization method.
First, (x²+5x+6),
= x²+2x+3x+6
= x(x+2)+3(x+2)
= (x+2) (x+3)
And 3x+6 = 3(x+2)
Substituting the simplified values to the given expression,
(x²+5x+6)/(3x+6),
= (x+2) (x+3) / {3(x+2)}
Factor out the common factor,
= (x+3)/2
Therefore, the simplified form is (x+3)/2.
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As you probably know, there is still a difference in wages for men vs. women in this country. Besides straight-up
discrimination and bias (which has been lessening over the decades), people point to many other factors that continue
to keep the average amount earned by a full-time, year-round female employee lower than males, on average (like
women taking more time off for maternity than men do for paternity, career selection, etc.).
Every ten years as part of the census, data is collected that gives the median income of "full-time year-round workers."
In 2010 the median income of FTYR workers was $42,800 for men, compared to $34,700 for women. In 1960, if you
adjust the wages to 2009 dollars, wages were $38,907 for men and $23,606 for women.
Based on this data, when might we predict women's wages might catch up to men's? Show all work you did to get
your answer. AND NO LINKS TO FILES OR ANYTHING LIKE THAT.
9514 1404 393
Answer:
year 2066
Step-by-step explanation:
In order to do this, we need to make some assumptions. We'll assume that the 2010 wages are also in 2009 dollars. (If not, there's an inflation factor that needs to be accounted for.) We also need to assume the form of the change in wages over time. The simplest assumption there is that wages change linearly.
Then we can write equations for men's and women's wages as follows:
Using the 2-point form of the equation for a line, we have ...
y = (y2 -y1)/(x2 -x1)(x -x1) +y1
Men's wages
y = (42800 -38907)/(2010-1960)(x -1960) +38907
y = 77.86(x -1960) +38907
y = 77.86x -113,698.6 . . . . . where x is the year
Women's wages
y = (34700 -23606)/(2010 -1960)(x -1960) +23606
y = 221.88x -411,278
These values are equal when ...
77.86x -113,698.6 = 221.88x -411,278
297,580.2 = 144.02x . . . . . . . add 411278 -77.86x
2066.2 = x . . . . . . . divide by the coefficient of x
Based on this data we predict women's wages might catch up to men's in the year 2066, about 56 years from 2010.
_____
Alternate solution
In the 50 years from 1960 to 2010, the fraction of men's wages that women receive has increased from 23606/38907 ≈ 0.606729 to 34700/42800 ≈ 0.810748. That is a change of about 0.204 of men's wages in 50 years. The remaining fraction of 1-0.810748 = 0.189 might be expected to be wiped out in another (0.189/0.204)(50 years) = 46.4 years. That would be the year 2056.
The different results come from different assumptions. For the second solution, we assumed that the fraction improved linearly. Under the first assumption, that wages improved linearly, the fractional improvement is non-linear, and decreases over time.
_____
Additional comment
The usual assumption regarding things financial is that they change exponentially over time. If we use an exponential model, instead of a linear one, wage parity is reached in about 2046.
Select the correct answer.
Steve is trying to determine the proper rectangular pan to use for his banana bread recipe. He has four different pans that he can use, each with the same length and width but all with different heights.
Which of the following formulas will show how Steve can determine the height of a rectangular pan?
I believe it's A
I hope this helps and if I'm wrong I apologize
Which facts are true for the graph of the function below? Check all that apply.
F(x) = 3 • 4*
A. The range of F(x) is y> 4.
B. The y-intercept is (0,4).
c. It is decreasing.
D. The domain of F(x) is all real numbers.
E. It is increasing.
F. The y-intercept is (0,3).
Which radicals are already in the simplest form?
Therefore , answering the questions, we can state that a factorial radicals is streamlined, or in its most basic form, when the user ’s behalf has no square components.
what is radicals?Radical is the name for the symbol for the scale factor or nth root. Root expressions are expressions that have square roots. Radicand: An expression or value enclosed by a radical symbol. Examples are the radicalism 7, 2y+1, and on and on. Radicals can also be described using the terms below: Equations that contain radicals are known as radical equations. The expression contained within the square root is referred to as the "root expression."
Here,
We refer to a sum of squares radical as being simplified or in its purest form when the radicand contains no square components.
The simplest form of a radical also exists when the user ’s behalf is not a fraction.
so that radical = 2√x / x
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Please help me this is timed
Answer:
118
Step-by-step explanation:
Answer: 118
Step-by-step explanation:
4(5)^2+3(6)
4(25)+3(6)
100+3(6)
100+18
118
Helpp!! Solve the system by graphing.
The graph of f(x) = |x| is transformed to g(x) = |x + 1| – 7. On which interval is the function decreasing?
Answer:
g is decreasing for all x less than or equal to -1
Step-by-step explanation:
The graph of the function y = |x| looks like a "vee."
g(x) = |x + 1| - 7 moves that graph 1 unit to the left (I know, it looks backwards!) and down 7 units. See attached image.
Function g(x) is decreasing for all [tex]x \le -1[/tex].
Answer:
on edg3
Step-by-step explanation:
what percent of 50 is 25 with solution
Answer:
50%
What is a percentage?A percentage is a ratio, or a number expressed in the form of a fraction of 100. Percentages are often used to express a part of a total.
Looking at the problem, we can take 25, and divide 50 by it.
25 ÷ 50 = 0.5
0.5 is equal to 5/10, which is also equal to 50%, meaning that 50% of 50 is 25.
Round 0.2275 to the nearest hundredth
Answer:
0.23 is the answer
I wish you luck in your assignments.
-15 POINTS-
What’s the length of GH
In a charity marathon to raise money for Typhoon Ulysses, Alex finished 43rd out of 200 entrants. Find his percentile rank.
The percentile rank in a charity marathon to raise money for Typhoon Ulysses is 21.5 percentile.
What is the Percentile?A percentile (or a centile) is a measure used in statistics indicating the value below which a given percentage of observations in a group of observations fall. For example, the 20th percentile is the value (or score) below which 20% of the observations may be found.
Rank of Alex is 43rd
Total Entrants is 200
Percentile = Rank of Alex X 100 / Total Entrants
= 43 X 100 / 200
= 21.5 percentile
Thus, the percentile rank in a charity marathon to raise money 21.5 percentile.
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Three long-sleeve T-shirts sell for $14.97 What is
the unit price? Write and solve an equation using
a variable
Answer:3x=4.99
Step-by-step explanation: 14.97/3= 4.99
Please helping faster if you know please?!!!!!!
I NEED THIS QUICK PLEASE!!!!!!!
20 POINTS!!!!
Answer:
option 4 (D)
Step-by-step explanation:
Select largest number from 16,48,8
Answer:
48.
Step-by-step explanation:
8 < 16 < 48
48 > 16 > 8
Answer:
Step-by-step explanation:
Select largest number from 16,48,8
What is the slope of a line that is parallel to the graph of the function below.
y = 1/4x-3
Answer:
The slope of a line that is parallel to the graph of the function below is 1/4x
Step-by-step explanation:
The only way you can have a line that stays parallel to another is if they have the same slope, and the slope of them both is 1/4x
Whoever answers the previous question after this gets 50 points and brainliest if correct.
Step-by-step explanation:
I said it I knew it I did it I submit for you so I'm the one that is if if you know me.
Given that XV = 11 and XQ = 3, is X the incenter or the circumcenter of /? Find XR. A. circumcenter; XR = 3 B. incenter; XR = 3 C. circumcenter; XR = 11 D. incenter; XR = 11
Answer:
The answer is C.
I did the practice.
ZAOC measures 150°. OC is 20° clockwise from the negative x-axis, as shown. If ZAOC is rotated
60° counterclockwise, what angle does OC make with the x-axis?
Answer:
40 degrees clockwise.
Step-by-step explanation:
If we rotate 150 degrees counterclockwise by 60 degrees , we would end up at 210 so
210-170=40 degrees
It would be clockwise.
8.
Does a triangle with these side lengths exist?20, 10,9
Da) Yes
I b) No
Answer:
yes
Step-by-step explanation: