The fourth power of the complex number 1 + i has an argument of π radians.
How to determine the argument of the power of a complex number
In this problem we find a complex number of the form z = (a + i b)ⁿ, where n is the grade of the power of the complex number, whose expanded form is obtained by the De Moivre's theorem:
(a + i b)ⁿ = rⁿ · (cos nθ + i sin nθ)
Where:
r - Norm of the complex number.θ - Argument of the complex number, in radians.And the norm and the argument of the complex number are, respectively:
Norm
r = √(a² + b²)
Argument
θ = tan⁻¹ (b / a)
First, determine the components of the complex number and its power:
a = b = 1; n = 4
Second, calculate the argument of the complex number:
θ = tan⁻¹ 1
θ = π / 4 rad.
Third, find the argument of the power of the complex number according to De Moivre's theorem:
θ' = 4 · (π / 4)
θ' = π
The argument of the power of the complex number is π radians.
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The mean incubation time of fertilized eggs is 20 days. Suppose the incubation times are approximately normally distributed with a standard deviation of 1 day. (a) Determine the 10th percentile for incubation times. (b) Determine the incubation times that make up the middle 95%.
Using the normal distribution, it is found that:
a) The 10th percentile for incubation times is of: 18.72 days.
b) The incubation times that make up the middle 95% are of: Between 18.04 and 21.96 days.
Normal Probability DistributionThe z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.The mean and the standard deviation for the incubation times are presented as follows:
[tex]\mu = 20, \sigma = 1[/tex]
The 10th percentile for the distribution is X when Z = -1.28, which is the value of Z with a p-value of 0.1, hence:
-1.28 = (X - 20)/1
X - 20 = -1.28
X = -1.28 + 20
Z = 18.72 days.
Considering the symmetry of the normal distribution, the bounds of the middle 95% of values are given as follows:
2.5th percentile: X when Z = -1.96.97.5th percentile: X when Z = 1.96.Hence the lower bound is:
-1.96 = (X - 20)/1
X - 20 = -1.96
X = -1.96 + 20
Z = 18.04 days.
The upper bound is:
1.96 = (X - 20)/1
X - 20 = 1.96
X = 1.96 + 20
Z = 21.96 days.
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The table shows the amount of storage y (in gigabytes) on a music-playing device when there are x songs on the device
A) Write an equation that models the amount of storage as a function of the number of songs
B) Interpret the slope and t-intercept of the line of fit
pls include work
From the given table
Part a
The equation of the function is y = ( - 0.7/277)x + 16
Part b
The slope of the line = - 0.7/277 and the y intercept of the line = 16
From the table
Choose two points
(242, 14.8) and (519, 14.1)
The slope of the line m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute the values in the equation
The slope of the line = (14.1 - 14.8) / (519 - 242)
= -0.7 / 277
The slope of the line = - 0.7/277
From the table at x = 0, the value of y = 16
Therefore the y intercept is 16
The slope intercept form is
y = mx + b
Substitute the values in the equation
y = ( - 0.7/277)x + 16
Part b
The slope of the line = - 0.7/277
The y intercept of the line = 16
Hence, from the given table
Part a
The equation of the function is y = ( - 0.7/277)x + 16
Part b
The slope of the line = - 0.7/277 and the y intercept of the line = 16
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The father is 37 years old and his son's age is 5 years.After how many years,the father's age will be five times that of his son?
Answer:Let the age of son be x.
Thus, age of father is 4x.
After 5 years, their ages will be x+5 and 4x+5 years respectively.
As per the question, we have
4x+5=3(x+5)
⇒4x+5=3x+15
⇒x=10
Age of father will be 4x=4×10=40 years.
Thus when son is 10 years old, father is 40 years.
Step-by-step explanation:
After 3 years father's age will be five times that of his son. Father age will be 40 years and son age will be 8 years .
Given,
Present age of father = 37 years.
Present age of son = 5 years.
Now,
Let the number of years be x after which the fathers age will be 5 times the age of his son.
So,
Ages after 3 years ,
Age of father = 40 years
Age of son = 8 years.
Thus age of father is 5 times the age of son.
Therefore after 3 years father's age will be five times that of his son.
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Fill in the blank
According to the Symmetric Property of Equality, if AB = then CD = AB
According to the Symmetric Property of Equality, if AB = CD then CD = AB.
According to the question,
We have the following information:
CD = AB then AB = ?
Now, in order to fill the given blank, we have to use the symmetric property of equality. According to the symmetric property of equality, there is no difference in the final result of an expression if we change the sides of the expression.
For example, if 2 = a then we can also say that a = 2.
So, when CD=AB then we can clearly state that AB = CD.
Hence, according to the Symmetric Property of Equality, if AB = CD then CD = AB.
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Seventy-five percent of the players in the basketball program are 5th graders. There are 80 players in the class. How many players are NOT 5th graders?
There are 20 players are not in 5th grades.
What is mean by Percentage?
A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
To Calculate the percent of a number , divide the number by whole number and multiply by 100.
Given that;
Total players in the class = 80
And, 75% of the players in the basketball program are 5th graders.
Now.
Number of players in the basketball program are 5th graders = 75% of 80
= 75/100 x 80
= 60
Thus, Number of players are not in 5th graders = 80 - 60
= 20
Therefore, There are 20 players are not in 5th grades.
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1. Griffin wants to go hiking, but the weather is not cooperating. Right now, there are 2 inches of snow on the ground and snow is falling at a rate of 0.25 in/hr.
(a) Write the linear equation that represents the total amount of snow, y, after x number of hours.
(b) How much snow will be on the ground after 4 hours? You must use your equation above to solve, and you must show all of your work.
(c) If Griffin does not want to be hiking when there are 6 inches of snow on the ground, how long does he have to complete his hike? Do you think he will finish his hike in time? You must use your equation above to solve, and you must show all of your work.
a) The linear equation that represents the total amount of snow, y, after x number of hours is: y = 2 + 0.25x.
b) 3 inches is the amount of snow that is on the ground after four hours.
c) The time until the snow reaches 6 inches is of 16 hours, which is enough to finish the hike, as they usually take at most five hours.
What is a linear function?The slope-intercept representation of a linear function is shown by the equation as follows:
y = mx + b
In which the parameters m and b of the linear equation are explained as follows:
m is the slope, representing the rate of change of the output relative to the input, in the context of this problem how much snow falls by hour.b is the y-intercept, which is the initial value of the function, that is, how much snow was there initially.Thus the values of these parameters are given as follows:
m = 0.25, b = 2.
The equation that represents the total amount of snow, y, after x number of hours is:
y = 0.25x + 2.
The numeric value of function after four hours is found replacing the lone instance of x on the function by 4, hence:
y = 0.25(4) + 2 = 3 inches.
To find when the amount will be of six inches, we have to solve for x when y = 6, hence:
2 + 0.25x = 6
0.25x = 4
x/4 = 4
x = 16 hours.
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Select the correct answer from each drop-down menu.
The GCF of the numbers in the expression (32 + 16) is
. The numbers left inside the parentheses after factoring out the GCF are
and
.
Using distributive law and the greatest common factor , the expression (32 + 16) can be factored as 16(2 + 1)
What is GCF(greatest common factor)?The GCF(greatest common factor) is defined as the largest number that is a factor of two or more numbers.
In a simpler term, the greatest number among all the common factors of two or more numbers is called the greatest common factor or GCF.
Using distributive law and the greatest common factor we can factor an expression.
Therefore, let's factor the expression (32 + 16).
The greatest common factor of 32 and 16 is 16.
Therefore, the expression can be express as follows:
(32 + 16) = 16(2 + 1)
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Suppose y varies directly with x, and y = 25 when x = 5. What is the value of y when x = 7 ?
Answer:
35
Step-by-step explanation:
y = 25 and x = 5
When two variable quantities have a constant ratio their relationship is called a direct variation. The formula for direct variation is y = kx, where k is called the constant of variation. If we know k we can find y given x or we can find x given y.
If we solve the equation y = kx for k, we get k = y/x. If we replace the variables x and y with the actual values from the problem we have:
k = 25/5, which is 5.
Now we can substitute this value for k into the equation y = kx to find y when x is 7:
y = (5) (7)
y = 35
Select the correct answer.
Which expression is equivalent to this polynomial expression?
(2a36) (2a²+ 66²) + (6a²b + 12ab² - 76³)
OA. 4a³ - 12a²b 24ab² 116³
B. 4a³+12a²b25b³
O c. 4a³+ 12a²b + 24ab²
O D. 4a³+24ab² - 256³
-
-
1
116³
Reset
Next
the expression equivalent to the given polynomial expression is 4a³+ 12a²b + 24ab² - 76³, which is option C.
what is expression ?
An expression is a mathematical phrase that contains numbers, variables, and/or mathematical operations. It does not have an equal sign, so it cannot be solved.
In the given question,
The correct answer is C.
To simplify the given polynomial expression using the distributive property, we need to distribute the first term (2a³) to each term in the second parentheses, and then add it to the third term.
So, we have:
(2a³) (2a²+ 66²) + (6a²b + 12ab² - 76³)
= 4a⁵ + 132a³ + 6a²b + 12ab² - 76³
Now, we can simplify further by combining like terms:
= 4a³ (a²+ 33) + 6ab (a + 2b) - 76³
Therefore, the expression equivalent to the given polynomial expression is 4a³+ 12a²b + 24ab² - 76³, which is option C.
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5. A line has a slope of zero. Which of the
following points could this line pass through?
A. (12, 9) and (12, 6)
B. (3, -6) and (7,-6)
C. (1, 4) and (2, 5)
D. (-9, 7) and (9, -7)
Answer: The correct answer is B.
Step-by-step explanation:
In a line with a slope of 0 the x can change but the y cannot in a (x, y).
Peter collected a total of 1,170 stamps. He collected 4 times as many US stamps as foreign
stamps. How many US stamps did he collect?
He collected 936 US stamps.
What is the solution to an equation?
In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.
Total number of stamps - 1170
US stamps - 4 times as many as foreign stamps
Let x be the number of foreign stamps.
4x as the number of US stamps.
To find the number of US and foreign stamps Peter collected, we are going to represent the given data as:
x + 4x = 1170.
x + 4x = 1170
5x = 1170
5x/5 = 1170/5
x = 234
Peter collected 234 foreign stamps.
US stamps = 4x
= 4(234)
= 936
Peter collected 936 US stamps.
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find a number such that 14 less than twice the number is 66
Answer:40
Step-by-step explanation:
so 14 less means that 14 was subtracted. So we need to add that to our main number, 66. When we do that we get 80. Then since 80 is twice the number we are looking for, we divide by 2 (twice is 2 times), and we get 40. Hope this helps
K
Solve the matrix equation AX = B for X.
1 1
[42]
X =
A =
ہلے
B=
23
78
Answer:
Step-by-step explanation:
I'm impressed that they make you do this in H.S. Linear Algebra. it's good for more complex math . so that's why i'm impressed. Is this an AP class?
Ax=B is our formula. we need to know something about x, it's size
so we look at rows and columns of A, 2x2 , also we need to know about B as well it's also 2x2
so now we know, that a matrix A, of size 2x2, *x = B of size 2x2
2x2*x=2x2 .... 2x2|2x2 since the two inside number match, we can do this multiplication, and the two ouside numbers tell us the size of x... it's also a 2x2. I know, a lot of explaining to just get 2x2. Maybe that is obvious, and i'm mansplaining, :DD , but I don't know what you know.
I'll put big subscripts on my matrix variable so you can see it well. You understand the subscript is the element location in the matrix , right? 1,1 is just the top left corner element of the matrix. ect , ect.
so now we need, a1,1 * x1,1 + a1,2 * x2,1 = 2 in b1,1
then we need a2,1 * x1,1 + a2,2 * x2,1 = 7 in b2,1
next we need a1,1 * x1,2 + a1,2 * x2,2 = 3 in b1,2
finally we need a2,1 * x2,1 + a2,2 * x2,2 = 8 in b2,2
X = [tex]\left[\begin{array}{ccc}\frac{3}{2} &1\\\frac{1}{2} &2\end{array}\right][/tex] I did that by observation. have you learned any RREF methods yet?
NEED ASAP THANKS EXPLANATION WOULD BE APRECIATED
IF x=2y and y=1/4 what does x equal
Answer:
[tex]x=\frac{1}{2}[/tex]
Step-by-step explanation:
replace y with 1/4
x=2(1/4)
x=2/4
x=1/2
Hopes this helps please mark brainliest
You start with $200 in bank account
and deposit $50 per week. Write an
equation for scenario.
Answer:
y= 50x + 200
Step-by-step explanation:
PLEASE HELP!!! QUESTION ON PICTURE
Answer:
120[tex]ft^{2}[/tex]
Step-by-step explanation:
4 yards is 12 feet
10(12) = 120
Answer:
120 square feet
1 ) We first need to convert the 4 yards into feet...
1 yard = 3 feet
so 4 yards = 12 feet
2 ) To find area we do length x width...
length = 10
width = 12
10 x 12 = 120
( 120 square feet )
Hope this helps! :)
Given: Line A // line B, ∠2≅∠4 Prove: ∠1≅∠3 line 2 and 3 have the same reason
∠1≅∠3 line 2 and 3 have the same reason.
∠1 and ∠3 are vertical angles, so they are formed by intersecting lines. Therefore ang1 and ∠2 are a linear pair, and ∠2 and ∠3 are a linear pair. By the Linear Pair Theorem, ∠1 and ∠2 are supplementary, and ∠2 and ∠3 are supplementary. So by the Congruent Supplements Theorem, ∠1 ≅ ∠3.
Statements - Reason
1. ∠1 and ∠3 are vertical angles - Given.
2. a and b are intersecting lines - definition of vertical angles
ang1 and ∠2 are a linear pair
3. ∠2 and ∠3 are a linear pair - definition of a line
4. ∠ 1 and 2 are supplementary ang2 and ang3 are supplementary - definition of linear pair.
5. ∠1 ≅ ∠3 - ≅ Supplements theorem
Hence the answer is ∠1≅∠3 line 2 and 3 have the same reason.
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Find X Find Y PLEASE HELP ME
The cost of two cell phones and three headphone sets is $286.00. The cost of two cell phones and six headphone sets is $392.50. What is the cost of one cell phone?
Answer: 89.75
Step-by-step explanation:
So 392.50 is the cost of 2 phones and 6 headphones and 286.00 is the cost of 2 cell phones and three headphones. so 392.50-286.00 is the cost of 3 headphones since you added three headphones to the price. so the price of 3 headphones is 106.50. Then you subtract 106.50 from 286.00 to get the cost of the two cell phones. And you get 179.50. Then, you divide 179.50 in order to get the price of one cell phone and you get 89.75. So the cost of one cell phone is $89.75.
S. Which equation represents the line that passes through the points (6, -12) and (16,-10)?
(A) y=-x-13
[B] y=x+13
[C] y=x-13
[D] y=-x+13²
The equation represents the line that passes through the points (6, -12) and (16,-10) is y = 1/5x - 13.2
The first point = (6, -12)
The second point = (16, -10)
The slope of the line m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute the values in the equation
The slope of the line m = (-10 -(-12) / (16 - 6)
= (-10 +12) / 10
= 2/10
= 1/5
The slope intercept form is
y = mx + b
Consider the point (6, -12)
-12 = (1/5)6 + b
-12 = 6/5 + b
b = -12 - 6/5
b = -13.2
The equation will be
y = 1/5x - 13.2
Hence, the equation represents the line that passes through the points (6, -12) and (16,-10) is y = 1/5x - 13.2
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rerrange 3g=d with the subject g
Step-by-step explanation:
[tex]3g = d[/tex]
[tex] \frac{3g}{3} = \frac{d}{3} \\ [/tex]
[tex]g = \frac{d}{3} \\ [/tex]
[tex]{ \purple{ \bold{g = \frac{d}{3}}}} [/tex]
Step-by-step explanation:
The given formula is [tex]{ \orange{ \sf{3g = d}}}[/tex]
In order to get formula for g, let us divide 3 on both the sides.
[tex]{ \orange{ \sf{ \frac{ \cancel3}{ \cancel3}g}}} = { \orange{ \sf{ \frac{d}{3}}}} [/tex]
Therefore, [tex]{ \boxed{ { \tt{g = \frac{d}{3}}}}} [/tex]
A radio station tower was built in two sections. From a point 27 m from the base of the tower, the angle of elevation of the top of the first section is 25º, and the angle of elevation of the top of the second section is 40º. To the nearest metre, what is the height of the top section of the tower?
Answer:13234
Step-by-step explanation:
13234 is
Graph the linear equation that passes through (-2, 5) and whose slope is 2/3.
let p1 and p2 be the respective proportions of women with iron-deficiency anemia in each of two developing countries. a random sample of 1800 women from the first country yielded 392 women with iron-deficiency anemia, and an independently chosen, random sample of 1700 women from the second country yielded 352 women with iron-deficiency anemia. can we conclude, at the 0.01 level of significance, that the proportion of women with anemia in the first country differs from the proportion of women with anemia in the second country? perform a two-tailed test. then answer the questions below.
According to the two tailed test, the difference between the first and second country is 40.
Two tailed test:
Two tailed test also means the two-sample t-test is used to determine if two population means are equal.
Given,
Let p1 and p2 be the respective proportions of women with iron-deficiency anemia in each of two developing countries. a random sample of 1800 women from the first country yielded 392 women with iron-deficiency anemia, and an independently chosen, random sample of 1700 women from the second country yielded 352 women with iron-deficiency anemia.
Here we need to find the the proportion of women with anemia in the first country differs from the proportion of women with anemia in the second country.
While we looking into the given question,
For the first country,
Number of samples = 1800
Number of women with iron-deficiency anemia = 392
And for the second country,
Number of samples = 1700
Number of women with iron-deficiency anemia = 352
So, there difference between them is calculated as,
=> 392 - 352
=> 40
And as per the two tailed test both countries doesn't have the same proportion and the sample values is also differs this situation.
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Find the missing angle measures
Answer:
145°
Step-by-step explanation:
Answer: y equals 145 degrees
Issac earns money tutoring kids on how to solve a Rubik’s cubes. He always saves 30% of his earnings and spends the rest. If he spent $80 last week, how much money did he earn in total
David opens a savings account with a 7.5% annual interest rate. Which choice best represents his monthly interest rate?
The choice that best represents David monthly interest rate is 0.625%. The correct option is C.
How to calculate the monthly interest?From the information, David opens a savings account with a 7.5% annual interest rate.
It should be noted that there are 12 months in a year.
Therefore, the monthly interest rate will be:
= Annual interest rate / Number if months in a year
= 7.5% / 12
= 0.625%
The interest is 0.625%.
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Complete question
David opens a savings account with a 7.5% annual interest rate. Which choice best represents his monthly interest rate?
A. 7.5%
B. 12%
C. 0.625%
D. 5%
pool empties at a rate of 12 quarts every 2 minutes. how many hours and minutes will it take to completely empty the pool which contains 12,000 gallons? (1 gallon
After the conversion, 133 hours and 33 minutes will it take to completely empty the pool which contains 12,000 gallons.
In the given question we have to find how many hours and minutes will it take to completely empty the pool which contains 12,000 gallons.
As given that pool empties at a rate of 12 quarts every 2 minutes.
In 12 quarts = empties in 2 minutes
As we know that 1 gallon = 4 quarts
So 1 quarts = 1/4 gallon
In 12 quarts = 12/4 gallon
12 quarts = 3 gallon
So 3 gallon = empties in 2 minutes
So 1 gallon = empties in 2/3 minutes
12,000 gallon = empties in 2/3 ×12,000 minutes
Simplifying
12,000 gallon = empties in 2×4,000 minutes
12,000 gallon = empties in 8,000 minutes
Now converting minutes in hours.
As we know that 1 minute = 1/60 hours
So 8000 minute = 8000/60 hours
8000 minutes = 133 hours 33 minutes
133 hours and 33 minutes will it take to completely empty the pool which contains 12,000 gallons.
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''24 hours per day''
Answer:
Step-by-step explanation:
365 day a year
24 hour per day
60 second in a minute
1440 minutes in a day
86400 second in a day!