Answers
Answer:The cube root of a negative number is a complex number because there is no real number that, when cubed, gives a negative result.
To find the cube root of -1, we can express it in exponential form as -1 = 1 * e^(iπ), where i is the imaginary unit and π is pi.
The cube root of -1 can be calculated by applying De Moivre's theorem, which states that (r * e^(iθ))^(1/n) = r^(1/n) * e^(iθ/n), where r is the magnitude and θ is the argument of the complex number.
For n = 3, the cube root of -1 becomes:
(-1)^(1/3) = (1 * e^(iπ))^(1/3) = 1^(1/3) * e^(iπ/3) = e^(iπ/3).
Therefore, the cube root of -1 is e^(iπ/3), which can also be expressed as cos(π/3) + i * sin(π/3).
In trigonometric form, the cube root of -1 is (√3/2) + i * (1/2).
Related Questions
A decagon is a 10-sided figure.
Divide the decagon into triangles.
Answers
Answer:
8 triangles
Step-by-step explanation:
PLEASE HELP I NEED THE ANSWER ASAP!!
(100 POINTS IF RIGHT!!!!!)
Answers
Answer:
1/2
Step-by-step explanation:
If the fraction of the box of pancake mix that Merida uses on Friday is not given, it is difficult to determine the exact fraction that she used on Saturday. However, if we assume that the fraction of the box of pancake mix used on Friday is 1/2 (which is a common amount for a recipe that serves 4-6 people), then we can solve for the fraction used on Saturday.
On Friday, Merida used 1/2 of the box of pancake mix.
On Saturday, she used 1 times as much pancake mix as Friday, or 1/2 * 1 = 1/2 of the box of pancake mix.
Therefore, Merida used 1/2 of the box of pancake mix on Saturday.
Note that if the fraction used on Friday is different, the fraction used on Saturday will also be different.
Which answer choice best represents 50/15
?
Answers
Answer:
3 1/3
Step-by-step explanation:
See attachment below
Answer:
Option (A) 3 1/3
Step-by-step explanation:
Let’s solve the improper fraction into a mixed fraction.
The simplified fraction will get a remainder but we I’ll not solve the remainder.
50/15
Quotient = 3
Remainder = 5
Fraction = 3 5/15
= 3 1/3
Hope my answer helps you ✌️
Mark BRAINLIEST
The language arts teacher wants to know whether the students in the entire school prefer a debate or an speech. The teacher draws a random sample from the following groups:
All teachers in the school
All boys in each grade
All students in the speech club
All students in each grade
Which group best represents the population she should take a random sample from to get the best results for her survey? (5 points)
a
All teachers in the school
b
All boys in each grade
c
All students in the speech club
d
All students in each grade
Johnny wants to know how many students in his school enjoy watching science programs on TV. He poses this question to all 26 students in his science class and finds that 75% of his classmates enjoy watching science programs on TV. He claims that 75% of the school's student population would be expected to enjoy watching science programs on TV. Is Johnny making a valid inference about this population? (5 points)
a
Yes, it is a valid inference because his classmates make up a random sample of the students in the school
b
Yes, it is a valid inference because he asked all 26 students in his science class
c
No, it is not a valid inference because he asked all 26 students in his science class instead of taking a sample from his math class
d
No, it is not a valid inference because his classmates do not make up a random sample of the students in the school
A researcher posts a magazine advertisement offering $30 in exchange for participation in a short study. The researcher accepts the first three people who respond to the advertisement. Which of the following statements is true about the sample? (5 points)
a
It is not a valid sample because it is not a random sample of the population.
b
It is a valid sample because the first three people were selected to participate.
c
It is a valid sample because money was offered to participants.
d
It is not a valid sample because it is only a short study.
Answers
Answer:
Q1: D
Q2: D
Q3: B
Step-by-step explanation:
Q1: It says it in the question.
Q2: He asked the ones in his science class so they would obviously prefer science, but that is not true for the rest of the students.
Q3: It is random because the first 3 people were chosen regardless of who they were, and it is still a valid sample even if the study is short.
can someone help me please? I know that I will be using the theoretical probability equation, but I just don’t know what to do
Answers
Answer:
Step-by-step explanation:
Hi there,
We know that a pair means two and so for each pair of socks he has, we are going to multiply that number by two to find the individual amount.
White socks: 2 pairs x 2 = 4 total white socks
Black socks: 4 pairs x 2 = 8 total black socks
Blue socks: 1 pair x 2 = 2 total blue socks.
Now, you add up the total amount of individual socks in the drawer.
4+8+2 = 14 socks.
We are trying the find the probability that he is going to pick a black sock. The amount of black socks is going to go on the numerator of the fraction and the total amount of socks in the drawer is going to go on the denominator.
8 black socks / 14 total socks
Now that we have this fraction, we need to simplify it. The number 8 and 14 are both divisible by 2, so we now have the fraction (4/7).
What this means is that, theoretically, if he randomly pulled out 7 socks, that 4 of the socks he pulls out should be black, leaving the probability he picks out black socks to be (4/7) of the time or about 57% likely to happen.
I hope this helps, let me know if you have questions :)
Find the surface area of the square pyramid shown. Label the net to help you.
I have to show work
Answers
Answer: 40 inches squared
Labels are in the pictures
Step-by-step explanation:
To find the surface area, find the area of each side.
Square (base) : side * side = 4*4 = 16
Triangle (sides) : (base * height)/2
Assuming each side is a isosceles triangle, the base 4/2 = 2
(2*6)/2 = 12/2 = 6
Since there are 4 triangles, we can multiply 6 by 4 to get the combined area. We then add the area of the square to get the final result.
6*4 + 16 = 24+16 = 40
Caden rolls two fair number cubes numbered from 1 to 6. He first defines the sample space, as shown below:
(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)
(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)
(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)
(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)
(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)
(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)
Based on the sample space, what is the probability of getting a total of 6? (5 points)
a. 5 over 36
Selected:b. 6 over 36This answer is incorrect.
c. 7 over 36
d. 8 over 36
Answers
Answer:
B. 6 over 36
Step-by-step explanation:
As we are given the sample space, the events that sum to 6 are:
{(1,5), (2,4), (3,3),(4,2),(5,1)}
Let n(S) be the number of items in sample space
n(S) = 36
Let E be the event the sum is 6
Then,
n(E) = 6
So,
P(Sum of two cubes is 6) = n(E) / n(S)
= 6/36
So, the correct answer is:
B: 6/36
Answer:
B. 6 over 36
Step-by-step explanation:
Identify all of the quadratic functions
Answers
Answer:
y=(x-2)^2 +4
y=1/4 x^2 +x-1
Compare the two groups of data. Which statement is true?
A. On average basketball players are 4 inches taller than baseball players
B. On average basketball players are 9 inches taller than baseball players
C. On average basketball players are 2 inches taller than baseball players
D. On average basketball players are 3 inches taller than baseball players
Answers
Answer: A
Step-by-step explanation:
If you graph the difference, it is 4 inches since you are looking at the middle of the graph
PLS HELPPPPPP *100 POINTS***
Answers
Answer:
6.9 if a triangle pyramid
Step-by-step explanation:
If triangle pyramid,
1/3(b)(h)
1/3(200)(h)=460
h=6.9
PLS HELP MEEE All of the number sentences are true except.
7 3 = 343
4 2 = 16
6 3 = 18
11 2 = 121
Answers
Answer:
I think its the second one, 4 2 = 16. If not then the third one.. I hope this helps!
7x7x7=343
4x4=16
6x6x6=216
11x11=121
At the sewing store, Samantha bought a bag of mixed buttons. She got 400 buttons in all. 400 of the buttons were large. What percentage of the buttons were large?
Answers
explanation
she got 400 buttons
400 were large
400/400 as a percent is 100%
Answer:100% of the buttons were large.
she got 400 buttons
400 were large
400/400 as a percent is 100%
Step-by-step explanation:
Explanation she got 400 buttons
400 were large
400/400 as a percent is 100%
Can you please help?
Answers
Answer:
30.68 cm²
Step-by-step explanation:
Area of the shaded region
= Area of rectangle - Area of semicircle
Given,
Height (h) = 4.5 cm
Base (b) = 9 cm
Diameter (d) = 5 cm
Formula
Area of the rectangle = bh
Area of the rectangle
= 9 x 4.5
= 40.5 cm²
Formula
Radius (r) = d/2
r = 5/2
r = 2.5 cm
Formula
Area of the semicircle = πr²/2
Note
The value of π is 3.14
Area of the semicirlce
= (3.14 x 2.5²)/2
= (3.14 x 2.5 x 2.5)/2
= 19.625/2
= 9.8125 cm²
Area of the shaded region
= Area of rectangle - Area of semicircle
= 40.5 - 9.8125
= 30.6875 cm²
~ 30.68 cm² approximately
pls help its over due
Answers
Your selected answer is correct. The 35 needs to be converted to 0.35 and then multiplied by 20.
___ is 35% of 20. So 0.35 x 20 = 7. The answer to the bottom left box is 7.
Answer:
The correct answer is 7
100 PTS *MIDDLE SCHOOL 7th GRADE***** HELP PLEASE!
Answers
Answer: x=108 degrees
Step-by-step explanation:
Since ST is a straight line, it measures 180 degrees.
This means that
x+(2/3)x=18
The simplified version is 5x/3=180. Now, we multiply both sides by 3. The equation becomes 5x=540 you would divide 5 by both sides which is ultimately x=108.
Answer:
x=108 degrees
Step-by-step explanation:
We know that since ST is a line, it equals a total of 180 degrees.
Let's write an equation:
[tex]180=x+\frac{2}{3}x[/tex]
simplify
[tex]180=\frac{5}{3} x[/tex]
divide both sides by 5/3
108=x
So, x=108 degrees.
Hope this helps! :)
HELPP!!
The table shows the possible outcomes of spinning the given spinner twice. Find the probability of the spinner landing on 1 at least once.
The probability is?
Type an integer or a fraction
Answers
Answer: 7/16
Step-by-step explanation:
Hope this helps! Just find the number that fit the criteria (at least 1 one), and divide it by total outcomes/possibilities.
YALL! WHAT IS THE ANSWER?! HELP ASAP!
q:
choose the different ways that a graph can be misleading (select all that apply)
a:
1- the y-axis starts at zero and uses consistent intervals
2- different bar heights are used on the same graph
3- the y-axis doesn't start at zero
4- the intervals on the y-axis are too large
5- different bar widths are used on the same graph
6- the y-axis starts at zero but has different intervals
Answers
Answer:
Step-by-step explanation:
6-The y -axis starts at zero but has different intervals.
5- Different bar widths are used on the same graph.
3- The y -axis doesn't start at zero.
At a recent football game of 8,450 in attendance, 150 people were asked what they prefer on a hot dog. The results are shown.
Ketchup Relish Chili
54 36 60
Based on the data in this sample, how many of the people in attendance would prefer chili on a hot dog?
5,070
3,380
2,986
2,084
Answers
Answer: 3,380
Step-by-step explanation: THIS IS MY GUESS.
Since we know that 150 people were surveyed, and only 60 wanted chili, we can write an equation to get the percentage of people who wanted chili as 60/150. We can simplify that to get 6/15 and then simplify again to get 2/5. 2/5 simplifies to 40% as a percentage. 40% of 8,450 (or 0.4 x 8,450) would be 3,380.
Explanation
We will find the ratio of 54 36 and 60 which is 9:6;10
So now total attendance is 8450.
So 8450 * 6 / 15= 3380
Which number describes the median of the data given in the table?
Responses
A 24.224.2
B 2323
C 2222
D 2828
Question 2
Which number describes the range of the data given in the table?
Responses
A 66
B 2323
C 2222
D 28
Answers
The number which describes the median of the data given in the table is 23. option B.
The number which describes the range of the data given in the table is 6. Option A.
What is the median and range of the data given in the table?Arrange the average gas mileage in ascending order
22, 22, 23, 26, 28
The median of a data refers to the middle number of the data set when arranged either in ascending order or descending order.
The median is 23
Hence, the range of the data set refers to the difference between the highest and lowest data.
= 28 - 22
= 6
Read more on median and range:
https://brainly.com/question/13278246
#SPJ1
please help me with these problems I will give brainlist
Answers
Step-by-step explanation:
Slope intercept form of a line is
y = mx + b where m = slope b = intercept
1) y = 2x + 4
3) y = -3/4 x + 0 = - 3/4 x
I think you can see how to do the other two now......
Pls answer this for me
Answers
In total, there are 100 blocks. There are 4 boxes.
100/4 = 25 therefore B would work.
D would also work as 41-16=25 and 9+16 is also 25, meaning boxes C and D would be equal. Boxes A and B would also be equal as 32-7=25 and 18+7=25.
A would NOT work as 41-21 is equal to 20, meaning box C would be lacking 5 blocks. C would NOT work as whilst A and B would be equal, C and D would not be. E would also NOT work as nothing would be equal at all.
Calculate the average (arithmetic mean) of the list of numbers shown in the table. (rounded to the nearest tenth)
Responses
A 39.139.1
B 44.044.0
C 39.039.0
D 35.235.2
E 39.2
Answers
Answer:
The answer is B. 39.0
Step-by-step explanation:
To find the average we add all the numbers then divide it by the total amount of numbers
= 23 + 33 + 33 + 27 +25 + 68 + 27 + 44 + 72/9
= 352/9
= 39.111111111
Round it of to the nearest tenth
= 39.0
Write each expression without the absolute value symbol. |7-(12-x)|
Answers
The expression without the absolute value symbol is given as follows:
If x > 5, then |7 - (12 - x)| = -5 + x.If x = 5, then |7 - (12 - x)| = -5 + x.If x < 5, then |7 - (12 - x)| = 5 - x.What is the absolute value function?The absolute value function is defined by the following piecewise rule, depending on the input of the function:
|f(x)| = f(x), x ≥ 0.|f(x)| = -f(x), x < 0.The expression for this problem is given as follows:
7 - (12 - x).
The critical value of x is obtained as follows:
7 - (12 - x) = 0
7 - 12 + x = 0
x = 5.
Hence the expression is given as follows:
If x > 5, then |7 - (12 - x)| = -5 + x.If x = 5, then |7 - (12 - x)| = -5 + x.If x < 5, then |7 - (12 - x)| = 5 - x.More can be learned about the absolute value function at https://brainly.com/question/3381225
#SPJ1
The stem-and-leaf plot below shows the percentage scores on a recent sixth-grade science test.
Use the stem-and-leaf plot to determine the mode of the test scores.
Answers
7 | 4 appears the most often.
100 PTS PLS HELP PLS PLS PLS PLSPLSPLPLSSPLSPLSLS
Answers
Answer:
D
Step-by-step explanation:
Lets go through each answer choice and check if it is correct.
A: False. 50% of 70 is not 31.
B: False. 17% of 70 is not 17.
C: False. The fraction 8/70 does not simplify to 2/25.
D: Correct. The fraction 14/70 simplifies to 2/10.
Answer:
The answer is D, On average, 2 out of 10 adults visited the museum most frequently.
Step-by-step explanation:
You can find this out by finding out how many adults there was total. You would do 31+14+17+8=70 and the you can see that 14 went to the museum so it would be 14/70. This fraction simplifies to 2/10.
whats the surface area? sorry if im annoying
Answers
Answer:
The surface area of a solid object is a measure of the total area that the surface of the object occupies.
Step-by-step explanation:
SA=2B+Ph
Find the area of each face. Add up all areas.
the table shows the possible outcomes of spinning the given spinner twice. Find the probability of the spinner landing on 1 at least once.
The probability is?
LOOK AT THE PICTURE AND PLEASE HELP!!
Answers
Answer: The probability or percentage of the spinner landing on 1 once is 36% or 9 out of 25.
Step-by-step explanation:
Please help I'll give u brainleist!
Answers
Answer:
Step-by-step explanation:
probability you roll a one is 1/6
probability you roll an 8 is 0/6
add them and the answer is 1/6
Work out the area of the trapezium
(some please help, i forgot how to do this )
Answers
Answer:
48cm
Step by step:
The area of a trapezoid can be found using the formula A=(1/2)(b1+b2)h, so we replace each variable with what is written on the trapezoid. A=(1/2)(7+9)(6), so once you simplify you get 48.
Answer:
The area of the Trapezium is 48cm².
Step-by-step explanation:
A trapezium has a pair of Parallel Lines.
Let’s mark the line that is on the top as A and the bottom one as B.
Length of line A (Base 1) = 7cm
Length of line B (Base 2) = 9cm
Height of Trapezium = 6cm
Area of Trapezium (Formula) = {( Base 1 + Base 2 ) / 2} * Height
= {( 7cm + 9cm ) / 2} * 6cm
= ( 16cm / 2 ) * 6cm
= 8 cm * 6cm
= 48cm²
The area of the Trapezium is 48cm².
Hope my answer helps you ✌️
Mark BRAINLIEST
Find the error(s) and solve the problem correctly.
Sarah was asked to solve the following problem. Identify her errors and explain how to correct her mistakes.
Answers
Answer:
[tex]5x^3-18x^2+2x+21[/tex]
Step-by-step explanation:
In the second step, -9x-21 should be 9x+21. This is because -3 in x-3, and -3x-7 in 5x²-3x-7 are both negative, so each term's product should be positive.
Also, in the third line, she wrote -3x²-15x² as -18x⁴ instead of -18x²,and similarly, she wrote -7x-9x as -16x² (however this is wrong anyway because step 2 was done incorrectly).
If we continued off from the second step with these corrected errors:
[tex]5x^3-3x^2-7x-15x^2+9x+21\\5x^3-18x^2+2x+21[/tex]
Therefore, the correct simplification is [tex]5x^3-18x^2+2x+21[/tex].
Answer:
5x^3-18^2 +2x +21
Step-by-step explanation: