It looks like the given complex number is
z = ((1 + i )¹⁰ - 1) / ((1 + i )¹⁰ + 1)
Let w = 1 + i, so we rewrite
z = (w ¹⁰ - 1) / (w ¹⁰ + 1)
Since w * = 1 - i, we get w w * = (1 + i ) (1 - i ) = 1 - (-1) = 2. Multiply z by ((w *)¹⁰ + 1) / ((w *)¹⁰ + 1). This gives
z = (2¹⁰ - 1 + w ¹⁰ - (w *)¹⁰) / (2¹⁰ + 1 + w ¹⁰ + (w *)¹⁰)
Now, writing w in polar form yields
w = √2 exp(i π/4)
==> w ¹⁰ = (√2)¹⁰ exp(i 10π/4) = 2⁵ exp(i 5π/2) = 2⁵ i
Similarly,
w * = √2 exp(-i π/4)
==> (w *)¹⁰ = -2⁵ i
So we have
w ¹⁰ + (w *)¹⁰ = 0
w ¹⁰ - (w *)¹⁰ = 2 × 2⁵ i = 2⁶ i
Then we end up with
z = (2¹⁰ - 1 + 2⁶ i ) / (2¹⁰ + 1) = (1023 + 64i ) / 1025
Can anyone help me with this problem
9514 1404 393
Answer:
8. A = {Delaware, New Jersey, Pennsylvania}
9. |B| = 3
Step-by-step explanation:
8. Dates prior to 1 Jan 1788 are those in 1787. The three states admitted in 1787 are listed as Delaware, Pennsylvania, New Jersey. It is usually convenient to list elements of a set in lexicographical order:
A = {Delaware, New Jersey, Pennsylvania}
__
9. The months June and July appear 3 separate times on the list, so there would be 3 elements in the set B.
|B| = 3
whats the difference between the lowest temperature -8 and the highest 6
Answer:
-14
Step-by-step explanation:
just like 8+6 = 14
-8-6 = -14
which exponential equation is equivalent to this logarithmic equation?
Answer:
the answer is A
Step-by-step explanation:
[tex] log_{x}(5 \times 12 ) = 7 \\ \: then \: log_{x}(60) = 7 \\ \: then \: {x}^{ log_{x}(60) } = {x}^{7} \\ {x}^{7} = 60[/tex]
4 in.
7 in.
O 124 6 in
87.9 in
O 97.5 in
O 78.9 in
5
6
7
Answer:
v=3.14 r 2 h
3.14 (2)(2)(7)= 87.9
Answer:
The answer for the Volume is 87.9 to 1d.p or 88in³ to the nearest tenth
Step-by-step explanation:
Volume of a cylinder =pir²h
r=d/2=4/2=2in
V=3.14×2²×7
V=3.14×4×7
V=87.92in³
V=87.9in³ to 1d.p
V=88in³ to the nearest tenth
Please help me
The amount of water dispensed by a water dispenser is normally distributed,
with a mean of 12.10 ounces and a standard deviation of 0.25 ounces. In
which range will the amount of water dispensed be found 95% of the time?
A. 11.85 ounces to 12.35 ounces
B. 11.35 ounces to 12.85 ounces
C. 11.60 ounces to 12.60 ounces
D. 11.10 ounces to 13.10 ounces
Answer:
C. 11.60 ounces to 12.60 ounces
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.
Approximately 95% of the measures are within 2 standard deviations of the mean.
Approximately 99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean 12.10, standard deviation 0.25.
In which range will the amount of water dispensed be found 95% of the time?
By the Empirical Rule, within 2 standard deviations of the mean. So
12.10 - 2*0.25 = 12.10 - 0.5 = 11.60
12.10 + 2*0.25 = 12.10 + 0.5 = 12.6
So the correct answer is given by option C.
What is the length of the base edge labeled x?
Answer:
It is six cm。
Step-by-step explanation:
a school held a tennis tournament. after each round one fourth of the players were eliminated. if there were 64 players at the start of the tournament, which equation models the number of players left after 6 rounds
Answer:
If there are 32 teams in the tournament and 1 winner, there were 31 games. So, 63 - 31 = 32 games.
Step-by-step explanation:
you would do 64/1 • 1/4 to get 16 so every round 16 people would leave.
All of the following relationships have the same y-intercept and slope except.
Answer:
D
Step-by-step explanation:
Plz help me. I need to ace this. Thxx
Answer:
Their intersection point is the only point where the same input into both functions yields the same output.
Step-by-step explanation:
In this case, x = 0 and y = 5.
How many meters are in 9 kilometers? 90,000 meters 9,000 meters 900 meters 90 meters
Answer:
9000 metres
Step-by-step explanation:
a kilometer has 1000 metres
so 9 kilometers has 9*1000 = 9000 metres
Answer:
Step-by-step explanation:
1 km=1000m
9 km=1000*9m
=9000 m
James Burke states that there is a 72% chance a polygraph test (lie detector test) will catch a person who is, in fact, lying. Furthermore, there is approximately a 7% chance that the polygraph will falsely accuse someone of lying.
Required:
a. Suppose a person answers 87% of a long battery of questions truthfully. What percentage of the answers will the polygraph wrongly indicate are lies?
b. Suppose a person answers 13% of a long battery of questions with lies. What percentage of the answers will the polygraph correctly indicate are lies?
Answer:
a) 6.09 %
b) 9.36 %
Step-by-step explanation:
a) Given
% of questions that are truthful = 87% = -.87
% of right questions that are falsely indicated as lies = 7%
Percentage of the answers that the polygraph wrongly indicate as lies = 0.87 * 0.07 = 0.0609 = 0.1 = 10%
b) % of answers that are lies = 13% = 0.13
% of answers that are correctly caught as lies = 72%
percentage of the answers that the polygraph will correctly indicate as lies
= 0.13 * 0.72 = 0.0936 = 0.1 = 10 %
Belts are made in sizes Small, Medium, Large and Extra Large.
Jenny needs to order more belts in June.
The modal size of belts sold is Small.
Jenny is going to order 4 of the belts in size Small.
The manager of the shop tells Jenny she should not order so many Small belts.
(b) Who is correct, Jenny or the manager?
You must give a reason for your answer.
Answer:
I think the manager is correct because Jenny should not order the belts according to its sold quantity or according to the demand of other people.She must choose the size according to her waist size and the other's for whom she is going to buy.
Will you mark it the brainliest please because I answered your question inspite of being in class:)
Solve for x, where x is a real number.
√x-5=6
How many solutions are there
Answer:
x=121
Step-by-step explanation:
1. Move the constant to the right-hand side and change its sign
square rootx = 6+5
2. Add the numbers
square rootx= 11
3. Square both sides of the equation
x=121
Check if the given value is the solution of the equation
square root 121 -5 =6
Simplify the expression
6=6
The equality is true, therefore x=121 is a solution of the equation
The volume of a cylinder is 72 pie cm3. If the radius is 3cm, what is the height of the cylinder?
Answer:
A
Step-by-step explanation:
maybe
Answer:
Step-by-step explanation:
2.55cm
Divide a line which is 20m long in the ratio 3:7
Answer: 6:14
Step-by-step explanation:
3 + 7 = 10x
10x of 20 = 20/10
10x of 20 = 2
3*2:7*2 = 6:14
Answer:
6:14
Step-by-step explanation:
3+7= 10... Double the numbers. The line should be drawn so that 6 is on one side and 14 are on the other.
Which statement is true?
A. All rectangles are parallelograms. Parallelograms have 2 pairs of parallel sides. Therefore, all rectangles have 2 pairs of parallel sides.
B. Only some rectangles are parallelograms. Parallelograms have exactly 1 pair of parallel sides. Therefore, only some rectangles have exactly 1 pair of parallel sides.
C. All rectangles are parallelograms. Parallelograms have exactly 1 pair of parallel sides. Therefore, all rectangles have exactly 1 pair of parallel sides.
D. Only some rectangles are parallelograms. Parallelograms have 2 pairs of parallel sides. Therefore, only some rectangles have 2 pairs of parallel sides.
Answer:
The correct answer is A I believe . . .
Answer:
A. All rectangles are parallelograms. Parallelograms have 2 pairs of parallel sides. Therefore, all rectangles have 2 pairs of parallel sides.
Step-by-step explanation:
Rectangles are parallelograms since they have 2 pairs of parallel sides. All rectangles also have 4 right angles and 2 pairs of opposites sides that are of equal lengths.
Graph the system of equations. { -x +2y = -8, 2x + y =6. Will Mark Brainliest. Need ASAP
Answer:
Graph the -x+2y=-8 as y=1/2x-4
and 2x+4=6 as y=-2x+6
Step-by-step explanation:
hope you understand how to graph y=mx+b equations.
Someone please help, having trouble with this
Answer:
C
Step-by-step explanation:
it describes how much the shown graph extends left and right.
Note that 4 is included, but -2 itself not. that's why it's empty and A isn't correct.
B and D are completely inapplicable
pls brainliest
A teacher assigns 10 questions for homework and wants to randomly pick 3 questions to be graded. He writes the numbers 1–10 on equally sized slips of paper and places them in a bag. He shakes the bag and selects 3 slips of paper. Is the sample of 3 questions a simple random sample? Yes, because the paper slips were equally sized. Yes, because the paper slips were equally sized and the bag was shaken. No, because there are only 10 questions. No, because the questions were selected using a bag.
Answer:
B:yes because the paper slips were equally size and the bag was shaken
Step-by-step explanation:
Taking the test
The table below shows the probability distribution of student ages in a high school with 1500 students. What is the expected value for the age of a randomly chosen student? Age 13 14 15 16 17 18 Probability 0.01 0.27 0.30 0.25 0.16 0.01 O A. 15.38 OB. 15.31 O C. 15.50 D. 15.35 SUBNET
Answer:
According to me it should be Option B, 15.31
Hope this helps!
The expected value for the age of a randomly chosen student is,
⇒ 15.38
What is mean by Probability?The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.
Given that:
Total number of students,
⇒ n = 1500,
And, Age : 13, 14, 15, 16, 17, 18
Probability : 0.01, 0.25, 0.27, 0.30, 0.16, 0.01
Now,
We can Calculate the expected value as shown below,
E = 13 × 0.01 + 14 × 0.25 + 15 × 0.27 + 16 × 0.30 + 17 × 0.16 + 18 × 0.01
E = 0.13 + 3.5 + 4.05 + 4.8 + 2. 72 + 0.18
E = 15.38
Therefore, The expected value for the age of a randomly chosen student is 15.
To know more about probability:
brainly.com/question/743546
#SPJ7
Find the trigonometric ratio for cos B may need to use Pythagorean theorem
Answer:
The answer is cos B = 2/3
I hope it will help you :)
An ornithologist has 4 bird feeders at separate locations. She wonders if birds are equally likely to visit each of the feeders. She recorded data for a sample of 300 recent visits. Here are the results:
Feeder 1 2 3 4
Observed visits 60 90 92 58
A test is performed to determine if these results suggest that birds visit one specific feeder more often than the other feeders. What is the xa test statistic?
a. 13.71
b. 0
c. 14.37
d. 3
e. 1028
Answer:
the x² test statistic 13.71
Option a) 13.71 is the correct answer.
Step-by-step explanation:
Given the data in the question;
Feeder 1 2 3 4
Observed visits; [tex]o_i[/tex] 60 90 92 58
data sample = 300
Expected [tex]e_i[/tex] = 300 / 4 = 75
the x² test statistic = ?
[tex]X^2_{stat[/tex] = ∑[ ([tex]o_i[/tex] - [tex]e_i[/tex])²/[tex]e_i[/tex]]
[tex]X^2_{stat[/tex] = [ (60 - 75)² / 75 ] + [ (90 - 75)² / 75 ] + [ (92 - 75)² / 75 ] + [ (58 - 75)² / 75 ]
[tex]X^2_{stat[/tex] = [ 3 ] + [ 3 ] + [ 3.8533 ] + [ 3.8533 ]
[tex]X^2_{stat[/tex] = 13.7066 ≈ 13.71
Therefore, the x² test statistic 13.71
Option a) 13.71 is the correct answer.
There are 88 marbles in a bin and 50 percent of the marbles are red how many red marbles are in the bin ?
Answer:
44
Step-by-step explanation:
50% is half of the whole
88/2=44
Answer:
44
Step-by-step explanation:
88/2
List the coefficients in the row of Pascal's triangle corresponding to n = 7.
9514 1404 393
Answer:
1 7 21 35 35 21 7 1
Step-by-step explanation:
Numbering from k=0 to k=7, the k-th coefficient in the row is ...
C(7, k) = 7!/(k!(7-k)!)
You know the first two in row 7 are 1 and 7. There are 8 in the row, and the row is the same forward and backward. This means you only need to find C(7, 2) and C(7, 3). These are ...
C(7, 2) = 7!/(2!(5!)) = 7·6/(2·1) = 21
C(7, 3) = 7!/(3!(4!)) = 7·6·5/(3·2·1) = 35
So, row 7 is ...
1, 7, 21, 35, 35, 21, 7, 1
Need help with this thanks
9514 1404 393
Answer:
x = 24
Step-by-step explanation:
The two angles are complementary, so their sum is 90°.
x° +(3x -6)° = 90°
4x = 96 . . . . . . . . . . . . divide by °, add 6
x = 24 . . . . . . . . . . . . . divide by 4
I appreciate if someone help me with this. is due today. Thanks
Answer:
Step-by-step explanation:
take 23 degree as reference angle
using tan rule
tan 23=opposite/adjacent
0.42=x/3.2
3.2*0.42=x
1.34=x
1.3=x
Answer:
x equals to about 1.36
Step-by-step explanation:
Okay so first of all list write out Sin Cos and Tan. SOH-CAH-TOA
Now lets see what we are given. For the reference angle we are given 23.
We are also given 3.2 which is the adjacent angle. And the angle opposite of the reference angle is x. So all in all we have <23, Adjacent length 3.2, opposite length x.
Now we see which one would fit for this. That would be Tan since it deals with adjacent and opposite angles.
Now lets write it out as an equation. tan(23)= x/3.2 | Okay now next to get x alone we move it to the right side. That would leave us with tan(23)*3.2 which equals to about 1.36 "1.35831941187". Remember to use degree and not radiant.
An image is also added.
Hope it helps.
At a pottery shop, there are 7 vases for every 3 planters.
Which of the following shows the ratio of planters to vases at the shop?
Answer:
3:7
Step-by-step explanation:
a ratio is a representation of a certain amount of two items. since there are 7 vases for every 3 planters, the amount of vases versus the amount of planters is represented by 3:7
Write an explicit formula for an, the nth term of sequence 2,4,8
Answer:
2^n will be your explicit formula for this sequence.
Step-by-step explanation:
By analyzing the sequence;
2=2^1
4=2^2
8=2^3
and so on
We find that the numbers of this sequence progresses with 2 to the power of the nth term such as for 3rd term we have 2^3 which is 8.
A store manager is marking down easels from $40 to $28. What is the discount, as a
percentage?
Write your answer using a percent sign (%).
Answer:
30% discount
that's a big discount!
Answer:
30%
Step-by-step explanation:
Shaquana went shopping for a new pair of sneakers because of a sale. The store was offering a 50% discount. What number should she multiply the prices on the tags by to find the price she would have to pay, before tax, in one step?
Answer:
.50
Step-by-step explanation:
50% is .50. The price of the item is .50 (100%-50% discount).