Answer:
The answer is C
Step-by-step explanation:
Correct answer shown on edge
The power of 5 of complex number z is (-16√3 + 16) + 4(-√3 + 3)i
What is a complex number?It is defined as the number which can be written as x+iy where x is the real number or real part of the complex number and y is the imaginary part of the complex number and i is the iota which is nothing but a square root of -1.
We have:
z = 1 + √3i
We have to find: z⁵
z⁵ = (1 + √3i)(1 + √3i)(1 + √3i)(1 + √3i)(1 + √3i)
z⁵ = (-2 + 2√3)(1 + √3i)(1 + √3i)(1 + √3i)
[tex]\rm z^5=\left(2\sqrt{3}-2\right)+2\left(3-\sqrt{3}\right)i(1+\sqrt{3}i)(1+\sqrt{3}i)[/tex]
[tex]\rm =\left(-4\sqrt{3}+4\right)+4\left(3-\sqrt{3}\right)i(1+\sqrt{3}i)[/tex]
z⁵ = (-16√3 + 16) + 4(-√3 + 3)i
Thus, the power of 5 of complex number z is (-16√3 + 16) + 4(-√3 + 3)i
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HELP PLS! ILL MARK BRAINLIEST!
Sean drink a slushy as fast as he could. The amount of Slushii left in a cup (in milliliters) as a function of time (in seconds) is graphed. How fast did Sean drink the slushy?
A. 8 mL per second
B. 0.8 mL per second
C. 1 mL per second
D. 10 mL per second
I NEED HELP THIS IS DUE IN THIRTY MINUTES
convert decimals to fractions
1.167
2.4
1.75
Answer:
1167/1000
24/10
175/100
Step-by-step explanation:
1.167
we consider the point is equal to 1. After that point, all numbers, we consider as zero.
so, the answer would become:
1167/1000
6) Which of the following angles is coterminal with -495 degrees?
45 degrees
135 degrees
225 degrees
315 degrees
Answer:
225 degrees
Step-by-step explanation:
-495 +360 until you get to one of the answers.
At the end of school, Josh's teacher handed out 27 coupons for bowling during the summer to each student. The third week of
summer, he accidentally threw away 15 of them when he cleaned his room. The last week of summer, he decided to use the
remaining coupons evenly over 3 days.
If he did not use any of the coupons until the last week of summer, how many coupons did he use on each of the 3 days?
The answer would be 4 Coupons
This trip the family will spend $117.96. The next trip they will spend $119.27. This is an increase of ($117.96 − $119.27) or an increase of $1.31.
What is the percent of increase?
Round your answer to the nearest whole percent. Type your answer into the space.
Answer:
1.11055% increase
Which of these expressions equal 15 when x=1/2 and y=3? Circle all that apply. Please help with this my teacher need me to work out xy+3 1/2+20x Btw guys 3 1/2 are mixed numbers if your wondering
Answer:
15
Step-by-step explanation:
First you would replace the x and y's with 1/2 and 3.
So it would look like: (1/2) (3) + 3 1/2 + 20 (1/2)
Next, you go by PEMDAS (parenthesis, exponents, multiplications, division, addition, subtraction)
So you would first multiply and the parenthesis that I added mean multiplication.
1.5 + 3.5 + 10
So then all that is left to do is add because I multiplied everything out.
So it is 5 + 10 which is 15
(1/2(7x3))^3= plz help
Answer:
1/2 X 7 X 3 X 3 = 31.5
Step-by-step explanation:
An SAT prep course claims to improve the test score of students. The table below shows the scores for seven students the first two times they took the verbal SAT. Before taking the SAT for the second time, each student took a course to try to improve his or her verbal SAT scores. Do these results support the claim that the SAT prep course improves the students' verbal SAT scores?
Let d=(verbal SAT scores prior to taking the prep course)−(verbal SAT scores after taking the prep course)d=(verbal SAT scores prior to taking the prep course)−(verbal SAT scores after taking the prep course). Use a significance level of α=0.1 for the test. Assume that the verbal SAT scores are normally distributed for the population of students both before and after taking the SAT prep course.
Student 1 2 3 4 5 6 7
Score on first SAT 500 380 560 430 450 360 560
Score on second SAT 540 470 580 450 480 400 600
Required:
a. State the null and alternative hypotheses for the test.
b. Find the value of the standard deviation of the paired differences. Round your answer to one decimal place.
c. Compute the value of the test statistic. Round your answer to three decimal places.
d. Determine the decision rule for rejecting the null hypothesis. Round the numerical portion of your answer to three decimal places.
e. Make the decision for the hypothesis test.
Answer:
Since the calculated value of t = -0.215 falls in the critical region so we accept Ha that SAT prep course improves the students' verbal SAT scores and reject the null hypothesis at significance level 0.05.
e. These results support the claim that the SAT prep course improves the students' verbal SAT scores.
Step-by-step explanation:
Student 1 2 3 4 5 6 7
Score on first SAT 500 380 560 430 450 360 560
Score on second SAT 540 470 580 450 480 400 600
Difference d -40 -90 -20 -20 -30 -40 -40 ∑ -280
d² 1600 8100 400 400 900 1600 1600 ∑14600
a. Let the hypotheses be
H0: ud= 0 against the claim Ha: ud ≠0
The degrees of freedom = n-1= 7-1= 6
The significance level is 0.05
The test statistic is
t= d`/sd/√n
The critical region is ║t║≤ t (0.025,6) = ±2.447
d`= ∑di/n= -280/7= -4
Sd²= ∑(di-d`)²/n-1 = 1/n-1 [∑di²- (∑di)²n]
= 1/6[14600-(-4)²/7] = [14600-2.2857/6]= 2432.952
b. Sd= 49.3249= 49.325
Therefore
c. t= d`/ sd/√n
t= -4/ 49.325/√7
t= -4/18.6435 = -0.2145= -0.215
d. Since the calculated value of t = -0.215 falls in the critical region so we accept Ha that SAT prep course improves the students' verbal SAT scores and reject the null hypothesis at significance level 0.05
e. These results support the claim that the SAT prep course improves the students' verbal SAT scores.
The side opposite from the right angle is called
Answer:
The side opposite from the right angle is called the hypotenuse.
3d - 5+4d +5=140 how do i solve this i need help
Answer:
3
−
5
+
4
+
5
=
1
4
0
3d{\color{#c92786}{-5}}+4d+{\color{#c92786}{5}}=140
3d−5+4d+5=140
3
+
4
=
1
4
0
3d+4d=140
3d+4d=140
2
Combine like terms
3
+
4
=
1
4
0
{\color{#c92786}{3d}}+{\color{#c92786}{4d}}=140
3d+4d=140
7
=
1
4
0
{\color{#c92786}{7d}}=140
7d=140
3
Divide both sides of the equation by the same term
7
=
1
4
0
7d=140
7d=140
7
7
=
1
4
0
7
\frac{7d}{{\color{#c92786}{7}}}=\frac{140}{{\color{#c92786}{7}}}
77d=7140
4
Simplify
Cancel terms that are in both the numerator and denominator
Divide the numbers
=
2
0
d=20
d=20
Solution
=
2
0
hope it help
Step-by-step explanation:
Answer:
the answer is 20
Step-by-step explanation: combine like terms
7d = 140
then divide
140/7
20
Can some one plz help i will give BRAINLIEST.
If there is a 10% chance of a certain flower species having blue petals, then is it possible to observe only 85 flowers with blue petals in a field of 1000 flowers? Explain your reasoning.
Answer:
Yes
Step-by-step explanation:
10% chance does not mean it is always 10 percent. 10 percent is the theoretical property. The experimental probability can be different than the theoretical property.
choir is selling Pringle chips to raise money for a field trip. The container has a diameter of 9 inches and a height of 32 inches . Which equation can be used to find the volume of the container?
1,,,,,,,V=pi(9)
2,...... V=pi(9)^2(32)
3,........V=pi(4.5)^2(32)
4,........V=pi(4.5)(32)
Please does anyone know the answer?
Answer:it’s V=pi(4.5)^2(32)
Step-by-step explanation:
The equation which can be used to find the volume of the container of Choir who is selling Pringle chips, is
[tex]V=\pi (4.5)^2(32)[/tex]
What is of volume of cylinder?Volume of cylinder is the amount of quantity, which is obtained by it in the 3 dimensional space.
Volume of cylinder is the can be given as,
[tex]V=\pi r^2h[/tex]
Here, (r) is the radius of the base of the cylinder and (h) is the height of the cylinder.
Choir is selling Pringle chips to raise money for a field trip. The container has a diameter of 9 inches and a height of 32 inches.
As the radius is half of the diameter. Thus, the radius of the container is,
[tex]r=\dfrac{9}{2}\\r=4.5\rm\; in[/tex]
As this container is in the shape of cylinder. Thus, the volume of container can be found out using the above formula as,
[tex]V=\pi (4.5)^2(32)[/tex]
Hence, the equation which can be used to find the volume of the container of Choir who is selling Pringle chips, is
[tex]V=\pi (4.5)^2(32)[/tex]
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Which polynomial can be factored using the binomial theorem?
81x2 + 117x + 169
81x2 + 234x + 169
6,561x4 – 9,477x3 + 13,689x2 – 19,773x + 28,561
6,561x4 – 18,954x3 + 27,378x2 – 39,546x + 28,561
Answer:
B.) 81x2 + 234x + 169
Step-by-step explanation:
What is 1/4 times 24.80
Answer:
6.2 is the answer you are looking for
What would you tip for a $22 meal if you wanted to leave 15%?
$18.70
$4.40
$3.30
$25.30
please help but right answers
Answer:
51=-3x+6 -6
45=-3x ÷(-3)
-15=x
Step-by-step explanation:
prove me wrong
Answer:
r=-15
Step-by-step explanation:
51-(-3r+6)=0
3r-6+51=0
3r+45=0
3r=-45
r=-45/3
r=-15
A system of equations is shown on the graph below How many solutions does this system have?
no solutions
one unique solution
two solutions
an infinite number of solutions
Answer:
There is only one solution.
Step-by-step explanation:
The two lines only cross once, so there is one solution.
If the lines did not cross at all, there would be no solutions.
If the lines crossed twice, then there would be two solutions.
If the lines were on top of one another, they would be the same line, and have an infinite amount of solutions.
A system of equations is shown on the graph below has Unique solution.
What is Line segment?
A line segment is a part of line having two endpoints and it is bounded by two distinct end points and contain every point on the line that is between its endpoint.
Given that;
The graph is shown in figure.
Now,
Since, In the graph the two line segment cut into one point.
Hence, The system of equation shown in graph has Unique solution.
Thus, A system of equations is shown on the graph below has Unique solution.
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Find the quotient: 8,358 ÷ 27 = ________.
309 r 15
309 r 26
310 r 15
310 r 26
Answer:
the answer is 309 r 15
Step-by-step explanation:
309 × 27 is 8343 and your left with 15
The ratio using a colon is
a ratio?
What numbers a provided
During a basketball game, the coach needs to select a player to make the free throw after a technical foul on the other team. There is a 68% chance that the coach will select you and a 26% chance that the coach will select your friend. What is the probability that you or your friend is selected to make the free throw?
For the probability of you or your friend add the probability of each together:
68% + 26% = 94% (0.94 if you need it as a decimal)
Answer: there's an 42 percent chance that your friend might make a free throw.
Step-by-step explanation: if u subtract u will get your answer that's bow i got this answer.
How many groups of 3/4 are in each of the following quantities?
Type your response in each box below.
1. 11/4 has __
groups of 3/4.
2. 6 1/2 has ___
groups of 3/4.
Answer:
vb\
Step-by-step explanation:
plx help i need to get this so I can be ungrounded
Answer:
2
Step-by-step explanation:
Twins Isaac and Isaiah were just born. Isaac weighs 6666 pounds 2222 ounces and Isaiah weighs 5555 pounds 4444 ounces.
Step-by-step explanation:
Kindly make the question clearer for assistance
Answer all questions and the topic is about ordering decimals and don't answer if u do not know.
Answer:
31. 0.93, 0.9, 0.33
27. 6.13, 6.14, 6.31
28. 3.09, 3.19, 3.9
29. 12.96, 12.83, 12.8
25. 9.06, 9.6, 9.66
26. 0.09, 0.67, 0.86
Step-by-step exp
The math clubs car can travel 9 meters in a second. The race track for the soap box derby is 63 meters long. How many seconds will it take the Math clubs car to make it around the track
Answer: it will take 7 seconds
Step-by-step explanation: 9 x 7 = 63
A giant tortoise moves at a slow but steady pace. It takes
the giant tortoise 3 seconds to travel 10.5 inches.
How many inches will the tortoise travel in 1 second?
Which of the following is a factor of x^4 - 5x^3 + 3x^2 + 15x - 2
A. 2x+3
B. x-3
C. 3x+1
D. Not factorable
Answer:
D. Not factorable
Step-by-step explanation:
Write an explicit formula for the sequence -13,-6,1,8, ...
A. an= -13n+7
B. an= -13+(n+7)
C. an= -13+7(n-1)
D. an= -13n+7
Answer:
7n-20 I believe
Step-by-step explanation:
hope this helps
Answer: A
lol need extra characters
i took the test btw
a man goes 10m due east and 24m due north find the distance from the starting(pls help )
Answer:
26m
Step-by-step explanation:
10^2+24^2=26^2
Someone please help! What is the domain and range of the relation?
Answer:
The domain is the set of all first elements of ordered pairs (x-coordinates).
The range is the set of all second elements of ordered pairs (y-coordinates).
Only the elements "used" by the relation or function constitute the range.