The correct value of (3cis(pi/6))³ is 27i.
What is Complex Number?Complex numbers are numbers that consist of two parts — a real number and an imaginary number. Complex numbers are the building blocks of more intricate math, such as algebra.
Given the complex number in polar coordinate expressed as
z = r(cos∅+isin∅)
zⁿ = {r(cos∅+isin∅)}ⁿ
According to DeMoivre’s Theorem;
zⁿ = rⁿ(cosn∅+isinn∅)
Given the complex number;
(3cis(pi/6))³
= {3(cosπ/6 + isinπ/6)}³
Using DeMoivre’s Theorem;
= 3³(cos3π/6 + isin3π/6)
= 3³(cosπ/2 + isinπ/2)
= 3³(0 + i(1))
= 27i
Thus, the correct value of (3cis(pi/6))³ is 27i.
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Which of the following expressions is equivalent to 14xy – 28x – 36y + 48? 2(7x – 6)(y – 2)(3y + 4) 2(7x – 6)(y – 2)(3y – 4) 2[7x(y – 2) – 6(3y – 4)] 2[7x(y – 2) – 6(3y + 4)]
The expression that is equivalent to 14xy – 28x – 36y + 48 is 2[7x(y-2)-6(3y-4)]
Factorizing expressionsFactorization is a way of separating the equations into two separate factors.
Given the expression below;
14xy – 28x – 36y + 48
Group
(14xy – 28x) – (36y + 48)
14x(y - 2) - 12(3y-4)
Factor out the value of 2 from both terms
2[7x(y-2)-6(3y-4)]
Hence the expression that is equivalent to 14xy – 28x – 36y + 48 is 2[7x(y-2)-6(3y-4)]
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Answer:
2[7x(y – 2) – 6(3y – 4)]
Step-by-step explanation:
I got it right on the test.
Question
The function defined by f(t)=12(1+0.03)t can be used to determine the population, in thousands, of a town t years since 1955. According to the function, what was the population of the town in 1955 and what was the percent increase in population from year to year?
Enter a number in each box to correctly complete the sentence.
The population of the town in 1955 was 12 thousand people, and the percent increase in population from year to year was 3%.
How to explain the population?A function assigns the value of each element of one set to the other specific element of another set. The function that gives the population of the town is given.
Since the year 1955 the value of t=0. Therefore, The population of the town in 1955 was 12 thousand. The percentage increase in population from year to year is 3%.
Therefore, the population of the town in 1955 was 12 thousand people, and the percent increase in population from year to year was 3%.
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what does it want me to put to 6 decimal places
They want you to solve the iterative process to a point where the value of x is greater than or equal to 6 decimal places.
What is an iterative process?An iterative process is a mathematical approach that employs an initial value to build a series of improving estimated solutions for a problem, where the nth-term estimation is generated from the prior ones.
You're required to put the value of x₁ = -1 into the equation:
[tex]\mathbf{x_{n+1}= \dfrac{(x_n)^3-1}{4}}[/tex]
where, [tex]x_1 = -1[/tex]So;
[tex]\mathbf{x_{2}= \dfrac{(-1)^3-1}{4}}[/tex]
[tex]\mathbf{x_{2}=-0.5}[/tex]
[tex]\mathbf{x_{3}= \dfrac{(-0.5)^3-1}{4}}[/tex]
[tex]\mathbf{x_{3}=-0.28125}[/tex]
[tex]\mathbf{x_{4}=\dfrac{(-0.28125)^3-1}{4}}[/tex]
[tex]\mathbf{x_{4}=-0.2555618286}[/tex]
x₄ ≅ -0.255562 ( to 6 decimal places)
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According to this factor tree, which of the following statements is true?
Answer:
option c
Step-by-step explanation:
a) NOT TRUE
A composite number is a positive integer that can be formed by multiplying two smaller positive integers.
3 and 7 are not composite numbers because each of them can only be divided by one and itself
b) NOT TRUE
2 is also a prime number so 3 and 7 are not the only numbers
c) TRUE
All the number listed are prime numbers hence why they are all at the bottom of the tree (only have 1 and itself as factors)
d) NOT TRUE
21 is not a prime number. The number 21 is divisible by 1, 3, 7, 21. For a number to be classified as a prime number, it should have exactly two factors. Since 21 has more than two factors, i.e. 1, 3, 7, 21, it is not a prime number.
The first two boxes I get but the last box I don’t know where to go for it
Answer:
add the size plus
Step-by-step explanation:
Sunday if you add sox
Multiple 4 by w then subtract v from the result
Answer:
4w-v
Step-by-step explanation:
Let the number be w.
Multiplying by 4:
4wSubtracting v,
4w-vIn two or more complete sentences, describe how to use technology to construct an appropriate regression model for the given data. you are not required to find the model, just choose the appropriate regression and explain how to use the technology. (-2,11), (1,1.7), (2,-0.2), (3,-1.5), (5,-2.3), (6,-1.8), (8,1)
The regression equation of the data values is y = 0.3x^2 - 2.8x +4.2
How to determine the regression equation?Using a technology such as a graphing calculator, we simply input the data values in the graphing calculator and then wait for the result.
The x coordinates must be entered into the x values and the y coordinates must be entered into the y values
Using a graphing technology, the regression equation of the data values is y = 0.3x^2 - 2.8x +4.2
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NEED HELP FAST! will mark Brain if first! Question 5!
Answer:
[tex]\boxed{\sf x = 11.7}[/tex]
[tex]\boxed{\sf b = 9.4}[/tex]
Sine Rule states:
[tex]\sf sin(x) = \dfrac{opposite}{hypotenuse}[/tex]
[tex]\hookrightarrow \sf sin(51) = \dfrac{x}{15}[/tex]
[tex]\hookrightarrow \sf x = 15sin(51)[/tex]
[tex]\hookrightarrow \sf x = 11.657 \ \ \approx \quad 11.7[/tex]
Additional, cosine rule:
[tex]\sf cos(x) = \dfrac{adjacent}{hypotenuse}[/tex]
[tex]\hookrightarrow \sf cos(51) = \dfrac{b}{15}[/tex]
[tex]\hookrightarrow \sf b = 15cos(51)[/tex]
[tex]\hookrightarrow \sf b = 9.4398 \quad \approx \ \ 9.4[/tex]
Lily has 655 coins that she wants to divide evenly for her 13 grandchildren.
How many coins will each grandchild receive? Will there be any leftover?
250
Answer:
Step-by-step explanation:
Each grandchild will receive 655/13 = 50 with 5 coins left over. She can keep the 5 coins and start again.
Answer
50 coins for each grandchild5 left over.Answer:
50 coins for each grandchild
5 left over.
Step-by-step explanation:
13x50=650
655-650=5
What is the area of a rectangle with a length of 3in and a with of 5 square root of 2
Answer:
The area of the rectangle = 15√2 in²
Step-by-step explanation:
What is the area of a rectangle with a length of 3in
and a width of 5√2.
……………………………………………
FORMULA :
area of a rectangle = length × width
===============================
Then
The area of the rectangle = 3 × 5√2 = 15√2
a computer purchased for $2 500 and its value depreciates at 5% per month. a).write the equation that models the situation. explain what each equation represent. b) determine the value of the computer after 2 years. c) in which month after it is purchased does the computer's worth fall below $1 000?
Answer:
a(y=-5x+2500) b(2,380) c(25months)
Step-by-step explanation:
someone point out if I'm wrong. I'm not so sure about "c".
(how I got b)
So 2 years=24 months
y=-5x+2500
So x would be 24.
-5(24)+2500
-120+2500
2,380
what is the product of the binomals below (2x+3) (3x+3)
Answer:
[tex]3*(2x+3)*(x+1)[/tex]
Step-by-step explanation:
pull like terms from the problem to re-arrange it into a product
[tex]\left(2x+3\right)\left(3x+3\right)\\3x + 3 = 3 \cdot (x + 1)\\3 \cdot (2x + 3) \cdot (x + 1)\\[/tex]
could someone pleasee help me will give brainliest
Question 5(Multiple Choice Worth 2 points)
(02.04 MC)
For the function f(x) = 3(x - 1)² + 2, identify the vertex, domain, and range.
Answer:
For the function f(x) = 3(x − 1)2 + 2, identify the vertex, domain, and range
Step-by-step explanation:
The vertex is (1, 2), the domain is all real numbers, and the range is y ≥ 2.
The vertex is (1, 2), the domain is all real numbers, and the range is y ≤ 2.
The vertex is (–1, 2), the domain is all real numbers, and the range is y ≥ 2.
Answer:
see explanation
Step-by-step explanation:
the equation of a parabola in vertex form is
f(x) = a(x - h)² + k
where (h, k ) are the coordinates of the vertex and a is a multiplier
f(x) = 3(x - 1)² + 2 ← is in vertex form
with vertex = (1, 2 )
The domain of a parabola exists for all real values of x
domain : x ∈ R
the range of the parabola are the values of y from the y- coordinate of the vertex, upwards.
range : y ≥ 2
Coach Sloan is responsible for recruiting male athletes to join the European
Masters track and field team. To improve his recruitment strategies, he wants to
investigate the connection between an athlete's height and 3000-meter run time.
Coach Sloan has recorded the heights of the men on the track and field team (in
centimeters), x, and their best 3000-meter times (in minutes), y.
The least squares regression line of this data set is:
y = -0.081x + 21.412
How quickly does this line predict a man who is 166 centimeters tall would run the 3000-
meters?
Round your answer to the nearest thousandth.
minutes
Using the line of best fit, it is found that the projected time for a man who is 166 cm tall is of 7.966 minutes.
What does the line of best fit gives?It gives the project time in minutes to run the 3000 meters for a men of a height of x centimeters, according to the following function:
y = -0.081x + 21.412.
Hence, for a men of 166 centimeters, x = 166 and the projected time in minutes is given as follows.
y = -0.081(166) + 21.412 = 7.966.
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Which is more, 20 inches or 1 foot?
Answer:
20 inches
Step-by-step explanation:
there is only 12 inches in a foot
5• (4 • x ) simplified
Step-by-step explanation:
= 5 • ( 4• x )
= 5 ( 4x )
= 20x
[tex]...[/tex]
NEED HELP QUICK DUE TMR MEAN AND MEDIAN
Suav left his house at time zero and drove to the store, which is 8 blocks away, at a speed of 4 blocks per minute. Then he stopped and went into the store for 2 minutes. From there, he drove in the same direction at a speed of 4 blocks per minute until he got to the bank, which is 16 blocks away from the store. He stopped at the bank for 4 minutes. Then he drove home at a speed of 6 blocks every minute. Make a graph of showing the number of blocks away from home that Suav is xx minutes after he leaves his house, until he gets back home.
The graph for Suav's trip is attached along with the values derived from the information provided.
What is the explanation for the graph?The key to understanding the graph is that every time spent while he was on the way to the back and back are all added cumulatively.
So when he stops at the store which is 8 blocks away from home, the time spent is recorded as 4 + 2 at location 8 blocks.
It is also to be noted that the time spent is plotted on the x-axis and the blocks away from home on the y-axis.
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What is the area of the circle
Answer:
201.062in²
Step-by-step explanation:
area for formula of a circle
[tex] {r}^{2} \pi[/tex]
we can now plug in the radius to solve
[tex] {8}^{2} \pi \\ 64\pi \\ 201.062[/tex]
that is the answer
- kan Academy Advance
help help help help help
Which graph does not represent a function of x?
To increase sales, an online clothing store began giving a 50% off coupon to random customers. Customers didn't know whether they would receive the coupon until after the final sale. The website claimed that one in five customers received the coupon. Six customers each made purchases from the website. Let X = the number of customers that received the 50% off coupon.
To increase sales, an online clothing store began giving a 50% off coupon to random customers Six customers each made purchases from the website the binomial random variable and mean and standard deviation of X is mathematically given as
[tex]X ~ Bin(n = 6, p = 0.2)[/tex]
x= 0.9798
What is a binomial random variable?
Generally, the equation for is mathematically given as
P(coupon) = 1/5
P(coupon)= 0.2
the binomial distribution
[tex]X ~ Bin(n = 6, p = 0.2)[/tex]
Therefore, The mean and standard deviation of X
[tex]пВ = np \\np= 6* 0.2 = 1.2\\[/tex]
[tex]x=\sqrt{ np(1 - p)} \\ x=\sqrt{ 6 * 0.2 + (1 -0.2)} \\[/tex]
x= 0.9798
In conclusion, mean and standard deviation of X
x= 0.9798
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It’s confusing, would the answer be square root 7 over 4?
Answer:
[tex]\tan U = 1[/tex]
Step-by-step explanation:
[tex]\text{Apply Pythagorean theorem,}\\\\~~~~~~\text{Hypotenuse}^2 = \text{Base}^2 + \text{Perpendicular}^2\\\\\implies UT^2 = UV^2 +VT^2\\\\\implies UV^2 = UT^2 -VT^2\\\\\implies UV^2 = \left(7\sqrt 2 \right)^2 - 7^2\\\\\implies UV^2 = 49(2)-49\\\\\implies UV^2 = 49\\\\\implies UV = \sqrt{49} \\\\ \implies UV = 7[/tex]
[tex]\text{Now,}\\\\~~~~~~~~\tan \theta = \dfrac{\text{Perpendicular}}{\text{Base}}\\\\\\\implies \tan U = \dfrac{7}{7}\\\\\\\implies \tan U = 1[/tex]
Why is P(A) •P(B/A) = P(B) • P(A/B)
HELP ME QUICK ASAP
Answer:
rawrrrrrrrrrrrrrrrrr
Step-by-step explanation:
Why is P(A) •P(B/A) = P(B) • P(A/B)
P/B + P = A
P/B/P
- A
What is the range of the function on the graph?
Answer:
2
Step-by-step explanation:
because (x,y)=(1,2)
Therefore, domine(d)=(x)=1
And, range(r)=(y)=2
So the ans is 2
PLEASE HELP ME!
The dimensions of a rectangular prism are shown below:
Length: 1 1/3 feet
Width: 1 foot
Height: 2 1 /3 feet
The lengths of the sides of a small cube are 1 over 3 foot each.
Part A: How many small cubes can be packed in the rectangular prism? Show your work. (5 points)
Part B: Use the answer obtained in part A to find the volume of the rectangular prism in terms of the small cube and a unit cube.
#Part A
L=1-1/3=4/3B=1H=2-1/3=7)3Volume of rectanglular prism
4/3(1)(7/3)28/9ft³Volume of one cube
side³(1/3)³1/27in³Total cubes
28/9÷1/2728/9×2728(3)84cubes#2
Volume=
No of cubes ×volume of 1 cube
84(1/27)28/9in³Answer:
A) 84 cubes
B) Volume = 4 x 3 x 7 = 84 small cubes
[tex]\sf Volume=3 \frac{1}{9}\:\:ft^3[/tex]
Step-by-step explanation:
Part AAs the lengths of each side of the small cube are ¹/₃ ft each, to find the number cubes in the rectangular prism, first find how many thirds are in each dimension of the prism:
[tex]\sf Length=1 \frac{1}{3}\:ft=\dfrac{4}{3}\:ft=4\:thirds[/tex]
[tex]\sf Width=1 \:ft=\dfrac{3}{3}\:ft=3\:thirds[/tex]
[tex]\sf height=2 \frac{1}{3}\:ft=\dfrac{7}{3}\:ft=7\:thirds[/tex]
Now simply multiply the number of thirds:
Number of cubes in prism = 4 x 3 x 7 = 84
Part BAs we have already found the dimensions of the prism in terms of the number of cubes, the volume of the prism in terms of the small cube is:
⇒ Volume = 4 x 3 x 7 = 84 small cubes
To find the volume of the prism in ft³, calculate the actual volume of the small cube:
[tex]\textsf{Volume of small cube}=\sf \dfrac{1}{3} \times \dfrac{1}{3} \times \dfrac{1}{3}=\dfrac{1}{27}\:ft^3[/tex]
Now multiply the volume in terms of number of cubes by the actual volume of a cube:
[tex]\begin{aligned}\textsf{Volume} &= \sf \textsf{Volume in cubes} \times \textsf{Volume of cube in ft}^3\\\\& = \sf 84 \times \dfrac{1}{27}\:ft^3\\\\& =\sf \dfrac{84}{27}\:ft^3\\\\& =\sf 3\frac{1}{9}\:ft^3\end{aligned}[/tex]
13. (a) In any triangle ABC, if C = 300,b= 4, a = 2 find A and B. [3] (b) If a = b = c and a,b,c are in G.P., show that x,y,z are in H.P. [2]
please, solve them
Step-by-step explanation:
oksosjaoqkqeand
[tex]66 \sqrt[3x9 \frac{ \sqrt[xx. \sqrt[36 \sqrt[3136(2 > kaki \: kwl{]{?} ]{?} ]{?} }{?} ]{?} [/tex]
4(x − 3) + 5x − x² for x = 2
Answer:
2
Step-by-step explanation:
Start by simplifying the expression:
[tex]4(x-3)+5x-x^2[/tex]
Use distribution:
[tex]4x-4(3)+5x-x^2\\4x-12+5x-x^2[/tex]
Add like terms:
[tex]9x-12-x^2[/tex]
Now, substitute the given value of x into the expression:
[tex]9(2)-12-2^2\\18-12-4\\6-4\\2[/tex]
Answer:
2
Step-by-step explanation:
Given: 4(x − 3) + 5x − x²
x = 2Substitute 2 for the value of x in the expression and simplify:
➜ 4(2 − 3) + 5(2) − (2)²
➜ 4(−1) + 10 − 4
➜ -4 + 10 - 4
➜ 2
Therefore, the value of the expression when x equals 2 is 2.
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DO,K = (9, 6) (3, 2) The scale factor is
Using proportions, it is found that the scale factor of the transformation is of 1/3.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
In this problem, during the transformation, each coordinate was divided by 3, hence, applying the proportion, the scale factor of the transformation is of 1/3.
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