[tex]i {}^{372} = 1 \\ i {}^{527 } = - i[/tex]
Step-by-step explanation:
Greetings !
Note that:-
[tex]i {}^{2n} = 1.\: if \: n \: is \: even \\ \: \: \: \: \: \: \: = - 1. \: if \: n \: is \: odd[/tex]
And also
[tex]i {}^{2n + 1} = i. \: if \: n \: is \: even \\ \: \: \: \: \: \: \: \: \: \: = - i.\: if \: n \: is \: dd[/tex]
Thus, remembering these general formula plug in values in the place of n and solve.
Therefore,
[tex]i {}^{2(186)} = i {}^{372} = 1[/tex]
where n is even thus its 1 from the above explanation
[tex]i {}^{2(263) + 1} = i {}^{527} = - i[/tex]
following the same procedure the values exceeds to be -i.
Hope it helps !!!
Can someone explain this to me?
What are the values of c for which f has a removable discontinuity?
1 only
5 only
1 and 7 only
1,5, and 7
Answer:
1 only
Step-by-step explanation:
1 only, as the other points have defined values.
Kira has a deck of 10 cards numbered 1 through 10. She is playing a game of chance.
This game is this: Kira chooses one card from the deck at random. She wins an amount of money equal to the value of the card if an even numbered card is drawn. She loses $5.50 if an odd numbered card is drawn.
a) find the expected value of playing the game.
___ dollars
b) what can Kira expect in the long run, after playing the game many times? (She replaces the card in the deck each time)
a) kira can expect to gain money. She can expect to win ___ dollars per draw
b) kira can expect to lose money. She can expect to lose ___ dollars per draw.
c) kira can expect to break even (neither gain nor lose money)
Answer:
A. The expected value of playing the game is 0.25
B. She can expect in the long run to gain 0.25 dollars per draw.
Step-by-step explanation:
On 10 draws with each card drawn once....
Winnings: 2+4+6+8+10=30
Losses: 5(5.50)=27.50
She gains an average of $2.50 in each group of 10 games, or $0.25 per game.
There are 20 flowers in a bouquet, and 2 of them are roses. What percent of the flowers are roses?
Answer:
10%
Step-by-step explanation:
firstly express as a fraction then multiply the fraction by 100% , that is
[tex]\frac{2}{20}[/tex] × 100% = 2 × 5 = 10% of the flowers are roses
Use the distributive property to multiply (3w + 5)(–2w – 7).
-6w^2+31w+35
6w^2-21w-35
-6w^2-31w-35
6w^2-21w+30
Answer:
[tex]=-6w^2-31w-35[/tex]
Step-by-step explanation:
Apply Foil.
[tex]\left(3w+5\right)\left(-2w-7\right)=3w\left(-2w\right)+3w\left(-7\right)+5\left(-2w\right)+5\left(-7\right)[/tex]
[tex]=3w\left(-2w\right)+3w\left(-7\right)+5\left(-2w\right)+5\left(-7\right)[/tex]
[tex]=-6w^2-31w-35[/tex]
guys!! please help me, I’ll give out brainliest just please help it’s my final question and it’s currently 4 in the morning .
(geometry)
what is the perimeter of the rectangle ABCD?
Answer:
Please disregard
Step-by-step explanation:
5. This diagram is a straightedge and
compass construction. Which triangle is
equilateral? Explain how you know.
The ΔVZW is Equilateral Triangle .
Equilateral Triangle is defined as the triangle in which all the three sides of the triangle are equal.
For Example ; if a triangle ABC has lengths AB=2cm , BC=2cm and CA=2cm then the triangle ABC can be called as an equilateral triangle as all sides have same length i.e. 2cm .
In the question ,
From the diagram, we have the radius of all the circles are of equal length ,
Since the radius of all the circles are equal in length , their diameter will also be equal in length .
We can see from the diagram that VZ , ZW and WV are the diameters of the circles , So they will be equal in length ,
which means VZ = ZW = WV.
In triangle VZW the sides VZ , ZW and WV are of equal length , hence the triangle will be an Equilateral Triangle.
Therefore , the Triangle VZW is Equilateral Triangle .
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A quadratic function is decreasing on (-∞, 3) and increasing on (3, ∞).
Will the vertex be the highest or lowest point on the graph of the parabola?
Explain.
Greetings from Brasil...
If X grows and Y grows, the function is increasing
If X increases and Y decreases, the function is decreasing
Besides that, according to the statement, we can conclude that the parabola has an upward concavity, that is, a > 0. In this case the vertex will be a minimum point
check the attachments
P.S. - vertex coordinate = (3; 0)
emiah The length of a ruler is 12 inches. There are approximately 25.4 millimeters in 1 inch. Which measurement is closest to the length of the ruler in millimeters? A 3,048 mm B 30.48 mm C304.8 mm D 3.048 mm
Answer:
C 304.8
Step-by-step explanation:
Answer:
C 304.8 mm
Step-by-step explanation:
12*25.4 = 304.8
In Euclidean geometry, the interior angles of any triangle add up to 180 degrees. Does this rule apply to triangles in spherical geometry? If not, is there another value that they would always sum to? Explain your answer.
The triangles are subject to this law. If another number were present, their sum would always be greater than 180 degrees.
What is geometry?It is defined as the branch of mathematics that is concerned with the size, shape, and orientation of two-dimensional figures.
It is given that:
In Euclidean geometry, the interior angles of any triangle add up to 180 degrees.
As we know,
Spherical trigonometry, which departs from conventional trigonometry in many ways, is created when angles between great circles are defined.
For instance, the total of the sides and angles of a hemispheric triangle is more than 180 degrees.
In spherical geometry, triangles are subject to this law. If another number were present, their sum would always be greater than 180 degrees.
Thus, the triangles are subject to this law. If another number were present, their sum would always be greater than 180 degrees.
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make a research about fibonacci sequence and its process kindly give at least five examples.
What is the Fibonacci sequence?
The Fibonacci sequence is a set of integers (the Fibonacci numbers) that starts with a zero, followed by a one, then by another one, and then by a series of steadily increasing numbers. The sequence follows the rule that each number is equal to the sum of the preceding two numbers.
The Fibonacci sequence begins with the following 14 integers:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233 ...
Each number, starting with the third, adheres to the prescribed formula. For example, the seventh number, 8, is preceded by 3 and 5, which add up to 8.
The sequence can theoretically continue to infinity, using the same formula for each new number. Some resources show the Fibonacci sequence starting with a one instead of a zero, but this is fairly uncommon.
Example 1: Starting with 0 and 1, write the first 5 Fibonacci numbers.
Solution: The formula for the Fibonacci sequence is Fn= Fn-1+Fn-2
The first and second terms are 0 and 1, respectively.
F0 = 0 and F1 = 1.
F2 = F0 + F1 = 0+1 = 1 is the third term.
F3 = F2+F1 = 1 + 1 = 2 is the fourth term.
F4 = F3+F2 = 1+2 = 3 is the fifth term.
The Fibonacci sequence’s first five terms are 0,1,1,2,3.
Example 2: Find the Fibonacci series’ next term: 0, 1, 1, 2, 3, 5…
Solution: The preceding two Fibonacci terms are the next term in the series.
As a result, the word that must be used is – 3 + 5 = 8
Example 3: What is the significance of Fibonacci numbers?
Solution: In financial statement analysis, Fibonacci numbers are pretty helpful. In addition, the Fibonacci number series may be utilized to provide valuable proportions or ratios for business people.
Example 4: Find the 12th term of the Fibonacci sequence if the 10th and 11th terms are 34 and 55, respectively.
Solution: Using the Fibonacci Sequence recursive formula, we can say that the 12th term is the sum of the 10th term and the 11th term
12th term = 10th term + 11th term
= 34 + 55
= 89
The 12th term of the Fibonacci sequence is 89.
Example 5: The 14th term in the sequence is 377. Find the next term.
Solution: We know that the 15th term = the 14th term × the golden ratio.
F15 = 377 × 1.618034
≈ 609.99 = 610
The 15th term in the Fibonacci sequence is 610.
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A farmer can plow a given field in 11 hours. If his son helps him, they can plow the vehicle together in 7 hours. How many hours would it take his son to plow the field alone? Express your answer as a fraction reduced to lowest terms, if needed
The total number of hours taken by farmer's son to plow the farm is 19 hours.
What is the concept of time and work?Time refers to the duration of any task or activity that occurs or continues.
Work is a process or set of tasks designed to achieve a specific result.
We can define work happening as follows: - If a person A completes a task in X days, the amount of work finished in 1 day is 1/x.Likewise, if a person B finished work in Y days, his work completed in 1 day will become 1/Y.We can conclude from the preceding two points that A and B can complete (1/(X+Y) amount of work in one day. As a result, A and B could really complete the task in X Y/(X+Y) days.For, the given question;
Let F be the number of hours taken by farmer to finish the work.
Let S be the number of hours taken by farmer' son to finish the work.
The amount of work finished in 1 hour by farmer is 1/F = 1/11.
The amount of work finished in 1 hour by farmer's son is 1/S.
The amount of work finished by both in 1 hours is;
1/F + 1/S = 1/7
1/S = 1/7 - 1/F
1/S = 1/7 - 1/11
Simplifying the given term;
1/S = 4/77
or, S = 77/4 = 19.25 hours.
S = 19 hours (fraction reduced to lowest terms)
Thus, the time taken by the farmer's son to complete the plow of field is 19 hours.
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9. Use the following data. 15, 24, 32, 46, 46, 58. Match the measures on the left with the values on the right.
1. median
2. mode
3. mean
4. range
Let f(X)=3√x
if g(x) is the graph of the f(x) shifted down 1 units and left 5 units write a formula for g(x)
g(x)=
g(x) = 3√(x-5) -1
The process of altering a graph to produce a different version of the preceding graph is known as graph transformation. The graphs can be moved about the x-y plane or translated. They may also be stretched, or they may undergo a mix of these changes.
Horizontal stretching: It means the graph is elongated or shrink in x direction.
Vertical stretching : It means the graph is elongated or shrink in y direction
Vertical translation : It means moving the base of the graph in y direction
Horizontal translation : It means moving the base of the graph in x direction
According to rules of transformation f(x)+c shift c units up and f(x)-c shift c units down.
Therefore, in order to move the graph down 1 units, we need to subtract given function by 1 , we get
g(x) = 3√x -1
According to rules of transformation f(x+c) shift c units left and f(x-c ) shift c units right.
Therefore, in order to move the graph left by 5 units, we need to add given function by 5 , we get
g(x) = 3√(x-5) -1
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What is 6.4% written as a decimal number? 64.0 6.4 0.64 0.064
Answer:
0.064
Step-by-step explanation:
To convert just muiltiply the percent by 100.
for small changes in temperature, the formula for the expansion of a metal rod under a change in temperature is: g-l=al(t-t), where g is the length of the object at temperature t, and l is the length at temperature t, and a is a constant which depends on the type of metal. a rod is 135 cm long at 115 degrees f and made of a metal with a=10^-3. write an equation giving the length of this rod at temperature t(because a=10^-3 is very small, give an exact answer: do not round expand multiplied numerical products to get rounded decimals).
Equation giving the length of this rod at temperature is g = 0.000085t + 84.991075 cm.
What is temperature ?
A temperature is a unit used to represent voguishness or coolness on any of a number of scales, including Fahrenheit and Celsius. According to temperature, heat energy will naturally move from a hotter( body with an advanced temperature) to a colder( body with a lower temperature)( one at a lower temperature).Given that,
Temperature denoted by T
G - L = aL(t - T)
G = aLt + L(1 - aT)
Slope = aL
Intercept = L(1 - aT)
g = 0.000085t + 84.991075 cm
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Question
Gabriel and Raj were running a lemonade stand at the local park. They decided to pay their sister to operate the stand. The
following values represent the profit y after a hours of the stand being open.
Using a calculator or statistical software, find the linear regression line for the data.
Enter your answer in the form y = mx +b, with m and b both rounded to two decimal places.
Provide your answer below:
y=x+
[
X
1
2
3
4
5
6
7
y
3.58
5.18
6.24
7.97
7.09
8.31
11.33
The linear regression equation for the data is given by:
y = 1.08x + 2.76.
How to find the equation of linear regression using a calculator?To find the equation, we need to insert the points (x,y) in the calculator.
For this problem, the points (x,y) are given as follows:
(1, 3.58), (2, 5.18), (3, 6.24), (4, 7.97), (5, 7.09), (6, 8.31), (7, 11.33).
Inserting these points into a calculator, the linear regression equation for the data is given by:
y = 1.08x + 2.76.
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pls answer if wrong i ban you
The coordinates of L are: (8,-4)
Here, triangle is rotated 270° counterclockwise. So the rule that we have to apply here is
(x, y) → (y, -x)
Based on the rule given in step 1, we have to find the vertices of the rotated figure.
(x, y) → (y, -x)
L(4,8) → L'(8.-4)
M(4,3) → M'(3,-4)
N(8,8) → N'(8,-8)
Vertices of the rotated figure are:
L'(8.-4) M'(3,-4) N'(8,-8)
Hence we get the desired result.
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Centre of rotation square
Answer:
Point of intersection of its diagonals
Step-by-step explanation:
Apply it
What is the value of the expression 4(x - y)
when x = 7 and y = 1?
A 26
7
B 29
C 32
D 48
Apply your thinking
Students, write your response!
Pear Deck Interactive Slide
Curriculum Associal Do not remove this bar
Answer:
USE AIR MATH!!
Step-by-step explanation:
Select all the triangles that have an area of 10 square units:
The triangles that have an area of 10 square units are triangles A and B
How to determine the triangles that have an area of 10 square units?The area of a triangle is calculated using
Area = 0.5 * Base * Height
Triangle 1
Base = 5
Height = 4
So, we have
Area = 0.5 * 5 * 4
Area = 10
Triangle 2
Base = 4
Height = 5
So, we have
Area = 0.5 * 5 * 4
Area = 10
Triangle 3
Base = 5
Height = 5
So, we have
Area = 0.5 * 5 * 5
Area = 12.5
Hence, the triangles that have an area of 10 square units are triangles A and B
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Help!!
Find the after-tax return to a corporation that buys a share of preferred stock at $49, sells it at year-end at $49, and receives a $4 year-end dividend. The firm is in the 21% tax bracket.
This is what I got so far:
Before-tax:
(49-49)+4 = 4,
4/49 = 0.0816,
After-tax:
0.0816 (1-021) = 0.06448 or 6.45%
After the tax return percent is 7.43%.
What is a tax return?
A tax return is a form or form filed with a duty authority that reports income, charges, and other material duty information. Tax returns allow taxpayers to calculate their duty liability, schedule duty payments, or request refunds for the remittance of levies. A tax return is the completion of attestation that calculates a reality’s or existent's income earned and the quantum of levies to be paid to the government or government associations or, potentially, back to the taxpayer. Taxation is one of the biggest sources of income for the government.The tax-return of the corporation will be calculated by providing a 70% of deduction to the preference dividend.
The total amount of preference dividend which will be taxable= (dividend amount*(1-.7)
= (4*.3)= 1.20.
The total amount of tax= (total preference dividend taxable*x tax rate)
= (1.2*.3)=.36
The total after tax amount of Return= (preference dividend-tax)= (4-.36)= 3.64.
There will be no capital gain because there is no change in the price of preference shares.
After tax return=(after tax dividend/purchase price)
= (3.64/49)
= 7.43%.
After the tax return percent is 7.43%.
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is X a positive, negative or zero? x + 5 = -8
Answer:
Negative
Step-by-step explanation:
x + 5 = -8
Subtract 5 from both sides to get x by itself
x = -13
Answer:
X is negative
Step-by-step explanation:
8/36 = /9 what number is missing to equal 9
Answer:
72
Step-by-step explanation:
I am pretty certain that the answer is 72.
Steps:
[tex]\frac{8}{36}[/tex] [tex]\frac{x}{9}[/tex]
Cross-Multiply and Divide.
8*9 = 72
72 / 36 = 2
2/9 = 0.222222
8/36 = 0.222222
2/9 = 0.2222222
find the distance between the two points in simplest radical form. (2,6) and (7,-6)
Answer:
13
Step-by-step explanation:
Use the distance formula to determine the distance between two points.
√[(x₂ - x₁)² + (y₂ - y₁)²]
The box plot represents the distribution of speeds, in miles per hour, of 100 cars as they passed through a busy intersection.
What is the first quartile? Interpret this value in the situation.
About *insert fraction* of the cars going through the intersection were going *Q1* or slower.
Answer:
Step-by-step explanation:
Given,
N= 100
Q1=?
We know that,
Q1= N/4
= 100/4
= 25
What is the graetest comon factor on 18 12
Answer: 6
Step-by-step explanation:
Answer:
GCF = 2
Step-by-step explanation:
what does 8+100-(7)/1^2 equal
Answer:
101
Step-by-step explanation:
Given that p=3i+j+2kand q=i-2j-4k are the position vectors
of points P and Q respectively, use the information to answer
Questions 2 and 3.
2.
Find an equation for the plane passing through Qand
perpendicular to liné PQ.
The equation for the plane passing through Q and perpendicular to line PQ is r (2 i + 3 j + 6 k) + 28 = 0.
Let position vector of point P be:
p = 3 i + j + 2 k
Let position vector of point Q be:
q = i - 2 j - 4 k
So, PQ = Q - P
PQ = n = i - 2 j - 4 k - (3 i + j + 2 k)
n = i - 2 j - 4 k - 3 i - j - 2 k
n = - 2 i - 3 j - 6 k
The Equation of plane passing through point Q and perpendicular to PQ will be:
(r - q).n = 0
r n = q n
q n = (i - 2 j - 4 k) . (- 2 i - 3 j - 6 k)
q n = - 2 + 6 + 24
q n = 28
r n = 28
r (- 2 i - 3 j - 6 k) = 28
r (2 i + 3 j + 6 k) + 28 = 0
Therefore the equation for the plane passing through Q and perpendicular to line PQ is r (2 i + 3 j + 6 k) + 28 = 0.
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Translate this phrase into an algebraic expression.
Three less than the product of 15 and Chrissy's score
Use the variable c to represent Chrissy's score.
Answer:
15c - 3
Step-by-step explanation:
Product means 'The answer when you Multiply' So we are working in multiplication ( x )
15 x c can also be written as 15c
'3 less than' means subtracting 3 off the answer.
So therefore the answer is:
15c - 3
Does 10x = 2.5x have one solution, no solutions, or infinite solutions?
Answer: One Solution
Step-by-step explanation:
Only the number 0 can solve this equation so it may be correct.
First approaching this problem, I would try to get x on one side of the equation by subtracting 2.5x from both sides.
This leaves us with 7.5x = 0
Therefore, this equation has only one solution, 0.
