The equivalent to the complex number i²⁷ is -i.
what is complex numbers?Every complex number may be represented in the form a + bi, where a and b are real numbers. A complex number is an element of a number system that extends the real numbers with a specific element labeled I sometimes known as the imaginary unit, and satisfying the equation
i² = 1.
Given that,
i²⁷ is a complex number
i²⁷ = i²⁴⁺³
i²⁷ = i²⁴ ₓ i³
i²⁷ = i⁴⁽⁶⁾ ₓ i²⁺¹
i²⁷ = (i⁴)⁶ . i².i
Here, we know that i² = -1
so, i⁴ = (i²)²
i⁴ = 1
Hence, 1⁶(-1)(i) = -i
Therefore, the equivalent to the complex number i²⁷ is -i.
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determine if the sequence is arithmetic. if it is find the common difference and the next 3 terms in the sequence 35, 32, 29, 26
Answer:
-3 and 23,20,17
Step-by-step explanation:
35-3=32,32-3=29
For f(x) = √x and g(x) = x + 9, find the following functions.
a. (f o g)(x) =
(Simplify your answer.)
b. (g o f)(x) =
(Simplify your answer.)
c. (f o g)(7) =
(Simplify your answer.)
d. (g o f)(7) =
(Simplify your answer.)
Show your work below.
Part a
[tex](f \circ g)(x)=f(g(x))=\sqrt{x+9}[/tex]
Part b
[tex](g \circ f)(x)=g(f(x))=\sqrt{x}+9[/tex]
Part c
[tex](f \circ g)(7)=\sqrt{7+9}=4[/tex]
Part d
[tex](g \circ f)(7)=\sqrt{7}+9[/tex]
A microwave raises the temperature of water by about 80°F in 5 minutes. Which graph has the slope that represents this rate of increase?
Since the microwave raises the temperature of water by about 80°F in 5 minutes, the graph that has the slope that represents this rate of increase is option A.
What is the temperature about?
Temperature is seen as a given unit used to stand for hotness as well as the coolness of a given object or thing, it is said to be mostly in Fahrenheit as well as Celsius.
Based on temperature, heat energy is one that tends to shift from a hotter part of a body to a colder part of the same body.
Note that:
Temperature = 80
Minutes = 5
Y = m
5m = 80
m = 80/5
m = 16
So y = 16x
Therefore, the graph that can give you the value above is graph A.
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Gina checked 20 markers. 7 of them were
working. What percent of her markers were
not working?
Step-by-step explanation:
1. find how many are not working
20 - 7 = 13
2. make this into a fraction:
13/20
3. make equivalent to x/100
do this by multiplying by 5
13/20 = 65/100
65/100 is 65% which don't work
Answer:
65%
Step-by-step explanation:
20-7=13, 13/20=0.65, 0.65*100=65 (Which leaves you with your answer)
Plot the image of point D under a dilation about the origin (0,0) with a scale factor of 2
The coordinates of the image of point D are (- 6, - 4) and a representation of the rigid transformation is shown in the picture attached below.
How to determine the location of the image of a point set on Cartesian plane
Herein we find the location of point D, which is set on Cartesian plane and must be modified by the use of a rigid transformation known as dilation. The general definition of the dilation rule is defined below:
D'(x, y) = O(x, y) + k · [D(x, y) - O(x, y)]
Where:
O(x, y) - Center of dilation.k - Scale factorD(x, y) - Coordinates of the point.D'(x, y) - Coordinates of the image.If we know that O(x, y) = (0, 0), D(x, y) = (- 3, - 2) and k = 2, then the coordinates of the image are:
D'(x, y) = (0, 0) + 2 · [(- 3, - 2) - (0, 0)]
D'(x, y) = (- 6, - 4)
Now we proceed to present the location of the image on the Cartesian plane.
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In a particular college class, 60% of the students are female. Of the female students, 75% have long hair. One student is picked randomly in the class. What is the probability that it is a female with long.
There is a 0.75 percent chance that the person is a woman with long hair.
What is probability?Probability can be used to define potential. The occurrence of a random event is the focus of this mathematical field. There is a 0 to 1 value range. The likelihood of anything happening is often referred to as probability. Utilize probability to gauge a situation's likelihood of happening. Numerous factors are difficult to forecast with absolute precision. Using it, we can only speculate on whether or how likely it is that an event will occur. A probability scale with a value of 0 for an impossibility and 1 for a certainty. In a sample space, there is a one probability for every event.
E is the probability of an event . Hence,
P(E) is the ratio of favorable results to all outcomes.
In probability, an event is deemed dependent if it is impacted by other occurrences, and independent if it is wholly unaffected by the occurrence of any other event.
By applying the literature and formulas previously mentioned, we have:
F should signify for the fact that the student is female, and L should stand for the fact that the student has long hair.
P(F)
= 0.60
P(L)
= 0.50
P(F AND L)
= 0.45
P(L|F)
= 0.75
There is a probability of 0.75 that a randomly chosen student has long hair.
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The Sum of the 1st in term of an A.p is 30 while the Sum of the it'st 7 term is 56 find the: a. the common difference b.the 1st term
The common difference of the AP is 4.33 and its first term is 30.
What is the formula to calculate the nth term of an Arithmetic Sequence ?
The formula to calculate the nth term of an Arithmetic Sequence is -
a(n) = a + (n - 1)da - first term of A.P.
d - Common difference of A.P.
n - position of term
Given is the 1st term of an AP as 30 while the Sum of the its first 7 terms is 56.
We have -
[a] = 30
and -
a + (7 - 1)d = 56
30 + (6)d = 56
6d = 56 - 30
6d = 26
d = 26/6
d = 13/3
d = 4.33
and
the first term of the AP is 30.
Therefore, the common difference of the AP is 4.33 and its first term is 30.
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suppose one person in your team has two x^{2}-tiles three x-tiles and one unit tile on his desk and another person has one x^{2}-tile five x-tiles and eight unit tiles on her desk. you decide to pull all of the tiles together on one desk. what is the name for this new group of tiles?
The name for this new group of tiles will be three x² tiles, eight x tiles and nine unit tiles.
How to illustrate the information?Based on the information, it should be noted that the following can be illustrated:
Number of x² tiles = 2 + 1 = 4
Number of x tiles = 3 + 5 = 8
Number of units tiles = 1 + 8 = 9
In this case, this is appropriately illustrated as three x² tiles, eight x tiles and nine unit tiles.. This will be the new name.
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What’s the answer plss
The height till which the ladder will reach the wall will be 3.84 m.
What is defined as the trigonometric identity?Trigonometric Identities come in handy when trigonometric functions are used in an expression or equation. Trigonometric identities hold for all values of variables on both sides of an equation. Geometrically, these identities involve one or more trigonometric functions (including such sine, cosine, and tangent). The principal trigonometry functions are sine, cosine, and tangent, whereas the other three functions are cotangent, secant, and cosecant. All six trig functions are used to derive the trigonometric identities.For the given question,
The distance between the base of the ladder and the wall is 1.4 m.
The angle made by base of the ladder to the floor is 70 degree.
Let the height till which the ladder goes be 'h'.
Then, applying the trigonometric identity.
tan 70 = h/1.4
h = 1.4 × tan 70
h = 3.84 m
Thus, the height till which the ladder will reach the wall will be 3.84 m.
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Write and equation of the line parallel to the given line that contains C
C(4,3) ; y=-2x+5
The equation of the required line is y = - 2x + 11
We need to find the equation of the line parallel to the given line y = -2x + 5 that contains C(4, 3)
Let m be the slope of the required line.
The slope of the line y = -2x + 5 is -2
We know that, the slope of the parallel lines is equal.
So, m = -2
The required line contains point C(4, 3)
Using point-slope form the equation of the line would be,
(y - y1) = m(x - x1)
y - 3 = -2(x - 4)
y - 3 = -2x + 8
y = -2x + 8 + 3
y = -2x + 11
Therefore, the equation of the required line is y = - 2x + 11
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how to divide 40 by 178
178/40
Answer: 0.224
Step-by-step explanation:
40/178= 0.224
work in the pic
This is a question from IXL. I need help! ASAP thanks
The image of triangle CDE after a rotation of 90º counterclockwise around the origin is graphed at the end of the answer.
What is a rotation?When a polygon undergoes a rotation, this rotation is over an angle measure, that defines the coordinate rule for each vertex of the polygon.
For triangle CDE, the vertices are given as follows:
D(-7,-1), C(-7,-7), E(-4,-8).
The rule for a rotation of 90º counterclockwise around the origin, for each vertex (x,y) of the polygon, is given by:
(x,y) -> (-y,x).
Hence, applying the rule above, the vertices of the image of triangle CDE will be given as follows:
D'(1,-7), C'(7,-7), E'(8,-4).
The triangle, with these vertices labeled, is graphed at the end of the answer.
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Which point is the BEST choice for the location of 377√?
The best choice for the location of the square root of 377 is B. less than 20.
How to illustrate the information?It should be noted that the square root of a number simply means the number that we can multiply but itself which will give the original number.
In this case, it should be noted that the square root of 377 is 19.4. It should be noted that this is close to 20.
Therefore based on the options given the correct option is B.
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Which point is the BEST choice for the location of ✓377?
Less than 15
Less than 20
Less than 14
More than 10
Answer:
B
Step-by-step explanation:
Evaluate.
0/−1.02 ⋅ (−4)
Enter your answer in the box.
suppose that buses are scheduled to arrive at a bus stop at noon but are always x minutes late, where x is an exponential random variable with mean of 4 minutes. suppose that you arrive at the bus stop precisely at noon. compute the probability that you have to wait for more than five minutes for the bus to arrive.
[tex]e^{-5 \lambda}[/tex] is the probability that we have to wait for more than 5 min for the bus to arrive.
What probability exactly is?Mathematical representations of the likelihood that an event will occur or that a statement is true are dealt with in the area of probability.A number between 0 and 1, where 0 roughly denotes impossibility and 1 roughly denotes certainty, is the probability of an event.Axiomatic, classical, empirical, and subjective are the four most popular approaches to probability.So, [tex]f_X(x)=\lambda e^{-\lambda x}, x \geq 0[/tex] ⇒ [tex]P(x \geq 5)=\int_5^{\infty} f_X(x) d x[/tex]
Now, solving the above function as follows:
[tex]\begin{aligned}&P(x \geq 5)=\int_5^{\infty} f_X(x) d x \\&=\int_5^{\infty} \lambda e^{-\lambda x} d x \\&=\left.\right|_5 ^{\infty} \frac{\lambda e^{-\lambda x}}{-\lambda} \\&=\left.\right|_5 ^{\infty}-e^{-\lambda x} \\&=e^{-5 \lambda}\end{aligned}[/tex]
Therefore, the probability that we have to wait for more than 5 min for the bus to arrive is [tex]e^{-5 \lambda}[/tex].
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The correct question is given below:
Suppose that the buses arrive are scheduled to arrive at a bus stop at noon are always X minutes late, where X is an exponential random variable with probability density function [tex]f_X(x)=\lambda e^{-\lambda x}, x \geq 0[/tex]. Suppose you arrive at the bus stop precisely at noon. Find the probability that you have to wait for more than 5 min for the bus to arrive
What is the sign of -3^40 - (5.6 ÷ 2.1)?
Choose 1 answer:
Positive
Negative
Zero
Answer:
Step-by-step explanation:
negative
Please help
Step by step
A wireless carrier offers the following plans that a person is considering.
The Family Plan: $90 monthly fee, unlimited talk and text on up to 8 lines, and data charges of $40 for each device.
The Mobile Share Plan: $120 monthly fee for up to 10 devices, unlimited talk and text for all the lines, and data charges of $35 for each device.
Use P for the number of devices that need data plans as part of their cost.
Find the model of the total cost of the Family Plan.
Find the model of the total cost of the Mobile Share Plan.
Assuming they stay under their data limit, find the number of devices that would make the two plans equal in cost.
If a family has 3 smart phones, which plan is more affordable?
Using linear functions, it is found that:
The model of the total cost of the Family Plan is: F(P) = 90 + 40P.The model of the total cost of the Mobile Share Plan is: M(P) = 120 + 35P.The costs will be the same for 6 devices.For 3 smartphones, the Family Plan is more affordable.What is a linear function in slope-intercept format, and why it is used in this problem?A linear function, in slope-intercept format, is modeled according to the following rule:
y = mx + b
In which:
The coefficient m is the slope of the function, which is the rate of change of the function, that is, the change in y divided by the change in x.The coefficient b is the y-intercept of the function, which is the the value of y when the function crosses the x-axis(x = 0).In the context of this problem, it is used because the rate of change for each plan is constant, that is, for each device, there is a constant increase in the plan charge.
For the plans in this problem, we have that:
The intercept is given by the monthly fee.The slope is given by the charges for each device.Hence the models for each plan are given as follows, with P representing the number of devices.
Family Plan: F(P) = 90 + 40P.Mobile Share Plan: M(P) = 120 + 35P.The costs will be the same when:
F(P) = M(P)
Hence we solve for P to find the number of plans as follows:
90 + 40P = 120 + 35P
5P = 30
P = 6 devices.
For 3 smartphones, the costs are given as follows:
F(3) = 90 + 40(3) = 210.M(3) = 120 + 35(3) = 225.210 < 225, hence the Family Plan is more affordable.
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Find the total surface area of this cone.
Leave your answer in terms of T.
25m
8m
SA = [?]π m²
Hint: Surface Area of a Cone = Tre + B
Where = slant height, and B = area of the base
Enter
Answer:
264
Step-by-step explanation:
The area of the base is [tex]\pi(8)^2=64\pi [/tex].
So, the surface area is [tex]\pi(8)(25)+64\pi=264\pi[/tex]
. Find the number which is when multiplied by 15 is increase by
196?
Answer: 14 is the number
Step-by-step explanation:
Write the function rule g(x) after the given transformations of the graph of f(x) = 6x.
reflection in the x-axis; vertical compression by a factor of
2
g(x) =
Given the transformations of the graph of f(x)=6x, the function rule g(x) is therefore g(x) = -1/2x.
What is transformation?A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location. Transformations can be divided into four categories: translation, rotation, reflection, and enlargement. You must be able to carry out each transformation and recognize which ones have already been done.
Given Data
f(x) = 6x
The resulting function will be f(x) = -6x if the function is not reflected over the x-axis.
The final function rule will be; if the resulting function is compressed by a factor of 1/12.
g(x) = 1/12(-6x)
g(x) = -1/2x
Given the transformations of the graph of f(x)=6x, the function rule g(x) is therefore g(x) = -1/2x.
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find the value of expression when y=4 6y-78
PLUG IN THE VALUE 4 IN THE PLACE OF Y AND SIMPLIFY
[tex] = 6(4) - 78 \\ = 24 - 78 \\ = - 54[/tex]
HOPE THIS HELPS
8 1/4 + 2 5/8 = ?
I REALLY NEED HELP!!!!!!!
Answer: the answer is 10.875
Hope this helped :D
Answer:
10 7/8 Here you go :) ten seven eights
Step-by-step explanation:
Please help me with math lol
Answer for 1: 16.4
Answer for 2: 10.095
Answer for 3: 7.431
Answer for 4: 2.31
Answer for 5: 42.74
Answer for 6: 10.224
Answer for 7: 4.436
Answer for 8: 20.574
Answer for 9: 35.626
Answer for 10: 31.042
Answer for 11: 84.708
Answer for 12: 53.066
Answer for 13: 0.0061
Answer for 14: 7.092
Answer for 15: 1.463
Answer for 16: 92.0898
I hope this helps :)
A plot of corn is 7 2/3 yards wide. It is 6 times as long as it is wide. How long is the plot of corn?
Answer:
length = 46 yards
Step-by-step explanation:
width = [tex]7\frac{2}{3}[/tex] yards
length = 6 times the width
[tex]7\frac{2}{3} *6 = 46[/tex]
length = 46 yards
Find all roots
y = 3x³ - 7x² − 14x + 24
Answer:
[tex]x=-2, x=\frac{4}{3}, x = 3[/tex]
Step-by-step explanation:
First, factor it.
[tex](x+2)(3x-4)(x-3)=0[/tex]
Use the Zero Factor Principle and equate them each to 0.
[tex]x+2=0\\x=-2\\\\3x-4=0\\x=\frac{4}{3}\\\\x-3=0\\x=3[/tex]
This is how you find the roots of [tex]3x^3-7x^2-14x+24[/tex].
Help please , THANKS!
:DD
Answer:
73°
Step-by-step explanation:
To find ∠QPS, just add ∠1 and∠2
∠QPS = ∠1 + ∠2
= 44° + 29°
= 73°
Answer:
∠QPS = 73°
Step-by-step explanation:
∠1 = 44°
∠2 = 29°
∠QPS = ∠1 + ∠2 = 44° + 29° = 73°
X=7/8t+3; t what does t equal?
Answer:
[tex]t=\frac{8x-24}{7}\\[/tex]
Step-by-step explanation:
[tex]\frac{7}{8}t+3=x\\\frac{7}{8}t=x-3\\7t=8x-24\\t=\frac{8x-24}{7}[/tex]
Pretty simple, basic algebra.
1. Switch the sides to make it easier to read
2. Subtract 3 on both sides
3. Divide both sides by 8 to cancel the denominator
4. Divide both sides by 7 to isolate the y
Estimate the quotient of 45 ÷ 1.5.
67.5
30
9
3
Answer:
30
Step-by-step explanation:
PLEASE HELP Which equation is equivalent to -2a + 6b = -8c + 16? A. a=-4b-10c+14 B. a=-3b+2c+8 C. a=3b+4c-8 D. a=4b-10c+14
Answer: a= 3b + 4c -8
Step-by-step explanation:
a= 3b + 4c -8
-2a + 6b = -8c + 16
-6b from the left the isolate a
-2a = -6b - 8c + 16
then divide by -2 to cancel it out
a = 3b + 4c -8
The equation is equivalent to -2a + 6b = -8c + 16 will be a= 3b + 4c -8
What is a linear equation?A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is of the form Ax + B = 0.
We are given the linear equation;
a= 3b + 4c -8
-2a + 6b = -8c + 16
-6b from the left the isolate a
-2a = -6b - 8c + 16
Then divide by -2 to cancel it out;
a = 3b + 4c -8
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