What is the distance on the unit circle between successive fourth roots of root3/2 - 1/2i
Answers
The distance between successive fourth roots of the complex number √3/2 - 1/2i on the unit circle is 5π/24 units.
To find the distance between successive fourth roots of a complex number on the unit circle, we can use the concept of the angle between the roots. Let's proceed step by step:
The given complex number is √3/2 - 1/2i. This complex number lies on the unit circle because its magnitude is equal to 1.
1. Convert the given complex number to trigonometric form:
√3/2 - 1/2i = cos(θ) + i*sin(θ)
By comparing the real and imaginary parts, we can determine the angle θ:
cos(θ) = √3/2
sin(θ) = -1/2
Using the unit circle, we can find that θ = 5π/6 (or 150 degrees). This angle represents the position of the given complex number on the unit circle.
2. Find the angle between successive fourth roots:
Since we are interested in the fourth roots, we divide the angle θ by 4:
θ/4 = (5π/6) / 4 = 5π/24
This angle represents the angular distance between two successive fourth roots on the unit circle.
3. Calculate the distance between the two points:
To find the distance, we multiply the angular distance by the radius of the unit circle (which is 1):
Distance = (5π/24) * 1 = 5π/24
Therefore, the distance between successive fourth roots of the complex number √3/2 - 1/2i on the unit circle is 5π/24 units.
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Related Questions
Based on the triangle shown, what is the approximate value of Cos(20)?
Use exact fractions. To receive credit for this question, you must show your work.
3
5
e
Answers
The value of cos 2θ will be;
⇒ cos 2θ = 7/25
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The sides of triangle are 3 , 5, 4
Now,
Since, In a triangle;
cos 2θ = 2cos²θ - 1 .....(i)
And, cos θ = Base / Hypotenuse
Substitute all the values, we get;
cos θ = Base / Hypotenuse
cos θ = 4 / 5
Substitute above value in equation (i), we get;
cos 2θ = 2cos²θ - 1
cos 2θ = 2(4/5)² - 1
cos 2θ = 32/25 - 1
cos 2θ = 7/25
Thus, The value of cos 2θ will be;
⇒ cos 2θ = 7/25
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A recent study found that people with insomnia are more likely to experience heart problems than people without insomnia.
a. What are the explanatory and response variables in this study?
b. Explain why amount of caffeine consumed might be a confounding variable in this study by explaining how caffeine consumption fits the two properties of confounding variables given in the box on page.
Answers
a. The explanatory variable in this study is insomnia and the response variable is the likelihood of experiencing heart problems. b. Amount of caffeine consumed could be a confounding variable in this study because it fits the two properties of confounding variables.
In this study, the explanatory variable is "insomnia" and the response variable is "heart problems." A confounding variable, such as "amount of caffeine consumed," might affect the relationship between insomnia and heart problems. Caffeine consumption fits the two properties of confounding variables as it is related to both the explanatory variable (insomnia) and the response variable (heart problems). Consuming more caffeine can lead to insomnia, and it can also increase the risk of heart problems independently. Therefore, caffeine consumption could be a confounding variable in this study, potentially influencing the observed relationship between insomnia and heart problems.
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Given the system of equations:
2x + 3y = 15
X + 3y = 0
What is x?
-15
-5
0
5
15
Answers
Answer:
Step-by-step explanation:
Given the system of equations:
2x + 3y = 15
X + 3y = 0
What is x?
2x + 3y = 15
X + 3y = 0 subtract the bottom equation fron the top one
2x - x + 3y - 3y = 15 - 0 see how the 3y - 3y equates to zero
2x - x = 15
x = 15 Now for extra credit what is y?
X + 3y = 0
15 + 3y = 0
15 - 15 + 3y = 0 - 15
3y = -15
3y/3 = -15/3
y = -5
-15
-5
0
5
15
Graph the system of equations.
2x−y=4
x−y=−2
Answers
Step-by-step explanation:
Given
The pair of lines are
\(2x-y=4\\x-y=-2\)
For the first line, if y=0, x=2
if x=0, y=-4
Similarly, for second line , if y=0, x=-2
if x=0, y=2
Plot the given point and draw the line.
From the graph the two lines meet at (6,8)
An icecream shop has 10 flavors. One can choose 4 different
flavors. What is the total number of possible flavor
combinations?
a.
252
b.
462
c.
120
d.
330
e.
210
2.
Answers
An ice cream shop has 10 flavors and one can choose 4 different flavors. The question asks for the total number of possible flavor combinations.Therefore, we need to find the number of ways in which 4 flavors can be chosen from 10 flavors.
In such cases where order does not matter and repetitions are not allowed, we can use the formula for combinations which is as follows:C(n, r) = n! / (r! (n - r)!)Where n is the total number of items, r is the number of items being chosen at a time and ! represents the factorial function.
Using this formula we can find the total number of possible flavor combinations. Substituting the values in the above formula, we get:C(10, 4) = 10! / (4! (10 - 4)!)C(10, 4) = (10 * 9 * 8 * 7) / (4 * 3 * 2 * 1)C(10, 4) = 210Hence, there are 210 possible flavor combinations when one can choose 4 different flavors
.Explanation:The formula to be used for this type of question is combination. Combination is the method of selecting objects from a set, typically without replacement (without putting the same item back into the set) and where order does not matter. The formula for combination is given by C(n,r)=n!/(r!(n-r)!).
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Simplify a^7 b^2 a^-9
Select one:
O a. a^2/ b²
O b. a^8 b^2
O c. a^2 b^2
O d. b^2/a ²
Answers
The answer to the given question is b²/a²
The power of a number tells us how many times that number must be multiplied. Exponents and indexes are other names for powers. For instance, 8² denotes "8 squared," "8 squared," or just "8 squared."
A power is just an expression that denotes repeatedly multiplying the same number or factor. The exponent value depends on how frequently the base has been multiplied by itself.
For instance, 8 x 8 x 8 x 8... times is 8. The phrase 8n above is pronounced as 8 raised to the power n. As a result, exponents are also sometimes referred to as power or indices.
a⁷ b² a⁻⁹
= a⁽⁷⁻⁹⁾ b²
= a⁻² b²
= b² / a²
Therefore, The value of the given equation is b²/a²
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Suppose you are building a storage box of volume 4368in^3. the length of the box will be 24 in. the height of the box will be 1 in. more than its width. find the height and the width of the box.
Answers
Answer:
height: 14 incheswidth: 13 inchesStep-by-step explanation:
The volume formula can be used to find the height and width of a box with volume 4368 in³ and height 1 in greater than width.
SetupThe volume formula is ...
V = LWH
Substituting given information, using w for the width, we have ...
4368 = (24)(w)(w+1)
SolutionWe want to find the value of w.
182 = w² +w . . . . . . . . divide by 24
182.25 = w² +w +0.25 = (w +0.5)² . . . . . . add 0.25 to complete the square
13.5 = w +0.5 . . . . . . . . take the positive square root
w = 13 . . . . . . . . . . . . subtract 0.5
h = w+1 = 14
The height of the box is 14 inches; the width is 13 inches.
__
Additional comment
By "completing the square", we can arrive at the exact dimensions of the box, as we did above. Note that we only added 0.25 to the equation to do this.
For numbers close together, the geometric mean (root of their product) is about the same as the arithmetic mean (half the sum):
\(\sqrt{w(w+1)}\approx\dfrac{w+(w+1)}{2}=w+\dfrac{1}{2}\\\\w\approx\sqrt{182}-\dfrac{1}{2}\approx12.99\)
Using this approximation to arrive at the conclusion w=13 saves the steps of figuring the value necessary to complete the square, then adding that before taking the root.
5 There are 150 men and 250 women in a crowd.
a What fraction of the crowd are men?
Write your answer in its simplest possible form.
b The ratio of married women to unmarried women is 3 to 2.
How many married women are in the crowd?
C More men arrive. The number of men increases by 20%.
How many men are in the crowd now?
d Some of the women leave.
There are now 60 women in the crowd.
What percentage of the women leave?
Answers
Answer:
men=150
women=250
total=400
Step-by-step explanation:
a) fraction of men
men/total=150/400=15/40
men/total =3/8
b)let married be x
so unmarried wil be 250-x
married/unmarried=3/2
x / 250-x =3/2
x =3(250-x)/2
2x =750-3x
5x=750
x=750/5
x =150
married =150
unmarried=250-150=100
c)20% of men will be :20x150
100
: 30
no of men =150+20%
=150+30
=180
d)no. of women decreased=250-60
=190
percentage of women leaved=% x 250
100
190x100/250=%
76 =%
76% women leaved
It took too much time
MARK ME BRAINLIEST THANKS MY ANSWER PLEASE
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Use the Central Limit Theorem to find the probability of the indicated event, assuming that the distribution of the population data is unknown. In a certain city, employees work an average of 18.9 hours of overtime every month, with a standard deviation of 7.8 hours. What is the probability that the average number of hours of overtime worked last month by a random sample of 140 employees in the city exceeds 20 hours? Provide a solution showing your calculations and submit your work for marking. Include a sketch as part of your complete solution. P(X > 20)=
Answers
The probability that the average number of hours of overtime worked last month by a random sample of 140 employees in the city exceeds 20 hours is approximately 0.9564, or 95.64%.
To find the probability that the average number of hours of overtime worked by a random sample of 140 employees exceeds 20 hours, we can use the Central Limit Theorem (CLT). The CLT states that for a large enough sample size, the sampling distribution of the sample mean approaches a normal distribution, regardless of the shape of the population distribution.
Given that the population mean is 18.9 hours and the population standard deviation is 7.8 hours, we can calculate the standard error of the mean using the formula: standard error = population standard deviation / sqrt(sample size).
For this problem, the sample size is 140, so the standard error is 7.8 / sqrt(140) ≈ 0.659.
To calculate the probability, we need to standardize the sample mean using the z-score formula: z = (sample mean - population mean) / standard error.
In this case, the sample mean is 20 hours, the population mean is 18.9 hours, and the standard error is 0.659. Plugging these values into the formula, we get z = (20 - 18.9) / 0.659 ≈ 1.71.
Now, we can use a standard normal distribution table or calculator to find the probability associated with a z-score of 1.71. Looking up this value in the table, we find that the probability is approximately 0.9564.
Therefore, the probability that the average number of hours of overtime worked last month by a random sample of 140 employees in the city exceeds 20 hours is approximately 0.9564, or 95.64%.
Here's a sketch to visualize the calculation:
|
|
|
| **
| * *
| * *
| * *
| * *
| * *
| * *
-------------------|--------------------------
18.9 | 20
The area under the curve to the right of 20 represents the probability we're interested in, which is approximately 0.9564 or 95.64%.
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I got the first part but i dont onow how to get the other ones
Answers
The value of x for this problem is given as follows:
x = 5.
Hence the angle measures are given as follows:
m < CAB = 32º.m < FDE = 32º.How to obtain the value of x?
We have that angles A and D are congruent for this problem, meaning that they have the same measure.
Hence the value of x is obtained as follows:
7x - 3 = 5x + 7
2x = 10
x = 5.
Hence the angle measures are given as follows:
m < CAB = 7(5) - 3 = 35 - 3 = 32º.m < FDE = 5(5) + 7 = 32º.More can be learned about angle measures at https://brainly.com/question/25716982
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Which word best describe reflection
A.Line of symmetry
B.Mirror-image
C.identical
D.All of the above
Answers
Answer:
B
Step-by-step explanation:
Which word best describe reflection
A.Line of symmetry
B.Mirror-image
C.identical
D.All of the above
(x + 7)^2 – 11 = 0
lesser =
greater =
Answers
Answer:
Lesser = -\(\sqrt{11}\) - 7 = -10.317
Greater = +\(\sqrt{11}\) - 7 = -3.683
Step-by-step explanation:
I am assuming you are asking for the lesser x solution and greater x solution.
(x + 7)^2 – 11 = 0
(x + 7)^2 = 11
x+7 = ±\(\sqrt{11}\)
x = ±\(\sqrt{11}\) - 7
Lesser = -\(\sqrt{11}\) - 7 = -10.317
Greater = +\(\sqrt{11}\) - 7 = -3.683
Answer:
lesser= -14
greater= 0 (:
It is known that the length of a certain product x is normally distributed with μ = 18 inches. How is the probability p(x > 18) related to p(x < 18)?
Answers
The probability of x being greater than 18 (p(x > 18)) is equal to the probability of x being less than 18 (p(x < 18)) in a normal distribution.
In a normal distribution, the probability of an event happening to the left of the mean (μ) is equal to the probability of the event happening to the right of the mean. This means that if we know the probability of x being less than 18 (p(x < 18)), we can use the property of symmetry to determine the probability of x being greater than 18 (p(x > 18)).
Since the probability distribution of x is symmetric around the mean, the area under the probability density function (PDF) to the left of the mean is the same as the area to the right of the mean. Therefore, we can say:
p(x > 18) = p(x < 18)
In other words, the probability of x being greater than 18 is equal to the probability of x being less than 18 in a normal distribution.
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Consider the expression 5a + (-4b), where bis a negative number and a
Answers
The sum is negative.
Identify the property that justifies the statement. OP = RS, RS= OP. Sym.
Answers
The property that justifies the statement "OP = RS, RS = OP" with "Sym" is symmetry. Symmetry refers to the property of an object or equation where it remains unchanged under certain transformations or operations.
In this case, if we reflect the circuit across the line of symmetry, the circuit will be exactly the same as the original circuit, except that the voltage source will be flipped over.
Therefore, if we take the voltage across the resistor (RS) and multiply it by the resistance of the voltage source (R), we will get the same result as if we take the voltage across the resistor (OP) and multiply it by the resistance of the resistor (R). This property is symmetric, and thus the statement "OP = RS, RS = OP" is true
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Answer:
Sym. Prop. of ≅ is the correct answer
As a part of your project studying tipping behavior, you ask people the question, How much should you tip a grocery bagger for carrying five bags to your car? The Grocery Bagger Surveys tab of this spreadsheet gives the responses to this question from 10 independent surveys, each with 50 respondents. The respondents were asked to round to the nearest quarter, since few people tip with pennies, nickels, and dimes. In the spreadsheet, you can calculate the mean, or average, of data using the Average function: Select the cell in which you want the mean to appear. Type =AVERAGE( in the formula bar. Select all the cells containing the values for which you want to find the average, and then press Enter. The average of the values in the cells will be calculated and displayed in the cell in which you entered the formula. Question 1 What is the sample mean of the responses in survey 1?
Answers
Answer:
The sample mean for survey 1 is $1.69.
Step-by-step explanation:
I just did this on edmentum plato.
How do you solve this?!!
Answers
Answer:
135°
Step-by-step explanation:
Step 1:
100° + 35° + 180° - ? = 180° Sum of a Δ/Vertical ∠'s
Step 2:
315° - ? = 180° Combine Like Terms
Step 3:
315° = 180° + ? Add ? on both sides
Step 4:
315° - 180° = ? Subtract
Answer:
? = 135°
Hope This Helps :)
1/4 of 7 and 1/3 of 7
Answers
Answer:
1/4 of 17 =4.25 in decimal form
1/3 of 7 = 2.3333 in decimal form
Step-by-step explanation:
I hope I helped
A certain basketball player scores 60% of the free-throw shots she attempts. during a particular game, she gets six free throws. what is the probability that she scores on exactly four of the six shots? choose one.
Answers
The probability of scoring exactly four out of the given six shots is 0.311, calculated using the concept of binomial distribution in probability theory.
What is a Binomial Distribution?
Binomial Distribution in probability theory is defined as getting x number of successes on repetition of trial n times, the formula for binomial distribution is C(n,r) × (p)x × (q)n - r, where p denotes the probability of success and q denotes the probability of failure.
Calculation of the probability of scoring exactly four shots out of six
Let p denote the probability of success and q denote the probability of failure, which is equal to 1 - p.
Using Binomial Distribution, we get,
P(x = r) = C(n,x) × (p)x × (q)n - x
Taking r = 4,
P(x = 4) = C(6,4) × (0.6)4 × (0.4)2
= 6! / (4! 2!) × (0.6)4 × 0.16
= 0.31104
~ 0.311
Hence, the required probability using binomial distribution is 0.311.
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Mary is designing a circular piece of stained glass with a diameter of 9 inches. She is going to sketch a square inside the circular region. Find to the nearest tenth of an inch, the largest possible length of a side of a square
Answers
Answer:
6.4 inches
Step-by-step explanation:
The diagonal of a square is equal to the diameter of the circle that can be inscribed in the square. So, if we can find the diameter of the circle, we can then find the length of the square's diagonal, which is also the largest possible length of a side of the square.
The diameter of the circle is 9 inches, so the radius is 4.5 inches. The diagonal of the square is the diameter of the circle, which is 9 inches.
Let's use the Pythagorean theorem to find the length of a side of the square:
a^2 + b^2 = c^2
where a and b are the sides of the square and c is the diagonal.
We know c = 9, so:
a^2 + b^2 = 9^2 = 81
Since we want the largest possible length of a side of the square, we want to maximize the value of a. In a square, a and b are equal, so we can simplify the equation to:
2a^2 = 81
a^2 = 40.5
a ≈ 6.4 (rounded to the nearest tenth of an inch)
Therefore, the largest possible length of a side of the square is approximately 6.4 inches.
Please help me with this question.
Answers
Answer:
aww i help u.....
Step-by-step explanation:
my answer is letter ~~B CAUSE STUDEN BIS CONDYCTION LIKR FREE AT THE SCORED
Write the rule for the linear function. Remember a function rule is written using using f(x). X -10 0 10 y -1 1 3
Answers
Rise: 3-1 equals 2
Run: 1-2 equals -1
This gives -2 as slope.
Pick a point to find b.
Use y=mx+b and (1,3). Y is same as f(x)
3=-2*1+b
5=b
Plug everything in: F(x) equals-2X plus 5
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zoe walks from her house to a bus stop that is 460 yards away. what would being the varying distances
Answers
Zoe walks from her house to a bus stop that is 460 yards away. The varying distances would depend on where Zoe begins her walk. if she starts closer to the bus stop, she would walk a shorter distance.
The varying distances would refer to the different distances Zoe might walk on different occasions. For example, she might take different routes or make detours, causing the actual distance she walks to vary.
However, without more information about Zoe's specific routes or circumstances, it is not possible to provide more detailed information about the varying distances.
However, if she starts closer to the bus stop, she would walk a shorter distance.
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What is the slope of the equation y = 5x - 7?
o
-7
o
7.
Answers
Answer:
slope = 5
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 5x - 7 ← is in slope- intercept form
with slope m = 5
Answer:
The slope is 5.
Step-by-step explanation:
y=mx+b is the equation used to plot a line, where m is the slope and b is the y intercept.
There are two cameras that take pictures of a traffic intersection. Camera A starts taking pictures at 6 AM and takes a picture every 11 minutes. Camera B starts taking pictures at 7 AM and takes pictures every 7 minutes. Camera A and Camera B take a picture at the same time at four different times before noon. When Camera A and Camera B take their last picture together, how many minutes before noon is it?
Answers
Answer:
41 minutes before noon
Step-by-step explanation:
The given parameters are;
The time camera A starts taking pictures = 6 AM
The frequency of picture taking by camera A = Once every 11 minutes
The time camera B starts taking pictures = 7 AM
The frequency of picture taking by camera B = Once every 7 minutes
The number of times both cameras take a picture at the same time before noon = 4 times
Let the time the two cameras first take a picture the same time be x, we have;
11·y - 60 = x
7·z = x
Taking the number of times after 7 camera A snaps and noting that the first snap is 6 minutes after 7, we have
11·b + 6 = x
7·z = x
x is a factor of 7 and 11·b + 6 and x is some minutes after 7
By using Excel, to create a series of values for Camera A based, on 11·b + 6, and dividing the results by 7 we have the factors of 7 at;
28, 105, 182, and 259 minutes after 7
Given that there are 60 minutes in one hour, we have;
259/60 = 4 hours 19 minutes, which is 11:19 a.m. or 41 minutes before noon.
Please can someone help geometry honors
Answers
Answer: THE FIRT ANSWER IS (C) AND THE SECOND ANSWER IS (A)
Step-by-step explanation:LEMME GET BRAINLIEST PLS AND THANK YOU
Answer:
number 2 is C
Number 3 is A
Step-by-step explanation:
hope this helps
What is 7 Roman numbers?
Answers
Answer:
VII
Step-by-step explanation:
Factor 25x2 10x 1. (5x 1)² (25x 1)(x 1) (5x 1)(5x - 1)
Answers
The answer is (5x + 1)².
The answer to the given question is (5x + 1)(5x + 1) which can be written as (5x + 1)². This can be solved by using the below method:Solve the equation by looking for two numbers that multiply to give you 25x2 and add up to give you 10x. To solve the equation, find factors of 25 that multiply to give you 25x2 and factors of 1 that multiply to give you 1. The expression that will be factored is 25x2 10x 1 and the factors that multiply to give 25x2 are 25x and x.
The factors that multiply to give 1 are 1 and 1. Thus, the factors of 25x2 10x 1 are (25x 1)(x 1).To factor the expression, first multiply 25x by 1 and add this result to the product of x and 1, which gives 25x + x = 26x. Next, set this sum equal to the middle coefficient of the original expression, which is 10x. Since 26x does not equal 10x, try different pairs of factors of the constant term 1 until one works. In this case, the pair that works is 5 and 1, since 5 + 5 + 1 + 1 = 12 and 5(1) + 5(1) = 10. Therefore, factor 25x2 10x 1 as (5x + 1)(5x + 1), which can be written as (5x + 1)².Hence, the answer is (5x + 1)².
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[100 POINTS] Find the values of x, y, and z.
![[100 POINTS] Find the values of x, y, and z.](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/cfQaLroXH6ecvOv38ItwXldpujCEF73r.png)
Answers
Y-90
Z-90
Hope this help I’m not sure if I’m right but hopefully
\(\qquad\qquad\huge\underline{{\sf Answer}}\)
Let's solve ~
x and y are values that represent the angle made by respective arcs on centre of the circle
that is :
x = 20°Here, Angle x + Angle z = 180°
[ because they form linear pair ]
z + x = 180z = 180 - xz = 180 - 20z = 160°Now, we can observe that angle made by Arc Y is equal to :
y = z + x = 160° + 20° = 180°Adele is 5 years older than Timothy. In three years, Timothy will be of Adele's age. What is Adele's current age? a) 8 years b) 11 years c) 13 years d) 16 years
Answers
Timothy is currently 7 years old and Adele's current age is 12 years old.
To solve this age problem involving Adele and Timothy, we can set up two equations based on the information given. Let A represent Adele's current age and T represent Timothy's current age. The problem states:
Adele is 5 years older than Timothy: A = T + 5
In three years, Timothy will be 2/3 of Adele's age: (T + 3) = (2/3)(A + 3)
First, let's rewrite equation 1 in terms of T: T = A - 5
Now, substitute this expression for T into equation 2:
(A - 5 + 3) = (2/3)(A + 3)
Simplify the equation:
A - 2 = (2/3)(A + 3)
Multiply both sides by 3 to eliminate the fraction:
3(A - 2) = 2(A + 3)
Expand:
3A - 6 = 2A + 6
Now, solve for A:
A = 12
So, Adele's current age is 12 years old. To find Timothy's age, we can use the equation T = A - 5:
T = 12 - 5 = 7
Thus, Timothy is currently 7 years old. Therefore, the correct answer is not among the given options, as Adele's current age is 12 years.
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