Answer:
a. v = 40 000 (3/ 5)^d
b. v = 40 000 (3/5)^(4/10)
c. 0.95
Explanation:
The exponential growth is modelled by
[tex]v=A(b)^d[/tex]We know that points (0, 40 000) and (1, 24 000) lie on the curve. This means, the above equation must be satsifed for v = 40 000 and d = 0. Putting v = 40 000 and d = 0 into the above equation gives
[tex]40\; 000=Ab^0[/tex][tex]40\; 000=A[/tex]Therefore, we have
[tex]v=40\; 000b^d[/tex]Similarly, from the second point (1, 24 000) we put v = 24 000 and d = 1 to get
[tex]24\; 000=40\; 000b^1[/tex][tex]24\; 000=40\; 000b^{}[/tex]dividing both sides by 40 000 gives
[tex]b=\frac{24\; 000}{40\; 000}[/tex][tex]b=\frac{3}{5}[/tex]Hence, our equation that models the situation is
[tex]\boxed{v=40\; 000(\frac{3}{5})^d\text{.}}[/tex]Part B.
Remember that the d in the equation we found in part A is decades. Since there are 10 years in a decade, we can write
t = 10d
or
d = t/10
Where t = number of years
Making the above substitution into our equation gives
[tex]v=40\; 000(\frac{3}{5})^{\frac{t}{10}}[/tex]Therefore, the car's value at t = 4 is
[tex]\boxed{v=40\; 000(\frac{3}{5})^{\frac{4}{10}}}[/tex]Part C:
The equation that gives the car's value after t years is
[tex]v=40\; 000(\frac{3}{5})^{\frac{t}{10}}[/tex]which using the exponent property that x^ab = (x^a)^b we can rewrite as
[tex]v=40\; 000\lbrack(\frac{3}{5})^{\frac{1}{10}}\rbrack^t[/tex]Since
[tex](\frac{3}{5})^{\frac{1}{10}}=0.95[/tex]Therefore, our equation becomes
[tex]v=40\; 000\lbrack0.95\rbrack^t[/tex]This tells us that the car's value is changing by a factor of 0.95 each year.
Enter your answer, rounded to the nearest tenth, in the box.
ANSWER:
-11.4
STEP-BY-STEP EXPLANATION:
We have the following function:
[tex]f\mleft(x\mright)=\frac{100}{-10+e^{-0.1x}}[/tex]We calculate the result when x = -2, just like this:
[tex]\begin{gathered} f(-2)=\frac{100}{-10+e^{-0.1\cdot-2}} \\ f(-2)=\frac{100}{-10+e^{0.2}} \\ f(-2)=\frac{100}{-10+1.22} \\ f(-2)=\frac{100}{-8.78} \\ f(-2)=-11.4 \end{gathered}[/tex]When x = -2, the value of the function is equal to -11.4
State weather the triangles are similar. If so write a similarity statement and that postulate or theorem you used. The diagram is not drawn to scale.
Given:
To prove the similarity.
Two triangles similarity condition:
If two triangles are similar then the corresponding sides are proportional.
[tex]\Delta\text{OKJ Similar to }\Delta ONM[/tex][tex]\begin{gathered} \frac{OK}{ON}=\frac{OJ}{OM}=\frac{KJ}{NM} \\ \frac{3}{3+1}=\frac{30}{30+10} \\ \frac{3}{4}=\frac{30}{40} \\ \frac{3}{4}=\frac{3}{4} \end{gathered}[/tex]From the given values the corresponding sides are proves as propotional.
[tex]\Delta\text{OKJ Similar to }\Delta ONM[/tex]What is the residual of a performance with a revenue of $700 and 70 seats occupied?
Marcia sells lemonade for $2 per cup and candy for $1.50 per candy bar. She earns $425 selling lemonade and candy bars. If marcia sold 90 bars of candy, which equation could be used to figure out how many cups of lemonade she sold?
Answer: 145 cups of lemonade
Step-by-step explanation:
hope it helped :)
What transformations were applied to the toolkit function to create the new function?
The parent functions is f(x) = 1/x
We have 1/(x+2) -1
The 1/(x+2) is f(x+2) which is a horizontal translation left 2 units
Then we have -1 which is f(x+2) -1 which is a vertical translation down 1 unit
The total transformation is a horizontal translation left 2 units and a vertical translation down 1 unit
Answer: left 2 units down 1 unit
the triangles are similar. find the similarity ratio of the first to the second
To get the similarity ratio between both triangles, write down a ratio between two similiar sides. Let's take the base, for example
[tex]4\colon6[/tex]Simplifying,
[tex]2\colon3[/tex]Thereby, the similarity ratio between both triangles is:
[tex]2\colon3[/tex]Ans: Option B
The scores at the end of a game are shown.List the scores in order from greatest to least.Scores:Vince:-0.5, Allison: 3/8, Mariah:-7/20
To arrange the numbers from greatest to least, let us begin by changing all the numbers to decimals.
Vince's Score: -0.5
Allison's Score: 0.375
By long division, we can convert the fraction to a decimal:
Mariah's Score: -0.35
By long division, we have:
Given that we have calculated the scores in decimal, we can clearly see the bigger and smaller numbers.
The order from biggest to smallest is:
Allison: 3/8, Mariah: -7/20, Vince: -0.5
i’m taking an algebra pretest & i’m very confused. i haven’t learned this material. please help!!
ANSWER
7 (Option D)
EXPLANATION
Given:
Number of times the traffic light Green = 6
Number of times the traffic light Yellow = 2
Number of times the traffic light Red = ?
Desired Outcome:
Number of times the traffic light Red
Total number of times for the traffic lights
[tex]\begin{gathered} \text{ Total times = Times for traffic light Red + Times for traffic light Green + Times for traffic light Yellow} \\ 15=Red+6+2 \\ 15=Red+8 \\ substract\text{ 8 from both sides} \\ 15-8=Red+8-8 \\ \text{ Times for traffic light Red = 7} \end{gathered}[/tex]Hence, the number of times the traffic light Red was 7.
Question 7b: Let g(x) be a polynomial function. Name all horizontal andvertical intercepts of the graphsg(x) = (x - 1)2 (x + 2)Horizontal intercepts: 1, -2; vertical intercepts: 2Horizontal intercepts: 2, vertical intercepts: 1,-2Horizontal intercepts: -1, 2, vertical intercepts: 4Horizontal intercepts: 4, vertical intercepts: -1,2
The given function is expressed as
g(x) = (x - 1)^2(x + 1)
It can be written as
y = (x - 1)^2(x + 1)
The horizontal intercept is also known as the x intercept. The x intercept is the value of x when y = 0
If we substitute y = 0 into the function, it becomes
0 = (x - 1)^2(x + 2)
This means that
(x - 1)^2 = 0 and x + 2 = 0
For (x - 1)^2 = 0, if we take the square root of both sides, it becomes
x - 1 = 0
x = 1
For x + 2 = 0,
x = - 2
Thus, the horizontal intercepts are 1 and - 2
The vertical intercept is also known as the y intercept. The y intercept is the value of y when x = 0
If we substitute x = 0 into the function, it becomes
y = (0 - 1)^2(0 + 2)
y = (- 1)^2(2)
y = 1 * 2 = 2
Thus, the vertical intercept is 2
Thus, the correct option is
Horizontal intercepts: 1, -2; vertical intercepts: 2
b) Use the graph to estimate the
value of x when y = 1
Answer:
Hey bro you're welcome.
Step-by-step explanation:
Part 2: Write limits given outputs.Use the graph of the function to write limit equations given limit values.Use the graph to write a limit equation for f(x) that satisfies each given condition. (2 points for each)a. b. c. d. e. Are there other values than what you chose for x where the limit of the function approaches 4? Is the graph continuous at these points? Explain your reasoning. (4 points)
a) From the graph, we see that the function takes the value y = 4 when x = 4, so we have:
[tex]\lim _{x\rightarrow4}f(x)=4.[/tex]b) We see that the curve tends to -∞ when x approaches zero from the left, so we have:
[tex]\lim _{x\rightarrow0^-}f(x)=-\infty.[/tex]c) We see that curve increases without limit when x tends to infinity, so we have:
[tex]\lim _{x\rightarrow\infty}f(x)=\infty.[/tex]d) From the graph, we see that the function tends to y = 0 when x approaches zero from the right, so we have:
[tex]\lim _{x\rightarrow0^+}f(x)=0.[/tex]e) Yes, there are two possible values of x for the limit of the function approaching 4:
• x = 2,
,• x = 4.
By definition, a function is continuous when its graph is a single unbroken curve.
We see that at the points x = 2 and x = 4 the curve is a single unbroken curve, so we conclude that the function is continuous at those points.
Answers
a, b, c, d
[tex]\begin{gathered} \lim _{x\rightarrow4}f(x)=4 \\ \lim _{x\rightarrow0^-}f(x)=-\infty \\ \lim _{x\rightarrow\infty}f(x)=\infty \\ \lim _{x\rightarrow0^+}f(x)=0 \end{gathered}[/tex]e. Yes, there are two possible values of x for the limit of the function approaching 4:
• x = 2,
,• x = 4.
By definition, a function is continuous when its graph is a single unbroken curve.
We see that at the points x = 2 and x = 4 the curve is a single unbroken curve, so we conclude that the function is continuous at those points.
this graphic organizer is being used to classify triangles based on their angle measures or sideways which list shows all of the ways that strangle could be classified
D
1) Examining the sides of that triangle, we can state that this is an equilateral triangle (at least 2 sides have the same measure). But Since isosceles is a triangle that has 2 sides with the same measure.
Then we can state that about their sides this is an equilateral and isosceles triangle.
2) Examining their angles. An equilateral triangle has 3 angles with 60º measure. A 60º angle is lesser than 90º, then we can classify this triangle as an acute triangle
3) Hence, the answer is D
How much money will he raise based on the two donations?
The neighbor will donate $0.25 for every 40ft run.
The aunt will donate $18 for every mile run.
To determine how much he will raise if he runs 5miles, you have to calculate the amount per donor and then add them:
Neighbor
1 mile is equal to 5280 feet
To determine how many feet correspond to 5 miles, multiply the distance by 5280
[tex]5\cdot5280=26400ft[/tex]Next, calculate how much we will make:
40ft → $0.25
26400ft → $x
[tex]\begin{gathered} \frac{0.25}{40}=\frac{x}{26400} \\ 26400\cdot\frac{0.25}{40}=26400\cdot\frac{x}{26400} \\ 165=x \end{gathered}[/tex]For running 5miles, Dustin will raise $165 from the neighbor.
Aunt
The aunt will donate $18 per mile run, to determine how much she will donate, multiply $18 by 5
[tex]18\cdot5=90[/tex]For running 5 miles, Dustin will raise $90 from the neighbor.
Next, add both amounts:
[tex]165+90=255[/tex]Dustin will raise $255 for running 5 miles.
A survey of 85 persons was conducted at TCC, and it was found that 54 persons carried a cell phone, 19 persons carried a tablet computer, and 16 carried both a cell phone and a tablet.How many people carried a cell phone or a tablet?How many people carried neither a cell phone nor a tablet?How many people carried a cell phone only?How many people carried a tablet but not a cell phone?
Answer:
The universal set is given below as
[tex]\xi=85[/tex]The number of people with cell phone is
[tex]n(C)=54[/tex]The number of persons with tablet is
[tex]n(T)=19[/tex]The number of people who carry both cellphone and tablet
[tex]n(C\cap T)=16[/tex]Step 1:
To figure our the number of students that carry cellphone or tablets will be
[tex]\begin{gathered} =38+16+3 \\ =57\text{ }people \end{gathered}[/tex]Hence,
The number of people that carried cell phone or tablet
[tex]\Rightarrow57people[/tex]Step 2:
How many people carried neither a cell phone nor a tablet?
[tex]\begin{gathered} =85-(38+16+3) \\ =85-57 \\ =28 \end{gathered}[/tex]Hence,
The number of people that carried neither cell phone nor a tablet is
[tex]\Rightarrow28people[/tex]Step 3:
How many people carried a cell phone only?
Hence,
The number of people who carried cell-phone only is
[tex]\Rightarrow38people[/tex]Step 4:
How many people carried a tablet but not a cell phone?
Hence,
The number of people that carried a tablet but not a cell phone is
[tex]\Rightarrow3people[/tex]hi help I've been trying to solve this for an hour and this is due in 10 minutes I just really need the correct answer please help
We have the following:
We can confirm the intercepts with the y-axis, since it is when x = 0, in the case of the first equation it is 2 and in the second equation it is 1
Therefore, we limit ourselves to the answers C and D, now we can calculate the slope as follows:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]The point are (0, 2) and (-6, -1)
[tex]m=\frac{-1-2}{-6-0}=\frac{-3}{-6}=\frac{1}{2}[/tex]The slope is 1/2, therefore, the equations are
[tex]\begin{gathered} y=\frac{1}{2}x+2 \\ y=\frac{1}{2}x+1 \end{gathered}[/tex]The answer is the option C
Find the perimeter of quadrilateral ABCD with vertices A(0,4), B(4,1), C(1, -3), and D(-3,0).25 units100 units5 units20 units
The perimeter is the sum of the length of each side of the quadrilateral. We would find the length of each side by applying the formula for finding the distance between two points which is expressed as
[tex]\text{Distance = }\sqrt[]{(x2-x1)^2+(y2-y1)^2}[/tex]Thus, we have
[tex]\begin{gathered} ForAB,x1=0,y1=4,x2=4,\text{ y2 = 1} \\ \text{Distance = }\sqrt[]{(4-0)^2+(1-4)^2\text{ }}\text{ = }\sqrt[]{16\text{ + 9}} \\ AB\text{ = 5} \\ \text{For BC, x1 = 4, y1 = 1, x2 = 1, y2 = - 3} \\ \text{Distance = }\sqrt[]{(1-4)^2+(-3-1)^2}\text{ = }\sqrt[]{9\text{ + 16}} \\ BC\text{ = 5} \\ \text{For CD, x1 = 1, y1 = - 3, x2 = - 3, y2 = 0} \\ \text{Distance = }\sqrt[]{(-3-1)^2+(0--3)^2}\text{ = }\sqrt[]{16\text{ + 9}} \\ CD\text{ = 5} \\ \text{For AD, x1 = 0, y1 = 4, x2 = - 3, y2 = 0} \\ \text{Distance = }\sqrt[]{(-3-0)^2+(0-4)^2\text{ }}\text{ = }\sqrt[]{9\text{ + 16}} \\ AD\text{ = 5} \end{gathered}[/tex]Perimeter = AB + BC + CD + AD = 5 + 5 + 5 + 5
Perimeter = 20 units
- 3/4 m - 1/2 = 2 + 1/4 m2345
what is the difference in a probability that the student will spin a factor of 83 times in a row in the probability that a student will spin a number greater than 63 times in a row
The number 8 has factors 1, 2, 4 and 8.
The only numbers in the spin greater than 6 are 7 and 8,
The probability that the student will spin a factor of 8 three times in a row is given by: (4/8)*(4/8)*(4/8) = (1/2)*(1/2)*(1/2) = 1/8
The probability that the student will spin a number greater than 6 three times in a row is given by (2/8)*(2/8)*(2/8) = (1/4)*(1/4)*(1/4) = 1/64
Then, the difference between these two probabilities is given by 1/8 - 1/64 = 7/64
b.InOut133171066co38Rule:
Suppose that the rule is of the form
[tex]y=mx+b[/tex]Where m is the slope and b is the intercept
The slope can be found using the formula
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]You can take any two consecutive x and y values from the given table.
[tex]\frac{17-3}{3-1}=\frac{14}{2}=7[/tex]Similarly,
[tex]\frac{66-17}{10-3}=\frac{49}{7}=7[/tex]As you can see, you will end up with the same slope.
Now let us find the intercept b.
Take any x, y coordinates from the table
[tex](x,y)=(1,3)[/tex]Now substitute them in the slope-intercept equation.
[tex]\begin{gathered} y=7x+b \\ 3=7(1)+b \\ 3=7+b \\ b=-7+3 \\ b=-4 \end{gathered}[/tex]So the rule is
[tex]y=7x-4[/tex]Verification:
Let us verify whether we got the correct rule or not
Substitute the input x coordinates into the rule and check the outputs y coordinates.
[tex]\begin{gathered} y=7(1)-4=7-4=3 \\ y=7(3)-4=21-4=17 \\ y=7(10)-4=70-4=66 \\ y=7(6)-4=42-4=38 \end{gathered}[/tex]As you can see, we have got the same results therefore, the rule is correct.
translate and simplify subtract 18 from -11 .enter only the simplified results
Problem
translate and simplify subtract 18 from -11 .enter only the simplified results
Solution
For this case we can do the following:
-11- 18= -29
Final answer: -29
Please just put the answer for this question On D
Answer
The liters of air takes in during 150 seconds is 25 liters
Step-by-step explanation:
A man takes in 5 liters of air in 30 seconds
Firstly, we need to find the rate
Given:
Volume = 5 liters
time = 30 seconds
Rate =?
Volume = rate x time
5 = rate * 30
rate = 5/30 liters / second
Find the volume of air takes in during 150 seconds at the same rate
Volume = rate * time
Volume = 5/30 * 150
Volume = 5 * 150 / 30
Volume = 25 liters
Hence, the liters of air takes in during 150 seconds is 25 liters
Which is the best estimate for 2 2/3 × 3 1/4
The best estimate of the real number expression; 2 ⅔ × 3 ¼ as given in the task content is; 8 ⅔.
What is the best estimate of the real number expression given?It follows from the task content that the best estimate of the real number expression given is to be determined.
On this note, the mixed numbers must be converted to fractions for ease of computation as follows;
Therefore; 2 ⅔ = 8 / 3.
And, 3 ¼ = 13 / 4.
Therefore, the required evaluation of the expression is;
2 ⅔ × 3 ¼ = 8 / 3 × 13 / 4
= 104/12
= 26 / 3
Hence, the best estimate for the given expression is; 26 / 3 Or 8 ⅔.
Read more on fractions multiplication;
https://brainly.com/question/7335118
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write an equation of a line passing through the point (-6,-3) and perpendicular to JK with J (-2, -7) and K (6,5)
EXPLANATION
Given the point: (-6,-3) and the vector JK with J=(-2,-7) K=(6,5)
First we need to the slope of the vector applying the slope formula:
[tex]\text{Slope}=\frac{(y_2-y_1)}{(x_2-x_1)}[/tex]Replacing the ordered pairs J=(-2,-7) and K=(6,5) give us the slope:
[tex]\text{Slope}=\frac{(5-(-7))}{(6-(-2))}=\frac{12}{8}=\frac{3}{2}[/tex]Now, we have the slope and we can use this to find the line that contains the point (-6, -3) applying the generic form:
y= -2x/3 + b where -2/3 is the negative and reciprocal slope perpendicular to the vector JK.
Finally, replacing the point (-6,-3) give us the y-intercept, b,
-3 = -2(-6)/3 + b
Multiplying terms:
-3 = 12/3 + b ---> -3 = 4 + b
Subtracting 4 to both sides:
-3 - 4 = b
Switching sides:
b= -7
The linear equation is y = (-2/3)x - 7 OPTION B
Find the probability of X successes, using Table B in Appendix A of the textbook or some other method.n = 10, p = 0.3, X = 7
SOLUTION
The probability is a binomial probability
The probability is given as
[tex]\text{nCxp}^xq^{n-x}[/tex]Where p= proability of succes=0.3
q=probability of failure=1-p=1-0.3=0.7
n=10, x=7
Then, substitute the parameters into the formula
[tex]10C_7(0.3)^7(0.7)^3[/tex][tex]\begin{gathered} 10C_7=120 \\ 120\times2.187\times10^{-4}\times0.343 \end{gathered}[/tex]Then we have
[tex]\begin{gathered} 9.0017\times10^{-3} \\ 0.0090017 \end{gathered}[/tex]The probability of x-success is 0.009
how would I solve the system of equations using elimination?8x - 5y = 114x - 3y =5
Using elimination. In elimination process the two system of equations are multiplied by a apropiate factor , in order to eliminate one of the variables
then
multiplicate first equation by 4
and multiplicate second equation by 8
once obtained both results, then substract them
So then
4• (8x-5y) = 4•11= 44
8• (4x-3y) = 8•5= 40
32x -20y= 44
32x - 24y= 40
4y= 4 then y=1
now replace y=1 in any of both equations
8x -5= 11. Then x= (11+5)/8= 2
x=2
1v=9. Which equation represents the equation of theparabola with focus (-3,3) and directrix y = 7?A),= (x+3)2 – 5B) y = 5(? – 3)2 +5C) y=-( + 3)2 +5D) y=-2 (2-3)2 +5
SOLUTION
From the focus (-3, 3) and the directrix y = 7 given, note that the vertex is usually between the focus and the directrix.
So, the vertex will have the same x-coordinate as the focus, which is -3, and the y-coordinate of the vertex becomes
[tex]\begin{gathered} \frac{3+7}{2} \\ that\text{ is 3 from the y-coordinate of the focus and 7 from the directrix} \\ y=7 \\ \frac{3+7}{2}=\frac{10}{2}=5 \end{gathered}[/tex]Hence coordinate of the vertex is (-3, 5)
Now, equation of a parabola is given as
[tex]\begin{gathered} (x-h)^2=4p(y-k) \\ where\text{ \lparen h, k\rparen is the coordinate of the vertex and p is the focal length} \\ y=k-p,\text{ so we have } \\ 7=5-p \\ p=5-7=-2 \end{gathered}[/tex]So putting in the values of h, k and p into the equation, we have
[tex]\begin{gathered} (x-h)^{2}=4p(y-k) \\ (x-(-3)^2=4(-2)(y-5) \\ (x+3)^2=-8(y-5) \\ -\frac{1}{8}(x+3)^2=y-5\text{ that is dividing through by -8} \\ making\text{ y the subject, we have } \\ y=-\frac{1}{8}(x+3)^2+5 \end{gathered}[/tex]Hence the answer is
[tex]y=-\frac{1}{8}(x+3)^{2}+5[/tex]Need help with number five. The question is solve each system
5)
The given equations are
- 4x - 2y + 3z = 7
- 3x + 5y - 3z = 13
- 5x + y - z = 11
From equation 3, we have
y = 11 + 5x + z
We would substitute y = 11 + 5x + z into equations 1 and 2. For equation 1, we have
- 4x - 2(11 + 5x + z) + 3z = 7
- 4x - 22 - 10x - 2z + 3z = 7
- 4x - 10x - 2z + 3z = 7 + 22
- 14x + z = 29
For equation 2, we have
- 3x + 5(11 + 5x + z) - 3z = 13
- 3x + 55 + 25x + 5z - 3z = 13
- 3x + 25x + 5z - 3z = 13 - 55
22x + 2z = - 42
Dividing both sides of the equation by 2, we have
11x + z = - 21
z = - 21 - 11x
Substituting z = - 21 - 11x into - 14x + z = 29, we have
- 14x - 21 - 11x = 29
- 14x - 11x = 29 + 21
- 25x = 50
x = 50/- 25
x = - 2
z = - 21 - 11(- 2) = - 21 + 22
z = 1
Substituting x = - 2 and z = 1 into y = 11 + 5x + z, we have
y = 11 + 5(-2) + 1
y = 11 - 10 + 1
y = 2
The solutions are
x = - 2, y = 2, z = 1
Find the area of each rectangle using the given information.(A=W x H)Question 9:6 and a height of 36 inches.
The rule of the area of a rectangle is
[tex]A=W\times H[/tex]W is the width
H is the height
Since the ratio between width and height is 9: 6 and the height is 36 inches, then we will use the ratio method
[tex]\begin{gathered} W\rightarrow H \\ 9\rightarrow6 \\ W\rightarrow36 \end{gathered}[/tex]By using the cross multiplication
[tex]\begin{gathered} W\times6=9\times36 \\ 6W=324 \end{gathered}[/tex]Divide both sides by 6
[tex]\begin{gathered} \frac{6W}{6}=\frac{324}{6} \\ W=54 \end{gathered}[/tex]Then the width of the rectangle is 54 inches
Substitute W by 54 and H by 36 in the rule of the area to find it
[tex]\begin{gathered} A=54\times36 \\ A=1944inches^2 \end{gathered}[/tex]The area of the rectangle is 1944 square inches
which function will have the greatest value of x equals 80
In order to solve this, we can replace 80 for x into each one of the three given functions, then we identify what value of y is the greatest, like this:
For the first function:
y = 4x
y = 4×80
y = 320
For the second function:
y = x² - 15x + 88
y = 80² - 15×80 + 88
y= 6400 - 1200 + 88
y = 5288
For the third function:
[tex]\begin{gathered} y=1.1135^{80} \\ y=5435.23 \end{gathered}[/tex]As you can see, at x = 80 the function that has the greatest value is the third one.
Chris tries to copy
The Chris's error is that he does not consider he can not draw the upper oblique line crosses trough the end the of the arc.
To coorect that, Chris must to draw the upper line crosses trough the center of the arc. In this way he is going to obtain a exact copy of angle ∠T.
By taking into account the previous specifications you obtain the following draw of the angle:
As you can notice, it is necessary that the upper line crosses trough the center of the arc.