Answer:
The 99% confidence interval for the proportion of adults who regularly lie to people conducting surveys is (0.116, 0.19).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
For this problem, we have that:
[tex]n = 623, \pi = \frac{95}{623} = 0.153[/tex]
99% confidence level
So [tex]\alpha = 0.01[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.575[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.153 - 2.575\sqrt{\frac{0.153*0.848}{623}} = 0.116[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.1525 + 2.575\sqrt{\frac{0.153*0.845}{623}} = 0.19[/tex]
The 99% confidence interval for the proportion of adults who regularly lie to people conducting surveys is (0.116, 0.19).
what is the gfc of 16 and 8
Answer:
Greatest common factor of 16 and 8 is 8 .....A ship traveled at an average rate of 25 miles per hour going west. It then traveled at an average rate of 19 miles per hour heading north. If the ship traveled a total of 145 miles in 7 hours, how many miles were traveled heading west?
Answer: 19.5 miles or 108.75 miles
Step-by-step explanation:
Let ship traveled to the west x hours and then to the north y hours. Total 7 hours. So we can write 1st equation
x+y=7 (1)
The ship traveled to the west x hours with speed 25 miles/h - the distance 25*x
The ship traveled to the north y hours with speed 19 miles/hour - the distance 19*y
Note that the angle between north and west directions is 90 degrees.
So if the initial traveling point is A, the final travelling point ic C and the point , where ther the ship has changed the travelling direction from West to North is B.
So we have the right triangle ABC, where B angle is right=90 degrees.
AB side=25*x, BC side= 19*y and AC side 145 miles.
According to Pithagor theorem we can write
AC^2=AB^2+BC^2
21025=625*x^2+ 361*y^2 (2)
Solve the system of equations (1) and (2)
y=7-x
625*x^2+361*(7-x)^2=21025
625*x^2+361*(49-14x+x^2)=21025
625*x^2+17689-5054*x+361*x^2=21025
986*x^2- 5054*x-3336=0 dividing on 2 we'll get
493*x^2-2527*x-1668=0
D=3096433 sqrt(D)=appr 1760
x1=(2527-1760)/493/2= appr 0.78 h
x2=(2527+1760)/493/2=appr 4.35 h
So the problem has 2 solutions :
heading west the ship traveled or 0.78*25= 19.5 miles
Or 4.35*25= 108.75 miles
Answer:
let w = time heading west at 25 mph
the total time is 7 hrs, therefore
(7-w) = time heading north at 19 mph
Distance = speed * time
25w + 19(7-w) = 145
25w + 133 - 19w = 145
25w - 19w = 145 - 133
6w = 12
w = 12/6
w = 2 hrs traveling west
therefore
2 * 25 = mile going west
Confirm this solution, 7 - 2 = 5 hrs going north
19 * 5 = 95mi
25 * 2 = 50mi
--------------
total dist 145 mi
Find the perimeter and total area of the composite shape shown below. All measurements are given in inches. Use pi = 3.14 in any formulas used.
Answer:
Step-by-step explanation:
The composite shape consists of a semi circle and a triangle. The formula for determining the perimeter of a semicircle is expressed as
Perimeter = 1/2 × 2πr = πr
Since radius, r = 3, then
Perimeter of semi circle = 3 × 3.14 = 9.42 inches
Perimeter of composite shape = 9.42 + 5 + 5 = 19.42 inches
Area of semi circle = 1/2 × πr²
Area of semicircle = 1/2 × 3.14 × 3² = 14.13 inches²
Area of triangle = 1/2 × base × height
Area of triangle = 1/2 × 6 × 4 = 12 inches²
Area of composite shape = 14.13 + 12 = 26.13 inches²
The perimeter and area of the composite shape is:
B. Perimeter = 19.42 inches; Area = 26.13 square inchesRecall:
Area of a circle = πr²
Perimeter of circle = 2πr
Area of triangle = 1/2(bh)
The composite shape given is composed of a triangle and a semicircle.
Perimeter of the composite shape = Perimeter of semicircle + the length of the two sides of the triangle
Perimeter = 1/2(2 × 3.14 × 3) + 2(5) = 19.42 inches
Area of the composite shape = area of semicircle + area of triangle
Area = 1/2(3.14 × 3²) + 1/2(6 × 4)
Are = 14.13 + 12
Area of the composite shape = 26.13 square inches.
Therefore, the perimeter and area of the composite shape is:
B. Perimeter = 19.42 inches; Area = 26.13 square inchesLearn more about area and perimeter of composite shapes on:
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Probability Models - Tutorial - Level G
If we want to know if my shuffler is playing an equal
number of slow jams, dance music, and jazz songs,
what do we need to collect data on exactly?
Answer:
Ima need the answer too
Step-by-step explanation:
Answer:
the genre
Step-by-step explanation:
PLEASE HELP! Two complementary angles measure (12x - 18) and (5x +23). What is the measure of the smaller angle? (1) 5 (2) 42 (3) 48 (4) 90
Answer:
5
Step-by-step explanation:
firstly, what are complementry angles.complementary angles are angles that su
m up to 90°
(12x-18)+(5x+23)=90
collecting like terms
12x+5x+23-18=90
17x-5-90=0
17x-95=0
17x=95
divide through by 17
x=5
The measure of the smaller angle when complementary angles are given is 42 degree.
Complementary AnglesWhat are complementary angles?Complementary angles are two angles whose total is 90 degrees in geometry. In other terms, complimentary angles are two angles whose sum is 90 degrees. 60° and 30°, for instance.
Calculation for the value of x in the given angles:The first angle of the triangle is (12x - 18).
The measure of the second angle of the triangle is (5x + 23).
As both angles are complementary, their sum would be equal to 90 degree.
(12x - 18) + (5x + 23) = 90
12x - 18 + 5x + 23 = 90
17x = 85
x = 5
Calculation for the angles.Substitute the value of x = 5 in the given angles.
(1) 12x - 18 = 12×5 - 18
= 42 degrees
(2) 5x + 23 = 5×5 +23
= 48 degrees
Therefore, the smaller angle is found to be 42 degrees.
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Equations and Functions
Answer:
Subtract the 2w to both sides of the equal sign.
Step-by-step explanation:
Since we want the equation to be in terms of l, we need to isolate the term first. To do so, we will need to subtract 2w on both sides to start out.
One of the space shuttle’s external tanks can carry up to 200,000 gallons of fuel. It used 170,000 gallons of fuel in this tank to leave the atmosphere. What percentage of the fuel capacity does the shuttle still have?
Answer:
15%
Step-by-step explanation:
The tank's capacity is 200,000 gallons.
170,000 gallons were used.
200,000 - 170,000 = 30,000
30,000 gallons of fuel are still there.
percent = part/total * 100%
percent = 30,000/200,000 * 100% = 15%
a.) The perimeter of a rectangular field is 354 m. If the length of the field is 95m, what is its width? b.) The area of a rectangular painting is 8439 cm^2. If the width of the painting is 87cm, what is its length?
Answer:
a) 82
b) 97
Step-by-step explanation:
a) 354 - (95+95)
354 - 190
164
164 ÷ 2 = 82
(82+82+95+95=254)
b) 8439 cm^2 = 87x
8439 cm^2 ÷ 87 = 87x ÷ 87
97 = x
If a person rolls a six-sided die and then draws a playing card and checks its color, describe the sample space of possible outcomes using 1, 2, 3, 4, 5, 6 for the die outcomes and B, R for the card outcomes.
Answer:
S = {1B, 2B, 3B, 4B, 5B, 6B, 1R, 2R, 3R, 4R, 5R, 6R}
Step-by-step explanation:
The sample space is the set of all possible outcomes in the experiment of rolling a six-sided die and then drawing a playing card and checking its color.
There are 6 possible outcomes for the die roll and two for the color of the card, which yields a total of 12 possible outcomes. The sample space is:
S = {1B, 2B, 3B, 4B, 5B, 6B, 1R, 2R, 3R, 4R, 5R, 6R}
Simplify: 1. 4x−(1−2x)+(2x−7) 2. (3−0.4a)−(10−0.8a)
Answer:1.8(x -1)
2.0.4a -7
Step-by-step explanation:
Let ƒ(x) = x + 1 and g(x) = 5x. Evaluate the composition (ƒ ∘ g)(–1). Question 2 options: A) (ƒ ∘ g)(–1) = 6 B) (ƒ ∘ g)(–1) = –4 C) (ƒ ∘ g)(–1) = 4 D) (ƒ ∘ g)(–1) = –6
Answer:
answer B
Step-by-step explanation:
hello,
[tex]f(x)=x+1\\g(x)=5x \ \ so\\(fog)(-1)=f(g(-1))=f(-5)=-5+1=-4[/tex]
so the winner is the answer B
hope this helps
Answer:
D)
(ƒ ∘ g)(–1) = –4
Step-by-step explanation:
A person who yells at an official who made a bad call is just displaying a competitive spirit. Please select the best answer from the choices provided. T F
Answer:
the answer is false
Step-by-step explanation:
FALSE. A person who yells at an official is not showing a competitive spirit.
What is a Competitive Spirit?A competitive spirit shows the following attributes:
Communicates respectShows sportsmanshipValues process among others.A person yelling at an official is not a way of communicating respect. Therefore, it is FALSE to say it is a display of competitive spirit.
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I can't figure this question out I've tried multiple times but only 2/3. Help, please.
Answer:
yes it is 2/3
Step-by-step explanation:
Samples of rejuvenated mitochondria are mutated (defective) in 1% of cases. Suppose 13 samples are studied, and they can be considered to be independent for mutation. Determine the following probabilities.
(a) No samples are mutated.
(b) At most one sample is mutated.
(c) More than half the samples are mutated.
Step-by-step explanation:
this isn't much I think so this isn't plus how come everything in March
Draw an array to find 21÷3
Answer:
21÷3 =9
3×9=21
Therefore the answer is 9 .
Step-by-step explanation:
Hope it works out!Three students are working to find the solution set of this system of equations:
3y = 6x + 6
y = 2x + 2
Use the drop-down menus to complete the statements about each of their methods.
Pedro Dropdown 1: Intersect, Do not Intersect, Are the same line.
Pedro Dropdown 2: One, Zero, Infinitely many
Amy Dropdown: is, is not
Matt Dropdown 1: Sometimes, Never, Always
Matt Dropdown 2: One, Zero, Infinitely Many
Answer:
Pedro Dropdown 1: they Do not Intersect, they Are the same line
Step-by-step explanation:
3y = 6x + 6
y = 2x + 2
3y-6x = 6... Equation one
y-2x = 2... Equation two
Dividing equation one by 3 gives
Y -2x = 2. Which is same thing with equation 2
So I think the two are same line and do not intersect.
Answer:
Pedro: are the same line, infinitely many
Amy: is
Matt: always, infinitely many
Step-by-step explanation:
PEDRO: Since the lines are on top of one another, there are infinitely many solutions. These lines are called coinciding lines.
AMY: 3y = 6x + 6 is a multiple of y = 2x + 2. When one equation is a multiple of the other, there are infinitely many solutions to the system.
MATT: When the equation 3y = 6x + 6 is divided by 3, the quotient is equal to the first equation. The equations are equivalent, so they describe the same graphed line.
Consider the initial value problem y' + 3y = 9t, y(0) = 7.
a. Take the Laplace transform of both sides of the given differential equation to create the corresponding algebraic equation. Denote the Laplace transform of y(t) by Y(s). Do not move any terms from one side of the equation to the other (until you get to part (b) below).
b. Solve your equation for Y(s).
Y(s) = L {y(t)} =
c. Take the inverse Laplace transform of both sides of the previous equation to solve for y(t).
y(t) =
Answer:
[tex]y(t) = 3x+8e^{-3x} -1[/tex]
Step-by-step explanation:
Recall that the following laplace transforms
[tex]L(y') = sY(s)-y(0)[/tex]
[tex]L(t) = \frac{1}{s^2}[/tex]
The laplace transform is linear, so, applying the laplace transform to the equation we get
[tex]L(y'+3y) = sY(s)-7+3Y(s) = L(9t) = \frac{9}{s^2}[/tex]
By some algebraic manipulations, we get
[tex] Y(s)(s+3) = \frac{9+7s^2}{s^2}[/tex]
which is equivalent to
[tex] Y(s) = \frac{9+7s^2}{s^2(s+3)} = \frac{9}{s^2(s+3)}+\frac{7}{s+3}[/tex]
By using the partial fraction decomposition, we get
[tex] \frac{9}{s^2(s+3)} = \frac{-1}{s} + \frac{3}{s^2} + \frac{1}{s+3}[/tex]
then
[tex]Y(s) = \frac{-1}{s} + \frac{3}{s^2} + \frac{1}{s+3} + \frac{7}{s+3} = \frac{8}{s+3} + \frac{3}{s^2}-\frac{1}{s}[/tex]
Using that
[tex] L(e^{-ax}) = \frac{1}{s+a}[/tex]
[tex]L(1) = \frac{1}{s}[/tex]
by taking the inverse on both sides we get
[tex] y(t) = L^{-1}(\frac{8}{s+3})+L^{-1}(\frac{3}{s^2})+L^{-1}(-\frac{1}{s}) = 8e^{-3x} + 3x-1[/tex]
Find the measure of angle angle AEB in the figure below. Enter only the number. PLEASE HELP ASAP
Answer:
42°
Step-by-step explanation:
AD is a line
AEC and DEC are both 90°
AEB and CEB make up 90°
AEB+CEB=AEC substitute
AEB+48=90 Next use Subtraction property of equality
AEB=42
Hope this helps, if so please give me brainliest, it helps a lot. :)
Have a good day!
Answer:
∠AEB=42
Step-by-step explanation:
∠AEB and ∠BEC are inside of ∠AEC.
∠AEC is a right angle, Since ∠AEC and ∠CED are on a straight line, they must add to 180 degrees. ∠CED is a right angle (the little square in the corner tell us this), so ∠AEC must also be a right angle. This is because a right angle is 90 degrees (∠CED+∠AEC=180 --> 90+∠AEC=180 --> ∠AEC=90)
Therefore, the 2 angles (AEB and BEC) inside of ∠AEC must add to 90 degrees.
∠AEB+ ∠BEC= 90
We know that ∠BEC=48
∠AEB+48=90
We want to find out what ∠AEB is. We must get ∠AEB by itself. 48 is being added, and the inverse of addition is subtraction. Subtract 48 from both sides.
∠AEB+48-48=90-48
∠AEB=90-48
∠AEB=42
Find the measure of the indicated angle to the nearest degree please. Thanks.
Answer:
? = 35°Step-by-step explanation:
Let the angle be x
To find the indicated angle we use sine
sin ∅ = opposite / hypotenuse
From the question
7 is the hypotenuse
4 is the opposite
sin x = 4/7
x = sin-¹ 4/7
x = 34.85
x = 35° to the nearest degree
Hope this helps you
I need help urgent plz someone help me solved this problem! Can someone plz help I’m giving you 10 points! I need help plz help me! Will mark you as brainiest!
Answer: L = 20.25
Step-by-step explanation:
[tex]T=2\pi \sqrt{\dfrac{L}{32}}[/tex]
Given: T = 5, π = 22/7
[tex]5=2\bigg(\dfrac{22}{7}\bigg)\sqrt{\dfrac{L}{32}}\\\\\\\dfrac{5}{2}\bigg(\dfrac{7}{22}\bigg)=\sqrt{\dfrac{L}{32}}\\\\\\\dfrac{35}{44}=\sqrt{\dfrac{L}{32}}\\\\\\\bigg(\dfrac{35}{44}\bigg)^2=\bigg(\sqrt{\dfrac{L}{32}}\bigg)^2\\\\\\\bigg(\dfrac{35}{44}\bigg)^2=\dfrac{L}{32}\\\\\\32\bigg(\dfrac{35}{44}\bigg)^2=L\\\\\\\large\boxed{20.25=L}[/tex]
Which is true about all quadratic equations that contain a difference of squares? Only the value of c is a perfect square. Only the value of a is a perfect square. The value b=0. The value |b|=2[tex]\sqrt{a} \sqrt{c}[/tex]
Answer:
b = 0
Step-by-step explanation:
The standard form of a regular quadratic equation is ax² + bx + c and the standard form of the difference of squares is ax² - c. This means that b = 0 because there is no x term.
i-Ready
Sofia
The area of a rectangle is 7/9 square feet. The width of the rectangle is 2 1/3 feet. What is the length of the rectangle?
Answer:
1/3 feet.
Step-by-step explanation:
The length = area / width
= 7/9 / 2 1/3
= 7/9 / 7/3
= 7/9 * 3/7
= 3/9
= 1/3 feet,
What the answer fast
Answer:
∠CDE
Step-by-step explanation:
Name it by the order of the letters with the point of the angle in the middle
What’s the difference between the polynomials ?
Answer:
7x^2-4x+3y^2 ( the ^ means the exponent EX: 5^2 is 5 squared. )
Step-by-step explanation:
Remove the parenthesis (a) = a
12x^2-11y^2-13x- (5x^2-14y^2-9x)
-(5x^2 - 14y^2 - 9x)
Distribute parenthesis
-(5x^2) - (14y^2) - (-9x)
Apply minus - plus rules
-5x^2 + 14y^2 + 9x
= 12x^2 - 11y^2 - 13x - 5x^2 + 14y^2 + 9x
Simplify
12x^2-11y^2-13x-5x^2+14y^2+9x
Group like terms
12x^2-5x^2-13x+9x-11y^2+14y^2
Add similar elements
7x^2-13x+9x-11y^2+14y^2
Add similar elements ( - 13x + 9x = -4x )
7x^2-4x-11y^2+14y^2
Add similar elements 11y^2 + 14y^2 = 3y^2
7x^2-4x+3y^2
The point P(7, −2) lies on the curve y = 2/(6 − x). (a) If Q is the point (x, 2/(6 − x)), use your calculator to find the slope mPQ of the secant line PQ (correct to six decimal places) for the following values of x.
(i) 6.9
mPQ = 1
(ii) 6.99
mPQ = 2
(iii) 6.999
mPQ = 3
(iv) 6.9999
mPQ = 4
(v) 7.1
mPQ = 5
(vi) 7.01
mPQ = 6
(vii) 7.001
mPQ = 7
(viii) 7.000
mPQ = 8
(b) Using the results of part (a), guess the value of the slope m of the tangent line to the curve at
P(7, −2).
m = 9
(c) Using the slope from part (b), find an equation of the tangent line to the curve at
P(7, −2).
The equation of the tangent line to the curve at P(7, -2) is y = 2x -16.
For each given value of x, we substitute the coordinates of P and Q into the slope formula to find the slope mPQ.
(i) For x = 6.9:
mPQ = (2/(6 - 6.9) - (-2)) / (6.9 - 7)
= 2.22
(ii) For x = 6.99:
mPQ = (2/(6 - 6.99) - (-2)) / (6.99 - 7)
= 2.020
(iii) For x = 6.999:
mPQ = (2/(6 - 6.999) - (-2)) / (6.999 - 7)
= 2.002002
(iv) For x = 6.9999:
mPQ = (2/(6 - 6.9999) - (-2)) / (6.9999 - 7)
= 2.000200
(v) For x = 7.1:
mPQ = (2/(6 - 7.1) - (-2)) / (7.1 - 7)
= 1.818182
(vi) For x = 7.01:
mPQ = (2/(6 - 7.01) - (-2)) / (7.01 - 7)
= 1.980198
(vii) For x = 7.001:
mPQ = (2/(6 - 7.001) - (-2)) / (7.001 - 7)
= 1.998002
(viii) For x = 7.0001:
mPQ = (2/(6 - 7.0001) - (-2)) / (7.0001 - 7)
= 1.999800
By observing the pattern in the calculated slopes, we can see that as x approaches 7, the slope of the secant line PQ approaches 2.
Using the point-slope form, we have:
y - y₁ = m(x - x₁)
Substituting the values of P(7, -2), we have:
y - (-2) = 2(x - 7)
y = 2x -16
Therefore, the equation of the tangent line to the curve at P(7, -2) is y = 2x -16.
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Rewrite the following statement in the form ∀x ______, if _______ then _______ (where each of the second two blanks are sentences involving the variable x) Every valid argument with true premises has a true conclusion.
Answer:
"Vx: if x is a valid argument with true premises then x has a true conclusion"
In a symbol form
Vx ( P(x) ⇒ 2(x) )
Step-by-step explanation:
The Following statement in the form ∀x ______, if _______ then _______ is a valid argument and this because any valid argument with "true premises" has a "true conclusion" as well
we will rewrite this statement in a universal condition statement form
assume x is a valid argument with true premises
then the following holds true
p(x) : x is a valid argument with true premises
q(x) : x has true conclusion
applying universal conditional statement
"Vx, if x is a valid argument with true premises then x has a true conclusion"
In a symbol form
Vx ( P(x) ⇒ 2(x) )
y = 2x^4 convert to polar form
Answer:
The polar form is sinθ = 2 r³cos⁴θ
Step-by-step explanation:
Explanation:-
Given function y = 2 x⁴
Parametric Form x = r cosθ ....(i)
and y = r sinθ ....(ii)
squaring x² = r² cos ²θ
y² = r² sin²θ
adding x² + y² = r² cos ²θ+r² s in²θ
= r²( cos ²θ+s in²θ)
= r²( 1)
x² + y² = r²
Given function y = 2 x⁴
Now convert into polar form
r sinθ = 2 (r cos θ )⁴
r sinθ = 2 (r )⁴cos θ )⁴
sinθ = 2 r ³cos⁴θ
Please answer this correctly
The correct answer is 5.5988 x [tex]10^{-3}[/tex] = 0.0055988
Explanation:
In mathematics and related areas, it is common the expression [tex]10^{n}[/tex] (n = a whole number) that multiplies a number, this is known as scientific notation, and it used to express long numbers concisely. This type of notation implies the exponent number or n represents the number of zeros in the number or the number of spaces after/before the decimal period.
Additionally, if the exponent is positive this means the zeros are placed to the right of the number, while a negative exponent shows the zeros are on the left. For example 7 x [tex]10^{3}[/tex] is equal to 7000 because the exponent indicates there are three zeros to the right of 7 or you need to move three spaces the period to the right, which is located right after 7. According to this, the expression 5.5988 x [tex]10^{-3}[/tex] indicates there are 3 zeros to the left of this number or that you need to move three spaces the period and add zeros in these spaces, which is equal to 0.0055988. Therefore, both numbers are equal (=)
Translate the following statements into symbolic form using capital letters to representaffirmative English statement.
If Maria Cantwell promotes alternative energy,then if Patty Murray supports wilderness areas, then Dianne Feinstein's advocating gun control implies that Susan Collins does so,too.
Answer:
Step-by-step explanation:
There are two distinct statements but put together, it is:
- If Maria Cantwell (MC) promotes Alternative Energy (AE) and if Patty Murray (PM) supports Wilderness Areas (WA) then Dianne Feinstein (DF) advocating Gun Control (GC), implies that Susan Collins (SC) does so too.
For Susan Collins, she advocates gun control too.
So the symbolic or algebraic representation is:
(SC = DF): (MC ~ AE), (PM ~ WA)
OR
(GC = GC): (MC ~ AE), (PM ~ WA)
Where ":" represents "such that" or "given that"
" ~ " represents "support or promotion of"
It can now be read thus;
Susan Collins has same or equal interest as Dianne Feinstein, given that Maria Cantwell promotes alternative energy and Patty Murray supports Wilderness Areas.
CAN SOMEONE HELP ME ASAP
A. 5
B. 53‾√53
C. 10
D. 103√3
Answer:
n = 5
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan theta = opp/ adj
tan 30 = n/ 5 sqrt(3)
5 sqrt(3) tan 30 = n
5 sqrt(3) * 1/ sqrt(3) = n
5 = n