Answer:
Bhāskara was a 7th-century mathematician and astronomer, who was the first to write numbers in the Hindu decimal system with a circle for the zero, and who gave a unique and remarkable rational approximation of the sine function in his commentary on Aryabhata's work.
Aryabhatta is the father of Indian mathematics. He was a great mathematician and astronomer of ancient India. His major work is known as Aryabhatiya. It consists of spherical trigonometry, quadratic equations, algebra, plane trigonometry, sums of power series, arithmetic.
Step-by-step explanation:
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I just need help with question one, but if you want to you can answer question 2 as well. I’ll give 100 points!
Explanation:
Given f(x) : (2, -3)
Translation's:f(x) + 2 then graph translates up by 2 units up = [tex]\boxed{\sf (2, -1)}[/tex]
f(x) - 3 then graph translates down 3 units down = [tex]\boxed{\sf (2, -6)}[/tex]
f(x + 5) then graph translates left 5 units = [tex]\boxed{\sf (-3, -3)}[/tex]
-f(x) then graph reflects over x axis = [tex]\sf \boxed{\sf (2, 3)}[/tex]
f(-x) then graph reflects over y axis = [tex]\sf \boxed{\sf (-2,-3)}[/tex]
f(2x) then graph has horizontal compression = (2/2, -3) = [tex]\boxed{\sf (1, -3)}[/tex]
2f(x) then graph has vertical compression = (2, (-3)2) = [tex]\boxed{\sf (2, -6)}[/tex]
-f(x - 4) then graph reflects over x axis, moves 4 units to right = [tex]\sf \boxed{\sf (6, 3)}[/tex]
Solution 2Parent function: y = x²
Graph function: f(x) = (x + 8)² - 4
After Identification:
D. The graph has a translation of 8 units left and 4 units down.
Answer:
Translations
For [tex]a > 0[/tex]
[tex]f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]
[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]
[tex]f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]
[tex]f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}[/tex]
[tex]y=a\:f(x) \implies f(x) \: \textsf{stretched parallel to the y-axis (vertically) by a factor of}\:a[/tex]
[tex]y=f(ax) \implies f(x) \: \textsf{stretched parallel to the x-axis (horizontally) by a factor of} \: \dfrac{1}{a}[/tex]
[tex]y=-f(x) \implies f(x) \: \textsf{reflected in the} \: x \textsf{-axis}[/tex]
[tex]y=f(-x) \implies f(x) \: \textsf{reflected in the} \: y \textsf{-axis}[/tex]
Question 1Given: [tex]f(x)=(2,-3)[/tex]
[tex]f(x)+2 \implies (x, y+2)= (2,-3+2)=(2,-1)[/tex]
[tex]f(x)-3 \implies (x,y-3)=(2,-3-3)=(2,-6)[/tex]
[tex]f(x+5)\implies (x-5,y)=(2-5,-3)=(-3,-3)[/tex]
[tex]-f(x) \implies (x,-y)=(2,-(-3))=(2,3)[/tex]
[tex]f(-x) \implies (-x,y)=(-(2),-3)=(-2,-3)[/tex]
[tex]f(2x) \implies \left(\dfrac{x}{2},y\right)=\left(\dfrac{2}{2},-3\right)=(1,-3)[/tex]
[tex]2f(x) \implies (x,2y)=(2,2 \cdot -3)=(2,-6)[/tex]
[tex]-f(x-4) \implies (x+4,-y)=(2+4,-(-3))=(6,3)[/tex]
[tex]\begin{array}{| c | c | c | c | c | c | c | c |}\cline{1-8} & & & & & & &\\f(x)+2 & f(x)-3 & f(x+5) & -f(x) & f(-x) & f(2x) & 2f(x) & -f(x-4)\\& & & & & & &\\\cline{1-8} & & & & & & &\\(2,-1) & (2,-6) & (-3,-3) & (2,3) & (-2,-3) & (1,-3) & (2,-6) & (6,3)\\& & & & & & &\\\cline{1-8} \end{array}[/tex]
Question 2Parent function: [tex]y=x^2[/tex]
Given function: [tex]f(x)=(x+8)^2-4[/tex]
[tex]f(x+8) \implies f(x) \: \textsf{translated}\:8\:\textsf{units left}[/tex]
[tex]f(x)-4 \implies f(x) \: \textsf{translated}\:4\:\textsf{units down}[/tex]
Therefore, a translation 8 units to the left and 4 units down.
The estimated distribution (in millions) of the population by age in a certain country for the year 2015 is shown in the
pie chart. Make a frequency distribution for the data. Then use the table to estimate the sample mean and the
sample standard deviation of the data set. Use 70 as the midpoint for "65 years and over."
The sample mean is x- (Round to two decimal places as needed.)
Under 4 years: 24.8
15-14 years: 422
15-19 years 194
20-24 years: 256
25-34 years 50.7
35-44 years: 35.7
45-64 years 75.2
65 years and over 54.3
The sample mean for the data is 21.38 and the sample standard deviation for the data is 56.19
The frequency distribution for the dataTo do this, we start by calculating the midpoint of each class using:
Midpoint= (Lower + Upper)/2
Using the above formula, we have:
Age (x) Frequency (f)
2 24.8
9.5 422
17 194
22 256
29.5 50.7
39.5 35.7
54.5 75.2
70 54.3
The sample mean for the dataThis is calculated using:
[tex]\bar x = \frac{\sum fx}{\sum f}[/tex]
So, we have:
[tex]\bar x = \frac{2*24.8 + 9.5*422 + 17*194 + 22*256 + 29.5*50.7 + 39.5*35.7 + 54.5*75.2+70*54.3}{24.8 + 422 + 194 + 256 + 50.7 + 35.7 + 75.2 + 54.3}[/tex]
Evaluate
[tex]\bar x = \frac{23793.8}{1112.7}[/tex]
[tex]\bar x = 21.38[/tex]
Hence, the sample mean for the data is 21.38
The sample standard deviation for the dataThis is calculated using:
[tex]\sigma_x = \sqrt{\frac{\sum f(x- \bar x)^2}{\sum f - 1}}[/tex]
So, we have:
[tex]\sigma_x = \sqrt{\frac{2*(24.8-21.38)^2 + .............+70*(54.3-21.38)^2}{24.8 + 422 + 194 + 256 + 50.7 + 35.7 + 75.2 + 54.3 - 1}}[/tex]
Evaluate
[tex]\sigma_x = \sqrt{\frac{3509508.4556}{1111.7}}[/tex]
[tex]\sigma_x = \sqrt{3156.88446128}[/tex]
[tex]\sigma_x = 56.19[/tex]
Hence, the sample standard deviation for the data is 56.19
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Use the following math quiz scores to answer the questions. 85%, 65%, 87%, 68%, 90%, 73%, 65%, 85%, 95%, 85% 17) What is the mean of these scores? 18) What is the median score? The point on the scale that divides the distribution of scores in half 19) What is the mode of these scores? The value that occurs most frequently in a set. 20) What is the range of these scores? The difference between the lowest and highest values
Answer:
79.8
Step-by-step explanation:
Solve the equation sin 79.5° = cos 2x
Answer:
x=5.24-9+180n,174.75+180n
Step-by-step explanation:
he graph of the function f(x) = –(x + 6)(x + 2) is shown below.
The domain of the function is all real numbers, the range of a function is y ≤ 4
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have a function:
f(x) = –(x + 6)(x + 2)
If we plot this function on the coordinate plane, we will see it is a graph of a quadratic function.
Here the no other details are given.
But we can say:
The domain of the function is all real numbers.The range of a function is y ≤ 4The x-axis intercept will be at (-6, 0) and (-2, 0).Thus, the domain of the function is all real numbers, the range of a function is y ≤ 4
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Can someone please help me with these questions!
The line that contains an example of assonance is C. He fell asleep under the oak tree, feeling fine.
What is Assonance?This refers to the similarity of sounds that can be found in nearby words in a sentence, between their vowels and/or consonants.
Furthermore, alliteration means the occurrence of similar words or sounds in a sentence at the beginning of closely connected words.
With this in mind:
The line that contains an example of alliteration is A. Tom tried learning a new tune.The line that contains an example of consonance is D. Phillipe hoped for a copper cup.Read more about alliteration here:
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D. -1 7. A weaver bought a bundle of grass for $50.00 from which he made 8 mats. If each mat was sold for $ 15.00, find the percentage profit. 10 %
Profit percentage for weaver after selling mat is equals to 140%.
What is percentage ?" Percentage is defined as the hundredth part of the whole given quantity. It is represented by symbol %."
Formula used
Profit% = [tex](\frac{Profit }{cost price} )[/tex]× 100
According to the question,
Given,
Cost price of bundle of grass = $50.00
Number of mats made = 8
Selling price of each mat = $15.00
Therefore,
Selling price of 8 mats = 15 × 8
= $120
Selling price > Cost price
Therefore,
Profit = Selling price - Cost price
= 120 - 50
= $70
Substitute the value in the formula to get profit percentage we get,
Profit% = [tex]\frac{70}{50}[/tex] ×100
= 140%
Hence, profit percentage for weaver after selling mat is equals to 140%.
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what are the solution of the quadratic equation (x-8)3-13x(x-8)+3=0? use u substitution to solve.
[tex]3(x - 8) - 13x(x - 8) + 3 = 0 \\ 3x - 24 - 13 {x}^{2} + 104x + 3 = 0 \\ - 13 {x}^{2} + 107x - 21 = 0 \\ x = \frac{ - b + - \sqrt{ {b}^{2} - 4ac } }{2a } \\ a = - 13 \\ b = 107 \\ c = - 21 \\ x = \frac{ - 107 + - \sqrt{ {107}^{2} - 4(13)( - 21)} }{2( - 13)} \\ x1 = \frac{107 - \sqrt{10357} }{26} \\ x2 = \frac{107 + \sqrt{10357} }{26} [/tex]
Hope it helps
Please give brainliest
QUICKKK
If $-3\le x+5 \le 8$ and $x$ is an integer, what is the sum of all the possible solutions?
Add -5 to each side of the inequality:
-3 ≤ x + 5 ≤ 8
-3 - 5 ≤ x + 5 - 5 ≤ 8 - 5
-8 ≤ x ≤ 3
Since x is an integer, there are 12 possible solutions belonging to {-8, -7, ..., 1, 2, 3}. In the sum of these solutions, the integers -3 to 3 cancel out, and the rest give
-8 - 7 - 6 - 5 - 4 = -30
which table represents an exponential function of the form y=bx when 0
The table that represents an exponential function of the form y = [tex]b^{x}[/tex] when 0 < b < 1 is Table - 2. See the attached tables.
What is an exponential function?
A function is exponential when its value is a constant that is raised to the power of the argument. This is so especially when the function of the constant is e.
What is the solution?Recall that the exponential function y = [tex]b^{x}[/tex] given that 0 < b < 1. Notice that the table number 2 see to the exponential function that has the following form:
y(x) = (1/3)ˣ
substituting the values of x into the equation, we have:
y(-3) = (1/3) ⁻³ = 27
x = -2; thus
y(-2) = (1/3) ⁻³ = 9
x = -1; thus
y(-1) = (1/3) ⁻³ = 3
x = 0; thus
y(0) = (1/3) ⁻⁰ = 1
x = 1; thus
y(1) = (1/3) ¹ = 1/3
x = 2; thus
y(2) = (1/3) ⁻² = 1/9
x = 3; thus
y(3) = (1/3) ⁻³ = 1/27
Therefore, according to the obtained values, one can summarize that the table that depicts the exponential function y = bˣ is table 2.
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f(x) = -3x+1
g(x) = 3x² + 4x - 15
Find: f(g(x))
4.
Solve the system of inequalities graphically. Label the solution set with an S.
Help asap
Answer:
Solution = (2,1)
Step-by-step explanation:
Make them equal each other and solve for x.
2x - 3 = 1
2x = 4
x = 2
2 * 2 - 3 = 1
Solution = (2,1)
Find the APR, rounded to the nearest tenth of a percent (one decimal place) for the loan. Purchase a living room set for $4,900 at 8% add-on interest for 4 years. Enter only the number without % sign.
The annual percent rate(APR) to purchase a living room set for $4,900 at 8% add-on interest for 4 years is 8. 6
How to calculate the annual interest rate
Using the formula
APR = ((Interest + Fees / Loan amount) / Number of days in loan term)) x 365 x 100
Note that Interest expense = Original amount / interest rate
Interest amount = $4, 900
Rate = 8% = 0. 08
Interest expense = $4, 900× 0. 08 = $392
Loan amount is also the principal amount , P = I / (RT)
where I is Interest Amount, R is Rate of Interest and T is Time Period.
Principal amount = $4, 900 ÷ 0. 08 × 4 = $4, 900 ÷ 0.32 = $ 15,313. 5
Substitute the values into the formula for APR
APR = [tex]\frac{392+ 4900}{15312.5} / 1460 * 365* 100[/tex]
APR = [tex]0.345 / 1460 *365*100[/tex]
APR = [tex]2. 36* 10^-4 *365* 100[/tex]
APR = [tex]8. 625[/tex]
To the nearest tenth is, 8. 6
Therefore, the annual percent rate(APR) is 8. 6
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In isosceles triangle ABC, AC=BC=20, the measure of angle A=68, and CD is the altitude to side AB. What is CD to the nearest 10th
Answer:
Step-by-step explanation:
Comment
The way the diagram looks when it is drawn is that you are going to need the sine function to solve for the side opposite which is CD.
Formula
Sin(A) = Sin(68 = opposite / hypotenuse Substitute values.
Solution
sin(68) = altitude (side opposite) / 20 multiply both sides by 20
20*sin(68) = 20* altitude / 20 substitute for sin(68)
20* 0.9272 = altitude
altitude = 18.5
Answer: 18.5 to the nearest tenth
HELP!!!!!!!!!!!!!!!!!!!!
Answer:
D is the answer hope
Step-by-step explanation:
hope this helped
Given Segment AC with point B contained on the segment, as shown below.
Write a complete two-column proof for following information:
Given: Segment AB = x + 16, Segment BC = 4x + 11
Segment AC = 77
Prove: AB = 26
It is true that the line segment AB equals 26
How to prove that line segment AB = 26?The given parameters are:
AB = x +16
BC = 4x + 11
AC = 77
The two-column proof is as follows:
AC = AB + BC Line segment formula
77 = x + 16 + 4x + 11 Substitution property of equation
77 = 5x + 27 Addition property of equation
5x = 50 Subtraction property of equation
x = 10 Division property of equation
AB = 10 +16 Substitution property of equation
AB = 26
Hence, the line segment AB has been proved to equal 26
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what is the mean of 12342634
Answer:
Mean = 3.125 ≈ 3.13
Step-by-step explanation:
Mean = Sum of numbers = 1 + 2 + 3 + 4 + 2 + 6 + 3 + 4 = 25 = 3.125≈3.13
Amount of number 8 8
Help please and thanks! I'll award brainliest if you show your work as well :)
Answer:
6 inches
Step-by-step explanation:
Formula for surface area of a cylinder:
[tex]SA=2\pi r^{2} +2\pi rh[/tex]
Plug in values and solve for the radius:
[tex]180\pi =2\pi r^{2} +2\pi r(9)\\[/tex]
Divide both sides by [tex]2\pi[/tex]
[tex]90=r^{2} +r(9)[/tex]
Subtract 90 from both sides
[tex]0=r^{2} +9r-90[/tex]
Use the quadratic equation to find the roots
[tex]x=(-b[/tex]±[tex]\sqrt{b^2-4ac})*\frac{1}{2a}[/tex] (sorry for formatting, Brainly doesn't
allow equations with ± in them)
[tex]x=\frac{-9+\sqrt{9^2-4*1*90} }{2(1)}[/tex] and [tex]x=\frac{-9-\sqrt{9^2-4*1*90} }{2(1)}[/tex]
[tex]x=\frac{(-9+\sqrt{81+360})}{2}[/tex] and [tex]x=\frac{(-9-\sqrt{81+360})}{2}[/tex]
[tex]x=\frac{(-9+\sqrt{441})}{2}[/tex] and [tex]x=\frac{(-9-\sqrt{441})}{2}[/tex]
[tex]x=\frac{(-9+21)}{2}[/tex] and [tex]x=\frac{(-9-21)}{2}[/tex]
[tex]x=\frac{12}{2}[/tex] and [tex]x=\frac{-30}{2}[/tex]
[tex]x=6[/tex] and [tex]x=-15[/tex]
We can't have a negative radius, so that leaves us with r=6 in.
Given the function f(x) = ³x – 1, evaluate f(-12).
Evaluation:
The answe for the function is -1.
Index Number:
b) A trader bought ar bags of rice at a cost, c= 24x+103 and sold them at a price.
x = 33x-x^2/20
(1)
Find the expression for the profit.
(i) If 20 bags of rice were sold, calculate the percentage profit.
The expression for the profit is -x^2/30 + 9x - 103 and the percentage profit on 20 bags of rice is 11.1%
How to determine the profit expression?The cost and the selling price are given as:
C(x) = 24x + 103
S(x) = 33x - x^2/30
The profit is calculated using:
P(x) = S(x) - C(x)
This gives
P(x) = 33x - x^2/30 - 24x - 103
Evaluate the like terms
P(x) = -x^2/30 + 9x - 103
Hence, the expression for the profit is -x^2/30 + 9x - 103
The percentage profitWhen x = 20, we have:
Cost: C(20) = 24 * 20 + 103 = 583
Profit: P(20) = -(20)^2/30 + 9(20) - 103 = 64.67
The percentage profit is then calculated as:
Percentage = P(x)/C(x) * 100%
This gives
Percentage = 64.67/583 * 100%
Evaluate
Percentage = 11.1%
Hence, the percentage profit on 20 bags of rice is 11.1%
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If 2,6 kg of potatoes cost R13,20, what will the cost of 3,3 kg be?
Answer:
[tex]\huge\boxed{\sf R. 16.75}[/tex]
Step-by-step explanation:
*Assuming commas are used for decimals.
Given that:2.6 kg potatoes = R 13.20
Using unitary methodDivide 2.6 to both sides
1 kg potatoes = R 13.20/2.6
1 kg potatoes = R 5.1
Multiply 3.3 to both sides
3.3 kg potatoes = R 5.1 × 3.3
3.3 kg potatoes = R 16.75
[tex]\rule[225]{225}{2}[/tex]
2. The number of hours you study for an exam impacts your grade. What is a reasonable value of the range?
70
-8
1.75
1/6
Answer:
62.
Step-by-step explanation:
because I subtract 70 to 8 equal to 62
Answer:
I think
Step-by-step explanation:
I think 62 hope you have a good day
What is the answer?
I want the explanation step by step
Help me
Chris and Hillary are remodeling their family room. They are deciding on the flooring, sofa and TV. How many possible combinations are shown in the tree diagram?
A. 10
B. 11
C. 12
D. 13
Answer:
its C ^^ makes more sense :D
Step-by-step explanation:
hope this helps
Use prime factorizations to find the GCF of 18 and 33.
Prime factorization of 18: 2 × 3 × 3
Prime factorization of 33: 3 x 11
The GCF of 18 and 33 is
Answer:
Use prime factorizations to find the GCF of 18 and 33.
Prime factorization of 18: 2 × 3 × 3
Prime factorization of 33: 3 x 11
The GCF of 18 and 33 is
Step-by-step explanation:
Use prime factorizations to find the GCF of 18 and 33.
Prime factorization of 18: 2 × 3 × 3
Prime factorization of 33: 3 x 11
The GCF of 18 and 33 is
Answer:
3 XD
Step-by-step explanation:
A train leaves Little Rock, Arkansas, and travels north at 85 kilometers per hour. Another train leaves at the same time and travels south at 85 kilometers per hour.
How long will it take before they are 680 kilometers apart?
Answer:
4hours
Step-by-step explanation:
1hour =85+85
=170km/h
time= distance÷
speed=170km/h
680÷170=time
=4h
Calculate the discriminant to determine the number of real roots of the equation.
y = x2 + 3x + 9
one real root
no real roots
three real roots
two real roots
find D which is the discriminant and with D < 0.
therefore the equation has an imaginary root and not a real root.
Consider two spinners I have the colors gray orange blue and yellow to make an area model what letter combination will go in the box highlighted in yellow below GB BB BG OY
Answer:
BB
Hope that helps!
Finding the slope from points
Answer:
m = -3
Step-by-step explanation:
The formula to find the slope of the line is :
slope = m = [tex]\frac{y_1 - y_2}{x_1-x_2}[/tex]
Given that the two coordinates of the line are :
( -1 , - 7 ) ⇒ ( x₁ , y₁ )
( 1 , -13 ) ⇒ ( x₂ , y₂ )
Let us solve now.
m = ( y₁ - y₂ ) ÷ ( x₁ - x₂ )
m = ( -7 - ( -13)) ÷ ( -1 - 1 )
m = ( -7 + 13 ) ÷ ( -2 )
m = 6 ÷ -2
m = -3
Answer:
m = -3
Step-by-step explanation:
Given two points:
(-1,-7) & (1,-13)To Find:
The slopeSolution:
Using slope's formulae,
[m denotes slope][tex] \boxed{ \rm{m = \cfrac{y_2 -y_1 }{x_2 - x_1} }}[/tex]
According to the question, on the formula:
(y_2,y_1) = (-13,-7)(x_2,x_1) = (1,-1)Substitute them onto the formulae:
[tex] \rm \: m = \cfrac{ - 13 - ( - 7)}{1 - ( - 1)} [/tex]
Simplify using PEMDAS:
P = ParenthesesE = exponentsM = MultiplicationD = DivisionA = additionS = subtraction[tex] \rm \: m = \cfrac{ - 13 + 7}{1 \ + 1} [/tex]
[tex] \rm \: m = \cfrac{ - \cancel6}{ \cancel2} = \boxed{ - 3}[/tex]
Hence, the slope of the line that passes through the given points in it's simplest form is -3.
A shipment of 50,000 transistors arrives at a manufacturing plant. The quality control engineer at the plant obtains a random sample of 500 resistors and will reject the entire shipment if 10 or more of the resistors are defective. Suppose that 4% of the resistors in the whole shipment are defective. What is the probability the engineer accepts the shipment? Do you believe the acceptance policy of the engineer is sound?
Step-by-step explanation:
remember, the number of possible combinations to pick m out of n elements is C(n, m) = n!/(m! × (n-m)!)
50,000 transistors.
4% are defective, that means 4/100 = 1/25 of the whole.
so, the probability for one picked transistor to be defective is 1/25.
and the probability for it to work properly is then 1-1/25 = 24/25.
now, 500 picks are done.
to accept the shipment, 9 or less of these 500 picks must be defective.
the probability is then the sum of the probabilities to get
0 defective = (24/25)⁵⁰⁰
1 defective = (24/25)⁴⁹⁹×1/25 × C(500, 1)
= 24⁴⁹⁹/25⁵⁰⁰ × 500
2 defective = (24/25)⁴⁹⁸×1/25² × C(500, 2)
= 24⁴⁹⁸/25⁵⁰⁰ × 250×499
3 defective = 24⁴⁹⁷/25⁵⁰⁰ × C(500, 3) =
= 24⁴⁹⁷/25⁵⁰⁰ × 250×499×166
...
9 defective = 24⁴⁹¹/25⁵⁰⁰ × C(500, 9) =
= 24⁴⁹¹/25⁵⁰⁰ × 500×499×498×497×496×495×494×493×492×491 /
9×8×7×6×5×4×3×2 =
= 24⁴⁹¹/25⁵⁰⁰ × 50×499×166×71×31×55×494×493×41×491
best to use Excel or another form of spreadsheet to calculate all this and add it all up :
the probability that the engineer will accept the shipment is
0.004376634...
which makes sense, when you think about it, because 10 defect units in the 500 is only 2%. and since the whole shipment contains 4% defect units, it is highly unlikely that the random sample of 500 will pick so overwhelmingly the good pieces.
is the acceptance policy good ?
that completely depends on the circumstances.
what was the requirement about max. faulty rate in the first place ? if it was 2%, then the engineer's approach is basically sound.
it then further depends what are the costs resulting from a faulty unit ? that depends again on when the defect is usually found (still in manufacturing, or already out there at the customer site, or somewhere in between) and how critical the product containing such transistors is. e.g. recalls for products are extremely costly, while simply sorting the bad transistors out during the manufacturing process can be rather cheap. if there is a reliable and quick process to do so.
so, depending on repair, outage and even penalty costs it might be even advisable to have a harder limit during the sample test.
in other words - it depends on experience and the found distribution/probability curve, standard deviation, costs involved and other factors to define the best criteria for the sample test.