Forecast for August with an alpha of 0.7 and forecast of June 164 are to be calculated using exponential smoothing.
Exponential smoothing is a forecasting method that uses a weighted average of past time-series values to forecast future values. In a time-series, data values are obtained over time, such as over months or years, and then plotted in sequence.
The weights decrease exponentially as the observations get older. The EWMA formula used in exponential smoothing is as follows:
St=α × Yt-1+(1-α) × St-1
where,St is the smoothed statistic for the current period tYt is the original observation for the current period tSt-1 is the smoothed statistic for the previous period t-1α is the smoothing parameter 0≤α≤1, and usually close to 0.1.The smoothed statistic is also called the exponentially weighted moving average (EWMA).Calculating the forecast for August with alpha=0.7 and forecast of June 164 as follows:
St=α × Yt-1+(1-α) × St-1St =0.7 × 164+(1-0.7) × 164St=164
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during a one-month promotional campaign, tiger films gave either a free dvd rental or a 12-serving box of microwave popcorn to new members. it cost the store $1 for each free rental and $2 for each box of popcorn. a total of 89 new members were signed up and the store's cost for the incentives was $135. how many of each incentive were given away?
By using system of equations, there are 43 free DVD rentals and 46 boxes of microwave popcorn were given away during the promotional campaign.
Let's use the following variables
x: the number of free DVD rentals given away
y: the number of boxes of microwave popcorn given away
We can set up a system of equations to represent the given information:
x + y = 89 (total number of new members signed up)
1x + 2y = 135 (total cost of the incentives)
We can solve for x or y in the first equation and substitute into the second equation
x = 89 - y
1(89 - y) + 2y = 135
89 - y + 2y = 135
y = 46
Substituting y = 46 into the first equation:
x + 46 = 89
x = 43
Therefore, 43 free DVD rentals and 46 boxes of microwave popcorn.
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Triangle TUV, with vertices T(-8,2), U(-2,8), and V(-9,9), is drawn inside a rectangle, as shown below.
The area of triangle TUV with vertices T(-8,2), U(-2,8), and V(-9,9) are 13.4 units.
What is triangle?A triangle is a closed two-dimensional plane figure that has three sides, three angles, and three vertices. The sum of the angles of a triangle is always 180 degrees. Triangles can be classified based on the length of their sides and the size of their angles. Some common types of triangles include equilateral, isosceles, scalene, acute, obtuse, and right triangles. Triangles are a fundamental concept in geometry and are used in many areas of mathematics and science.
Here,
To find the area of triangle TUV, we can use the formula:
Area = 1/2 * base * height
We can choose any two sides of the triangle as the base and the corresponding height. Let's choose TU as the base and the perpendicular distance from V to TU as the height.
First, let's find the length of TU:
TU = √[(8 - 2)² + (-2 - (-8))²]
= √[6² + 6²]
= 6√(2)
Next, let's find the slope of TU:
mTU = (8 - 2) / (-2 - (-8))
= -3/2
The line perpendicular to TU passing through V has a slope equal to the negative reciprocal of mTU:
mVQ = 2/3
The equation of the line passing through V and perpendicular to TU is:
y - 9 = (2/3)(x + 9)
Solving for x and y at the point where this line intersects TU, we get:
y = (2/3)x + 19
(2/3)x + 19 = -3x/2 + 7
x = -8/7
y = 94/21
The perpendicular distance from V to TU is the absolute value of y - 8:
|94/21 - 8| = 2/21
So, the area of triangle TUV is:
Area = 1/2 * TU * (2/21)
= (1/21)√(2)
To find the area of rectangle QRS, we need to find the length and width. We can use the distance formula to find the length QR and the width QS:
QR = √[(9 - (-8))² + (9 - 2)²]
= √[289]
= 17
QS = √[(9 - (-9))² + (2 - 2)²]
= √[324]
= 18
So, the area of rectangle QRS is:
Area = QR * QS
= 17 * 18
= 306
Area of triangle QRS = Area of rectangle QRS - Area of triangle TUV
= 306 - (1/21)√(2)
≈ 13.4 units
So, the answer is (C) 13.
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Complete question:
Triangle TUV, with vertices T(-8,2), U(-2,8), and V(-9,9), is drawn inside a rectangle. What is the area, in square units, of the triangle TUV?
A. 7
B. 10
C. 13
D. 18
Describe the pay at the digital source. Use complete sentences and include at least one specific example from the table that you made for part a
The pay at the Digital Source is a variable amount that depends on the employee's job position and experience level. The pay is represented in dollars per hour, and it ranges from $12 per hour for a new employee in a low-level position to $60 per hour for a senior developer with extensive experience.
For example, if we look at the table created in part a, we can see that a junior developer with less than a year of experience will earn $18 per hour, while a senior developer with more than 10 years of experience will earn $60 per hour. This means that the pay at the Digital Source is directly related to the employee's experience and job position.
Additionally, the table also shows that the pay rate increases as the employee gains more experience and moves up the career ladder. For instance, a junior developer with less than a year of experience will earn $18 per hour, but a mid-level developer with 3-5 years of experience will earn $35 per hour. This shows that employees are rewarded for their skills and experience, and they have the opportunity to advance their careers and earn higher pay rates.
In summary, the pay at the Digital Source is a variable amount that depends on the employee's job position and experience level. The pay rate ranges from $12 per hour to $60 per hour, and it increases as the employee gains more experience and moves up the career ladder. The company values the skills and expertise of their employees and rewards them accordingly.
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a sample of test scores is normally distributed with a mean of 120 and a standard deviation of 10. what score is located 2 standard deviations below the mean? g
The score located 2 standard deviations below the mean is 100. This score can be found by subtracting 2 standard deviations (20) from the mean (120).
The normal distribution is a bell-shaped curve that is symmetrical around the mean. This means that if you calculate the number of standard deviations away from the mean, you can use the same number to calculate how many standard deviations away from the mean the score is.
For example, in this question, the mean is 120 and the standard deviation is 10. To find the score located 2 standard deviations below the mean, subtract 2 standard deviations from the mean. This means the score is 120 - 20 = 100.
In general, the formula for calculating the score located x standard deviations away from the mean is:
Score = Mean + (x * Standard Deviation)
For example, to find the score located 4 standard deviations away from the mean, the formula is:
Score = Mean + (4 * Standard Deviation)
In this example, the score is 120 + (4 * 10) = 160.
In summary, to find the score located x standard deviations away from the mean, use the formula:
Score = Mean + (x * Standard Deviation)
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if one flag pole is y feet tall and casts a shadow x feet long, then how tall is another nearby flag pole that casts a shadow p feet long at the same time of day?
If one flag pole is y feet tall and casts a shadow x feet long, and another nearby flag pole casts a shadow p feet long at the same time of day, we can use similar triangles to determine the shadow of the second flag pole.
In this scenario, the two flag poles and the ground form two similar right triangles. The height of the first flag pole (y) corresponds to one leg of the first triangle, and the length of its shadow (x) corresponds to the other leg.
Similarly, the height of the second flag pole (h) corresponds to one leg of the second triangle, and the length of its shadow (p) corresponds to the other leg.
Therefore, the height of the second flag pole is equal to the product of the height of the first flag pole and the length of the shadow of the second flag pole, divided by the length of the shadow of the first flag pole.
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A triangle with side lengths 7, 6, 4 is
Acute
Right
Obtuse
Right
so 7 is the hypotenuse because it is the biggest. so you have to use 6 and 4 in the formula to see if they equal 7.
(a)²+(b)²=c²
(6)²+(4)²=c²
36+16=c²
(square root) 52=c²
the square root of 52 is 7
so therefore it is a right triangle.
During a catered lunch, an average of 4 cups of tea are poured per minute. The lunch will last 2 hours. How many gallons of tea should the caterer bring if there are 16 cups in one gallon? _____ gallons
Answer:30 gallons
Step-by-step explanation:
Answer:
30 gallons of tea
Step-by-step explanation:
Step 1:
First, before we do anything, let's convert 2 hours into minutes. There are 60 minutes in an hour, so we would multiply 60 and 2 to get 120 minutes.
Step 2:
Since we know that 4 cups of tea are poured every minute, we must multiply 4 by 120 because it is poured every 1 minute, and 4 × 120 = 480.
Step 3:
We also know that there are 16 cups of tea in one gallon, so we would divide 480 by 16 because we are trying to get how many gallons there are. 480 ÷ 16 = 30, so there are 30 gallons of tea poured in two hours.
Solve for x 8 x + 3 ≥ 19
Answer:
x ≥ 2
Step-by-step explanation:
8x + 3 ≥ 19
8x ≥ 19 - 3
8x / 8 ≥ 16 / 8
x ≥ 2
Answer:
Sure, I can solve for x:8x + 3 ≥ 19Subtracting 3 from both sides:8x ≥ 16Dividing both sides by 8:x ≥ 2Therefore, the solution is x ≥ 2.
help i need help with this its very hard
Answer:
3a + 2b
Step-by-step explanation:
Let the unknown side have length X.
X + X + 5a - b + 5a - b = 16a + 2b
2X + 10a - 2b = 16a + 2b
2X = 6a + 4b
X = 3a + 2b
Answer: 3a + 2b
if you're good at quadratics...
Therefore, the correct answer is: [tex](x+10)^2=82[/tex]. ( right hand side of the equation).
What is equation?An equation is a mathematical statement that indicates that two expressions are equal. It typically contains variables, which are represented by letters, and may also include constants and operators. The general format of an equation is:
expression = expression
For example, the equation x + 2 = 6 means that the expression x + 2 is equal to the expression 6. The goal of solving an equation is to find the value(s) of the variable(s) that make the equation true.
To solve the quadratic equation by completing the square, Jamie needs to follow the steps:
Move the constant term to the right-hand side of the equation:
[tex]x^2 + 20x = -18[/tex]
Add and subtract the square of half the coefficient of x to the left-hand side of the equation:
[tex]x^2 + 20x + (20/2)^2 - (20/2)^2 = -18[/tex]
[tex](x+10)^2 - 100 = -18[/tex]
Simplify the right-hand side of the equation:
[tex](x+10)^2 = 82[/tex]
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xiao aims to get 8 hours of sleep per week night on monday night he slept for 6 1/2 hrs, on tuesday night 7 1/2 on wednesday night 5 3/4 and on thursday night 8 1/4 hours.
a. state the difference between the amount of sleep he got and his goal
b. after 4 nights, how much is xiao ahead or behind in his sleep goal?
a) Xiao is 13 hours short of his sleep goal for the week.
b) After 4 nights, Xiao is 5 hours short of his sleep goal.
a) Given,Xiao's goal is to get 8 hours of sleep per weeknight, which means he aims to get 40 hours of sleep (8 hours per night x 5 weeknights) during the week. To find the difference between the amount of sleep he got and his goal, we need to calculate the total amount of sleep he got during the week and subtract it from his goal:
Total sleep = [tex]6 \frac{1}{2} + 7 \frac{1}{2} + 5 \frac{3}{4} + 8 \frac{1}{4} = 27[/tex]
Difference from goal = 40 - 27
= 13
Therefore, Xiao is 13 hours short of his sleep goal for the week.
b. After 4 nights, Xiao has slept for a total of:
Total sleep = 27
Since he aims to get 8 hours of sleep per weeknight, he would have gotten a total of 32 hours of sleep (8 hours per night x 4 weeknights) if he had met his goal. To find out how much he is ahead or behind in his sleep goal, we need to calculate the difference between the total amount of sleep he got and his goal:
Difference from goal = 32 - 27 = 5
Therefore, after 4 nights, Xiao is 5 hours short of his sleep goal.
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-5x - 3y + 7x + 21y Simplify
Answer:
2x + 18y
Step-by-step explanation:
-5x - 3y + 7x + 21y ----> (combine like terms)
2x - 3y + 21 y ---> (combine like terms)
2x + 18y
Answer:
[tex]\huge\boxed{\sf 2(x + 9y)}[/tex]
Step-by-step explanation:
Given expression:= -5x - 3y + 7x + 21y
Combine like terms= -5x + 7x - 3y + 21y
= 2x + 18y
Common factor = 2So, take 2 as a common factor
= 2(x + 9y)[tex]\rule[225]{225}{2}[/tex]
A house plan has concrete stairs leading down into the garage. How much concrete is needed to make the stairs? 3 ft 2 ft 8 ft 5 ft [? ] ft ³ 2 ft 8 ft 1 ft
The amount of concrete needed to make the stairs that leads to the garage is 64 cubic feet
Calculating the amount of concrete needed to make the stairs?The missing information is added as an attachment
The concrete needed to make the stairs is the volume of the stairs and this is calculated using
Volume = Base area * Height
Where
Base area = 3 * 2 + 2 * 1
Base area = 8
And
Height = 8
So, we have
Volume = 8 * 8
Evaluate
Volume = 64
Hence, the amount needed is 64 cubic feet
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Is r=4q-5 a linear function ?
Answer:
yes
Step-by-step explanation:
replace r and q with y and x:
y = 4x - 5
It is a line.
a chord is drawn perpendicular to the radius of the circle. if the radius is 5 inches and the point of intersection between the chord and the radius is 2 inches away from the circumference of the circle, find the length of the chord.
The length of the chord is approximately 7.62 inches.
Let's call the center of the circle point O, the radius of the circle 5 inches, the point where the chord intersects the radius point A, and the point where the chord intersects the circle point B.
Since the chord is perpendicular to the radius, we know that angle AOB is a right angle. Also, since OA is 5 inches and AB is 2 inches, we can use the Pythagorean theorem to find the length of OB
OB^2 = OA^2 + AB^2
OB^2 = 5^2 + 2^2
OB^2 = 25 + 4
OB^2 = 29
OB = sqrt(29) ≈ 5.39 inches
Now that we know the length of OB, we can use it to find the length of the chord. Let's call the length of the chord CD, where C and D are the points where the chord intersects the circle. Since OB is perpendicular to CD, we can use the Pythagorean theorem again to find the length of CD
CD^2 = 2OB^2
CD^2 = 2(29)
CD^2 = 58
CD = sqrt(58) ≈ 7.62 inches
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how to factor a trinomial when a is greater than 1
To factor a trinomial when a is greater than 1, we can use the AC method
To factor a trinomial when a is greater than 1, follow these steps
Multiply the coefficient of a (the first term) by the constant (the third term).
Find two numbers that multiply to the product obtained in step 1 and add up to the coefficient of b (the second term).
Replace the middle term with the two terms found in step 2.
Factor the resulting four-term polynomial by grouping.
Factor out the greatest common factor from each group.
Factor the resulting binomials.
Combine the factors to obtain the final factorization of the trinomial.
This method is known as the AC method, and it can be used to factor trinomials of the form ax^2 + bx + c, where a is greater than 1.
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what is the value of t?
Answer:
t=36°
Step-by-step explanation:
90-54=36
opposite angles are equal so t=36°
Write an equation of a line in slope-intercept form that is parallel to y=-3x-5 and goes through the point (-1,8)
Answer:
y=-3x+5
Step-by-step explanation:
A line that is parallel to y=-3x-5 will have the same slope, which is -3.
Using the point-slope form, we can write the equation of the line as:
y - 8 = -3(x + 1)
Simplifying:
y - 8 = -3x - 3
Adding 8 to both sides:
y = -3x + 5
Therefore, the equation of the line in slope-intercept form that is parallel to y=-3x-5 and goes through the point (-1,8) is y = -3x + 5.
i need help pleaseeeeeee
By using the definition of inverse functions we can see that:
a) g(7) = -10
b)(-10,7) is a point on h(x).
c)(7, -10) is a point on j(x)
How to evaluate the functions?Remember that if two functions f(x) and g(x) are inverses, then:
f(y) = x
g(x) = y
And also g(f(x)) = x = g(f(x)).
Here we know that functions h(x) and j(x) are inverses, and we also know that:
h(-10) = 7
So for the input -10, we have the output 7.
Then, by using the relation written above, we know that for the inverse function we must have:
j(7) = -10
That is the answer for a.
And for b and c the notation is (input, output), then:
(-10, 7) is a point on h.(7, -10)is a point on jThese are the answers of points B and C of the question.
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when is it appropriate to take a pulse by counting the heart rate for 30 seconds and multiplying by two?
It is appropriate to take a pulse by counting the heart rate for 30 seconds and multiplying by two when a rapid or irregular pulse is suspected, or when it is difficult to count the pulse for a full minute.
Counting the heart rate for a full minute is the most accurate way to determine the heart rate. However, there are situations when it may be more appropriate to count the heart rate for 30 seconds and multiply by two.
For example, if a person's pulse is rapid or irregular, it may be difficult to accurately count the pulse for a full minute. In such cases, it may be more appropriate to count the pulse for 30 seconds and multiply by two to get an estimate of the heart rate.
Another situation where it may be appropriate to count the pulse for 30 seconds is when time is limited, such as in an emergency situation. In such cases, counting the pulse for 30 seconds and multiplying by two can provide a quick estimate of the heart rate.
However, it is important to note that counting the pulse for 30 seconds and multiplying by two may not be as accurate as counting the pulse for a full minute.
Therefore, if possible, it is recommended to count the pulse for a full minute to obtain the most accurate measurement of the heart rate.
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A business owner applies for a credit card to cover $14,000 in emergency expenses. The credit card charges 16.99% annual interest compounded continuously. If no payments are made for 2 years, what will the balance on the card be, rounded to the nearest penny?
Credit card charges $19665.33 will the balance on the card be, rounded to the nearest penny.
What is interest in simple words?
When you borrow money, you must pay interest, and when you lend money, you must charge interest. The most common way to represent interest is as a percentage of a loan's total amount per year. The interest rate for the loan is denoted by this proportion.
Interest is the cost of borrowing money and is typically stated as a percentage, such an annual percentage rate (APR). Lenders may charge interest to borrowers for the use of their funds, or borrowers may charge interest to lenders for the use of their funds.
amount applied for = $14,000
interest rate = 16.99%
the balance after 2 years
P₀ = $1400
r = 16.99% = 0.1699
t = 2
[tex]P_{0} = P_{0}e^{rt}[/tex]
[tex]P_{2} = 1400e^{0.1699 * 2}[/tex]
≈ $19665.33
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the volume of a cube decreases at a rate of 6 m 3 / s . find the rate at which the side of the cube changes when the side of the cube is 4 m . answer exactly or round to 2 decimal places.
The rate at which the side of the cube changes when the side of the cube is 4 m is -1/8 m/s (or approximately -0.125 m/s).
Let's use the formula for the volume of a cube:
V = s³
where V is the volume and s is the length of one side of the cube. To find the rate of change of the side length, we need to differentiate this formula with respect to time t:
dV/dt = d/dt (s³) = 3s² ds/dt
We know that dV/dt = -6 m³/s (the negative sign indicates that the volume is decreasing), and when s = 4 m, we have:
-6 = 3(4²) ds/dt
Simplifying this equation gives us:
ds/dt = -6 / (3*4²) = -1/8 m/s
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When the temperature drops below 15°C in a building, the furnace turns on.
At what temperatures will the heater turn on? Write an inequality to represent
this situation, and graph the solution on a number line.
The inequality to represent this situation is T < 15°C, where T is the temperature.
What is inequality?Inequality is a statement that two values, expressions, or quantities are not equal. Inequality is usually represented by the symbols ">", "<", "≥", or "≤".
This inequality can be graphed on the number line by representing 15°C as a point on the number line. Any values to the left of 15°C, such as 14°C, 13°C, and so on, would be represented as points to the left of 15°C on the number line.
Less than inequality is used to compare two values to see if one is less than the other. In this case, the inequality T < 15°C states that the temperature T must be less than 15°C in order for the furnace to turn on.
Graphically, the solution to this inequality is represented by a number line with a point at 15°C and all points to the left of 15°C represented in the solution set.
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(-3m+3d):3 пожалуйста срочноооооо!!!!!!!!!
Answer:
-m + d
Step-by-step explanation:
(-3m + 3d) : 3 =
(-3m + 3d) x 1/3 =
-m + d
A party tent is used for an outdoor event. Ropes of equal length support each tent pole. The angle each rope makes with the ground is 52°.
What is the height of each tent pole?
Therefore, the height of each tent pole is approximately 8.07 meters.
What is trigonometry?Trigonometry is a branch of mathematics that deals with the study of the relationships between the sides and angles of triangles. It is used to solve problems involving triangles, such as finding the length of a side or the measure of an angle. Trigonometry is based on the use of trigonometric functions, which are ratios of the sides of a right triangle.
Here,
We can use trigonometry to solve this problem. Let's call the height of the tent pole "h" and the length of the rope "r". Then, we can use the tangent function to find the height:
tan(52°) = h/r
Rearranging this equation, we get:
h = r * tan(52°)
We know that the length of each rope is equal, so we can choose any arbitrary length for r. For simplicity, let's assume that each rope is 10 meters long. Then, we can plug in the values into the equation:
h = 10 * tan(52°)
Using a calculator, we get:
h ≈ 8.07 meters
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26. In the given figure, OP || RS. ZPQR = 60° and QRS = 130°. Then what is the measure of ZOPQ? S P 60% R 130⁰
Answer: The answer is 60.
Step-by-step explanation:
Using the fact that OP || RS, we know that∠RWV = 180° − 130° 1. ∠RWV = 50° We know that,∠PWQ = ∠RWV = 50° (Since, opposite angles of intersecting lines are equal) Also, for line OP∠OQP + θ = 180° θ = 180° − ∠OPQ = 180° − 110° 2. θ = 70°
Answer:
The measure of ∠OPQ is 110°.
Step-by-step explanation:
Draw a line parallel to OP from point Q. Label a point on the line T. (See attached diagram).
Angles SRQ and TQR are alternate interior angles, and so according to the Alternate Interior Angles Theorem, they are congruent.
⇒ m∠TQR = m∠SRQ = 130°
Given m∠PQR = 60° and m∠TQR = 130° then:
⇒ m∠TQP + m∠PQR = m∠TQR
⇒ m∠TQP + 60° = 130°
⇒ m∠TQP = 70°
Angles OPQ and TQP are same-side interior angles, and so according to the Same-side Interior Angles Theorem, they are supplementary (sum to 180°).
⇒ m∠OPQ + m∠TQP = 180°
⇒ m∠OPQ + 70° = 180°
⇒ m∠OPQ = 110°
Therefore, the measure of ∠OPQ is 110°.
What is the value of k?
127.3°
PLEASE HURRY !! I NEED HELP!!!
Answer:$10
Step-by-step explanation: We are given the ratio 9:1. Meaning for every 9 dollars he spends on healthy food, he can spend a dollar on snacks. If he intends on paying 100 dollars total, how much will he spend on snacks?
He would have spent 90 dollars on healthy food, and 10 dollars on snack food. Totaling 100 dollars.
What is the endpoint of a line segment with these points? Endpoint: Z(–21, 15) Midpoint: M(–13, 29) (–5, 43) (–17, 22) (–27, 21) (–29, 1)
Answer: A - (-5, 43)
Step-by-step explanation:
QUESTION 1. Assume we are testing a function with 3 variables:
Variable A: has values 0 and 1
Variable B: has values 0 and 1
Variable C: has values 0 and 1
What is the total 2-way variable value configuration coverage achieved by the following tests:
A=0; B=0; C=1
A=0; B=1; C=1
A=1, B=0, C=0
The total 2-way variable achieved by the given tests is 6.
How to find 2-way variable?
There are three pairs of variables, and each pair can have two possible values, resulting in 2-way variable value configurations. Therefore, the total 2-way variable value configuration coverage achieved by the given tests is 6, as follows:
A=0, B=0
A=0, C=1
B=0, C=1
A=0, B=1
A=1, B=0
A=1, C=0
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