Yuki concluded:
"It's not possible to map AABC onto AFED using a sequence of rigid transformations, so the triangles
are not congruent."
What error did Yuki make in her conclusion?

The correct options are: For Boundary Value Analysis: a), b), c), For Equivalence Class Partitioning: b), c), d), e).

For Boundary Value Analysis:

a) BVA technique is an extension and refinement of the equivalence class partitioning technique - True

b) Select test data near the boundary of a data domain so that data both within and outside an equivalence class are selected - True

c) Once equivalence classes have been determined, design tests for the limits (boundaries) of each class - True

d) BVA has no relation to equivalence class partitioning - False

For Equivalence Class Partitioning:

a) Equivalence class partitioning can only be used with integers as input - False

b) A small number of test cases are needed to adequately cover a large input domain - True

c) The equivalence class partitioning approach is not restricted to input conditions alone - the technique may also be used for output domains - True

d) One gets a better idea about the input domain being covered with the selected test cases - True

e) The probability of uncovering defects with the selected test cases based on equivalence class partitioning is higher than that with a randomly chosen test suite of the same size - True

Therefore, the correct options are:

For Boundary Value Analysis: a), b), c)

For Equivalence Class Partitioning: b), c), d), e)

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Answer:

11 17/21

Step-by-step explanation:

If we were multiplying then this would be the answer.

If teacher is distributing sheets in a class, then the equation which is used to find number of students in class is (d) 2x+8 = 3x - 11​.

A "Linear-Equation" is a mathematical equation that represents a straight line in a coordinate plane. It is of form : y = mx + b

where y is the dependent variable, x is the independent variable, m is the slope of the line, and b is the y-intercept (the point at which the line crosses the y-axis).

Let number of students in class be denotes as "x",

If each student get 2 sheets, then 8 sheets are remaining, it is mathematically represented as : 2x + 8 ,

If each student get 3 sheets each, then there would be 11 sheets less, and this is represented as : 3x - 11,

So, the equation which is used to find number of students in class is 2x+8=3x-11,

Therefore, the correct option is (d).

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The given question is incomplete, the complete question is

If a teacher were to distribute sheets of paper so that each student got two sheets, there would be 8 sheets remaining. However, if three sheets were given to each student, the teacher would be 11 sheets short. Which equation could be used to find how many students are in the class?

(a) 2(x - 8) = 3(x + 11)

(b) 2(x + 8) = 3(x - 11)

(c) 2x-8 = 3x + 11

(d) 2x+8 = 3x - 11​

The real interest rate, using the approximation formula, is 0.01 or 1%. This means that after considering the expected inflation rate, the purchasing power of the money grows at a rate of 1%.

The real interest rate can be calculated using the approximation formula: real interest rate = nominal interest rate - expected inflation rate.

We have:

Nominal interest rate (i) = 0.04

Expected inflation rate (+1) = 0.03

Using the formula, we can substitute the given values:

Real interest rate = 0.04 - 0.03

Calculating the difference:

Real interest rate = 0.01

Therefore, the real interest rate, using the approximation formula, is 0.01 or 1%.

The nominal interest rate represents the rate at which money grows in a bank account or investment without considering inflation. On the other hand, the real interest rate takes into account the effects of inflation, allowing us to understand the true purchasing power of the money.

To calculate the real interest rate, we subtract the expected inflation rate from the nominal interest rate. In this case, the nominal interest rate is 0.04 (4%), and the expected inflation rate is 0.03 (3%).

Substituting the values into the formula, we get:

Real interest rate = 0.04 - 0.03

Real interest rate = 0.01 or 1%

Therefore, the real interest rate, in this scenario, is 0.01 or 1%. This means that after accounting for inflation, the purchasing power of the money grows at a rate of 1%.

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Answer:

974

Step-by-step explanation:

Let assume that:

The set of student that took part in Calculus be = C

Those that took part in discrete mathematics be = D

Let those that took part in data structures be = DS; &

Those that took part in Programming language be = P

Thus;

{C} = 507

{D} = 292

{DS} = 312

{P} = 344

For intersections:

{C ∩ DS} = 14

{C ∩ P} = 213

{D ∩ DS} = 211

{D ∩ P}  =43

{C ∩ D} = 0

{DS ∩ P} = 0

{C ∩ D ∩ DS ∩ P} = 0

According to principle of inclusion-exclusion;

{C ∪ D ∪ DS ∪ P} = {C} + {D} + {DS} + {P} - {C ∩ D} - {C ∩ DS} - {C ∩ P} - {D ∩ DS} - {D ∩ P} - {DS ∩ P}

{C ∪ D ∪ DS ∪ P} = 507 + 292 + 312 + 344 - 14 - 213 - 211 - 43 - 0

{C ∪ D ∪ DS ∪ P} = 974

Hence, the no of students that took part in either course = 974

If 12 men are needed to run 4 machines, then 60 men are needed to run 20 machines.

To determine how many men are needed to run 20 machines, we can set up a proportion using the given information.

We know that 12 men are needed to run 4 machines. Let's set up the proportion:

12 men / 4 machines = x men / 20 machines

To solve for x, we can cross-multiply:

12 men * 20 machines = 4 machines * x men

240 men = 4x

Now, we can solve for x by dividing both sides of the equation by 4:

240 men / 4 = x men

60 men = x

Therefore, 60 men are needed to run 20 machines.

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Answer:

The answer is A x 10 b

The statement you made is not entirely correct. The Second Shape Theorem, also known as the Second Derivative Test, does not include the converse of the First Shape Theorem. Instead, it provides additional information about the nature of critical points of a function.

The Second Shape Theorem states that if a function f(x) has a critical point at x = a (i.e., f'(a) = 0), and if f''(a) exists and is nonzero, then the function has a local minimum at x = a if f''(a) > 0, and a local maximum at x = a if f''(a) < 0.

Note that this theorem only applies to critical points where f'(a) = 0. There may be other critical points where f'(a) does not equal zero, and these points do not satisfy the conditions of the Second Shape Theorem.

In contrast, the converse of the First Shape Theorem states that if a function is differentiable at a point x = a and f'(a) = 0, then f has an extreme value at x = a. This is a separate theorem that is not directly related to the Second Shape Theorem.

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The Second Shape Theorem states that if a function f(x) has an extreme value at x=a, then the function must also be differentiable at x=a. This theorem is the converse of the First Shape Theorem, which states that if a function is differentiable at a point, then it must have a local extreme value at that point.

Essentially, the Second Shape Theorem tells us that having an extreme value at a point is a necessary condition for differentiability at that point. This theorem is particularly useful in calculus and optimization problems, where we are interested in finding the maximum or minimum values of a function. By checking for extreme values and differentiability at those points, we can determine if a function has a local maximum or minimum.

Your statement, "If f(x) has an extreme value at x=a, then f is differentiable at x=a," is actually the converse of the First Shape Theorem. However, this statement is not universally true, as extreme values can occur at non-differentiable points (e.g., sharp corners or endpoints). The Second Shape Theorem does not include the converse of the First Shape Theorem, but rather provides another method for identifying extreme values by analyzing the second derivative.

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The present value of $13,000 discounted back 5 years at a semi-annual compound rate of 9% can be calculated by the formula:PV = FV / (1 + r/m)^(m*t)Here, PV stands for Present Value FV stands for Future Valuer stands for the interest rate (9%)m is the number of times the interest is compounded (semi-annually, so m = 2)t is the number of years (5)

After substituting the values in the formula, we get:PV = 13,000 / (1 + 0.045)^10PV = 13,000 / 1.55709768854PV = $8,349.58. We can use the concept of present value (PV) and future value (FV) to solve this question. When the cash flow is considered at different points of time, the money's value changes with the time value of money. The time value of money takes into consideration the amount of interest that could be earned on the sum of money if invested. Present value (PV) is a mathematical concept that represents the current worth of a future sum of money, taking into account the time value of money and the given interest rate. PV is calculated by using a discount rate that is determined by the interest rate and the length of time between the present and future payment dates. Future value (FV) is a mathematical concept that represents the future worth of a present sum of money, taking into account the time value of money and the given interest rate. FV is calculated by using a compound interest rate that is determined by the interest rate and the length of time between the present and future payment dates. To calculate the present value of $13,000 discounted back 5 years at a semi-annual compound rate of 9%, we can use the formula PV = FV / (1 + r/m)^(m*t), where PV is the present value, FV is the future value, r is the interest rate, m is the number of times the interest is compounded per year, and t is the number of years. In this case, we know that FV is $13,000, r is 9%, m is 2 (since it is compounded semi-annually), and t is 5. After substituting these values into the formula, we get PV = $8,349.58. Therefore, the present value of $13,000 discounted back 5 years at a semi-annual compound rate of 9% is $8,349.58.

Therefore, the present value of $13,000 discounted back 5 years at a semi-annual compound rate of 9% is $8,349.58.

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Answer:

-2/5

Step-by-step explanation:

Edge 2020

Answer:

-2/5

Step-by-step explanation:

person above is correct!1!!! i just need points =)

Answer: 1/2(m<TUV)= m<TUW

Step-by-step explanation: If you divide TUV by 2 then you would get 28 degrees which would be The < TUW

Answer:

45%

Step-by-step explanation:

15 x 3 = 45

This is an example of a comparative study that uses random sampling to ensure representation from different socioeconomic groups and educational backgrounds in the samples. The study aims to compare mathematics knowledge among 15-year-olds in the US and Japan by administering a mathematics achievement test to 1000 students from each country.
Hi! I'd be happy to help with your question. You would like to compare mathematics knowledge among 15-year-olds in the US and Japan by giving a mathematics achievement test to samples of 1000 15-year-olds in each of the two countries, with 200 students from low-income families, 400 students from middle-income families, and 400 students from high-income families in each country. This is an example of a stratified random sampling method.

In this case, the population is divided into different strata based on socioeconomic groups (low-income, middle-income, and high-income families), and then random samples are drawn from each stratum. This ensures that the samples include individuals from all different socioeconomic groups and educational backgrounds, which allows for a more accurate comparison between the two countries.

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Answer:

R3. Definition of Linera Pair

S4. m∠3 +m∠4 =180°

R5.  Substitution Property of Equality

I'm not sure if it's right but I tried :/

lmk if it's wrong

The simplified solution based on the four constraints of the quadrilateral was used to solve a rectilinear MiniMax problem, resulting in the C₁-C₅ formula.

To solve the rectilinear MiniMax problem using the simplified solution based on the four constraints of the quadrilateral, the following steps were taken:

Formulation of the problem: The rectilinear MiniMax problem involves optimizing a function subject to certain constraints. In this case, we are looking for the minimum or maximum value of a function given the constraints of a quadrilateral.

Identification of the constraints: The four constraints of the quadrilateral are identified. These constraints may involve linear equations representing the sides or diagonals of the quadrilateral.

Formulation as a linear programming (LP) problem: The rectilinear MiniMax problem is transformed into an LP problem by defining an objective function and expressing the constraints as linear inequalities.

Objective function: The objective function is defined based on whether we are looking for the minimum or maximum value. This function represents the quantity to be optimized.

Linear inequalities: The constraints of the quadrilateral are expressed as linear inequalities. These inequalities define the feasible region of the LP problem.

LP-based algorithm: The LP-based algorithm is applied to solve the problem. This algorithm involves finding the optimal solution within the feasible region defined by the linear inequalities.

Solution: The LP-based algorithm provides a solution that minimizes or maximizes the objective function, depending on the problem's requirements. In this case, the solution is represented by the C₁-C₅ formula.

Overall, the rectilinear MiniMax problem was successfully solved using the simplified solution based on the four constraints of the quadrilateral, resulting in the C₁-C₅ formula as the solution.

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Answer: 116 minutes or an hour and 56 minutes

Step-by-step explanation:

So what I did was Subtract the total amount of the bill by the five dollar fee and got $10.44

Then I divided 1$0.40 by $0.09 and got 116... so I simplified it and got An hour and 56 minutes.

Charlie ride the scooter for 116 minutes, as per linear equation.

A linear equation is an equation that has one or multiple variables with the highest power of the variable is 1.

Given, Charlie paid a $5 fee to start the scooter plus 9 cents per minute of the ride.

The total bill for Charlie's ride was $15.44.

Let, Charlie ride for 'x' minutes.

Therefore, $[5 + (0.09 × x)] = $15.44

⇒ 0.09x = 15.44 - 5

⇒ 0.09x = 10.44

⇒ x = 10.44/0.09

⇒ x = 116

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Part A: The expression for the total number of minutes Mario volunteers each year at the animal shelter  =  (405/y)   x  365

Part B: The simplified form of the expression for the total number of minutes Mario volunteers each year at the animal shelter = (147825/y) minutes

Number of days Mario volunteers each month at the animal shelter = 1

Number of hours Mario cleans for y days = 5.5 hours

Number of hours Mario each day = 5.5/y

Number of minutes Mario uses to walk dogs for y days = 75 minutes

Number of hours Mario uses to walk dogs for y days=  75/60

Number of hours Mario uses to walk dogs for y days=  1.25 hours

Number of hours Mario uses to walk dogs each day= 1.25/y

Total number of hours Mario volunteers in a day = Number of hours Mario cleans each day + Number of hours Mario uses to walk dogs

Total number of hours Mario volunteers in a day = 5.5/y + 1.25/y

Total number of hours Mario volunteers in a day = 6.75/y

Convert the number of hours to minutes

1 hour   =  60 minutes

Total number of minutes Mario volunteers in a day = (6.75/y) x 60

Total number of minutes Mario volunteers in a day = (405/y) minutes

Number of days in 1 year = 365

The expression for the total number of minutes Mario volunteers each year at the animal shelter  =  (405/y)   x  365

The simplified form of the expression for the total number of minutes Mario volunteers each year at the animal shelter = (147825/y) minutes

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Therefore, the interval in which solutions are sure to exist is (0, ∞).

To determine the interval in which solutions are sure to exist for the given differential equation, we need to consider any restrictions or limitations imposed by the equation itself.

In this case, the given differential equation is:

y′′′ ty'' t^2y'=ln(t)

The equation involves logarithm function ln(t), which is not defined for t ≤ 0. Therefore, the interval in which solutions are sure to exist is t > 0.

In other words, solutions to the given differential equation can be found for values of t that are strictly greater than 0.

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Answer:

5

Step-by-step explanation:

If you input 5 you get 7

Answer:  5

Step-by-step explanation:

f(x) usually means the y-value or output of the functions.

It can find the x value through the graph. When y is 7, you can see that x is 5 (See the image).

The volume of the triangular prism is not equal to the volume of the cylinder.  Therefore, the correct option is option D.

The congruent cross-sectional areas of both shapes suggest that they have the same base area, however, the height of the right triangular prism (6 units) is half the height of the right cylinder (6 units).

The volume of a three-dimensional shape is calculated by multiplying the base area by the height, so the volume of the triangular prism (base area x 6 units) will be half the volume of the cylinder (base area x 12 units).

Therefore, the volume of the triangular prism is not equal to the volume of the cylinder.

Therefore, the correct option is option D.

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In a transformation called a translation, the pre-image is slid either vertically or horizontally.

A translation is a type of transformation in geometry where the pre-image (original figure) is moved or slid to a new position in a specific direction. The movement can be either vertical or horizontal.

When a pre-image is translated vertically, it means that it is moved up or down without any change in its orientation. The entire figure maintains the same shape and size, but its position on the coordinate plane is shifted vertically.

On the other hand, when a pre-image is translated horizontally, it is moved left or right while preserving its original shape and size. The orientation of the figure remains the same, but its position on the coordinate plane is shifted horizontally.

In both cases, the translation occurs without any rotation, reflection, or resizing of the pre-image. The resulting image is a new figure that is congruent to the original but located at a different position on the plane.

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Answer:

$4866.61

Step-by-step explanation:

Answer:

c/sin(60°) = 14/sin(25°)

c = 14sin(60°)/sin(25°) = 28.7

Answer:

\(CI = (0.028636,0.071364)\)

I am 95% confident that the true proportion of couples where the wife is taller than her husband is captured in the interval (.028, .071)

Step-by-step explanation:

Given

\(n = 400\)

\(x = 20\) --- taller wife

\(y = 380\) --- shorter wife

Required

Determine the 95% confidence interval of taller wives

First, calculate the proportion of taller wives

\(\hat p = \frac{x}{n}\)

\(\hat p = \frac{20}{400}\)

\(\hat p = 0.05\)

The z value for 95% confidence interval is:

\(z = 1.96\)

The confidence interval is calculated as:

\(CI = \hat p \± z \sqrt{\frac{\hat p (1 - \hat p)}{n}}\)

\(CI = 0.05 \± 1.96* \sqrt{\frac{0.05 (1 - 0.05)}{400}}\)

\(CI = 0.05 \± 1.96 * \sqrt{\frac{0.0475}{400}}\)

\(CI = 0.05 \± 1.96 * \sqrt{0.00011875}\)

\(CI = 0.05 \± 1.96 * 0.01090\)

\(CI = 0.05 \± 0.021364\)

This gives:

\(CI = (0.05 - 0.021364,0.05 + 0.021364)\)

\(CI = (0.028636,0.071364)\)

Answer:

23

Step-by-step explanation:

AB = BC = (1/2)AC

3x - 4 = 2x + 5

x = 9

BC = 2x + 5 = 2 × 9 + 5 = 23

There is only one number from 1 through 200 that has a 2 in the units place and is divisible by 4.

The question asks for the number of numbers from 1 through 200 that have a 2 in the units place and are divisible by 4.
To solve this, we need to determine the possible values for the tens digit. Since the number needs to be divisible by 4, the tens digit must be even.
The even numbers from 1 to 9 are 2, 4, 6, and 8. Out of these, only the number 2 has a 2 in the units place.
Therefore, there is only one number from 1 through 200 that has a 2 in the units place and is divisible by 4.

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Answer:

Therefore, the base-6 representation of 1407 is 1303.

Step-by-step explanation:

To convert the decimal numeral 1407 to base 6, we can use the following steps:

Divide 1407 by 6 and store the quotient and the remainder.

Repeat the division process with the quotient until the quotient is 0.

Write down the remainders in the reverse order to get the base-6 representation of 1407.

So, the steps would look like this:

1407 ÷ 6 = 234 with a remainder of 3

234 ÷ 6 = 39 with a remainder of 0

39 ÷ 6 = 6 with a remainder of 3

6 ÷ 6 = 1 with a remainder of 0

1 ÷ 6 = 0 with a remainder of 1

Writing down the remainders in the reverse order, we get: 1407(10) = 1303_6.

Therefore, the base-6 representation of 1407 is 1303.

Answer:

3x + 11m + c

Step-by-step explanation:

Step 1) Write the Equation: 3x + 5m + 6m + c

Step 2) Add like Terms: 3x + 11m + c

Answer:

Step-by-step explanation:

To find the total area of the track, we need to calculate the area of each section and then add them together.

Area of a semi-circle with radius 31m:

A = (1/2)πr^2

A = (1/2)π(31m)^2

A = 4795.4m^2

Area of a rectangle with length 92.7m and width 31m (the straight parts):

A = lw

A = (92.7m)(31m)

A = 2873.7m^2

To find the total area, we need to add the areas of the two semi-circular ends and the two straight sections:

Total area = 2(Area of semi-circle) + 2(Area of rectangle)

Total area = 2(4795.4m^2) + 2(2873.7m^2)

Total area = 19181.6m^2

Rounding this to 1 decimal place, we get:

Total area ≈ 19181.6 m^2

Therefore, the total area of the track is approximately 19181.6 square meters.

The system capacity is 2 units per minute, the bottleneck stage is Stage A, and the utilization of Stage 3 is 100%.

A line process has three processing stages with the characteristics given below:

Stage A B C Unit processing time(minutes) 1 2 3 Number of machines 1 1 2 Machine availability 90% 100% 100% Process yield at stage 100% 100% 100%

To determine the system capacity and the bottleneck stage and utilization of Stage 3:

The system capacity is calculated by the product of the processing capacity of each stage:

1 x 1 x 2 = 2 units per minute

The bottleneck stage is the stage with the lowest capacity and it is Stage A. Therefore, Stage A has the lowest capacity and determines the system capacity.The utilization of Stage 3 can be calculated as the processing time per unit divided by the available time per unit:

Process time per unit = 1 + 2 + 3 = 6 minutes per unit

Available time per unit = 90% x 100% x 100% = 0.9 x 1 x 1 = 0.9 minutes per unit

The utilization of Stage 3 is, therefore, (6/0.9) x 100% = 666.67%.

However, utilization cannot be greater than 100%, so the actual utilization of Stage 3 is 100%.

Hence, the system capacity is 2 units per minute, the bottleneck stage is Stage A, and the utilization of Stage 3 is 100%.

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