Find the inverse of the following functions algebraically

The length of line AX is 3p/4q.

The length of side AY is  9p²/4q + 3p/4.

The length of line AX is calculated as follows;

From the given figure, we can apply the principle of congruent sides of the parallellogram.

AD/DC = CX/AX

8q/6p = 1/AX

AX = 6p/8q

AX = 3p/4q

The length of side AY is calculated by applying the following formula as shown below.

Apply similar principle of congruent sides;

AX/CX = AY/CY

3p/4q / 1 = AY/(3p + q)

AY = 3p/4q(3p + q)

AY = 9p²/4q + 3p/4

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The value of the function n(x) = -1 -x + 4 when x = -2,0, and 5 are  respectively.

Function:

A function is defined as a relationship between a set of inputs having one output each.

It can be represented as f(x).

Given,

Here we have the function

n(x) = -1 -x + 4

And we need to find the value of the function when x takes the values -2, 0 and 5.

To solve this one, then we have to put the value of x on the function and then we have to simplify it in order to get the value of the function.

For that first we have to put the value of x = -2, then we get,

n(-2) = -1 - (-2) + 4

n(-2) = -1 + 2 + 4

n(-2) = -1 +6

n(-2) = 5

Now we have to apply the value of x as 0, then we get the value of function as,

n(0) = -1 - 0 + 4

n(0) = -1 + 4

n(0) = 3

Finally we gave to apply the value of x as 5, then we get the value of n(5) as,

n(5) = -1 - 5 + 4

n(5) = -6 + 4

n(5) = -2

Therefore, the resulting values are 5, 3 and -2.

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Answer:

Step-by-step explanation:

A system of equations

y = x -1 _ _ _ _ _ _(1)

y=-2x+5_ _ _ _ _ _(2)

we get,

x -1 = y

-(-2x +5 = y)

__________

3x -6 = 0

3x = 6

x = 6/3

x = 2

___________

y= 2-1

y= 1

We will solve this through graphical way

Graph both equations

Solution is

Graph attached

Answer:

2

Step-by-step explanation:

Step-by-step explanation:

8)

describe y in terms of x

y=5+x

so now replace y with terms of x

5+x+3x=37

4x=32

x=8

y=13

9)

do the same here

x=y+1

2y+x=19

2y+y+1=19

3y=18

x=6

y=7

A measure of goodness of fit for the estimated regression equation is the residual standard error (RSE)

It is a measure of goodness of fit for the estimated regression equation. It measures the average amount that the response variable (y) deviates from the estimated regression line, in the units of the response variable.

The RSE is calculated as the square root of the sum of squared residuals divided by the degrees of freedom. A smaller RSE indicates a better fit of the regression line to the data.

It represents the proportion of the variation in the dependent variable that is explained by the independent variable(s) in the model. The value of R-squared ranges from 0 to 1, with higher values indicating a better fit of the model to the data.

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The standard deviation lies in the range of 0 to 1. The numerical value of standard deviation can never be negative.

The standard deviation is a measure of amount of variation or dispersion of a set of values. When we compare two unequal observations, the result is always greater than zero i.e., always positive.

Standard deviation is the square root of the variance of the observations and the root always gives values either positive or zero, it can never be negative.

Therefore, the numerical value of the standard deviation can be positive. The value of standard deviation is always greater or equal to zero.

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The equation r = 2w, when solved to find, the amount of white fabric w, is solved as: w = r/2.

To solve an equation for a given variable, it implies that we have to make a variable the subject of the formula by moving the variable to one side of the equation using the appropriate properties of equality.

The equation that models the amount of red fabric needs as much as white fabric is given as, r = 2w, to solve for the equation for the amount of white fabric, w, do the following:

r = 2w [given]

Divide both sides by 2 to isolate variable w:

r/2 = 2w/2 [division property of equality]

r/2 = w

Rewrite

w = r/2

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By applying the Simplex Method or Big M Method to the given problem, the optimal solution for minimizing the objective function Z = 4x₁ + 2x₂ subject to the given constraints is obtained. The optimal solution for the given problem is Z = -27, x₁ = 6, and x₂ = 3.

To solve the given problem using the Simplex Method or Big M Method, we follow these steps:

Step 1: Convert the problem into standard form:

Introduce slack variables to convert inequalities into equations.

Express any unrestricted variables as the difference of two non-negative variables.

The given problem can be converted into the following standard form:

Minimize Z = 4x₁ + 2x₂

subject to:

3x₁ + x₂ + s₁ = 27

-x₁ - x₂ = 21

x₁ + 2x₂ + s₂ = 30

x₁, x₂, s₁, s₂ ≥ 0

Step 2: Set up the initial Simplex tableau:

Construct the initial tableau using the coefficients of the objective function and the constraints:

  | Cj   | x₁ | x₂ | s₁ | s₂ | RHS |

------------------------------------

Z  | -4   |  0 |  0 |  0 |  0 |  0  |

------------------------------------

s₁ |  0   |  3 |  1 |  1 |  0 | 27  |

------------------------------------

s₂ |  0   |  1 |  2 |  0 |  1 | 30  |

------------------------------------

Step 3: Perform iterations of the Simplex Method:

We start with the initial tableau and iterate until we reach an optimal solution. I will provide the final tableau directly:

| Cj   | x₁ |  x₂ |  s₁ |  s₂ |  RHS |

----------------------------------------

Z  | -2   | 0  |  0  |  1  | -2  |  -27 |

----------------------------------------

x₁ |  1   | 1  |  0  | -1  |  1  |   6  |

----------------------------------------

s₂ |  0   | 0  |  1  | -0.5|  0.5|   3  |

----------------------------------------

The optimal solution is obtained when all the coefficients in the Z row (except Cj) are non-positive. I

n this case, Z = -27, x₁ = 6, and x₂ = 3. The objective function is minimized when x₁ = 6 and x₂ = 3, resulting in Z = -27.

Therefore, the optimal solution for the given problem is Z = -27, x₁ = 6, and x₂ = 3.

Note: The steps provided above show the general process of solving a linear programming problem using the Simplex Method or Big M Method. The exact calculations and iterations may vary depending on the specific values and coefficients in the problem.

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Answer:

  (b)

Step-by-step explanation:

The hundredths place is immediately to the left of the thousandths place. In our base-10 number system, moving a digit to the left one place increases its value by a factor of 10.

The value of 7 in the hundredths place is 10 times the value of 7 in the thousandths place.

Answer:

The value of the 7 in the hundredth place is 10 times​ the value of the 7 in the thousandth place.

Step-by-step explanation:

Answer:

x = 6 , y = 18

Step-by-step explanation:

By adding up all the possible ways to distribute the coupon and subtracting it from the possible ways to distribute the 10 coupons to the 15 men, we can determine the total number of ways at least a woman can receive a coupon.

- The entire number of options for dividing the coupons among the 20 customers is the same as the total number of ways to choose a subset of 10 items from a set of 20.

In other terms, 20/10 = 20!/ 10!10 is the combinatorial number of 20 and 10.

- We must use the same calculation as above, but with a set of 15 items rather than 20, to get the total number of alternatives for distributing the coupons among the 15 males.

We now have 15/10, which is 15!/10!5! possibilities.

To ensure that at least one woman receives a coupon, we have 20/10 - 15/10 distribution options.

A combination is made up of r items chosen without replacement from a set of n items, where the order is irrelevant.

The amount of circular permutations of n other objects, taken r at a time, is nPr 2r if clockwise and anti-clockwise configurations are not considered to be distinct. Combinations are various groups or choices made from a variety of items, either all or some of them.

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One ounce of food contains average  about 28 grams of carbs.

One of the three macronutrients that the body needs for energy, carbohydrates can be found in a wide variety of foods. Sugar, starch, and fiber are the three elements that make up carbohydrates. Weight is measured in ounces, which weigh 28.35 grams. As a result, one ounce of food contains about 28 grams of carbs. Carbohydrates are crucial for supplying the body with the 4 calories per gram of energy it needs to function, fuel physical activity, and help with digestion. Foods like fruits, vegetables, grains, nuts, and dairy products all naturally include ounces of carbs. It is crucial to remember that there are several kinds of carbs, some of which are healthier than others.

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The complete question is

How many grams of carbs in an ounce of food ?

The approximate probability that one of the 1000 books published this week will contain almost 3 pages with errors is 0.414 or 41.4%. Note that this is an approximation because the Poisson distribution assumes independence between the trials, but errors may be correlated within a book or across books.

To solve this problem, we can use the Poisson distribution, which approximates the probability of rare events occurring over a large number of trials. In this case, the rare event is a page containing an error, and the large number of trials is the 1000 books published.
The average number of pages with errors per book is p * number of pages = 0.005 * 500 = 2.5. Using the Poisson distribution, we can find the probability of having almost 3 pages with errors in one book:
P(X = 3) = (e^(-2.5) * 2.5^3) / 3! = 0.143
This is the probability of having exactly 3 pages with errors. To find the probability of having almost 3 pages (i.e., 2 or 3 pages), we can sum the probabilities of having 2 and 3 pages:
P(X = 2) = (e^(-2.5) * 2.5^2) / 2! = 0.271
P(almost 3 pages) = P(X = 2) + P(X = 3) = 0.271 + 0.143 = 0.414
Therefore, the approximate probability that one of the 1000 books published this week will contain almost 3 pages with errors is 0.414 or 41.4%. Note that this is an approximation because the Poisson distribution assumes independence between the trials, but errors may be correlated within a book or across books.

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The caller function is do_twice().

The explanation for 3rd and 4th line is passed as the first argument to do_twice().

The reason for the 4th line we write add(add(x,y),add(x,y)) is used to pass the arguments to the function

In order to write function after return statement insted of (x+y+x+y )=30 use add() function

In programming, a function is a reusable block of code that performs a specific task. It takes inputs, processes them, and returns an output. The code you provided defines two functions: add(x, y) and do_twice(func, x, y).

The caller in this code is the print() function, which is used to display the result of the do_twice() function.

The third line defines the do_twice() function, which takes three arguments: a function (func), and two values (x and y). It then calls the function twice with the arguments (x, y), and returns the result.

In the fourth line, the add() function is passed as the first argument to do_twice(). The add() function takes two arguments (x and y), and returns their sum. So, when do_twice() calls add() twice with the arguments (a, b), it computes (a+b) + (a+b) = 2(a+b).

We could have written the return statement as return x + y + x + y instead of using the add() function twice, but using the add() function makes the code more modular and reusable.

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Answer:

b is you answer hope it helps you

The value of the additional data point is 36

To find the value of the additional data point, we can use the concept of the sample mean.

Given the data set: 23, 28, 20, 33, 42, 12, 19, 50, 36, 25, 19.

The sample mean of this data set is 26.5.

To find the value of the additional data point, we can use the formula for the sample mean:

(sample mean) = (sum of all data points) / (number of data points)

In this case, we have 11 data points in the original data set. Let's denote the value of the additional data point as x.

Therefore, we can set up the equation:

26.5 = (23 + 28 + 20 + 33 + 42 + 12 + 19 + 50 + 36 + 25 + 19 + x) / 12

Multiplying both sides of the equation by 12 to eliminate the fraction, we have:

318 = 282 + x

Subtracting 282 from both sides of the equation, we find:

x = 318 - 282

x = 36

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.

Answer:

6C2 = 15

# of ways to select two from the bag: 20C2 = 190

---

P(2 red) = 15/190 = 3/38

Step-by-step explanation:

Answer:

All angles are supplementary

Step-by-step explanation:

All are supplementary angles because they all add up to 180 degrees.

The variance for this sample of 5 scores with the sum of squared errors (deviations)  20 is 5.

Variance is a measure of the spread of the data around the mean. It can be calculated from the sum of squared deviations (SSE) as follows:

Variance = SSE / (n - 1)

where n is the number of scores in the sample.

In this case, n = 5 and SSE = 20, so the variance is:

Variance = 20 / (5 - 1) = 20 / 4 = 5

So the variance for this sample is "5".

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The minimum perimeter of a rectangle with an area of 80 ft2 is 56 ft. The dimensions of this rectangle would be 8 ft x 10 ft.

explanation: Let length be L and breadth be B of the rectangular room. A = L × B, given A = 80 ft² (Area of the room)The perimeter of the rectangle, P = 2(L + B) = 2L + 2BTo minimize P, we need to express one variable in terms of the other.

Let's consider L as the variable, and write B in terms of L from the given equation.=> B = (A/L)Therefore, P = 2L + 2B= 2L + 2(A/L) => P = 2(L² + 40/L)Differentiate P w.r.t L to find the critical point.= 2[(d/dL)(L²) + (d/dL)(40/L)]= 2(2L – 40/L²)For the critical point, dP/dL = 0=> 2L – 40/L² = 0=> L = ±2√10

Therefore, L = 2√10 (since L cannot be negative)Thus, B = (A/L) = 80/(2√10) = 4√10The dimensions of the room are 2√10 × 4√10 = 8.94ft × 35.76ft (rounded to the nearest hundredth).

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C. -6, -7, -8

\( \: \: \: \)

The equation of the line from the given figure is y=-7.

We need to find the equation of the line from the given figure.

The equation of a line is an algebraic form of representing the set of points, which together form a line in a coordinate system. The numerous points which together form a line in the coordinate axis are represented as a set of variables x and y to form an algebraic equation, which is referred to as an equation of a line.

From the given figure, we can see that the line is passing through the point (0, -7).

The slope (m) of the line is 0.

Put m=0 and (0, -7) in y=mx+c and simplify.

That is, -7=c

Now, substitute c=-7 in y=mx+c.

Thus, y=-7

Therefore, the equation of the line from the given figure is y=-7.

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As the sample size increases, the probability of a Type II error tends to decrease. Type II error occurs when we fail to reject a null hypothesis that is actually false.

It represents the probability of not detecting a true effect or difference between groups. The probability of committing a Type II error is influenced by various factors, including the level of significance (α), effect size, and sample size.

When the sample size increases, it provides more information and reduces the variability in the data. This increased precision improves the power of the statistical test, which is the ability to detect a true effect. With a larger sample size, the statistical test becomes more sensitive and has a higher chance of correctly rejecting the null hypothesis when it should be rejected. Consequently, as the sample size increases, the probability of a Type II error decreases.

In summary, by increasing the sample size, researchers can decrease the probability of a Type II error. A larger sample size enhances the power of the statistical test, increasing the likelihood of correctly detecting a true effect or difference.

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The reduced gradient is analogous to the residual for linear models.

In linear regression, the residual represents the difference between the observed values and the predicted values of the dependent variable. Similarly, in optimization, the reduced gradient represents the difference between the current solution and the optimal solution. It is a measure of how far the current solution is from the optimal solution in the direction of the search. By minimizing the reduced gradient, we can move closer to the optimal solution.

The reduced gradient is a widely used optimization technique in non-linear programming that allows for efficient computation of the descent direction at each iteration while accounting for constraints. It involves calculating a partial derivative of the objective function with respect to the variables that are not restricted by the constraints, and then projecting the resulting gradient onto the space defined by the constraints. The resulting vector is called the reduced gradient, and it points in the direction of the steepest descent that is feasible.

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Answer:

I am pretty sure the answer would be 8. if x is 1, then you need to multiply 8x1, which, as you may know, anything multiplied by 1 is the same as before, So, 8x1 is 8. I hope this helps!!

The set P consists of the elements {1, 4, 7, 10, 13, 16}, all of which form an arithmetic sequence with a common difference of 3.

What is roster method?

The roster method is a way of defining a set by listing its elements inside curly braces.

For example, the set A = {2, 4, 6, 8} is defined using the roster method, where the elements 2, 4, 6, and 8 are listed inside curly braces. This is a convenient way to specify small, finite sets.

In the set P, the first element is 1. To get the next element in the set, we add 3 to the previous element. So the second element in the set is 1 + 3 = 4.

Similarly, to get the third element in the set, we add 3 to the second element, which gives us 4 + 3 = 7. We can repeat this process to obtain the rest of the elements in the set.

Specifically, the next three elements in the set are obtained by adding 3 to the previous element:

The fourth element in the set is 7 + 3 = 10.

The fifth element in the set is 10 + 3 = 13.

The sixth element in the set is 13 + 3 = 16.

Therefore, the set P consists of the elements {1, 4, 7, 10, 13, 16}, all of which form an arithmetic sequence with a common difference of 3.

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Answer:

4

Step-by-step explanation:

(x1,y1)(x2,y2)

(2,8)   (0,0)

0-8 / 0-2 = -8/-2

simplify -8/-2 = 4

Answer:

4.

Step-by-step explanation:

Slope = (y2-y1)/(x2-x1)

-  that is rise / run.

We use the points (2, 8) and (2,0) ( - the last point is vertically below (2,8) and is on the x axis)

Here y2 = 8, y1 = 0, x2 = 2 and x1 = 0.

So the slope = (8-0)/(2-0)

= 4