The annual income of a sole proprietor of a grocery shop is Rs 10,00,000. If the tax is exempted up to Rs 4,50.000, what is his/her taxable income?​

According to the question The Simplex method to solve the following LP The optimal solution for the given LP is x₁ = 3, x₂ = 0, and the minimum value of z is -3.

To solve the given linear programming problem using the Simplex method, we first convert it into standard form. The objective function is to minimize z = -x₁ - 3x₂, subject to the constraints -x₁ + x₂ ≤ 3 and x₁ - 2x₂ ≤ 4, with the non-negativity conditions x₁, x₂ ≥ 0.

We set up the initial Simplex tableau with the coefficients and variables, as well as the right-hand side (RHS) values. The tableau is then modified through iterations to find the optimal solution.

In the first iteration, we choose the most negative coefficient in the z-row, which is -3 corresponding to x₂. We select the s₁-row as the pivot row since it has the minimum ratio of the RHS value (3) to the coefficient in the pivot column (1). We perform row operations to make the pivot element 1 and other elements in the pivot column 0. Therefore, the optimal solution for the given LP is x₁ = 3, x₂ = 0, and the minimum value of z is -3.

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The Simplex method is used to solve linear programming problems by iteratively improving the objective function value until the optimal solution is reached.

To solve the given linear programming problem using the Simplex method, we will follow these steps:

Step 1: Convert the problem into standard form:
  - Introduce slack variables, s₁ and s₂, for the two inequalities.
  - Rewrite the constraints as: -x₁ + x₂ + s₁ = 3 and x₁ - 2x₂ + s₂ = 4.
  - Introduce surplus variables, x₃ and x₄, for the negative variables in the objective function: z = -x₁ - 3x₂ + x₃ + x₄.

Step 2: Set up the initial tableau:
  - Create the initial simplex tableau by writing the coefficients of the decision variables and the right-hand side of the constraints.
  - Include the coefficients of the surplus variables, x₃ and x₄, in the objective function row.

Step 3: Perform the simplex method iterations:
  - Identify the pivot column by selecting the most negative coefficient in the objective function row.
  - Determine the pivot row by finding the minimum positive ratio between the right-hand side and the corresponding pivot column elements.
  - Perform row operations to make the pivot element equal to 1 and the other elements in the pivot column equal to 0.
  - Update the tableau by applying the row operations.

Step 4: Repeat the iterations until there are no more negative coefficients in the objective function row or the ratios become negative.

Step 5: Read the solution from the final tableau:
  - The optimal solution occurs when all coefficients in the objective function row are non-negative.
  - The values of the decision variables (x₁, x₂) are obtained from the corresponding columns in the tableau.
  - The optimal value of the objective function (z) is the negative of the value in the last column.

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Answer:

6.4 inches

Step-by-step explanation:

Area= (a+b)/2 x h

64 in^2= (8+12)/2 x h

= 20/2 x h

= 10 x h

64 in^2 / 10 = height of 6.4 inches

Answer:

Answer:

42

Step-by-step explanation:

30/5 + ( 9)(5)−32

= 6 + ( 9)(5)−32

= 6 + 45−32

= 51 − 32

= 51 − 9

= 42

hope I helped!!

Answer:

The specific surface area of soil and soil constituents can range from less than 0.1 m 2 g −1 (1 × 10 2 m 2 kg −1 ) for coarse sands to more than 800 m 2 g −1 (8 × 10 5 m 2 kg −1 ) for expandable clay minerals such as montmorillonite

The median of the given data is 52, the lower quartile (Q1) is 41, the upper quartile (Q3) is 74, and the interquartile range (IQR) is 33.

Median: 52

Q1: 41

Q3: 74

IQR: 33

1. Arrange the numbers in ascending order: 38, 41, 42, 47, 48, 51, 72, 74, 74, 77, 82, 129

2. Count the number of data points: 12

3. Calculate the median by adding the two middle numbers and dividing by two: (47 + 48) / 2 = 52

4. Calculate the lower quartile (Q1) by finding the median of the lower half of the data: 41

5. Calculate the upper quartile (Q3) by finding the median of the upper half of the data: 74

6. Calculate the interquartile range (IQR) by subtracting the lower quartile from the upper quartile: 74 - 41 = 33

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Answer:

$3.87

Step-by-step explanation:

$123.84 / 32 = $3.87

So, each individual person's lunch costs $3.87

Answer:

when dividing fractions folow these steps:

first, you need to switch the denom and num of the second fraction:

3/4 ÷ 1/3---> 3/4 ÷ 3/1

Next you just switch the sign of the negative to a multiplication sign and multiply:

3/4 ÷ 3/1---> 3/4 x 3/1

3/4 x 3/1 -----> 9/4

9/4, 2 1/4 - these are your answers. Either are correct

Step-by-step explanation:

Answer:

2 1/4

Step-by-step explanation:

30% off every item and an additional 10% off of an object is not equal to 40% discount on an object.

Given that, a store has a sale with 30% off every item. When you enter the store, you receive a coupon that states that you receive an additional 10% off.

The discount equals the difference between the price paid for and its par value. A discount is a kind of reduction or deduction in the cost price of a product.

Let us assume the cost of an object is $100.

If the 30% off an object, then the discount of the object= 30% of 100

=30/100 × 100=$30

The cost of the object =100-30=$70

Additional 10% off, then 10% of 70=10/100 ×70 =$7

The cost of the object=70-7=$63

Now, 40% discount of an object= 40% of 100

=40/100 ×100=40

The cost of the object =100-40=$60

Therefore, 30% off every item and an additional 10% off of an object is not equal to 40% discount on an object.

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Answer: A. -1

Explanation: 4-5/5-4= -1/1 = -1

Answer:

B

Step-by-step explanation:

Answer:

$4.20 Per month = $4.2/1month

Step-by-step explanation:

1 year = 12 months

Proportions:

12 months ⇒ $48.24

1 month ⇒ $P

P = 48.24*1/12

P = $4.2

The inequality that represents the problem is x < 100 which means that Britney wants to spend less than $100 at restaurants  in June.

Inequality:

In math, inequality defines the non equal relationship between the expression.

Given,

Britney sets a limit on how much money she can spend at restaurants during the month of June. She divides the total amount evenly among the 5 times she expects to go to restaurants. Britney determines she should spend less than $20 each time.

Here we need to find the inequality that refers the given problem.

Let x represent how much Britney wants to spend at restaurants in June.

Here we know that, the number of time she goes in the restaurant is 5.

And the amount limit for each time is less than $20.

So, it can be written as,

=> x/5 < 20

While we solve the inequality then we get

=> x < 100

Therefore, Britney wants to spend less than $100 at restaurants in June.

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Answer:

V = £21,012.50

Step-by-step explanation:

Compound interest formula

\(\sf A=P(1+\frac{r}{n})^{nt}\)

where:

Given:

Substituting given values into the formula:

\(\sf \implies V=20000(1+\frac{0.025}{1})^{(1 \times 2)}\)

\(\sf \implies V=21012.5\)

Answer:

(If you like this answer i would appreciate if u give brainliest but otherwise, i hope this helped ^^)

Step-by-step explanation:

The correct statement that describes how the slope relates to the height of the water in the pool is:

The height of the water increases 2 inches per minute.

The slope of the line represents the rate of change of the height of the water with respect to time. In this case, since the slope is 2, it indicates that for every minute that passes, the height of the water in the pool increases by 2 inches.

The coordinates of the point that corresponds to -π/3 on the unit circle are (x, y) = (1/2, √3/2)

A unit circle is a circle in which the value of the radius is equal to 1 unit.

The coordinates of a point with angle Ф on a unit circle are given by

To find the coordinates of the point that corresponds to -π/3 on the unit circle, since we have the coordinates of a point on a unit circle as

substituting Ф = -π/3 into both equations, we have that the x - coordinate is

Also, we have that the y - coordinate is

So, the coordinates of the point are (x, y) = (1/2, √3/2)

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a. The table value of z 0.99 is given as 2.58.

b. we use σ = 2.30 minutes.

c. The value of Z is given as 0.609.

d. The confidence interval is (23.391, 24.609) minutes.

a) To find the z-score for a 0.99 confidence interval, we need to find the z-score that leaves 0.5% (since it's two-tailed, we split the 1% or 0.01 of the data that's not within the confidence interval into two) in each tail. The z-score for 0.995 (0.5% in the upper tail) is approximately 2.58 in standard normal distribution tables. So, Z_0.99 is 2.58.

b) Therefore, we use σ = 2.30 minutes.

c) The standard error of the mean (SE) is given by σ/√n, where n is the sample size.

Here, σ = 2.30 minutes and n = 95.

Therefore, SE = σ/√n

= 2.30/√95

= 0.236 minutes.

Multiply this by the z-score to find Z * σ/√n.

Therefore, Z * σ/√n = 2.58 * 0.236 ≈ 0.609.

d) The 0.99 confidence interval for μ

Here, x is the sample mean which is 24 minutes.

So the confidence interval is approximately

= (24 - 0.609, 24 + 0.609)  

= (23.391, 24.609) minutes.

This is the range of values we are 99% confident that the true population mean (μ) falls in.

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The rule which describe the composition of transformations that

maps ΔBCD to ΔB"C"D" is:

Reflection across the y-axis composition translation of 6 units x,

negative 5 units y ⇒ last answer

Step-by-step explanation:

Let us revise the reflection across the y-axis , horizontal translation

and vertical translation

1. If point (x , y) is reflected across the y-axis, then its image is (-x , y)

2. If point (x , y) is translated h units to the right, then its image is

  (x + h , y), if translated h units to the left, then its image is (x - h , y)

3. If point (x , y) is translated k units up, then its image is (x , y + k),

  if translated k units down, then its image is (x , y - k)

∵ The vertices of triangle BCD are (1 , 4) , (1 , 2) , (5 , 3)

∵ The vertices of triangle B'C'D' are (-1 , 4) , (-1 , 2) , (-5 , 3)

∵ The x-coordinates of the vertices of Δ B'C'D' have the same

  magnitude of x-coordinates of Δ BCD and opposite signs

∴ Δ B'C'D' is the image of Δ ABC after reflection across the y-axis

∵ The vertices of triangle B'C'D' are (-1 , 4) , (-1 , 2) , (-5 , 3)

∵ The vertices of triangle B''C''D'' are (5 , -1) , (5 , -3) , (1 , -2)

∵ The image of -1 is 5 and the image of -5 is 1

∴ The x-coordinates of the vertices of triangle B'C'D' are added by 6

∵ The image of 4 is -1 , image of 2 is -3 and the image of 3 is -2

∴ The y-coordinates of the vertices of triangle B'C'D' are subtracted

  by 5

∴ Δ B"C"D" is the image of Δ B'C'D' by translate 6 units to the right

 and 5 units down ⇒ (x + 6 , y - 5)

The rule which describe the composition of transformations that

maps ΔBCD to ΔB"C"D" is:

Reflection across the y-axis composition translation of 6 units x,

negative 5 units y

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The composition of transformations that maps BCD to B"C"D" is described by the following rule:

Composition translation of 6 units x, negative 5 units y across the y-axis last response

Let us rewrite the y-axis reflection, horizontal translation, and vertical translation.

1. If point (x, y) is mirrored across the y-axis, the image of that point is (-x , y)

2. If point (x, y) is translated h units to the right, its image is (x + h, y), and if it is translated h units to the left, its image is (x + h, y) (x - h , y)

3. If point (x, y) is translated k units up, its image is (x, y + k), but if it is translated k units down, its image is (x , y - k)

∵ Triangle BCD has (1, 4) vertices, (1, 2) vertices, and (5, 3) vertices. Triangle B'C'D' has (-1, 4) vertices, (1, 2) vertices, and (5, 3) vertices. The x-coordinates of the B'C'D' vertices have the same magnitude as the x-coordinates of BCD and opposite signs. B'C'D' is the picture of ABC after it has been reflected across the y-axis.

The vertices of triangle B'C'D' are (-1, 4), (-1, 2), (-5, 3), (1, -2)

The vertices of triangle B"C"D" are (5, -1), (5, -3), (1, -2)

The x-coordinates of the triangle B'C'D' vertices are added by 6.

The image of 4 is -1, the image of 2 is -3, and the image of 3 is -2.

The y-coordinates of triangle B'C'D' vertices are subtracted by 5.

∴ Δ B"C"D" is the image of Δ B'C'D' by translating 6 units to the right

and 5 units down ⇒ (x + 6 , y - 5)

The rule which describe the composition of transformations that

maps ΔBCD to ΔB"C"D" is:

Reflection across the y-axis composition translation of 6 units x,

negative 5 units y

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The information shows that f(4)=f(30) tells us that the weight of a particular female panda at 4 years old is the same as her weight at 30 years old.

It is a mathematical expression, rule, or law that establishes the relationship between an independent variable and a dependent variable (the dependent variable).

In this case, Dr. Coleman is a zoologist who studies giant pandas. Giant pandas are very tiny when they are born but grow to be quite large. The function f(x) gives the weight, in pounds, of a particular female panda when she was x years old.

The function illustrated shows that the weights are the same.

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Explanation:

The Conditional reasoning and logical equivalence of the statements could read;

1. If the investigation continues, then new evidence is brought to light.

C ⇒ N

2. If new evidence is brought to light, then several leading citizens are implicated.

N ⇒ I

3. If several leading citizens are implicated, then the newspapers stop publishing the case.

I ⇒ S

4. If continuation of the investigation implies that the newspaper stop publicizing the case, then the bringing to light of new evidence implies that the investigation continues.

C ⇒ S: ⇒ N ⇒ C

5. The investigation does not continue. Therefore, new evidence is not brought to light.

not C ⇒ not N

To find various values related to the vectors (u, v) and (kv, w), such as cos, ||v||, d(u, v), and ||u - kv||, within the range C[-1,1].

(i) To find cos, we need to compute the dot product of the vectors (u, v) and divide it by the product of their magnitudes.
(ii) To determine kv, we scale the vector v by a factor of k, and then calculate the dot product with w.
(c) Since C[-1,1], we can infer that the cosine of the angle between the two vectors is within the range [-1, 1].
(iii) Adding the vectors (u + v) results in a new vector.
(iv) The magnitude of vector v, denoted as ||v||, can be found using the Pythagorean theorem.
(v) The distance between vectors u and v, represented as d(u, v), can be calculated using the formula for the Euclidean distance.
(vi) To find the magnitude of vector u - kv, we subtract kv from u and compute its magnitude using the Pythagorean theorem.

The angle between the vectors f(x) = x + 1 and g(x) = x² can be determined by finding the angle between their corresponding direction vectors. The direction vector of f(x) is (1, 1), while the direction vector of g(x) is (1, 2x). By calculating the dot product of these vectors and dividing it by the product of their magnitudes, we can find the cosine of the angle.


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Answer:

y = 14

Step-by-step explanation:

\(y = 5x + 4\)

When x = 2:

\(y = 5 \times 2 + 4\)

\(y = 14\)

That's it. :)

Answer:

C

Step-by-step explanation:

Answer:

(3,4), (4,-3)

Step-by-step explanation:

When finding a point on a graph, do the x-axis first, then the y-axis. For this equation, move three to the right on the x-axis, then move upward 4 times to get to the point. Or move up 4 times, then 3 to the right. Hope this helps!

For the given graph, the gradient of the given blue line in the graph is equal to 2.

As given in the question,

For the given graph,

Consider two pairs of coordinates on the blue line of the given graph,

( x₁ , y₁ ) = ( 2, 2 )

( x₂ , y₂ ) = ( 3, 4 )

Gradient is nothing but slope of the line

Formula to calculate the gradient of the given blue line of the graph is given by:

Gradient = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substitute the value in the formula we get,

Gradient = ( 4 - 2 ) / ( 3 - 2 )

              = 2 / 1

              = 2

Therefore, for the given graph, the gradient of the given blue line in the graph is equal to 2.

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Answer:

A

Step-by-step explanation:

it is A for every output y , there is only one input x

Answer:

A

Step-by-step explanation:

Because all the x-intercepts are different. Whereas all the other ones have repeats of numbers in the x-intercepts.

The area of pyramid base with a dimension of x + 2 and x - 1 is given as x² + x - 2

An equation is an expression that shows the relationship between two or more numbers and variables.

Let us assume that the base of the pyramid has a dimension of x + 2 and x - 1, hence:

Area of pyramid base = (x + 2)(x - 1) = x² + x - 2

The area of pyramid base with a dimension of x + 2 and x - 1 is given as x² + x - 2

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Answer:

D)6 x squared StartRoot 3 EndRoot units2

Step-by-step explanation: on edge

A quartic polynomial with a negative leading coefficient

scaled 1/x function with horizontal offset

The wiggles of section 1 can be attributed to a number of different functions. Perhaps the simplest is a 4th-degree polynomial. In order to have downward-trending end behavior, it would need to have a negative leading coefficient.

__

The curve of section 2 looks like it might be a scaled and translated version of 1/x, or it could be an exponential function. The latter would be expected to approach the horizontal asymptote more quickly than shown here, so we prefer a version of 1/x.

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Answer: x = 157

Step-by-step explanation:

\(1056=6\left(x+19\right)\)

Switch sides:

\(6\left(x+19\right)=1056\)

Divide both sides by 6:

\(\frac{6\left(x+19\right)}{6}=\frac{1056}{6}\)

Simplify:

\(x+19=176\)

\(x+19-19=176-19\)

\(x=157\)

From the given options, it appears that option C, \( X = (\bar{A} \cdot \bar{B}) + (B \cdot C) \), best describes the action of the circuit based on the logical operations performed.

To determine which of the given Boolean equations describes the action of the circuit, let's analyze each equation step by step.

A. \( X = (\overline{A \cdot B}) + (B \cdot C) \)

In this equation, \( X \) is the output of the circuit. The first term, \( (\overline{A \cdot B}) \), represents the negation of the logical AND operation between \( A \) and \( B \). The second term, \( (B \cdot C) \), represents the logical AND operation between \( B \) and \( C \). The two terms are then summed using the logical OR operation.

B. \( X = (A \cdot B) \cdot (B + C) \)

In this equation, \( X \) is the output of the circuit. The first term, \( (A \cdot B) \), represents the logical AND operation between \( A \) and \( B \). The second term, \( (B + C) \), represents the logical OR operation between \( B \) and \( C \). The two terms are then multiplied using the logical AND operation.

C. \( X = (\bar{A} \cdot \bar{B}) + (B \cdot C) \)

In this equation, \( X \) is the output of the circuit. The first term, \( (\bar{A} \cdot \bar{B}) \), represents the negation of \( A \) ANDed with the negation of \( B \). The second term, \( (B \cdot C) \), represents the logical AND operation between \( B \) and \( C \). The two terms are then summed using the logical OR operation.

It's important to note that without additional context or a specific circuit diagram, we can't definitively determine the correct equation for the circuit. The given equations represent different logic configurations, and the correct equation would depend on the specific circuit design and desired behavior.

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Step-by-step explanation:

A method for this would be the tree diagram

20

/. \

10 x 2 ( u circle 2,times with 1 will times into itself)

/ \. (nothing goes into 2)

5x2 (same goes for 5 and the rest)

5x2x2= 20

3. (cant times into itself)

so 2x5x3 = 30

LCM = 30

The answer is B Your welcome!!!!

To determine whether the series converges or diverges, we need to analyze the given series. The series is:

Σ (5^n / (4n - 2)), from n = 1 to infinity.

To check for convergence, we can apply the Ratio Test, which involves finding the limit of the ratio between consecutive terms. Let's denote the term a_n as (5^n / (4n - 2)). Then, we'll compute the limit as n approaches infinity:

lim (n→∞) (a_(n+1) / a_n) = lim (n→∞) ((5^(n+1) / (4(n+1) - 2)) / (5^n / (4n - 2)))

Simplifying this expression, we get:

lim (n→∞) (5^(n+1) / 5^n) * ((4n - 2) / (4(n+1) - 2))

The first part of the limit simplifies to:

lim (n→∞) 5 = 5

The second part of the limit becomes:

lim (n→∞) ((4n - 2) / (4n + 2)) = 1

Multiplying both limits, we get:

5 * 1 = 5

Since the limit is greater than 1, the Ratio Test indicates that the series diverges.

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