In how many months the amount of Rs1000 at the rate of 10%will be RS1200
​

17. The equation can be rewritten as 2x²-8x+1=0.

18. The axis of symmetry is x = 5. The parabola opens up and has a maximum at the vertex (5, 6). The quadratic equation has two solutions, x = 4 and x = 6.

17.

The equation can be rewritten as 2x²-8x+1=0.

Vertex:

The vertex is (4, -1). A minimum.

Axis of symmetry:

The axis of symmetry is x = 4.

The parabola opens up.

The graph has 1 solution.

18. How many solutions does the quadratic

have?

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17. The equation can be rewritten as 2x²-8x+1=0. 18. The axis of symmetry is x = 5. The parabola opens up and has a maximum at the vertex (5, 6). The quadratic equation has two solutions, x = 4 and x = 6.

17. The equation can be rewritten as 2x²-8x+1=0.

Vertex:

The vertex is (4, -1). A minimum.

Axis of symmetry:

The axis of symmetry is x = 4.

The parabola opens up.

The graph has 1 solution.

18. The coefficient of x, which is -10, is multiplied by two to determine the axis of symmetry, which is x = 5.

This is due to the fact that the axis of symmetry is always located halfway between the two x-intercepts.

The parabola widens, indicating that the vertex is where its maximum is located. The vertex is (5, 6), which is determined by solving for y while changing x = 5 in the equation.

There are two answers to the quadratic equation: x = 4 and x = 6. The equation must be made equal to 0 in order to get the solutions.

Either factoring or applying the quadratic formula can be used to accomplish this.

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Based on given data, Mean is 4, missing number can be 4,2,7., So the arrangement is c,4,6,8.

The mean of numbers is the average value of given numbers.

Given numbers are 4,2,5

Mean is 4

Mean = sum of numbers/ total number of values given

4 = (4+2+5+x) /4

16 = 11 +x

x = 5

Therefore the missing number is 5.

  Mode is the number which is most frequently repeated in a list of numbers.

Given numbers are 4,2,7 and x

Mode is given as 2

So x can be any number from the given values since any number can be repeated twice.

Therefore missing number can be 4,2,7.

 The median of the set is the middle number after the numbers are arranged from least to greatest.

There are four numbers given. So the median is the average of middle numbers.

To get the median of 5 the middle numbers should be 4 and 6.

So the arrangement is c,4,6,8

Therefore the missing number can be any number less than or equal to 4.

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Answer: The empirical rule states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, approximately 95% falls within two standard deviations, and approximately 99.7% falls within three standard deviations.

So, using the empirical rule, we can say that approximately 99.7% of housing prices in this small town fall within 3 standard deviations of the mean.

To find the range of prices that this corresponds to, we can use the following formula:

(mean - (3 x standard deviation), mean + (3 x standard deviation))

Plugging in the given values:

(157,000 - (3 x 8,000), 157,000 + (3 x 8,000))

(141,000, 173,000)

So, approximately 99.7% of housing prices in this small town are between $141,000 and $173,000.

Step-by-step explanation:

Step-by-step explanation:

To show that the function f(x,y) = 2x^2 − xy is differentiable at any point (a,b), we need to show that the partial derivatives of f with respect to x and y exist and are continuous at that point.

The partial derivative of f with respect to x is:

∂f/∂x = 4x - y

The partial derivative of f with respect to y is:

∂f/∂y = -x

We can see that both of these partial derivatives are continuous functions of x and y and are defined for all (x,y) in the domain of f. Therefore, f is differentiable at any point (a,b).

The derivative of f at (a,b) is the gradient vector of f evaluated at (a,b), which is given by:

Gradient vector of f(a,b) = ∇f(a,b) = ( ∂f/∂x, ∂f/∂y ) = (4a-b, -a)

So the derivative of f at (a, b) is (4a-b, -a).

The total cost of his groceries in dollars and cents is 91.35 on 8.75% sales tax.

A sales tax is a fee that is paid to the government when specified goods and services are sold. Typically, laws permit the vendor to charge the customer the tax at the time of purchase. Use taxes are typically used to describe taxes on goods and services that consumers pay directly to a governing authority.

Sales tax is an indirect fee that is always applied at the point of exchange or purchase and is calculated as a percentage of the item's worth. Retail, manufacturing, wholesale, use, and value-added taxes are the various types of sales taxes (VAT). Note: As of July 1, 2017, the Goods and Services Tax (GST) has taken the place of the Sales Tax.

Sales tax = 8.75%

⇒  8.75/100 × 84

⇒ 7.35

Total price = 7.35 + 84

⇒ $ 91.35

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a. The total cost C as a function of the number of units produced is C = $12.13x + $92,000

b. The revenue R as a function of the number of units sold is R = $17.10x

c. The profit P as a function of the number of units sold is P = $5.97x - $92,000

(A) The total cost for a business is the sum of the variable cost and the fixed costs.

The variable cost per unit is $12.13, so the total variable cost for x units produced is $12.13x.

The fixed costs are $92,000 and do not change with the number of units produced, so the total cost C as a function of the number of units produced is given by -

C = $12.13x + $92,000

(B) The revenue is the total amount of money earned from selling the product. The product sells for $17.10 per unit, so the revenue R as a function of the number of units sold is given by -

R = $17.10x

(C) The profit is the difference between the revenue and the total cost. Using the equations from (A) and (B), the profit P as a function of the number of units sold is given by -

P = R - C = $17.10x - ($12.13x + $92,000) = $5.97x - $92,000

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A histogram of the weights of all 2,000 athletes would be a graph with two normal distributions, one for offense and one for defense.

The offense distribution would have a bell shaped curve centered at 200 pounds, with a range of 150-250 pounds. The defense distribution would have a bell shaped curve centered at 300 pounds, with a range of 250-350 pounds. Each of the distributions would have the same area, representing 1,000 athletes in each group. The total area of the histogram would represent the combined 2,000 athletes with weights ranging from 150-350 pounds. It is important to note that the histogram would not represent the exact weights of the athletes, but rather the relative frequency of each weight.

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The number of selections that will contain no defective printers can be found using the nCr formula as well, but with n being the number of non-defective printers (34) and r being the number of items selected (2). So nCr = 34!/(2!(34-2)!) = 34!/(2!32!) = 5,832.

(a) There are 6,632 selections that can be made.

(b) There are 5,832 selections that will contain no defective printers.

(a)The number of selections can be found using the nCr formula: nCr = n!/(r!(n-r)!), where n is the total number of items (42) and r is the number of items selected (2). So nCr = 42!/(2!(42-2)!) = 42!/(2!40!) = 6,632.

(b) The number of selections that will contain no defective printers can be found using the nCr formula as well, but with n being the number of non-defective printers (34) and r being the number of items selected (2). So nCr = 34!/(2!(34-2)!) = 34!/(2!32!) = 5,832.

There are 6,632 selections that can be made when two printers are chosen from a shipment of 42, including 8 that are defective. Out of these selections, 5,832 will contain no defective printers.

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BFS has an exponential space complexity with respect to d because it stores all the nodes at the same depth level before moving on to the next level

DFS doesn't have an exponential space complexity with respect to d because it only stores the nodes that need to be visited next.

The space complexity of breadth-first search (BFS) is O([tex]b^d[/tex]) and the space complexity of depth-first search (DFS) is O(bd), where b is the maximum branching factor of the search tree and d is the maximum depth of the tree.

The reason for the difference in the space complexities is that BFS uses a queue to store the nodes to be visited, while DFS uses a stack.

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The greatest common factor (GCF) of two or more expressions is the largest monomial that divides each expression exactly.

To find the GCF of 36x^2 and 18xy^2, we can factor out the greatest common factor from each expression.

The prime factorization of 36 is 2^2 * 3^2 and of 18 is 2*3^2

The GCF of 36x^2 and 18xy^2 is 18x^2y^2 = 2*3^2 * x^2 * y^2

So, the GCF of 36x^2 and 18xy^2 is 18x^2y^2

Answer:

18xy

Step-by-step explanation:

By applying the rule of sin, it can be concluded that the length of the sides of the triangle is 15.48 cm, 39.68 cm, and 44.84 cm.

Triangle is a 2D shape that is bounded by three sides and has three vertices. The perimeter of a triangle is the sum of the lengths of the three sides of the triangle.

Perimeter = a + b + c, where a, b, and c are the sides of the triangle

One of the most important properties of a triangle is that the sum of the angles in a triangle equals 180°.

The rule of sin describes the ratio of the angles corresponding to the side lengths of the sine function.

a / sin A = b / sin B = c / sin C, where A, B, and C are the angles of the triangle

If the ratio of the angles is 1 : 3 : 5 and let x be the smallest angle, then we can put this information into the following equation:

Total angle = A + B + C

           180° = x + 3x + 5x

           180° = 9x

                x = 20°

Then we can calculate the other angles:

A = 20°

B = 3x = 3 * 20° = 60°

C = 5x = 5 * 20° = 100°

Now we put the value of A, B, and C into the rule of sin equation:

  a / sin A = b / sin B

a / sin 20° = b / sin 60°

   a / 0.34 = b / 0.87

              a = 0.34 * b / 0.87

              a = 0.39b

    c / sin C = b / sin B

c / sin 100° = b / sin 60°

    c / 0.98 = b / 0.87

               c = 0.98 * b / 0.87

               c = 1.13b

Then we go back to the perimeter formula:

perimeter = a + b + c

          100 = 0.39b + b + 1.13b

          100 = 2.52b

              b = 39.68 cm

Then we can calculate the length of the other sides, a and c:

a = 0.39b

  = 0.39 * 39.68

  = 15.48 cm

c = 1.13b

  = 1.13 * 39.68

  = 44.84 cm

Thus, the length of the sides of the triangle is 15.48 cm, 39.68 cm, and 44.84 cm.

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The area of the shaded region and the length of the boundary is 86.59 cm^2 and 44cm respectively.

A semicircle is a shape that is half of a circle. It is defined by a center point and a radius, and it is made up of an arc that is 180 degrees of the full circle.

The circumference of a semicircle is given by the formula: C = π * d, where C is the circumference and d is the diameter of the semicircle.

Diameter of the biggest semi-circle = 14cm.

Diameter to two small semi-circles = 3.5cm.

Diameter of other semi-circle = 14 - 2(Diameter to two small semi-circles)

                                                 =14 - 7 cm

                                                = 7cm

Length of boundary = Circumference of bigger semi-circle + Circumference of small semi-circle + 2 ×circumference of the smaller semi-circles

∴Length of boundary= [tex]\pi R+\pi r_{1}+2\pi r_{2}[/tex]

=> Length of boundary=[tex]\pi (R+r_{1})+2\pi r_{2}[/tex]

=> [tex]\frac{22}{7}(7+3.5)+2X\frac{22}{7}X1.75[/tex]

=> 44cm

Area of the biggest semi-circle = [tex]\frac{1}{2}\pi (7)^{2} cm^{2}[/tex]

Area of two small semi-circles = [tex]\pi (1.75)^{2}cm^{2}[/tex]

Area of other semi-circle= [tex]\frac{1}{2}\pi (3.5)^{2}cm^{2}[/tex]

Area of shaded region= π×(24.5−3.0625+12.25)

                                      =π×27.5625 cm^2 =86.59 cm^2

Therefore, the area of the shaded region and the length of the boundary is 86.59 cm^2 and 44cm respectively.

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Triangles are shown to be congruent by the statement that "Angles are congruent by vertical angles."

Triangles are said to be congruent if, under a correspondence, two of a triangle's sides and the angle that connects them are equal to two of another triangle's sides and the angle that connects them.

Given two triangles, Where the base of these triangles are same

And also given that the two angles are the same.

Since,

Two intersecting lines form a pair of vertical angles. The vertical angles are opposite angles with a common vertex (which is the point of intersection).

Thus, the third angle is also equal

From AAS:

AAS stands for Angle-Angle-Side. When two angles and a non-included side of a triangle are equal to the corresponding angles and sides of another triangle, then the triangles are said to be congruent

Therefore. "Angles are congruent by vertical angles" is used to show the triangles are congruent by AAS,

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The length of the rectangle be 12 and Width be 6.

With four sides, four corners, and four right angles (90°), a rectangle is a closed 2-D object. A rectangle's opposing sides are equal and parallel. Since a rectangle is a two-dimensional form, it has two dimensions: length and width.

A quadrilateral is a shape with two opposed sides that are equal and parallel. It is a polygon with four sides and four 90-degree angles. The shape of a rectangle is two dimensional.

4 sides, 4 corners, and 4 right angles make up the 2D shape of a rectangle. A rectangle's diagonal sides are equal in length, with one pair being longer than the other.

Let the equation be L = 2W and

P = 36 = 2 × ( L + W )

simplifying the equation, we get

⇒ 18 = L + W

⇒ 18 = 2W + W

⇒ 6 = W and L = 2 × W = 2 × 6 = 12

Therefore, the length of the rectangle be 12 and Width be 6.

The complete question is:

The length of a rectangle is twice the width. The perimeter of the rectangle is 36. What is the length and width of the rectangles?

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The area of the glacier at the beginning of the last year is given as follows:

56.31 km².

The area of the glacier is obtained applying the proportions in the context of this problem.

The current area is given as follows:

56.20 km².

The percentage of this area relative to the area at the beginning of the last year is given as follows:

100 - 0.2 = 99.8% = 0.998.

Hence the area at the beginning of the last year is obtained as follows:

0.998x = 56.20

x = 56.20/0.998

x = 56.31 km².

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The coordinate of the circumcentre of ΔABC is (-1, 0.15).

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

Triangle ABC.

A = (-5, -4)

B = (3, -4)

C = (-1, 6)

The circumcentre of a triangle is the point where the perpendicular bisectors of the sides of the triangle intersect.

Now,

Let the circumcentre be M = (x, y).

The length from each side of the triangle to the circumcentre is equal.

So,

AO² = BO² = CO²

Now,

AO² = BO²

(x + 5)² + (y + 4)² = (x - 3)² + (y + 4)²

x² + 10x + 25 + y² + 8y + 16 = x² - 6x + 9 + y² + 8y + 16

10x + 25 = -6x + 9

16x + 16 = 0

x + 1 = 0

x = -1

BO² = CO²

(x - 3)² + (y + 4)² = (x + 1)² + (y - 6)²

x² - 6x + 9 + y² + 8y + 16 = x² + 2x + 1 + y² - 12y + 36

-6x + 9 + 8y + 16 = 2x + 1 - 12y + 36

20y - 8x + 25 - 36 = 0

20y - 8x - 11 = 0

20y = 11 + 8x

y = (11 + 8x)/20

y = (11 - 8)/20

y = 3/20

y = 0.15

Thus,

Circumcentre M = (-1, 0.15)

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The percent by mass of a solution is  29.21.

To calculate the percent by mass of a solution, divide the mass of the solute (13.687 grams) by the total mass of the solution (46.833 grams). Then, multiply this value by 100 to get the percent.

% by mass = (mass of solute/total mass of solution) x 100

% by mass = (13.687/46.833) x 100 = 29.21.This calculation can be used to determine the amount of a solute in a given solution. It is important to know the percent by mass of a solution in order to make sure the solution is composed of the desired amount of solute. Knowing the percent by mass can also be used to compare the solutions of different concentrations.

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Null hypothesis for the investigation Ha=0.38

The null hypothesis is a kind of hypothesis which explains the population parameter whose purpose is to test the validity of the given experimental data.

This hypothesis is either rejected or not rejected based on the viability of the given population or sample.

In other words, the null hypothesis is a hypothesis in which the sample observations results from the chance.

It is said to be a statement in which the surveyors wants to examine the data. It is denoted by H0.

Here, the hypothesis test formulas are given below for reference.

The formula for the null hypothesis is:

H0:  p = p0

The formula for the alternative hypothesis is:

Ha = p >p0, < p0≠ p0

The formula for the test static is:

[tex]z=\frac{p-p0}{\sqrt{\frac{p0(1-p0)}{n} } }[/tex]

Remember that,  p0 is the null hypothesis and p – hat is the sample proportion.

38 percent of people living in region w have the blood type o positive.

w region

38% - o positive

x region

100 random sample

35 o positive

means 35/ 100*100

35% 0 positive

a hypothesis test to investigate whether the percent of people in region x with o positive blood is different from that of in region w

The formula for the null hypothesis is:

H0:  p = p0 =0.38

Ha = p >p0, < p0≠ p0

Ha=0.38

Null hypothesis for the investigation Ha=0.38

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Answer: The slope between two points (x1, y1) and (x2, y2) is given by the formula:

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

We are given that the slope between (8, y) and (14, -13) is -2/3. So we can use this information to set up the equation:

-2/3 = (-13 - y) / (14 - 8)

To find y, we can solve for y:

-2/3 = (-13 - y) / 6

-2 = -13 - y

y = 11

So the value of y is 11.

Step-by-step explanation:

The percentage of scores below 112 is equal to 78.81.

Let X represent a test's score. X is regularly distributed, hence

P(X < 112)

= P[(X - 100)/15 < (112 - 100)/15]

= P[ SNV < 0.8] .8]

SNV stands for Standard Normal Variable,

A normal distribution with a mean of 0 and a standard deviation of 1 is the standard normal distribution. When referring to a random variable that has this typical normal distribution, the letter Z is frequently employed.

z = (X – μ) / σ

If X is a normal random variable, represents its mean, and represents its standard deviation. The normal distribution formula is also available here.

and the value is 0.7881.

Thus, the percentage of scores below 112 is equal to 78.81.

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The full question

If the scores for a test have a mean of 100 and a standard deviation of 15, what is the percentage of scores that will fall below 112? Assuming a normal distribution

(a) The number of four-digit numbers with distinct digits in {1, 2, 3, 4, 5, 6} is 6543 = 360.

(b) The number of four-digit numbers in {1, 2, 3, 4, 5, 6} that are even is (3543)/2 = 270.

(c) The number of four-digit numbers in {1, 2, 3, 4, 5, 6} that are even and have distinct digits is (321*1)/2 = 3.

For (a) the total number of four-digit numbers with digits in {1, 2, 3, 4, 5, 6} is 6 options for the first digit, 5 for the second, 4 for the third and 3 for the last one. So, 654*3 = 360.

For (b) since digits in {1, 2, 3, 4, 5, 6} the even digits are 2,4,6. for each of the even digits we have 5 options for the second digit, 4 for the third and 3 for the last one. In total, we have 354*3= 270 even numbers.

For (c) The total number of four-digit numbers with distinct digits that are even is 211 = 2, since there are 2 even digits in {1,2,3,4,5,6} and only one of each can be used. However, this count is double-counting the numbers, so we divide by 2 to get 3.

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An example of a question that can be solved using the associative method is : (2/5) * (3/4) * (5/6)

One example of a problem involving multiplication of fractions that can be made easier using the associative property is:

(2/5) * (3/4) * (5/6)

Using the associative property of multiplication, we can change the grouping of the fractions to make the problem easier. The associative property states that the way we group the numbers being multiplied does not change the product. For example,

(2/5) * (3/4) * (5/6) = (2/5 * 3/4) * (5/6) = (6/20) * (5/6) = 30/120

This simplification makes it easier to see that the final answer is 1/4.

By using the associative property, we can first multiply (2/5) * (3/4) = (6/20) which is easier to cancel out the common factor and then multiply it with (5/6) = (5/6) * (6/20) = (30/120) = 1/4 which is the final answer

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The number of feet that should be on each side of the painting is 4 feet.

An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.

Let x be the number of feet on each side of the painting.

The equation to determine the number of feet on each side of the painting would be:

x + 5 + x = 13

So x = (13-5)/2

x = 4

So there should be 4 feet on each side of the painting.

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The domain is [0,100].[0,100]. The range is [0,1500] [0,1500]

(a) To find the cost of making 25 items substitute

x=25 in the equation

=10+500(25)

=10(25)+500(25)=750

c(x)=10x+500

c(25)=10(25)+500

c(25)=750

the cost of making 25 items is

$750

(b)

Since the maximum cost allowed is

$1500  

10+500≤1500

10x+500≤1500

To solve this inequality

First, subtract 500 from both sides

10≤1000

10x≤1000

Divide both sides by 10

≤100x≤100

This means you can make at most 100 items.

The domain is

[0,100].[0,100].

The range is

[0,1500] [0,1500].

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Answer:

= -6x + 24

Step-by-step explanation:

6(4-x) = 6*4 + 6*-x

= 24 - 6x

= -6x + 24

The solution set to inequality - 5 ≤ (1 / 2) · (2 · m + 2) ≤ 14 is equal to - 6 ≤ m ≤ 13. (Correct choice: A)

Herein we find a simultaneous inequality, that is, the combination of two inequalities. We find the following case below by algebra properties:

- 5 ≤ (1 / 2) · (2 · m + 2) ≤ 14

(1 / 2) · (2 · m + 2) ≥ - 5 and (1 / 2) · (2 · m + 2) ≤ 14

Now we proceed to determine the solution set to this inequality by algebra properties:

2 · m + 2 ≥ - 10 and 2 · m + 2 ≤ 28

2 · m ≥ - 12 and 2 · m ≤ 26

m ≥ - 6 and m ≤ 13

- 6 ≤ m ≤ 13

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Answer: y = 2-4x

Step-by-step explanation:

There are many similarities between Vanguard and Fidelity, but there are also some significant distinctions. Vanguard focuses primarily on long-term, buy-and-hold investing.

Fidelity, on the other hand, caters to investors who prefer a more hands-on approach.

There are more than 8,300 domestic investment-grade bonds held by the Vanguard Total Bond Market ETF.

Therefore, You'll need to study two (or more) sets of statements, keep track of several phone numbers, access a number of websites, and comprehend and keep track of hundreds of different funds.

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There are many similarities between Vanguard and Fidelity, but there are also some significant distinctions. Vanguard focuses primarily on long-term, buy-and-hold investing. Fidelity, on the other hand, caters to investors who prefer a more hands-on approach.

Bonds are issued by borrowers to attract capital from investors ready to extend a loan to them for a specific period of time. When you purchase a bond, you are making a loan to the issuer, which could be a corporate, government, or municipality.

By purchasing a bond, you are effectively lending the issuer money. In exchange, they commit to repay you the face amount of the loan on a particular date and to make periodic interest payments—typically twice a year—along the way. Unlike stocks, which grant you ownership rights, bonds issued by corporations do not.

Therefore, Vanguard's primary investment strategy is long-term buy-and-hold investing. On the other hand, Fidelity caters to investors who favor a more active strategy.

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Answer:

Is this what youre asking?

Step-by-step explanation:

Price before tax: $ 590.00

+ Sales tax (32.45%): $ 191.46

Total price including tax: $ 781.46