Two cars start at the same point and travel in opposite directions. The first car travels 10
miles per hour faster than the second. In 3 hours, they are 342 miles apart. The formula
below determines the rate of the second car. What is the rate of the second car?
3(r+ 10) + 3r = 342

The amount 6424.66 invested at 14% and amount 5221.33 invested at 8%.

We have,

Investment at 14%= $11,646

Investment at 8%= $1317.16

Let x be the amount invested at 14% and y be the amount invested at 8%.

So, x + y = 11646

0.14x + 0.08y = 1317.16

Now, solving the equation we get

x= 6424.66 and y = 5221.333

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The explanatory variable is; A. square footage.

The correct scatter diagram of the data is: B. scatter diagram.

The linear correlation coefficient between square footage and asking price is 0.91.

In this scenario, the square footage (x) would be plotted on the x-axis of the scatter plot while the selling price (y) would be plotted on the x-axis of the scatter plot.

By critically observing the scatter plot (see attachment) which models the relationship between the square footage (x) and the selling price (y), an equation for the linear regression is given by:

y = 13.762782 + 0.156710276x

Correlation coefficient, r = 0.904601208 ≈ 0.91.

In conclusion, there is a strong correlation between the data because the correlation coefficient (r) approximately equals to 1;

0.7＜|r| ≤ 1   (strong correlation)

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The value of m for the quadratic equation, 2x² - 28x + 7m = 0  to have one solution is 14.

She said the quadratic equation 2x² - 28x + 7m = 0 has only one solution for some value of m.

Therefore, the exact value of m which give the quadratic equation exactly one solution can be calculated as follows:

Therefore, a quadratic equation has one solution when the discriminant is zero.

Hence,

b² = 4ac

a = 2

b = -28

c = 7m

Therefore,

(-28)² = 4 (2)(7m)

784 = 56m

divide both sides by 56

m = 784 / 56

m = 14

Therefore,

m = 14

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Answer:

A.

Step-by-step explanation:

Peter should choose to base his report card percentage on the median if he wants to have the highest percentage possible. To calculate the median, Peter would first order the scores from lowest to highest: 44%, 64%, 71%, 75%, 84%, 90%, 98%. Then, he would select the middle score as the median, which is 75%. If Peter drops his lowest score (44%), his percentage based on the median would be 80% ((64%+71%+75%+84%+90%+98%)/6). If he were to choose the mean, his percentage would also be 80%. However, since the median is not affected by extreme values like the 44% score, it is a more reliable measure of central tendency in this case.

I did this on homework b4 and got It right so this Is 100 percent right.

Answer:

Peter should choose the median after dropping one test score so he can have the highest percentage possible.

If we calculate the mean of all seven test scores, we get:

(84+71+64+90+75+44+98)/7 = 73.14%

If we calculate the median of all seven test scores, we get:

Arrange the scores in ascending order:

44, 64, 71, 75, 84, 90, 98

The median is 75.

If we drop the lowest score (44) and calculate the mean of the remaining six test scores, we get:

(84+71+64+90+75+98)/6 = 80.5%

If we drop the lowest score (44) and calculate the median of the remaining six test scores, we get:

Arrange the scores in ascending order:

64, 71, 75, 84, 90, 98

The median is 79.5%.

Therefore, Peter should choose the median after dropping one test score to have the highest possible percentage.

1a. Inferring from the facts that Sample 2—which is larger than Sample 1—received the most votes,

we may infer that "Butterflies and Ladybirds" would be the most widely chosen option for the spring window show.

1b. This hypothesis is plausible given that a bigger sample size often yields more accurate results and can more accurately reflect the population as a whole.

Furthermore, the fact that "Butterflies and Ladybirds" garnered the most votes across the board implies that it is a widely accepted pick.

2a. The statistics should not be used to draw the conclusion that the spring window displays "Flower Garden" and "April Showers" are unpopular options.

They got fewer votes than "Butterflies and Ladybirds," but they still got a lot of votes from both samples.

2b. This conclusion should not be drawn since the data only reflects the opinions of the chosen samples and might not fairly represent the opinions of the general community.

Personal prejudices and preferences may have also had a role in the outcomes, and there may be more variables (such as cost or availability) that might have an impact on the decision about the spring window display.

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Complete question:

Two random samples of people were selected to help choose a spring window display for a department store. The results are shown in this table.

"Flower Garden"

Number of Votes from Sample 1 =35

Number of Votes from Sample 2=21

"April Showers"

Number of Votes from Sample 1 =16

Number of Votes from Sample 2=15

"Butterflies and Ladybugs"

Number of Votes from Sample 1 =27

Number of Votes from Sample 2=42

1a. What prediction can you make from the data?

1b. Explain why your prediction is reasonable.

2a. What conclusion should not be made from the data?

2b. Explain why the conclusion should not be made.

To eliminate the y-terms in this system of equations, we can multiply the second equation by 2 and add it to the first equation.

We have,

To eliminate the y-terms in this system of equations, we can multiply the second equation by 2 and add it to the first equation.

This will result in the y-terms canceling out, and we will be left with only x-terms on one side of the equation, which we can then solve for x.

So, multiplying the second equation by 2, we get:

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

6x + 8y = 10

Now, adding this to the first equation, we get:

4x - 8y + 6x + 8y = 20 + 10

10x = 30

Dividing both sides by 10, we get:

x = 3

Now, we can substitute this value of x back into either of the original equations to solve for y.

4x - 8y = 2

So,

4(3) - 8y = 20

12 - 8y = 20

-8y = 8

y = -1

Therefore,

The solution to the system of equations is (x, y) = (3, -1).

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The value of probability that they win the next game is,

⇒ 6/13

We have to given that;

The NY Knicks won 35 games out of 65 games.

Now, We can simplify as;

The possible value of to win next game is,

⇒ 65 - 35

⇒ 30

Thus, The value of probability that they win the next game is,

⇒ 30 / 65

⇒ 6/13

So, The value of probability that they win the next game is,

⇒ 6/13

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The answer is below., the town's tax status should change within the next 3 years.

An exponential decrease can be represented by the formula:

y = ab^x

where a is the initial amount and b < 1.

Let p represent the population after t years, hence:

p = ab^t

Since the population decreases exponentially at a rate of 14.3% each year, hence:

b = 100% - 14.3% = 85.7% = 0.857

b = 0.857

Also, a = 9400 people

Therefore the equation is:

p = 9400(0.857)^t

The town's tax status will change once the population is below 6,000 people, therefore:

9400(0.857)^t < 6000

for the tax status to change.

At t = 3 years:

p = 5917

so, 5917< 6000

the town's tax status should change within the next 3 years.

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1) b. quota

2) d. they make foreign products cheaper to U.S. shoppers

3) a. it sets the value of its currency in relation to a specific amount of gold

4) c. $3,040 per person

5) b. low population growth

We have,

1)

A limit imposed by the government on the quantity of a good or product that can be brought into the country is called a quota.

Tariffs, on the other hand, are taxes imposed on imported goods, while foreign bills of exchange refer to payment methods in international trade, and value-added tax (VAT) is a tax on the value added to goods and services.

2)

The argument that enacting trade restrictions makes foreign products cheaper to U.S. shoppers is not effective because it is contradictory.

Trade restrictions, such as tariffs or quotas, are intended to make foreign products more expensive and protect domestic industries from foreign competition.

3)

If a country is on the gold standard, it means that it sets the value of its currency in relation to a specific amount of gold.

The value of the currency is directly linked to the amount of gold held in reserves by the government and can be exchanged for gold at a fixed rate.

4)

Economists tend to classify a country as less developed if the country's average level of income is less than $3,040 per person.

This is the World Bank's definition of low-income countries, which are typically characterized by high levels of poverty, limited access to education and healthcare, and underdeveloped infrastructure.

5)

Low population growth is not considered a barrier to economic development.

In fact, some economists argue that high population growth can put a strain on resources and hinder economic development.

Barriers to economic development typically include factors such as political corruption, lack of investment capital, and low levels of education and human capital.

Thus,

1) b. quota

2) d. they make foreign products cheaper to U.S. shoppers

3) a. it sets the value of its currency in relation to a specific amount of gold

4) c. $3,040 per person

5) b. low population growth

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Answer: B, 83.

Step-by-step explanation: Just use long division as shown below, hope this helps! :)

The formula for this function is y = 0.9 * cos((2π/3) x + π/2) - 1.2

From the image attached, that looks like a cosine graph with 3 periods. 2 highs and 1 low. Also, it should be noted that it is a cosine function.

Therefore to derive the formula for the graph, we use a cosine function with a phase shift and amplitude adjustment.

The general formula for a cosine function is:

f(x) = A * cos(Bx + C) + D

where

A = amplitude,

B = frequency,

C = phase shift,

D = vertical shift.

To get the Amplitude:

We want the function to oscillate between 2.1 and 0.3, which is a difference of 1.8. Since the sine function oscillates between -1 and 1, we need to multiply it by half the desired difference to get the right amplitude. Therefore,

A = 1/2 *1.8 = 0.9.

To get the Frequency:

Since there are only three periods in the interval, then

frequency =  2π/3.

Therefore B = 2π/3.

To get the Phase shift:

We want the function to peak at x = 0, so we need a phase shift of π/2.

Therefore C = π/2.

To get Vertical shift:

We want the function to have a trough at y = 0.3, which means we need to shift it down by 1.8/2 + 0.3 = 1.2. We set D = -1.2.

Putting all these parameters together, we get the following formula:

f(x) = 0.9 * cos((2π/3) x + π/2) - 1.2

This function will oscillate between 2.1 and 0.3 over three periods, with a peak at x = 0 and a trough at y = 0.3.

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The measure of the line segment XY is 54 units.

Since,

A line segment is a path between two points that can be measured. Since line segments have a defined length, they can form the sides of any polygon.

Given that,

W is between X and Y, WX = 38 and WY = 16.

Here, Length of segment XY is sum of measure of line segments WX and WY, we get

XY=WX+WY

XY=38+16

XY = 54 units

Therefore, the measure of XY is 54 units.

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"Your question is incomplete, probably the complete question/missing part is:"

Find the length of XY if W is between X and Y, WX = 38 and WY = 16. XY = ?

Answer:

AB is not a tangent. The lengths 4, 12, and 13 do not form a right triangle.

√(4^2 + 12^2) = √160, which is not equal to 13.

Answer:

No

Step-by-step explanation:

if AB is a tangent the the angle BAC = 90°

using Pythagoras' theorem

then square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

BC² = 13² = 169

AB² + AC² = 12² + 4² = 144 + 16 = 160

since BC²≠ AB² + AC²

then Δ ABC is not a right triangle so AB is not a tangent

a.  The magnitude of earthquake 7 is 1.259 times stronger than a magnitude 6 earthquake

b.  The magnitude of earthquake 9 is 1.995 times stronger than a magnitude 6 earthquake

The magnitude of an earthquake is given by M = 10㏒(A/A₀) where A = intensity of eartquake and A₀ = standard intensity

a. To find out how much stronger is a magnitude 7 earthquake than a magnitude 6 earthquake, we proceed as folllows.

For a magnitude of 7,

So, M = 10㏒(A'/A₀)

7 = 10㏒(A'/A₀)  (1)

For a magnitude of 6,

So, M = 10㏒(A'/A₀)

6 = 10㏒(A"/A₀) (2)

Subtracting (2) from (1), we have that

7 - 6 = 10㏒(A'/A₀) - 10㏒(A"/A₀)

1 = 10㏒[(A'/A₀) ÷ (A"/A₀)]

1 = 10㏒[(A'/A")

㏒[(A'/A")  = 1/10

Taking inverse logarithm, we have

(A'/A") = ¹⁰√10

= 1.259

So, it is 1.259 times stronger

b. To find out how much stronger is a magnitude 9 earthquake than a magnitude 6 earthquake, we proceed as folllows.

For a magnitude of 9,

So, M = 10㏒(A'/A₀)

9 = 10㏒(A'/A₀)  (1)

For a magnitude of 6,

So, M = 10㏒(A'/A₀)

6 = 10㏒(A"/A₀) (2)

Subtracting (2) from (1), we have that

9 - 6 = 10㏒(A'/A₀) - 10㏒(A"/A₀)

3 = 10㏒[(A'/A₀) ÷ (A"/A₀)]

3 = 10㏒[(A'/A")

㏒[(A'/A")  = 3/10

Taking inverse logarithm, we have

(A'/A") = 10⁰°³

= 1.259

So, it is 1.995 times stronger

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Answer:

Step-by-step explanation:

3/4 : 1/8 =

3/4 x 8 =

24/4 =

6

A polygon is a geometric object with two dimensions and an infinite number of sides.  Drawing of each regular polygon: equilateral triangle, square, and regular hexagon can be drawn in the image.

A polygon is a geometric object with two dimensions and an infinite number of sides. A polygon's sides are made up of segments of straight lines that are joined end to end. As a result, a polygon's line segments are referred to as its sides or edges.

Vertex or corners refer to the intersection of two line segments, where an angle is created. Having three sides makes a triangle a polygon.  Drawing of each regular polygon: equilateral triangle, square, and regular hexagon can be drawn in the image.

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There are 300 grams in 1500 ml of the 20% solution.

We can use the concept of proportions to solve this problem.

A 20% solution contains 20 grams in 100 ml.

This means that for every 100 ml of solution, there are 20 grams of the solute.

To find out how many grams are in 1500 ml of the solution, we can set up a proportion:

20 grams/100 ml = x grams/1500 ml

where x is the number of grams in 1500 ml.

To solve for x, we can cross-multiply and simplify:

100x = 20 × 1500

100x = 30,000

x = 300 grams

Therefore, there are 300 grams in 1500 ml of the 20% solution.

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The gradients for each line are given as follows:

The slope-intercept representation of a linear function is given by the equation presented as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

The gradient of each line represents the slope, hence they are given as follows:

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The surface area of the right cone is 800.7 squared unit.

The surface area of a three-dimensional object is the total area of all its faces.

To calculate the surface area of the right cone, we use the formula below

Formula:

From the question,

Given:

From the question,

Given:

Substitute these values into equation 1

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The difference between area and volume is that:

8. Area describes the space taken up by two-dimensional objects whereas volume describes the space taken up by three-dimensional objects. The area can be measured in square meters (m²) and square kilometers (km²), whereas, volume can be measured in cubic millimeters (mm³), and cubic meters (m³).

9. The volume of the cube is D. 12 cubic units.

To calculate the volume of a cube, we multiply all three sides. The formula is V = S³.

So, for the cube shape with the given three sides, we can obtain the volume by executing the following operation:

1 × 2 × 6

12 cubic units. Option D is thus correct.

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Sally can solve minimum of 35 calculus problem and maximum of 50 calculus problem.

We know,

Calculus is a branch of mathematics that focuses on rates of change, to put it simply. For instance, you might want to determine how quickly a car will slow down as it approaches a stop sign. Calculus can assist you in calculating that change. Calculus introduces movement into math, that's correct!

Calculus is useful in many different fields, including engineering, medicine, biological research, economics, architecture, space science, electronics, statistics, and pharmacology.

minimum = 35

maximum=50

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complete question:

Sally completely solves at least 7 calculus problems per hour and at most 10 calculus problems per hour. Based on this information, what is a possible number of calculus problems that Sally can completely solve in five hours?

To conclude, $2,755,000 was invested at 12% interest, $1,275,000 was invested at 3.8% interest and $1,290,000 was invested at 3% interest.

The elimination method is a useful process in solving a system of equations especially when the terms in the equations contain coefficients. By elimination method, the equations may be reduced to an equation containing only one of the unknowns and may be used to solve for the first value. The remaining unknowns are derived using the original equations and the first value.

Let x be the amount invested in stocks at 12%  interest, y be the amount invested at bonds at 3.8% interest and z be the amount invested in CD at

3% interest.

The total investment amounts to $190000

x + y + z = $190000__eq.(1)

The total interest from the three investments is $11250

0.12x + 0.038y + 0.03z = 11250 ___eq.(2)

Country Days invests $15000 more in bonds than in CDs.

y = z + $15000

y - z = $15000 ____eq.(3)

Use elimination method for the first and second equation to eliminate x.

x + y + z = $190000                [ Multiply both sides by 0.12 ]

-[0.12x + 0.038y + 0.03z = 11250]      

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

 0.12x + 0.12y + 0.12z = $ 22,800

-[0.12x + 0.038y + 0.03z = 11250]      

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

          0.082y  +   0.09z  = $11,550

Perform another elimination method for the derived equation above and Equation 3 to eliminate z.

 0.082y  +   0.09z  = $11,550

-[y - z = $15000]   [ Multiply both sides by 0.09 ]

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

0.082y  +   0.09z  = $11,550

-[0.09y - 0.09z= $1350]

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

- 0.008y = $10,200

y = - $1,275,000

Substitute the value of y to Equation 2.

y - z = $15000    [ Substitute y in Equation 3 ]

-1275000 - z = 15000

-z = 15000 + 1275000

z = -$1,290,000

Substitute the value of y and z to Equation 1.

x + y + z = $190000

x - $1,275,000 - $1,290,000 = $190000

x = $190000 + $2565000

x = $2,755,000

To conclude, $2,755,000 was invested at 12% interest, $1,275,000 was invested at 3.8% interest and $1,290,000 was invested at 3% interest.

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Yes, its possible to have s path through the house that uses door way once and the path is BADC.

In the given graph the vertices represents the rooms.

A, B, C and D are the rooms

the edges represent doorways connecting the rooms.

Vertex represents the outdoors.

Yes, its possible to have s path through the house that uses door way once.

The path is BADC.

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The tank holds approximately 994,040 liters.

The volume of a right circular cylinder is given by the formula:

V = πr^2h

Where

The cylinder's diameter is specified as 13 m, hence the radius may be computed using the formula: r = d/2 = 13/2 = 6.5 m

The cylinder is described as having a 6 m length.

These values are substituted into the volume calculation to produce the following result:

V = π(6.5)^2(6)

V ≈ 994.04 cubic meters

Since 1 cubic meter equals 1000 liters, we can convert the volume to liters by multiplying by 1000.

V = 994.04 cubic meters x 1000 liters/cubic meter

V = 994,040 liters

Therefore, the tank holds approximately 994,040 liters.

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The height of the plane to the nearest metres is 243 metres.

An airplane pilot over the Pacific sights a ship at an angle of depression of 3 degrees. The horizontal distance from the airplane to the ship is 4629 meters.

Therefore, the height of the plane can be found as follows:

Hence, using trigonometric ratios,

tan 3 = opposite / adjacent

Therefore,

tan 3° = x / 4629

cross multiply

x = 4629 tan 3°

x = 242.595610301

Therefore,

height of the plane = 243 metres.

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The value of the integration are:

∫(√(2 + (cos x)²) / sec x - cosec x) dx = 3 ln|cos x - sin x| + √2 + C

∫arc tan√x dx = √x arc tan √x - ln|1 + x| + C

We have,

∫(√(2 + (cos x)²) / sec x - cosec x) dx:

We can simplify the expression in the integral as follows:

√(2 + (cos x)²)

= √(1 + (cos² x)) + √1

= √(sin² x + cos² x + cos² x) + 1

= √(2cos² x + 1) + 1

So the integral becomes:

∫[(√(2cos² x + 1) + 1) / (1/cos x - 1/sin x)] dx

= ∫[(√(2cos² x + 1) + 1) / ((sin x - cos x)/ (sin x cos x))] dx

= ∫[(√(2cos² x + 1) + 1) / ((sin x cos x - cos² x)/ (sin x cos x))] dx

= ∫[(√(2cos² x + 1) + 1) sin x / (cos x - sin x)] dx

Now we can make the substitution u = cos x - sin x, which gives us

du = (-sin x - cos x) dx, or -du = (sin x + cos x) dx.

Making this substitution and simplifying, we get:

∫[(√(2u² + 2) + 2) / u] du

= ∫[(√2(u² + 1) + √2) / u] du

= √2 ∫[(u² + 1)^(1/2) / u] du + 2 ∫(1/u) du

Using integration by substitution,

let w = u^2 + 1, then dw = 2u du, and we have:

= √2 ∫(1/w) dw + 2 ln|u|

= √2 ln|u| + 2 ln|u| + C

= 3 ln|cos x - sin x| + √2 + C

where C is the constant of integration.

And,

∫arc tan√x dx:

We can make the substitution u = √x, which gives us du = (1/2√x) dx, or 2u du = dx.

Substituting these into the integral, we get:

∫arc tan√x dx = ∫arc tan u x 2u du

Now, using integration by parts with u = arc tan u and dv = 2u du, we get:

∫arc tan u  2u du = u arc tan u - ∫(1 + u²)/(1 + u²)² du

= u arc tan u - ∫1/(1 + u²) du

= u arc tan u - ln|1 + u²| + C

Substituting back u = √x, we get:

∫arc tan√x dx = √x arc tan √x - ln|1 + x| + C

where C is the constant of integration.

Thus,

The value of the integration are:

∫(√(2 + (cos x)²) / sec x - cosec x) dx = 3 ln|cos x - sin x| + √2 + C

∫arc tan√x dx = √x arc tan √x - ln|1 + x| + C

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Answer:

  192.7 cm³

Step-by-step explanation:

You want the volume of a regular pentagonal prism with a base side length of 4 cm and a height of 7 cm.

The area of a regular n-gon is given by the formula ...

  A = n·s²/(4·tan(180°/n))

For n=5 and s=4 cm, the area of the prism base is ...

  A = 5·(4 cm)²/(4·tan(36°)) = 20/tan(36°) cm² ≈ 27.528 cm²

The volume of a prism is ...

  V = Bh

where B is the base area, and h is the height. Here, we have h=7 cm, so the volume is ...

  V = (27.528 cm²)(7 cm) ≈ 192.7 cm³

The volume of the interior of the box is about 192.7 cm³.

Answer:

b)

Step-by-step explanation:

a) y = 4x +1 y= -4x + 1

Different slopes; same y-intercept; lines intersect at 1 point; there is 1 solution.

b) y= 2x + 7 y= 2x - 7

Same slopes; different y-intercepts; parallel lines do not intersect; no solution.

c) 3x + y =1 6x + 2y =2

Equations are the same; infinite number of solutions.

d) 5x + y =3 x + 5y = 15

Different slopes; lines intersect at 1 point; there is 1 solution.

Answer: b)

The total price including sales tax that Brayden has to pay is $114.15

Sales tax is a tax charged to the buyer of a product based on the product's price.

From the case, we know that:

Sales tax = 6%

price = $18.70

Sales tax to be paid = Sales tax x product price

Sales tax to be paid = 6% x $18.70

Sales tax to be paid = $112.2

Total price to be paid = Product price + Sales tax to be paid

Total price to be paid = $112.2+ $1.95

Total price to be paid = $114.15

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