Consider the following symbolic logic statement: ¬ (∃x)(P(x) ∧ Q(x)) ∧ (∀y)(R(y) → P(y))
a) Translate the statement into English using proper syntax and semantics.
b) Identify and explain any potential ambiguities in the translated statement.
c) Rewrite the statement in a way that eliminates any ambiguities and maintains the original meaning.

Donald traveled approximately 100 kilometers on each of his trips to the amusement park.

Now, the distance Donald traveled on each of his trips to the amusement park.

If he drove a total of 399 kilometers over the course of four trips, we can find the average distance he traveled per trip by dividing the total distance by the number of trips.

So, We get;

= 399 divided by 4

= 399 / 4

= 99.75 kilometers per trip

≈ 100 kilometers per trip.

Therefore, Donald traveled approximately 100 kilometers on each of his trips to the amusement park.

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a) The area of the rectangular shaped bathroom floor is A = 30.375 feet²

b) The number of boxes of tiles = 25 boxes

Given data ,

Jordan is putting new tile on the bathroom floor. The width of the floor is 4 2/4 feet and the length is 6 3/4 feet

Now , Area of Rectangle = Length x Width

On simplifying , we get

Width = 4 2/4 feet = (4 x 4 + 2)/4 = 18/4 feet

Length = 6 3/4 feet = (6 x 4 + 3)/4 = 27/4 feet

Area = (18/4) x (27/4) = (18 x 27)/(4 x 4) = 30.375 feet²

Therefore , the area of bathroom floor is A = 30.375 feet²

Now , the number of boxes is given by

Number of boxes of tiles = Total area of bathroom floor / Area covered by each box of tiles

B = 30.375 / 5

B = 6.075

B = 6 tiles

Hence , the area of bathroom floor is A = 30.375 feet²

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In a case whereby A ship travels due west for 94 miles. It then travels in a northwest direction for 119 miles and ends up 173 miles from its original position the degrees north of west it turned is 72°

From trigonometry, the law of cosines states  the side c of a triangle can be found as

c² = a² + b² - 2abcos(C)

where

C = angle opposite to side c.

a and = lengths of the other sides.

a = 94, b = 119, c = 173.

c² = a² + b² - 2abcos(C)

173² = 94² + 119² - 2 x 94 x 119cos(C)

22327cos(C) = -6932

cos(C) = -6932/22327

C = arccos(-6932/22327)

C = 108º.

Then,

T = 180 - C

= 180 - 108 = 72º.

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1. The proportion is; x/4 = 12/18

2. The height of the mailbox is 2.7 feet

In mathematics, a proportion is an equation that states that two ratios are equal. It expresses the relationship between the quantities in terms of their relative sizes or magnitudes. Proportions are used in various areas of mathematics and real-life applications, such as ratios

We have;

Length of the mail box shadow = 4 feet

Length of the tree shadow = 18 feet

Height of the mail box = x

Height of the tree = 12 feet

Thus;

x/4 = 12/18

x = 4 * 12/18

x = 2.7 feet

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The surface area of the rectangular prism is (26/3) times larger than the surface area of the cube.

Given data ,

Let the surface area of the cube be S₁

Let the surface area of the rectangular prism be S₂

Let the volume of the cube be V₁

Let the volume of the prism be V₂

On simplifying , we get

The side length of cube = x

So , surface area of cube = 6x²

The volume of cube = x³

And , the surface area of prism = 2 ( 12x² + 8x² + 6x² )

S₂ = 52x²

And , volume of prism = l x w x h

V₂ = ( 2x ) ( 3x ) ( 4x ) = 24x²

So , S₂ = ( 26/3 ) S₁

52x² = ( 26/3 ) ( 6x² )

52x² = 52x²

Hence , The rectangular prism's surface area is (26/3) times greater than the cube's surface area.

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The complete question is attached below :

The dimensions of a cube and a rectangular prism are shown below.

Which statement is true?

A The surface area of the rectangular prism is 24 times larger than the surface area of the cube.

The surface area of the rectangular prism is times larger than the surface area of the cube.

C The volume of the rectangular prism is 48 times larger than the volume of the cube.

D The volume of the rectangular prism is 3 times larger than the volume of the cube.

The amount of poster board left over will be 1275 square inches, the equation used is  A = (b₁ + b₂)h/2.

To calculate the amount of poster board that will be left over after Ole cuts out a piece of poster board that is the same size as the window,

we need to find the area of the trapezoid window and subtract it from the area of the poster board.

The formula to find the area of a trapezoid is A = (b₁ + b₂)h/2, where b₁ and b₂ are the lengths of the parallel sides and h is the height.

Let's assume that the length of the top parallel side of the trapezoid is 20 inches, the length of the bottom parallel side is 10 inches, and the height is 15 inches.

Using the formula, we get A = (20 + 10) x 15 / 2 = 225 square inches. This is the area of the window.

To find the area of the poster board, we multiply the length and width, which gives 25 x 60 = 1500 square inches.

Finally, we subtract the area of the window from the area of the poster board using the equation:

1500 - 225 = 1275 square inches.

Therefore, the amount of poster board left over will be 1275 square inches.

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The complete question is

Ole has a window that has the dimensions and shape like the trapezoid shown below. He also has a large rectangular piece of poster board that measures 25 inches by 60 inches. If Ole cuts out a piece of poster board that is exactly the same size as the window, which equation can be used to calculate the amount of poster board that will be left over?

The exponential function that model this situation is [tex]A(t) = 2500(1 + 0.035)^t.[/tex]

The account will have $5000 in 20 years.

Let A be the amount in the account after t years.

Then, we can model this situation with the function A(t) = 2500(1 + 0.035)^t with the use of compound intererst formula which is [tex]P = A*(1+r)^t[/tex]

To find when the account will have $5000, we can set A(t) = 5000 and solve:

5000 = 2500(1 + 0.035)^t

2 = (1.035)^t

Taking the natural logarithm:

ln(2) = t ln(1.035)

t = ln(2)/ln(1.035)

t = 20.148791684

t = 20 years.

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Answer:

1)  21 years

2) 26 years

Step-by-step explanation:

To model the account balance of Vanessa's account at t years, we can use an exponential function in the form:

[tex]\large\boxed{A(t) = A_0(1 + r)^t}[/tex]

where:

Given Vanessa invested $2500 into the account and it will increase in value by 3.5% each year:

Substitute these values into the formula to create an equation for A in terms of t:

[tex]A(t) = 2500(1 + 0.035)^t[/tex]

[tex]A(t) = 2500(1.035)^t[/tex]

To find when the account balance will be $5000, set A(t) equal to $5000 and solve for t:

[tex]A(t)=5000[/tex]

[tex]2500(1.035)^t=5000[/tex]

[tex](1.035)^t=\dfrac{5000}{2500}[/tex]

[tex](1.035)^t=2[/tex]

[tex]\ln (1.035)^t=\ln 2[/tex]

[tex]t \ln 1.035=\ln 2[/tex]

[tex]t=\dfrac{\ln 2}{ \ln 1.035}[/tex]

[tex]t=20.1487916...[/tex]

[tex]t=20.15\; \sf years\;(2\;d.p.)[/tex]

Therefore, it will take approximately 20.15 years for Vanessa's account to reach a value of $5000.

Since the interest rate is an annual rate of 3.5%, it means that the interest is applied once per year, at the end of the year. Therefore, we need to round up the number of years to the next whole number.

So Vanessa's account will have $5,000 after 21 years.

Note: After 20 years, the account balance will be $4,974.47. After 21 years, the account balance will be $5,148.58.

[tex]\hrulefill[/tex]

To model the increase in movie ticket prices over time, we can use an exponential function in the form:

[tex]\large\boxed{P(t) = P_0(1 + r)^t}[/tex]

where:

Given the initial price of the ticket was $4.22 and the price has increased by 3.1% each year:

Substitute these values into the formula to create an equation for P in terms of t:

[tex]P(t) = 4.22(1 + 0.031)^t[/tex]

[tex]P(t) = 4.22(1.031)^t[/tex]

To find how many years until tickets cost $9.33, we can set P(t) equal to $9.33 and solve for t:

[tex]P(t)=9.33[/tex]

[tex]4.22(1.031)^t=9.33[/tex]

[tex](1.031)^t=\dfrac{9.33}{4.22}[/tex]

[tex]\ln (1.031)^t=\ln \left(\dfrac{9.33}{4.22}\right)[/tex]

[tex]t \ln (1.031)=\ln \left(\dfrac{9.33}{4.22}\right)[/tex]

[tex]t =\dfrac{\ln \left(\dfrac{9.33}{4.22}\right)}{\ln (1.031)}[/tex]

[tex]t=25.9882262...[/tex]

Therefore, it will take approximately 26 years for movie ticket prices to reach $9.33, assuming the annual growth rate remains constant at 3.1%.

The correct option is D, the parent quadratic function is:

f(x) = x²

First, we define the parent functions as the simplest function for each type.

For example, the parent linear function is.

y = x

The parent square root function is:

y = √x

The parent absolute value function is:

y = |x|

And so on.

So the parent quadratic function is a polynomial of degree 2 where we only have the quadratic term (and no coefficient).

Thus, the correct option is D; f(x) = x²

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The length of the shortcut is 1 mile

The total length of your walk in the park is 1.4 miles

Given that you walk along the outside of a park starting at point P to point Q

The point P is at (0, 0)

The point Q is located at (0.6, 0.8)

We have to find the length of the shortcut

Distance=√(x₂-x₁)²+(y₂-y₁)²

PQ=√(0.6-0)²+(0.8)²

=√0.36+0.64

=√1 units

=1 mile

The total length of the park is PR+RQ

PR=√(0.6-0)²

=0.6

RQ==√(0.8-0)²

=0.8

The total length is 0.6+0.8

Which is 1.4 miles

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The solutions of the given inequality is: x ≥ -1 or x ≤ -5, the correct number line is 2nd.

To solve the inequality |x + 3| ≥ 2, we need to consider two cases:

Case 1: (x + 3) ≥ 2

If x + 3 is greater than or equal to 2, then the absolute value of (x + 3) will also be greater than or equal to 2. Solving this case:

x + 3 ≥ 2

x ≥ 2 - 3

x ≥ -1

So, for this case, the solution is x ≥ -1.

Case 2: -(x + 3) ≥ 2

If -(x + 3) is greater than or equal to 2, then the opposite of (x + 3) will also be greater than or equal to 2. Solving this case:

-(x + 3) ≥ 2

x + 3 ≤ -2

x ≤ -2 - 3

x ≤ -5

So, for this case, the solution is x ≤ -5.

Combining the solutions from both cases, we have the final solution:

x ≥ -1 or x ≤ -5

Hence the number line showing the given inequality is 2nd.

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a) The correct option is C. Construct a 99% confidence interval for μ in order to see the magnitude of the difference between 115 and your sample results.

b) The correct option is B. Use a very small level of significance.

c) The correct option is B. The sample size is small.

d) The lack of statistical significance at the 0.10 significance level suggests that the observed doubling of survival time may not be practically significant as the actual increase is only two years.

(a) To assess the practical significance of the results, the most helpful approach would be to construct a 99% confidence interval for the population mean, μ. This would provide a range of values within which the true population mean is likely to fall. By comparing this interval to the hypothesized value of 115, you can evaluate the magnitude of the difference and determine if it is practically significant.

Therefore, the correct option is C. Construct a 99% confidence interval for μ in order to see the magnitude of the difference between 115 and your sample results.

(b) When the consequences of rejecting the null hypothesis are very serious, it is important to be cautious and use a very small level of significance. The level of significance determines the threshold for rejecting the null hypothesis. By using a very small level of significance, you are setting a higher standard for rejecting the null hypothesis, reducing the likelihood of making a Type I error (false positive). This ensures that strong evidence is required to support rejecting the null hypothesis when the consequences are significant.

Therefore, the correct option is B. Use a very small level of significance.

(c) In this scenario, the explanation for the lack of statistical significance at the 0.10 significance level, despite the survival time doubling, is likely due to the small sample size. With only three subjects, the sample may not provide enough statistical power to detect a significant difference. The variability in survival times within the sample might also influence the lack of significance. A larger sample size would provide more reliable and statistically significant results.

Therefore, the correct option is B. The sample size is small.

d) The explanation for the lack of statistical significance in this scenario is that although the survival time has doubled from two years to four years, the actual increase is still only two years. This means that the difference between the standard treatment and the new treatment is not as substantial as it may initially seem.

When conducting statistical tests, it is important to consider both statistical significance and practical significance. While the survival time doubling may be a positive outcome, if the actual increase is only two years, it may not be considered practically significant in the context of cancer treatment.

Statistical significance is determined by conducting hypothesis tests and examining the p-value. In this case, even at the 0.10 significance level, the results are not statistically significant, indicating that the observed difference in survival times could likely be due to chance.

It is important to interpret the results in the context of the specific situation and consider factors such as sample size, variability, and clinical significance. In this case, the small sample size of three subjects may limit the statistical power to detect a significant difference. Additionally, the placebo effect or other factors may also play a role in limiting the statistical significance of the results.

In summary, the lack of statistical significance at the 0.10 significance level suggests that the observed doubling of survival time may not be practically significant as the actual increase is only two years.

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The claims are this year some of their clients will have a starting salary of at least $38,500 and last year at least one of their clients had a starting salary of exactly $38,500. Correct options are A and B.

Based on the given information, option A can be true. This is because the average starting salary of the job placement agency's clients was $38,500 last year, which means some clients had a starting salary equal to or greater than that amount.

Option B is also true because the mean includes all values, including the value of $38,500, so it is likely that at least one client had that starting salary.

Option C cannot be determined from the given information as it is unclear what percentage of clients had a starting salary above $38,500. Option D is not necessarily true as there is no information on the starting salary of any client exceeding $42,000.

Option E is also not true as the average salary of $38,500 does not guarantee that all clients had that same starting salary. Therefore, the correct answer is A and B, and the rest cannot be determined from the given information.

Correct options are A and B.

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Answer:

1 1/6 metre

Step-by-step explanation:

1/3 pink + 5/6 purple

To add, we need to get a common denominator

1/3 *2/2 = 2/6

2/6 + 5/6

7/6

Change from an improper fraction to a mixed number

1 1/6 metre

Jasper has a total of 135 possible combinations for his outfit.

To calculate the total number of combinations that Jasper can pick for his outfit, we need to multiply the number of options for each category: tops, pants, shoes, and jackets.

For tops, Jasper has three options: t-shirt, polo, or sweatshirt.

For pants, he has five options: khakis, jeans, sweatpants, corduroys, or shorts.

For shoes, he has three options: boots, tennis shoes, or sandals.

For jackets, he has three options: ski coat, raincoat, or wool coat.

To calculate the total number of combinations, we multiply the number of options for each category:

3 (tops) × 5 (pants) × 3 (shoes) × 3 (jackets) = 135

Jasper has a total of 135 possible combinations for his outfit.

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The correct answer is, Cougars; they have a larger median value of 22 inches.

Calculating the median and mean for each data set, we get:

Cougars:

Median = 22 inches

Mean = 22.3 inches

Panthers:

Median = 22.5 inches

Mean = 22.2 inches

Since the median of the Cougars data set is larger than the median of the Panthers data set, we can conclude that the Cougars have the largest overall size hat for their players.

Therefore, the correct answer is, Cougars; they have a larger median value of 22 inches.

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The length of a side of the square garden is 5.75 feet.

(x+10)(x+5) - x² + (x+13)(x+8) - x² = 700

Simplifying and solving for x, we get:

2x^2 + 46x - 177 = 0

Using the quadratic formula, we can solve for x:

x = (-46 ± ✓46² - 4(2)(-177))) / (2(2))

x = (-46 ± 26) / 4

x = 5.75

The length of a side of the square garden is 5.75 feet.

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Answer:

Step-by-step explanation:

To estimate the original volume of the pyramid in Figure 15.28, we can use the formula for the volume of a frustum of a pyramid. The frustum is the portion of the pyramid between the top and bottom, created by removing the top section.

The formula for the volume of a frustum of a pyramid is:

V = (1/3) * h * (A + sqrt(A * B) + B)

Where:

V = Volume of the frustum

h = Height of the frustum (vertical distance between the top and bottom)

A = Area of the top base

B = Area of the bottom base

Given the dimensions provided, we can calculate the areas of the bases:

Area of the top base (A) = 4 m * 4 m = 16 m²

Area of the bottom base (B) = 20 m * 20 m = 400 m²

The height of the frustum (h) is given as 12 m.

Now we can plug these values into the formula:

V = (1/3) * 12 m * (16 m² + sqrt(16 m² * 400 m²) + 400 m²)

Calculating the square root and simplifying:

V = (1/3) * 12 m * (16 m² + 20 m² + 400 m²)

V = (1/3) * 12 m * (436 m²)

V = 1744 m³

Therefore, the estimated original volume of the pyramid in Figure 15.28 is approximately 1744 cubic meters.

Answer:

3

Step-by-step explanation:

factorize whats common in the question

division turns to multiplication by Inverwing the fraction

at the end of the day you will be left with 3

I hope you understand

a. The value of sin θ = 13/18

b. The size of sin θ is 46.2 degrees

First, we need to know the different trigonometric identities.

These trigonometric identities are listed thus;

From trigonometric relations, we have that the ratio for sine identity is represented as;

sin θ = opposite/hypotenuse

Then, we have from the information given that;

Hypotenuse side = 18cm

Opposite side = 13cm

Substitute the values, we have;

sin θ = 13/18

Divide the values

sin θ = 0. 7222

Find the sine inverse value, we have;

so, θ = sin⁻¹(13/18) = 46. 2 degrees

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Answer:

47703169206

Step-by-step explanation:

7 x 787 x 9999 x 866 = 47703169206 via the process of multiplication

Answer:

8,9740 that is your answer and then I hope you have a good day and hope this helps

Mean: Mean = (8,336,817 + 979,576 + 2,693,976 + 2,320,268 + 1,680,992 + 1,584,064 + 1,547,253 + 1,423,851 + 1,343,573 + 1,021,795 + 978,908 + 911,507) / 12=2688602

Median =  1,643,032

Mode: Determine the value(s) that appear most frequently in the population list. In this case, there is no mode as none of the population values repeat.

Range = 8,336,817 - 911,507 = 7,425,310.

Standard Deviation = √( Σ ( xi - μ )² / N )

To find the mean, median, mode, range, and standard deviation of the given population data for the top twelve largest cities in the U.S., we can perform the following calculations:

Performing these calculations will yield the mean population, median population, mode (if any), range, and standard deviation of the given population data for the top twelve largest cities in U.S .

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Band B-1 is a band of the electromagnetic spectrum that is used for cellular communications. It is located in the 2100 MHz frequency range.

Band B-2 is also a band of the electromagnetic spectrum that is used for cellular communications. It is located in the 1900 MHz frequency range.

The main difference between band B-1 and band B-2 is their range. Band B-1 has a longer range than band B-2. This is because it is located in a higher frequency range. Higher frequency ranges have shorter wavelengths, which means that they can travel through objects more easily. This makes them better for use in areas where there are a lot of obstacles, such as buildings and trees.

Band B-2 has a shorter range than band B-1, but it is better for use in areas where there are a lot of people. This is because it is located in a lower frequency range

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Answer:

130 degrees

Step-by-step explanation:

DE+DA=130

The solution to the System of equations is x = -9 and y = 8

We have the equation x - y = -1 and the equation x = -9. We can use the second equation to substitute the value of x in the first equation and solve for y.

Given x = -9, we substitute this value into the first equation:

(-9) - y = -1

Simplifying, we have:

-9 + y = -1

To isolate y, we can add 9 to both sides of the equation:

-9 + 9 + y = -1 + 9

This gives us:

y = 8

Therefore, the solution to the system of equations is x = -9 and y = 8.

We can check this solution by substituting the values of x and y back into the original equations:

Equation 1: x - y = -1

Substituting x = -9 and y = 8:

-9 - 8 = -1

Simplifying, we have:

-17 = -1

The equation is true, so our solution is valid.It is important to note that the solution provided is derived from the given equations and standard algebraic methods.

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We are 98% confident that the true mean amount of money spent per month on home maintenance by all homeowners is between $70.19 and $75.81.

A confidence interval is a range of values that is likely to contain the true value of the population parameter with a given level of confidence. A confidence interval for the population mean μ can be constructed as follows:

μ = sample mean ± margin of error where the margin of error is given by:margin of error = (critical value) x (standard error)

Here, we want to construct a 98% confidence interval for the mean amount of money spent per month on home maintenance by all homeowners. We are given that a survey of 81 randomly selected homeowners finds that they spend a mean of $73 per month on home maintenance.

The population standard deviation is assumed to be $10 per month.

Therefore, the standard error of the mean is given by:standard error = σ / sqrt(n) = 10 / sqrt(81) = 10 / 9 = 1.11

where σ is the population standard deviation and n is the sample size.To find the critical value, we need to look up the t-distribution table with 80 degrees of freedom and a significance level of 0.01 (since we want a 98% confidence interval).

The corresponding value is 2.527.

Therefore, the margin of error is:margin of error = (critical value) x (standard error) = 2.527 x 1.11 = 2.81

Finally, we can construct the confidence interval as follows:73 ± 2.81 = (70.19, 75.81)The confidence interval is rounded to the nearest cent.

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The result of the expression (A ∩ B) - C is [-2, 5] U [13, 18] is [-2,5,13,18].

To find the result of the expression (A ∩ B) - C, where A, B, and C are sets, we need to perform the following steps:

Given the sets:

A = < - 7, 5 ] U [10, 18 >

B = [ - 2, 8 > U < 13, 23 >

C = < 1, 15 >

1.Find the intersection of sets A and B (A ∩ B):

2. Subtract set C from the intersection (A ∩ B):

Subtracting set C = <1, 15> from the intersection [-2, 5] U [13, 18] means removing any elements that are present in set C from the intersection.

Since set C = <1, 15> does not overlap with either [-2, 5] or [13, 18], the subtraction (A ∩ B) - C results in the same set as the intersection:

(A ∩ B) - C = [-2, 5] U [13, 18].

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The quadrilateral given on the image can be said to be a parallelogram because the diagonals bisect each other.

An effective way to check if a four-sided figure is a parallelogram is through the diagonal test, which involves inspecting its diagonals. According to the examination, if the two diagonals of a four-sided shape intersect at their midpoint, the shape is classified as a parallelogram.

The two diagonals in a parallelogram intersect at their midpoint, although they may not have the same length. This implies that the intersection point of every diagonal bisects the diagonal into two identical parts. Despite the unequal length of its diagonals, the parallelogram is still considered as such due to the bisecting property.

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Answer:

hey it is

Step-by-step explanation:

22 × 18 or 12 into 18

Wendy's marginal tax brackets in 2022 while she is still in school is 12 percent and it will be also 12 percent when she graduates.

Hence the correct option is (D).

Given that Wendy is Single.

So the effective taxable income regime will be which is on the second column.

It is given that at her school days she earns a taxable income of $ 12,000.

So $12000 falls in the slab of $ 10276 - $ 41775.

So the tax rate for her in her school days is 12%.

When she will graduates the taxable per year income will be $35,000.

Clearly, $35,000 also falls into the slab of $ 10276 - $ 41775.

So the tax rate for her when she will graduate will be same 12 percent.

Hence the correct option will be (D).

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