Paula comió un tercio de una pizza, Sofia un cuarto y Isabella el sexto. ¿Cuánto queda de pizza para Nicole?​

The matrix A or the linear transformation it represents to determine whether the transformation is onto or not.

We cannot determine whether the linear transformation given by matrix A is onto based solely on the information provided about the matrix A.

Recall that a linear transformation is onto if and only if its range is equal to its codomain.

In other words, for every vector b in the codomain, there exists at least one vector x in the domain such that [tex]T(x) = b[/tex], where T is the linear transformation.

If A is a matrix representing a linear transformation from[tex]R^2[/tex] to[tex]R^3[/tex], then the codomain is[tex]R^3[/tex], and the range of the transformation is a subspace of [tex]R^3[/tex].

If the matrix A is 1-to-1, then its nullspace only contains the zero vector. This implies that the columns of A are linearly independent, which means that the column space of A has dimension 2.

The range of the transformation has dimension at most 2.

The codomain has dimension 3, it is possible for the range to be a proper subspace of the codomain, in which case the transformation would not be onto.

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Required value of cosy is 12/13.

What is Complementary angle?

Two angles are said to be complementary if their addition is 90°.Let if one angle is x then the other angle will be 90° – x. Hence, we use these complementary angles for trigonometry ratios, where one ratio is complementary to another ratio by 90 degrees such as,

[tex]sin(x) = \cos(\frac{\pi}{2} - x) \\ \tan(x) = \cot(\frac{\pi}{2} - x) \\ \sec(x) = \csc(\frac{\pi}{2} - x) \\ \cos(x) = \sin(\frac{\pi}{2} - x) \\ \cot(x) = \tan(\frac{\pi}{2} - x) \\ \csc(x) = \sec(\frac{\pi}{2} - x)[/tex]

Given, here x and y are complementary.

So, we can say that

[tex]x + y = {90}^{o} \\ y = {90}^{o} - x[/tex]

So,

[tex] \sin( x) = \frac{12}{13} \\ \sin( {90}^{o} - y) = \frac{12}{13} \\ \cos(y) = \frac{12}{13} [/tex]

Therefore, required value of cosy is 12/13.

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Answer: See Below

Step-by-step explanation:

A slope of 0 simply means a straight line. Since we want the point (8,0), we need to shift our graph to the right 8. Therefore, the equation would be...

x = 8

Answer:

first one is 18 second one is 45

Step-by-step explanation:

add 18 and 45 to get 63

area is 63

Answer:

Step-by-step explanation:

Let X be the number of adults who had their faces painted.

Therefore, the number of kids who had their faces painted is 8*X.

Given that 56 kids had their faces painted, we can write an equation as:

8*X = 56

Solving for X:

X = 7

So, there were 7 adults who had their faces painted and 56 kids who had their faces painted.

Altogether, there were 7 + 56 = 63 people who had their faces painted.

The graph of g(x)=(x – 2)²+10 is a translation of the parent function f(x) = x²by² units to the right and 10 units up.

A linear function is defined as a function that has either one or two variables without exponents. It is a function that graphs to a straight line.

The graph of the function g(x) = (x-2)² +10 is a transformation of the parent function f(x) = x² that has been shifted 2 units to the right and 10 units up.

To see this, consider the vertex of the graph of g(x), which occurs at the point (2, 10). This vertex represents the minimum value of the function and is located 2 units to the right and 10 units up from the vertex of the parent function f(x), which is at the origin (0, 0). Therefore, we can say that the graph of g(x) is a translation of the graph of f(x) by a vector (2, 10).

Therefore, The graph of g(x) = (x-2)² +10 is a translation of the parent function f(x) = x²by² units to the right and 10 units up. The vertex of g(x) is located at (2, 10), which is 2 units to the right and 10 units up from the vertex of f(x) at (0, 0).

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The ladder should she placed 12 feet from the base of her house

From the question, we have the following parameters that can be used in our computation:

Using the above as a guide, we have the following:

We make use of the pythagoras theorem to calculate how far the ladder should be placed

Represent this with x

So we have

x^2 = 20^2 - 16^2

Evaluate

x^2 = 144

So, we have

x = 12

Hence. the ladder should she placed 12 feet from the base of her house

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The maximum profit will be $87,000.

To find the quantity of things that will augment the benefit, we want to find the vertex of the parabola addressed by the given capability.

The vertex of a parabola in the form of[tex]y = ax^2 + bx + c[/tex] is located at the point [tex](-b/2a, c - b^2/4a)[/tex].

So for the function [tex]P(x) = -3x^2 + 12x + 75,[/tex] the coefficient of [tex]x^2[/tex] is -3, the coefficient of x is 12, and the constant term is 75.

Therefore, the number of items that will maximize the profit is:

x = -b/2a = -12 / 2(-3) = 2

The second derivative test is something we can use to make sure that this is a maximum. The vertex is a maximum when the second derivative of P(x) is -6, which is negative.

Since x is in thousands, the maximum profit occurs when 2,000 items are produced, and the maximum profit is:

[tex]P(2) = -3(2)^2 + 12(2) + 75 = 87[/tex]

Hence, the business will boost its benefit by making 2,000 things, and the most extreme benefit will be $87,000.

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The proportion (p) of adults who received a parking ticket in the last year is 0.1 or 10%.

The standard error for the proportion (P hat) is given as 0.015, which provides a measure of the precision of our estimate.

To find the proportion (p) of adults who received a parking ticket in the last year, we will use the information provided in the survey.
Determine the number of adults who received a parking ticket (given as 40).
Determine the total number of adults surveyed (given as 400).
Now, calculate the proportion (p) using the formula:
p = (number of adults with parking tickets) / (total number of adults surveyed)
p = 40 / 400
p = 0.1

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Answer: The First Graph and the Last Graph

Step-by-step explanation:

So all of these are inverses of a function. But as for how do you tell if the inverse is a function...

Well, it has to pass the test that all functions have to pass: the Vertical Line Test.

Any time you draw a vertical line down a graph, it should ONLY PASS THROUGH ONE POINT.

Your pictures are a little blurry, but as far as I can tell, Graph 1 is pretty linear, and a vertical line drawn would only intersect one point on the graph.

The second one however... well it seems pretty obvious why the vertical line test wouldn't work there. A vertical line drawn on the right half would intersect two points, which does not pass the test.

Same thing for Graph 3.

Graph 4 looks like it would pass the vertical line test. I cannot see the section on the y-axis that well, but it looks like it doesn't double back on itself.

Just check them with the Vertical Line Test! It's really useful for figuring out if something's a function or not.

The width of the path is 24 meters.

Let's call the width of the path "x".

The dimensions of the inner rectangle (the lawn without the path) are 46m by 34m. The dimensions of the outer rectangle (the lawn with the path) are (46+2x) by (34+2x).

Area of path = Area of outer rectangle - Area of inner rectangle

425m² = (46+2x)(34+2x) - (46)(34)

Simplifying and solving for x:

425m² = (2x+46)(2x+34)

425m² = 4x² + 80x + 1564

4x² + 80x - 1161 = 0

We only want the positive value for x, so:

x = (-80 + 272) / 8

x = 24m

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Answer:

Step-by-step explanation:

You want to know the number of panels and posts needed for a 40 ft fence comprised of 8 ft panels, with a post between panels and at each end of the fence.

The number of panels needed is ...

  (40 ft)/(8 ft/panel) = 40/8 panels = 5 panels

The 5 panels will have 2 ends and 4 spaces, requiring 2 + 4 = 6 posts.

  o ---- o ---- o ---- o ---- o ---- o

Answer:

20 hours

Step-by-step explanation:

for 1 week 560/2

=260

calculation for working hours

Total wage=Rate per hour × actual time spend on working.

Let actual working hours be (x)

260=13×X

260/13=X

20=X

20 hours

The probability that the secretary will receive 6 calls next hour is approximately 0.090 or 9.0%.

The Poisson distribution is a probability distribution that describes the number of events occurring in a fixed time interval, given the average rate at which events occur and the independence of events. In this case, the average rate of calls is 3 calls per hour.

The probability of receiving exactly 6 calls next hour can be calculated using the Poisson probability formula:

[tex]P(X = 6) = (e^(-λ) * λ^6) / 6![/tex]

where λ is the average rate of calls, e is the base of the natural logarithm, and 6! is the factorial of 6.

Substituting the values, we get:

[tex]P(X = 6) = (e^(-3) * 3^6) / 6! ≈ 0.090[/tex]

Therefore, the probability that the secretary will receive 6 calls next hour is approximately 0.090 or 9.0%.l

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The probability that the secretary will receive 6 calls next hour is approximately 0.0504, or 5.04%

To calculate the probability that the secretary will receive 6 calls next hour, given that the average is 3 calls per hour

and the Poisson distribution applies, follow these steps:

Identify the given information: λ (average calls per hour) = 3, k (number of calls to calculate the probability for) = 6.

Use the Poisson probability formula:

P(k) =[tex](e^{(-\lambda)} \times\lambda^k) / k!,[/tex]

where P(k) is the probability of k calls,

e is the base of the natural logarithm (approximately 2.71828),

λ is the average rate (3 calls per hour), and

k! is the factorial of k (6 in this case).

Calculate [tex]e^{(-\lambda)}: e^{(-3)} = 0.04979.[/tex]

Calculate [tex]\lambda^k: 3^6 = 729.[/tex]

Calculate k!: 6! = 6 × 5 × 4 × 3 × 2 × 1 = 720.

Substitute these values into the formula: P(6) = (0.04979 × 729) / 720 ≈ 0.0504.

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The typical number of points from the histogram for scored in 2008 is 11 points.

The typical number of points from the histogram for scored in 2016 is 9 points

A histogram is described as an approximate representation of the distribution of numerical data.

We take note of the following pints while determining the number of points:

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The volume of  the solid is 761.97 in².

The mistake the student made is that the student did not subtract the square of the radius of the inner hollow cylinder  from the square of the radius of the main cylinder.

The volume of the solid can be found by adding the volume of hollow cylinder and the volume of the cone. That is:

Volume of solid = volume of hollow cylinder + volume of the cone

Volume of solid = π(R²-r²)H + 1/3πR²h

where R = 8/2 = 4 in, r = 2 in, H = 18 in and h = 5 in

Volume of solid = [3.14 * (4²-2²) * 18] + [1/3 * 3.14 * 4² * 5]

Volume of solid = 678.24 + 83.73

Volume of solid = 761.97 in²

The mistake the student made is that the student did not subtract the square of the radius of the inner hollow cylinder  from the square of the radius of the main cylinder.

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Angles complementary to ∠BEA are ∠BED and ∠ABE.

Angles supplementary to ∠BFC are ∠AFB and ∠EFC.

Angle supplementary to ∠CAE is ∠FCD.

Complementary angles are defined as two angles whose sum is 90 degrees.

Complementary angles sum up to 90 degrees.

Supplementary angles are those angles that sum up to 180 degrees.

Therefore, the sum of the angles is 180 degrees.

Let's find the angles that are supplementary or complementary to the highlighted angles.

Therefore,

Angles complementary to ∠BEA are ∠BED and ∠ABE.

Angles supplementary to ∠BFC are ∠AFB and ∠EFC.

Angle supplementary to ∠CAE is ∠FCD.

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The area, in square inches, of the composite figure is: 112.125 square inches.

To obtain the area in square inches of the composite figure, we can start by calculating the area of the rectangle to be

= length x width = 14 x 2

= 28 square inches

The leg length of 25 will be divided by 2 to give 12.5. Next we find the area of the isosceles right triangle as follows:

= (leg length)^2 / 2 = (12.5)^2 / 2 = 78.125 square inches.

The combined area = Area of rectangle + Area of isosceles right triangle

= 28 + 78.125

= 106.125 square inches

So, the area of isosceles triangle = (base x height) / 2

= (4 x 3) / 2

= 6 square inches

Now we can add up the areas of the individual shapes to find the total area of the composite figure:

Total area = Combined area + Area of isosceles triangle

= 106.125 + 6

= 112.125 square inches

Complete Question:

Find the area, in square inches, of the composite figure. A composite figure consisting of an isosceles right triangle, a rectangle, and an another isosceles triangle. The combined length of the right triangle and the rectangle is 25 inches. The length of only the rectangle is 14 inches. The base of the other isosceles triangle, which is the same as the width of the rectangle, is 2 inches plus 2 inches, and the height of the isosceles triangle is 3 inches

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According to the concept of inequality, the maximum value of A is obtained when a = 2 and c = 28.

Let's assume that each minute of advertising attracts 40,000 viewers and each minute of comedy attracts 45,000 viewers. Therefore, the total audience (in thousands) that can be reached is given by:

A = 40a + 45c

Firstly, we know that the total time allotted for advertising and comedy cannot exceed 30 minutes. Therefore, we can rewrite the inequality as:

a + c ≤ 30

Solving for c, we get:

c ≤ 30 - a

Now, we can substitute this expression for c in the equation for A:

A = 40a + 45c

A = 40a + 45(30 - a)

A = 1350 - 5a

To maximize A, we need to find the value of a that will result in the maximum value of A. Taking the derivative of A with respect to a and setting it equal to zero, we get:

dA/da = -5 = 0

a = 0

This does not make sense, as a cannot be zero. Therefore, we need to check the endpoints of the interval [2,4] to see if they give a maximum value for A.

When a = 2, we get:

A = 40(2) + 45c

A = 80 + 45c

Substituting c = 30 - a, we get:

A = 80 + 45(30 - 2)

A = 80 + 1350

A = 1430

When a = 4, we get:

A = 40(4) + 45c

A = 160 + 45c

Substituting c = 30 - a, we get:

A = 160 + 45(30 - 4)

A = 160 + 1215

A = 1375

This means that the producer should allocate 2 minutes for advertising and 28 minutes for the comedy program in order to maximize the number of viewers.

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The null hypothesis represents the default assumption or the status quo, while the alternative hypothesis represents the alternative possibility or the hypothesis that is being tested.

These two hypotheses are mutually exclusive, meaning that if one is true, the other must be false.

The null and alternative hypotheses divide all possibilities into two non-overlapping sets.

In statistical hypothesis testing, the null and alternative hypotheses divide all possibilities into two non-overlapping sets.

These two hypotheses represent different explanations or theories about the data, and they are used to make inferences about the population from the sample data.

The null hypothesis represents the default assumption or the status quo. It states that there is no significant difference or relationship between two variables, or that the observed data is due to random chance alone. The alternative hypothesis, on the other hand, represents an alternative explanation or theory about the data.

It states that there is a significant difference or relationship between two variables, or that the observed data is not due to random chance alone.

The null and alternative hypotheses are mutually exclusive, meaning that if one hypothesis is true, the other hypothesis must be false.

They are also exhaustive, meaning that they cover all possible explanations for the observed data.

By dividing all possibilities into two non-overlapping sets, the null and alternative hypotheses allow us to make a decision about which hypothesis is more likely to be true based on the evidence provided by the sample data.

In order to test the null and alternative hypotheses, we use statistical methods to calculate the probability of obtaining the observed data if the null hypothesis were true.

This probability is called the p-value, and it represents the likelihood of obtaining the observed data or a more extreme result if there were no true effect or relationship in the population.

If the p-value is small enough, we reject the null hypothesis in favor of the alternative hypothesis.

The null and alternative hypotheses divide all possibilities into two non-overlapping sets and provide a framework for making inferences about the population based on sample data.

By testing the null hypothesis and calculating the p-value, we can make decisions about which hypothesis is more likely to be true based on the evidence provided by the sample data.

In statistical hypothesis testing, we use evidence from the data to decide whether to reject the null hypothesis in favor of the alternative hypothesis or not.

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For the given data, The correct statement is: A refrigerator with 3.75 ft³ of refrigerator space will have 1.5 ft³ of freezer space.

We can compute the refrigerator space ratio for each model by dividing the refrigerator space by the freezer space:

[tex]\text{For Model A: Space ratio = Refrigerator space / Freezer space} = 15.75 \;ft^3 / 6.3 ft^3 \approx 2.5[/tex]

[tex]\text{For Model B: Space ratio = Refrigerator space / Freezer space }= 10.25 ft^3 / 4.1 ft^3\approx 2.5\\\\\text{For Model C: Space ratio = Refrigerator space / Freezer space }= 15.25 ft^3 / 6.1 ft^3 \approx 2.5[/tex]

We can use this ratio to compute the freezer space for a particular refrigerator with a known refrigerator space because all refrigerators have the same space ratio of around 2.5.

Now for given statements:

Using the space ratio of 2.5, if a refrigerator has 3.25 ft³ of refrigerator space, the freezer space will be= [tex]3.25 ft^3 / 2.5 \approx 1.3 ft^3[/tex], not 1.2 ft³. So, statement a is not true.

Using the space ratio of 2.5, if a refrigerator has 3.25 ft³ of refrigerator space, the freezer space will be [tex]3.25 ft^3 / 2.5 \approx 1.3 ft^3[/tex], not 1.5 ft³. So, statement b is not true.

Using the space ratio of 2.5, if a refrigerator has 3.75 ft³ of refrigerator space, the freezer space will be [tex]3.75 ft^3 / 2.5 \approx 1.5 ft^3[/tex], not 1.2 ft³. So, statement c is not true.

Using the space ratio of 2.5, if a refrigerator has 3.75 ft³ of refrigerator space, the freezer space wii be[tex]3.75 ft^3/ 2.5 \approx 1.5 ft^3[/tex] So, statement d is true.

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Answer: Since we don't have the actual table, we can't provide an exact answer. However, we can explain the general method for solving this type of problem.

Let's say that Julie rented three types of bicycles: type A, type B, and type C. Let's also say that she rented a certain number of each type, and received a certain amount of money from each type. We can set up the following equations based on this information:

Cost to rent type A bike = (Amount received for type A rentals) / (Number of type A bikes rented)

Cost to rent type B bike = (Amount received for type B rentals) / (Number of type B bikes rented)

Cost to rent type C bike = (Amount received for type C rentals) / (Number of type C bikes rented)

We can then solve for each cost by plugging in the given numbers from the table. For example, if the table shows that Julie rented 10 type A bikes and received $200 in rental fees, we would have:

Cost to rent type A bike = $200 / 10 = $20

We can do this for each type of bike to find the cost to rent each kind of bicycle.

It's worth noting that the actual equations may look slightly different depending on the specific information provided in the table. For example, if the table gives the total number of bikes rented and the total amount received, we would need to use slightly different equations to solve for the individual costs.

Thus, the value of the  x- and y-intercepts for the given linear equation is (-30, 0) and (0, 15)

A nonlinear function's intercepts can be defined algebraically or graphically. The points on a graph where a nonlinear function crosses both x and y axes are known as the intercepts.

Given that-

linear equation:  -x + 2y = 30

x-intercept: It occurs when y = 0,

-x + 2(0) = 30

-x = 30

x = -30

y-intercept: It occurs when x = 0,

-0 + 2y = 30

2y = 30

y = 15

Thus, the value of the  x- and y-intercepts for the given linear equation is (-30, 0) and (0, 15).

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The standard deviation of the sample mean weight will decrease by a factor of √2, so the answer is C) It will decrease by a factor of 2. The mean of the sample mean weight will remain unchanged, so the answer is E) It will remain unchanged. It is a correct statement, and it is a result of the Central Limit Theorem, so the answer is C) It is a correct statement, and it is a result of the Central Limit Theorem.

When the sample size is doubled, the standard deviation of the sample mean weight decreases by a factor of √2 according to the formula σ/√n, where σ is the standard deviation of the population and n is the sample size. So, The correct answer is C).

The mean of the sample mean weight is an unbiased estimator of the population mean and is not affected by the sample size. Therefore, doubling the sample size will not change the mean of the sample mean weight.  So, The correct answer is E).

The Central Limit Theorem states that the distribution of the sample mean approaches a normal distribution as the sample size increases, regardless of the underlying distribution of the population. Therefore, the statement is correct and a result of the Central Limit Theorem.  So, The correct answer is C).

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The solution of the expression is x = (-1 ± i√3)/2 and the domain of the expression is all values of x l x ≥ 0 (option c).

The given equation is -x² = √x. To solve this equation, we need to isolate x on one side of the equation. We begin by squaring both sides of the equation to eliminate the radical:

(-x²)² = (√x)²

x⁴ = x

Now we have a quartic equation, which we can solve by factoring:

x(x³ - 1) = 0

We can further simplify this equation by factoring the cubic term using the difference of cubes formula:

x(x - 1)(x² + x + 1) = 0

From this factorization, we can see that the solutions are x = 0, x = 1, and the solutions of the quadratic factor x² + x + 1 = 0. To find the solutions of the quadratic, we can use the quadratic formula:

x = (-1 ± √1 - 4(1)(1))/2(1)

x = (-1 ± i√3)/2

Therefore, the solutions to the equation -x² = √x are x = 0, x = 1, and x = (-1 ± i√3)/2.

Now let's consider the domain of the solutions, which is determined by the inequality x ≥ 0. This inequality means that the solutions must be greater than or equal to 0. We can see that x = 0 and x = 1 satisfy this inequality.

For the solution x = (-1 ± i√3)/2, we can see that it does not satisfy the inequality x ≥ 0 because it is negative. Therefore, the solutions to the equation -x² = √x in the domain x ≥ 0 are x = 0 and x = 1.

Finally, let's consider the inequality x ≤ 0. This inequality means that the solutions must be less than or equal to 0. We can see that x = 0 satisfies this inequality. However, x = 1 and x = (-1 ± i√3)/2 do not satisfy this inequality. Therefore, the solutions to the equation -x² = √x in the domain x ≤ 0 are x = 0.

Hence the correct option is (c).

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Complete Question:

Solve the expression -x² = √x . And identify the domain of the expression,

A. all values of x

B. all values of x l x ≥ 1

C. all values of x l x ≥ 0

D. all values of x l x ≤ 0

Answer:

10

20,00/2000=10

Step-by-step explanation:

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Answer: 10 tons.

Step-by-step explanation: There are 2000 pounds in one ton. Hence:

20000 lb ÷ 2000 lb/ton = 10 tons

The lateral surface-area of the cone with dimensions 12 cm height and 5 cm radius is 65π cm² using the formula πrl.

What is surface-area?

The overall surface area of a solid shape, item, or three-dimensional figure.It can have a flat or curved surface. Cone and cylinder surfaces are curved, but those of solid structures like the cube and cuboid have flat surfaces. The surface area of the cube is provided by 6 times side times side, which equals the area of each face side times side. The cube and cuboid have 6 faces, 12 equal edges, and 8 corners or vertices.

Given that the dimensions of cone:

Radius(r)=5 cm

Height(h) = 12 cm

slant height l =[tex]\sqrt{r^{2} +h^{2} }[/tex]

                      =[tex]\sqrt{(5)^{2} +(12)^{2} }[/tex]

                      =[tex]\sqrt{25+144}[/tex]

                      =[tex]\sqrt{169}[/tex]

                      =13 cm

Slant height (l) = 13 cm

lateral area of cone= πrl.

                                =π (5) (13)

                                =65 π cm²

The lateral surface area of cone=65 π cm²

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If the trapezium "ABCD" have "AD || BC", AD as 24 cm, BC as 10, then the measure of the angle CDA will be 32.27°.

A "Trapezium" is defined as a polygon with "four-sides", where one pair of opposite sides are parallel and the other pair of opposite sides are non-parallel.

Let point "M" be on AD, So, Height = 6 cm ⇒ BM = 6 cm,

We Apply Pythagoras-Theorem in Triangle AMB,

So, AM² = AB² - BM²

⇒ AM² = (7.5)²- (6)²,

⇒ AM  = 4.5,

Let "N" be a point on "AD", such that "CN ⊥ AD",

So, the base AD will be =  AM +  MN + ND,

MN = BC = 10 and CN = BM = 6 (height)

⇒ 24 = 4.5 + 10 + ND,

⇒ ND = 9.5

In triangle-CDN, Tan(∠CDN) = CN/ND,

From the figure , we see that, ∠CDN = ∠CDA,

So, Tan(∠CDA) = 6/9.5,

⇒ ∠CDA =  32.27°.

Therefore, the measure of the angle CDA is 32.27°.

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The given question is incomplete, the complete question is

ABCD is a trapezium. In which AD || BC, AD = 24 cm  BC = 10, AB = 7.5 and Height = 6 cm.

Find out the size of angle CDA.

The numbers that could be added to 1/12 to make the sum greater than 1/2 are 9/24 and 4/9.

To make the sum greater than 1/2, we need to find the number that, when added to 1/12, gives a result greater than 1/2.

1/2 is the same as 6/12, so we need to find the number that, when added to 1/12, gives a result greater than 6/12.

1/12 + 5/12 = 6/12, which is not greater than 1/2.

1/12 + 9/24 = 1/12 + 3/8 = 11/24, which is greater than 1/2.

1/12 + 1/3 = 1/12 + 4/12 = 5/12, which is not greater than 1/2.

1/12 + 4/9 = 3/36 + 16/36 = 19/36, which is greater than 1/2.

Therefore, the numbers that could be added to 1/12 to make the sum greater than 1/2 are 9/24 and 4/9.

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