Sam started the week with a balance of -$10 in his checking account. Then he deposited some money into the account. The ending balance was $70. How much did sam deposit?

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

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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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 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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The correct answer is (d) No, it is not continuous because lim x→3 f(x) ≠ lim x→3 f(x).

To determine if the function f(x) = (x+3)/(x²-9) is continuous at x=3, we need to check if the limit of the function exists as x approaches 3 from both the left and the right, and whether this limit is equal to the value of the function at x=3.

First, we can check the limit as x approaches 3 from the left:

lim x→3- f(x) = lim x→3- (x+3)/(x²-9) = (-3)/(0-) = ∞

Next, we can check the limit as x approaches 3 from the right:

lim x→3+ f(x) = lim x→3+ (x+3)/(x²-9) = (6)/(0+) = ∞

Since both one-sided limits are infinite, the limit as x approaches 3 does not exist.

Therefore, the function f(x) = (x+3)/(x²-9) is not continuous at x=3.

The correct answer is (d) No, it is not continuous because lim x→3 f(x) ≠ lim x→3 f(x).

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Answer:

5

Step-by-step explanation:

6.5 / x = 1.3

multiply by x on each side to cancel it out

6.5 = 1.3x

/1.3   /1.3

x = 5

1.3 x 5 = 6.5

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

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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Answer:

-4. my answers need to be 20 characters+ soooo

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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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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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.

Answer:

17/12

Step-by-step explanation:

What is the missing number in [_] -3/4=2/3?

Let the missing number be x

We have

x - 3/4 = 2/3

x = 2/3 + 3/4

x = 8/12 + 9/12

x = 17/12

So, the missing number is 17/12

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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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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1. Chicken became the key product that drove the creation of the Interstate Highway System, which led to the dominance of American trucks in the US truck market.

2. A party may want to impose a tariff to protect domestic industries from foreign competition or to generate revenue for the government.

3. A party is usually trying to protect domestic industries, but a tariff on automobiles would hurt both domestic consumers who would pay higher prices and foreign producers who would face reduced demand.

4. Competition encourages innovation by providing incentives for companies to improve their products and services to stay ahead of their rivals; American trucks stayed the same because they faced little competition due to protectionist policies.

5. Foreign companies tried to get around American-imposed tariffs on automobiles by establishing factories in the US, forming joint ventures with American companies, or exporting through third countries.

6. The methods used to get around tariffs can be efficient in the short term, but they may not be sustainable or desirable in the long term as they can lead to trade imbalances and undermine the competitiveness of domestic industries.

7. Tariffs can be used as a bargaining chip to negotiate better trade deals, but they should be imposed judiciously and only as a last resort to avoid damaging the economy and harming consumers.

1. In the podcast, chicken is cited as the reason why American trucks dominate the truck market in the United States.

This is because in the 1960s, the government imposed regulations on the trucking industry that limited the amount of weight a truck could carry.

To get around these regulations, the industry started using smaller trucks to transport goods, which were often not strong enough to handle the weight.

However, they found that if they put chicken on the back of the trucks, the weight of the cargo would distribute more evenly and the smaller trucks could handle the load.

This led to the development of the modern pickup truck, which is now a staple of the American automobile market.

2. Parties may want to impose tariffs for various reasons, such as to protect domestic industries and jobs from foreign competition, to raise revenue for the government, or to level the playing field in international trade.

Two specific reasons for imposing tariffs could be to protect national security interests or to address unfair trade practices by other countries.

3. Tariffs are usually imposed to protect domestic industries and jobs, and the parties that are being protected are typically the producers of the goods or services in question.

However, tariffs can also harm consumers who may have to pay higher prices for imported goods or may have fewer choices in the marketplace. For example, if a tariff is imposed on automobiles, domestic car manufacturers may benefit, but consumers may have to pay more for cars, and foreign automakers may lose market share.

4. Competition encourages innovation by creating incentives for companies to improve their products or services to gain a competitive advantage.

In the case of American trucks, the lack of competition may have contributed to their lack of innovation over the years. Since they dominated the market, there was little pressure to improve or innovate, and as a result, they have largely stayed the same.

However, the rise of foreign competition in recent years has led American truck manufacturers to invest more in innovation to stay competitive.

5. Foreign companies have tried to get around American-imposed tariffs on automobiles in various ways, such as by moving production to countries not subject to the tariffs, by exporting parts and assembling them in the United States, or by lobbying the government for exemptions or tariff reductions.

6. The methods used by foreign companies to get around tariffs may not be efficient for the economy as a whole because they can lead to higher costs and inefficiencies in the supply chain.

However, they may be necessary for individual companies to remain competitive in the short term.

Ultimately, a more efficient solution would be to address the root causes of the trade imbalances that lead to tariffs in the first place.

7. A tariff can be used as a bargaining chip by threatening to impose tariffs on imports from a country unless they make concessions in trade negotiations.

While this can be an effective strategy in certain situations, it can also lead to a trade war and harm both economies.

In general, tariffs should be used sparingly and as a last resort, and efforts should be made to address underlying trade issues through diplomacy and negotiation.

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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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The type of skewness that can be observed in an histogram are positive and negative skewness.

An histogram can display both positive and negative skewness.

A positive skew means that the tail of the histogram is longer on the positive side of the distribution, indicating that there are more data points with smaller values, and fewer data points with larger values.

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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

The total amount of water Keisha drinks in 12 days is 12 + 18 = 30 quarts.

Algebra is a branch of mathematics that involves using letters and symbols to represent numbers and quantities in mathematical equations and formulas. It includes a variety of topics, such as solving equations, manipulating expressions, working with functions and graphs, and studying abstract structures such as groups and rings.

At its core, algebra is about understanding the relationships between numbers and how they can be manipulated using various operations such as addition, subtraction, multiplication, and division. Algebraic expressions can be used to model real-world situations and solve problems in fields such as physics, engineering, and finance.

To find the total amount of water Keisha drinks in 12 days, we need to add up the amounts of water she drinks each day:

1 1/2 + 2 1/4 + 2 + 1 1/2 + 1 3/4 + 1 1/2 + 1 1/4 + 2 + 2 1/4 + 1 1/2 + 2 + 1 1/2

We can simplify the mixed numbers by converting them to improper fractions:

3/2 + 9/4 + 2 + 3/2 + 7/4 + 3/2 + 5/4 + 2 + 9/4 + 3/2 + 2 + 3/2

Then we can add the fractions together:

(3/2 + 3/2 + 3/2 + 2 + 2 + 2) + (9/4 + 7/4 + 5/4 + 9/4 + 3/2 + 3/2)

Simplifying the sum of the whole numbers, we get:

12

Simplifying the sum of the fractions, we get:

(18/4 + 14/4 + 10/4 + 18/4 + 6/4 + 6/4) = 72/4 = 18

So the total amount of water Keisha drinks in 12 days is:

12 + 18 = 30 quarts.

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The complete  question is:

For 12 days, Keisha keeps track of how much water she drinks per day. 1 1/2 quarts, 2 1/4 quarts, 2 quarts, 1 1/2 quarts, 1 3/4 quarts, 1 1/2 quarts, 1 1/4 quarts, 2 quarts, 2 1/4 quarts, 1 1/2 quarts, 2 quarts, 1 1/2 quarts. What is the total amount of water that Keisha drinks the 12 days?

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 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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Answer:

s < [tex]\frac{1}{7}[/tex]

Step-by-step explanation:

8s + 8 < s + 9

7s + 8 < 9

7s < 1

s < [tex]\frac{1}{7}[/tex]

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

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:

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 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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