1. What is one of the solutions to the system of equations graphed here?
O (-5,-4)
O (2,4)
O (0,4)
O (4,0)

Answer:

To divide two mixed numbers, we first need to convert them into improper fractions.

Converting 3 1/5 to an improper fraction:

3 1/5 = (3 × 5 + 1) / 5 = 16/5

Converting 1 7/9 to an improper fraction:

1 7/9 = (1 × 9 + 7) / 9 = 16/9

Now we can rewrite the division problem as a multiplication problem by taking the reciprocal of the second fraction:

16/5 ÷ 16/9 = 16/5 × 9/16

We can simplify the expression by canceling out the common factor of 16 in the numerator and denominator:

(16 ÷ 16) / (5 ÷ 1) × (9 ÷ 16) / (1 ÷ 1) = 1 / 1 × 9 / 16 = 9/16

Therefore, 3 1/5 ÷ 1 7/9 = 9/16 in simplest form.

Step-by-step explanation:

Solution of expression  3 1/5 divided by 1 7/9 are, 9/5

We have,

To find 3 1/5 divided by 1 7/9 in simplest form.

Now, We can divide,

3 1/5 divided by 1 7/9

3 1/5 ÷ 1 7/9

16/5 ÷ 16/9

16 / 5 × 9/16

9 / 5

Therefore, Solution of expression are, 9/5

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The value of the expression [tex]5x + 1 / 4 y^2\\[/tex] when x = 3 and y = 2 is 16.

When someone is experiencing "joy," for instance, the user wants them to feel shocked or very happy. The user will be positively impression if you convey surprise or extreme joy. When someone is experiencing "fright," they want them to feel extremely saddened or disgusted.

A phraseme is a multi-word , multi-morphemic statement whose components contain at least a single word that is selectionally limited. It is also known as a set phrase, persist longer, idiom phrase, multiword expression, or idiom.

To evaluate the expression [tex]5x + 1 / 4 y^2[/tex] when x = 3 and y = 2, we substitute x = 3 and y = 2 into the expression and simplify as follows:

[tex]5x + 1/4 y^2 = 5(3) + 1/4 (2)^2[/tex](substitute x = 3 and y = 2)

= 15 + 1/4(4)

= 15 + 1

= 16

Therefore, the value of the expression [tex]5x + 1 / 4 y^2[/tex]when x = 3 and y = 2 is 16.

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question

What is the value of the expression[tex]5x + 1 /4 y^2[/tex] when x = 3 and y = 2?

Answer:

The lower limit and upper limits of the athlete's height can be calculated by subtracting and adding the absolute error, respectively.

Lower Limit = 165.5 cm - 0.1 cm = 165.4 cm

Upper Limit = 165.5 cm + 0.1 cm = 165.6 cm

Therefore, the athlete's height lies between 165.4 cm and 165.6 cm, inclusive.

After the collision, cart a moves in the negative x direction with a speed of 4 m/s, and cart b moves in the positive x direction with a speed of 2 m/s.

In a perfectly elastic collision, the total momentum of the system is conserved, as well as the total kinetic energy. This means that the sum of the momenta of the carts before the collision is equal to the sum of the momenta after the collision. In this case, since cart b is initially at rest, its initial momentum is zero.

We can use conservation of momentum to determine the final velocities of the carts. Let the velocity of cart b after the collision be v, then the velocity of cart a after the collision is -4 m/s. The momentum of cart a before the collision is m(4 m/s) = 4m, and the momentum of cart b after the collision is 3mv.

Using conservation of momentum, we have:

m(4 m/s) + 0 = m(-4 m/s) + 3mv

Simplifying this equation, we get:

8m = 3mv + 4m

Dividing both sides by 3m, we get:

v = (8/3) - (4/3)v

Solving for v, we get:

v = 2 m/s

So after the collision, cart a moves in the negative x direction with a speed of 4 m/s, and cart b moves in the positive x direction with a speed of 2 m/s. We can verify that this satisfies conservation of momentum:

m(4 m/s) + 0 = m(-4 m/s) + 3m(2 m/s)

4m = 4m

This result shows that in a perfectly elastic collision, even though the carts exchange momentum, the total momentum of the system is conserved.

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The cost of 1 bottle of water when sold in a 24-pack case with a case price of $7.50 is $0.3125 or 31.25 cents.

The given equation is 24b = t, where b is the cost of one bottle of water and t is the price of a case of 24 bottles.

We are given that the price of the case is $7.50. Substituting this value in the equation, we get:

24b = 7.50

To solve for b, we need to isolate it on one side of the equation. We can do this by dividing both sides by 24:

b = 7.50/24

Simplifying this expression, we get:

b = 0.3125

Therefore, the cost of 1 bottle of water when sold in a 24-pack case with a case price of $7.50 is $0.3125 or 31.25 cents. In other words, if you were to buy a case of 24 bottles of water for $7.50, each bottle of water would cost you about 31.25 cents.

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The vertices of net that represents a container is 8 vertices.

A cuboid is a three-dimensional geometric shape that is formed by six rectangular faces or sides. It is also known as a rectangular prism. A cuboid has six faces, twelve edges, and eight vertices. The opposite faces of a cuboid are congruent and parallel to each other.

A cuboid can be defined by its length, width, and height, which are the three dimensions of the cuboid. The length is the longest side, the width is the shorter side, and the height is the distance between the two parallel faces.

Cuboids are common in many everyday objects, such as boxes, buildings, and books. They are also important in geometry and engineering as they have a simple shape that is easy to work with and can be used to represent more complex shapes.

The figure which is shown below is a cuboid. Net has 12 edges, 6 faces and 8 vertices.

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The complete question is:

The net below represent a container. What solid figure does it show?

How many vertices does the container have?

Answer: We can simplify the given equation as follows:

sin(x/2) = sqrt(2) - sin(x/2)

2sin(x/2) = sqrt(2)

sin(x/2) = sqrt(2)/2

x/2 = pi/4 or x/2 = 3pi/4 (using the standard angles for sin)

x = pi/2 or x = 3pi/2

However, we need to check if these solutions satisfy the original equation since we simplified it along the way.

For x = pi/2, we have:

sin(pi/4) = sqrt(2) - sin(pi/4)

sqrt(2)/2 = sqrt(2) - sqrt(2)/2

sqrt(2)/2 = sqrt(2)/2

This is true, so x = pi/2 is a solution.

For x = 3pi/2, we have:

sin(3pi/4) = sqrt(2) - sin(3pi/4)

-sqrt(2)/2 = sqrt(2) - (-sqrt(2)/2)

-sqrt(2)/2 = sqrt(2)/2

This is not true, so x = 3pi/2 is not a solution.

Therefore, the only solution in the interval [0, 2pi) is x = pi/2.

Step-by-step explanation:

1. The probability that an infected patient’s length of stay will be greater than 7 days is 0.3085.

2. The 70th percentile in stay length for a patient given that they have a

post-operative infection is 7.04.

3. The probability that the average stay length of the next 2 infected patients is less than 5.5 days is 0.3632.

4. The probability that a patient is infected and then stays for 3 to 4 days is  0.1587.

1. Probability of an infected patient staying more than 7 days:

We can standardize the normal distribution using the formula: Z = (X - μ) / σ, where X is the length of stay, μ is the mean length of stay, and σ is the standard deviation of the length of stay.

So, Z = (7 - 6) / 2 = 0.5.

Using a standard normal distribution table or calculator, we can find the probability that a patient will stay longer than 7 days as:

P(Z > 0.5) = 0.3085.

2. The 70th percentile in stay length for an infected patient:

We can use the inverse standard normal distribution function to find the Z-score corresponding to the 70th percentile.

Using a standard normal distribution table or calculator, we find that the Z-score corresponding to the 70th percentile is approximately 0.52.

So, Z = 0.52 = (X - 6) / 2.

Solving for X, we get:

X = 6 + 0.52 * 2 = 7.04.

3. Probability that the average stay length of the next 2 infected patients is less than 5.5 days:

The average length of stay of 2 infected patients can be modeled by a normal distribution with a mean of 6 days (the mean of a single infected patient's length of stay) and a standard deviation of σ/√2, where σ is the standard deviation of the length of stay of a single infected patient.

So, the standard deviation of the average length of stay of 2 infected patients is:

σ/√2 = 2/√2 = 1.414 days.

Using the standardized normal distribution formula, we get:

Z = (5.5 - 6) / 1.414 = -0.3536.

Using a standard normal distribution table or calculator, we can find the probability that the average stay length of the next 2 infected patients will be less than 5.5 days as:

P(Z < -0.3536) = 0.3632.

4. Probability that a patient is infected and then stays for 3 to 4 days:

We can standardize the normal distribution as before using the formula:

Z = (X - μ) / σ, where X is the length of stay, μ is the mean length of stay, and σ is the standard deviation of the length of stay.

For X = 3 days, Z = (3 - 6) / 2 = -1.5.

For X = 4 days, Z = (4 - 6) / 2 = -1.

Using a standard normal distribution table or calculator, we can find the probability that a patient is infected and then stays for 3 to 4 days as:

P(-1.5 < Z < -1) = P(Z < -1) - P(Z < -1.5) = 0.1587

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Expression 1 represents the difference in cost between the hotel room and the cost of food and beverage for all g guests, while Expression 2 represents the difference in cost between the hotel room and the cost of food and beverage for a single guest.

Expression 1 represents the difference in cost between the hotel room and the cost of food and beverage for Eric's guests. The first part of the expression (326 + 37g) represents the cost of the hotel room for all g guests, while the second part of the expression (287 + 23g) represents the cost of food and beverage for all g guests. To calculate the total cost of the hotel room and food and beverage, we can use the following formula: (326 + 37g) - (287 + 23g) = 39 + 14g.Expression 2, on the other hand, represents the difference in cost between the hotel room and the cost of food and beverage for a single guest. The first part of the expression (38 + 14g) represents the cost of the hotel room for one guest, while the second part of the expression (287 + 23g) represents the cost of food and beverage for one guest. To calculate the total cost of the hotel room and food and beverage for one guest, we can use the following formula: 38 + 14g.In conclusion, Expression 1 represents the difference in cost between the hotel room and the cost of food and beverage for all g guests, while Expression 2 represents the difference in cost between the hotel room and the cost of food and beverage for a single guest.

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To determine the number of milliliters (mLs) of Erythromycin sup 500mg/10mL needed to administer Erythromycin 0.4g bid for infection, we can use the following formula:

To calculate the adecuated dose of Erythromycin we have to follow the following procedure:

Where:

First, we need to convert the ordered dose from grams to milligrams (mg), as the concentration of Erythromycin sup is given in milligrams. 0.4g is equal to 400mg.

Next, we can substitute the values into the formula:

Therefore, the number of mLs of Erythromycin sup 500mg/10mL needed to administer Erythromycin 0.4g bid for infection is 8 mLs. It is important to note that the medication should be administered as prescribed by a healthcare provider, and the patient should complete the entire course of treatment, even if symptoms improve.

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Volume of sphere with radius r = 7 m is [tex]v_1=1,436.026 \ \text{m}^3[/tex].

Step-by-step explanation:

We know that volume of sphere  [tex]=\dfrac{4}{3}\pi r^3[/tex] given that [tex]\pi =3.14,\ r=7 \ \text{ft}[/tex].

volume of sphere  [tex]=\dfrac{4}{3}\pi r^3=v_1[/tex]

[tex]\implies v_1=\dfrac{4}{3}\pi r^3[/tex]

[tex]\implies v_1=\dfrac{4}{3}\pi(7)^3[/tex]

[tex]\implies v_1=\dfrac{4}{3}\pi (343)[/tex]

[tex]\implies v_1=\dfrac{4}{3}(3.14)(343)[/tex]

[tex]\implies v_1=1,436.026 \ \text{m}^3[/tex]

∴ Volume of sphere with radius r = 7 m is [tex]v_1=1,436.026 \ \text{m}^3[/tex].

It would be important to have more information about the driving conditions, types of vehicles, and other factors that could influence gas mileage in order to draw more conclusive insights from this data.

Based on the graph provided, it appears that both Amy and Laura's average gas mileage fluctuated over the course of the four weeks. Amy's average gas mileage started at around 30 miles per gallon (mpg), decreased in week 2, and then increased again in weeks 3 and 4. Laura's average gas mileage started at around 25 mpg, increased in week 2, decreased in week 3, and then increased again in week 4.

However, one could make some tentative observations. For example, Amy's average gas mileage appears to be consistently higher than Laura's over the four-week period, and both of their average gas mileage values appear to be somewhat volatile, with significant changes occurring from week to week.

Overall, it would be important to have more information about the driving conditions, types of vehicles, and other factors that could influence gas mileage in order to draw more conclusive insights from this data.

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The x-intercept is 26. This means that if Stanley were to buy only pizzas (and no sub sandwiches), he would need to buy 26 pizzas to spend exactly $130 on food.

What do you mean by Algebraic expression ?

An algebraic expression is a mathematical phrase that contains one or more variables, numbers, and operations such as addition, subtraction, multiplication, division, and exponentiation.

The given equation is 5x + 6.50y = 130. To find the x-intercept, we set y = 0 and solve for x.

5x + 6.50(0) = 130

5x = 130

x = 26

Therefore, the x-intercept is 26. This means that if Stanley were to buy only pizzas (and no sub sandwiches), he would need to buy 26 pizzas to spend exactly $130 on food.

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The surface area of the given triangular prism having an isosceles triangle   base with sides 40,41 and 43 cm, is 2274 cm².

Area is a measure of the size of a two-dimensional shape or surface, such as a rectangle, triangle, circle, or any other shape that has length and width. It is usually expressed in square units, such as square meters, square centimeters, square feet, or square inches.

To find the surface area of a triangular prism, we need to find the area of each face of the prism and add them up.

The triangular base of the prism is an isosceles triangle with sides of 40 cm, 41 cm, and 43 cm.We may use Heron's formula to determine the area of this triangle:

s = (40 + 41 + 43) / 2 = 62

A = √(s(s-40)(s-41)(s-43)) = √(622221*19) = 798

Therefore, the area of the triangular base is 798 cm².

The height of the prism is given as 18 cm, which is also the length of the rectangular side of the prism.

The two other faces of the prism are rectangles with lengths equal to the base of the triangle (41 cm), and widths equal to the height of the prism (18 cm). The area of each rectangle is:

A = lw = 4118 = 738

Therefore, the area of both rectangles is 2*738 = 1476 cm².

The total surface area of the prism is the sum of the area of the base and the area of both rectangular sides:

Total surface area = Area of base + 2*(Area of rectangle)

Total surface area = 798 + 2*738

Total surface area = 2274 cm².

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Answer:

28

Step-by-step explanation:

a = b * h

a = 4 * 7 = 28

We want to copy the original triangle using only two of its sides and the included angle. To do this, we'll create a new triangle with the same side lengths and angle measures as the original triangle.

To copy a triangle using two of its sides and the included angle, follow these steps:

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The number of male students that went on the school trip given that there are 30 female students is 24

Given that we have the following statement:

Every teacher is assigned 4 male students and 5 female students

The above statement means that we have the following ratio

Ratio = Male : Female

So, we have the following equation

Male : Female = 4 : 5

When the number of female students is 30, we have the following

Male : 30 = 4 : 5

Express as fraction

Male/30 = 4/5

So, we have

Male = 4/5 * 30

Evaluate

Male = 24

Hence, the number of male students is 24

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(a) The probability of rain on January 1st is 0.614. (b) The probability of rain for the first time in the New Year on January 3rd is 0.136*0.614 = 0.083. (c) the probability that people of Seattle get to wait at least 3 days until it rains for the first time in the New Year is 0.053. (d) They wait for the first day of rain in the New Year is 1/0.614 ≈ 1.63 days. (e) The distribution of X is a geometric distribution.

a) The probability that it will rain on January 1st can be estimated using the information provided by komonews.com, which states that the chances of rain on any day in the first week of January in Seattle is about 0.614. Assuming that the probability of rain is constant across all days of the week, the probability of rain on January 1st is also 0.614.

b) The probability that it will rain for the first time in the New Year on January 3rd can be calculated by considering the probability of no rain for the first two days, followed by rain on the third day. The probability of no rain for the first two days is [tex](1-0.614)^2[/tex] = 0.136, and the probability of rain on the third day is 0.614. Therefore, the probability of rain for the first time in the New Year on January 3rd is 0.136*0.614 = 0.083.

c) The probability that the people of Seattle get to wait at least 3 days until it rains for the first time in the New Year can be calculated by considering the probability of no rain for the first three days. The probability of no rain for the first three days is [tex](1-0.614)^3[/tex] = 0.053. Therefore, the probability that people of Seattle get to wait at least 3 days until it rains for the first time in the New Year is 0.053.

d) The expected value or average of the number of days people in Seattle wait for the first day of rain in the New Year can be calculated by using the formula E(X) = 1/p, where p is the probability of rain on any given day. Therefore, the expected value or average number of days people in Seattle wait for the first day of rain in the New Year is 1/0.614 ≈ 1.63 days.

e) The number of days until it rains for the first time in the New Year, X, is a geometric random variable since it represents the number of trials until the first success (rain). The probability of success (rain) remains constant over time, and the trials (days) are independent of each other. Therefore, the distribution of X is a geometric distribution.

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Answer:

Step-by-step explanation:

Approach: If four numbers a, b, c and d are in proportion then a:b = c:d. The solution is to sort the four numbers and pair up the first 2 together and the last 2 together and check their ratios this is because, in order for them to be in proportion, the product of means has to be equal to the product of extremes.

Answer:

x=3, y=2

Step-by-step explanation:

First Add both equations

3x-y=7                     ---1

x+y=5                      ---2

----------

so we get, 4x=12

so x=3

Now plug x back into equation 2 so we get y=2

Step-by-step explanation:

that means we optionally multiply one or both equations with some factors, so that one variable term has the same coefficient in both equations but with different signs.

and then we add both equations giving us one equation in the other variable, which we can solve.

and then we use that with any of the original equations to solve for the first variable.

in this case we don't need the multiplication step, as the terms in y have already the same coefficient (1) with different signs.

so, we add both equations

3x - y = 7

+ x + y = 5

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

4x 0 = 12

4x = 12

x = 12/4 = 3

x + y = 5

3 + y = 5

y = 5 - 3 = 2

Answer:

Cannot be determined

Step-by-step explanation:

Without any additional information, we cannot accurately determine the probability that the code number for a new customer will begin with the number 7.

To calculate the probability, we would need to know the total number of possible code numbers that can be assigned to new customers and how many of those code numbers start with the number 7. If we have that information, we can calculate the probability as follows:

Probability = Number of code numbers starting with 7 / Total number of possible code numbers

For example, if there are 1000 possible code numbers and 50 of them start with the number 7, the probability of a new customer's code number starting with 7 would be:

Probability = 50 / 1000

Probability = 0.05 or 5%

Answer:196 possible committees

Step-by-step explanation:

Part (a): Three cases:

Case 1: 3 men and 5 women: (7 C 3) * (5 C 5) = 35 * 1 = 35; or

Case 2: 4 men and 4 women: (7 C 4) * (5 C 4) = 35 * 5 = 175; or

Case 3: 5 men and 3 women: (7 C 5) * (5 C 3) = 21 * 10 = 210

35 + 175 + 210 = 420 possible committees

Part (b): Six cases:

Cases 1–3: Oldest man included (but not oldest woman):

Case 1: 3 men and 5 women: Not possible**; therefore, 0; or

Case 2: 4 men and 4 women: 1 * (6 C 3) * (4 C 4) = 20 * 1 = 20; or

Case 3: 5 men and 3 women: 1 * (6 C 4) * (4 C 3) = 15 * 4 = 60; or

Cases 4–6: Oldest woman included (but not oldest man):

Case 4: 3 men and 5 women: (6 C 3) * (5 C 5) = 20 * 1 = 20; or

Case 5: 4 men and 4 women: (6 C 4) * 1 * (4 C 3) = 15 * 4 = 60; or

Case 6: 5 men and 3 women: (6 C 5) * 1 * (4 C 2) = 6 * 6 = 36

0 + 20 + 60 + 20 + 60 + 36 = 196 possible committees

Answer:

4500

Step-by-step explanation:

250 x 18 = 4500

Answer:

Step-by-step explanation:

a) 2x-6 is equivalent to 1) -6+2x

b) 5/3-x+1/3 is equivalent to 4) x-3+x

c) 2x-3 is equivalent to 3) -6.9++4.9

d) 3x+0 is equivalent to 2) 3x

e) 3/5-13/5 is equivalent to 5) 3/2x+2+1/2x

Answer:0.65

Step-by-step explanation:

The standard error of the sample mean is approximately 0.682, rounded to the hundredths place.

To calculate the standard error of the sample mean, we need to find the sample mean and the standard deviation of the data. Then we can divide the standard deviation by the square root of the sample size.

First, let's calculate the sample mean:

Mean = (64.5 + 64 + 66.5 + 64 + 62.5 + 61 + 63) / 7 = 64.14

Next, let's calculate the standard deviation. We will use the sample formula for standard deviation (Bessel's correction):

Calculate the squared differences from the mean for each temperature:

(64.5 - 64.14)² = 0.1904

(64 - 64.14)² = 0.0204

(66.5 - 64.14)² = 5.5376

(64 - 64.14)² = 0.0204

(62.5 - 64.14)² = 2.6836

(61 - 64.14)² = 9.8324

(63 - 64.14)² = 1.2696

Calculate the sum of the squared differences:

Sum = 0.1904 + 0.0204 + 5.5376 + 0.0204 + 2.6836 + 9.8324 + 1.2696 = 19.5544

Calculate the variance:

Variance = Sum / (n - 1) = 19.5544 / (7 - 1) = 3.25907

Calculate the standard deviation:

Standard Deviation = sqrt(Variance) = sqrt(3.25907) = 1.80597

Finally, let's calculate the standard error of the sample mean:

Standard Error = Standard Deviation / sqrt(n) = 1.80597 / sqrt(7) ≈ 0.682

Therefore, the standard error of the sample mean is approximately 0.682, rounded to the hundredths place.

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Answer:

50, because yes

Answer: 7/20

Step-by-step explanation:

35+17=52

80-52=28

28/80=7/20

Answer:

28

Step-by-step explanation:

35+17=52

80-52=28

so your answer is 28

Answer: See below

Step-by-step explanation:

To solve this problem, we need to assign each digit from 0 to 9 to a unique letter so that each letter represents a single digit. We can then use this mapping to solve the addition problem:

Let's assign the letters A, B, C, D, E, F, G, H, I, and J to the digits 0 to 9, respectively.

Then, the addition problem becomes:

A B C

D E F

We know that the sum of each column must be the same, so:

C + F = 10 + B

B + E = 10 + A

We can rewrite these equations as:

C - B + F = 10

B - A + E = 10

Since we are given that the sum of the two numbers is the same, we know that:

C + F + D + E = 1112

We can substitute C and F in terms of A and B using the equations above:

C = 10 + B - F

F = 10 + C - B

Substituting these expressions into the equation for the sum, we get:

10 + B - F + C + D + E = 1112

Simplifying this equation, we get:

B - F + C + D + E = 1102

Now we can substitute in the expressions for C and F in terms of A and B:

B - (10 + B - F) + (10 + C - B) + D + E = 1102

Simplifying and canceling out terms, we get:

F - C - D - E = -92

We know that each digit is unique, so we can assume that A is not equal to 0 (otherwise the number would not have 4 digits). We can also assume that D is not equal to 0, since it is the leftmost digit of the second number.

Trying different values for A and D, we find that A = 2 and D = 3 works:

A B C

D E F

2 7 9

1 7 3

The sum of each column is 3 + 7 + 2 = 1 + 9 + 7, which is equal to 12. Therefore, the solution is:

2 7 9

1 7 3

4 5 2