You mix gas and oil to obtain 2 and 1/2 gallons of mixture for an engine. The mixture is 40 parts gasoline and 1 part oil. How much gasoline must be added bring the mixture to 50 parts gasoline and 1 part oil?

Using trigonometric identities, we found that sec Φ = -7/(2√10), sin Φ = 3/7, tan β = √11/5, and sin β = √11/6 for the given values of csc Φ, cot Φ, and sec β.

1. We can start by using the Pythagorean identity to find the values of sin Φ:

[tex]sin^2[/tex] Φ + [tex]cos^2[/tex] Φ = 1

Since csc Φ = 1/sin Φ, we can substitute and solve for sin Φ:

1/(7/3) = sin Φ

sin Φ = 3/7

Next, we can use the fact that cot Φ = cos Φ/sin Φ:

cot Φ = cos Φ/(3/7) = - (2√10)/(3)

Simplifying this expression, we get:

cos Φ = - (2√10)/(3) * (3/7) = - 2√10/7

Finally, we can use the fact that sec Φ = 1/cos Φ:

sec Φ = 1/(- 2√10/7) = -7/(2√10)

2. We can use the fact that sec β = 1/cos β to find the value of cos β:

sec β = 6/5

cos β = 5/6

Next, we can use the Pythagorean identity to find the value of sin β:

[tex]sin^2[/tex] β + [tex]cos^2[/tex] β = 1

sin β = √(1 - [tex]cos^2[/tex] β) = √(1 - 25/36) = √(11/36) = √11/6

Finally, we can use the fact that tan β = sin β/cos β:

tan β = (√11/6)/(5/6) = √11/5

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The total area of the garden is 56 square feet and the perimeter of the garden is 30 feet

Given the diagram of a rectangle

The opposite sides of a rectangle are equal

So, the values that complete the missing dimensions are

3 ft and 5 ft

Also, we have the area to be

Area = Sum of area of each garden

This gives

Area = 7 * 3 + 7 * 5

Area = 56

The perimeter is the sum of the lengths

So, we have

Perimeter = 7 + 5 + 3 + 7 + 3 + 5

Evaluate

Perimeter = 30

Hence, the perimeter is 30 feet

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The length of the segment PD obtained using the relationship between similar right triangles is; PD = 7.5 units

A right triangle is a triangle that has an interior angle of 90° (a right angle) and the side opposite the right angle (90°) interior angle is known as the hypotenuse side, while the other two sides of the triangle are the legs of the right triangle.

The possible drawing in the question, obtained from a similar online question, created with MS Word is attached.

The equation of the line that passes through the points A and D, y = -2·x + 6, indicates;

The coordinates of the y-intercept of the line of the equation, is; (0, 6)

The y-intercept indicates that OD = 6 units

The x-intercept coordinates of the graph of the equation, can therefore be obtained as follows; 0 = -2·x + 6

2·x = 6

x = 6/2 = 3

x = 3

The x-intercept is; (0, 3)

The x-intercept indicates that OA = 3 units

The length of the side of the square, s, is therefore;

s = √(s²) = √(6² + 3²) = 3·√5

OA = The length of the x-intercept of ; y = -2·x + 6

The ∠DAO ≅ ∠OPA, and m∠DOA = m∠POA = 90°

Therefore;

∠DOA  ≅ ∠POA

ΔOPA is similar to ΔOAD, by Angle-Angle similarity postulate

The ratio of corresponding sides of similar triangles indicates;

OP/OA = OA/OD

Therefore;

OP/OA = OA/OD

OP/3 = 3/6

OP = 3 × 3/6 = 1.5

PD = OP + OD (Segment addition postulate)

PD = 1.5 + 6 = 7.5

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Answer:

Step-by-step explanation:

Answer:

= 3x - 5/(6x)

Step-by-step explanation:

El triple de x es: 3x

La expresión es:

3x - 5/(6x)

By using chi-squared test, we can conclude that there is evidence of an association between breed and milk yield at the 5% significance level.

What is chi-squared test?

To perform a chi-squared test for independence between breed and milk yield, we need to set up the hypotheses:

Null hypothesis: There is no association between breed and milk yield.

Alternative hypothesis: There is an association between breed and milk yield.

We will use a significance level of 0.05.

To calculate the expected counts for each cell, we will use the formula: (row total x column total) / grand total.

The observed counts and expected counts are:

The grand total is 100.

The degrees of freedom for the test are (number of rows - 1) x (number of columns - 1) = (2 - 1) x (3 - 1) = 2.

Using a chi-squared distribution table or calculator, we find the critical value for a chi-squared test with 2 degrees of freedom and a 0.05 significance level to be 5.99.

To calculate the test statistic, we use the formula:

chi-squared = [tex]sum((observed\ count - expected\ count)^2 / expected\ count)[/tex]

The calculated value of chi-squared is:

[tex]chi-squared = ((32-25.76)^2 / 25.76) + ((20-19.04)^2 / 19.04) + ((16-13.20)^2 / 13.20) + ((10-16.24)^2 / 16.24) + ((18-18.96)^2 / 18.96) + ((4-4.80)^2 / 4.80) = 10.92[/tex]

The degrees of freedom for the test are 2, and the critical value is 5.99.

Since the calculated value of chi-squared (10.92) is greater than the critical value (5.99), we reject the null hypothesis.

Therefore, we can conclude that there is evidence of an association between breed and milk yield at the 5% significance level.

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The expression is true for all values of a between 0 and -5 (inclusive)

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a complete sentence. Any one of the following mathematical operations can be used. A sentence has the following structure: Number/variable, Math Operator, Number/Variable is an expression.

The expression is given as:

|a+5|= -5–a

The absolute value expression is always positive.

So, we have:

a +5 = -5 -a or -5 - a = -5 - a

For the expression a +5 = -5 -a we have:

a + a = -5 - 5

Evaluate like terms

2a =- 10

Divide both sides by 2

a = -5

For the expression -5 - a = -5 - a, we have:

0 = 0

So, we have:

0 = 0 or a = -5

This means that, the expression is true for all values of a between 0 and -5 (inclusive)

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The inequality can be solved to get 2 > x, and the graph on the number line can be seen in the image at the end.

Here we have an inequality and we want to sole it, to do so, we just need to isolate the variable in the inequality.

Here we have:

10 > 5x

To isolate the variable we can divide both sides of the inequality by 5, then we will get:

10/5 > 5x/5

2 > x

So x is the set of all values smaller than 2.

That is the inequality solved, to graph this, drawn an open circle at x = 2 and a line that goes to the left. The graph is the one you can see in the image below.

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Answer: We can use the DuPont Model to calculate the total assets turnover and equity multiplier:

ROE = ROA × Equity Multiplier

Equity Multiplier = Total Assets / Total Equity

Profit Margin = Net Income / Sales

Total Assets Turnover = Sales / Total Assets

Given:

ROA = 12%

Profit Margin = 8%

ROE = 19%

To find the Total Assets Turnover:

Profit Margin = Net Income / Sales

0.08 = Net Income / Sales

Net Income = 0.08 x Sales

ROA = 12%

ROA = Net Income / Total Assets

0.12 = 0.08 x Sales / Total Assets

Total Assets Turnover = Sales / Total Assets = 0.08 / 0.12 = 0.67

Therefore, the total assets turnover is 0.67.

To find the Equity Multiplier:

ROE = ROA x Equity Multiplier

0.19 = 0.12 x Equity Multiplier

Equity Multiplier = 0.19 / 0.12 = 1.58

Therefore, the equity multiplier is 1.58.

Note: The total assets turnover and equity multiplier are related to each other through the DuPont model. The product of these two ratios should be equal to the ROE. In this case, 0.67 x 1.58 = 1.06, which is approximately equal to 1.9 (ROE in decimal form). This confirms that our calculations are correct.

Step-by-step explanation:

The value of x round to the nearest 10th is 28.

One of the most significant areas of mathematics is trigonometry, which has numerous applications. The study of the relationship between the sides and angles of the right-angle triangle is the main objective of the branch of mathematics known as "trigonometry." Trigonometric identities, functions, and formulas can be used to determine the angles or sides of a right triangle that are unknown or missing. Angles can be expressed in trigonometry as either degrees or radians. The five most frequently used trigonometric angles in calculations are 0°, 30°, 45°, 60°, and 90°.

In the given right-angled triangle the angle is 41 degrees and the altitude is 32 units.

So, the trigonometry ratio is -

[tex]tan \theta=\frac{32}{x}\\\\x= 32 tan41\\\\x=28[/tex]

the value of x=28

The complete question is'

Find the value of x in a given triangle, and round to the nearest tenth,

image of the triangle is attached,

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The volume of the cylinder in terms of π is  128π centimetres³.

The cylinder below has a height of 8 centimetres and a diameter of 8 centimetres. Therefore, the volume of the cylinder can be found as follows:

volume of the cylinder = πr²h

where

Therefore,

r = 8 / 2 = 4 centimetres

h = 8 centimetres

volume of the cylinder = π × 4² × 8

volume of the cylinder = 128π centimetres³

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The values of y and z which makes triangle (△) QRS exactly the same (≅) as triangle (△) WVX is

We must note here that the sign, ≅ means exactly the same. Thus,

Line VW = Line QR

The following were obtained from the question:

Line VW = Line QR

31  = y + 20

Collect like terms

y = 31 - 20

y = 11

Thus, the value of y is 11

We can obtain the value of z as follow:

Line QS = Line WX

y + 3z + 28 = 6y + z - 5

11 + 3z + 28 = 6(11) + z - 5

11 + 3z + 28 = 66 + z - 5

3z + 39 = z + 61

Collect like terms

3z - z = 61 - 39

2z = 22

Divide both sides by 2

z = 22 / 2

z = 11

Thus, the value of z is 11

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Therefore, cos(K) = √(17)/9, sin(L) = 8/9, and cos(K) and sin(L) together are (√(17)/9, 8/9) are trigonometric ratios as fractions in simplest terms.

It is possible to calculate trigonometric ratios for various orientations. However, we memories the trigonometric ratios of a few particular angles, such as 0°, 30°, 45°, 60°, and 90°, to make computations easier. The numbers of the ratios at these angles can be found in the trigonometric ratios table.

The Pythagorean formula can be applied to the illustration to determine the length of the third side:

c²= a²+ b²

c²= 8² + √(17)²

c²= 64 + 17

c² = 81

c = 9

We can now calculate the trigonometry ratios of angles K and L:

cos(K) = adjacent/hypotenuse = √(17)/9

sin(L) = opposite/hypotenuse = 8/9

Using the same hypotenuse number of 9, we can calculate both cos(K) and sin(L) as follows:

cos(K) = adjacent/hypotenuse = √(17)/9

sin(L) = opposite/hypotenuse = 8/9

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Answer:

Its b,

Step-by-step explanation:

I had this test before i chose b and it was right

Answer:

(1, 6), (2, 12), (3, 18), (4, 24)

The probability of waiting between 2 and 3 minutes to use the ABC Ban ATM machine is 1/4 or 0.25, which means that approximately 25% of the time a customer has to wait between 2 and 3 minutes to use the ATM.

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a numerical value between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to occur. For example, the probability of flipping a fair coin and getting heads is 1/2 or 0.5.

Since the waiting time for the ABC Ban ATM machine is uniformly distributed between 1 and 5 minutes, the probability density function is given by:

f(x) = 1/(5-1) = 1/4 for 1 ≤ x ≤ 5

To find the probability of waiting between 2 and 3 minutes, we need to find the area under the probability density function between 2 and 3. This is given by the definite integral of the probability density function over the interval [2, 3]:

P(2 ≤ x ≤ 3) = ∫2^3 f(x) dx

= ∫2^3 (1/4) dx

= (1/4) [x]2^3

= (1/4) (3-2)

= 1/4

Therefore, the probability of waiting between 2 and 3 minutes to use the ABC Ban ATM machine is 1/4 or 0.25, which means that approximately 25% of the time a customer has to wait between 2 and 3 minutes to use the ATM.

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The required set of numbers 5, 9, 11, and 14 satisfies all the given conditions.

In mathematics, a set is a logically arranged group of items that can be represented in either set-builder or roster form. Sets are typically denoted by curly brackets; for instance, A = 1, 2, 3, 4 is a set.

a set of four whole numbers that satisfies the given conditions:

5, 9, 11, 14

To check that this set meets the requirements:

The range of the original set (12 - 4 = 8) increased by 2 to become 10 (14 - 4 = 10).

The mean of the original set ((4 + 9 + 10 + 12) / 4 = 8.75) remains the same in the new set ((5 + 9 + 11 + 14) / 4 = 8.75).

The median of the original set is 9.5 (the average of 9 and 10), and the median of the new set is 10 - 1 = 9.

Therefore, the set of numbers 5, 9, 11, and 14 satisfies all the given conditions.

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Answer:

This should be a permutation

Step-by-step explanation:

P (n, r) = n!/(n-r)!

P (12,5) = 12!/(12-5)!

P (12,5) = 12!/7!

P(12,5) = 95040

Since we are given the lengths of the two legs of the triangle, 14 and 16 respectively, the area of the triangle is 152.97 square units.

To find the area of a triangle, we can use the formula: area = (1/2) x base x height

In this case, we are given the lengths of the two legs of the triangle, 14 and 16, so we can use the Pythagorean theorem to find the length of the base:

a^2 + b^2 = c^2

14^2 + 16^2 = c^2

196 + 256 = c^2

452 = c^2

c = √452

c ≈ 21.26

To find the height, we need to drop a perpendicular from the apex to the base, forming two right triangles. Using the Pythagorean theorem again, we have:

(1/2) x base x height = area

(1/2) x 21.26 x height = area

Let's use the right triangle with legs 14 and height h as our reference. Then we have:

h^2 + 7^2 = 16^2

h^2 + 49 = 256

h^2 = 207

h = √207

h ≈ 14.39

Therefore, the area of the triangle is:

= (1/2) x 21.26 x 14.39

= 152.9657

= 152.97².

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Step-by-step explanation:

The average weight of a male African elephant is 15,000 pounds.

To convert pounds to tons, we divide the weight in pounds by 2,000 (the number of pounds in a ton):

15,000 pounds ÷ 2,000 pounds/ton = 7.5 tons

Therefore, the weight of a male African elephant is approximately 7.5 tons.

So the closest answer to this question is "7 tons".

Answer:

7 tons

Step-by-step explanation:

The average weight of a male African elephant is 15,000 pounds. To convert this weight into tons, we need to divide it by 2,000 (since there are 2,000 pounds in a ton).

So, 15,000 ÷ 2,000 = 7.5 tons.

Therefore, the answer is 7 tons (since there are no fractions of tons in the options given).

Therefore, there is a 12.12% chance that the chosen party will be made up exclusively of Republicans.

The likelihood or chance of an occurrence occurring is measured by probability. The occurrence is expressed as a number between 0 and 1, where 0 denotes an impossibility and 1 denotes a certainty. By dividing the number of favorable outcomes by the total number of potential outcomes, the probability of an occurrence is determined. Numerous disciplines, including statistics, mathematics, science, finance, and engineering, heavily rely on probability to make predictions and judgments about the chance of various events happening.

given

A. The combination formula can be used to determine how many options there are to choose three individuals from a group of eleven:

C(11, 3) = 11! / (3! (11-3)!) = 165

There are 165 different methods to choose three from this group of eleven people.

b. The combination formula gives the number of options to choose three Republicans from the group of six Republicans:

C(6, 3) = 6! / (3! (6-3)!) = 20

To choose three Republicans from this set of six Republicans, there are 20 possible options.

c. The ratio of the number of ways to choose three Republicans from the group of six Republicans to the total number of ways to choose three people from the group of eleven determines the likelihood of choosing three Republicans out of the group of eleven.

P(3 Republicans) = C(6, 3) / C(11, 3), which translates to 20 / 165 = 0.1212 or roughly 12.12%.

Therefore, there is a 12.12% chance that the chosen party will be made up exclusively of Republicans.

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Answer:

Step-by-step explanation:

The BAC (Blood Alcohol Concentration) of a person depends on several factors, such as the amount of alcohol consumed, the time over which the alcohol was consumed, and the weight and gender of the person. For this problem, we will assume that the woman has a normal metabolism and that the alcohol is completely absorbed into her bloodstream.

To calculate the BAC at 8 pm, we need to know the amount of alcohol that the woman consumed and the time over which she consumed it. We are given that she had 2 mixed drinks between 7-8 pm, which contained a total of 2 ounces of liquor. We are also given that she had a glass of wine at 10 pm, but we don't need to consider this for the BAC at 8 pm.

Using the Widmark formula, we can calculate the BAC at 8 pm:

BAC = (Alcohol consumed / (Body weight x r)) - (0.015 x Hours since first drink)

where r is the gender constant (0.55 for females) and 0.015 is the rate at which the liver metabolizes alcohol.

Plugging in the values we know, we get:

BAC = (2 oz / (130 lbs x 0.55)) - (0.015 x 1 hour)

BAC = 0.0208 - 0.015

BAC = 0.0058

Therefore, the woman's BAC at 8 pm was approximately 0.0058, which is below the legal limit for driving in most states in the US.

The total cost to fence the rectangular yard is given as follows:

$1,610.28.

The perimeter of a rectangle is the total distance around its outer boundary. To find the perimeter of a rectangle, you need to add up the lengths of all four sides.

If a rectangle has length l and width w, then its perimeter P is given by the equation presented as follows:

P = 2l + 2w

Considering the scale factor of 0.75, the distance represented by each unit on the graph is given as follows:

0.75 x 12 = 9 yards.

Hence the dimensions of the rectangle are given as follows:

The perimeter of the fence is then given as follows:

2 x (72 + 54) = 252 yards.

It costs $6.39 per yard, hence the total cost to fence the yard is given as follows:

252 x 6.39 = $1,610.28.

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Answer:

0 degrees

Step-by-step explanation:

To find m/YAI, we need to first find the measure of angle KAI, which is the sum of angles KAY and LAI. Then, we can find the measure of angle YAI by subtracting the measure of angle KAI from 180 degrees.

Using the angle addition postulate, we know that:

m/KAY + m/LAI = m/KAI

Substituting the given values, we get:

4x + 39 + 12x - 9 = m/KAI

Simplifying the expression, we get:

16x + 30 = m/KAI

Now, we need to solve for x. To do this, we can use the fact that angles KAY and LAI are supplementary (add up to 180 degrees) since they form a straight line. Thus:

m/KAY + m/LAI = 180

Substituting the given values, we get:

4x + 39 + 12x - 9 = 180

Simplifying the expression, we get:

16x + 30 = 180

Subtracting 30 from both sides, we get:

16x = 150

Dividing both sides by 16, we get:

x = 9.375

Now that we know x, we can substitute it back into the equation we found earlier:

16x + 30 = m/KAI

16(9.375) + 30 = m/KAI

150 + 30 = m/KAI

m/KAI = 180

So, we know that angle KAI measures 180 degrees. To find m/YAI, we need to subtract the measure of angle KAI from 180 degrees:

m/YAI = 180 - m/KAI

m/YAI = 180 - 180

m/YAI = 0

Therefore, we can conclude that the measure of angle YAI is 0 degrees. This means that YAI is not an angle, but a line segment, and it does not have a measure in degrees.

Answer:

g(x)= log(x-1)

Step-by-step explanation:

g(x) = f(x-1)

The value of x in the rectangle is 36.

A rectangle is a quadrilateral with opposite sides equal to each other and opposite sides parallel to each other.

All angles measure 90∘ in a rectangle. The sum of angles in a rectangle is 360 degrees.

Therefore, let's find the value of x in the angles.

Hence,

∠2 = x + 30

∠5 = 2x - 48

Therefore,

∠2 + ∠5 = 90°

x + 30 + 2x - 48 = 90

3x - 18 = 90

3x = 90 + 18

3x = 108

divide both sides by 3

x = 108 / 3

x = 36

Therefore,

x = 36

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The correct graph of the inequality -0.4x - 2 < - 1.2 is option 2.

Equation containing a relational operator and a linear expression is known as a linear inequality. In a coordinate plane or space, regions that satisfy a linear inequality are defined. A linear inequality defines a half-plane in two dimensions, which, depending on the inequality, can be either above or below a line. A linear inequality defines a half-space in three dimensions, which, depending on the inequality, is either above or below a plane. The goal of optimization problems is to determine the maximum or minimum value of a linear function under a set of constraints, which are typically represented by linear inequalities.

The given inequality is -0.4x - 2 < - 1.2.

-0.4x - 2 < - 1.2

Adding 2 on both sides of the equation we have:

-0.4x < -1.2 + 2

-0.4x < 0.8

-x < 2

x > -2

Hence, the correct graph of the inequality is option 2.

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Earn 56 units of currency after 8 hours of work.

What is independent variable?

The independent variable is the variable that you change and control in your experiment.

The independent variable is the number of hours worked, h. The dependent variable is the amount of pay earned, P.

To find how much you earn after 8 hours of work, we can simply substitute h = 8 into the equation and evaluate:

P = 7h

P = 7(8)

P = 56

So you would earn 56 units of currency after 8 hours of work.

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Answer:

Each tile would be 8.5 in

Step-by-step explanation:

Area of parallelogram is A=bh, so 4.25*2= 8.5

The mathematical expression to be evaluated is:

[tex]2 \frac{3}{6} - \frac{1}{3}[/tex]

To simplify the expression, we first convert the mixed fraction to an improper fraction:

[tex]2 \frac{3}{6} = \frac{(2 \times 6) + 3}{6} = \frac{15}{6}[/tex]

Substituting this value back into the original expression, we get:

[tex]2 \frac{3}{6} - \frac{1}{3} = \frac{15}{6} - \frac{1}{3}[/tex]

Now we need to find a common denominator for the two fractions:

[tex]\frac{15}{6} - \frac{1}{3} = \frac{15}{6} \times \frac{2}{2} - \frac{1}{3} \times \frac{2}{2} = \frac{30}{12} - \frac{2}{6}[/tex]

We can simplify the second fraction:

[tex]\frac{30}{12} - \frac{2}{6} = \frac{30}{12} - \frac{4}{12} = \frac{26}{12}[/tex]

Finally, we can simplify the fraction by dividing both the numerator and denominator by their greatest common factor, which is 2:

[tex]\frac{26}{12} = \frac{13}{6}[/tex]

Therefore, the simplified value of the mathematical expression is:

[tex]2 \frac{3}{6} - \frac{1}{3} = \frac{13}{6}[/tex]

Answer:

[tex]2\frac{1}{6}[/tex]

Step-by-step explanation:

First, write the fractions as improper fractions.

[tex]\sf2\frac{3}{6} -\frac{1}{3} \\\\\sf\frac{15}{6} -\frac{1}{3}[/tex]

To, subtract the fractions make the denominators the same.

For that, multiply both sides of 1/3 by 2.

[tex]\sf\frac{15}{6} -\frac{1*2}{3*2} \\\\\sf\frac{15}{6} -\frac{2}{6}[/tex]

Subtract.

[tex]\frac{13}{6}[/tex]

Write it as a mixed number.

[tex]2\frac{1}{6}[/tex]