A pharmacy has determined that a healthy person should receive 70 units of
proteins, 100 units of carbohydrates and 20 units of fat daily. If the store carries
the six types of health food with their ingredients as shown in the table below,
what blend of foods satisfies the requirements at minimum cost to the
pharmacy? Make a mathematical model for the given problem.
Foods Protein units Carbohydrates
units
Fat units Cost per unit
A 20 50 4 2
B 30 30 9 3
C 40 20 11 5
D 40 25 10 6
E 45 50 9 8
F 30 20 10 8

a)  The thrust of the propeller is  23,834 lbf

b)  The induced velocity is 8.44 mph

c)  The velocity in the downstream far field away from the propeller disc     is 161.56 mph

d) The power absorbed by the fluid is  42.7 hp

e)  the propeller power (thrust flight speed) is  4,844.08 hp

f)  The propeller efficiency is 113.6%

a)The thrust of the propeller can be calculated using the equation,

Thrust = 2πρR^2V^2, where ρ is the air density, R is the propeller radius, and V is the average velocity of the propeller disc. For sea level at a speed of 150 mph, the air density is about 0.002377 slugs/ft^3.

the thrust of the propeller can be calculated as: Thrust = 2π x 0.002377 x (6 ft)^2 x (170 mph)^2 = 23,834 lbf

b)The induced velocity can be calculated using the equation v_ind = (1/2) V ∞ [1–(V_∞/V_tip)^2]^(1/2), where V_∞ is the free stream velocity and V_tip is the tip velocity of the propeller. For the given problem, the induced velocity can be calculated as: v_ind = (1/2) x 150 mph x [1–(150 mph/170 mph)^2]^(1/2) = 8.44 mph

c) The velocity in the downstream far field can be calculated using the equation V_∞ = V_tip – v_ind, where V_tip is the tip velocity of the propeller and v_ind is the induced velocity. For the given problem, the velocity in the downstream far field can be calculated as: V_∞ = 170 mph – 8.44 mph = 161.56 mph

d)The power absorbed by the fluid can be calculated using the equation P_fluid = (1/2) ρ V_ind^3 A_disc, where ρ is the air density, V_ind is the induced velocity, and A_disc is the area of the propeller disc. For the given problem, the power absorbed by the fluid can be calculated as P_fluid = (1/2) x 0.002377 x (8.44 mph)^3 x (π x (6 ft)^2) = 42.7 hp

e)The power absorbed by the propeller can be calculated using the equation P_prop = T x V, where T is the thrust of the propeller and V is the flight speed of the aircraft. For the given problem, the power absorbed by the propeller can be calculated as: P_prop = 23,834 lbf x 150 mph = 3,575,500 ft-lbf/s = 4,844.08 hp

f)The efficiency of the propeller can be calculated using the equation η = P_prop/P_fluid, where P_prop is the power absorbed by the propeller and P_fluid is the power absorbed by the fluid. For the given problem, the efficiency of the propeller can be calculated as: η = 4,844.08 hp/42.7 hp = 113.6%

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From the figure the constant of proportionality when y is directly proportional to x² is 1/2

The ratio between two quantities that are directly proportional is the constant of proportionality.

When two quantities grow and reduce at the same rate, they are directly proportional.

The constant of proportionality is solved by taking points from the graph\

using point (2, 2)

y is directly proportional to x² writing in equation form

y α x²

y = kx²

k = y / x²

plugging in values from the graph

k = 2 / 2²

k = 2 / 4

k = 1/2

The constant of proportionality is equal to 1/2

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Answer:-98

Step-by-step explanation:

bc i said so ;)

Answer:

-98 is my answer

The two variables to have a negative correlation are x and y.

Negative correlation is the relationship where x grows as y decreases.

Given,

Here, negative correlation is used to describe the relationship between two variables that results in independent variables moving in one direction while dependent variables move in another.

Positive correlation

Positive correlation is when the value of the variable x rises as the value of the variable y rises.

Negative Correlation

Negative correlation is the relationship where x grows as y decreases.

No correlation

No correlation exists between the two variables.

That example, the term "no-correlation" refers to the absence of a connection between two variables.

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The question is improper. Proper question is given below;

What two variables are likely to have a negative correlation

The values of the expression (1)  (r*s)(x) is 4x²+22x+10 (2) (r-s)(x) is -3x +3 (3) (r+s)(1) is 5x +7

The given parameters that will help us to calculate the values are

r(x) = x+5

s(x) = 4x +2

(1)  r*s(x) will be

(x+5)(4x+2)

Opening the brackets we have

4x²+2x+20x+10

= 4x²+22x+10

(2) (r-5)(x)

Putting the values of r and s

(x+5)- (4x+2)

Open the brackets to have

x+5-4x-2

Collecting like terms to get

-3x+3

(3) (r+s)(x)

By substitution we have

x+5+4x+2

⇒5x +7

In conclusion the values of the expressions are (1)  (r*s)(x) is 4x²+22x+10 (2) (r-s)(x) is -3x +3 (3) (r+s)(1) is 5x +7

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The two different expressions to represent the total cost of 3 liters of shampoo where L is the regular price of a liter bottle are;

Let

Total cost = Regular price of 2 liters of shampoo + discounted price of the 3rd liter

= (L × 2) + (L - 30% of L)

= 2L + (L - 0.3L)

= 2L + (0.7L)

Total cost = 2.7L

In conclusion, the expressions which can be used to represent the situation are;

2L + (L - 0.3L)

2.7L

Complete question:

Emilio buys liter bottles of shampoo when the store has the promotion shown. Write an expression in two different ways to represent the total cost 0f 3 liters of shampoo. Let L be the regular price of a liter bottle.

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There are three line segments in a triangle. Since there are three vertices in a triangle, they form three line segments.

Consider a triangle ABC. It has three vertices A, B, and C.

And it has three angles ∠A, ∠B, and ∠C.

So, the line segments formed by these three vertices are [tex]\overline{AB}[/tex], [tex]\overline{BC}[/tex], and [tex]\overline{CA}[/tex].

So, a closed figure will form by connecting these three vertices. That closed figure is said to be a triangle.

Therefore, there are 3 line segments in a triangle.

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The degrees of freedom (df): For a chi-square test of independence, the df is (number of variable 1 groups − 1) * (number of variable 2 groups − 1).

Under the null speculation and sure conditions (mentioned below), the check statistic follows a Chi-Square distribution with stages of freedom identical to ( r − 1 ) ( c − 1 ) , wherein is the quantity of rows and is the quantity of columns.

The quantity of levels of freedom in a chi-rectangular goodness-of-healthy check is the quantity of classes minus the quantity of parameters anticipated. The quantity of levels of freedom in a chi-rectangular goodness-of-healthy check is the quantity of classes minus the quantity of parameters anticipated minus one.

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Complete question:

what degrees of freedom should be used to conduct a chi-squared test of independence using this table?

The angles COA and POC are 22.5 and 67.5 degrees respectively as POA is a right angled triangle.

POA is a right angle so it is 90 degrees.

POC +COA = 90  .....(1)

Also, POC is 3 times as large as COA.

Let's take COA, "x"

POC = 3x

Substituting the values in equation (1) as follows:

x + 3x = 90

4x = 90

x= 22.5

Therefore,

COA = 22.5°

POC = 22.5*3 = 67.5°

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At m = 26 only the equation will be true, And the values 3, 78, and 126 will not satisfy the equation and make the equation false.

The substitution method is a quick and easy way to algebraically solve a set of linear equations and determine the variables' solutions.

Finding the value of the x-variable in terms of the y-variable from the first equation and then substituting or replacing the value of the x-variable in the second equation.

Here we have

8m − 15 = 5m + 63

=> 3m = 78

And set of possible solution, S = {3, 26, 78, 126}

Here we use the Substitution method to find at what value the equation will be false

At m = 3  

=>  3m = 78  

=>  3(3) = 78  [ which is not true]

At m = 26

=> 3(26) = 78 [ which is true ]

At m = 78

=> 3(78) = 78 [ which is not true ]

At m = 126

=> 3(126) = 78  [ which is not true ]

From the above calculations,

At m = 26 only the equation will be true, And the values 3, 78, and 126 will not satisfy the equation and make the equation false.

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According to the data provided, the regression line equation is given by

y=2.83+0.52x.  The non-linear characteristics of data is ignored by the regression line.

The most popular statistical method for simulating a link between two sets of variables is linear regression. As a result, a linear regression equation that can be applied to data is created.

The required formula is:

[tex]y= a + b_{yx}x[/tex]

[tex]b_{yx} = \frac {n \sum xy - \sum x \sum y}{n \sum x ^ {2} - (\sum x) ^ {2}}[/tex]

[tex]a = \bar y - b_{yx} \bar x[/tex]

[tex]\bar x = 8.81 \\\bar y = 7.45\\\sum x ^ {2} =947\\\sum xy = 770.95[/tex]

[tex]b_{yx} = 0.52[/tex]

[tex]a=2.83[/tex]

y=2.83+0.52x .

In scatter plot, Non-linear characteristics is ignored by the regression line.

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She needs to bike for 66 miles on the last day so that her mean is 54 miles per day.

Mean, in terms of math, is the total added values of all the data in a set divided by the number of data in the set.

To calculate the miles Marthina needs to bike so that her mean is 54 mile per day, we use the formula below.

Formula:

Where:

Let y be the miles she biked for the last day.

From the question,

Given:

Substitute these values into equation 1 and solve for y

Hence, she needs to bike for 66 miles on the last day.

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The properties of the unique solution of the system AX=B depend on the matrix of the system. That is, it depends only on the coefficients on the left side. RHS configuration is not the issue.

The method of least squares is an important statistical technique practiced to find the regression line or the best fit line for a particular pattern. This procedure is described by an equation with specific parameters. The method of least squares is used liberally in analysis and regression. In regression analysis, this method is a standard approach to approximating a system of equations using more equations than unknowns.

The least squares method actually defines a solution to minimize the resulting sum of squares or error for each equation. Find the formula for the sum of squared errors to help find the variation in the observed data.

The least squares method is often used in data fitting. A best fit result is assumed to reduce the sum of squared errors or residuals reported as the difference between the observed or experimental values ​​and the corresponding fitted values ​​in the model.

Linear System of Equation:

A system of linear equations (or linear system) is a collection of one or more linear equations involving the same variables.

A linear system of three variables determines the collection of levels. Intersection is the solution.

For example,

3x + 2y -z =1 , 2x - 2y + 4z =-2

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The evidence suggests that the average distance hiked by each visitor has decreased to less than 25 kilometers, so the null hypothesis is rejected.

The p-value is the probability of getting a test statistic result at least as extreme as the one observed, given that the null hypothesis is true. If the p-value is less than the chosen level of significance (which is 0.05 in this case), then the null hypothesis is rejected. In this case, since the p-value is less than 0.05, the null hypothesis is rejected. This means that there is enough evidence to conclude that the mean distance hiked by each visitor is now less than 25 kilometers.

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Answer:

47. 18

48. 13

49. Candy A

Step-by-step explanation:

47. To find the number of groups of 25 people, you can divide the total number of employees by the size of each group. In this case, you would divide 425 employees by 25 people per group to get 17 groups. However, since you can't have a fraction of a group, you would need to round up to the nearest whole number. In this case, you would have 18 groups of 25 people.

48. he average number of customers contacted each day can be calculated by adding the total number of customers contacted during the week and dividing by the number of days in the week. In this case, the total number of customers contacted during the week is 15 + 12 + 14 + 11 + 13 = 65. Dividing this by the number of days in the week, which is 5, gives an average of 13 customers per day.

The method used to calculate the average in this case is the mean, which is the sum of all the values divided by the number of values. The mean is the most commonly used measure of central tendency and is a good choice for finding the average when the data is evenly distributed and there are no extreme values (outliers).

49. the question is cut off but if its ....the most popular and should be included in the most number of kits?

Candy A is the most popular candy, as it is sold in the greatest quantity on an average day. It should be included in the most number of kits in order to maximize sales.

Answer:

b

Step-by-step explanation:

The factors of 16 are: 1, 2, 4, 8, 16

The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24

The factors of 32 are: 1, 2, 4, 8, 16, 32

The factors of 40 are: 1, 2, 4, 5, 8, 10, 20, 40

Then the greatest common factor is 8

Answer:

13

Step-by-step explanation:

-11+2/3x(-12)+4/1/8 Identify the sign

-11-\\\2/3x12+4/1/8 multiplying and inverting

-11-2/3x12+4x8 Simplify

-11 -2x4+4x8

-11-8+32

13

By solving a linear equation, it can be calculated that the value of 3x - 4 is 8

What is linear equation?

At first it is important to know about equation

Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.

A one degree equation is known as linear equation.

The given linear equation is

[tex]\frac{3}{4}x - 2 = 1\\\frac{3}{4}x = 1 + 2\\\frac{3}{4}x = 3\\x = \frac{3 \times 4}{3}\\x = 4\\[/tex]

Value of 3x - 4  = [tex]3 \times 4 - 4 \\[/tex]

                          = 12 - 4

                          = 8

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The exact value of the expression is 4.15

What is a trigonometric expression?

The trigonometric functions in mathematics are real functions that connect the right-angled triangle's angle to the ratios of its two side lengths. They are extensively employed in all fields of geometry-related study, including geodesy, solid mechanics, celestial mechanics, and many others.

We are given an expression

cosec 30^0 + cosec 60^0 + cosec 90^0

We know that cosec x= 1/sinx

Substituting this in the above equation we get

1/sin30^0 + 1/sin60^0 + 1/sin90^0

Now we know from the trigonometric table

sin30^0 = 1/2

sin60^0 = [tex]\frac{\sqrt{3} }{2}[/tex]

Sin90^0 = 1

Substituting this values in the equation we get

2+ [tex]\frac{2}{\sqrt{3} }[/tex]+1

3+1.15

= 4.15

The exact value of the expression is 4.15

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The equation that represents the employee’s salary, S, after t years since the employee began working with the company is S(t) = 35400 * (1.08)^t

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

Initial salary = 35400

Raise = 8%

Number of years = t

The equation that represents the employee’s salary is calculated as

Salary = Initial salary * (1 + raise)^Number of years

Substitute the known values in the above equation, so, we have the following representation

Salary = 35400 * (1 + 8%)^t

So, we have

S(t) = 35400 * (1.08)^t

Hence, the equation is S(t) = 35400 * (1.08)^t

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The correlation coefficient for x1 and y is 0.91, The correlation coefficient for x2 and y is 0.55 and The correlation coefficient for x1 and x2 is -0.33

Calculating the Correlation Coefficient for x1 and y:

Step 1: Calculate the mean of x1:  Mean of x1 = (30 + 46 + 24 + 51 + 41 + 51 + 74 + 37 + 60 + 77) / 10  Mean of x1 = 47.1

Step 2: Calculate the mean of y:  Mean of y = (94 + 109 + 112 + 178 + 94 + 176 + 171 + 117 + 142 + 212) / 10  Mean of y = 134.1

Step 3: Calculate the standard deviation of x1:  Standard Deviation of x1 = √(((30 - 47.1)2 + (46 - 47.1)2 + (24 - 47.1)2 + (51 - 47.1)2 + (41 - 47.1)2 + (51 - 47.1)2 + (74 - 47.1)2 + (37 - 47.1)2 + (60 - 47.1)2 + (77 - 47.1)2) / 10)

Standard Deviation of x1 = 17.43  

Step 4: Calculate the standard deviation of y:  Standard Deviation of y = √(((94 - 134.1)2 + (109 - 134.1)2 + (112 - 134.1)2 + (178 - 134.1)2 + (94 - 134.1)2 + (176 - 134.1)2 + (171 - 134.1)2 + (117 - 134.1)2 + (142 - 134.1)2 + (212 - 134.1)2) / 10)

Standard Deviation of y = 38.82  

Step 5: Calculate the covariance of x1 and y:  Covariance of x1 and y = ((30 - 47.1) × (94 - 134.1) + (46 - 47.1) × (109 - 134.1) + (24 - 47.1) × (112 - 134.1) + (51 - 47.1) × (178 - 134.1) + (41 - 47.1) × (94 - 134.1) + (51 - 47.1) × (176 - 134.1) + (74 - 47.1) × (171 - 134.1) + (37 - 47.1) × (117 - 134.1) + (60 - 47.1) × (142 - 134.1) + (77 - 47.1) × (212 - 134.1)) / 10  

Covariance of x1 and y = 393.3

Step 6: Calculate the correlation coefficient of x1 and y:

Correlation Coefficient of x1 and y = Covariance of x1 and y / (Standard Deviation of x1 × Standard Deviation of y)  = 393.3 / (17.43 × 38.82)

Correlation Coefficient of x1 and y = 0.91

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consider the following data for a dependent variable y and two independent variables, x1 and x2. x 1 x 2 y 30 12 94 46 11 109 24 17 112 51 16 178 41 6 94 51 19 176 74 7 171 37 13 117 60 13 142 77 16 212 round your all answers to two decimal places. enter negative values as negative numbers, if necessary. Show the correlation coefficient for each variable

An odd degree polynomial with a negative leading coefficient would have endpoint behavior of "as x approaches -∞, y approaches ∞ and as x approaches ∞, y approaches -∞.

What is a polynomial?

A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables. x² - 4x + 7 is an illustration of a polynomial with a single indeterminate x.

The leading coefficient and the degree of the monomial n have an impact on the final behavior.

The function behaves the same at both "ends" when n is even. They both either approach + ∞ or they both approach depending on the sign of the leading coefficient.

The behaviour of the function at both "endpoints" is the reverse when n is odd. Which one is +∞and which one is depends on the sign of the leading coefficient.

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27. 5 minutes is the amount of time I would have to wait to be able to use the merry go round

For the merry go round the wait time for 84 people is said to be 11 minutes.

If 84 persons are to wait for = 11 minutes

How many minutes would you have to wait with 210 people in line?

We would have to cross multiply

84 = 11

210 = ?

84 * ? = 11 * 210

84 ? = 2310

? = 2310 / 84

= 27.5

Hence if 210 are line, the number of minutes that I would have to wait would be 27. 5 minutes on the line before it would get to my turn.

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The wait time for two different rides at a fair are listed in the table. If there are 210 people in line for the merry-go-round, how long can you expect to wait to ride the merry-go-round?

Ride

Tilt-a-whirl

Wait Times

6 minutes for 54 people

Merry-go-round

11 minutes for 84 people in

line

The logarithmic function that models the data is given as follows:

y = 1.0994 + 5.6403 ln(x).

The logarithmic function is used as from the table, the data has a initial fast increase and then the rate of the increase decreases, as the graph reaches it's horizontal asymptote.

The function is defined using a logarithmic regression calculator, inserting the points of the data-set.

From the table, the points are given as follows:

(0, 0.5), (1, 1.4), (2, 4.1), (3, 7.6), (4, 9.1), (5, 10).

(as x represents the number of years after 2005).

Inserting these points into the logarithmic regression calculator, the equation is given as follows:

y = 1.0994 + 5.6403 ln(x).

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Equivalent expression is (x-1)/2x for ((1 -1/x)/2), So Option 1 is correct.

If two expressions can be written similarly or can be combined into a single, simpler phrase, then those two expressions are comparable. Additionally, you can tell if two expressions are equal if you substitute values for the variable in both and they get the same result. The numerator and denominator of equivalent fractions can be written by multiplying or dividing them both by the same value.

This is the rationale for why these fractions simplify to the same number. Equivalent ratios are two ratios that have identical values. Divide or multiply both amounts by the same number to arrive at an equivalent ratio. The method is the same as determining equivalent fractions.

Here expression is ((1 -1/x)/2)

take x as lcm then (x-1)/2x

correct option is (A).

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Correct Question:

Which expression is equivalent to the following complex fraction?

(1-1/x)/2

A) x-1/2x

B) -1/2

C) 2x-2/x

D) 2x/x-1

Answer:

3K

Step-by-step explanation:

The length of the unknown side is 6 units

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

Triangles ABC and QRS

This triangles are similar triangles

This means that

AB : AC= QR : QS

Substitute the known values in the above equation, so, we have the following representation

5 : 3 = 10 : QS

Multiply the first ratio by 2

So, we have

10 : 6 = 10 : QS

By comparison, we have

QS = 6

Hence, the length is 6 units

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The area of this rectangle is 0.105C that can be calculated by implementing the dimensions of length and breadth.

The area of rectangle involves the length and breadth.

Suppose length of rectangle be a,

Height of rectangle (1-a)^3

Area, A= a*(1-a)^3

dA/da = -3a(1-a)^2+(1-a)^3 = 0

a = 1, 0.25

Thus, Area (max) = 0.25*0.75^3 = 0.105

In this case

Height of rectangle C(1-a)^3

Area, A= Ca*(1-a)^3

dA/da = C[-3a(1-a)^2+(1-a)^3] = 0

a = 1, 0.25

Thus, Area (max) = 0.25*0.75^3*C = 0.105C

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It is possible to think of the set of hexadecimal digits, which includes one through four digits, as being divided into disjoint subsets: s, Sa, and so forth, strings in S,, strings in fourth, where each S, is made up of the strings with k hexadecimal digits. There are v rules, there are S2 total strings, and so on.

Hexadecimal number system is one of many sorts of ways for representing numbers that has a base-16 value. Hexadecimal numerals therefore contain 16 symbols or digital values, namely 0 through 1, 2, 3, 4, 5, 6, 7, 8, 9, A–F. Single bit representations of 10, 11, 12, 13, 14, and 15 are A, B, C, D, E, and F, respectively.

It can occasionally be spoken as "hex." There are only 16   used to represent hexadecimal integers. A, B, C, D, E, and F are the following values or symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.

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The value of the surd when simplified is 1/6

We should recall that surd is the square root of all irrational numbers, simplification involves making it more simpler.

The given question is [tex]\frac{1}{(1-\sqrt{5 })^{2} } + \frac{1}{(1+\sqrt{5} )^{2} }[/tex]

We shall be simplifying the expression in parts

From difference of two squares

(1)/[(1-√5)(1+√5) = 1+5 = 1/6

The second part is 1/[(1+√5)(1+√5) = 1/(1+√10+5)

= 1/(6+√10)

Joining the two parts to get

1/6 + 1/(6+√10

Simplifying the fractions

(√10+1)/(6+√10)

= 1/6

Therefore the value of the expression is 1/6

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