A rectangle has a length of 10 3/16 inches and a width of 6 7/8 inches. what is the perimeter of the rectangle?​

Function g has non-constant elasticity of substitution and does not satisfy the Inada condition for all inputs. Therefore, it is not a homothetic function.

A homothetic function is a function of a particular form in economics and mathematics. It is a function where the structure remains the same even when the magnitudes change. This means that it does not change its properties even when there is a proportional change in the inputs or the parameters. Hence, it is a class of functions in which the ratio of the parameters determines the outcomes. Therefore, it is said that homothetic functions possess constant elasticity of substitution (CES) and satisfy the Inada condition for all inputs.

A homothetic function, f is a production function or utility function that has constant returns to scale. Hence, it is said that a homothetic function has a unique property of constant elasticities of substitution. The homothetic functions have a certain form of homogeneity that leads to scale invariance. Hence, it implies that the functions that have the same form as the homothetic function but have different coefficients, are still homothetic functions. Thus, if a function has the same structure and elasticity of substitution, it is considered a homothetic function.

Given the two functions:

f(x1,...,xn) = A(8₁x₁ +82x2 + ... + ₂x)
g(x1, x2) = 2logr1 + 5logr2

The functions f and g are not homothetic. This is because f is a homogeneous function that satisfies the property of constant elasticity of substitution and the Inada condition for all inputs, whereas g does not.

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The functions f and g are not homothetic. This is because f is a homogeneous function that satisfies the property of constant elasticity of substitution and the Inada condition for all inputs, whereas g does not.

Here, we have,

Function g has non-constant elasticity of substitution and does not satisfy the Inada condition for all inputs. Therefore, it is not a homothetic function.

A homothetic function is a function of a particular form in economics and mathematics. It is a function where the structure remains the same even when the magnitudes change. This means that it does not change its properties even when there is a proportional change in the inputs or the parameters. Hence, it is a class of functions in which the ratio of the parameters determines the outcomes. Therefore, it is said that homothetic functions possess constant elasticity of substitution (CES) and satisfy the Inada condition for all inputs.

A homothetic function, f is a production function or utility function that has constant returns to scale. Hence, it is said that a homothetic function has a unique property of constant elasticities of substitution. The homothetic functions have a certain form of homogeneity that leads to scale invariance. Hence, it implies that the functions that have the same form as the homothetic function but have different coefficients, are still homothetic functions. Thus, if a function has the same structure and elasticity of substitution, it is considered a homothetic function.

Given the two functions:

f(x₁,...,xₙ) = A(8₁x₁ +8₂x₂ + ... + ₂x)

g(x₁, x₂) = 2logr₁ + 5logr₂

The functions f and g are not homothetic. This is because f is a homogeneous function that satisfies the property of constant elasticity of substitution and the Inada condition for all inputs, whereas g does not.

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Answer:

80

Step-by-step explanation:

Let the total number of statues be s.  Then 0.75s = 60, and s = (4/3)(60 statues) = 80

He has 80 statues total.

Answer:

5.87

Step-by-step explanation:

I figured it out. Do 10 x sin (36) to get the answer. I would explain, but it's kinda of hard to in this case.

The probability that the mean of the first sample will be larger than the mean of the second sample is approximately 0.976 or 97.6%.

To find the probability that the mean of the first sample will be larger than the mean of the second sample, we can use the central limit theorem and the formula for the standard error of the difference between two means:

SE = sqrt[(s1^2/n1) + (s2^2/n2)]

Where SE is the standard error, s1 and s2 are the standard deviations of the two populations, n1 and n2 are the sample sizes, and ^2 represents squared.

Plugging in the given values, we get:

SE = sqrt[(12^2/30) + (15^2/36)]
SE = 3.535

Next, we need to standardize the difference between the two sample means by dividing it by the standard error:

z = (x1 - x2) / SE

Where z is the z-score, x1 and x2 are the sample means, and SE is the standard error.

In this case, we want to find the probability that the mean of the first sample is larger than the mean of the second sample, so we are interested in the area to the right of the z-score we calculate. Using a standard normal distribution table or calculator, we can find this probability to be:

P(z >  -1.971) = 0.976

Therefore, the probability that the mean of the first sample will be larger than the mean of the second sample is approximately 0.976 or 97.6%.

For your question about the probability that the mean of the 1st random sample (size 30, mean 78, standard deviation 12) will be larger than the mean of the 2nd random sample (size 36, mean 85, standard deviation 15) from two different populations, we need to calculate the difference in the means and the standard error of the difference.

First, we find the difference in means: μ1 - μ2 = 78 - 85 = -7

Next, we calculate the standard error of the difference: SE = sqrt[(σ1²/n1) + (σ2²/n2)] = sqrt[(12²/30) + (15²/36)] ≈ 3.39

Now we need to find the z-score associated with the difference in means: z = (X1 - X2 - (μ1 - μ2)) / SE = (0 - (-7)) / 3.39 ≈ 2.06

Finally, we look up the probability associated with this z-score in a standard normal table or use a calculator. For z = 2.06, the probability that the mean of the 1st sample will be larger than the mean of the 2nd sample is approximately 0.0197, or 1.97%.

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Answer:

1716

Step-by-step explanation:

These ribbons be awarded to 3 of 13 pigs in 1716

We have given that,

13 pigs are entered in the best pig competition at the country fair the judges will award very special pigs with blue, red, and white ribbons

We have to determine how many different ways can these ribbons be awarded to 3 of 13 pigs.

A permutation of a set is, loosely speaking, an arrangement of its members into a sequence or linear order, or if the set is already ordered, a rearrangement of its elements.

So the judges are going to pick 3 pigs from the 13 to give a ribbon. Since the ribbons are different, the order does matter.

So this is a permutation. This can be set up like this:

Therefore we get,

13*12*11=1716

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Percent cost of the total spent on

each equipment = 14.23%,fees=62.45% and transportation = 23.32%.

As given in the question,

Money spent on

Each equipment = $36

Fees = $158

Transportation = $59

Total money spent = $( 36 + 158 + 59)

                             = $253

Percent cost of the total spent on

Each equipment = (36/253) × 100

                          = 14.23%

Fees = (36/253) × 100

        = 62.45%

Transportation =(36/253) × 100

                       = 23.32%

Therefore, percent cost of the total spent on

each equipment = 14.23%,fees=62.45% and transportation = 23.32%.

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Answer:

Multiplication property of equality

Step-by-step explanation:

x/4=36/16

Cross product

16*x=36*4

16x=144

Divide both sides by 16

x=144/16

=9

What property allowed her to go from

x/4=36/16

To

x/4*4=36/16*4

Multiplication property of equality would allow her to go from

x/4=36/16

To

x/4*4=36/16*4

Answer:

multiplication property of equality

Step-by-step explanation:

Answer: A=78

Step-by-step explanation: 936/12=78

936 eggs were produced last year by the sizable dairy farm. 78 dozen eggs are produced by this farm. The answer is option (A).

The study of symbols for math and the procedures for using them to solve equations and comprehend the relationships between variables is the subject of the branch of mathematics known as algebra. When representing quantities and their relationships using letters and symbols, algebra uses graphs, functions, and expression manipulation in addition to equation and inequalities solving.

Numerous branches of science, technology, economics, and other disciplines make considerable use of algebraic concepts and methods. It is a fundamental area of mathematics that is frequently studied as a pre-requisite for more difficult maths and science courses.

Algebraic concepts that are important to know include:

Addition, subtraction, multiplication, and division are operations using numbers and variables.

Using variables to solve equations and inequalities

Algebraic expressions manipulation and simplification

Knowing how to graph both linear and nonlinear functions

Utilising matrices and vectors

studying trigonometric, rational, and polynomial functions

We must divide the total number of eggs by 12 to determine the number of dozen eggs produced.

936/12 = 78

We must divide the total number of eggs by 12 to determine the number of dozen eggs produced.

The answer is A) 78.

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Answer:

2 real solutions

Step-by-step explanation:

Get all the terms to one side

10n^2 = 10 - 8n

10n^2 +8n -10 =0

ax^2 +bx+c =0

The discriminant is

b^2 -4ac

8^2 - 4(10)(-10)

64 +400

464

If the discriminant is greater than 0 we have 2 real solutions

Answer:

i think it's 13.44

Step-by-step explanation:

im not really sure, but let me know if im wright pls!!

hope this helped!!

Answer: C

Step-by-step explanation:

Answer: I think the answer is A.

Step-by-step explanation:

1. 3x + y = 3:

Equation in slope-intercept form: y = -3x + 3, with a slope of -3 and a y-intercept of 3.

Graph: The graph will have a slope of -3 and intersect the y-axis at the point (0, 3).

2. y - 4x = -3:

Equation in slope-intercept form: y = 4x - 3, with a slope of 4 and a y-intercept of -3.

Graph: The graph will have a slope of 4 and intersect the y-axis at the point (0, -3).

3. -10x + 7y = 35:

Equation in slope-intercept form: y = (10/7)x + 5, with a slope of 10/7 and a y-intercept of 5.

Graph: The graph will have a slope of 10/7 and intersect the y-axis at the point (0, 5).

4. 3x + 4y = 12:

Equation in slope-intercept form: y = (-3/4)x + 3, with a slope of -3/4 and a y-intercept of 3.

Graph: The graph will have a slope of -3/4 and intersect the y-axis at the point (0, 3).

To write each equation in slope-intercept form (y = mx + b), we need to rearrange the equations to solve for y.

Once we have them in this form, we can identify the slope (m) and the y-intercept (b) and graph the equations.

3x + y = 3:

Rearranging the equation, we get:

y = -3x + 3

The slope (m) is -3, and the y-intercept (b) is 3.

Graph:

The graph of this equation will have a slope of -3 and intersect the y-axis at the point (0, 3).

y - 4x = -3:

Rearranging the equation, we get:

y = 4x - 3

The slope (m) is 4, and the y-intercept (b) is -3.

Graph:

The graph of this equation will have a slope of 4 and intersect the y-axis at the point (0, -3).

-10x + 7y = 35:

Rearranging the equation, we get:

7y = 10x + 35

y = (10/7)x + 5

The slope (m) is 10/7, and the y-intercept (b) is 5.

Graph:

The graph of this equation will have a slope of 10/7 and intersect the y-axis at the point (0, 5).

3x + 4y = 12:

Rearranging the equation, we get:

4y = -3x + 12

y = (-3/4)x + 3

The slope (m) is -3/4, and the y-intercept (b) is 3.

Graph:

The graph of this equation will have a slope of -3/4 and intersect the y-axis at the point (0, 3).

By plotting the respective y-intercepts and using the slopes as a guide, we can graph each equation accurately on a coordinate plane.

In summary:

Equation: y = -3x + 3, Slope: -3, Y-intercept: 3.

Equation: y = 4x - 3, Slope: 4, Y-intercept: -3.

Equation: y = (10/7)x + 5, Slope: 10/7, Y-intercept: 5.

Equation: y = (-3/4)x + 3, Slope: -3/4, Y-intercept: 3.

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Answer:

Step-by-step explanation:

600*24%=144 are girls

600-144= 456 are boys

Answer:

456

Step-by-step explanation:

There are 144 girls. There are 600 students and 144 of them are girls, that means that 456 students are boys.

Answer:

of course ,the refree or the umpire

The value of the constant "a" is -1/4.

To find the value of the constant "a", we need to use the given information that the definite integral of the function 2x^2 + x - a over an unspecified interval is equal to 24.

The integral can be evaluated using the power rule of integration:

fo(2x^2 + x - a) dx = (2/3)x^3 + (1/2)x^2 - ax + C

where C is the constant of integration.

Since we are given that the integral equals 24, we can substitute this value into the above equation and solve for "a":

(2/3)x^3 + (1/2)x^2 - ax + C = 24

Simplifying and setting C = 0 (since it's an unspecified constant), we get:

(2/3)x^3 + (1/2)x^2 - ax = 24

Now, we don't have enough information to solve for "a" yet, as we don't know what interval the definite integral is taken over. However, we can use the fact that the integral is linear, meaning that if we multiply the integrand by a constant, the value of the integral will also be multiplied by that constant.

In other words, if we let f(x) = 2x^2 + x - a, then fo f(x) dx = 24 is equivalent to:

fo (2f(x)) dx = 48

Now we can solve for "a" using the same method as before:

(2/3)x^3 + x^2 - 2ax = 48

Again, we don't know the interval over which the integral is taken, but that doesn't matter for finding "a". We can now compare the coefficients of x^2 to get:

1/2 = -2a

Solving for "a", we get:

a = -1/4

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To set up the artificial variable LP (Phase I LP) for the given problem, we introduce an artificial variable, LP, to the objective function with a coefficient of 1. The artificial variable is used to identify infeasible solutions.

To set up the artificial variable LP (Phase I LP), we modify the objective function as follows:

Maximize Z = 4x1 + 7x2 + x3 + LP

The artificial variable LP is introduced to the objective function with a coefficient of 1. This allows us to track its value during the iterations.

The initial constraints remain the same:

2x1 + 3x2 + x3 = 20

3x1 + 4x2 + x3 + x4 = 40

8x1 + 5x2 + 2x3 - x5 = 70

The initial basic variables (BV) are the slack variables corresponding to the equality and inequality constraints, namely, x3 and x4. The artificial variable LP is initially a non-basic variable.

The initial artificial variables' basic variable (BVB) values are set to the right-hand side values of the constraints:

x3 = 20

x4 = 40

The initial artificial variable LP's value is set to 0.

Next, the artificial variable LP is selected as the entering variable, as it has a positive coefficient in the objective function. To determine the leaving variable, we perform the ratio test using the ratios of the right-hand side values and the entering column values (coefficients of LP) for the respective constraints.

The leaving variable is determined based on the minimum ratio, ensuring that the corresponding row represents a valid pivot element. If no valid pivot element is found, the problem is infeasible.

This completes the setup of the artificial variable LP (Phase I LP) without performing a complete pivot. Further steps would involve applying the simplex method and iteratively pivoting to find the optimal solution or identify infeasibility.

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$1,192.67

Interest is the amount of money that an initial investment earns.

Compound Interest

The question states that the interest is compounded monthly. Compound interest is when the amount of interest earned increases periodically. In this case, since the interest is compounded monthly, it is compounded 12 times a year. This means that the interest will increase at a faster rate than simple interest. With the information we were given, we can use a formula to find the total balance after 10 years.

Compound Interest Formula

The formula for compound interest is as follows:

In this formula, P is the principal (initial investment), r is the interest rate as a decimal, n is the number of times compounded per year, and t is the time in years. So, to find the total balance, all we need to do is plug in the information we were given.

So, after 10 years, the balance will be $1,192.67.

The angle between two vectors a = 5i + j and b = 2i - 4j is approximately 52.125°.

The angle between two vectors can be calculated using the following formula: cosθ = (a · b) / (||a|| ||b||)

where θ is the angle between the vectors, a · b is the dot product of the vectors, and ||a|| and ||b|| are the magnitudes of the vectors.

In this case, the dot product of the vectors is 13, the magnitudes of the vectors are √29 and √20, and θ is the angle between the vectors. So, we can calculate the angle as follows:

cos θ = (13) / (√29 * √20) = 0.943

The inverse cosine of 0.943 is approximately 52.125°. Therefore, the angle between the two vectors is approximately 52.125°.

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Answer:

x=2

Step-by-step explanation:

Counting by 0.5 pattern

After 4 hours of discharging, the volume left in the tank would be 500 liters. The correct option is C.

Initially, the tank has a water capacity of 1500 liters.

After three hours of discharging, half of the water is discharged, which means 1500/2 = 750 liters have been removed from the tank.

To find the volume left after 4 hours of discharging, we need to subtract the additional amount discharged in the fourth hour.

Since the discharge rate remains the same, we can calculate the amount discharged in one hour as 750/3 = 250 liters.

Therefore, in the fourth hour, 250 liters would be discharged. Subtracting this from the remaining water after three hours (750 liters), we get 750 - 250 = 500 liters.

Therefore, the correct answer is c. 500 liters.

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Answer: (-2,8) and (2,8)

For solving the given equations we will elimination method

This method involves removing variables from the equations.  Variables are removed successively until only a single last  variable is left, i.e. until there is one equation with one unknown.  This equation is then solved for the one unknown.  The solution is then used in finding the second to last variable. The procedure is repeated by adding back variables as their solutions are found.

-x2  + 3y = 20 ……..(1)

3x2  + 6y = 60 ……………. (2)

Step -1 :  Multiply the first equation by 3 this gives:

         -3x2 + 9y = 60 …….(3)

          3x2 + 6y = 60 ………….(2)

Step- 2 : Add the two equations. This gives

       15y = 120

           y = 8

Step – 3 : Solve for x in either of the original equations

         -x2 + 3(8) = 20

         -x2 + 24 = 20

                x2 = 4

                x = +2, -2

hence the solutions of the given equations are (2,8) and (-2,8)

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Answer:

20:43

Step-by-step explanation:

Answer:

the woodpecker was 7m above the ground

The height where the bird pecked is 7m above the ground.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, A woodpecker pecked at a 17 m wooden pole until it cracked and the upper part fell with the top hitting the ground 10 m from the foot of the pole.

Therefore, If the length of the pole that fell down is 10m then the length of the remaining pole is,

= (17 - 10)m.

= 7m.

So, The bird pecked away where the pole had cracked is 7m.

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Answer:

7<1+x

1+x>7

x>7-1

x>6

Step-by-step explanation:

hope this helps a little

Answer:

The surface area is:

276cm^2

Step-by-step explanation:

10x5=50x2=100

4x5=20x2=40

10x4=40x2=80

100+40+80=220

6x2=12x4=48

2x2=4x2=8

48+8=56

220+56=276

The formula for finding the standard deviation for a binomial distribution is σ2=npq. f.

What means binomial distribution?

When each trial has the same probability of achieving a given value, the number of trials or observations is summarized using the binomial distribution.

For each random variable X, the binomial distribution formula is given by;

P(x:n,p) = nCx px (q)n-x

Where,

n = the number of experiments

x = 0, 1, 2, 3, 4, …

p = Probability of Success in a single experiment

q = Probability of Failure in a single experiment = 1 – p

formula for finding standard deviation of a binomial distribution is npq. f.

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The answer is c. The population must be experiencing both demographic and environmental stochasticity.

Demographic stochasticity refers to random fluctuations in the population size due to chance events, such as variations in birth and death rates, migration, or dispersal. Environmental stochasticity refers to fluctuations in the population size due to random variations in environmental conditions, such as changes in climate, resource availability, or natural disasters.

Chaotic population fluctuations are characterized by complex and seemingly unpredictable patterns of change. If the population size is observed to vary in a chaotic manner, it is likely that both demographic and environmental stochasticity are playing a role in driving the fluctuations.

In some cases, even when environmental and demographic conditions do not change, chaotic population fluctuations can occur. This occurs when small fluctuations are amplified and result in larger, more complex fluctuations. In these cases, chaotic population fluctuations are a result of the interactions between demographic and environmental factors, rather than changes in these factors themselves.

Probability is a branch of mathematics that deals with the study of random events and the likelihood or chance of their occurrence. It provides a numerical measure of the uncertainty associated with an event, expressed as a value between 0 and 1.

A probability of 0 means that an event is impossible and will never occur, while a probability of 1 means that an event is certain to occur. For example, the probability of rolling a six on a standard six-sided die is 1/6, and the probability of not rolling a six is 5/6.

Probability is used in a wide range of fields, including statistics, finance, engineering, and the natural sciences, to make predictions, model real-world systems, and analyze data.

The theory of probability is based on the concept of sample space, which is the set of all possible outcomes of a random event. The probability of a specific event is defined as the ratio of the number of favorable outcomes to the total number of possible outcomes in the sample space.

There are various methods for finding probabilities, including classical probability, empirical probability, and subjective probability. The choice of method depends on the specific problem being addressed and the type of information available.

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Answer:

What is the question

Step-by-step explanation:

The answer would be C because X=5,y=\(\frac{17}{3}\) Is equivalent to the missing values