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Answer:

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We are going to use the triangle inequality theorem, which says that any side of the triangle must be shorter than the other sides added together.

a) 14 ioge

Efficiency refers to the extent to which resources, such as time, money, or energy, are utilized effectively and productively to achieve a desired outcome.

The fuel efficiency, in miles per gallon, of an American-made car: Continuous. Fuel efficiency can be measured in decimals and have a range of values.

(b) The temperature of a burrito served to a customer in a local Mexican restaurant: Continuous. Temperature can be measured in decimals and have a range of values.

(c) The actual length of a roll of plastic wrap is advertised to be 30 feet long: Continuous. Length can be measured in decimals and have a range of values.

(d) The number of children in a household: Discrete. The number of children can only be whole numbers (e.g., 0, 1, 2, 3).

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The original short-run supply curve shifts left, causing the market price to decrease to P2 and the quantity to decrease to Q2.

As a result, some firms exit the market, causing the short-run supply to shift back to the right and the market to return to equilibrium at a lower quantity, Q3, and the same price, P2.

When demand decreases, the original short-run supply curve shifts leftward as firms reduce production to meet the lower demand. This causes the market price to decrease to P2 and the quantity to decrease to Q2.

At this lower price, some firms may exit the market if they are unable to cover their costs, causing the short-run supply curve to shift back to the right.

As a result, the market quantity decreases further to Q3, and the market returns to equilibrium at the same price, P2. In the long run, the supply curve may shift further to accommodate the lower demand, resulting in a new equilibrium price and quantity.

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Answer: A) 1716   B) 1235520

Step-by-step explanation:

\(^nC_r=\dfrac{n!}{r!(n-r)!}\)

\(^nP_r=\dfrac{n!}{(n-r)!}\)

Given, Total distinct letters = 13

To choose = 6 letters

A) Number of ways to choose (if order does not matter)=\(^{13}C_6\)

\(=\dfrac{13!}{6!7!}=\dfrac{13\times12\times11\times10\times9\times8\times7!}{(720)\times 7!}\\\\= $$1716\)

B) Number of ways to choose (if order matters)=\(^{13}P_6\)

\(=\dfrac{13!}{7!}=\dfrac{13\times12\times11\times10\times9\times8\times7!} 7!}\\\\= $$1235520\)

Hence, A) 1716   B) 1235520

Answer: 0.045%

Step-by-step explanation:

Answer:

Santos should run approximately 36.145 meters along the shore

Step-by-step explanation:

The given parameters are;

The distance along the shore of the child = 50 meters

The distance from the shore of the child = 60 meters

The rate at which Santos can run = 4 m/s

The rate he can swim = 0.9 m/s

Let 'x' represent the distance he runs along the shore

We have;

The time he spends running on the shore, t₁ = x/4

The time he spends swimming, t₂ = (√(60² + (50 - x)²)/0.9

The total time, T = t₁ + t₂ = x/4 + (√(60² + (50 - x)²)/0.9

To find the maximum, we have;

dT/dx = 0 = d(x/4 + (√(60² + (50 - x)²)/0.9)/dx = 1/4 - (50 - x)/(0.9·(√(60² + (50 - x)²) = 0

1/4 - (50 - x)/(0.9·(√(60² + (50 - x)²) = 0

Simplifying using a graphing calculator gives;

\(\dfrac{x - 2000}{9} = \sqrt{x^2-100\cdot x+6,100}\)

1519·x² - 151900·x + 3505900 = 0

x = (151900 ± √((-151900)² - 4×1519×3505900))/(2 × 1519)

x ≈ 63.86 m or x ≈ 36.145 m

We note that the distance from a point x = 63.83 meters and 36.145 meters from where Santos spots the girl to the location of the girl are the same

Therefore, Santos should run approximately 36.145 meters along the shore before jumping into to the water in order to save the child

The greatest number of different cards based on the permutations is 144.

From the information given, there are 4 versions which are either roses, daisies, tulips, or sunflowers and this is further divided into either Happy birthday, anniversary, or holidays.

Therefore, the greatest number of different cards will be:

= 4! × 3!

= 24 × 6

= 144

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The provided questions cover various aspects of a 2-period production economy, including the household's problem, firm's problem, market clearing conditions, Social Planner's Problem, competitive equilibrium, and welfare theorems.

(a) The Household's problem is to maximize its utility over two periods subject to its budget constraint. The household's problem can be formulated as follows:

Max U(Co, C1) = log(Co) + ß log(C1)

subject to the budget constraint:

Co + (1+r)C1 ≤ (1+r)Ko + W0 + W1,

where Co and C1 are consumption in period 0 and 1 respectively, ß is the discount factor, r is the interest rate, Ko is the initial capital endowment, W0 and W1 are the wages in periods 0 and 1 respectively.

(b) The Firm's problem is to maximize its profit by choosing the optimal combination of capital and labor. The firm's problem can be formulated as follows:

Maximize F(K, L) - RK - WL,

where F(K, L) is the production function, K is capital, L is labor, R is the rental rate of capital, and W is the wage rate.

(c) The market clearing conditions are:

Capital market clearing: K1 = (1 - δ)K0 + S - C0, where δ is the depreciation rate, S is savings, and C0 is consumption in period 0.

Labor market clearing: L = L0 + L1, where L0 and L1 are labor supplies in periods 0 and 1 respectively.

(d) The Social Planner's Problem is to maximize social welfare, which is the sum of the household's utility and the firm's profit. The Social Planner's Problem can be formulated as follows:

Maximize U(C0, C1) + F(K, L) - RK - WL,

subject to the production function F(K, L) and the market clearing conditions.

(e) A Competitive Equilibrium is a situation where all markets clear and agents (household and firm) make optimal decisions based on prices and market conditions. It is characterized by the following conditions:

Household's problem is solved optimally.

Firm's problem is solved optimally.

Market clearing conditions hold.

(f) To solve the Social Planner's Problem, we need to set up the Lagrangian and solve for the optimal values of consumption, capital, and labor. The Lagrangian can be written as:

L = U(C0, C1) + F(K, L) - RK - WL + λ1[(1+r)K0 + W0 + W1 - Co - (1+r)C1] + λ2[K1 - (1 - δ)K0 + S - C0] + λ3[L - L0 - L1],

where λ1, λ2, and λ3 are the Lagrange multipliers.

(g) To solve the Competitive Equilibrium, we need to determine the prices of capital (R) and labor (W) that clear the markets. This can be done by equating the demand and supply of capital and labor, and solving the resulting equations.

(h) The First Welfare Theorem states that under certain conditions, a competitive equilibrium is Pareto efficient. It implies that a competitive equilibrium is a socially optimal allocation of resources. To verify the theorem, we need to demonstrate that the competitive equilibrium allocation is Pareto efficient.

(i) The Second Welfare Theorem states that any Pareto efficient allocation can be achieved as a competitive equilibrium with appropriate redistribution of initial endowments.

To verify the theorem, we need to show that given an initial Pareto efficient allocation, we can find prices and redistribution of endowments that lead to a competitive equilibrium that achieves the same allocation.

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Answer:

6

Step-by-step

You're welcome!

:)

Answer:

It's 6.

Step-by-step explanation:

1

5

×30

=  

1

5

×30

=  

1 × 30

5 × 1

=  

30

5

=  

30 ÷ 5

5 ÷ 5

= 6

Answer:

x=9 ⇒AC=24

Step-by-step explanation:

vì DE//B C⇒ΔABC  Tương ung ti tỉ lệ vớiv  ΔADE

⇒DB/AB=EC/AC

⇒AC=(EC.AB)/DB

⇒AC=24

Given: 15 different shirts with 5 different colours

To Determine: The bar chart represent the different colours

Solution

Let us get the frequecy table representing the number of the different colors

From the given picture, we can note that

Similarly,

In the same way, we have

and finally,

The weight range that contains at least 75% of all residents' annual garbage goes between 420 pounds and 787.5 pounds.

Given that the average resident of Metro City produces 630 pounds of solid waste each year, and the standard deviation is approximately 70 pounds, to determine the weight range that contains at least 75% of all residents' annual garbage weights, the following calculation must be performed:

Therefore, the weight range that contains at least 75% of all residents' annual garbage goes between 420 pounds and 787.5 pounds.

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Answer:

 5/13 and Cos(x) = 12/13 and so Sin(x) + Cos(x) =

5/13 + 12/13 = 17/13. Simple really.

Step-by-step explanation:

The term that describes an event that increases the likelihood of a response being repeated is known as reinforcement.

Reinforcement can be defined as any consequence that strengthens or increases the probability of a behavior occurring again in the future. This can include positive reinforcement, which involves adding a desirable consequence after a behavior, or negative reinforcement, which involves removing an aversive consequence after a behavior. Both types of reinforcement have been shown to be effective in increasing the likelihood of a behavior being repeated.

Overall, understanding the concept of reinforcement is essential in the field of psychology, particularly in the areas of behaviorism and behavior modification. By providing positive consequences after desired behaviors, individuals can be motivated to continue engaging in those behaviors, which can lead to long-term positive changes. Reinforcement can also be used to shape new behaviors or replace unwanted behaviors with more desirable ones.

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For a closed curve encircles several conductors. If the line integral around this curve is then the net current in the conductors is equals to the 334 Ampere.

Ampere’s Law is stated as ‘the line integral of a Magnetic field \(\vec B\) along a closed path is equals to the \( \mu_0\) (permeability of free space) times the total current 'I' enclosed by closed path or curve, mathematically form, we can say that \(\int \vec B. \vec dl = \mu_0 I\)

where, I --> total or net current.

It is used to describe a relationship between the current and the Magnetic field that it generates around itself. Now, we have the line integral around closed curve, \(\int \vec B.\vec dl \)

= 4.20×10⁻⁴ T-m

We have to determine value of the net current in the conductors. Using the ampere's law, for a closed loop carrying current, \( 4.20 × 10^{-4} = \mu_0 I\).

plug the value of constant of permeability of free space, \(\mu_0\) = 4π× 10⁻⁷ T-m/A

=> I × 4π× 10⁻⁷ T-m/A = 4.20 × 10⁻⁴ T-m

=> I = ( 4.20/4π) 10⁻⁴⁺⁷ A

=> I = 0.334× 10³ A

=> I = 334 A

Hence, required value is 334 A.

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Complete question:

a closed curve encircles several conductors. the line integral around this curve is int B.dl = 4.20×10-4 T-m. What is the net current in the conductors?

Triangulation is the method of finding the location of an object based on the measurements made from the two other locations. The above statement is true statement.

Triangulation is the division of a face or plane polygon into a series of triangles, usually with the limitation that each side of a triangle is fully shared by two adjacent triangles. In geometry, triangulation is the division of planar objects into triangles, or more broadly, the division of high-dimensional geometric objects into simplifications. Triangulation of a 3D volume involves subdivision into packed tetrahedra that directly measure distances to points. It is a method for finding the location of the object.

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Sure! Here's a code snippet in Octave to calculate \(c_j - z_j\) for all the variables in the Linear Programming Problem (LPP) table:

```octave

% Variables and coefficients

c = [coefficients]; % Replace [coefficients] with the actual coefficients for the variables

z = [coefficients]; % Replace [coefficients] with the actual coefficients for the objective function

% Calculate c_j - z_j

cj_minus_zj = c - z;

% Display the result

disp(cj_minus_zj);

```

In the code, you need to replace `[coefficients]` with the actual coefficients for the variables and the objective function. The variable `c` represents the coefficients of the variables, while `z` represents the coefficients of the objective function.

The calculation of \(c_j - z_j\) involves subtracting the coefficients of the objective function from the coefficients of the variables. This difference indicates the marginal improvement (or degradation) in the objective function value if the corresponding variable is increased by one unit while keeping other variables constant. By executing the code, you will get the values of \(c_j - z_j\) for all the variables, indicating their impact on the objective function. A positive value suggests that increasing the corresponding variable will increase the objective function value, while a negative value suggests a decrease in the objective function value.

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Horizontal translation: 2 units right.

Vertical translation: 5 units up

Stretch/compression: stretched by a factor of 3.

Reflection: not reflected.

10:20 and 7:14. They all are 1/2 and the ratio 1:2 equals one half

To find the probability of the event "the first die is 6 or the sum is 8," we need to count the number of outcomes that satisfy this event and divide it by the total number of possible outcomes.

To find the probability of the event "the first die is 6 or the sum is 8," we need to consider the total possible outcomes when rolling two dice and the favorable outcomes for this event.

Total possible outcomes: 6 sides on each die, so there are 6 x 6 = 36 possible outcomes.

Favorable outcomes:
1. First die is 6: There are 6 possible outcomes (6,1), (6,2), (6,3), (6,4), (6,5), and (6,6).
2. Sum is 8: There are 5 possible outcomes (2,6), (3,5), (4,4), (5,3), and (6,2).

However, (6,2) is counted twice, so we should subtract 1 from the total favorable outcomes: 6 + 5 - 1 = 10.

Probability = Favorable outcomes / Total possible outcomes = 10/36. Simplifying the fraction gives 5/18.

So, the probability of the event "the first die is 6 or the sum is 8" is 5/18.

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The first step to solve the equation is;

⇒ ''Change 14 1/10 to 14.1''

What is Mixed fraction?

A fraction which is represented with its quotient and remainder is called a mixed fraction.

The problem is given as,

40.8 - 14 1/10

Now, To solve the equation we have firstly change 14 1/10 as

40.8 - 14 1/10

40.8 - 14.1

Then, Subtract the numbers as,

26.7

Solution of the problem is 26.7.

So, The first step to solve the equation is;

⇒ ''Change 14 1/10 to 14.1''

Option 4 is true.

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Answer:

$125.00

Step-by-step explanation:

4 walls (2 at 18 foot and 2 at 15 foot). height of each wall = 10 foot.

total area of 2 wide walls = 2 (10 X 15) = 300 square foot.

total area of 2 long walls = 2 (10 X 18) = 360 square foot.

area of ceiling = 18 X 15 = 270 square foot.

total area = 930 square foot.

200 square foot for one gallon of paint.

she will need 930/200 = 4.65 tins of paint = 5 tins.

one tin costs $25.

she will have to budget 5 X 25 = $125.00  

The required pounds of Bolivian coffee and Colombian coffee are 2500 and 1500 respectively.

A equation is supposed to be linear equation in two factors in the event that it is written as ax + by + c=0, where a, b and c are genuine numbers and the coefficients of x and y, i.e an and b separately, are not equivalent to nothing. For instance, 10x+4y = 3 and - x+5y = 2 are direct conditions in two factors.

Let x be the pound of Bolivian coffee and y is that of Colombian coffee.

Bolivian coffee sells for $4.59 per pound, and Colombian coffee sells for $5.95 per pound and whole mixture sells for $5.10.

So,  4.59x + 5.95y = 5.10(4000)

4.59x + 5.95y = 20400--------------------(1)

and x + y = 4000-----------------------------(2)

On solving above two equation, we get

x = 2500 pounds and y = 1500 pounds

Thus, required pounds of two coffees are 2500 and 1500.

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