According to a circle graph about favorite outdoor activities, 50% of votes were for "Swimming." What is the measure of the central angle in the "Swimming" section?

Answer:

An equation in the form y = mx + b is in the 'slope y-intercept' form where m is the slope and b is the y-intercept. We can rewrite our equation, y = 4, in slope y-intercept form as follows: y = 0x + 4. Here, it is clear that the slope, or m, is zero. Therefore, the slope of the horizontal line y = 4 is zero

Answer: $88.90

Step-by-step explanation:

$39.95 x 2 + 0.06 x 150

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:

5

Step-by-step explanation:

3x = 15 (you add the 6 over)

x = 5 (you divide by 3)

Answer:

x = -8

Step-by-step explanation:

-2.5x - 2 = 18.

Add 2 to both sides.

-2.5x = 20.

Divide both sides by -2.5.

x = -8

Answer:

20 maybe

Step-by-step explanation:

Answer:

20 because you have to cross multiple

The waiter tip is 8.175$

If we do 23+25+(3.25)×2

The sum of all the bought,

It will equal to 54.5

So if we do as the waiter planned

We must to 54.5×15%=8.175$

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Answer:

it is B on edge 2021

Step-by-step explanation:

The required graph is decreasing in -1 <x <0 and 0 < x < 1. Options b and c are correct.

Given that,
A graph of the function is shown it the domain at which the function is decreasing is to be determined.

The domain is defined as the values of the independent variable for which there is a certain value of the dependent variable exists in the range of the function.

Here,
Since in the initial stage, the function is increasing, from -3 < x < -1 after that function starts decreasing from -1 < x < 1 and afterward again increasing,

Thus, The required graph is decreasing in -1 <x <0 and 0 < x < 1. Options b and c are correct.

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Truth statement are statements or assertions that is true regardless of whether the constituent premises are true or false. See below for the definition of Euclidean Postulates.

There are five Euclidean Postulates or axioms. They are:

1. Any two points can be joined by a straight line segment.

2. In a straight line, any straight line segment can be stretched indefinitely.

3. A circle can be formed using any straight line segment as the radius and one endpoint as the center.

4. Right angles are all the same.

5. If two lines meet a third in a way that the sum of the inner angles on one side is smaller than two Right Angles, the two lines will inevitably collide on that side if they are stretched far enough.

The right angle in the first page of the book shown and the right angles in the last page of the book shown are all the same. (Axiom 4);

If the string from the Yoyo dangling from hand in the picture is rotated for 360° such that the length of the string remains equal all thought, and the point from where is is attached remains fixed, it will trace a circular trajectory. (Axiom 3)

The swords held by the fighters can be extended into infinity because they are straight lines (Axiom 5)

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The value of K is 2.

Let's denote the scale factor as K. The surface area of a solid after dilation is directly proportional to the square of the scale factor.

We are given that the initial surface area of the solid is 50 units^2, and after dilation, the surface area becomes 200 units^2.

Using the formula for the surface area, we have:

Initial surface area * (scale factor)^2 = Final surface area

50 * K^2 = 200

Dividing both sides of the equation by 50:

K^2 = 200/50

K^2 = 4

Taking the square root of both sides:

K = √4

K = 2

Therefore, the value of K is 2.

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Answer:

24+4x

Step-by-step explanation:

4(6)= 24

4(x)= 4x

The expressions for the lengths of the segments obtained using vectors notation are;

a. i. \(\overrightarrow{LA}\) = q - (1/2)·p  ii. \(\overrightarrow{AN}\) = (2/7)·(p - q)

b. The expressions for \(\overrightarrow{MN}\), \(\overrightarrow{LA}\), and \(\overrightarrow{AN}\) indicates;

\(\overrightarrow{MN}\) = (1/84)·(46·q - 11·p)

A vector is a quantity that has magnitude and direction and are expressed using a letter aving an arrow in the form, \(\vec{v}\)

a. i. \(\overrightarrow{LA}\) = \(\overrightarrow{BA}\) - \(\overrightarrow{LB}\) =  \(\overrightarrow{BA}\) - (1/2) × \(\overrightarrow{CB}\)

\(\overrightarrow{BA}\) - (1/2) × \(\overrightarrow{CB}\) = q - (1/2)·p

\(\overrightarrow{LA}\) = q - (1/2)·p

ii. \(\overrightarrow{AC}\) = \(\overrightarrow{BC}\) - \(\overrightarrow{BA}\)

\(\overrightarrow{AN}\) = (2/7) × \(\overrightarrow{AC}\)

\(\overrightarrow{AN}\) = (2/7) × \(\overrightarrow{BC}\) - \(\overrightarrow{BA}\)

\(\overrightarrow{AN}\) = (2/7) × (p - q)

b. \(\overrightarrow{MN}\) = \(\overrightarrow{MA}\) + \(\overrightarrow{AN}\)

\(\overrightarrow{MA}\) = (5/6) × \(\overrightarrow{LA}\)

\(\overrightarrow{LA}\) = q - (1/2)·p

\(\overrightarrow{AN}\) = (2/7) × (p - q)

Therefore;

\(\overrightarrow{MN}\) = (5/6) × ( q - (1/2)·p) + (2/7) × (p - q)

\(\overrightarrow{MN}\) = (1/84) × ( 70·q - 35·p + 24·p - 24·q) = (1/84)(46·q - 11·p)

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The correct trigonometric function cos²47° = (1 + cos94°)/2 thus, option (A) is correct.

The fundamental 6 functions of trigonometry have a range of numbers as their result and a domain input value that is the angle of a right triangle.

The trigonometric function is very good and useful in real-life problems related to the right-angle triangle.

It is known that,

cos2x = 2cos²x - 1

2cos²x = 1 + cos2x

cos²x = (1 + cos2x)/2

Put x = 47°

cos²47° = (1 + cos94°)/2

Hence "The correct trigonometric function cos²47° = (1 + cos94°)/2".

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Answer:18

Step-by-step explanation:

Answer:

64ft

Step-by-step explanation:

The distance between the lions and the monkeys is; 64 ft

From the given diagram, we see two triangles;

Triangle one formed by Zebras, Monkeys, lions.

Triangle two formed by tigers, elephants, lions

Now, from the given triangles we can see that they are similar and using the given dimensions, we can use proportion to find distance between the lions and the monkeys as;

52/78 = x/96

where x is the unknown distance we are looking for

We cross multiply to get;

4992 = 78x

Divide both sides by 78 to get;

x = 64 ft

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Answer: 16 hours

Step-by-step explanation::

4 machines complete a large order in 32 hours

8 machines complete the same large order in x hours ( x is the unknown number of hours)

(4 machines)(32 hr/order) = (8 machines)( x hr/order)

128 machine·hr/order = (8 machine·hr/order) (x  hr)

solve for x:

x = 128 / 8 = 16 hr

Answer:

$456.25 each month

Step-by-step explanation:

Fund for 3 months 3750 * 3 = 11250

Start with 300 => 11250 - 300 = 10950

Within 24 months to reach 10950 => each month = 10950 / 24 = 456.25

She needs to save $456.25 each month for the next 24 months to reach her goal.

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

In other words, an equation is a set of variables that are constrained through a situation or case.

Monthly expenses = $3,750

For 3 months = 3 × 3750 = $11250 need to save total.

Since she started with $300 so

11250 - 300 = $10950 need to save total.

Let's say the amount per month is x

24x = 10950

x = 456.25.

Hence "She needs to save $456.25 each month for the next 24 months to reach her goal".

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The probability of leaving it in any given class is 1/4, the probability of leaving it in the 5th class is 1/4, or\(0.250 (25.0%).\)

The probability that the student left her iClicker device in the 5th class is 0.250 (25.0%). This is because the probability of leaving it in any given class is 1/4, and as she attends 5 different classes,

there is 5/4 or 1.25 chances of her leaving it in the 5th class.

To explain further, the probability of an event can be calculated by dividing the number of ways the event can occur by the total number of possible outcomes. In this case, the event is leaving the iClicker device in the 5th class, and the total number of possible outcomes is 5 (for the 5 classes).

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The measure of ∠6 is 54 degrees.

When parallel lines are cut by a transversal, angle relationship are formed. Therefore,

∠6 = 5x + 9 (vertically opposite angles)

∠6 = ∠2

Hence,

∠2 + 13x + 9 = 180

5x + 9  + 13x + 9 = 180

18x = 162

x = 162 / 18

x = 9

Hence,

∠6 = 5(9) + 9  54°

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For the polynomials p(x) = 1 - x + 4x² and q(x) = x - x², (p, q) = 10, ||p|| = √18, ||a|| = √18, and d(p, q) cannot be determined. For the vectors u = (0, 2, 3) and v = (2, 3, 0), (u, v) = 6, ||u|| = √13, ||v|| = √13, and d(u, v) cannot be determined.

In the first scenario, we have p(x) = 1 - x + 4x² and q(x) = x - x². To find (p, q), we substitute the coefficients of p and q into the inner product formula:

(p, q) = (1)(0) + (-1)(2) + (4)(3) = 0 - 2 + 12 = 10.

To calculate ||p||, we use the formula ||p|| = √((p, p)), substituting the coefficients of p:

||p|| = √((1)(1) + (-1)(-1) + (4)(4)) = √(1 + 1 + 16) = √18.

For ||a||, we can use the same formula but with the coefficients of a:

||a|| = √((1)(1) + (-1)(-1) + (4)(4)) = √18.

Lastly, d(p, q) represents the distance between p and q, which can be calculated as d(p, q) = ||p - q||. However, the formula for this distance is not provided, so it cannot be determined. Moving on to the second scenario, we have u = (0, 2, 3) and v = (2, 3, 0). To find (u, v), we use the given inner product formula:

(u, v) = (0)(2) + (2)(3) + (3)(0) = 0 + 6 + 0 = 6.

To find ||u||, we use the formula ||u|| = √((u, u)), substituting the coefficients of u:

||u|| = √((0)(0) + (2)(2) + (3)(3)) = √(0 + 4 + 9) = √13.

Similarly, for ||v||, we use the formula with the coefficients of v:

||v|| = √((2)(2) + (3)(3) + (0)(0)) = √(4 + 9 + 0) = √13.

Unfortunately, the formula for d(u, v) is not provided, so we cannot determine the distance between u and v.

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The last sentence of the proof states, "By the Pythagorean theorem, since a squared plus b squared equals c squared, the sum of f and e is equal to c."

The proof establishes the proportions and similarities between the triangles in the diagram. It shows that the ratios of corresponding sides in the similar triangles hold true, leading to the proportions a/c = c/a and b/c = c/e. These proportions can be rearranged to obtain a2 = cf and b2 = ce.

The next step in the proof adds b2 to both sides of the equation a2 = cf, resulting in a2 + b2 = cf + b2. Since b2 = ce, we substitute ce into the equation, giving us a2 + b2 = cf + ce.

The final step applies the converse of the distributive property, which states that if a + b = c, then a(b + d) = ab + ad. In this case, we have a2 + b2 = cf + ce, which can be rewritten as a2 + b2 = c(f + e).

Therefore, the last sentence of the proof concludes that because a2 + b2 = c2 (as derived from the previous steps), it follows that f + e = c. This statement completes the proof and establishes the relationship between the lengths of the sides and the altitude in the right triangle. Option C is correct.

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Answer:

I think 1

I think 2

I think 3

I think 4

Answer and Explanation:

Given the function:

ℎ(t)= −16t+5t+250

Where the variable t is measured in seconds. We can plug in t=20 seconds in the function to measure the height in feet of the bungee jumper after 20 seconds.

h(t)= -16×20+5×20+250

h(t)= -320+100+250

h(t)=350-320

h(t)= 30feet

height in feet of the bungee jumper after 20 seconds = 30 feet

Answer:

The scale on the map is incorrect.

Step-by-step explanation:

y equals 50° since there is a 90° and a 30°

Answer:

cos^-1 (9/15)

Step-by-step explanation:

Answer:

$1.80

Step-by-step explanation:

2/3x = 1.2

x = 1.2 / (2/3)

x = 1.2 * (3/2)

x = 1.80

By the use of factor decomposition and algebra properties, we conclude that the rational number 48/192 is equal to the rational number 1/4.

In this question we should simplify a rational number into its simplest form based on two facts. First, that all natural numbers except 1 and the prime numbers are products of prime numbers and, second, the simplification of the fraction can be done by using the following algebra property:

(a · c)/(b · c) = a/b, where a, b, c are natural numbers.     (1)

Along with power properties.

Now we proceed to simplify the rational number:

48/192 = (2⁴ × 3) / (2⁶ × 3)

48/192 = 1 / 2²

48/192 = 1 / 4

By the use of factor decomposition and algebra properties, we conclude that the rational number 48/192 is equal to the rational number 1/4.

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Answer:

4

Step-by-step explanation:

Part A: The relationship between the temperature of Naomi’s city and the number of popsicles she sold daily is direct and proportional. This implies that as the temperature of the city increases, the number of popsicles sold per day also increases. This is confirmed by the upward trend of the graph, which shows an increase in the number of popsicles sold per day as the temperature increases.

Part B: The line of best fit is a straight line that is used to represent the trend of a scatter plot. The line of best fit can be used to make predictions about the value of the dependent variable based on the value of the independent variable. To create the line of best fit for this graph, we need to identify the slope and y-intercept.

The slope of the line of best fit can be calculated using the formula:

slope = (y2 - y1)/(x2 - x1)
where (x1, y1) and (x2, y2) are any two points on the line of best fit. We can choose two points on the line of best fit, such as (20, 25) and (40, 75), and substitute the values into the formula:
slope = (75 - 25)/(40 - 20)
slope = 50/20
slope = 2.5
The approximate slope of the line of best fit is 2.5.
The y-intercept of the line of best fit can be calculated by substituting the slope and one of the points on the line of best fit into the formula:
y - y1 = m(x - x1)

where m is the slope and (x1, y1) is one of the points on the line of best fit. We can choose the point (20, 25) and substitute the values into the formula:
y - 25 = 2.5(x - 20)
y - 25 = 2.5x - 50
y = 2.5x - 25
The y-intercept of the line of best fit is -25.
Therefore, the line of best fit for the graph is:
y = 2.5x - 25.

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