Economic equilibrium is a condition or state in which economic forces are balanced. In effect, economic variables remain unchanged from their equilibrium values in the absence of external influences.
Economic equilibrium is also referred to as market equilibrium. Economic equilibrium is the combination of economic variables (usually price and quantity) toward which normal economic processes, such as supply and demand, drive the economy. The term economic equilibrium can also be applied to any number of variables such as interest rates or aggregate consumption spending. The point of equilibrium represents a theoretical state of rest where all economic transactions that “should” occur, given the initial state of all relevant economic variables, have taken place.
In a competitive market, demand for and supply of a good or service determine the equilibrium price.
Equilibrium:MARKETS:
Equilibrium is achieved at the price at which quantities demanded and supplied are equal. We can represent a market in equilibrium in a graph by showing the combined price and quantity at which the supply and demand curves intersect.
For example, imagine that sellers of squirrel repellant are willing to sell 500 units of squirrel repellant at a price of $5 per can. If buyers are willing to buy 500units of squirrel repellent at that price, this market would be in equilibrium at the price of $5 and at the quantity of 500 cans.
Disequilibrium:Whenever markets experience imbalances—creating disequilibrium prices, surpluses, and shortages—market forces drive prices toward equilibrium.
A surplus exists when the price is above equilibrium, which encourages sellers to lower their prices to eliminate the surplus.
A shortage will exist at any price below equilibrium, which leads to the price of the good increasing.
For example, imagine the price of dragon repellent is currently $6 per can. People only want to buy 400 cans of dragon repellent, but the sellers are willing to sell 600 cans at that price. This creates a surplus because there are unsold units. Sellers will lower their prices to attract buyers for their unsold cans of dragon repellant.
Changes in equilibrium :Changes in the determinants of supply or demand result in a new equilibrium price and quantity. When there is a change in supply or demand, the old price will no longer be an equilibrium. Instead, there will be a shortage or surplus, and price will subsequently adjust until there is a new equilibrium.
For example, suppose there is a sudden invasion of aggressive unicorns. There will be more people who want to buy unicorn repellent at all possible prices, causing demand to increase. At the original price, there will be a shortage of unicorn repellant, signaling sellers to increase the price until the quantity supplied and quantity demanded are once again equal.
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(b)
Simplify
45e6f8
5ef²
A school district telephone system has three-digit extensions. How many unique extensions are there with no
repeated digits, if the first digit cannot be zero and the last number is a nine?
A.72
B.64
C.504
E.None of the above
64 unique extensions are there with no repeated digits.
What is Combination?Combinations are decisions that are made by choosing some or all of a group of objects, regardless of how they are arranged.
For the 3-digit area code, the first digit can be any digit from 2 through 9, and each of the two digits that follow can be any digit from 0 through 9. That's a total of 8 × 10 × 10 = 800 different combinations.
Given:
A school district telephone system has three-digit extensions.
So, first digit cannot be zero then we have possibility of total 8 digits.
and the last number is a nine.
unique extensions are there with no repeated digits
= 8 x 8 x 1
= 64
Hence, 64 unique extensions are there with no repeated digits.
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4u+8v=-3u+2v
pleaseeee
Answer:
solve for u= 6v/7
solve for v= 7u/6
Step-by-step explanation:
36 is 40% of what number?
[tex]\fbox{90}[/tex]
In order to find 36 is 40% of what number, we will need to use the following formula:
[tex]number\times100/Percent[/tex]
[tex]\frac{36\times100}{40}[/tex]
[tex]36\times100=3,600[/tex]
[tex]3,600\div40[/tex]
[tex]=90[/tex]
The solution of the number in the expression ''40% of a number is 36'' is 90.
Given that,
To find the solution for 40% of that number is 36.
Used the concpet of percentage which stated that,
A number or ratio that can be expressed as a fraction of 100 or a relative value indicating the hundredth part of any quantity is called a percentage.
Let us assume that the solution of the given condition is x.
So, it can be written as,
[tex]40\% \times x = 36[/tex]
[tex]\dfrac{40}{100} \times x = 36[/tex]
Multiply both sides by 100,
[tex]40x = 36 \times 100[/tex]
[tex]40x = 3600[/tex]
Divide both sides by 40,
[tex]x = \dfrac{3600}{40}[/tex]
[tex]x = 90[/tex]
So, the solution for the number is 90.
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aaron collects 54 rocks at the beach. he wants to give an equal number of rocks to 6 of his friends. how many rocks did each of aaron's friends get? if r represents the number of rocks each friend will get, which equation could be used to solve the problem?
Each of Aaron's pals receives nine (9) rocks in total.
The question states that,
Aaron collects a total of 54 rocks at the beach.
He wants to give an equal number of rocks to six (6) of his friends.
It is given that let 'r' be the number of rocks each of his friends gets.
The required equation is;
Rock's Aaron's friends get,
→ 6*r = 54
r = 54/6
r = 9
The total number of rocks each of Aaron's friends get is 9.
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Dominique uses a car service company to travel to work and back home. She uses the same route each way. The company charges a ride fee of $3.00 and $1.25 per mile. Dominique pays $11.75 for transportation each way. Select all of the equations that model the total amount of money Dominique spends on travel each day if her route to work is x miles long.
The equation that model the total amount of money Dominique spends on travel each day if her route to work is x miles long is 3 + 1.25x = 11.75.
What is an equation?An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
In this case, Dominique uses a car service company to travel to work and back home.
The company charges a ride fee of $3.00 and $1.25 per mile. The appropriate equation will be:
3 + 1.25(x) = 11.75
where x = number of miles
3 + 1.25(x) = 11.75
3 + 1.25x = 11.75
This illustrates the equation.
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tan(x+pie) + sin(x+pie) + sin (x-pie) = 0
Answer:
[tex]x=\dfrac{\pi }{3}+2\pi n, \quad x=\dfrac{5\pi }{3}+2\pi n,\quad x=2\pi n,\quad x=\pi+2\pi n[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{6.5 cm}\underline{Trigonometric Double Angle Identities}\\\\$\sin (A \pm B)=\sin A \cos B \pm \cos A \sin B$\\\\$\cos (A \pm B)=\cos A \cos B \mp \sin A \sin B$\\\\$\tan (A \pm B)=\dfrac{\tan A \pm \tan B}{1 \mp \tan A \tan B}$\\\end{minipage}}[/tex]
Given equation:
[tex]\tan (x + \pi) + \sin(x + \pi) + \sin(x - \pi)=0[/tex]
Simplify using the double angle identities:
[tex]\implies \dfrac{\tan x + \tan \pi}{1 -\tan x \tan \pi} + \sin x \cos \pi+\cos x \sin \pi + \sin x \cos \pi -\cos x \sin \pi=0[/tex]
[tex]\implies \dfrac{\tan x + 0}{1 -\tan x(0)} + \sin x (-1)+\cos x (0) + \sin x(-1) -\cos x (0)=0[/tex]
[tex]\implies \dfrac{\tan x}{1} -\sin x - \sin x=0[/tex]
[tex]\implies \tan x-2\sin x =0[/tex]
Use the tan identity to rewrite tan(x) in terms of sin(x) and cos(x):
[tex]\implies \dfrac{\sin x}{ \cos x}-2\sin x=0[/tex]
Multiply both sides by cos(x):
[tex]\implies \dfrac{\sin x\cos x}{ \cos x}-2\sin x\cos x=0(\cos x)[/tex]
[tex]\implies \sin x-2\sin x \cos x=0[/tex]
Factor out sin(x) from the left side of the equation:
[tex]\implies \sin x(1-2 \cos x)=0[/tex]
Apply the zero-product property.
Case 1
[tex]\implies \sin x=0[/tex]
[tex]\implies x=\sin^{-1}(0)[/tex]
[tex]\implies x=2\pi n, \; \pi+2\pi n[/tex]
Case 2
[tex]\implies 1-2 \cos x=0[/tex]
[tex]\implies 1=2 \cos x[/tex]
[tex]\implies \cos x=\dfrac{1}{2}[/tex]
[tex]\implies x= \cos ^{-1} \left(\dfrac{1}{2}\right)[/tex]
[tex]\implies x=\dfrac{\pi }{3}+2\pi n, \;\dfrac{5\pi }{3}+2\pi n[/tex]
Solution
[tex]x=\dfrac{\pi }{3}+2\pi n, \quad x=\dfrac{5\pi }{3}+2\pi n,\quad x=2\pi n,\quad x=\pi+2\pi n[/tex]
the measure of the middle ordinate of a yaw mark is 6 ft. the radius of the arc is 70 ft. what was the length of the chord used in this situation? round the answer to the nearest tenth of a foot.
The length of the chord used in this situation is approximately 40.54 ft.
To find the length of the chord used in the situation, we can use the formula for the chord length in a circular arc:
Chord length = 2√(r² - (r - h)²)
where r is the radius of the arc and h is the measure of the middle ordinate.
Given that the radius of the arc is 70 ft and the measure of the middle ordinate is 6 ft, we can substitute these values into the formula:
Chord length = 2√(70² - (70 - 6)²)
Chord length = 2√(4900 - 4489)
Chord length = 2√(411)
Chord length ≈ 2 * 20.27
Chord length ≈ 40.54 ft
Therefore, the length of the chord used in this situation is approximately 40.54 ft.
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Dominic needs a new bike mirror. His old mirror was a square with a side length of 9 cm. He wants the new mirror to have an area as close as possible to his old bike mirror.
The new mirror must have at least 81 cm² of the area.
What is the area of the square?The area of the square is defined as the product of the length and width.
As per the given question, we have
Dominic requires a new bicycle mirror. His old mirror was a square with a 9-cm side length.
He wants the replacement mirror to have an area that is as near to his previous bike mirror as feasible.
We have to determine the area of the previous bike mirror.
The area of the previous bike mirror = (side length)²
The area of the previous bike mirror = (9)² = 9 x 9
The area of the previous bike mirror = 81 cm²
So the new mirror must have greater than 81 cm² of area.
Thus, the new mirror must have at least 81 cm² of the area.
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Answer:
5 cm
Step-by-step explanation:
hope this helps
Here is a correlation, does it also represent causation? Explain you answer.
The miles driven and the amount of gasoline used.
Yes the miles driven and the amount of gasoline used can be said to have a causation as well as a correlation.
What is causation in statistics?The strength and direction of a relationship between two or more variables are described by the statistical measure of correlation, which is given as a number. However, a correlation between two variables does not necessarily imply that a change in one variable is the reason for a change in the values of the other.
There is a causal relationship between the two occurrences, which means that causation shows that one event is the outcome of the occurrence of the other event. This concept is also known as cause and effect.
When the amount of gasoline is small, it would cause the miles covered to be just a few miles. Or if there is no gas, then no mile would be covered.
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How do you use distributive property to express the expression as the multiple of a sum of two whole numbers with no common factor? 27 + 99, 99+36, 3+33, 33+27, 10+50
7. 55 is what percent of 100?
8. 22% of what number is 24.2?
9. 19 is 50% of what number?
10. 25 is 32% of what number?
11. 40% of what number is 28?
12. 30 is what percent of 60?
This is due tmr please help!
(7) 55 is 181.81% of 100
(8) 22% of 110 is 24.2
(9) 19 is 50% of 38
(10) 25 is 32% of 78.125
(11) 40% of 70 is 28.
(12) 30 is 200% of 60.
What is percent?
A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.", "pct.", and occasionally "pc" are also used to indicate it, while the percent symbol, "%," is most frequently employed. A % has no dimensions and no standard measurement.
(7) Suppose 55 is x% of 100.
So,
55x/100 = 100
x/100 = 100/55
x = 1.8181 x 100
x = 181.81%
Therefore, 55 is 181.81% of 100.
(8) Suppose 22% of x is 24.2
So,
x(22)/100 = 24.2
x = 24.2 x 100/22
x = 110
Therefore, 22% of 110 is 24.2
(9) Suppose 19 is 50% of x.
So,
19 = 50(x)/100
x = 19 x 100/50
x = 38
Therefore, 19 is 50% of 38.
(10) Suppose 25 is 32% of x.
So,
25 = 32(x)/100
x = 25 x 100/32
x = 78.125
Therefore, 25 is 32% of 78.125
(11) Suppose 40% of x is 28
So,
40(x)/100 = 28
x = 28 x 100/40
x = 70
Therefore, 40% of 70 is 28.
(12) Suppose 30 is x% of 60
So,
30(x)/100 = 60
x = 60 x 100/30
x = 200
Therefore, 30 is 200% of 60.
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(3x-19)
what is the value of x
What does 3x-19 equal? You can find x without it being an equation
The solution is, the value of x is 6.33.
What is simplification?Simplify simply means to make it simple. In mathematics, simply or simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.
here, we have,
given that,
(3x-19) = 0,
here, we have to make the given expression simple, as we have to find the value of x.
so, we get, by isolating the variable & numbers,
adding 19 on both sides we get,
3x = 19
dividing both sides by 3, we get,
or, x = 19/3
or, x = 6.33
Hence, The solution is, the value of x is 6.33.
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Deshaun's gas tank is 1/10 full. After he buys 6 gallons of gas, it is 2/5 full. How many gallons can Deshuan's tank hold?
Answer:
20 gallons
Step-by-step explanation:
2/5 = 4/10
3/10 = 6 gallons
1/10 = 6 : 3= 2 gallons
10/10 = 2 * 10 = 20 gallons
according to the almanac of questionable statistics, vol 4 (2012), the probability of a mass squirrel uprising in any given year is 0.47 and the probability that cats and dogs will sign a peace treaty allowing them to live together peacefully in any given year is 0.61. if we presume that these two events are independent, what is the probability of both happening next year?
If the two events described in the questions are independent events, the probability of both happening next year is 28.67%.
Independent events refer to events whose occurrence is not interdependent. In other words, if the probability of occurrence of event A is not influenced by the probability of occurrence of event B, then A and B are independent events. Mathematically, independent events are represented as P(A│B) and is calculated by multiplying the individual probabilities of the two events. The formula of probability of two independent events is:
P(A│B) = P(A)*P(B)
Hence,
P(A│B) = 0.47*0.61
P(A│B) = 0.47*0.61
P(A│B) = 0.2867
The probability of two events happening next year is 28.67%.
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consider this confidence interval interpretation: we are 95% confident the mean sodium content for all beef hot dogs is between 353.2 and 449.1 mg. what needs to be done to fix this statement?
"We are 95% confident that the mean sodium content for all beef hot dogs is between 353.2 and 449.1 mg." is the correct statement.
The true parameter must be properly and contextually stated.
We are researching confidence intervals for population means rather than for particular observations. The parameter is, to put it in plain English, the average sodium content of all beef hot dogs. The phrase "We are 95% confident" would be a better translation.
Thus the correct statement is as mentioned above.
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what is the acceleration of a softball if it had a mass of .50kg and has a force of 70N when it hits the catchers glove
Answer:
the answer is 1.4N/kg
Determine whether each of these functions from {a,b,c,d} to itself is bijection if it is than find f -¹.
f(a)=b, f(b)=a, f(c)=d, f(d)=c
f(a)=a, f(b)=b, f(c)=c, f(d)=d
Only function (a) is one-to-one.
What is a one-one function?A mathematical function with individuality known as an injective function, injective, or one-one function never translates discrete components of its domain to equivalent elements of its codomain. We can say that each element of the codomain is only a representation of a single element in the domain.acc to our question-
If every element of the range of the function corresponds to exactly one element of the domain, then the function is called one-to-one.
The elements of a function are
A = {a,b,c,d}
Therefore, this function is one-to-one.
(b).f (a) = b, f (b) = b, f (c) = d, f (d) = c.
Here, the value of function is b for x=a and x=b. For two domains the functions has same range.
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d) The rent of a room for 4 months is Rs 20,000. (i) What is the rent for 7 months? (ii) How long would a tenant hire the room for Rs 55,000 at the same rate of rent?
The rent for seven months is 35000 and a tenant hire the room for Rs 55,000 at the same rate of rent for 11 months
The rent of a room for 4 months is Rs 20,000.
The rent of a room for 1 month is Rs 20,000./4
The rent of a room for 1 month is Rs 5000
The rent of a room for 7 months is Rs 5000 x 7
The rent of a room for 7 months is Rs 35000
Now we need to calculate the number of month a tenant hire the room for Rs 55,000 at the same rate of rent
The rent is 5000 for 1 month
The rent will be 55000 for 1/5000 x 55000 = 11 months
Therefore, the rent for seven months is 35000 and a tenant hire the room for Rs 55,000 at the same rate of rent for 11 months
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The total cost for laundry service, in dollars, depends on the weight of the laundry, in pounds. This relationship is proportional, as it costs $22.25 for 25 pounds of laundry and $36.49 for 41 pounds of laundry. In words, describe the graph of the proportional relationship.
The proportional relationship between the cost and weight is given as y = 0.89x.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The absolute expense for clothing administration, in dollars, relies upon the heaviness of the clothing, in pounds. This relationship is corresponding, as it costs $22.25 for 25 pounds of clothing and $36.49 for 41 pounds of clothing.
The equations are given below.
22.25 = 25m + c ...1
36.49 = 41m + c ...2
From equations 1 and 2, then we have
41m - 25m = 36.49 - 22.25
16m = 14.24
m = 0.89
Then the value of c will be given as,
22.25 = 25 (0.89) + c
c = 0
The proportional relationship between the cost and weight is given as y = 0.89x.
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help asap please. . . . .
initially, a $65$-foot ladder rests against a vertical wall such that the top of the ladder is $60$ feet from the ground. then, naoki moves the base of the ladder farther out from the wall so that the top of the ladder slides down until resting against the wall at a point $52$ feet above the ground. given that the wall is perpendicular to the ground, how many feet did naoki move the base of the ladder?
Naoki shifted the base of ladder by 14 feet as the updated distance is 39 feet and old distance was 25 feet.
What is trigonometry?Trigonometry is the branch of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six common trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and abbreviations (csc). Finding the elements of vectors, modeling the mechanics of waves (both electromagnetic and physical), summarizing the strength of fields, and using dot and cross products are all physics applications of trigonometry. You can use trigonometry quite a bit in projectile motion.
Here,
The length of ladder= 65 foot
It rest at a wall at height of 60 foot.
So distance of foot of ladder from wall,
=√(65²-60²)
=√625
=25 foot
Now, as the ladder is shifted, it rest on the wall at height of 52 foot.
=√(65²-52²)
=√1521
=39 foot
Shift in the base of ladder,
=39-25
=14 foot
As the updated distance is 39 feet and the previous distance was 25 feet, Naoki moved the base of the ladder up by 14 feet.
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events which can never occur together in probability theories then it is classified as? a. mutually exclusive events b. collectively exclusive events c. mutually exhaustive events d. none of these
In probability theories, events which can never occur together are classified as "mutually exclusive events" that is option A.
What is mutually exclusive event?Two events are mutually exclusive or disjoint in logic and probability theory if they cannot both occur at the same time. The results of a single coin toss, which can result in either heads or tails but not both, serve as an obvious illustration. Events that do not take place at the same time are said to be mutually exclusive. For instance, if a coin is tossed, the outcome will either be head or tail; we cannot get both outcomes. Since they do not occur at the same time, such events are also known as disjoint events.
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PLEASEE HELP ME !! Find the volume of each shape and then compare do not reduce your fractions.
Answer:
1.) 150/512 in.
2.) 64/125 in.
Step-by-step explanation:
1.) V = l x w x h That's the formula to find the volume of a rectangle
V = 6/8 x 5/8 x 5/8 in. Plug in the numbers
V = 150/512 in. Multiply
V = 75/256 in. Simplify
Since you're asked to not reduce don't write this answer. I only put it to show that it can be simplified.
2.) V = l^3 This is the formula to find the volume of a cube
V = (4/5)^3 in. Plug in the numbers
V = 64/125 in. Miltuply
Select all of the following equation(s) that are quadratic in form. x4 – 6x2 – 27 = 0 3x4 = 2x 2(x + 5)4 + 2x2 + 5 = 0 6(2x + 4)2 = (2x + 4) + 2 6x4 = -x2 + 5 8x4 + 2x2 – 4x = 0
The equations that are quadratic in form are:
x4 – 6x2 – 27 = 0
6(2x + 4)2 = (2x + 4) + 2
6x4 = -x2 + 5
How can the quadratic functions be written?The concept that is been used here is quadratic functions which can be written in three ways :
Standard Form: [y = ax^2 + bx + c ]Factored Form: [y = a ( x − r 1 ) ( x − r 2 ) ](x−r2)Vertex Form: [y = a ( x − h ) 2 + k ]Where vertical line x = h and a not equal to zero, Hence we can see that the three selected options above followed the concept that is decribed as the quadratic function.
Therefore, the first, fourth and fifth options are correct.
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Answer:
A, D, E
Step-by-step explanation:
A model of a car is 1 feet wide and 3 feet long. If the actual car is 15 feet long, what is the width of the actual car?
A. 3 feet
B. 5 feet
C. 15 feet
D. 45 feet
Answer:
5 feet.
Step-by-step explanation:
if we see that 3 feet is the model and 15 feet is the actual, we find the ratio is 3:15 or 1:5. since the width is 1 foot, then we see the actual is 5 feet long.
A utility pole has a support wire that reaches from the top of the pole to the ground, forming a right triangle. Ryan has measured the angle of elevation to the top of the pole formed by the wire and the ground to be 59°. He also knows that the horizontal distance from the base of the pole to the wire is 7 meters. What is the approximate height of the utility pole? A. 8 meters B. 12 meters C. 11 meters D. 14 meters
The height of utility poles is B. 12 meters.
The height of the utility pole will be calculated by the formula -
tan theta = perpendicular ÷ base, where theta is the angle of elevation, perpendicular is the height of utility pole and base is the distance from the base of pole to the wire.
Keep the values in formula to find the height of utility pole.
tan 59 = perpendicular ÷ 7
Perpendicular = tan 59 × 7
Perpendicular = 1.66 × 7
Performing multiplication on Right Hand Side of the equation
Perpendicular = 11.65 metres
On rounding off, we get 12 metres.
Thus, the height is B. 12 meters.
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If y = 3x2 - 9, what is its inverse?
Answer:
f^-1(x) = √((y +9)/3)
Step-by-step explanation:
You want the inverse function of y = 3x² -9.
Inverse functionThe given relation will only have an inverse function if its domain is restricted to values x ≥ 0.
We can find that inverse function by interchanging the variables x and y, then solving for y:
x = 3y² -9
x +9 = 3y² . . . . . . . add 9
(x +9)/3 = y² . . . . . . divide by 3
y = √((x+9)/3) . . . . . take the square root
The inverse function is f^-1(x) = √((x +9)/3).
Allan i meauring hi dining room table to make a tablecloth. The table i 0. 45 meter longer than it i wide. If it i 1. 06 meter wide,how long i it?
The length of the table is 1.51 meters.
Allan is measuring his dining room table to make a tablecloth. The table is 0.45 meter longer than it is wide. The width of the table is 1.06 meter. We need to find out the length of the table.
Let the length of the table be represented by the variable "L". In the context of a mathematical problem or experiment, a variable is a quantity that may vary. The length of the table is the sum of the width of the table and the difference between the two quantities.
L = 1.06 + 0.45
L = 1.51
Hence, the length of the table is 1.51 meters.
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the faa now figures the average checked bag to weigh 30 pounds. this is up from a previous figure of 26 pounds. find the amount of increase and the percent of increase, to the nearest whole percent.
The amount of weight of bag increase is 4 pounds. The percent of increase is 13,33 %. The result is obtained by calculating the change of two numbers.
How to find the percent of change?A number can increase or decrease to another number. This change can be counted by subtracting the first number from the second number. If the result is positive, it is an increase. If the result is negative, it is a decrease.
The percent of change would be the ratio of the amount of change to first number times 100.
Given the first figure of bag is 26 pounds and the last figure is 30 pounds.
What is the amount of increase?What is the percent of increase?The amount of increase is subtracting 26 from 30.
30 - 26 = 4 pounds.
The percent of increase is
[tex]= \frac{4}{30} \times 100[/tex] %
[tex]= 0.1333 \times 100[/tex] %
[tex]= 13.33[/tex] %
Hence, the amount of weight of bag increase is 4 pounds. The percent of increase is 13,33 %.
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