"Karen wants to buy a new smartphone that costs $46. She currently has some money saved up, represented by the expression 6x - 4, where x is the number of weeks she has been saving. Can Karen buy the smartphone now, or does she need to save for more weeks? Use the inequality 6x - 4 < 46 to help you answer the question."
Describe Algebraic Expression?In mathematics, an algebraic expression is a combination of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. Algebraic expressions are used to represent and solve problems in various areas, including science, engineering, economics, and mathematics.
An algebraic expression can contain one or more variables, which represent unknown or changing quantities, and one or more constants, which represent fixed values. The variables are usually represented by letters, such as x, y, or z. The operations of addition, subtraction, multiplication, and division are represented by the symbols +, -, ×, and ÷, respectively. Parentheses are also used to group terms and indicate the order of operations.
For example, the algebraic expression 3x + 2y - 5 represents a combination of two variables, x and y, and three constants, 3, 2, and 5. The terms 3x and 2y are the variables multiplied by their coefficients, while -5 is a constant term.
Algebraic expressions can be simplified by combining like terms, which are terms that have the same variable raised to the same power. For example, in the expression 3x + 2y - 5 + 4x - 3y, the like terms are 3x and 4x, and 2y and -3y. Combining these terms yields the simplified expression 7x - y - 5.
Algebraic expressions are used in various mathematical operations, such as solving equations, graphing functions, and evaluating formulas. They are also used in real-world applications, such as calculating interest rates, solving optimization problems, and modeling physical phenomena.
Sure, here's a word problem that fits the inequality 6x - 4 < 46:
"Karen wants to buy a new smartphone that costs $46. She currently has some money saved up, represented by the expression 6x - 4, where x is the number of weeks she has been saving. Can Karen buy the smartphone now, or does she need to save for more weeks? Use the inequality 6x - 4 < 46 to help you answer the question."
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In the image below if m <1 = 90° and m <1 = M<2 = m
<3 = M<4 = m<5 = m<6 = m<7 = m<8, which of the
following below represents a line parallel to line b?
The line parallel to the line b is the line a
How to determine the parallel line to line bFrom the question, we have the following parameters that can be used in our computation:
The figure
Also, we have
Angle 1 = 90 degrees
The measure of angle 1 and angle 5 are congruent
This is so because they are corresponsing angles
So, we have
Angle 5 = 90 degrees
The above implies that line a and line b are parallel lines
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How far away is 1 km?
To convert 1km into other measurements: 1) 1000 meter, 2) 3280.84, 3) 1e+6 millimeter, 4) 100000 centimeter, 5) 39370.1 inch, 6) 1093.61 yard1 km, 7) 0.621371 mile.
It is necessary to measure these quantities using units of measurement. Sometimes the units of measurement chosen don't match the standards needed for a specific procedure or application, as well as the measurement preference and ease of use.
It's essential to convert these units in a way that enables proper comprehension and use. When converting between different units in the metric system, a decimal point must typically be moved. If you remember what the prefixes mean, you can convert between different units of measurement within the metric system fairly quickly by simply multiplying or dividing the number by the prefix's value.
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The following system of equations is designed to determine concentrations (the c's in g/m³) in a series of coupled reactors as a function of the amount of mass input to each rector (right hand sides in g/day): 10c2c₂cy -3c-6c₂+2c3=-61.5 C₂+503
Solve this problem with the Jacobi's iterative method to 5%.
The solution for the system of equations is Ax = b as the matrix is invertible (or non-singular) if and only if its determinant is not zero.
To solve a system of equations, we can use matrix algebra. We can write the system of equations in matrix form as follows:
Ax = b
where A is the matrix of coefficients, x is the vector of unknowns (the concentrations), and b is the vector of right-hand sides (the mass inputs).
To solve for x, we can multiply both sides by the inverse of A:
x = [tex]A^{-1}b[/tex]
where [tex]A^{-1}[/tex] is the inverse of A.
However, not all matrices have inverses. A matrix is invertible (or non-singular) if and only if its determinant is not zero. So, before we can solve for x, we need to check if A is invertible by calculating its determinant.
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A carpet in Frank’s house has a length of 2 1/4 meters and a width of 1 1/5 meters. What is the area of the carpet? 6 9/10 meters 2 1/20 square meters 2 7/10 square meters 2 7/20 meters
The area of the carpet is [tex]2 7/20[/tex] square meters.
The size of a patch on a surface is determined by its area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.
To find the area of the carpet, we need to multiply its length by its width.
The mixed numbers must first be transformed into improper fractions:
Length: 21/4 = 9/4
Width: 11/5 = 6/5
Then we can multiply:
Area = length x width
Area = (9/4) x (6/5)
Area = 54/20 or 27/20 square meters
Therefore, the area of the carpet is 27/20 square meters.
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what is 1 8 in decimal
1/8 in a decimal, divide the denominator by the numerator to get 1/8 as a decimal 1/8 is 0.125.
We divide the numerator by the denominator to convert a fraction to a decimal number. This results in a decimal value because, when dividing, we add the decimal place and then add the necessary number of zeros to finish the division.
1/8
1/2 x 1/2 x 1/2
0.5 x 0.5 x 0.5
0.125
To convert a fraction to a decimal, all you have to do is divide the numerator by the denominator. We position the number over its place value when converting a decimal to a fraction.
Just dividing the numerator by the denominator is all that is required to convert a fraction to a decimal.
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how to convert 250 grams to pounds?
250 grams is approximately equal to 0.5511 pounds ( rounded to four decimal places )
The conversion factor to convert grams to pounds is 0.00220462
1 gram = 0.00220462 pounds
The conversion is the process of changing the unit of one quantity to another units
The conversion factor is defined as the number that is used to change one unit to another units by multiplying or dividing
The mass in pounds = The mass in grams × conversion factor
Substitute the values in the equation
1 gram = 0.00220462 pounds
250 grams = 250 × 0.00220462
Multiply the numbers
= 0.5511 pounds ( rounded to four decimal places )
Therefore, 250 grams is 0.5511 pounds
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Consider the line
Find the equation of the line that is perpendicular to this line and passes through the point (5, 6).
The equation of the line that's vertical to the given line and passes through the point(,6) is y = (-2/3) x28/3.
To find the equation of a line vertical to a given line, we need to use the fact that the pitches of two vertical lines are negative reciprocals of each other.
Let's start by chancing the pitch of the given line. The equation of a line in pitch- intercept form is y = mx b, where m is the pitch and b is the y- intercept. We can rewrite the given line 3x- 2y = 5 in pitch- intercept form by working for y
3x- 2y = 5
- 2y = -3 x 5
y = (3/2) x-5/2
So the pitch of the given line is3/2.
The pitch of a line vertical to this line is the negative complementary of3/2, which is-2/ 3.
Now we can use the point- pitch form of the equation of a line to find the equation of the line that passes through the point(,6) and has pitch-2/ 3. The point- pitch form is
y- y1 = m( x- x1)
where( x1, y1) is the point the line passes through and m is the pitch.
Substituting in the values we know, we get
y- 6 = (-2/3)( x- 5)
Expanding the right side, we get
y- 6 = (-2/3) x10/3
Adding 6 to both sides, we get
y = (-2/3) x28/3
So the equation of the line that's vertical to the given line and passes through the point(,6) is y = (-2/3) x28/3.
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List two different ways you could break up the factors in 239 x 64 to find the product. Explain why the two ways would have the same product.
The two different ways to find the product of 239×64 are,
(240 - 1)×64 and 239×(60 + 4).
What are some alternative names for arithmetic operations?Addition is also known as the sum, subtraction is also known as the difference, multiplication is also known as the product, and division is also known as the factor.
Given, A product of 239×64.
The first way is,
239×64.
= (240 - 1)×64.
= 15360 - 64.
= 15296.
Another way to find the product of 239×64 is,
= 239×(60 + 4).
= 14340 + 956.
= 15296.
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on a car trip, jane ate some pretzels. after spilling and losing half of the pretzels, she at 14. her sister then ate on more than half the remaining pretzels, after which there was 3
The number of pretzels in the beginning was 44 pretzels solving the equation.
What is an Equation?An equation is a mathematical statement containing two expressions on either sides which are connected with an equal to sign.
Either sides of an equation is called as left hand side and right hand side.
Let the total number of pretzels = x
Pretzels has been spilled and lost half of the pretzels.
Remaining pretzels = x - x/2
Jane ate 14 pretzels.
Remaining pretzels = x - x/2 - 14
Her sister then ate one more than half the remaining pretzels.
Remaining pretzels = x - x/2 - 14 - [1/2 (x - x/2 - 14) + 1]
Remaining pretzels is 3.
So we get an equation,
x - x/2 - 14 - [1/2 (x - x/2 - 14) + 1] = 3
Solve for x.
x - x/2 - 14 - (x/2 - x/4 - 7 + 1) = 3
x - x/2 - x/2 + x/4 - 14 + 7 - 1 = 3
x/4 - 7 - 1 = 3
x/4 - 8 = 3
x/4 = 11
x = 44
Hence the total number of pretzels was 44.
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Your question is incomplete. The complete question is as follows.
On a car trip, Jane ate some pretzels. After spilling and losing half of the pretzels, she ate 14. Her sister then ate one more than half the remaining pretzels, after which there was 3 pretzels.
How many pretzels was there?
In ΔABC, a = 6 inches, mm∠A=121° and mm∠B=36°. Find the length of b, to the nearest 10th of an inch.
Using a calculator, we find that b ≈ 3.9 inches (rounded to the nearest 10th of an inch).
What is the Law of Sines?
The Law of Sines, also known as the sine rule, is a trigonometric formula used to find unknown sides or angles in a triangle.
To solve this problem, we can use the Law of Sines, which states that for any triangle ABC,
a/sin(A) = b/sin(B) = c/sin(C)
where a, b, and c are the side lengths opposite the corresponding angles A, B, and C, respectively.
Using this formula, we can set up the following proportion:
b/sin(B) = a/sin(A)
Plugging in the values we know, we get:
b/sin(36°) = 6/sin(121°)
Solving for b, we get:
b = (6 sin(36°))/sin(121°)
Using a calculator, we find that b ≈ 3.9 inches (rounded to the nearest 10th of an inch).
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Find the length of CYT given that m/CAT=128° and CA =10 in Circle A.
3.14 in your calculation and round to the nearest tenth.
The length of arc CYT is solved to get
= 40.12
How to solve for length of arcLength of arc CYT is calculated using the formula for length of arc
= theta / 360 * 2πR
From the problem, we have that
theta = 360 - 128 = 230
R = radius = CA = 10
π = 3.14sds
plugging in the values we have
= 230 / 360 * 2 * 3.14 * 10
= 23/36 * 20 * 3.14
= 40.1222
= 40.12 (to the nearest tenth)
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Find the area of the shaded region. Round to the nearest square unit when applicable. Show appropriate work. formules, and substitutions.
The areas of the composite figures are listed below:
516 55π cm² 96 m² (29.5π + 77) m² 58 ft² 588 cm²How to determine the areas of composite figures
In this problem we need to determine the areas of composite figures, which are the result of adding and subtracting geometric figures, whose area formulas are listed below:
Rectangle
A = b · h
Triangle
A = 0.5 · b · h
Circle
A = π · r²
Semicircle
A = 0.5π · r²
Quarter of a circle
A = 0.25π · r²
Square
A = l²
Where:
b - Baseh - Heightl - Side lengthr - RadiusA - AreaNow we proceed to determine the area of each figure:
Area 1
A = 30 · 20 - 6 · 14
A = 600 - 84
A = 516
Area 2
A = π · (8 cm)² - π · (3 cm)²
A = (64 - 9) · π cm²
A = 55π cm²
Area 3
A = (14 m)² - 4 · (5 m)²
A = 196 m² - 100 m²
A = 96 m²
Area 4
A = 0.5π · (7 m)² + 0.5 · (14 m) · (11 m)
A = 29.5π m² + 77 m²
A = (29.5π + 77) m²
Area 5
A = (7 ft) · (10 ft) + (3 ft) · (4 ft)
A = 70 ft² - 12 ft²
A = 58 ft²
Area 6
A = (28 cm)² - 4 · 0.25π · (14 cm)²
A = 784 cm² - 196π cm²
A = 588 cm²
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A stained glass window is in the shape of a semi circle. What is the distance around the window in inches if the diameter is 40 in. Don't forget to add all parts of the distance around the window to get the entire distance.
Answer:
The distance around the window in inches is 80 inches. This is because the circumference of a semi-circle is equal to π times the diameter (C = πd). So, 40 x π = 80 inches.
Please help me
Nine times the sum of a number and 17 is at least -23. Translate the sentence into an inequality
Answer:
9(x + 17) ≥ -23
Step-by-step explanation:
Let's start by breaking down the sentence:
"A number": We can represent this as a variable, say "x".
"The sum of a number and 17": This is x + 17.
"Nine times the sum of a number and 17": This is 9(x + 17).
"Is at least -23": This means the expression on the left-hand side of the inequality is greater than or equal to -23.
Putting it all together, we get the inequality:
9(x + 17) ≥ -23
This year Boris watched 60 movies. He thought that 33 of them were very good. Of the movies he watched, what percentage did he rate as very good?
Answer:
55%
Step-by-step explanation:
To get 55 I just divided 33/60 and multiplied it buy 100
What is the image point of
(
−
7
,
(−7,5) after a translation right 5 units and up 4 units?
The image point of (-7, 5) after the translation is (-2, 9).
What is the translation in the coordinate system?
A translation in the Cartesian plane can be described by a rule that indicates how to move each point of a figure to its image under the translation. The rule is usually given as a pair of numbers (a, b), where a is the horizontal distance to move each point (positive to the right, negative to the left), and b is the vertical distance to move each point
To find the image point of the point (-7, 5) after a translation right 5 units and up 4 units, we need to add 5 to the x-coordinate and add 4 to the y-coordinate.
The new x-coordinate will be -7 + 5 = -2, since we're moving the point to the right 5 units.
The new y-coordinate will be 5 + 4 = 9, since we're moving the point up 4 units.
Hence, the image point of (-7, 5) after the translation is (-2, 9).
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How to convert 112 kg to lbs?
The required value of 112 kilograms into pounds using standard conversion relation is equal to 112 kilograms = ( 246. 92 ) pounds ( round up to two decimal places )
Units pounds and kilograms are used to measure the mass of a given things.One kilograms is equal to 2.20462 pounds.
We need to convert 112 kilograms into pounds :
This implies :
⇒ 112 kilograms = ( 112 × 2.20462 ) pounds
⇒ 112 kilograms = ( 246.91744 ) pounds
⇒ 112 kilograms = ( 246. 92 ) pounds ( round up to two decimal places )
Therefore, the converting value of kilogram to pounds is given by :
112 kilograms = ( 246. 92 ) pounds ( round up to two decimal places ) .
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can somebody help me with this
Answer:
-4
Step-by-step explanation:
7(-1)³ + 5(-1)² -2 = ?
-7 + 5 -2 = ?
-2 -2 = ?
? = -4
Solve.
x−2/5=1/5
Responses
13
12
2
3
Answer:
Step-by-step explanation:
To solve for x in the equation:
x - 2/5 = 1/5
We can start by isolating x on one side of the equation. We can do this by adding 2/5 to both sides:
x - 2/5 + 2/5 = 1/5 + 2/5
Simplifying, we get:
x = 3/5
Therefore, the solution is:
x = 3/5
the hypergeometric distribution should be used instead of the binomial distribution when: a. each trial is independent b. there are more than two outcomes on a single trial c. there is a fixed number of trials d. sampling does not involve replacement
The hypergeometric distribution should be used instead of the binomial distribution. The correct option is d. Sampling does not involve replacement,
What is binomial distribution ?
The binomial distribution is a probability distribution that describes the probability of getting a certain number of successes in a fixed number of independent trials, where each trial has only two possible outcomes: success or failure.
The probability of getting exactly k successes in n trials with probability of success p is given by the formula:
[tex]P(k) = (n choose k) * p^k * (1 - p)^(n - k)[/tex]
where (n choose k) is the binomial coefficient, which gives the number of ways to choose k items out of n, and is equal to:
[tex](n choose k) = n! / (k! * (n - k)!)[/tex]
where n! represents n factorial, which is the product of all positive integers up to n.
Given by the question:
The correct answer is d. sampling does not involve replacement.
Therefore, when sampling does not involve replacement, the hypergeometric distribution should be used instead of the binomial distribution.
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Molly si selling bracelets and necklace at a crack fair . The cost of 4 bracelets and 3 neckclace is 23.50. The cost of 5 bracelets and 2 necklace is 21.50. A custumer bought 1 bracelet and 1 necklace. How Mich money did the custumer spend?
Word problems
Simultaneous equation
4b + 3n = $23.50 x2
5b + 2n = $21.50 x3
We solve this equation using the elimination method. By removing necklaces, we can find the cost of a bracelet.
8b + 6n = $47 --- eqn 1
15b + 6n = $64.5 --- eqn 2
Subtract eqn 1 from eqn 2
7b = 17.5
1b = 17.5/7
1b = $2.50
Substitute the value of bracelet into eqn 1 to find the cost of 1 necklace
8(2.5) + 6n = $47
20 + 6n = $47
6n = 47 -20
6n = 27
1n = 27/6
1n = $4.5
1b + 1n = ?
2.50 + 4.50 = $7
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Don’t know answer can u please help me understand this and give me the answers
The value of the expression is 1/c - 5
How to simply the expressionNote that algebraic expressions are described as expressions that are composed of terms, variables, coefficients, factors and constants.
From the information given, we have that;
c/ c² - 7c + 10 - (2/ c² - 7c + 10)
Find the lowest common factors
c - 2/ c² - 7c + 10
solve the quadratic equation
c - 2/ c² - 5c - 2c + 10
Factor the expression, we get;
c- 2/c(c - 5) - 2(c - 5)
Factor the terms
c-2/(c-2)(c-5)
Divide the values
1/c - 5
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need help asap
Which ordered pair (from the table in part A) represents the initial value? What does the initial value represent in this problem? (1-2
sentences)
Part D:
What is the rate of change in this equation? What does the rate of change represent in this problem? (1-2 sentences)
Table from part A:
The table of values for y = -128x + 3840 is:
xy
0 3840
5 3200
8 2816
10 2560
30 0
C) The ordered pair that represents the initial value of the function is of (0,3840), meaning that the graph of the function crosses the y-axis at the value of y = 3840.
D) The rate of change of the equation is of -128, meaning that when x increases by one, y is decreased by 128.
How to define a linear function?The following is the definition of a linear function's slope and intercept:
y = mx + b.
In which:
m is the slope, representing the rate of change, that is, by how much y changes when x is increased by one.
The value of y at x=0 is represented by the intercept, b. Hence the ordered pair is of (0,b).
The function is defined as follows for this problem:
y = -128x + 3840.
The slope and intercept are therefore given as follow:
m = -128, b = 3840.
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Are the two triangles similar ?
Yes or no?
How do you know ?
The grand staircase has 13 steps. The
priest wants to know if he can climb this a
different way each day for a year using the
same rules as the priestess.
Is it possible?
How many ways are there of ascending the
grand staircase?
Explain why your answer is correct.
Find the solution of the system of equations. -2x-3y= −2x−3y= \,\,-28 −28 -2x+2y= −2x+2y= \,\,22 22
The quadratic equation of [tex]x^{2}[/tex]-6x+9=0 is C) (x-2)(x+3).
What is equation?Equation is a physical and mathematical statement that describing physical phenomena and the relationship between different physical quantity typically consist of variable simple presenting physical quantity and then it personal variable may be pointed such as your energy.
This equation is an example of a quadratic equation, which is an equation of the form a[tex]x^{2}[/tex]+bx+c=0, where a, b, and c are real numbers, and a is not equal to 0. In this equation, a is equal to 1, b is equal to -6, and c is equal to 9. To solve this equation, we need to use the quadratic formula, which states that the solutions to the equation are x= -b ± [tex]\sqrt[1]{b^{2}-4ac }[/tex] / 2a. Therefore, the solutions to this equation are x= -(-6) ± [tex]\sqrt{(-6)^{2} -(4)(1)(9) }[/tex]) / 2(1), which simplifies to x=3 ± [tex]\sqrt{3}[/tex] /2, or x=3 ± [tex]\sqrt{9}[/tex] /2. This simplifies to x=3 ± [tex]\sqrt{3}[/tex], or x=3 ± 1. Therefore, the solutions to this equation are x=2 and x=4. The factored form of this equation is (x-2)(x+3), which is option C.
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What is A divided by 6 is equal to a whole number?
Answer:
4
Step-by-step explanation:
I think and I hope I got it right sorry if I didnt
The answer I think is right is a=24
a/6=?
24/6=4
The radius of a semicircle is 2 millimeters. What is the semicircle's perimeter?
Answer:
required perimeter is 12.57mm
what does a rhombus look like
A rhombus with opposite sides are parallel and equal, and opposite angles are equal looks like Diamond.
A closed two-dimensional plane figure is a rhombus. It is regarded as a peculiar parallelogram, and due to its distinctive characteristics, it acquires a distinct identity as a quadrilateral. Due to its equal length sides, a rhombus is also known as an equilateral quadrilateral. The name "rhombus" is derived from the Greek word "rhombos," which really refers to a spinning object.
Due to the fact that it is a quadrilateral with two pairs of parallel sides, a rhombus can be considered a particular parallelogram. A rhombus also has equal sides on all four sides, exactly like a square. Because of this, it is often referred to as a tilted square. To comprehend the relationship between the rhombus shape, parallelogram, and square, look at the graphic below.
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Select the two situations with the highest total surplus. 1.) Bonnie buys flowers for $2.25 less than she was willing to pay. She bought them from a seller would have been willing to receive $3 less from the sale. 2.) Don wanted to buy a scooter for no more than $5, but was only able to find a producer who would sell for $15.
1) Jay buys a house for $40,000 less than he is willing to pay. He bought a house from a seller who received $2,000 more than he was willing to sell.
4) Kevin wanted to spend $50 on a dishwasher and bought it for $45 from a manufacturer hoping to get $40.
Economic Surplus:
Economic surplus, also known in mainstream economics as general welfare or general public welfare or Marshall's surplus (after Alfred Marshall), is one of two related quantities. Pay.
Producer surplus or producer surplus is the amount a producer receives by selling at a market price higher than the lowest price they are willing to sell. This roughly equals profit margin (because producers are usually unwilling to sell at a loss and are generally uninterested in selling at a break-even price).
Total economic surplus = supplier surplus + consumer surplus
supplier surplus is the difference between the minimum price that a seller would take for his/her products and the actual selling priceconsumer surplus is the difference between the maximum price that a consumer would be willing to pay for a product and the actual priceOn scenario 1, total economic surplus = $40,000 + $2,000 = $42,000
On scenario 2, total economic surplus = $2.25 + $3 = $5.25
On scenario 3, total economic surplus = $0
On scenario 4, total economic surplus = $5 + $5 = $10
Complete Question:
Select the two situations with the highest total surplus. correct answer(s) jay buys a house for $40,000 less than he was willing to pay. he bought his home from sellers who received $2,000 more than they were willing to sell for. bonnie buys flowers for $2.25 less than she was willing to pay. she bought them from a seller would have been willing to receive $3 less from the sale. don wanted to buy a scooter for no more than $5, but was only able to find a producer who would sell for $15. kevin wanted to spend $50 on a dishwasher and bought one at $45 from a producer who was hoping to receive $40.
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