The sum is greater than 8 wrote as a fraction in the simplest form
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The fraction in simplest form that represents the linear inequality "The sum is greater than 8" is y/1 > (8 - x)/1.
What are linear inequalities, exactly?
Linear inequalities are mathematical expressions that describe a relationship between two values or variables, where one value is greater than, less than, or equal to the other value. They are similar to linear equations, but instead of an equal sign, they contain an inequality symbol (<, >, ≤, or ≥).
A linear inequality can be written in the form:
ax + b < c
or
ax + b > c
where "x" is the variable, "a" and "b" are constants, and "c" is a constant value.
Now,
The sum is greater than 8 can be written as the inequality:
x + y > 8
To write this as a fraction in simplest form, we need to convert it into an equation in the form of "numerator/denominator".
y > 8 - x
Then, we can write this as a fraction by putting "y" over "1":
y/1 > (8 - x)/1
To simplify this fraction, we can divide both the numerator and denominator by their greatest common factor (GCF), which is 1:
y/1 > (8 - x)/1
y > 8 - x
So the fraction in simplest form that represents the inequality "The sum is greater than 8" is:
y/1 > (8 - x)/1
or equivalently:
y > 8 - x
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Related Questions
What is the surface area of this cone round to the nearest hundreth
Answers
Given:
Diameter of cone = 4 mm
Slant height (l) = 7 mm
Find-: Surface area of the cone.
Sol:
The surface area of a cone is:
\(A=\pi r(r+\sqrt{r^2+h^2})\)Where,
\(\begin{gathered} r(\text{ radius\rparen}=\frac{\text{ Diameter}}{2} \\ \\ h=\text{ Height} \end{gathered}\)Height of cone:
\(\begin{gathered} l^2=r^2+h^2 \\ \\ h^2=l^2-r^2 \\ \\ h^2=7^2-2^2 \\ \\ h^2=49-4 \\ \\ h=\sqrt{45} \end{gathered}\)So, the surface area of a cone is:
\(\begin{gathered} A=\pi r(r+\sqrt{r^2+h^2}) \\ \\ A=\pi(2)(2+\sqrt{2^2+45}) \\ \\ A=2\pi(2+\sqrt{49}) \\ \\ A=2\pi(9) \\ \\ A=18\pi \\ \\ A=18\times3.14 \\ \\ A=56.52 \end{gathered}\)So, the surface area of a cone is 56.52
Will do a brainly! help me with this, please.
Answers
Answer:
C
Step-by-step explanation:
So, we want to find the equation of the line graphed.
To do so, let's first find the slope. Let's pick two points from the graph. I'm going to use (-2,2) and (0,-1).
The formula for slope is:
\(m=\frac{y_2-y_1}{x_2-x_1}\)
Let's let (-2, 2) be (x₁, y₁) and let's let (0,-1) be (x₂, y₂). So, substitute:
\(m=\frac{-1-2}{0-(-2)}\)
Subtract:
\(m=\frac{-3}{2}\)
So, our slope is -3/2.
Now, we can use the point-slope form, which is:
\(y-y_1=m(x-x_1)\)
Where m is the slope and (x₁, y₁) is any point on the graph.
Since our answer choices are using the values 2 and 4, this means we can use the point (2,-4).
So, (2,-4) is our (x₁, y₁).
Also, our m is -3/2. So, substitute these into the point-slope form:
\(y-(-4)=-\frac{3}{2}(x-2)\)
Simplify:
\(y+4=-\frac{3}{2}(x-2)\)
Therefore, our answer is C.
And we're done!
What is a outlier in math example?
Answers
In a dataset or graph, outliers are extreme values that greatly deviate from the dominant pattern of values.
How do you find the outlier in math?In order to identify the outlier, search for a value that is significantly greater or smaller than all the other values. Due to its extreme size compared to all other numbers, the number 267 is an outlier.
a value that "lies outside" (i.e., is significantly smaller or substantially bigger) most of the other values in a set of data For instance, both 3 and 85 in the scores 25, 29, 3, 32, 85, 33, 27 and 28 are "outliers".
A data point that is an outlier in a data graph or dataset you are dealing with is one that is extraordinarily high or extraordinarily low in comparison to the nearest data point and the rest of the nearby coexisting values. Outliers in a dataset or graph are extreme values that stand out significantly from the main pattern of values.
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Which of the following could be an example of a function with a domain
(-∞0,00) and a range (-∞,4)? Check all that apply.
A. V = -(0.25)* - 4
-
□ B. V = − (0.25)*+4
c. V = (3)* +4
□ D. V = − (3)* — 4
-
Answers
The correct options that could be an example of a function with a domain (-∞0,00) and a range (-∞,4) are given below.Option A. V = -(0.25)x - 4 Option B. V = − (0.25)x+4
A function can be defined as a special relation where each input has exactly one output. The set of values that a function takes as input is known as the domain of the function. The set of all output values that are obtained by evaluating a function is known as the range of the function.
From the given options, only option A and option B are the functions that satisfy the condition.Both of the options are linear equations and graph of linear equation is always a straight line. By solving both of the given options, we will get the range as (-∞, 4) and domain as (-∞, 0).Hence, the correct options that could be an example of a function with a domain (-∞0,00) and a range (-∞,4) are option A and option B.
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when estimating a population​ mean, are you more likely to be correct when you use a point estimate or an interval​ estimate? explain your reasoning.
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In estimating a population mean, an interval estimate is more likely to be correct than a point estimate. An interval estimate provides a range of values within which the true population mean is likely to fall, while a point estimate provides only a single value.
When estimating a population mean, using an interval estimate is more likely to be correct because it accounts for the uncertainty associated with the estimate. A point estimate, on the other hand, provides a single value that is assumed to represent the true population mean. However, due to sampling variability and potential errors in measurement, a point estimate is prone to error and may not accurately reflect the true population mean.
By using an interval estimate, which includes a range of values, we have a measure of uncertainty. The range is typically constructed based on a certain level of confidence, such as a 95% confidence interval. This means that if we were to repeat the sampling and estimation process many times, the true population mean would be expected to fall within the estimated interval in 95% of those repetitions.
The interval estimate takes into account the variability in the data and provides a more realistic representation of the true population mean. It provides a margin of error and acknowledges that the point estimate is just one possible value among many that could have been obtained through sampling.
Therefore, when estimating a population mean, an interval estimate is preferred because it not only provides a point estimate but also quantifies the uncertainty associated with that estimate, leading to a higher likelihood of being correct.
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Consider the given pseudo code. Write the function T(n) in terms of the number of operations, and then give the asymptotic (big Oh) complexity of the algorithm, show all the work you do. [ write the summation formula and solve it, or use the "Look for pattern"method. a. Matrix Multiplication
Answers
The function T(n) in terms of the number of operations is:
T(n) = 2n^3 + 3n^2 + 2n + 1 and the asymptotic complexity of the matrix multiplication algorithm is O(n^3).
To analyze the provided pseudo code for matrix multiplication and determine the function T(n) in terms of the number of operations, we need to examine the code and count the number of operations performed.
The pseudo code for matrix multiplication may look something like this:
```
MatrixMultiplication(A, B):
n = size of matrix A
C = empty matrix of size n x n
for i = 1 to n do:
for j = 1 to n do:
sum = 0
for k = 1 to n do:
sum = sum + A[i][k] * B[k][j]
C[i][j] = sum
return C
```
Let's break down the number of operations step by step:
1. Assigning the size of matrix A to variable n: 1 operation
2. Initializing an empty matrix C of size n x n: n^2 operations (for creating n x n elements)
3. Outer loop: for i = 1 to n
- Incrementing i: n operations
- Inner loop: for j = 1 to n
- Incrementing j: n^2 operations (since it is nested inside the outer loop)
- Initializing sum to 0: n^2 operations
- Innermost loop: for k = 1 to n
- Incrementing k: n^3 operations (since it is nested inside both the outer and inner loops)
- Performing the multiplication and addition: n^3 operations
- Assigning the result to C[i][j]: n^2 operations
- Assigning the value of sum to C[i][j]: n^2 operations
Total operations:
1 + n^2 + n + n^2 + n^3 + n^3 + n^2 + n^2 = 2n^3 + 3n^2 + 2n + 1
Therefore, the function T(n) in terms of the number of operations is:
T(n) = 2n^3 + 3n^2 + 2n + 1
To determine the asymptotic (big O) complexity of the algorithm, we focus on the dominant term as n approaches infinity.
In this case, the dominant term is 2n^3. Hence, the asymptotic complexity of the matrix multiplication algorithm is O(n^3).
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if 4 -letterwords'' are formed using the letters a, b, c, d, e, f, g, how many such words are possible for each of the following conditions:(a) no condition is imposed.
Answers
The number of 4-letter words that can be formed without any condition imposed is 8,064.
To determine the number of 4-letter words that can be formed without any conditions, we can use the concept of permutations. Since we have 8 options (a, b, c, d, e, f, g) for each letter position, we can multiply the number of options for each position to find the total number of possibilities.
For the first letter position, we have 8 options to choose from. Similarly, for the second, third, and fourth positions, we also have 8 options each. Therefore, the total number of possibilities is:
8 options for the first position × 8 options for the second position × 8 options for the third position × 8 options for the fourth position = 8 × 8 × 8 × 8 = 8,064.
Hence, there are 8,064 possible 4-letter words that can be formed without any conditions imposed.
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Change the following algebraic expressions to the statement in words: i. 3mn +7 ii. xy + (x+y)
Answers
Answer:
i) 3*m*n + 7
Then we can write the first term as:
"3 times the product between two numbers"
Where the product of two numbers is m*n
And after that we need to add 7, then the complete sentence is:
"3 times the product between two numbers, increased by 7"
ii) x*y + (x + y)
The first part, x*y, can be written as:
"the product of two numbers"
where the two numbers are the number x and the number y.
After that, we add the sum of these two numbers, then the complete sentence can be:
"the product of two numbers, plus the sum of these two numbers"
students are conducting an experiment to determine if the amount of sunlight affects the size of clover leaves. they plant clover in two identical pots, placing one next to a window and one inside a cupboard. they water each pot daily with 10 ml of water. which is the independent variable?
Answers
In the experiment, the independent variable is the amount of sunlight received by the clover plants.
The amount of sunlight the clover plants receive throughout the experiment serves as the independent variable, as it is being manipulated by the experimenters to determine its effect on the size of the clover leaves.
The dependent variable is the size of the clover leaves, which is being measured as a result of the change in the independent variable (amount of sunlight). The water is a controlled variable, as it is kept constant across both conditions to eliminate its effect on the outcome.
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ANALYZE In Europe, fuel economy is measured in liters per 100 kilometers. On a 2500 km road trip a car used 150 liters of fuel. The car used an average of how many liters per 100 km?
Answers
To find out the car's average fuel consumption in liters per 100 kilometers, we need to use the following formula:
Fuel consumption (liters per 100 km) = (Total fuel used / Total distance traveled) x 100
Using the information given, we know that the car traveled 2500 km and used 150 liters of fuel. Plugging these values into the formula, we get:
Fuel consumption (liters per 100 km) = (150 / 2500) x 100 = 6
Therefore, the car used an average of 6 liters of fuel per 100 kilometers on its 2500 km road trip.
It is important to note that fuel economy is an important factor in Europe, where fuel prices are generally higher than in other parts of the world.
By measuring fuel consumption in liters per 100 kilometers, European consumers can easily compare the fuel efficiency of different vehicles and make more informed purchasing decisions.
Additionally, analyzing fuel consumption data can help drivers identify ways to improve their fuel efficiency, such as reducing their speed, maintaining proper tire pressure, and avoiding excessive idling.
This not only saves money on fuel costs, but also reduces carbon emissions and contributes to a more sustainable transportation system.
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Need help quick please!!!
Answers
Answer:
b = 12 Km
Step-by-step explanation:
using Pythagoras' identity in the right triangle
the square on the hypotenuse is equal to the sum of the squares on the other 2 sides , that is
b² + 16² = 20²
b² + 256 = 400 ( subtract 256 from both sides )
b² = 144 ( take square root of both sides )
b = \(\sqrt{144}\) = 12
what is -4(x+3) - 12x + 5 distributed
Answers
-4x -12- 12x + 5 (Distributed)
-16x - 7 ( Combine like terms)
Answer-16x - 7.
2 +2 - 6 + 8 and then 2
Answers
Step-by-step explanation:
2+2 = 4 - 6= -2+8=6+2=8
Answer: 8
Answer:
48
Step-by-step explanation:
First add 2 + 2 = 4
Next subtract 4 - negative 6 = -2
Then add -2 + 8 = 6
Last multiply 6 * 8 = 48
From 1, 2, . . . 15, Alice and Bob each choose a number that is different from each other's. We know that Alice’s number can be divided by 5, then what is the probability that Alice’s number is larger than Bob’s?
Answers
The probability that Alice's number is greater than Bob's number given that Alice's number is divisible by 5 is 1/7.
To solve this problem, we first need to determine the total number of possible outcomes. Since Alice and Bob choose a number each, there are 15 options for Alice's first choice and 14 options remaining for Bob's first choice. Therefore, the total number of possible outcomes is 15 x 14.
The probability of Alice's number being greater than Bob's number given that Alice's number is divisible by 5 is then given by the ratio of the number of favorable outcomes (30) to the total number of possible outcomes (15 x 14):
Probability = favorable outcomes / total outcomes
Probability = 30 / (15 x 14)
Probability = 30 / 210
Probability = 1 / 7
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use calculus to find the area a of the triangle with the given vertices. (0, 0), (6, 1), (3, 7) a =
Answers
The area of the triangle is approximately 36.83 square units.
To find the area of a triangle using calculus, we can use the formula:
A = (1/2) ∫(x2 - x1)dy
Where x1 and x2 are the x-coordinates of the vertices, and dy is the change in the y-coordinate.
First, we need to find the equations of the lines that make up the sides of the triangle. The line between (0,0) and (6,1) has the equation y = (1/6)x. The line between (6,1) and (3,7) has the equation y = -2x + 13. The line between (3,7) and (0,0) has the equation y = (7/3)x.
Now we can use the formula to find the area of the triangle. We'll integrate from y = 0 to y = 1 for the first side, from y = 1 to y = 7 for the second side, and from y = 7 to y = 0 for the third side:
A = (1/2) ∫(x2 - x1)dy
= (1/2) ∫[(6x - 0) - (0 - 0)]dy from y = 0 to y = 1
+ (1/2) ∫[(13 - 2x) - (6x - 0)]dy from y = 1 to y = 7
+ (1/2) ∫[(0 - 0) - (7x/3 - 0)]dy from y = 7 to y = 0
= (1/2) ∫6xdy from y = 0 to y = 1
+ (1/2) ∫(13 - 8x)dy from y = 1 to y = 7
+ (1/2) ∫(-7x/3)dy from y = 7 to y = 0
= (1/2) [(3 - 0) + (49 - 8) + (-49/3 - 0)]
= (1/2) [(3) + (41) + (-49/3)]
= (1/2) [(147/3) + (123/3) + (-49/3)]
= (1/2) [(221/3)]
= 36.83
So the area of the triangle is approximately 36.83 square units.
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what is liters to pounds?
Answers
Answer:1 l = 2.2 lb wt.
Step-by-step explanation:
In a Binomial distribution, where the sample size is 9 and the probability of a success is .45, what is the value of q
Answers
The value of q in a Binomial distribution with a sample size of 9 and a probability of success of .45 is 0.55.
The Binomial distribution is a probability distribution that represents the number of successes in a fixed number of independent trials with the same probability of success in each trial. The probability of success in each trial is represented by the letter p and the probability of failure is represented by the letter q, which is equal to 1 minus the probability of success.
In this case, the sample size is 9 and the probability of success is .45, so the probability of failure would be 1 - .45 = .55. Therefore, the value of q in this Binomial distribution is 0.55.
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a) prove that there exists an s such that for any r > s there exists an m 2 n such that for all n m we have xn < r.
Answers
Hence the given statement that there exists an s such that for any r > s there exists an m 2 n such that for all n m we have x n < r is proved.
What is non-decreasing sequence?
Non-decreasing sequences are a generalization of binary covering arrays, which has made research on non-decreasing sequences important in both math and computer science.
Proof:
For n 2 N, let s = sup x n.
Then, there exists a m 2 N such that x m r for any r > s.
Given that x n is a non-decreasing sequence, we get x n r for any n > m.
As a result, there is a m 2 N such that for any n > m, x n r for any r > s.
Hence proved.
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the slide part of a water slide is 89 feet long and makes a 42 angle of depression with the ground, how high up in the air do you start your ride?
Answers
In a case whereby the slide part of a water slide is 89 feet long and makes a 42 angle of depression with the ground, the lenght or how high up in the air is 73.6 feet
How can the height ber calculated?We know that the length of the slide AB is 89 feet, and the angle of depression from A to B is 42 degrees. We want to find the height h of point A above the ground.
The tangent of an angle is defined as the ratio of the opposite side to the adjacent side. In this case, the opposite side is h (the height we're looking for), and the adjacent side is AB (the length of the slide). So we can write base on trigonometery as ;
tan(42) = h / 89
h = 89 * tan(42)
h ≈ 73.6 feet
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How to convert minutes and seconds into grades.
Answers
Answer:
Step-by-step explanation:
To convert time to time, kernel time with 24 (number of time in a day).
To convert time to minutes, kernel with time with 1440 (number of minutes in a day = 24 * 60).
To convert s to seconds, multiply the time by 86400 (number of s in a day = 24 * 60 * 60).
find the force on a square loop (side a), lying in the yz plane and centered at the origin, if it carries a current i, flowing counterclockwise, when you look down the x axis.
Answers
The force on the square loop is F = i(a²)(B), where B is the strength of the magnetic field in the x direction.
What is the Current-carrying loop?A current-carrying loop refers to a closed circuit consisting of a conductor (usually a wire) bent into the shape of a closed loop, through which an electric current flows. The loop may be any shape or size, but its geometry and the amount of current flowing through it determine the magnetic field it produces.
When a current-carrying loop is placed in a magnetic field, a force is exerted on the loop due to the interaction between the magnetic field and the current. The force on the loop can be calculated using the following formula:
=> F = iABsinθ
where F is the force on the loop, i is the current flowing through the loop, A is the area of the loop, B is the magnetic field, and θ is the angle between the normal to the loop and the direction of the magnetic field.
In this case, the loop is in the yz plane and centered at the origin. The magnetic field is assumed to be in the x direction. Since the loop is perpendicular to the x direction, the angle between the normal to the loop and the magnetic field is 90 degrees.
The area of the loop is given by A = a².
The current flowing through the loop is i.
Thus, the force on the loop is given by:
F = iABsinθ = i(a^2)(B)(sin90) = i(a^2)(B)
Therefore, the force on the square loop is F = i(a^2)(B), where B is the strength of the magnetic field in the x direction.
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Help again please!!! qwq
Answers
Answer:
Option (4)
Step-by-step explanation:
Step - 1 : 5(x² - 8x + 3)
Step - 2 : 5(x²- 8x + 16 - 16 + 3)
Step 3 : 5[(x - 4)²- 16 + 3]
Step 4 : 5[(x - 4)² - 13]
Step 6 : 5(x - 4)² - 65
Therefore, Cedric made a mistake in step 3, he incorrectly wrote the square as (x + 4)². He should have written as (x - 4)².
Option (4) will be the correct option.
A Galapagos tortoise can 1/5 mile in an hour. How many hours would it take the tortoise to walk 1/6?
Answers
Answer:
5/6 hours
Step-by-step explanation:
Create a proportion where x is the number of hours it will take to walk 1/6 of a mile:
\(\frac{1/5}{1}\) = \(\frac{1/6}{x}\)
Cross multiply and solve for x:
1/5x = 1/6
x = 5/6
So, it will take the tortoise 5/6 hours to walk 1/6 of a mile
In bus x passengers have taken tickets of rupees 5 each and y passengers taken tickets of rupees 10 each. Find total number of passengers and total fare received by the conductor
Answers
The total number of passengers = x + y and total fare received by the conductor = 5 (X + 2Y) rs.
Given: X Passengers purchased tickets for Rs. 5 each, while Y Passengers purchased tickets for Rs. To determine: The total number of passengers and the conductor's total revenue. Calculation: = x + y total number of passengers.
Fare from X Passenger Received: 5X Rs
Fare from Y Passenger Received: 10Y Rs
The conductor's overall tip is equal to 5X plus 10Y. = 5(X + 2Y) Rs.
Hence, The total number of passengers = x + y and total fare received by the conductor = 5 (X + 2Y) rs.
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Find each sum.
6 2/5+4 3/10
Answers
The sum of \(6 \dfrac{2}{5}+4 \dfrac{3}{10}\) using rules of simplification is 10.7 in decimal form and \(10\dfrac{7}{10}\) in mixed fractions.
Mixed fraction is a combination of a whole number and a proper fraction Example \(3\dfrac{3}{8}\) which consists 3 as a whole number and \(\dfrac{3}{8}\) as a proper fraction.
The set of the number system which includes all positive numbers from zero and ends at infinity are called whole numbers.
Example = 0,1,2,3,4,5,6,7…….∞.
To add fractions with different denominators, we will take LCM (least common multiple) of denominator. In this case, the common denominator is 10.
\(6 \dfrac{2}{5}+4 \dfrac{3}{10}\)
First we will convert the given mixed fraction into improper fraction which results to
\(\dfrac{32}{5}+\dfrac{43}{10}\)
The LCM is 10 so we will multiply 32 by 2 and 43 by 1 to make denominators same
\(\dfrac{64+43}{10}\)
\(\dfrac{107}{10}\)
which results to 10.7 in decimal form and \(10\dfrac{7}{10}\) in fractions.
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how have income levels for most americans changed in recent years apex?
Answers
Answer:
from 2015 to 2018 us household income has increased from 70,200 to 74,600
Step-by-step explanation:
Sam's preferences over cake, c, and money, m, can be represented by the utility function.
u(c,m)=c+m+μ(c-rc)+μ(m-rm)
where rc is his cake reference point, rm is his money reference point, and the function μ(⋅) is defined as
μ(z)={z z ≥ 0
{vz z < 0
where v > 0
1. If his reference point is the status quo (that is, his initial endowment), what is the maximum price Sam would be willing to pay to buy a cake?
2. If his reference point is the status quo, what is the minimum price Sam would be willing to accept to sell a cake he already owned?
3. If his reference point is the status quo, what is the minimum amount of money Sam would be willing to accept instead of receiving a cake (that he did not already own)? In other words, if Sam were a "chooser," how much money would he demand to compensate for not accepting a cake?
4. Find a condition on λ such that we can say that Sam exhibits the endowment effect.
Answers
Sam's maximum willingness to pay to buy a cakeIf the reference point is the status quo, Sam's utility function is given by;u(c,m) = c + m + μ(c - rc) + μ(m - rm)The marginal utility of a good is its derivative, thus.
∂u/∂c = 1 + μ′(c - rc)∂u/∂m
= 1 + μ′(m - rm)The maximum amount Sam is willing to pay to buy a cake will occur where the marginal utility of the cake is equal to the price. That is;∂u/∂c = 0⇒ 1 + μ′(c - rc)
= 0⇒ μ′(c - rc)
= -1⇒ c - rc
= -1/μ′Since μ(z) is decreasing and convex, we haveμ′(z) ≤ 0, μ′′(z) ≥ 0Hence, if the reference point is the status quo, Sam will not buy a cake whose price is more than rc.2. Sam's minimum willingness to accept to sell a cakeIf Sam wants to sell his cake, he would do so for a price that would give him at least as much utility as eating the cake himself.
That is;∂u/∂c = 0⇒ 1 + μ′(c - rc)
= 0⇒ μ′(c - rc)
= -1⇒ c - rc
= -1/μ′Therefore, the minimum amount that Sam will be willing to accept to sell his cake is rc - 1/μ′.3. Sam's minimum compensation in moneyIf Sam is offered a cake, then the minimum amount of money he will accept in exchange for the cake would be such that the utility from the money is at least as much as the utility from the cake. That is;u(c,m) = u(c, m')⇒ c + m + μ(c - rc) + μ(m - rm)
= c + m' + μ(c - rc) + μ(m' - rm)⇒ m - m'
= μ-1[μ(m' - rm) - μ(m - rm)]Thus, the minimum amount of money that Sam would demand in compensation for not accepting the cake would be given by m - μ-1[μ(m' - rm) - μ(m - rm)].4. The endowment effectSam exhibits the endowment effect when his willingness to sell his cake is less than his willingness to buy the same cake.
The endowment effect occurs when people demand more to give up a good than they are willing to pay to acquire the same good.Let λ be the marginal utility of money. Sam's willingness to pay for a cake can be expressed as;∂u/∂c = 1 + μ′(c - rc)
= 0⇒ μ′(c - rc)
= -1⇒ c - rc
= -1/μ′The willingness to sell the cake will be given by the minimum amount that Sam will accept for the cake, which is;∂u/∂c = 1 + μ′(c - rc)
= 0⇒ μ′(c - rc)
= -1⇒ c - rc
= -1/μ′Hence, Sam exhibits the endowment effect when;rc - 1/μ′ < rc + 1/λ, μ′ < λ.
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ABCD is a parallelogram with diagonals AC and BD intersecting at O
Prove that the diagonals bisect one another
Answers
Step-by-step explanation:
See the attached image. I numbered angles differently so as not to make an assumption that angles numbered the same are congruent.
\(\overline{AB} \parallel \overline{CD}\\\angle1 \cong \angle3\) (alternate interior angles are congruent)
\(\overline{AD} \parallel \overline{BC}\\\angle 2 \cong \angle 4\) (alternate interior angles are congruent)
\(\overline{AB} \cong \overline{CD}\) (opposite sides of a parallelogram are congruent)
\(\triangle{ABO \cong \triangle{CDO}\) (ASA - side/angle/side)
\(\overline{AO} \cong \overline{CO}\\\overline{BO} \cong \overline{DO}\) (corresponding parts of congruent triangles are congruent)
The diagonals bisect each other!
Calculate the missing terms in each proportion.
◼:11 = 11:121
5:2:1 = ◼:14:◼
1.5:◼:2.4 = 6:5:◼
Please Help me!
Answers
Answer:
1:11=11:121
5:2:1=35:14:7
1.5:1.25:2.4=6:5:9.6
Step-by-step explanation:
x/11=11/121 so x equals 1
5/2=x/14 so x equals 35
1.5/x=6/5 so x equals 1.25
1.25:2.4=5/x so x equals 9.6
Which compound inequality has a solution set of all real numbers?
x > -2 or x < 1
x < -1 and x > 2
x > -4 and x < 5
x < -3 or x > -2
Answers
The compound inequality that has a solution set of all real numbers is: x > -2 or x < 1
A mathematical expression known as a compound inequality consists of two or more inequalities linked together by the logical operators "and" or "or." It represents a set of values that simultaneously meet each of the stated inequalities. Take the compound inequality 2x + 3 7 and x - 4 > -2, for instance. We treat this compound inequality as two separate inequalities, 2x + 3 7 and x - 4 > -2, in order to solve it. We first determine the intersection of the solution sets after solving each inequality separately. The values of x in this situation that meet both inequality are: 0 x 3.
1. A compound inequality is an inequality that combines two or more simple inequalities using the words "and" or "or."
2. The solution set of all real numbers means that any number on the number line is a solution to the inequality.
3. In the given inequality, x > -2 or x < 1, we have two simple inequalities connected by "or."
4. If x > -2, we have all numbers greater than -2 (to the right of -2 on the number line) as solutions.
5. If x < 1, we have all numbers less than 1 (to the left of 1 on the number line) as solutions.
6. Since we're using "or," a number only needs to satisfy one of these conditions to be a solution. So, all real numbers satisfy either x > -2 or x < 1, making this the compound inequality with a solution set of all real numbers.
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