2. Consider this scatter plot.
(a) How would you characterize the relationship between the hours spent on homework and the test scores? The more hours spent on studying, the higher the test score
(b) Paul uses the function y = 8x + 40 to model the situation. What score does the model predict for 3 h of homework?
(c) What does the number 40 in Part (b) mean in the context of the situation?
Answers
Therefore, according to Paul's model, a student who spends 3 hours on homework is predicted to get a test score of 64.
What is function?In mathematics, a function is a rule or relationship that maps each input value (also known as the "argument" or "independent variable") to a corresponding output value (also known as the "value" or "dependent variable").
In other words, a function is a way to describe how one set of values (the inputs) are transformed into another set of values (the outputs). Functions are often represented using algebraic equations or graphical representations, such as graphs or charts.
For example, the function f(x) = 2x + 1 maps each input value x to the output value 2x + 1. So, if we input x=2, the output value would be f(2) = 2(2) + 1 = 5. Similarly, if we input x=3, the output value would be f (3) = 2(3) + 1 = 7.
(a) Based on the scatter plot, we can see a positive linear relationship between the hours spent on homework and the test scores. As the number of hours spent on homework increases, the test scores also tend to increase.
(b) To use Paul's function to predict the test score for 3 hours of homework, we can substitute x = 3 into the equation:
\(y = 8x + 40\)
\(y = 8(3) + 40\)
\(y = 24 + 40\)
\(y = 64\)
Therefore, according to Paul's model, a student who spends 3 hours on homework is predicted to get a test score of 64.
(c) In the context of the situation, the number 40 in Paul's model represents the baseline or minimum test score that a student would get if they didn't study at all. This is the y-intercept of the line and indicates that a student who does not spend any time on homework is predicted to get a score of 40.
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Related Questions
The length of a common housefly has approximately a normal distribution with mean µ= 6.4 millimeters and a standard deviation of σ= 0.12 millimeters. Suppose we take a random sample of n=64 common houseflies. Let X be the random variable representing the mean length in millimeters of the 64 sampled houseflies. Let Xtot be the random variable representing sum of the lengths of the 64 sampled houseflies
a) About what proportion of houseflies have lengths between 6.3 and 6.5 millimeters? ______
b) About what proportion of houseflies have lengths greater than 6.5 millimeters? _______
c) About how many of the 64 sampled houseflies would you expect to have length greater than 6.5 millimeters? (nearest integer)?______
d) About how many of the 64 sampled houseflies would you expect to have length between 6.3 and 6.5 millimeters? (nearest integer)?________
e) What is the standard deviation of the distribution of X (in mm)?________
f) What is the standard deviation of the distribution of Xtot (in mm)? ________
g) What is the probability that 6.38 < X < 6.42 mm ?____________
h) What is the probability that Xtot >410.5 mm? ____________
Answers
(a) Proportion of houseflies have lengths between 6.3 and 6.5 millimeters is 0.5934.
(b) Proportion of houseflies have lengths greater than 6.5 millimeters is 20.33%.
c) 64 sampled houseflies would expect to have length greater than 6.5 millimeters is 13 .
d) 64 sampled houseflies would expect to have length between 6.3 and 6.5 millimeters is 38 .
e) The standard deviation of the distribution of X is 0.015 millimeters.
f) The standard deviation of the distribution of X to t is 0.96 millimeters.
g) The probability that 6.38 < X < 6.42 mm is 0.1312 .
h) The probability that Xtot >410.5 mm is 0 .
(a) To determine the proportion of houseflies with lengths between 6.3 and 6.5 millimeters, we need to calculate the area under the normal distribution curve between these two values.
Using the Z-score formula:
Z = (X - µ) / σ
For X = 6.3 mm:
Z₁ = (6.3 - 6.4) / 0.12 = -0.833
For X = 6.5 mm:
Z₂ = (6.5 - 6.4) / 0.12 = 0.833
Now we can use a standard normal distribution table or calculator to find the proportion associated with the Z-scores:
P(-0.833 < Z < 0.833) ≈ P(Z < 0.833) - P(Z < -0.833)
Looking up the values in a standard normal distribution table or using a calculator, we find:
P(Z < 0.833) ≈ 0.7967
P(Z < -0.833) ≈ 0.2033
Therefore, the proportion of houseflies with lengths between 6.3 and 6.5 millimeters is approximately:
0.7967 - 0.2033 = 0.5934
(b) To find the proportion of houseflies with lengths greater than 6.5 millimeters, we need to calculate the area under the normal distribution curve to the right of this value.
P(X > 6.5) = 1 - P(X < 6.5)
Using the Z-score formula:
Z = (X - µ) / σ
For X = 6.5 mm:
Z = (6.5 - 6.4) / 0.12 = 0.833
Using a standard normal distribution table or calculator, we find:
P(Z > 0.833) ≈ 1 - P(Z < 0.833)
≈ 1 - 0.7967
≈ 0.2033
Therefore, approximately 20.33% of houseflies have lengths greater than 6.5 millimeters.
c) The number of houseflies with lengths greater than 6.5 millimeters can be approximated by multiplying the total number of houseflies (n = 64) by the proportion found in part (b):
Expected count = n * proportion
Expected count = 64 * 0.2033 ≈ 13 (nearest integer)
Therefore, we would expect approximately 13 houseflies out of the 64 sampled to have lengths greater than 6.5 millimeters.
d) Similarly, to find the expected number of houseflies with lengths between 6.3 and 6.5 millimeters, we multiply the total number of houseflies (n = 64) by the proportion found in part (a):
Expected count = n * proportion
Expected count = 64 * 0.5934 ≈ 38 (nearest integer)
Therefore, we would expect approximately 38 houseflies out of the 64 sampled to have lengths between 6.3 and 6.5 millimeters.
(e) The standard deviation of the distribution of X (the mean length of the 64 sampled houseflies) can be calculated using the formula:
Standard deviation of X = σ /√(n)
σ = 0.12 millimeters and n = 64, we have:
Standard deviation of X = 0.12 / √(64)
= 0.12 / 8
= 0.015 millimeters
Therefore, the standard deviation of the distribution of X is 0.015 millimeters.
f) The standard deviation of the distribution of Xtot (the sum of the lengths of the 64 sampled houseflies) can be calculated using the formula:
Standard deviation of Xtot = σ * √(n)
Given σ = 0.12 millimeters and n = 64, we have:
Standard deviation of Xtot = 0.12 * √(64)
= 0.12 * 8
= 0.96 millimeters
Therefore, the standard deviation of the distribution of Xtot is 0.96 millimeters.
g) To find the probability that 6.38 < X < 6.42 mm, we need to calculate the area under the normal distribution curve between these two values.
Using the Z-score formula:
Z₁ = (6.38 - 6.4) / 0.12 = -0.167
Z₂ = (6.42 - 6.4) / 0.12 = 0.167
Using a standard normal distribution table or calculator, we find:
P(-0.167 < Z < 0.167) ≈ P(Z < 0.167) - P(Z < -0.167)
P(Z < 0.167) ≈ 0.5656
P(Z < -0.167) ≈ 0.4344
Therefore, the probability that 6.38 < X < 6.42 mm is approximately:
0.5656 - 0.4344 = 0.1312
(h) To find the probability that Xtot > 410.5 mm, we need to convert it to a Z-score.
Z = (X - µ) / σ
For X = 410.5 mm:
Z = (410.5 - (6.4 * 64)) / (0.12 * (64))
= (410.5 - 409.6) / 0.015
= 60
Using a standard normal distribution table or calculator, we find:
P(Z > 60) ≈ 1 - P(Z < 60)
≈ 1 - 1
≈ 0
Therefore, the probability that Xtot > 410.5 mm is approximately 0.
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assume that jessie and lester have formed a contract whereby jessie agrees to deliver 10,000 dozen grade a large eggs to be shipped in paper cartons. a shortage of paper makes paper cartons much more expensive, so jessie uses styrofoam cartons and ships the eggs. lester is entitled to cancel the contract based on a material breach of the contract. True or false?
Answers
The statement given by Lester is true, he can terminate the contract as Jessie didn't follow the protocol.
What is Contract?
A contract is an agreement between parties, creating mutual obligations that are enforceable by law. The basic elements required for the agreement to be a legally enforceable contract are: mutual assent, expressed by a valid offer and acceptance; adequate consideration; capacity; and legality.
For example :-A promise by one party to another that they will or will not perform a specific action in the future. Example: I will pay you $3,500 for the purchase of your vehicle. Acceptance . Usually mirrors the terms of the offer—an expression, through words or deeds, that both parties agree to the terms of the contract
So, the answer is true since Lester have the authority to terminate the agreement due to a substantial breach.
Thus, the given statement is true.
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-8.3 + x = -12
I will give brainliest
Answers
Answer:
x = -3.7
Step-by-step explanation:
so in this equation we are trying to find the variable x and to do so we have only have the variables on one side of the equal sign and numbers on the other. SO the equation is:
-8.3 + x = -12
So we are going to only have x on the left side of the equal sign, so we are going to add 8.3 to -8.3 and -12 because what you do to one side you do to the other:
-8.3 + x = -12
+8.3 +8.3
to make the equation look like this:
x = -3.7
Now to check our work we are going to replace where the x variable is in the equation -8.3 + x = -12 with -3.7
-8.3 + (-3.7) = -12
-12 = -12
Hope this helps!!!
24.
What is the slope of a line through (-3, 4) and
(5, 6)?
PLEASE help if you can!!
Answers
Answer:
slope = 2 : 8 or 1:4
Step-by-step explanation:
a(-3, 4)
b(5, 6)
slope = rise / run
slope (6-4, 3+5))
slope = 2 : 8 or 1:4
Answer:
Slope =¼
Step-by-step explanation:
\((-3, 4) \: (5, 6) \\ x _{1} = - 3 , y_1 = 4 \\ x_2 = 5 \\ y_2 = 6\)
\(m = \frac{y_2 - y_1}{x_2 - x_1} \\ m = \frac{6 - 4}{5 - ( - 3)} \\ m = \frac{2}{8} = \frac{1}{4} \)
Pls answer. Will give brainliest...
Answers
Answer:
45 square meters
Step-by-step explanation:
Area of a rectangle= length*width
A=9*5
A=45
A social networking site currently has 40,912 active members per month, but that figure is dropping by 5% with every month that passes. How many active members can the site expect to have in 10 months?
Answers
Answer:
24496
Step-by-step explanation:
40912 * (1-5%) ^10 = 24495.5
becuase they are humans, so round up to 24496
You and your friend are selling magazine subscriptions for a fundraiser. After w weeks, you have sold (7w+6) subscriptions and your friend has sold (9w+2) subscriptions
after 8 weeks your friend has sold how many more than you have
Answers
Which graph shows the solution to the system of linear inequalities?
x – 4y < 4
y < x + 1
On a coordinate plane, 2 straight lines are shown. The first solid line has a positive slope and goes through (0, negative 1) and (4, 0). Everything above the line is shaded. The second dashed line has a positive slope and goes through (negative 1, 0) and (0, 1). Everything below the line is shaded.
On a coordinate plane, 2 straight lines are shown. The first dashed line has a positive slope and goes through (negative 1, 0) and (0, 1). Everything above of the line is shaded. The second solid line has a positive slope and goes through (0, negative 1) and (4, 0). Everything above the line is shaded.
On a coordinate plane, 2 straight lines are shown. The first solid line has a positive slope and goes through (0, negative 1) and (4, 0). Everything above the line is shaded. The second solid line has a positive slope and goes through (negative 1, 0) and (0, 1). Everything below the line is shaded.
On a coordinate plane, 2 straight lines are shown. The first solid line has a positive slope and goes through (0, negative 1) and (4, 0). Everything below the line is shaded. The second dashed line has a positive slope and goes through (negative 1, 0) and (0, 1). Everything below the line is shaded.
Answers
Answer:
SOLUTION: .−5x + 4y = 20. 10x − 8y = −40.
Step-by-step explanation:
First, solve the first equation for y. Then, substitute for y in the second equation. This equation is an identity
solve for x!! helppppp
Answers
180 = 86 + 52 + x + 50
180 = x + 188
X = -8
Hope this is right and helps you out!
The table below shows the value of a particular car over time
Answers
The model that is more appropriate for modelling the data would be an exponential model.
Why is the exponential model better ?An exponential function aptly captures the dynamics of a changing dependent variable (in this scenario, the car's value) at an accelerating or decelerating pace over time. As the years accumulate, the car's value experiences a decrement, showcasing a trend that aligns harmoniously with the principles of exponential decay.
Conversely, a linear function assumes a fixed rate of change, which might not adequately represent the descending trajectory of the car's value across time. Linear functions imply a consistent devaluation year by year, whereas the available information suggests a gradual diminishing of the rate of decrease.
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The question is:
Determine whether a linear or exponential function is more appropriate for modeling this data. Explain your choice.
intersecting lines r, s, and t are shown below. s t 23° r 106° x° what is the value of x ?
Answers
To find the value of x, we need to use the fact that when two lines intersect, the sum of the adjacent angles formed is equal to 180 degrees.
In this case, the angle formed between lines s and t is 23 degrees, and the angle formed between lines r and s is 106 degrees. Let's denote the angle between lines t and r as x.
Using the information given, we can set up the equation:
(106 degrees) + (23 degrees) + x = 180 degrees
Combine the known values:
129 degrees + x = 180 degrees
To isolate x, subtract 129 degrees from both sides of the equation:
x = 180 degrees - 129 degrees
x = 51 degrees
Therefore, the value of x is 51 degrees.
In conclusion, the value of x, the adjacent angles formed between intersecting lines t and r, is 51 degrees.
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Determine whether the distribution represents a probability distribution. X 3 6 0.3 0.4 P(X) Oa. Yes b. No 9 0.3 0.1
Answers
The distribution does not represent a probability distribution. The correct option is b.
A probability distribution should satisfy two main conditions: (1) the sum of the probabilities for all possible outcomes should be equal to 1, and (2) the probabilities for each outcome should be between 0 and 1 (inclusive).
In this distribution, the probabilities for the outcomes are 0.3, 0.4, 0.3, and 0.1 for the values of X as 3, 6, 9, and 0, respectively. However, the sum of these probabilities is 1.1, which violates the first condition of a probability distribution.
Therefore, this distribution does not meet the requirements of a probability distribution and is not a valid probability distribution. The correct answer is option b.
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What is the answer for this question please
Answers
Answer:
74
Step-by-step explanation:
92-18=74
Answer: Barry has 92 so 92 - 18 = Heidi. Heidi has 74
Step-by-step explanation:
i just wanted to make sure my answers are correct could someone tell me if they are or not correct or tell me which ones are wrong?
Answers
14. Is B
16. Is B
correct
Find the derivative of y with respect to t.
y= t(ln 10t)^2
Answers
Derivative of y with respect to t \(y= t(ln 10t)^2\) is y' = 2t·ln 10t + (ln 10t)².
We have, \(y= t(ln 10t)^2\)
Recall that the derivative of u² is \(2u\( · \(\ u'\).
By applying this rule. Differentiating y with respect to t
\(y' = [t(\frac{d}{dt})(ln 10t)^2] + [(ln 10t)^2 (\frac{d}{dt} )(t)]\)
Now, simplifying the above expression by taking care of the derivative of \(ln 10t^2\).
Recall that the derivative of \(ln \ u\) with respect to t is (1/u)·du/dt.
By applying this rule.
\(y' =[t(2ln\ 10t)(\frac{1}{10t} )(10)]+[(ln\ 10t)^2 (1)]\)
\(y' = [2t(ln 10t)] + [(ln 10t)^2]\)
So, the final derivative is, y' = 2t·ln 10t + (ln 10t)².
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What is the area of the region on the xy-plane which is bounded from above by the curvey=e*, from below by y = cos x and on the right by the vertical line X = ? (a) 2 cos(e* - 5) (b) 14.80 (c) 27/3 (d) 22.14 (e) 31.31
Answers
The area of the region bounded by the curves is d) 22.14.
To find the area of the region bounded by the curves y = \(e^x\), y = cos(x), and x = π on the xy-plane, we need to integrate the difference between the upper and lower curves with respect to x over the specified interval.
The upper curve is y = \(e^x\), and the lower curve is y = cos(x). The vertical line x = π bounds the region on the right.
To find the area, we integrate the difference between the upper and lower curves from x = 0 to x = π:
A = ∫[0, π] (\(e^x\) - cos(x)) dx
To evaluate this integral, we can use the fundamental theorem of calculus:
A = [\(e^x\) - sin(x)] evaluated from 0 to π
A = (\(e^\pi\) - sin(π)) - (\(e^0\) - sin(0))
A = (\(e^\pi\) - 0) - (1 - 0)
A = \(e^\pi\) - 1
Calculating the numerical value:
A ≈ 22.14
Therefore, the area of the region bounded by the curves y = \(e^x\), y = cos(x), and x = π on the xy-plane is approximately 22.14.
The correct answer is (d) 22.14.
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Someone please help!
Answers
Answer:
RU is 8
Step-by-step explanation:
In a basketball game, Alana scores twice as many points as Taylor. Taylor scores four points fewer than Nancy, and Nancy scores three
times as many points as Molly. If Molly scores 6 points, how many points did Alana score?
Determine your answer by first determining how many points each other player scored:
1. Nancy scores
2. Taylor sco res
3. Alana scores
points.
points.
points.
Answers
1. Molly scores 6 points.
2. Nancy scores three times as many points as Molly, so Nancy scores 3 * 6 = 18 points.
3. Taylor scores four points fewer than Nancy, so Taylor scores 18 - 4 = 14 points.
4. Alana scores twice as many points as Taylor, so Alana scores 2 * 14 = 28 points.
Therefore, Alana scored 28 points in the basketball game.
A pilot is flying a helicopter at a constant altitude. She decides to make the helicopter rise vertically. It rises 32ft every 4s. After 10s the helicopter is at an altitude of 180ft. The helicopters altitude in feet, y, is a function of the time in seconds, x. How many feet does the helicopter rise each second? Find the rate of change
Answers
The distance covered by helicopter rise each second is 8 feet.
And, the rate of change would be 24.7.
Used the concept of rate of change of equation that states,
Rate of change problems can be approached using the formula,
R = D/T
Or the rate of change equals the distance traveled divided by the time it takes to do so.
Given that,
A pilot is flying a helicopter at a constant altitude.
And, It rises 32ft every 4s. After 10s the helicopter is at an altitude of 180ft.
Let us assume that,
The helicopter's altitude in feet, y, is a function of the time in seconds, x.
Here, It rises 32ft every 4s.
Hence, the distance covered by helicopter rise in each second is,
32 ft / 4
8 feet
And, the rate of change would be,
\(m = \dfrac{(180 - 32)}{(10 - 4)}\)
\(m = \dfrac{148}{6}\)
\(m = 24.67\)
So, the rate of change would be 24.7.
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if a scatter plot displays data that shows a positive correlation, then the correlation coefficient will be closest to what whole number?
Answers
If a scatter plot displays data that shows a positive correlation, then the correlation coefficient will be closest to +1.
The correlation coefficient is a numerical measure of the strength and direction of the linear relationship between two variables. It ranges from -1 to +1, with -1 indicating a perfect negative correlation, +1 indicating a perfect positive correlation, and 0 indicating no correlation.
Since the scatter plot displays data that shows a positive correlation, the correlation coefficient will be positive and closer to +1 than to 0 or -1. The exact value will depend on the strength of the correlation. If the data points are tightly clustered around a straight line, the correlation coefficient will be closer to +1, indicating a strong positive correlation. If the data points are more spread out, the correlation coefficient will be smaller, but still positive, indicating a weaker positive correlation.
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3. Triangle RST has angle measures as shown. S 5(x+3) 25° 62 R (a) What is the value of x? Show your work. (b) What is the measure of angle S? Show your work.
Answers
Answer:
X=2
Step-by-step explanation:
12x + 5y = -24 13x - 5y = 14 Linear Equations By Elimination
Answers
Let,
\(\begin{gathered} 12x+5y=-24\ldots(1) \\ 13x-5y=14\ldots(2) \end{gathered}\)Perform the operation (1)+(2),
\(\begin{gathered} 12x+5y+(13x-5y)=-24+(14) \\ 12x+13x+5y-5y=-10 \\ 25x+0y=-10 \\ 25x=-10 \\ x=\frac{-10}{25} \\ x=\frac{-2}{5} \end{gathered}\)Substitute the value of x=-2/5 in the expression (1).
\(\begin{gathered} 12\times\frac{-2}{5}+5y=-24 \\ 5y=-24+\frac{24}{5} \\ 5y=\frac{-96}{5} \\ y=\frac{-96}{5\times5} \\ y=\frac{-96}{25} \end{gathered}\)Thus, the value of x is -2/5 and value of y is -96/25.
Sarah is working as a truck driver. She gets paid $100 everyday and then $22 per hr driving. How many hours does sarah have to work to make $276 in one day
Answers
Answer:8
Step-by-step explanation: she makes $100 a day so you would subtract that from the total (276) then you would divide the remainder (176) by the amount she makes an hour (22) then you would end up with 8 hours
Answer:
8 hours
Step-by-step explanation:
For $22=1 hour
For $1=1/22 hours
For $176=176/22 hours=8 hours
And she gets also $100 extra
So for $276 she works 8 hours.
What is inverse of Tangent called?.
Answers
Arctan or tan-1 are used to denote the inverse of Tangent.
The ratio of the perpendicular of the triangle and the base of the triangle with respect to the required angle is know as the tangent of the angle. Specifically, tan = (opposite side) / (adjacent side). The inverse tan formula is thus = tan-1[(opposite side) / (adjacent side)] according to the definition of inverse tan.
The reciprocal of the tangent is the cotangent. It is basically just the reciprocal of the tangent, it means that it can be written as the ratio of the base to the perpendicular.
Arccosine is another name for inverse cosine. It is the cos function's opposite. Also known as "arccos," occasionally. When two sides of a right triangle's length are known, it is used to measure the unknown angle.
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Work out the value of 8^2+4^3, 5^3-7^2
Answers
Answer:
302
Step-by-step explanation:
what is it called when you describe the steps that are necessary for finding a solution to a problem in programming?
Answers
The process of describing the steps necessary for finding a solution to a problem in programming is commonly referred to as algorithm design.
Algorithm design is an essential aspect of programming, as it allows programmers to devise a systematic approach to problem-solving. When faced with a programming problem, the first step is to analyze and understand the problem requirements thoroughly.
Once the problem is understood, the next step is to design an algorithm that outlines the sequence of steps needed to solve the problem.
In algorithm design, programmers typically consider factors such as efficiency, correctness, and maintainability. They aim to devise algorithms that produce accurate results, optimize resource usage, and are easy to understand and maintain.
The process involves selecting appropriate data structures, determining control flow, and defining the specific operations or computations required at each step.
By describing the steps in an algorithm, programmers can effectively communicate their approach to solving a problem and provide a roadmap for implementing the solution in code.
Well-designed algorithms help streamline the programming process, improve code quality, and facilitate the development of reliable and efficient software systems.
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What is the value of 5/6+(-4/9)-(-2)
Answers
China and Germany specialize in the production of silk and automobiles respectively. They are considered the best at their specializations. Assume that China chooses not to trade silk with Germany in exchange for automobiles. Which perspective is China using in regards to not trading to another country which provides a specialization they do not have? O absolute advantage O comparative advantage O new trade theory O porter's model
Answers
both countries can benefit from trade by specializing in the goods and services that they are relatively more efficient at producing and exchanging them with each other.
Explain about comparative advantage.China is using the comparative advantage perspective in regards to not trading silk with Germany in exchange for automobiles. According to the theory of comparative advantage, a country should specialize in producing and exporting the goods or services that they can produce more efficiently or at a lower opportunity cost compared to other goods and services.
According to question;In this case, China has a comparative advantage in producing silk and a comparative disadvantage in producing automobiles compared to Germany, which has a comparative advantage in producing automobiles and a comparative disadvantage in producing silk.
Hence, both countries can benefit from trade by specializing in the goods and services that they are relatively more efficient at producing and exchanging them with each other.
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Select the correct answer. what is the value of the third quartile of the data set represented by this box plot? a box plot with lower quartile, median and upper quartile values as 21, 26, and 29, respectively. the whiskers on both the ends end at 19 (minimum) and 33 (maximum). a. 19 b. 21 c. 26 d. 29
Answers
Answer:
D. 29
Step-by-step explanation:
just did the test and got it correct. Edmentum, Plato.
In the figure below, find the exact value of y.
Answers
9514 1404 393
Answer:
2
Step-by-step explanation:
y is the geometric mean of the segment lengths.
y = √(4·1)
y = 2
_____
You can also get there by considering the similarity of the triangles:
short side / long side = y/4 = 1/y
y^2 = 4 . . . . . . . multiply by 4y\
y = √4 = 2 . . . . take the square root