The linear model representing the information is y = 600x + 1500.
To produce 12 solar heaters it cost $8,700.
The domain of the linear model is [1, 80].
What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
10 solar heaters = $7500
20 solar heaters = $13,500
The linear model can be in the form of y = mx + c
m = (13,500 - 7500)/(20 - 10)
m = 6000/10
m = 600
Now,
(10, 7500) = (x, y)
7500 = 600 x 10 + c
c = 7500 - 6000
c = 1500
Now,
The linear model is y = 600x + 1500.
Where y is the cost of x solar heaters.
Now,
x = 12,
y = 600 x 12 + 1500
y = 7200 + 1500
y = 8700
Now,
y ≤ 50,000
We see that,
x = 81
y = 600 x 81 + 1500 = 48600 + 1500 = 50,100
x = 80
y = 600 x 80 + 1500 = 48000 + 1500 = 49,500
The domain is from x = 1 to x = 80.
Thus,
The linear model is y = 600x + 1500.
$8,700 is the cost to produce 12 solar heaters.
The domain is [1, 80].
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what is the word used to describe a vector that always points toward the center of a circular path?
"Centripetal is the word used to describe a vector that always points toward the centre of a circular path."
The centripetal acceleration vector is an acceleration in the radial direction that is directed towards the centre of the circular line of motion. It runs perpendicular to the linear motion, or v.
The direction of the velocity shift for a ball travelling around a curve is in the direction of the curve's centre. Centripetal acceleration is the acceleration that is directed towards the centre of a curved or circular route.
Any force that changes the path of motion towards the centre of a circular motion is known as a centripetal force. The portion of the force that produces the centripetal force is the part that is perpendicular to the velocity.
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Each day that a library book is kept past its due date, a $0.30 fee is charged at midnight. Which ordered pair is a
viable solution if x represents the number of days that a library book is late and y represents the total fee?
O(-3,-0.90)
O(-2.5, -0.75)
(4.5, 1.35)
57:43
O (8,2.40)
Answer:(8,2.4)
Step-by-step explanation:
Lana put an end table with a triangular top next to her sofa. The length of the base of the top is 26 inches, and the height is 16 inches.
What is the area of the top of the table?
Answer:
208
Step-by-step explanation:
Took the quiz and got 100%
Lin is comparing the graph of two functions g and f. The function g
is given by g(x) = f(x - 2). Lin thinks the graph of g will be the same as
the graph of f, translated to the left by 2. Do you agree with Lin? Explain
your reasoning.
Lin is correct in thinking that the graph of g will be the same as the graph of f, translated to the left by 2 units.
The function g(x) = f(x - 2) is obtained by shifting the graph of f to the right by 2 units, which means that the point (a, f(a)) on the graph of f is mapped to the point (a - 2, f(a)) on the graph of g. Therefore, the shape of the graph of f remains the same, but its position is shifted to the right by 2 units to obtain the graph of g.
This can be seen by considering the effect of the transformation on the key features of the graph of f, such as its intercepts, maxima, and minima. For example, if f has a maximum at x = c, then g will have a maximum at x = c + 2. Similarly, if f intersects the x-axis at x = d, then g will intersect the x-axis at x = d + 2.
Therefore, Lin's reasoning is correct, and the graph of g will be the same as the graph of f, translated to the left by 2 units.
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what is foci of ellipse calculator?
An ellipse's form is determined by two locations inside the ellipse known as its foci.
The lengths of the main and minor axes of an ellipse may be used to calculate its foci.
The foci of an ellipse may be calculated using a variety of online calculators.
These calculators normally ask the user to enter the main and minor ellipse axes' lengths before calculating the foci's coordinates. Depending on the calculator in question, some may additionally ask for more details like the ellipse's eccentricity or center of rotation.
Understanding an ellipse's shape and characteristics requires knowing its foci since they are what characterize an ellipse.
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HELPPPPPP PLEASEeeeeeeeeeeeeee
Answer:
x-5 that is the answer na
50 POINTS SOLVE FAST
Answer:
u get it done?
Step-by-step explanation:
what is 106348 + 674? so hard!
Answer:
Its 107,002
Step-by-step explanation:
Answer:
107022
Step-by-step explanation:
yeah totally... it was really hard (sarcasm)
Brainliest??? Plz!!!
investment risk investors not only desire a high return on their money, but they would also like the rate of return to be stable from year to year. an investment manager invests with the goal of reducing volatility (year-to-year fluctuations in the rate of return). the following data represent the rate of return (in percent) for his mutual fund for the past 12 years. 13.8 15.9 10.0 12.4 11.3 6.6 9.6 12.4 10.3 8.7 14.9 6.7 (a) verify that the data are normally distributed by constructing a normal probability plot. (b) determine the sample standard deviation. (c) construct a 95% confidence interval for the population standard deviation of the rate of return. (d) the investment manager wants to have a population standard deviation for the rate of return below 6%. does the confidence interval validate this desire?
The normal probability plot suggests the data is approximately normally distributed. The sample standard deviation of given data is 3.13. The 95% confidence interval for the population standard deviation is (1.85, 6.28). The investment manager's desire for a population standard deviation below 6% is validated by the confidence interval.
To construct a normal probability plot, we first need to sort the data in ascending order:
6.6, 6.7, 8.7, 9.6, 10.0, 10.3, 11.3, 12.4, 12.4, 13.8, 14.9, 15.9
Then we can plot the ordered data against the expected values of a normal distribution with the same mean and standard deviation as the sample. The plot shows that the points follow a roughly straight line, which suggests that the data is roughly normally distributed.
To determine the sample standard deviation, we can use the formula:
s = sqrt[(∑(xi - x)²) / (n - 1)]
where xi is the rate of return for each year, x is the sample mean, and n is the sample size.
Sample mean:
x = (13.8 + 15.9 + 10.0 + 12.4 + 11.3 + 6.6 + 9.6 + 12.4 + 10.3 + 8.7 + 14.9 + 6.7) / 12 = 11.433
Sample standard deviation:
s = sqrt[((13.8 - 11.433)² + (15.9 - 11.433)² + ... + (6.7 - 11.433)²) / (12 - 1)]
= 3.059
Therefore, the sample standard deviation is 3.059.
To construct a 95% confidence interval for the population standard deviation of the rate of return, we can use the formula:
CI = [(n - 1) * s² / χ²(α/2, n-1), (n - 1) * s² / χ²(1-α/2, n-1)]
where n is the sample size, s is the sample standard deviation, χ² is the chi-square distribution, and α is the level of significance (1 - confidence level).
For a 95% confidence level and 11 degrees of freedom (n - 1), α = 0.05/2 = 0.025. From the chi-square distribution table with 11 degrees of freedom, we can find the critical values as follows:
χ²(0.025, 11) = 2.201 and χ²(0.975, 11) = 23.337
Plugging in the values, we get:
CI = [(12 - 1) * 3.059² / 23.337, (12 - 1) * 3.059² / 2.201]
= [1.946, 26.557]
Therefore, we can say with 95% confidence that the population standard deviation of the rate of return is between 1.946 and 26.557.
The investment manager wants to have a population standard deviation for the rate of return below 6%. The confidence interval (1.946, 26.557) does not validate this desire, as it includes values above 6%. Therefore, based on the sample data, the investment manager cannot be confident that the population standard deviation is below 6%.
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Let B and C be nonnegative real numbers and A a complex number. Suppose that 0B-2 Re(A) + 12C for all complex numbers λ. Conclude that |A| ^ 2 <= BC (Hint: If C = 0 show that A = 0 If C0, then choose λ = A/C.)
Let B and C be non-negative real numbers, and A is a complex number, and it is given that 0 < B - 2 Re(A) + 12C for all complex numbers λ. To conclude that |A|² ≤ BC. If C = 0, then 0 < B - 2 Re(A). This can only be true if A = 0 (since Re(A) is a real number and B is positive).
So, in this case, we have A = 0 and C = 0. Therefore, the inequality is always true.Now, let's consider the case where C > 0. Then, choose λ = A/C. Since λ is a complex number, we have 0 < B - 2 Re(A/C) + 12C ⇒ 0 < B - 2 Re(A)/C + 12C. Simplifying this inequality by multiplying both sides by C, we get0 < BC - 2C Re(A) + 12C².
Dividing both sides by 4C², we get0 < (BC/4C²) - (Re(A)/C) + 3. Hence, we have(BC/4C²) > (Re(A)/C) - 3 = |Re(A)/C - 3| .(Note that the absolute value of a complex number is always a real number.)
Now, since |z| ≤ |Re(z)| + |Im(z)| for any complex number z, we have|A/C| = |λ| ≤ |Re(A/C)| + |Im(A/C)| ≤ |Re(A)/C| + |Im(A)/C| = |Re(A)/C| + |A|/(C|) .
Therefore, |Re(A)/C| ≥ |λ| - |A|/(C|) = |A/C| - |A|/(C|) .But, |A/C| = √(Re(A)/C)² + (Im(A)/C)² by the modulus formula.
Therefore, we have |Re(A)/C| ≥ √(Re(A)/C)² - |A|/(C|).
Squaring both sides, we get(Re(A)/C)² ≥ (Re(A)/C)² - |A|²/(C²|).
Therefore, we have proved that |A|² ≤ BC when 0 < B - 2 Re(A) + 12C for all complex numbers λ.
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Suppose there are two types of individuals: healthy and unhealthy individuals. Unhealthy individuals have a 5% chance of experiencing a heart attack each year, while health individuals have only a 1% chance. There are an equal number of healthy and unhealthy people, and the cost of a heart attack is $50,000. a) Suppose an insurance company knows each individual's type with certainty. What is the actuarially fair premium for each type? b) Now suppose there is asymmetric information so that the insurance company does not know the individual's type. Would the company continue to sell insurance? Why or why not? What is the term for this type of asymmetric information problem?
This type of asymmetric information problem is known as adverse selection, where individuals with higher risks are more likely to purchase insurance. To mitigate adverse selection, the insurance company may need to implement risk assessment measures or gather more information about the individuals to accurately price the premiums.
a) The actuarially fair premium for each type can be calculated by considering the expected cost of a heart attack for each type of individual.
For unhealthy individuals, the probability of experiencing a heart attack is 5%. So, the expected cost for an unhealthy individual would be 5% of $50,000, which is $2,500.
For healthy individuals, the probability of experiencing a heart attack is 1%. Therefore, the expected cost for a healthy individual would be 1% of $50,000, which is $500.
Since there are an equal number of healthy and unhealthy individuals, the actuarially fair premium for each type would be the expected cost of a heart attack for that type. Hence, the actuarially fair premium for unhealthy individuals is $2,500, and for healthy individuals, it is $500.
b) If there is asymmetric information, where the insurance company does not know the individual's type, the company may not continue to sell insurance. This is because individuals who are aware that they are unhealthy have a higher probability of experiencing a heart attack, making them more likely to seek insurance. As a result, the insurance pool would be filled with a higher proportion of unhealthy individuals, leading to higher costs for the insurance company.
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a line with a slope of 1 passes through the point (5,10). what is the equation in this slope-intercept form?
Answer:
y=x+5
Step-by-step explanation:
So first you need to plug everything into the point-slope formula which is
y-y1=m(x-x1)
m being the slope and y1 and x1 being the point (5,10)
So once you plug it in it should look like this: y-10=1(x-5)
Now you solve it
First you need to distribute 1 in 1(x-5) which is (x-5)
Now you have y-10=x-5
Then you add 10 to both sides which is y=x+5
Your answer is y=x+5
Please help!!
Find the value of x!
Answer:
x = \(\frac{16}{3}\)
Step-by-step explanation:
Since the triangles are similar then the corresponding sides are congruent.
EF and BC are corresponding sides , then
8x - 3 = 5x + 13 ( subtract 5x from both sides )
3x - 3 = 13 ( add 3 to both sides )
3x = 16 ( divide both sides by 3 )
x = \(\frac{16}{3}\)
Jose earns $3680 per month, of which 22% is taken out of his paycheck for federal and state income taxes and other required deductions, Last month he spent $775 for rent and $86.12 for clothing. What percent of his take
home pay did he spend on rent and clothing combined?
Answer:
30%Step-by-step explanation:
Step one:
monthly earnings= $3680
22% of the earnings is
=22/100*3680
=0.22*3680
=$809.6
Jose's take home will be
3680-809.6
=$2870.4
Step two:
Required
percentage spent on rent and clothing
but the total cost of rent and clothing is
=775+86.12
=$861.12
percentage of rent and cloth is
=(861.12/2870.4)*100
=0.3*100
=30%
The percentage is 30% of the take home
Brandee makes an hourly wage. In the last pay period, she earned $800 for regular hours and $240 for overtime hours. Her overtime rate of pay is 50% more than her regular rate of pay "r". Write and simplify an expression in terms of "r" that represents the number of hours "h" Brandee worked in the pay period. Show your work.
Step-by-step explanation:
Overtime rate= r+50%= 1.5r
Regular hours= 800/r
Overtime hours= 240/1.5r
Total hours worked
h=800/r+240/1.5rh= 800/r+160/rh=960/rr=960/hSolve the inequality 4(k − 5) + 12k ≥ −4.
Solution for the given Inequality 4(k − 5) + 12k ≥ − 4 is 1
What is Inequality:Inequality simply means that two things aren't equal. One of the items could be inferior to, superior to, greater than, or equivalent to the other things. We often use algebraic operations like addition, subtraction, multiplication, and division to solve linear simple inequalities.
Here given Inequality is 4(k − 5) + 12k ≥ −4
We can simply solve the above inequality as given below
=> 4(k − 5) + 12k ≥ −4
Multiply the terms and remove the bracket
=> 4k − 20 + 12k ≥ −4
Add 'k' terms
=> 16k − 20 ≥ −4
Add 20 on both sides
=> 16k − 20 + 20 ≥ −4 +20
=> 16k ≥ 16
Divide by 16 into both sides
=> 16k/16 ≥ 16/16
=> k ≥ 1
Therefore,
Solution for the given Inequality 4(k − 5) + 12k ≥ −4 is 1
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let $p$ be a point inside rectangle $abcd$ such that $pa = 1$, $pb = 7$, and $pc = 8$. find $pd$.
To find the length of \(PD\) in the given rectangle \(ABCD\), we can use the Pythagorean theorem.
The length of \(PD\) is \(\sqrt{} 79\)units.
Given that \(PA = 1\), \(PB = 7\), and \(PC = 8\), we need to find \(PD\).
Since \(P\) is inside the rectangle, we can consider the right-angled triangles \(PAB\), \(PBC\), and \(PCD\).
Using the Pythagorean theorem, we have:
In triangle \(PAB\):
\(PA^2 + AB^2 = PB^2\)
In triangle \(PBC\):
\(PB^2 + BC^2 = PC^2\)
In triangle \(PCD\):
\(PC^2 + CD^2 = PD^2\)
Since the rectangle has equal side lengths, \(AB = BC = CD\), so we can denote them as \(s\).
Now let's substitute the given lengths:
\(1^2 + s^2 = 7^2\) (Equation 1)
\(7^2 + s^2 = 8^2\) (Equation 2)
\(8^2 + s^2 = PD^2\) (Equation 3)
Simplifying Equations 1 and 2, we have:
\(s^2 = 7^2 - 1^2\) (Equation 4)
\(s^2 = 8^2 - 7^2\) (Equation 5)
Solving Equations 4 and 5:
\(s^2 = 48\)
\(s^2 = 15\)
From Equation 5, we find that \(s^2 = 15\), so \(s = \sqrt{15}\).
Substituting this value into Equation 3, we can solve for \(PD\):
\(8^2 + (\sqrt{15})^2 = PD^2\)
\(64 + 15 = PD^2\)
\(79 = PD^2\)
Taking the square root of both sides, we find:
\(PD = \sqrt{79}\)
Therefore, the length of \(PD\) is \(\sqrt{79}\) units.
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A 15 ft tree casts a 9 foot shadow on the ground. What is the angle of elevation formed by the tree’s shadow and the sun? (Round to the nearest hundredth)
Answer:
59.04
Step-by-step explanation:
If you were to make a right triangle, 15 would be the altitude (height), and 9 would be the base. You need the angle of elevation which is going the angle of the hypotenuse going upwards. (Bottom Left/Right Corner.) From that angle you need to solve for arctan (Used for solving the measure of angle.) Simply plug into your calculator arctan(15/9) to get the answer.
A pet store has 80 geckos and anole lizards altogether.
The ratio of geckos to anole lizards is 3:5.
How many geckos does the pet store have?
Answer:
The pet store has 30
Step-by-step explanation:
okay the ratio is 3:5 if you add them you get 8.
8 to get to 80 gets multiplied by 10.
so 3: 5 x 10 equals 30: 50
the 30 is geckos the 50 is lizards
A trapezoid has an area of 24 square feet. The bases are 5
feet and 7 feet. Write an equation to determine the height of of
the trapezoid. Then determine the height.
\(\textit{area of a trapezoid}\\\\ A=\cfrac{h(a+b)}{2}~~ \begin{cases} h~~=height\\ a,b=\stackrel{parallel~sides}{bases~\hfill }\\[-0.5em] \hrulefill\\ a=5\\ b=7\\ A=24 \end{cases}\implies 24=\cfrac{h(5+7)}{2} \\\\\\ 24=\cfrac{h(12)}{2}\implies 24=6h\implies \cfrac{24}{6}=h\implies 4=h\)
the measure of the supplement of an angle is 39° more then the angle. find the measure of the angle and it’s supplement.
Step-by-step explanation:
s = a+39
s+a = 180
a+39+a = 180
2a = 180-39
2a = 141
the angle = 70.5°
the supplement = 109.5°
the angles of a triangle are in the ratio 3:5:4 calculate the size of each angle
The 3 angles in a triangle always add up to be 180.
Call the smallest angle as x
-> The 3 angles are x, 4/3x and 5/3x
-> 4x = 180
-> 45
So, the sizes of the 3 angles are 45, 60 and 75.
Can anyone help me on question 2?
Answer:
yes
Step-by-step explanation:
-3x - 7y =2
Substitute the point into the equation
-3(4) -7(-2) =2
-12 +14=2
2=2
This is true so the point is a solution to the equation
Answer:
Sure, I can help you with question 2.
Step-by-step explanation:
Original equation:
-3x-7y=2
Substitute x and y values
-3(4)-7(-2)=2
-12+14=2
2=2
This is true, thus (4, -2) is a solution to the given equation.
Lynn and Trey each stood at a different location on a field and threw a ball. Lynn threw to the 24-yard line and Trey threw to the 19-yard line. Who threw farther, and how do you know?
Lynn threw a ball farther because 24 yard line > 19 yard line
In this question we have been given Lynn and Trey each stood at a different location on a field and threw a ball.
Lynn threw to the 24-yard line and Trey threw to the 19-yard line.
We need to determine who threw a ball farther.
As we know 24 yards > 19 yards
So, Lynn threw a ball farther
Therefore, Lynn threw a ball farther because 24 yard line > 19 yard line
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88 is increased by 25 what is the new value but with expination
In response to the question, we may say that Hence, when 88 is expression multiplied by 25, the new result is 113.
what is expression ?An expression in mathematics is a collection of representations, numbers, and conglomerates that mimic a statistical correlation or regularity. A real number, a mutable, or a mix of the two can be used as an expression. Mathematical operators include addition, subtraction, fast spread, division, and exponentiation. Expressions are often used in arithmetic, mathematics, and form. They are employed in the depiction of mathematical formulas, the solving of equations, and the simplification of mathematical relationships.
To discover the new value of 88 after it has been multiplied by 25, just add 25 to 88:
88 + 25 = 113 is the new value.
Hence, when 88 is multiplied by 25, the new result is 113.
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For each type of effect listedâmain effects, two-way interactions, and three-way interactionsâidentify the maximum number of possible effects that could be tested in a 2 Ã 2 Ã 2 factorial design. - 3 main effects- 1 three- way interaction- 3 two-way interactions
The maximum number of possible effects that could be tested in a 2x2x2 factorial design with 3 main effects, 3 two-way interactions, and 1 three-way interaction is 7.
In a 2 x 2 x 2 factorial design, we can test the following maximum number of possible effects:
Main effects:
There are 3 main effects in this design, one for each factor (A, B, and C). You would analyze the effect of each factor independently on the outcome variable.
Two-way interactions:
There are 3 possible two-way interactions that can be tested in this design: AxB, AxC, and BxC.
These interactions examine the combined effects of two factors on the outcome variable.
Three-way interactions:
There is 1 possible three-way interaction that can be tested in this design: AxBxC.
This interaction examines the combined effect of all three factors (A, B, and C) on the outcome variable.
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Write an inequality to represent the graph
Answer:
B
Using gradient of two points and equation of a straight line graph.
-7/8 is at most the difference of twice a number m and 5/4
Answer:
Step-by-step explanation:
The given inequality can be written as 2m - 5/4 ≤ -7/8.
An inequality -7/8 is at most the difference of twice a number m and 5/4 which is 2m - 5/4 ≤ -7/8.
Difference of twice a number 'm' and 5/4 is 2m - 5/4 and this is at most -7/8 means less than or equal to.
∴ The given statement can be written as 2m - 5/4 ≤ -7/8
Answer:
2m - 5/4 ≤ -7/8
Step-by-step explanation:
hope this helps
In the analysis of variance procedure (ANOVA), factor refers to _____.
a. the critical value of F b. the independent variable c. the dependent variable d. different levels of a treatment
In the analysis of variance procedure (ANOVA), "factor" refers to the independent variable, which is manipulated in order to observe its effect on the dependent variable.
In the analysis of variance procedure (ANOVA), factor refers to:
b. the independent variable
In ANOVA, a factor is an independent variable that is manipulated or controlled to investigate its effect on the dependent variable. Different levels of a factor represent the variations in the independent variable being tested. The different levels of a treatment are often created by manipulating the factor.
In contrast, independent variables are not considered dependent on other variables in various experiments. [a] In this sense, some of the independent variables are time, area, density, size, flows, and some results before the affinity analysis (such as population size) to predict future outcomes (dependent variables).
In both cases it is always a variable whose variable is examined through a different input, statistically also called a regressor. Any variable in an experiment that can be assigned a value without assigning a value to another variable is called an independent variable.
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Which of the following domains are closed and which are bounded?
(a) {(x,y)∈R2:x2+y2≤1}
(b) {(x,y)∈R2:x2+y2<1}
(c) {(x,y)∈R2:x≥0}
(d) {(x,y)∈R2:x>0,y>0}
(e) {(x,y)∈R2:1≤x≤4,5≤y≤10}
(f) {(x,y)∈R2:x>0,x2+y2≤10}
(a) The domain closed and bounded.
(b) The domain bounded.
(c) The domain closed.
(d) The domain bounded.
(e) The domain closed and bounded.
(f) The domain closed and bounded.
In this question, we have been given some domains.
We need to check which domains are closed and which are bounded.
A domain of function is said to be closed if the region R contains all boundary points.
A bounded domain is nothing but a domain which is a bounded set.
(a) {(x,y)∈R2:x^2+y^2≤1}
The domain of x^2+y^2≤1 contains set of all points (x, y) ∈R2
so, the domain closed and bounded.
(b) {(x,y)∈R2:x2+y2<1}
The domain of x^2+y^2 < 1 contains set of all points (x, y) ∈R2
so, the domain is bounded.
(c) {(x,y)∈R2: x ≥ 0}
The domain of x ≥ 0 is R2 - {x < 0}
So, the domain is closed.
(d) {(x, y) ∈ R2 : x > 0,y > 0}
The domain is R2 - {(x, y) ≥ 0}
So, the domain is bounded.
(e) {(x, y) ∈ R2 : 1 ≤ x ≤ 4, 5 ≤ y ≤ 10}
The domain is closed and bounded.
(f) {(x,y)∈R2:x>0,x^2+y^2≤10}
The domain is closed and bounded.
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