The domain of the area function is 0 < x ≤ 300, and the range is A > 0. The total area enclosed by a rectangular fence, given a fixed amount of fencing, can be expressed as a function of the length of one side.
The domain and range of this area function depend on the constraints imposed by the amount of fencing available.
a) To express the total area enclosed as a function of the length x, we need to consider that the perimeter of a rectangle is twice the sum of its length and width. Since the farmer has 600m of fencing, we can write the equation:
2x + 2y = 600
Solving for y, we can express it in terms of x:
y = (600 - 2x) / 2
The area of the rectangle is given by the product of its length and width:
A = x * y = x * (600 - 2x) / 2
b) The domain of the area function is determined by the values of x that satisfy the constraints of the problem. Since x represents the length of one side of the rectangle, it must be positive (x > 0). Additionally, the sum of the lengths of all four sides must be less than or equal to the available fencing, which gives us the constraint: 2x + 2y ≤ 600.
The range of the area function represents the possible areas of the enclosed rectangle. Since both x and y are positive, the range is also positive.
Therefore, the domain of the area function is 0 < x ≤ 300, and the range is A > 0.
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The U.S.A. Olympic Synchronized Swimming Team is designing a routine for their upcoming competition. From the center of the pool, they moved 2 feet to the right and 4 feet up to create the center of their formation (Point C). From the center of their formation, they then formed a circle that goes through a point 3 feet to the left and 4 feet up (Point D). What is the equation of the circle?
Answer:
The equation of the circle is;
(x - 2)² + (y - 4)² = 5²
Step-by-step explanation:
We note that the general equation of a circle is given as follows;
(x - h)² + (y - k)² = r²
Where;
(h, k) = The coordinates of the center of the circle
r = The radius of the circle
The given parameters are;
The location of the center of the pool to the center of their formation = 2 feet to the right and 4 feet up from the center of the pool
The point through which the circle which they form goes through = A point 3 feet to the left and 4 feet up from the center of their formation
Taking the center of the pool as the origin of the coordinate plane system, we have;
The coordinate of the center of the circle = The coordinate of their motion from the center of the circle
∴ The coordinate of the center of the circle = (2, 4)
∴ (h, k) = (2, 4)
h = 2, k = 4
The coordinate of the point through which the circle passes = (2 - 3, 4 + 4) = (-1, 8)
∴ The length of the radius, 'r', can be found as, r = √((-3)² + 4²) = 5 or r = √((-1 - 2)² + (8 - 4)²) = 5
r = 5
The equation of the circle is therefore presented by substituting the values of 'h', 'k', and 'r', as follows;
(x - 2)² + (y - 4)² = 5².
Let p, q, and r be the propositions You get an A on the final exam. You do every exercise in this book. You get an A in this class. p 9: r: (3 pts) Express as an English sentence: q-p b) (p) Express as an English sentence: ar - (-p A-q) Pe 2 c) (4 pts) Write the proposition below using the propositions p, q or r as well as logical connectors (including negation): "To get an A in this class or get an A on the final exam, you need to do every exercise in the book." 7. (pt) Use truth table to determine whether [-p Apv q)] →q is a tautology. (you may not need to use all the rows and columns available below.) 8. (4 pts) Use truth table to determine whether [(pv q) Apr)^(q→r)] →r (you may not need to use all the rows and columns available below.) is a tautology.
q - p can be expressed as "If you do every exercise in this book, then you get an A on the final exam."
¬(p ∨ ¬q) can be expressed as "You need to do every exercise in this book and not get an A on the final exam."
The proposition "To get an A in this class or get an A on the final exam, you need to do every exercise in the book" can be written as "(r ∨ p) → q."
q - p: This proposition states that if you do every exercise in this book (q), then you get an A on the final exam (p).
¬(p ∨ ¬q): This proposition states that you need to do every exercise in this book (q) and not get an A on the final exam (¬p).
"(r ∨ p) → q": This proposition expresses that to get an A in this class (r) or get an A on the final exam (p), you need to do every exercise in the book (q). It is a conditional statement, where the antecedent is (r ∨ p) and the consequent is q.
For the truth table analysis:
[-p ∨ (p ∧ ¬q)] → q: The truth table should be constructed using the propositions p, q, and r, along with logical connectors. However, the given proposition doesn't involve the proposition r, so it cannot be analyzed using the truth table.
[(p ∨ q) ∧ r) ∧ (q → r)] → r: The truth table should be constructed using the propositions p, q, and r, along with logical connectors. However, the given proposition doesn't involve the proposition p, so it cannot be analyzed using the truth table.
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Joseph's front porch is rectangular. The length is 8 feet more than the width. The
perimeter of the porch is 52 feet. What is the width of the porch?
A. 9 feet
B. 14 feet
C. 17 feet
D. 22 feet
whats the answer to this?
Answer:
x=6
Step-by-step explanation:
Can someone please respond to this
Answer:
that's easy, use the 6969 equation, with a some 420's and that will do it
Which of the following number lines best represents the value, 144/2
Answer:
C
Step-by-step explanation:
sqrt of 144 is 12
then 12 divided by 2 is 5
C has the point of 6
A sprinkler waters a circular area. The sprinkler sprays 30 gallons of water per minute.
Select as few quadrants as possible that would allow you to create a graph of the total number of gallons of water,
y, sprayed by the sprinkler after x minutes.
Quadrant 1
Quadrant 2
Quadrant 3
Quadrant 4
Answer:
Quadrant 1
Step-by-step explanation:
The number of gallons of water sprayed after x minutes would never be negative, nor would time be negative, so the first quadrant would be all that you need
If Lin runs 21 laps at the same rate, how long does it take her?
minutes
What is the value of f(x) = 4x -9
Answer:
i believe its ()=4−9
Step-by-step explanation:
Answer:
f=4x-9
Step-by-step explanation:
f(x) = 4x-9
f(x)= 4x-9
x x
f=4x-9
How do you find the radius of a circle?
Answer:
Divide the diameter by two
example if the diameter is 25 you divide 25 by 2 to get 12.5 as your radius .
A map has a scale of 1 inch : 40 miles. Use the given map distance to find the actual distance.
1.) 12 inches
2.) 1 foot
Answer:
480 miles
Step-by-step explanation:
If one inch equals 40 miles, then 12 times that would be 4800 miles.
1 Inch 12 Inches
---------- = ------------------
40 Miles 480 Miles.
Leo flips a paper cup 50 times and records how the cup landed each time. The table below shows the results.
RESULTS OF FLIPPING PAPER CUP
Outcome Right-side UP Upside Down On its Side
Frequency
10
18
22
Based on the results, how many times can he expect the cup to land on its side if it is flipped 1,000 times?
333
440
550
786
N
Previous
Answer:
440
Step-by-step explanation:
i did the test already
What method did you use? Why? Solve. for x: 47° 13
Answer:
Step-by-step explanation:
Givens
You have the hypotenuse: 13
You seek the adjacent side: x
You have the angle enclosing the 2: 47 degrees.
The relationship is the Cosine
Solution
Cos(47) = opposite / hypotenuse
Cos(47) = 0.6820 From your calculator
Cos(47) = x / 13 Multiply both sides by 13
13*cos(47) = x
x=8.866
LOOK RIGHT HERE! HELP FASSST EMERGENCY! Don't go past go to this question right here and no Decimal answers plz. Thanks the answer is not 144 BTW. Thank you.
Answer: 140cm^3
Step-by-step explanation:
8-2(4×3-5)
does this equal -4?
Answer:
-6
Step-by-step explanation:
Answer:
No -6
Step-by-step explanation:
The population of a city and 2005 was 18,000. By 2010, the cities population has grown to 32,800. It’s a population grows flow a linear model, what is the projected population for 2015?
Answer:
47,600
Step-by-step explanation:
The rate is (32,800 - 18,000) = 14,800 per 5 years
therefore :
in 2015 = 2010 + 5 years
the pop. will be :
32,800 + 14,800 = 47,600
The answer is 47,600.
Hope this helped :)
Consider the following argument by analogy.
Some doctors recommend that people over the age of 40 should get a physical every year. As one physician argued, "People take their car in for servicing every few months without complaint. Why shouldn’t they take similar care of their bodies?" [U.S. News & World Report, Aug. 11, 1986]
Analyze and evaluate this argument by doing the following: 1) Identify the two things being compared (A and B) and the property P attributed to B in the conclusion. 2) Identify the (unstated) properties (S) that are supposed to make A and B similar. 3) Analyze the argument into its inductive and deductive elements. The deductive step with be a valid syllogism with a universal major premise. 4) Evaluate the inductive generalization in the inductive step: a) Consider its initial plausibility given our other knowledge; b) Look for additional positive instances besides the one stated; c) Look for counterexamples.
The argument draws an analogy between car servicing and regular physicals for people over 40, highlighting the need for preventive care and maintenance. The deductive step is a valid syllogism with a universal major premise, and the inductive generalization is plausible given the potential benefits of regular check-ups, although individual circumstances may vary.
1) In this argument by analogy, two things are being compared: A) taking a car in for servicing every few months, and B) getting a physical every year for people over the age of 40. The property P attributed to B in the conclusion is the need for regular care or check-ups.
2) The unstated properties (S) that are supposed to make A and B similar include the idea that both cars and bodies require regular maintenance to ensure proper functioning and longevity. The argument assumes that just as neglecting car maintenance can lead to breakdowns and costly repairs, neglecting regular physical check-ups can lead to health problems and potential medical issues.
3) The deductive step of the argument can be formulated as follows:
Major premise: Cars need regular servicing to prevent breakdowns and maintain optimal performance.
Minor premise: Bodies are similar to cars in the sense that they require regular check-ups to prevent health issues and maintain optimal well-being.
Conclusion: People over the age of 40 should get a physical every year.
4) The inductive generalization in the argument relies on the plausibility of the comparison between car maintenance and physical check-ups. To evaluate its validity, we can consider the following:
a) The initial plausibility of the generalization: Given our knowledge that regular check-ups can help detect health problems early and promote overall well-being, it is reasonable to argue that regular physicals are beneficial, similar to regular car servicing.
b) Additional positive instances: We can find support for the generalization by examining medical recommendations and practices that emphasize the importance of regular check-ups for preventive care.
c) Counterexamples: While some individuals may not experience health issues or see the need for frequent physicals, the argument assumes that the general population will benefit from regular check-ups.
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A line passes through the points (-1, 10) and (3, 2). Which shows the graph of this line?
8
8
4
2
- 108
2
46
8 10
X
12
-8
-10
10
6
Answer:
C
Step-by-step explanation:
EDGE 2021
Consider a Markov chain with state space S = {1, 2, 3, 4, 5, 6} and transition probability matrix P = [ 0 0.5 0 0.1 0.4 0]
[ 0 1 0 0 0 0 ]
[ 0.3 0 0.2 0.1 0 0.4]
[0 0.7 0 0 0.3 0 ]
[0 0 0 0 1 0]
[0 0 0 0 0 1 ]
(a) Compute Pˣ. (b) If the process starts in state 3, what are the probabilities that it will be absorbed in state 2, state 5, and state 6, respectively?
a)Pˣ = [tex]\begin{bmatrix}0.1 & 0.5 & 0.04 & 0.28 & 0.03 & 0.05\\0 & 1 & 0 & 0 & 0 & 0\\0.22 & 0 & 0.33 & 0.17 & 0.1 & 0.19\\0.7 & 0 & 0.43 & 0.3 & 0 & 0.57\\0 & 0 & 0 & 0 & 1 & 0\\0 & 0 & 0 & 0 & 0 & 1\end{bmatrix}[/tex] in matrix form, using eigen-values.
b)state 2 is 0.75; state 5 is 0 and ;state 6 is 0.25.
a)In order to calculate the value of Pˣ, follow the below-given steps:
Step 1: Compute the eigen-values of the matrix P.
Here, we get λ = 1, λ = 0.6, λ = 0.4, λ = 0.1, λ = 0, λ = 0.
Step 2: Compute the eigen-vectors corresponding to each eigenvalue of the matrix P.
Step 3: Compute the diagonal matrix D and the transition matrix T. [tex]\begin{matrix}1 & 0 & 0 & 0 & 0 & 0\end{matrix}0.6[/tex]
[tex]\begin{matrix}0.58 & 0.25 & 0.72 & 0 & 0 & 0\end{matrix}0.4.[/tex]
[tex]\begin{matrix}0.07 & 0 & 0.04 & 0.7 & 0 & 0\end{matrix}0.1.[/tex]
[tex]\begin{matrix}0.35 & 0.75 & 0.56 & 0 & 1 & 0\end{matrix}0.[/tex]
[tex]\begin{matrix}0 & 0 & 0 & 0.3 & 0 & 1\end{matrix}[/tex]
Pˣ = T . Dˣ . T⁻¹
We get the following matrix as a result.
Pˣ = [tex]\begin{bmatrix}0.1 & 0.5 & 0.04 & 0.28 & 0.03 & 0.05\\0 & 1 & 0 & 0 & 0 & 0\\0.22 & 0 & 0.33 & 0.17 & 0.1 & 0.19\\0.7 & 0 & 0.43 & 0.3 & 0 & 0.57\\0 & 0 & 0 & 0 & 1 & 0\\0 & 0 & 0 & 0 & 0 & 1\end{bmatrix}[/tex]
b)If the process starts in state 3,
the probability that it will be absorbed in state 2 is 0.75,
the probability that it will be absorbed in state 5 is 0, and
the probability that it will be absorbed in state 6 is 0.25.
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The rent for an apartment was $6,600 per year in 2012. If the rent increased at a rate of 4% each year thereafter, use an exponential equation to find the rent for the apartment in 2021
Answer:
$9,393.78
Step-by-step explanation:
Using the equation:
A = P(1+r)^t
Where,
A = final amount
P = initial amount = $6,600
r = rate of increase = 4% = 0.04
t = time in years = 9 years (2012-2021)
A = 6,600(1 + 0.04)^9
= 6,600(1.04)^9
= 6,600(1.4233)
= 9,393.78
A = $9,393.78
yo i need help please i need the correct answer i will give u a brainliest to please just help me
Answer:
a
Step-by-step explanation:
Jeremy wants to determine the number of solutions for the equation below without actually solving the equation. -3(x+1)+3x=-3(x-1)+3 Which method should Jeremy use? Determine whether the equation has the form a = a, and if it does, the equation has infinitely many solutions. Determine whether the equation has the form a = b, and if it does, the equation has no solution. Determine whether the equation has the form x = a, and if it does, the equation has one solution. Determine whether the equation has the form x = 0, and if it does, the equation has no solution.
Answer:C
Step-by-step explanation:
I have taken a test and it was right sorry if it isn’t right
Answer:
C
Step-by-step explanation:
determine whether the equation has the form x=a, and if it does, the equation has one solution
Suppose the random variables X and Y have the following joint PDF: fxy(x, y) = cxy ,0 < x < b < 1 Determine the value of c.
The random variables X and Y have the value of c is 2/b².
Considering that the joint PDF of X and Y as fxy(x, y) = cxy ,0 < x < b < 1. Integrating the given PDF over its domain is necessary in order to determine the value of c. To find the worth of c, we utilize the accompanying integral:∫∫fxy(x, y)dxdy = 1,where the mix is done over the whole area of x and y. Therefore, cxy dxdy = 1. (1) For x, the integration limits are (0 to b) and for y, they are (0 to 1).
Therefore, by substituting these limits into equation (1), we obtain: 01 0b cxy dxdy = 1 c * [x2/2]0r1[y2/2]0rb = 1 c = 2 / b2 The value of c is therefore 2/b².
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residents of the town smithfield like to consume pizzas, but each pizza requires 10 people to produce it and takes a month. if the town has a total of 100 people, what is the maximum amount of pizza the residents can consume in a year?
The number of pizzas the people of the town will produce in a year, obtained using the simple mathematical operations, is 120 pizzas.
What are mathematical operations?Mathematical operations include operations of additions, subtraction, division, and multiplication.
The number of pizzas produced in a year can be obtained using mathematical operations as follows;
The number of people required to produce one pizza in a month = 10 people
The number of people in the town = 100 people
The number of pizza'a that the people in the town can produce in a month is therefore;
Number of pizza's produced in a month = 100/10 = 10
The number of months in a year = 12 months
The number of pizzas the people in the town can produce in a year = 10 × 12 = 120 pizzas
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The lifetime of an electronical component is to be determined; it is assumed that it is an ex- ponentially distributed random variable. Randomly, users are asked for feedback for when the component had to be replaced; below you can find a sample of 5 such answers (in months): 19,23,21,22,24.
Fill in the blanks below.
(a) Using the method of maximum likelyhood, the parameter of this distribution is estimated to λ = ________WRITE YOUR ANSWER WITH THREE DECIMAL PLACES .
(b) Let L be the estimator for the parameter of this distribution obtained by the method of moments (above), and let H be the estimator for the parameter of this distribution obtained by the method of maximum likelyhood. What comparison relation do we have between L and M in this situation? Use one of the symbols
< = or > to fill in the blank. L ________M
(a) Using the method of maximum likelihood, the estimated parameter of the exponential distribution is λ = 0.050.
(b) Comparing the estimators obtained by the method of moments (L) and the method of maximum likelihood (M), we have L < M.
(a) The maximum likelihood estimation involves finding the parameter that maximizes the likelihood function based on the given data. In this case, using the sample of replacement times (19, 23, 21, 22, 24), the estimated parameter λ of the exponential distribution is calculated to be 0.050.
(b) Comparing the estimators obtained by the method of moments (L) and the method of maximum likelihood (M), we can determine the relationship between them. In general, the method of maximum likelihood tends to provide more efficient and precise estimators compared to the method of moments. Therefore, we have L < M, indicating that the estimator obtained by the method of maximum likelihood (M) is expected to be greater than the estimator obtained by the method of moments (L) in this situation.
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Billy made 2 gallons of juice for a picnic. He said that he made
2
4
quarts of juice.
Answer:
2/4 quarts of juice is 0.125 Gallons of juice for
Step-by-step explanation:
Please Give Brainliest
Answer:
He divided instead of using multiplication
Step-by-step explanation:
PLEASE HELP for a TEST EXPLAIN ANSWER pls give you brainlest!!!!
Answer:
B
Step-by-step explanation:
Answer:
a-4
Step-by-step explination:
hope this helps!
Find the sum of all the two-digit numbers that divide 170 with a remainder of 5.
WILL MARK BRAINLIEST IF ITS RIGHT!!! PLEASE HELLPP!!!!!
Answer:
114
Step-by-step explanation:
To find - Find the sum of all the two-digit numbers that divide 170 with a remainder of 5.
Proof -
The 2 digit number is 11
170 = 11(15) + 5
The two digit number is 15
170 = 15(11) + 5
The two digit number is 33
170 = 33(5) + 5
The two digit number is 55
170 = 55(3) + 5
∴ we get
The two digit numbers are
11, 15, 33, 55
Their sum is equals to
11 + 15 + 33 + 55 = 114
PLEASE HELP I AM BEING TIMED I NEED THE RIGHT ANSWER AND A EXPLAINTION PLEASE I WILL HIVE YOU THE CROWN
Answer:
B
Step-by-step explanation:
Dependent values would be the numbers on the y axis
Let A and B be disjoint compact subspaces of a Hausdorff space X. Show that there exist disjoint open sets U and V, with A⊂U and B⊂V.
In Hausdorff-space "X", if A and B are disjoint "compact-subspaces", then there exist disjoint "open-sets" U and V such that A is contained in U and B is contained in V, because Hausdorff property ensures the existence of disjoint open neighborhoods for any two distinct points.
To prove existence of disjoint "open-sets" U and V with A⊂U and B⊂V, where A and B are "compact-subspaces" (disjoint) of "Hausdorff-space" X, we use the steps:
Step (1) : Since A and B are disjoint compact subspaces, we use the Hausdorff property to find open sets Uₐ and [tex]U_{b}[/tex] such that A⊂Uₐ and B⊂[tex]U_{b}[/tex], and Uₐ∩[tex]U_{b}[/tex] = ∅. This can be done for every pair of points in A and B, respectively, since X is Hausdorff.
Step (2) : Consider the set U = ⋃ Uₐ, where "union" is taken over all of Uₐ for each point in A. U is = union of "open-sets", hence open.
Step (3) : Consider the set V = ⋃ [tex]U_{b}[/tex], where union is taken over for all [tex]U_{b}[/tex] for "every-point" in B. V is also a union of open-sets and so, open.
Step (4) : We claim that U and V are disjoint. Suppose there exists a point x in U∩V. Then x must be in Uₐ for some point a in A and also in [tex]U_{b}[/tex] for some point b in B. Since A and B are disjoint, a and b are different points. However, this contradicts the fact that Uₐ and [tex]U_{b}[/tex] are disjoint open sets.
Therefore, U and V are disjoint open sets with A⊂U and B⊂V.
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