Read the following excerpt from Pointed Roofs by Dorothy Richardson. Then, respond to the question that follows. In a well-written paragraph of 5–7 sentences, explain how the author uses stream of consciousness and one other narrative technique to enhance her writing. Be sure to include specific textual evidence to support the narrative techniques you discuss in your response
In "Pointed Roofs," Dorothy Richardson makes use of conversation and stream of consciousness to improve her writing. Using stream of consciousness, in the given expert.
An excerpt is indeed a quotation from that other resource that the author introduces with fresh language in a sentence. This phrase is taken from Thomas Jefferson's 1801 inaugural speech: As he warned his audience, "I may often go wrong by defect of judgement," Jefferson admitted the fallibility of human nature. "I shall frequently err through lack of judgement" is the excerpt.
In "Pointed Roofs," Dorothy Richardson makes use of conversation and stream of consciousness to improve her writing. Using stream of consciousness, the author lets readers peek inside the protagonist, Miriam, to understand her feelings and thoughts as they happen. For instance, readers can feel Miriam's mild dizziness
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If TRAP is an isosceles trapezoid, what is the value of X?
6x"
(2x + 4)"
Answer:
The answer is 22.
Step-by-step explanation:
6x+2x+4=180
8x+4=180
8x=176
x=22
(a) How do the brightnesses of the three bulbs compare to each other? Explain your reasoning.
(b) What happens to the brightness of each of the three bulbs when bulb A is unscrewed and removed from its socket? Explain your reasoning.
(c) What happens to the current through points 3, 4 and 5 when bulb A is unscrewed? Explain your reasoning.
(a) The brightness of the three bulbs in a series circuit is the same. The reason for this is that a series circuit is designed to have the same amount of electric current flow through each component in the circuit. When the electric current flows through each component in the circuit, it transfers electrical energy to light energy which makes the bulbs light up. Since the same amount of electric current flows through each bulb in a series circuit, they have the same brightness.
(b) When bulb A is unscrewed and removed from its socket, the brightness of bulbs B and C will decrease. The reason for this is that bulb A acts as a resistor in the series circuit. When bulb A is unscrewed and removed from its socket, the electrical resistance of the circuit decreases which leads to an increase in electric current flowing through the circuit. As a result, more electric current flows through bulbs B and C, causing them to become brighter. However, if the resistance of bulb A is too high, the circuit may become open, meaning that there is no current flow and none of the bulbs will light up.
(c) When bulb A is unscrewed, the electrical resistance of the circuit decreases which leads to an increase in electric current flowing through the circuit. As a result, more electric current flows through points 3, 4, and 5. Since the same amount of electric current flows through each component in the circuit, the increase in electric current flowing through points 3, 4, and 5 will be the same.
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The center of a circle is located at (4, 2). A point on the circle is located at (1, 2). What is the approximate area of the circle?
Answer: 9π≈28.26 squared units
Step-by-step explanation: The distance between the two points, 3 units, is the radius. And then we use that to find the area by squaring and multiplying by pi.
A quarterback throws an incomplete pass. The height of the football at time t is modeled by the equation h(t) = –16t2 + 40t + 7. Rounded to the nearest tenth, the solutions to the equation when h(t) = 0 feet are –0.2 s and 2.7 s. Which solution can be eliminated and why?
A quarterback throws an incomplete pass. The height of the football at time t is modeled by the equation h(t) = –16t² + 40t + 7. Rounded to the nearest tenth, the solutions to the equation when h(t) = 0 feet are –0.2 s and 2.7 s.
the solution to be eliminated is -0.2s this is because time do not have negative values
What is a quadratic equation?ax² + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a.
It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be real or complex.
Considering the given function, the answer is both real one is negative the other is positive.
The solution in this case represents time, and time of negative value do not apply in real life
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there are 12 zodiac signs. assume that each of the zodiac signs is equally likely. in a group of 9 random people, what is the chance that there is at least 1 zodiac sign match? (i.e., at least 2 people share a zodiac sign.)
The probability that in a group of 9 friends, at least two share the same astrological sign will be 0.985 as defined "Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of events that follow a probability distribution."
What is probability?Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of events that follow a probability distribution. A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to express probabilities. The number of favorable events to all the events in an experiment is the ratio that makes up the probability formula. Theoretical probability, Experimental probability, and Axiomatic probability are the three categories into which probability can be divided.
Here,
The probability that in a group of 9 friends, at least two share the same astrological sign,
= 1 - the probability that all 9 friends have different astrological signs
=1-12P9/12^9
=1-79833600/5,15,97,80,352
=1-0.0154
=0.985
In a group of nine friends, there is a 0.985 percent chance that at least two of them will have the same astrological sign. "Probability is simply the likelihood that something will happen. The likelihood or likelihood of various outcomes can be discussed when we don't know how an event will turn out. The study of events that fit into a probability distribution is known as statistics."
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how many gallons are equivalent to 20 points
Answer:
2.31964e-7
Step-by-step explanation:
Answer:
3 gallons
Step-by-step explanation:
While standing exactly halfway between two tall trees, Nikki spots a blue jay at the top of one tree and a cardinal at the top of the other. From Nikkis point of view, the angles of elevation to the blue gay and to the cardinal are 60 degrees and 50 degrees, respectively. The trees are 40m apart. If nikki is 1. 5 m tall, find the height of each tree
The height of both trees is 34.641 meters and 23.835 meters respectively.
We can calculate the height using the following method,
We have been given the following values,
Distance between the two trees is 40m
Let the tree with Blue jay be A and the tree with cardinal be B.
The observer is 1.5 m tall, therefore the base of the angles is 1.5 m above the ground.
Observer is standing in the middle, thus distance from each tree is 20m.
Now, base of each triangle= 20m
The angle of elevation of tree A= 60
The angle of elevation of tree B= 50
Height of tree A= tan A * distance from the tree
= tan 60 * 20
= 34.641 m
Similarly, Height of tree B= tan B * distance from the tree
= tan 50 * 20
= 23.835 m
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Y=inxCan you please give a graph use color for function, asymptotes, etc.A short table of easy pointsThe domain and rangePlease identify and label the asymptotes (Please work this as if you didn’t have a calculator)
To graph the natural logarithm function, without using a calculator, and using a short table of easy points, we can proceed as follows:
1. We need to remember that the logarithm function is not defined for negative numbers. We cannot find any exponent that raised to a positive number that result in a negative number.
2. The logarithm function is not defined for x = 0. Therefore, we will have an asymptote at x = 0. It is a vertical asymptote, x = 0.
3. The value for ln(1) = 0, and we also know that the value of ln(e) = 1.
We need to remember that e is, approximately, 2.7182818284...
Now, using this information, we will have the following table:
x - values ---------- y-values
Negative values ---- the function is not defined
0 ------------- The function has a vertical asymptote
1 ------------- 0
e (approx. 2.72) ------------ 1
We can see the table of these values in the following drawing:
Now we can sketch a graph of this function as follows:
The domain of the natural logarithm function is, in interval notation:
\(D=(0,\infty)\)And the range is (in interval notation too) as follows:
\(R=(-\infty,\infty)\)let's denote new intpair(5, 7) as [5 7]. you've got a list of intpairs: [3 7], [4 6], [3 4] you sort them using intpair.compareto. what is their sorted order?
*A* [2 9], [3 2], [5 7]
B [5 7], [3 2], [2 9]
C [3 2], [5 7], [2 9]
D [2 9], [5 7], [3 2]
The sorted order of the impairs [3 7], [4 6], [3 4] using impair. compare to would be:
[C] [3 2], [4 6], [3 7]
When comparing in pairs using impair. compare to, the first element taking priority over the second element. So, in the list [3 7], [4 6], [3 4], the impair [3 2] would come first because 3 is smaller than both 4 and 3, and the second element (2) is also smaller than the second element of the other in pairs. Then, the impair [4 6] would come next as it has the second smallest first element, and finally, the impair [3 7] would come last as it has the largest first element. Therefore, the sorted order is [3 2], [4 6], [3 7], denoted as option C.
To sort the given list of in pairs ([3 7], [4 6], [3 4]) using impair. compared, follow these steps:
1. Compare the first elements of the in pairs (3, 4, and 3). If there is a tie, move to step 2.
2. Compare the second elements in pairs with the same first elements (7 and 4).
3. Arrange the impairs in ascending order based on the comparison results.
The sorted order is [3 4], [3 7], [4 6]. However, this order is not present in the given options. Please check the question for any discrepancies or provide the correct in pairs to sort.
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The sorted order of the impairs [3 7], [4 6], [3 4] using impair. compare to would be:
[C] [3 2], [4 6], [3 7]
When comparing in pairs using impair. compare to, the first element taking priority over the second element. So, in the list [3 7], [4 6], [3 4], the impair [3 2] would come first because 3 is smaller than both 4 and 3, and the second element (2) is also smaller than the second element of the other in pairs. Then, the impair [4 6] would come next as it has the second smallest first element, and finally, the impair [3 7] would come last as it has the largest first element. Therefore, the sorted order is [3 2], [4 6], [3 7], denoted as option C.
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Mrs. Rodriquez has 24 students in her class. Ten of the students are boys. Jeff claims that the ratio of boys to girls in this class must be 5:12. What is Jeff’s error and how can he correct it? Jeff found the ratio of the number of boys to the total number of students. He needed to first find that there are 14 girls to get a ratio of 10:14 or 5:7. Jeff found the ratio of the number of boys to the total number of students. He needed to first find that there are 14 girls. The ratio would be 14:10 or 7:5. Jeff did not write the ratio in the correct order. He should have written it as 24:10. Jeff did not write the ratio in the correct order. He should have written it as 12:5.
Answer:
Jeff found the ratio of boys to students. He needed to first find that there are 14 girls to get a ratio of 10:14 or 5:7.....answer is the first one
Step-by-step explanation:
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Answer:
A- Jeff found the ratio of the number of boys to the total number of students. He needed to first find that there are 14 girls to get a ratio of 10:14 or 5:7.
Good Luck-
maggbaron765
A line passes through the point (8,-7) and has a slope of -1/3 write an equation in slope intercept form for this line
Answer:
y= -1/3x-13/3
Step-by-step explanation:
(Refer to picture)
Use the general point-slope formula and plug in y1 and x1, then simplify
(I hope my handwriting isn't too bad, is so, I'll clarify any numbers you can't read.)
please answare all of them by putting eather true or false
Put (T)rue or (F)alse in the brackets in front of each of the following statements (Correct \( =+2 \) points, Wrong \( =-1 \) points, Unanswered \( =0 \) points) ] (a) A delta modulator has a quantize
(a) It is False a delta modulator does not have a fixed number of quantization levels. It uses a 1-bit quantizer, resulting in a binary decision for each sample.
(b) It is False the bandwidth of a VSB (Vestigial Sideband) signal is greater than that of the corresponding SSB (Single Sideband) signal, but it is also greater than the bandwidth of the corresponding DSBSC (Double Sideband Suppressed Carrier) signal.
(c) It is False a zero-ISI pulse satisfies p(t) = 1 when t = 0, and p(t) = 0 for all other values of t. This ensures that there is no interference between adjacent symbols at the receiver.
(d) It is False wideband FM has a wider bandwidth than AM for the same message signal. The bandwidth of FM depends on the modulation index and the frequency deviation.
(e) It is False Line coding is necessary for DSBSC demodulation to recover the original message signal. It ensures proper synchronization and provides a method to represent binary data.
(f) It is true FM is more resistant to non-linearity distortion than AM. FM modulation spreads the signal energy across a wider frequency range, reducing the impact of non-linearities.
(g) It is False in a Quadrature Amplitude Modulator (QAM), two signals are transmitted at different frequencies but at the same time, allowing them to coexist without interference.
(h) It is true DSBSC demodulators can be used for demodulating AM signals because DSBSC is a special case of AM where the carrier is suppressed.
(i)It is False the minimum bandwidth required for transmitting 10 PCM (Pulse Code Modulation) bits/second depends on the sampling rate and the specific encoding scheme used.
(j)It is False the bandwidth of an anti-aliasing filter is determined by the Nyquist-Shannon sampling theorem and is typically set to half the sampling frequency to prevent aliasing. It is not equal to the sampling frequency.
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COMPLETE QUESTION - Put (T)rue or (F)alse in the brackets in front of each of the following statements (Correct =+2 points, Wrong =−1 points, Unanswered =0 points) ] (a) A delta modulator has a quantizer with 256 quantization levels ] (b) The bandwidth of a VSB signal is greater than the BW of the corresponding SSB and less than the BW of the corresponding DSBSC signal. ] (c) When transmitting bits at a rate of 1/T b , a zero-ISI pulse p(t) must satisfy p(t)={ 0, 1,t=±T b ,±2T b ,±3T b ,…t=0] (d) Wideband FM has the same bandwidth as AM for the same message signal. 1 (e) Line coding is not required for DSBSC demodulation. ] (f) FM is more resistant to non-linearity distortion than AM. ] (g) In a Quadrature Amplitude Modulator (QAM), two signals are transmitted at the same frequency without interfering with each other. ] (h) DSBSC demodulators can be used for demodulating AM signals (DSB with carrier) ] (i) The minimum bandwidth required for transmitting 10PCM bits/second is 20 Hz. ] (j) The bandwidth of an anti-aliasing filter is equal to the sampling frequency.
help msnohskgdjdshyatu
Answer:
I dont even know myself
Step-by-step explanation:
T^T
Perform the calculation and report your results to the correct number of significant figures. (10.52)(0.6721)
(19.09−15.347)
The results of the calculations are approximately 7.07 and 3.74, respectively, to the correct number of significant figures.
Performing the calculation:
(10.52)(0.6721) = 7.0671992
Rounding to the correct number of significant figures, we have:
(10.52)(0.6721) ≈ 7.07
Next, let's calculate (19.09 - 15.347):
(19.09 - 15.347) = 3.743
Rounding to the correct number of significant figures, we have:
(19.09 - 15.347) ≈ 3.74
Therefore, the results of the calculations are approximately 7.07 and 3.74, respectively, to the correct number of significant figures.
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1) Solve the following equations for 0° ≤x≤ 360°.
(i) cosec x=1
(ii) sec x=2
(iii) cot x=4
The solutions of the given equations are,
(i) \(x=\frac{\pi }{2} , x= \frac{5\pi }{2} , x= \frac{9\pi }{2} , x = \frac{13\pi }{2} , x = \frac{17\pi }{2}\)
(ii) x = 0, x = 2π, x = 4π, x = 6π, x = 8π.
(iii)
\(x = cot^-^1(4), x = cot^-^1(4)+\pi , x = cot^-^1(4)+2\pi , x = cot^-^1(4)+3\pi , \\x = cot^-^1(4)+4\pi\)
What is solution of the equation?
In order to make the equation's equality true, the unknown variables must be given values as a solution. In other terms, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transform the equation into an equality.
(i) cosec x = 1 for 0 ≤ x ≤ 360°
Since, the general solution for
cosec x = 1 is, \(x = \frac{\pi }{2} +2n\pi\)
The range for the solution is 0 ≤ x ≤ 360°
Hence,
\(x=\frac{\pi }{2} , x= \frac{5\pi }{2} , x= \frac{9\pi }{2} , x = \frac{13\pi }{2} , x = \frac{17\pi }{2}\)
(ii) sec x = 2
Since, the general solution for
sec x = 1 is, x = 0 + 2πn
The range for the solution is 0 ≤ x ≤ 360°
Hence,
x = 0, x = 2π, x = 4π, x = 6π, x = 8π.
(iii) cot x = 4
⇒ \(x = cot^-^1(4)\)
The range for the solution is 0 ≤ x ≤ 360°
Hence,
\(x = cot^-^1(4), x = cot^-^1(4)+\pi , x = cot^-^1(4)+2\pi , x = cot^-^1(4)+3\pi , \\x = cot^-^1(4)+4\pi\)
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here is a set of sample data: 1009.85 1587.04 1984.87 2281.95 2337.80 2994.27 3554.64 3748.54 4487.25 4533.82 4559.06 4882.61 4951.68 4995.65 6428.17 6658.12 6789.12 7009.47 which one will be the best design of the units of stem and leaf for a stem-and-leaf display?
The one that will be the best design of the units of stem and leaf for a stem-and-leaf display is 1's for stem unit and 0.1's for leaf unit (option b).
In this case, we are given a set of sample data and asked to determine the best design for the units of stem and leaf. We are given four options: 100's for stem unit and 10's for leaf unit, 1's for stem unit and 0.1's for leaf unit, 10's for stem unit and 1's for leaf unit, and 1000's for stem unit and 100's for leaf unit.
Option b) uses 1's for the stem unit and 0.1's for the leaf unit. This design would work well if the data had a small range and many values, which is the case here. Using 1's for the stem unit and 0.1's for the leaf unit would result in a compact and easy-to-read display, with each stem having only a few leaves.
Therefore, option b) is the best design for the units of stem and leaf for this set of data.
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Complete Question:
Here is a set of sample data:
1009.85 1587.04 1984.87 2281.95 2337.80 2994.27 3554.64 3748.54 4487.25 4533.82 4559.06 4882.61 4951.68 4995.65 6428.17 6658.12 6789.12 7009.47
Which one will be the best design of the units of stem and leaf for a stem-and-leaf display?
a) 100's for stem unit and 10's for leaf unit
b) 1's for stem unit and 0.1's for leaf unit
c) 10's for stem unit and 1's for leaf unit
d) 1000's for stem unit and 100's for leaf unit
The CPI is currently 153. If a coffee maker costs $31. 90 today, how much did one cost in 1983, to the nearest cent? a. $20. 85 b. $21. 20 c. $26. 60 d. $48. 81.
The cost of one coffee maker in 1983, to the nearest cent, was $20.80. Hence, the correct option is (a) $20.85.
To find the cost of a coffee maker in 1983, we can use the formula for inflation:
Initial cost = Current cost × Initial CPI ÷ Current CPI
Given:
Current cost = $31.90
Current CPI = 153
We need to find the Initial cost and the Initial CPI.
According to the table, the CPI for 1983 is 99.6.
Substituting the values into the formula:
Initial cost = $31.90 × 99.6 ÷ 153
Simplifying the calculation:
Initial cost = $20.80 (approx)
Therefore, the cost of one coffee maker in 1983, to the nearest cent, was $20.80.
Hence, the correct option is (a) $20.85.
Note: Inflation is a measure of the rise in the general level of prices of goods and services in an economy over a period of time.
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14) Coterminal angle
The range of angles typically used in trigonometry is from 0 to 360 degrees or 0 to 2π radians, so when finding coterminal angles, we usually choose the angle that falls within this range.
Two angles in standard position (angles that have their initial side on the positive x-axis) are called coterminal if they have the same terminal side. In other words, two angles are coterminal if they end at the same point on the unit circle.
To find coterminal angles, we can add or subtract any multiple of 360 degrees or 2π radians to or from the given angle. This is because adding or subtracting a full revolution (360 degrees or 2π radians) results in an angle that ends at the same point on the unit circle.
For example, if we are given an angle of 150 degrees, we can find coterminal angles by adding or subtracting multiples of 360 degrees. Adding 360 degrees gives us 510 degrees, which is coterminal with 150 degrees. Subtracting 360 degrees gives us -210 degrees, which is also coterminal with 150 degrees. We can continue to find additional coterminal angles by adding or subtracting multiples of 360 degrees.
It is important to note that the range of angles typically used in trigonometry is from 0 to 360 degrees or 0 to 2π radians, so when finding coterminal angles, we usually choose the angle that falls within this range.
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The diameter of the hubcap of a tire is 46 cm find the area in square centimeters of this hubcap write your answer in the terms of pi 
Answer:
\(529\pi\) cm²
Step-by-step explanation:
\(d=46 \implies r=23 \\ \\ A=\pi r^2=\pi (23^2)=529\pi\)
the joint pdf of x and y is f(x,y) = x y, 0 < x < 1; 0 < y < 1. are x and y independent?
Since the joint pdf \(\(f(x,y)\)\) cannot be expressed as the product of the marginal pdfs \(\(f_X(x)\) and \(f_Y(y)\),\)we conclude that x and y are not independent.
What is the determination of independence?
The determination of independence refers to the process of assessing whether two or more random variables are statistically independent of each other. Independence is a fundamental concept in probability theory and statistics.
When two random variables are independent, their outcomes or events do not influence each other. In other words, the occurrence or value of one variable provides no information about the occurrence or value of the other variable.
To determine whether x and y are independent, we need to check if the joint probability density function (pdf) can be expressed as the product of the marginal pdfs.
The joint pdf of \(x\) and \(y\) is given as:
\(\[ f(x,y) = xy, \quad 0 < x < 1, \quad 0 < y < 1 \]\)
To determine the marginal pdfs, we integrate the joint pdf over the range of the other variable. Let's start with the marginal pdf of x
\(\[ f_X(x) = \int_{0}^{1} f(x,y) \, dy \]\[ = \int_{0}^{1} xy \, dy \]\[ = x \int_{0}^{1} y \, dy \]\[ = x \left[\frac{y^2}{2}\right]_{0}^{1} \]\[ = x \left(\frac{1}{2} - 0\right) \]\[ = \frac{x}{2} \]\)
Similarly, we can calculate the marginal pdf of y:
\(\[ f_Y(y) = \int_{0}^{1} f(x,y) \, dx \]\[ = \int_{0}^{1} xy \, dx \]\[ = y \int_{0}^{1} x \, dx \]\[ = y \left[\frac{x^2}{2}\right]_{0}^{1} \]\[ = y \left(\frac{1}{2} - 0\right) \]\[ = \frac{y}{2} \]\)
Since the joint pdf \(\(f(x,y)\)\) cannot be expressed as the product of the marginal pdfs\(\(f_X(x)\\)) and \(\(f_Y(y)\)\), we conclude that x and y are not independent.
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Which number, when placed in the blank, makes the inequality FALSE? _____ > 8
Hi!
I can help you with joy!
Recall that the sign ">" means "greater than"
So, we need to find a number that would make the inequality false.
Is it 9? Nope, 9 is greater than 8, so 9 would make the inequality true.
So, we need to find a number less than 8.
Is it 7? Yes, 7 is less than 8, so 7 would make the inequality false.
7>8 (False)
Hope it helps!
Enjoy your day!
\(\bf{GracefulGirl\)
Answer:
Anything under 8.
Step-by-step explanation:
Anything under 8, (7, 6, 5, 4, etc.) would make the inequality false. "Inequality" means difference in size, degree, circumstances, etc.; lack of equality. ">" means greater than, so, to make the equation false, insert something less than 8.
Write the equation of the line fully simplified slope-intercept form.
Answer:
Using the points (0,8)(2,5)(4,2)(6,-1)
Step-by-step explanation:
y=mx+b form/ slope intercept is -3/2x+8
solpe is -3/2
Y-intercept is (0,8)
Select the correct answer from each drop-down menu. Which system of inequalities does the graph represent? Which test point satisfies both of the inequalities in that system? The graph represents the system of inequalities . The test point satisfies both of the inequalities in the system represented by the graph.
The system of inequality that the graph represents is E. 2x + 3y is less than or equal to 4 and 2x + 2y is less than or equal to 3
How to illustrate the graph?In the graph, when 2x + 3y = 4
3y = 4 - 2x
y = -2/3x + 4/3
When 2x + 2y = 3
2y = -2x + 3
y = -x + 3/2
On the graph, -2/3x + 4/3 is illustrated on the first line while -x + 3/2 is illustrated on the second line.
Therefore, the correct option is E.
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HELP ME IT'S URGENT I COULD FAIL
Answer:
undefined
Step-by-step explanation:
i think its undefined
Find the equation for the plane through the points \( P_{0}(-4,-5,-2), Q_{0}(3,3,0) \), and \( R_{0}(-3,2,-4) \). Using a coefficient of \( -30 \) for \( x \), the equation of the plane is (Type an eq
The equation of the plane is 1860x - 540y - 1590z - 11940 = 0
To find the equation of the plane through the points P0(-4,-5,-2), Q0(3,3,0), and R0(-3,2,-4), we can use the cross product of the vectors PQ and PR to determine the normal vector of the plane, and then use the point-normal form of the equation of a plane to find the equation.
Vector PQ is (3-(-4), 3-(-5), 0-(-2)) = (7, 8, 2).
Vector PR is (-3-(-4), 2-(-5), -4-(-2)) = (-1, 7, -2).
The cross product of PQ and PR is (-62, 18, 53).
So, the normal vector of the plane is (-62, 18, 53).
Using the point-normal form of the equation of a plane, where a, b, and c are the coefficients of the plane, and (x0, y0, z0) is the point on the plane, we have:
-62(x+4) + 18(y+5) + 53(z+2) = 0.
Multiplying through by -30, we get:
1860x - 540y - 1590z - 11940 = 0.
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find the area of the region enclosed by one loop of the curve r = 8 sin 3θ.
The area of the region enclosed by one loop of the curve r = 8 sin 3θ is \(\frac{\pi a^{2} }{12}\)
given that
r = 8sin3θ
The radius of the curve will only be altered by changing the value of a.
Set r = 0 since this is where the curve is at its origin to determine where the curve starts and where it finishes.
if asin3θ = 0 then sin3θ = 0 since sinθ =0 at θ = 0,\(\pi\),2\(\pi\),....... we see that for sin3θ ,it will be 0 at 0,\(\pi\)/3,2\(\pi\)/3.......
So, the curve in the first quadrant varies from θ=0 to \(\pi\)/3
The expression for the area of any polar equation r from θ=α to θ = β
is given by
\(\frac{1}{2}\)\(\int\limits^\beta _\alpha\)\(r^{2}\) dθ
For one loop of the given equation, the corresponding integral is then
\(\frac{1}{2}\)\(\int\limits^\frac{\pi }{3} _0\)(asin3θ)^2 dθ
Working this integral:
\(\frac{1}{2}\)\(\int\limits^\frac{\pi }{3} _0\)(asin3θ)^2 dθ
= \(\frac{1}{2}\)\(\int\limits^\frac{\pi }{3} _0\)\(a^{2}\)(sin3θ)^2 dθ
we know that cos2θ = 1-2((sinθ)^2) we can rewrite it as (sinθ)^2 = 1/2(1-cos2θ)
we can write (sin3θ)^2 = 1/2(1-cos6θ)
then the integration is:
= \(\frac{1}{2}\)\(\int\limits^\frac{\pi }{3} _0\)\(a^{2}\)( 1/2(1-cos6θ))dθ
=\(\frac{a^{2} }{4}\)\(\int\limits^\frac{\pi }{3} _0\)(1-cos6θ)dθ
we need to integrate that
=\(\frac{a^{2} }{4}\)(θ - \(\frac{1}{6}\)sin6θ)with θ = \(\pi\)/3 to 0
=\(\frac{a^{2} }{4}\)[\(\frac{\pi }{3}\) - \(\frac{1}{6}\)sin2\(\pi\) - (0 - \(\frac{1}{6}\)sin0)]
=\(\frac{a^{2} }{4}\)(\(\frac{\pi }{3}\))
=\(\frac{\pi a^{2} }{12}\)
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What ratios are equivalent to 4:3?
7:2
12/42
28:21
42:12
show that if one set is a subset of another then the other's complenet is a subset of the first's complement
To show that if one set is a subset of another then the other's complement is a subset of the first's complement, we can use the definition of set complement and subset.
Let's assume that A is a subset of B, which means that every element of A is also an element of B. We want to show that the complement of B, denoted by B', is a subset of the complement of A, denoted by A'.
To prove this, we need to show that every element of B' is also an element of A'. Let x be an arbitrary element of B'. By definition, x is not an element of B. Since A is a subset of B, x cannot be an element of A either. Therefore, x must be an element of A', which means that B' is a subset of A'.
In summary, if A is a subset of B, then B' is a subset of A'.
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A band must pay a $2500 entrance fee, It will split the cost between its 25 members. How much will each member pay?
Please help quick
Answer $100 each
Step-by-step explanation:
2500/25
Answer: 2500/25
Each member pays $100
============================================
Explanation:
The slash symbol means division. It's the same as saying 2500 ÷ 25
The expression 2500/25 simplifies to 100, which means that each member must pay $100. If you had 25 members paying $100 each, then 25*100 = 2500 dollars is the total amount of money paid.
So in short, you divide the total cost over the number of members.