(20 pts) Q2) Determine the Fourier Transform of the following signals (Show your work, Don't use FT Table): 1) X(t) = u(t-2) +t X(t) = e-2|t| |t1= (10 pts) Q3) Determine the average power of the signal f(t)= A cos(wot)
Answers
Q2) Fourier Transform of the given signals:
1) X(t) = u(t-2) + t
To find the Fourier Transform of this signal, we can use the properties of the Fourier Transform.
Using the time-shifting property, we can write the signal X(t) as:
X(t) = u(t-2) + (t-2) + 2
The Fourier Transform of u(t-a) is 1/(jω) * e^(-jaω), where ω is the angular frequency.
Applying the Fourier Transform to each term separately, we get:
FT{u(t-2)} = 1/(jω) * e^(-j2ω)
FT{(t-2)} = j/(ω^2) * (1 - e^(-j2ω))
FT{2} = 2πδ(ω)
Combining these results, we have:
FT{X(t)} = 1/(jω) * e^(-j2ω) + j/(ω^2) * (1 - e^(-j2ω)) + 2πδ(ω)
2) X(t) = e^(-2|t|)
The absolute value function |t| can be defined as a piecewise function:
|t| = -t for t < 0
|t| = t for t >= 0
Using this definition, we can write X(t) as:
X(t) = e^(-2(-t)) for t < 0
X(t) = e^(-2t) for t >= 0
Now, let's find the Fourier Transform of each part separately:
For t < 0:
FT{e^(-2(-t))} = FT{e^(2t)}
= 1/(jω - 2)
For t >= 0:
FT{e^(-2t)} = 1/(jω + 2)
Combining these results, we have:
FT{X(t)} = 1/(jω - 2) for t < 0
= 1/(jω + 2) for t >= 0
Q3) Average power of the signal f(t) = A * cos(w0t):
To determine the average power of this signal, we need to calculate the mean square value of the signal.
The mean square value of a continuous-time signal f(t) is defined as:
P_avg = (1/T) * ∫[f^2(t)] dt
In this case, the signal f(t) = A * cos(w0t), where A is the amplitude and w0 is the angular frequency.
Substituting the signal into the mean square value formula, we get:
P_avg = (1/T) * ∫[(A * cos(w0t))^2] dt
= (1/T) * ∫[A^2 * cos^2(w0t)] dt
= (1/T) * A^2 * ∫[cos^2(w0t)] dt
Using the trigonometric identity cos^2(x) = (1 + cos(2x))/2, we can simplify the integral:
P_avg = (1/T) * A^2 * ∫[(1 + cos(2w0t))/2] dt
= (1/T) * A^2 * [(t/2) + (sin(2w0t)/(4w0))] + C
Where C is the constant of integration.
The average power is given by the limit as T approaches infinity:
P_avg = lim(T→∞) [(1/T) * A^2 * [(t
/2) + (sin(2w0t)/(4w0))] + C]
Since the signal is periodic with period T = 2π/w0, we can rewrite the average power as:
P_avg = (1/(2π/w0)) * A^2 * [(t/2) + (sin(2w0t)/(4w0))] + C
Simplifying further, we have:
P_avg = (w0/2π) * A^2 * [(t/2) + (sin(2w0t)/(4w0))] + C
The average power of the signal f(t) = A * cos(w0t) is (w0/2π) * A^2.
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Related Questions
A 75-hp, 850 r/min, 500-V series motor has an efficiency of 90.2 percent
when operating at rated conditions. The series field has 30 turns/pole, and
the motor parameters are:
Armature
0.1414 ohms
IP + CW
0.0412 ohms
Series
0.0189 ohms
Resistance,
The motor has a maximum safe speed of 1700 r/min. Is it safe to operate the
motor with a 10-hp shaft load? Use the magnetization curve in Figure
11.16, and show all work. Neglect changes in windage and friction
Answers
It is not safe to operate the motor with a 10-hp shaft load.
Explanation :
Solution-
First, determine the rated speed and current of the motor:
Rated speed = 850 r/min
Rated current = 500 V / (0.1414 ohms + 0.0412 ohms + 0.0189 ohms) = 30.22 A
Next, determine the speed and current for a 10-hp shaft load:
Speed = 1700 r/min
Current = 10 hp / (75 hp * 0.902) = 0.1343 A
Finally, determine whether it is safe to operate the motor with the 10-hp shaft load using the magnetization curve. we can see that the current at 1700 r/min is 0.1264 A, which is less than the current for the 10-hp shaft load (0.1343 A).
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Wood is which one of the following composite types: (a) CMC, (b) MMC, or (c) PMC?
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Wood is a composite type of CMC. What is Wood. Wood is a natural composite that is formed from cellulose fibers embedded in a matrix of lignin.
It is a natural material that has been used for thousands of years to make structures, furniture, and other useful items. What are Composites. Composite materials are made up of two or more materials with distinct and they can be made by combining any type of material. The goal of combining different materials is to create a new material with better overall properties than any of the individual components. Wood is made up of cellulose fibers embedded in a matrix of lignin. Wood, which is a natural composite, is an example of a composite made up of organic materials. CMC (Ceramic matrix composites) and MMC (Metal matrix composites) are the other two composite types.
Wood is a natural composite material and does not fall under the categories of (a) CMC (Ceramic Matrix Composite), (b) MMC (Metal Matrix Composite), or (c) PMC (Polymer Matrix Composite).
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A "calorie" is a unit of energy, defined as the amount of energy needed to raise the temperature of one gram of water by one degree Celsius. The nutritional labels on food products typically tell you how many calories of digestible energy are in one serving of food, where "digestible" means that the energy stored in the chemical bonds of the molecules comprising the food can be extracted by your body. (Water for example has energy, but that energy is not chemically accessible via digestion.) To simplify understanding for typical consumers, the "calories" reported on nutritional labels actually represent kilocalories: a 170 calorie can of beer actually contains 170,000 calories of digestible energy.
i) If a student foolishly decides to binge drink 21 beers on their 21t birthday, how many gallons of water could they have heated from room temperature (24 °C) to boiling (100 C) using an equivalent amount of digestible energy in the beer? Recall that one gallon of water is roughly 8 pounds.
ii) What is this energy equivalent to in BTU? A "BTU" or British Thermal Unit is also a unit of energy, defined as the amount of energy needed to raise the temperature of one pound of water by one degree Fahrenheit
iii) If you had purchased an equivalent amount of electrical energy in kW-hr from the utility company, how much would you have to pay? Is this cheaper than buying beer?
Answers
A "calorie" is a unit of energy that is defined as the usually inform you of the number of calories of digestible energy present in one serving of food. 21 beers times 17 calories per beer equals 357 calories.
What is "calorie"?Calories are units of energy that a food or drink provides. You can usually find calorie counts listed on food items, and wearables like the best fitness trackers allow you monitor how many calories you're burning by doing different activities. Certain foods, such as fatty, fried, or processed foods, tend to have more calories. Other foods, such as fresh fruit and vegetables, tend to have fewer calories. However, some healthy fruits and vegetables can be high in calories, while low-calorie foods, such as diet soda, don’t provide any nutritional value. We need calories to give us enough energy to move around, stay warm, grow, work, think, and play. Even our blood circulation and digestion need the energy gained from calories in order to function well.To learn more about blood circulation refer to:
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Which of the following is a Dashboard Scoreboard for alignment of the business where information is constantly flowing through the Tiers so immediate actions can be taken?
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Answer:
What is a dashboard?
A dashboard is an information management tool used to track KPIs, metrics, and key data points that are relevant to your business, department, or a specific process. Dashboards aggregate and visualize data from multiple sources, such as databases, locally hosted files, and web services. Dashboards allow you to monitor your business performance by displaying historical trends, actionable data, and real-time information.
Dashboards actually take their name from automobile dashboards and they are used in much the same way. For the sake of an analogy, let’s look at a car. There may be hundreds of processes that impact the performance of your vehicle if you look under the hood. Your car’s dashboard summarizes this using visualizations so you can focus on what matters most: safely driving your vehicle.
For businesses, there are hundreds of processes that impact your performance if you look ‘under the hood’, so to speak. And with a wealth of data made available these days, managing and extracting value from it can be difficult. Simplifying data analysis and distribution through tools like dashboards is a way to help businesses rev their engines and make smarter, better, faster data-driven decisions.
And a well designed dashboard levels up your approach to information management. Everyone in the business, regardless of role, has questions about your company performance, whether it be campaign performance, new wins, or churn rate. Dashboards bring everyone (and your metrics) together in one place to answer these questions.
Explanation:
An inventor claims to have developed a device requiring no work or heat transfer input yet able to produce hot and cold air streams at steady state.
a. True
b. False
Answers
Answer:
a. True
Explanation:
Apply the principle of conservation of mass.
and also the expression for the steady flow energy equation.
kinetic and potential energy effects can be neglected.
The given statement by the inventor who is claiming the development of a device that requires no work or heat transfer input yet is able to produce hot and cold air streams at a steady state is definitely false.
What is heat transfer?Heat transfer may be characterized as a type of process which involves the migration of heat from one object or component to another by numerous mechanisms like conduction, convection, and/or radiation.
The process of heat transfer may occur where there is a temperature difference between two objects exist. It significantly utilizes the mechanism of exchanging thermal energy between two or more physical systems.
According to the concept of physics, no object or thing has the ability to perform its function without the utilization of any source of heat or energy. Then, how it is possible for that device to produce hot and cold air streams at a steady state.
Therefore, the given statement by the inventor is absolutely false.
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Consider these two sentences: "The boy was sick from eating so much ice cream," and, "That boy ate so much ice cream, it made him sick." These sentences have similar ------ but different syntax.
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The given sentences have similar semantic meaning but different syntax.
Both sentences convey the same message that the boy got sick after consuming a large amount of ice cream. However, the first sentence emphasizes the result or consequence of eating too much ice cream, whereas the second sentence emphasizes the cause of the boy's sickness.
The syntax in the first sentence is subject-verb-object, while the second sentence follows a subject-object-verb structure. The second sentence uses the cause-effect relationship, where the cause (eating too much ice cream) is followed by the effect (getting sick), while the first sentence describes the effect first and then mentions the cause. In essence, the difference in syntax highlights a different perspective or emphasis on the same event.
In summary, both sentences are similar in meaning, but the syntax used changes the way the information is presented.
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MyLinkedList> +comparisons : long +contains (item : Type) : boolean +sort() Field summary • comparisons - Stores the total number of comparisons made by the contains method. . Method summary contains - This function should be upgraded to use Comparable.compare To(Type) to compare elements. sort - Sorts the list in ascending order. You may select any sorting procedure you like from this list: a. Bubble Sort - This method should run in O(n?) time. b. Insertion Sort - This method should run in O(n) time. C. Selection Sort - This method should run in O(n?) time. d. Merge Sort - This method should run in O(nlogn) time. e. Quick Sort - This method should run in O(nlogn) time.
Answers
Based on the provided information, the MyLinkedList class has the following fields and methods:
Fields:
- comparisons: a long variable that stores the total number of comparisons made by the contains method.
Methods:
- contains(item: Type): a boolean method that checks if the list contains a specific item. The method should be upgraded to use the Comparable.compare method to compare elements.
- sort(): a method that sorts the list in ascending order. There are several sorting procedures to choose from:
a. Bubble Sort: This method should run in O(n^2) time.
b. Insertion Sort: This method should run in O(n) time.
c. Selection Sort: This method should run in O(n^2) time.
d. Merge Sort: This method should run in O(n log n) time.
e. Quick Sort: This method should run in O(n log n) time.
You can select any of the mentioned sorting procedures to implement the sort() method. The choice depends on factors such as the size of the list and the desired time complexity for sorting.
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explain why it is not advisable to wear Ornament like ring at work shop
Answers
The reason that it is not advisable to wear Ornament like ring at work shop is that rings can be easily get caught and fingers or the hands of the person can be injured, cut, scared etc.
Why should you not wear a ring at work?Jewelry is known to bring about a lot of safety hazards for people working around chemicals and others.
Note that the reason that it is not advisable to wear Ornament like ring at work shop is that rings can be easily get caught and fingers or the hands of the person can be injured, cut, scared etc.
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a voltage amplifier with an input resistance of 40 kn, an output resistance of i 00 n, and a gain of 300 v n is connected between a 10-kn source with an open-circuit voltage of to m v and a i 00-n load.
Answers
In this circuit, we have two resistors and we are required to determine the voltage across the load resistance.
The voltage across the 100 nΩ load resistor is,
\(3.98 μV or 3.98 * 10^-6V.\)
Voltage division formula is given as;
V x is the voltage drop across the resistor Rx
V t is the total voltage applied to the resistive circuit
RT is the equivalent resistance of the circuit
To solve the given problem, we can use the voltage division concept, which is given as:
\($$V_{load}=\frac{R_{load}}{R_{load}+R_{out}}*\frac{R_{in}}{R_{in}+R_{source}}*V_{source}$$\)
Putting all these values in the above-given equation, we get:
\($$V_{load}=\frac{0.1}{0.1+100}*\frac{40}{40+10000}*10*10^{-3}$$$$\)
\(=\frac{0.1}{100.1}*4*10^{-3}$$$$\)
\(=3.98*10^{-6}V$$\)
\(3.98 μV or 3.98 * 10^-6V.\)
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I will rate 5 stars/brainliest if you help me!!! A company produces A, B, and C and can sell these products in unlimited quantities at the following unit prices: A, $10; B, $56; C, $100. Producing a unit of A requires 1 hour of labor; a unit of B, 2 hours of labor plus 2 units of A; and a unit of C, 3 hours of labor plus 1 unit of B. Any A that is used to produce B cannot be sold. Similarly, any B that is used to produce C cannot be sold. A total of 40 hours of labor are available. Formulate an LP to maximize the company’s revenues. (Please solve the LP with Lindo or Excel).
Answers
Answer: 0
Explanation: i need to add it up to get what u want
12. Some engine blocks are made of _______, but its high cost prohibits use in average-priced vehicles. A. cast iron B. aluminum C. magnesium alloy D. hydrocarbon
Answers
What is the eye an example of?
sense organ
stimulus
a relay neuron
Answers
sens organ is the eye example
A single fixed pulley is used to lift a load of 400N by the application of an effort of 480N in 10s through a vertical height of 5m. Determine the V.R, M.A and efficiency of the machine.
Answers
Answer:
(a) the velocity ratio of the machine (V.R) = 1
(b) The mechanical advantage of the machine (M.A) = 0.833
(c) The efficiency of the machine (E) = 83.3 %
Explanation:
Given;
load lifted by the pulley, L = 400 N
effort applied in lifting the, E = 480 N
distance moved by the effort, d = 5 m
(a) the velocity ratio of the machine (V.R);
since the effort applied moved downwards through a distance of d, the load will also move upwards through an equal distance 'd'.
V.R = distance moved by effort / distance moved by the load
V.R = 5/5 = 1
(b) The mechanical advantage of the machine (M.A);
M.A = L/E
M.A = 400 / 480
M.A = 0.833
(c) The efficiency of the machine (E);
\(E = \frac{M.A}{V.R} \times 100\%\\\\E = 0.833 \ \times \ 100\%\\\\ E = 83.3 \ \%\)
A turbine in a simple ideal Rankine cycle with water as the working fluid operates with an inlet temperature of 500°C and pressure of 600 kPa and an exit temperature of 45°С. Find the turbine work in MW if the mass flow rate of the steam is at 11 kg/s.
Answers
Answer:
the turbine work in MW is \(\mathbf{W_t = 10.47299 \ kW}\)
Explanation:
Given that:
the inlet temperature = 500°C
pressure = 600 kPa
exit temperature = 45°С
mass flow rate = 11 kg/s
The objective is to find the turbine work in MW given that the mass flow rate of the steam is at 11 kg/s.
From the steam tables, the data obtained for the enthalpies at the inlet temperature of 500°C and a pressure of 600 kPa is:
\(\mathtt{h_1 : 3482.7 \ kJ/kg}\)
The turbine expansion process is also the isentropic process, as such:
Inlet entropy \(\mathbf{s_1}\) = Exit entropy \(\mathbf{s_2}\)
The data obtained from the steam table for \(\mathbf{s_1}\) = 8.003 kJ/kg.K
\(s_2 = s_{f2}+ x_2 *s_{fg2}\)
The data obtained from the steam tables for this entities are as follows:
\(\mathsf{s_{f2} = 0.638 \ kJ/Kg/K }\)
\(\mathtt{s_{fg2}=7.528 \ kJ/kg/K}\)
since \(\mathbf{s_1}\) = \(\mathbf{s_2}\) = 8.003 kJ/kg.K
Therefore;
\(8.003 = 0.638 + x_2 * 7.528\)
\(8.003 -0.638 = 7.528x_2\)
\(7.365= 7.528x_2\)
\(x_ 2= \dfrac{ 7.365}{7.528}\)
\(x_2 = 0.978\)
From the steam tables, the data obtained for the enthalpies at the exit temperature of 45°C and a pressure of 600 kPa is:
\(h_{f2}\) = 188.4
\(h_{fg2\) =2394.9
Thus;
\(h_ 2= 188.4 +0.978*2394.9\)
\(h_ 2=2530.61\) kJ/kg
The workdone for the turbine process can be computed as:
\(\mathsf{W_t = m(h1-h_2)}\)
\(\mathsf{W_t = 11(3482.7-2530.61)}\)
\(\mathsf{W_t = 11(952.09)}\)
\(\mathsf{W_t = 10472.99}\) kW
To MW, we have
\(\mathbf{W_t = 10.47299 \ kW}\)
In poor weather you should___ your following distance
Answers
"Regression) What percent of work satisfaction is explained by interest and wage? (Write your answer as a decimal with one place after zero. For example, if you get 0.1243 then write 12.4). Please enter a valid real number.
Answers
90.2% the proportion of job happiness that can be accounted for by interest. Similar to the majority of multivariate statistics, regression analysis.
Enables you to infer that two or more variables are related to one another. As numerous variables, not only the ones being researched, create variance, these connections are rarely exact. If you claim that students who study more earn better grades, you are actually speculating that there is a favourable correlation between studying and grades. By collecting a sample of data from a small number of students and using regression analysis to see whether the association in the sample is strong enough to infer that there is a relationship in the population, you can then complete your inference and test your hypothesis.
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Rocks in mountains can be weathered by breaking them apart. How can they be eroded?
A. Pieces of rocks are moved by the deep roots of plants.
B. Pieces of rocks are moved by water and gravity.
C. Rocks expand by the temperature changes in the mountains.
D. Rocks are smoothed by the flowing water and ice.
NO LINKS PLEASE!
Answers
Answer: If you look up its definition of eroded it'll tell you the answer should be B
Explanation:
T or F Often, parallel compressor systems employ a satellite or booster compressor.
Answers
The statement is True, parallel compressor systems often employ a satellite or booster compressor.
In parallel compressor systems, multiple compressors are used together to provide the required refrigeration capacity. These systems are commonly used in large-scale industrial and commercial refrigeration applications. In such systems, it is common to include a satellite or booster compressor.
A satellite or booster compressor is an additional compressor that works in conjunction with the main compressors in the parallel system. Its purpose is to provide additional refrigeration capacity and improve system efficiency. The satellite compressor is typically smaller in size compared to the main compressors and is strategically positioned within the system to optimize refrigerant flow and balance the load among the compressors. The use of a satellite or booster compressor in a parallel compressor system allows for better control over refrigeration capacity modulation, enhanced system performance, and improved energy efficiency.
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Hard steering can be caused by
Answers
Answer:
Lack of fluid oil – lack of fluid oil in your vehicle, or a fluid leakage, can lead to heavy steering. If there is a lack of fluid oil, or a leak, this can reduce the pressure in the system, meaning the steering wheel does not receive enough supply of fluid to perform freely.
Hey guys can anyone list chemical engineering advancement that has been discovered within the past 20 years
Answers
Nanopesticides. The world population keeps growing. ...
Enantio selective organocatalysis. ...
Solid-state batteries. ...
Flow Chemistry. ...
Porous material for Water Harvesting. ...
Directed evolution of selective enzymes. ...
From plastics to monomers. ...
Tech A says that LED brake lights illuminate faster than incandescent bulbs. Tech B says that LED brake lights have
more visibility and last longer. Who is correct?
Answers
Answer:
Both
Explanation:
Hi,
I'm paying for this monthly and I'm receiving this upgrade message.
Answers
I'm here if you need help with a math question
when sizing beams, you should stick with 2x6 to 2x12 members because:
Answers
When sizing beams, you should stick with 2x6 to 2x12 members because they are readily available and easy to handle. You may have to consider larger size members when spans exceed the lengths that 2x6 to 2x12 can handle. In addition, larger size members may be required to support the load carried by a beam.
The size of beams used in construction varies depending on the span, the weight of the load it is going to support, the species of lumber used, and the spacing between joists.Consequently, larger beams may be necessary to support larger loads or spans. Furthermore, larger beams may be necessary to support the load carried by a beam. Typically, 2x6 to 2x12 is the most commonly used beam size due to their availability and ease of handling.
In summary, it's recommended that you stick to 2x6 to 2x12 beam sizes when sizing beams due to their ease of handling and availability. Nevertheless, when spans exceed the lengths that 2x6 to 2x12 can handle, larger size members may be needed.
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write a program that prompts the user to enter the month and year and displays the number of days in the example, if the user entered month 2 and year 2012, the program should display
Answers
To write a program that prompts the user to enter the month and year and displays the number of days,
Begin by prompting the user to enter the month and year . Read the values entered by the user. Determine if the year is a leap year or not. A leap year is divisible by 4 but not divisible by 100, unless it is also divisible by 400. This is important because February can have 28 or 29 days depending on whether it's a leap year or not. Based on the month entered by the user, calculate the number of days in that month. For example, January, March, May, July,
August, October, and December each have 31 days, while April, June, September, and November each have 30 days. If it's February, check if it's a leap year to determine if it has 28 or 29 days. Display the number of days in the entered month to the user. Here's an example of how the main answer could be implemented in Python:
```python
# Prompt the user to enter the month and year
month = int(input("Enter the month (1-12): "))
year = int(input("Enter the year: "))
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Can someone help me plz!!
Answers
When measuring the resistance of an electrical load, connect the meter ____ the load.
Answers
Answer:
multimeter
Explanation: in parallel
How to measure the quality of the output signal in ADC?
A. Signal-to-noise ratio
B. Quantization error
C. Signal-to-quantization-noise ratio
D. Bit error rate
Answers
Answer:
C. Signal-to-quantization-noise ratio
Explanation:
Is a 10 foot ladder long enough to safely reach a landing that is 9 feet above the adjacent floor
Answers
Answer:
Definitely not
Explanation:
You should have 1-2 feet of extra ladder on a flat surface so 1 foot on an adjacent floor is a no no
The Switch In The Circuit Has Been Open A Long Time Before Closing At T=0. Find 1 (T), Vclt), 11(T), 12(T) Fort 20 12 1002 20 MA
Answers
An electric circuit's state can be changed by a switch, which is a component.
Where does a switch go in a circuit?Anywhere you place the switch will cause the circuit to operate. A requirement of the electrical code for residential wiring is that the switch must always be placed between the hot conductor and the load. Safety justifies this.An electric circuit's switches are used to turn on or off connected devices and appliances. In order to prevent the passage of the 220 V voltage carried by the live wire, which can be stopped by turning the circuit off, switches are always connected to the live wire.Most circuits have an on/off switch as the most basic form. Many circuits have switches in addition to the on/off switch that regulate the operation of the circuit or activate various aspects of the circuit.To Learn more About switch refer to;
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The Environmental Protection Agency (EPA) has standards and regulations that says that the lead level in soil cannot exceed the limit of 400 parts per million (ppm) in public play areas designed for children. Mike is an inspector, and he takes 50 randomly selected soil samples from a site where they are considering building a playground.
These data show a sample mean of x = 390.25 ppm and standard deviation of Sx = 30.5 ppm. Answer the following:
1. Determine the critical t value and along with the confidence interval for 95% level of
confidence. 2. What does this interval suggest?
Answers
Answer:
See below
Explanation:
Check One-Sample T-Interval Conditions
Random Sample? √
Sample Size ≥30? √
Independent? √
Population Standard Deviation Unknown? √
One-Sample T-Interval Information
Formula --> \(CI=\bar{x}\pm t^*(\frac{S_x}{\sqrt{n}})\)Sample Mean --> \(\bar{x}=390.25\)Critical Value --> \(t^*=2.0096\) (given \(df=n-1=50-1=49\) degrees of freedom at a 95% confidence level)Sample Size --> \(n=50\)Sample Standard Deviation --> \(S_x=30.5\)Problem 1
The critical t-value, as mentioned previously, would be \(t^*=2.0096\), making the 95% confidence interval equal to \(CI=\bar{x}\pm t^*(\frac{S_x}{\sqrt{n}})=390.25\pm2.0096(\frac{30.5}{\sqrt{50}})\approx\{381.5819,398.9181\}\)
This interval suggests that we are 95% confident that the true mean levels of lead in soil are between 381.5819 and 398.9181 parts per million (ppm), which satisfies the EPA's regulated maximum of 400 ppm.