A student takes 60 voltages readings across a resistor and finds a mean voltage of 2.501V with a sample standard deviation of 0.113V. Assuming that errors are due to random processes, how many of the readings are expected to be greater than 2.70V?

Answers

Answer 1
Answer:

Answer:

There are 2 expected readings greater than 2.70 V

Solution:

As per the question:

Total no. of readings, n = 60 V

Mean of the voltage, \mu = 2.501 V

standard deviation, \sigma = 0.113 V

Now, to find the no. of readings greater than 2.70 V, we find:

The probability of the readings less than 2.70 V, P(X\leq 2.70):

z = (x - \mu)/(\sigma) = (2.70 - 2.501)/(0.113) = 1.761

Now, from the Probability table of standard normal distribution:

P(z\leq 1.761) = 0.9608

Now,

P(X\geq 2.70) = 1 - P(X\leq 2.70) = 1 - 0.9608 = 0.0392 = 3.92%

Now, for the expected no. of readings greater than 2.70 V:

P(X\geq 2.70) = (No.\ of\ readings\ expected\ to\ be\ greater\ than\ 2.70\ V)/(Total\ no.\ of\ readings)

No. of readings expected to be greater than 2.70 V = P(X\geq 2.70)* Total\ no.\ of\ readings

No. of readings expected to be greater than 2.70 V = 0.0392* 60 = 2.352 ≈ 2


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1.19. A gas is confined in a 0.47 m diameter cylinder by a piston, on which rests a weight. The mass of the piston and weight together is 150 kg. The local acceleration of gravity is 9.813 m·s−2, and atmospheric pressure is 101.57 kPa. (a) What is the force in newtons exerted on the gas by the atmosphere, the piston, and the weight, assuming no friction between the piston and cylinder? (b) What is the pressure of the gas in kPa? (c) If the gas in the cylinder is heated, it expands, pushing the piston and weight upward. If the piston and weight are raised 0.83 m, what is the work done by the gas in kJ? What is the change in potential energy of the piston and weight?\

Answers

In this exercise we have to use the knowledge of force to calculate the required energies, so we have to:

a) 19094 N

b) 110.055 kPa

c) 1222 J

What is the concept of force?

In the field of physics, force is a physical action that causes deformation or that changes the state of rest or movement of a given object.

a) Knowing that the force formula is defined by:

F = P + p * A\nF = m * g + p *\pi /4 * d^2\nF = 150 * 9.813 + 101570 * \pi /4 * 0.47^2 = 19094 N

b) Knowing that the force exerted by an area is equal to the pressure in that area, we have:

p_1 = F / A\np_1 = F / (\pi /4 * d^2)\np_1 = 19094 / (\pi /4 * 0.47^2) = 110055 Pa = 110.055 kPa

c)So calculating the potential energy we have:

\Delta E_p = m * g * \Delta h\n\Delta E_p = 150 * 9.813 * 0.83 = 1222 J

See more about force at brainly.com/question/26115859

Answer:

a) 19094 N

b) 110.055 kPa

c) 1222 J

Explanation:

The force on the gas is the weight plus the atmospheric pressure multiplied by the piston area

F = P + p * A

F = m * g + p * π/4 * d^2

F = 150 * 9.813 + 101570 * π/4 * 0.47^2 = 19094 N

The pressure is the force divided by the area of the piston

p1 = F / A

p1 = F / (π/4 * d^2)

p1 = 19094 / (π/4 * 0.47^2) = 110055 Pa = 110.055 kPa

variation of gravitational potential energy is defined as

ΔEp = m * g * Δh

ΔEp = 150 * 9.813 * 0.83 = 1222 J

A rectangular channel with a width of 2 m is carrying 15 m3/s. What are the critical depth and the flow velocity

Answers

Answer:

The critical depth of the rectangular channel is approximately 1.790 meters.

The flow velocity in the rectangular channel is 4.190 meters per second.

Explanation:

From Open Channel Theory we know that critical depth of the rectangular channel (y_(c)), measured in meters, is calculated by using this equation:

y_(c) = \sqrt[3]{(\dot V^(2))/(g\cdot b^(2)) }(Eq. 1)

Where:

\dot V - Volume flow rate, measured in cubic meters per second.

g - Gravitational acceleration, measured in meters per square second.

b - Channel width, measured in meters.

If we know that \dot V = 15\,(m^(3))/(s), g = 9.807\,(m)/(s^(2)) and b = 2\,m, then the critical depth is:

y_(c) = \sqrt[3]{(\left(15\,(m^(3))/(s) \right)^(2))/(\left(9.807\,(m)/(s^(2)) \right)\cdot (2\,m)^(2)) }

y_(c) \approx 1.790\,m

The critical depth of the rectangular channel is approximately 1.790 meters.

Lastly, the flow velocity (v), measured in meters, is obtained from this formula:

v = (\dot V)/(b\cdot y_(c))(Eq. 2)

If we know that \dot V = 15\,(m^(3))/(s), b = 2\,m and y_(c) = 1.790\,m, then the flow velocity in the rectangular channel is:

v = (15\,(m^(2))/(s) )/((2\,m)\cdot (1.790\,m))

v = 4.190\,(m)/(s)

The flow velocity in the rectangular channel is 4.190 meters per second.

The Clausius inequality expresses which of the following laws? i. Law of Conservation of Mass ii. Law of Conservation of Energy iii. First Law of Thermodynamics iv. Second Law of Thermodynamics

Answers

Answer:

(iv) second law of thermodynamics

Explanation:

The Clausius  inequality expresses the second law of thermodynamics it applies to the real engine cycle.It is defined as the cycle integral of change in entropy of a reversible system is zero. It is nothing but mathematical form of second law of thermodynamics . It also states that for irreversible process the cyclic integral of change in entropy is less than zero

Write a program to accept a one-line string (maximum of 100 characters) from the keyboard. Edit the string entered in Part 1a (with code that you write) to remove all the white space,digits, punctuation, and other special characters, leaving only the letters. Print out the resulting compressed string to the screen.

Answers

Answer:

// This program is written in C++ programming language

// Comments are used for explanatory purpose

/* The aim of this program is to to remove all the white space,digits, punctuation, and other special characters, leaving only the letters. */

// Program starts here

#include <stdio.h>

#include<iostream>

using namespace std;

int main()

{

// Declare Variable of 100 characters

char word[100];

// Prompt user for input

cout<<"Your input goes here (max, 100 characters)";

cin>>word;

// Iterate through string to check for non alphabetic characters

for (int i = 0; word[i] != '\0'; ++i) {

// Check for uppercase and lowercase letters

while (!((word[i] >= 'a' && word[i] <= 'z') || (word[i] >= 'A' && word[i] <= 'Z') || word[i] == '\0')) {

for (int j = i; word[j] != '\0'; ++j) {

word[j] = word[j + 1];

}

word[j] = '\0';

}

}

cout<<"The resulting compressed string: "<<word;

return 0;

}

Answer:

w = str(input("input your values: "))

values = ' '.join(filter(str.isalpha, w))

while len(w) < 100:

       print(values)

       break

Explanation:

The code is written in python

w = str(input("input your values: "))

This code ask the user to input any string values with characters, numbers, line spaces , letters etc.

values = ' '.join(filter(str.isalpha, w))

This code filters the inputted value to bring only letters. All the letter are then joined together

while len(w) < 100:

The code check if the inputted value is less than 100 characters. While it is less than 100 characters. If it is less than 100 character the next code will function.

print(values)

This code prints the joined letters after checking with  a while loop to confirm the length of character is less than 100

break

The break function breaks the code whether it print the values or not.

Generally, the letters will only be printed if the character inputted is less than 100 and later break the while loop or will not print any letter if the character is greater than 100 and later break.

Select the true statements regarding rigid bars. a. A rigid bar can bend but does not change length.
b. A rigid bar does not bend regardless of the loads acting upon it.
c. A rigid bar deforms when experiencing applied loads.
d. A rigid bar is unable to translate or rotate about a support.
e. A rigid bar represents an object that does not experience deformation of any kind.

Answers

Answer:

option b and E are true

Explanation:

A lever is an example of a rigid bar that can rotate around a given point. In a rigid material, the existing distance does not change whenever any load is placed on it. In such a material, there can be no deformation whatsoever. Wit this explanation in mind:

option a is incorrect, given that we already learnt that no deformation of any kind happens in a rigid bar.

option b is true. A rigid bar remains unchanged regardless of the load that it carries.

option c is incorrect, a rigid bar does not deform with loads on it

option d is incorrect. A lever is a type of rigid bar, a rigid bar can rotate around a support.

option e is true. A rigid bar would not experience any deformation whatsoever.

A power plant burns natural gas to supply heat to a heat engine which rejects heat to the adjacent river. The power plant produces 800 MW of electrical power and has a thermal efficiency of 38%. Determine the heat transfer rates from the natural gas and to the river, in MW.

Answers

A. The heat transfer rate from natural gas is 2105.26 MW

B. The heat transfer rate to river is 1305.26 MW

Efficiency formula

Efficiency = (power output / power input) × 100

A. How to determine the heat transfer from natural gas

  • Efficiency = 38%
  • Power output = 800 MW
  • Power input =?

Power input = Power input / efficiency

Power input = 800 / 38%

Power input = 800 / 0.38

Power input = 2105.26 MW

Thus, the heat transfer from natural gas is 2105.26 MW

B. How to determine the heat transfer to the river

  • Total heat = 2105.26 MW
  • Heat used by plant = 800 MW
  • Heat to the river =?

Heat to the river = 2105.26 – 800

Heat to the river = 1305.26 MW

Learn more about efficiency:

brainly.com/question/2009210

Answer:

heat transfer from natural gas is 2105.26 MW

heat transfer to river is 1305.26 MW

Explanation:

given data

power output Wn = 800 MW

efficiency = 38%

solution

we know that efficiency is express as

\eta = (Wn)/(Qin)    ......................1

put here value we get

38% = (800)/(Qin)  

Qin  = 2105.26 MW

so heat supply is 2105.26

so we can say

Wn = Qin - Qout

800 = 2105.26 - Qout

Qout = 2105.26 - 800

Qout = 1305.26 MW

so heat transfer from natural gas is 2105.26 MW

and heat transfer to river is 1305.26 MW

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