Let Σ = {a} be a one-element alphabet and L ⊆ Σ^* be an arbitrary language over Σ = {a}. Show that L^* is regular [duplicate]

Answers

Answer 1

To show that L^* is regular, we need to construct a regular expression or a finite automaton that accepts L^*. Let's start by defining L^* as the set of all possible concatenations of strings in L, including the empty string.



Since Σ is a one-element alphabet, L can only contain strings of the form a^n, where n is a non-negative integer. Thus, L^* can be expressed as the set of all possible combinations of strings in L, where each string is of the form a^n.

To construct a regular expression for L^*, we can use the formula:

L^* = ε + L + LL + LLL + ...

where ε represents the empty string, and the concatenation operator (+) represents the union of all possible combinations of strings in L.

To construct a finite automaton for L^*, we can start with a single state, which is the initial and accepting state. From this state, we can add transitions to itself for each possible string in L. We can continue adding transitions for each combination of strings in L until we have covered all possible concatenations.

Overall, both the regular expression and the finite automaton for L^* can be easily constructed, demonstrating that L^* is indeed a regular language.

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Answer 2

This is a classic problem in formal language theory, and the fact that L^* is regular for any language L over a one-element alphabet is a well-known result. Here's a proof:

Let's start by defining a regular expression R for L. Since Σ = {a}, R can only contain the symbol a, along with the usual operators (concatenation, union, and Kleene star). We can assume that R is in a particular normal form (such as the star normal form or the sum of products normal form), which guarantees that R can be expressed as a finite sum of products of symbols from Σ and operators. For example, if L is the language of all strings that contain at least two a's, we can take R = aaa*.

Now consider the language L^. By definition, L^ is the set of all strings that can be formed by concatenating zero or more strings from L. We can express L^* as the union of all possible powers of L:

L^* = ∪_{i≥0} L^i

where L^i is the set of all strings that can be formed by concatenating i strings from L. In other words, L^i is the i-th power of L.

Let's focus on a particular power L^i, for some i ≥ 0. We can think of L^i as the language of all strings that can be formed by concatenating i copies of strings from L. For example, if L is the language of all strings that contain at least two a's, then L^2 is the language of all strings that contain at least four a's.

We can express L^i as the concatenation of i copies of L:

L^i = L.L.L...L (i times)

Using the regular expression R for L, we can express each copy of L as a concatenation of symbols from Σ and operators:

L = R

Therefore, we can express L^i as a finite sum of products of symbols from Σ and operators, each product having i factors:

L^i = R.R.R...R (i times)

Since there are only finitely many products of symbols and operators involved, we can combine them all into a single regular expression S for L^*, using the union operator:

S = ∪_{i≥0} L^i

This expression S represents the language L^*, which is therefore regular.

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Related Questions

When making routine transponder code changes, pilots should avoid inadvertent selection of which code?

Answers

When making routine transponder code changes, pilots should avoid inadvertent selection of  code. 7700.

What are the  transponder code that pilot  should  avoid?

Under normal as well as non-emergency operations, it is very essential  for pilot to make sure he  avoid using the transponder codes of 7500,  as well as 7600, and 7700.

Especially  while switching  codes,  It is easy in switching by  pilot to  go to of these 3 codes on accident.

In this case, When making routine transponder code changes, pilots should avoid inadvertent selection of  code. 7700.

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Which data protection process provides prebuilt capabilities, mapped to specific regulations, to create the necessary resources to implement and demonstrate compliance with these regulations

Answers

The data protection process  that provides prebuilt capabilities, mapped to specific regulations, to create the necessary resources to implement and demonstrate compliance with these regulations is known as The European Union General Data Protection Regulation (GDPR).

Who are held responsible for your compliance with data protection laws and processes?

Employers are known to be people who must be held accountable for data processing works while also working and complying with data protection principles.

The General Data Protection Regulation (GDPR) is known to be one of the hardest privacy and security law in the globe as it is known to be a body that imposes obligations onto its firm anywhere.

Hence, The data protection process  that provides prebuilt capabilities, mapped to specific regulations, to create the necessary resources to implement and demonstrate compliance with these regulations is known as The European Union General Data Protection Regulation (GDPR).

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We initialize the parameters to all zero values and run the linear perceptron algorithm through these points in a particular order until convergence. The number of mistakes made on each point are shown in the table below. (These points correspond to the data point in the plot above)

Answers

The main aim of running the parameters in the linear perceptron algorithm is to be able to develop a machine learning algorithm for binary classification tasks.

What is a linear perceptron algorithm?

This refers to the linear classification algorithm that is used in machine learning.

This is done in order to learn a decision boundary that divides different classes using a hyperplane.

Hence, we can see that your question is incomplete because the parameters are not included, hence a general overview was given to give you a better understanding of the concept.

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scheduling is approximated by predicting the next CPU burst with an exponential average of the measured lengths of previous CPU bursts.

Answers

SJF scheduling is approximated by predicting the next CPU burst with an exponential average of the measured lengths of previous CPU bursts.

What is SJF in operating system?

SJF is a term that connote Shortest Job First. It is said to be a type of CPU scheduling whose algorithm is linked with each as it is said to process the length of the next CPU burst.

Note that for one to be able to know the time for the next CPU burst to take place, one need to take the SJF into consideration as that is its function.

Hence, SJF scheduling is approximated by predicting the next CPU burst with an exponential average of the measured lengths of previous CPU bursts.

See options below

A) Multilevel queue

B) RR

C) FCFS

D) SJF

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A _______ engine is a specialized program that assists you in locating information on the web and the internet.

Answers

Answer:

search

Explanation:

A search engine is a type of software that is used to carry out web searches. It works by "crawling" through the World Wide Web one web page at a time and indexing the pages.

To generate a control break report, your input records must be organized in ____ order based on the field that will cause the breaks.

Answers

To generate a control break report, your input records must be organized in directory order based on the field that will cause the breaks.

What is directory?

Directory serves as guide in locating a particular item.

The directory is written in a way for an individual or an employee to understand and be able to retrieved needed information.

Therefore, to generate a control break report, your input records must be organized in directory order based on the field that will cause the breaks.

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For the IPv4 CIDR address 153.10.22.56 /22 What is the... Netmask: [ Select ] Network Address: [ Select ] Host Mask: [ Select ] Broadcast Address: [ Select ] Number of possible hosts: [ Select ] Host Number: [ Select ]

Answers

Netmask:

The netmask is calculated by putting the number of 1’s equal to the given mask value (here 22).

Netmask = 11111111.11111111.11111100.00000000

= 255.255.252.0

Therefore, the netmask is equal to 255.255.252.0

Network Address:

The network address is obtained by performing the AND operation of the bits in the given IP address with the bits of the netmask.

IP address (153.10.22.56) = 10011001.00001010.00010110.00111000

Netmask (255.255.252.0) = 11111111.11111111.11111100.00000000

Network address = 10011001.00001010.00010100.00000000

= 153.10.20.0

Therefore, the network address is equal to 153.10.20.0

Host Mask:

The remaining or the unused bits in the netmask are used as the host mask. In other words, the host mask is obtained by complementing each bit of the netmask.

Netmask = 11111111.11111111.11111100.00000000

Host mask = 00000000.00000000.00000011.11111111

= 0.0.3.255

Therefore, the host mask is equal to 0.0.3.255

Broadcast address:

The broadcast address is used to send the packages to all the hosts in the network. It is obtained by setting all the bits after the network address to 1.

Network address (153.10.20.0) = 10011001.00001010.00010100.00000000

Broad cast address = 10011001.00001010.00010111.11111111

= 153.10.23.255

Therefore, the broadcast address is equal to 153.10.23.255

The number of possible hosts:

The number of possible hosts is computed as follows:

Possible hosts = 2n, where n is the number of host bits.

Out of the above 2n hosts, 2 are reserved and hence the number of usable hosts is equal to 2n – 2.

Number of hosts = 210 – 2 = 1024 – 2 = 1022

Host number:

Host number is the decimal equivalent of the host bits in the IP address.

Ip address (153.10.22.56) = 10011001.00001010.00010110.00111000

Host bits = 10.00111000

Host number = 29 + 0 + 0 + 0 + 25 + 24 + 23 + 0 + 0 + 0

= 512 + 32 +16 + 8

= 568

Hence, the host number is equal to 568.

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Define a function SwapRank() that takes two char parameters passed by reference and swap the values in the two parameters. The function does not return any value. Ex: If the input is A C, then the output is: C A

Answers

The program that takes two char parameters passed by reference and swap the values in the two parameters is illustrated below.

What is a program?

A computer program is a sequence of instructions in a programming language for a computer to execute.

The program is illustrated below:

void SwapGrade(char &g1, char &g2)

{

char t = g1;

g1= g2;

g2 = t;

}

Output

B

C

C B

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The system log daemon, rsyslogd, creates a socket for other system processes to write to. what is the path to this socket?

Answers

If the system log daemon, rsyslogd, creates a socket, the path to this socket is known to be /dev/log.

What is the system log daemon?

The syslog daemon is known to be a kind of a server process that is known to often gives or provides a form of message logging tools that is made for application and system processes.

Note that the syslog daemon is said to be one that begins by the Internet Daemon and it is also one that tend to receives messages on well-known port such as  514.

Note that The syslog daemon must be on before any application program and as such, If the system log daemon, rsyslogd, creates a socket, the path to this socket is known to be /dev/log.

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See full question below

The System Log Daemon, rsyslogd, creates a socket for other system processes to write to. What is the path to this socket?

Select one:

a. /etc/rsyslog.socket

b. /var/log.sock

c. /tmp/log

d. /dev/log

What is a "Top-Level Domain Name"?

Answers

A top-level domain is known to be an aspect of a domain that quickly follows the last dot symbol that is seen in a domain name.

What is a "Top-Level Domain Name"?

This is known to be the biggest level in terms of the hierarchical Domain Name System of the Internet.

Note that TLD (top-level domain) is said to be the most generic domain that is seen on the Internet's hierarchical DNS (domain name system) as A top-level domain is known to be an aspect of a domain that quickly follows the last dot symbol that is seen in a domain name.

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True or false? you should avoid using your power point slides as handouts, according to the text.

Answers

true, you should avoid using power point notes always

What is the correct syntax for defining an __init__() method that takes no parameters?

Answers

The correct syntax for defining an __init__() method that takes no parameters is: def __init__(self): pass

What is a syntax?

The set of guidelines known as syntax establishes the meaning of the different symbol combinations.

This instructs the machine on how to decipher the code.

When writing code, the idea of syntax deals with a very precise collection of words and a very strict sequence for those words when we offer instructions to the machine.

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Assembler Language
CSCI 360-1 Assignment 4 Name_____________________
Spring 2019 ABENDs and Dump Reading
25 points
This programming assignment does not require any further coding or documentation than what is provided. The program will ABEND and your task is to learn how to investigate what happened so that you can debug your own Assembler programs in the future. To begin, run the following program on the Marist mainframe using the ASSIST JCL used previously. Be sure you type it or copy it EXACTLY as shown below:
DUMP1 CSECT
USING DUMP1,15 ESTABLISH REG 15 AS BASE REG
*
SR 2,2 CLEAR REG 2
*
LA 3,NUM1 LOAD ADDRESS OF NUM1 INTO REG 3
LA 4,NUM2 LOAD ADDRESS OF NUM2 INTO REG 4
*
A 2,0(,3) ADD NUM1 TO REG 2
A 2,0(,4) ADD NUM2 TO REG 2
*
LA 5,SUM LOAD ADDRESS OF SUM INTO REG 5
ST 2,0(,5) STORE THE SUM OF NUM1 & NUM2 AT SUM
*
XDUMP , SET REG 2 TO 35
*
LTORG
*
SUM DC F'0' FULLWORD OF ZERO TO LATER HOLD SUM
*
NUM1 DC F'1206000000' VARIOUS FULLWORD INTEGER VALUES
NUM2 DC F'972460'
NUM3 DC F'1344335922'
*
END DUMP1
Use the resulting ABEND dump output to answer the questions below. Each is worth 2 points except question 11 which is worth 5 points.
Did this error occur (a) while the program was being assembled or (b) when it was being run?
________________________________________________________________________________
What is the address of the next instruction which would have been executed?________________________________________________________________________________
What is the value of the condition code at the time of the ABEND?
________________________________________________________________________________
What is the length of the instruction that caused the ABEND (number of bytes)?
_______________________________________________________________________________
What is the address of the instruction that caused the abend?
_________________________________________________________________________________
What type of error occurred (number and name)?
_________________________________________________________________________________
What usually causes this error?
_________________________________________________________________________________
What does the value in register 2 represent at the time of the ABEND dump?
__________________________________________________________________________________
What instruction needs to be added to fix this ABEND?
_________________________________________________________________________________
What does the value stored at location counter value 00002C represent?
_________________________________________________________________________________
What exactly happened here to cause the ABEND? Be detailed but succinct in your description.
_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________

_________________________________________________________________________________

Answers

hello thnks

Explanation:

Write the first line of a function named Days. The function should return an integer value. It should have three integer parameters: intYears, intMonths, and intWeeks. All arguments should be passed by value.

Answers

Answer:

Program:

Module Module1

Function Days(intYears As Integer, intMonths As Integer, intWeeks As Integer) As Integer

' 1 year = 365days

' 1 month=30.417 days

' 1 week = 7 days

Days = 365 * intYears + 30.417 * intMonths + 7 * intWeeks

End Function

Sub Main()

Dim years, months, weeks As Integer

Console.Write("Enter the number of years: ")

years = Convert.ToInt32(Console.ReadLine())

Console.Write("Enter the number of months: ")

months = Convert.ToInt32(Console.ReadLine())

Console.Write("Enter the number of weeks: ")

weeks = Convert.ToInt32(Console.ReadLine())

Console.WriteLine("Days: " & Days(years, months, weeks))

Console.ReadKey()

End Sub

End Module

which computer can be used where is no electricity ?​

Answers

Answer:

mechanical computers

Explanation:

A mechanical computer is built from mechanical components such as levers and gears rather than electronic components. The most common examples are adding machines and mechanical counters, which use the turning of gears to increment output displays.

Answer:

Non-electric computers.

A mechanical computer is a computer built from mechanical components such as levers and gears rather than electronic components

The command-line interface tells a user that it's ready to receive commands by displaying a specific set of characters called a(n) _____

Answers

Answer:

it's called the prompt, mean yeah

During the merge sort operation for the list {90 7 9 43 62 12 21 36}, at what left and right partition position is 21 added to the temporary list

Answers

The point at left and right partition position to add 21 is Left position is 1 and right position is 7.

How do you solve merge sort?

The Algorithm for Merge Sort operations are:

First one need to find the middle index of the array. Then one has to Divide the array from the middle. Then do Call merge sort for the second half of the array. Then one can finally merge two sorted halves into one sorted array.

Hence, The point at left and right partition position to add 21 is Left position is 1 and right position is 7.

See Group of answer choices

Left position is 2 and right position is 6

Left position is 1 and right position is 7

Left position is 4 and right position is 7

Left position is 2 and right position is 5

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The cell tower’s base transmission station is connected to a mobile ____ station.

Answers

The cell tower’s base transmission station is connected to a mobile switching station.

What is a switching station?

A switching station is known to be a kind of a substation that is known to be without transformers and it is one that often operate  only based or at a single voltage level.

Note that Switching stations are known to be often used as collector and they also acts as a distribution stations.

Hence,  The cell tower’s base transmission station is connected to a mobile switching station.

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A touch screen _____.

Answers

A touch screen is known to be a kind of a display device that gives room for its users to be able to interact with a computer through the use of their finger or stylus.

What is a Touch Screen?

Touch screen are regarded as output device as a person can be able to touch and  use screen that displays the content in their mobile.

Hence, A touch screen is known to be a kind of a display device that gives room for its users to be able to interact with a computer through the use of their finger or stylus.

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If you try to add a new item to a full stack the resulting condition is called a(n)?

Answers

Answer:

it's called an overflow

The _________________ can be used to repair common causes of unbootable operating systems. It is based on the Windows Preinstallation Environment (Windows PE).

Answers

The Windows Recovery Environment (Windows RE or WinRE) can be used to repair common causes of unbootable operating systems. It is based on the Windows Preinstallation Environment (Windows PE).

What can be used to repair common causes of unbootable operating system?

The use of the Windows Recovery Environment (WinRE) is known to be a kind of tools that is often used in the recovery environment that is said to often helps in the repair of the common issues of unbootable operating systems.

Hence, The Windows Recovery Environment (Windows RE or WinRE) can be used to repair common causes of unbootable operating systems. It is based on the Windows Preinstallation Environment (Windows PE).

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What are the three advantages of using blockchain technology? multiple choice all of the answer choices are correct. digital trust internet of things integration immutability

Answers

The  three advantages of using blockchain technology are:

digital trust internet of thingsimmutability

What is blockchain technology?

A Blockchain is known to be a kind of a chain of blocks that is made up of information.

Note that the data that are said to be stored inside a block is one that is based on the type of blockchain. Blockchain  is seen as a kind of a shared, form of immutable ledger that quickens the process of putting down or recording transactions and helps in the tracking of assets in a business network.

Hence, The  three advantages of using blockchain technology are:

digital trust internet of thingsimmutability

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You have a user remotely connecting to the corporate network from a client location. They can connect to the corporate network file server. But they cannot access files and folders they need on the client LAN in order to work on their project. What would you enable in order to allow the user to access resources on both networks while the VPN is connected

Answers

I don't really get this question but I will go with hotspot

When using spanning tree protocol. What is the first step in selecting paths through a network?

Answers

The first step in selecting paths through a network is STP must first select the root bridge, or master bridge.

Which one is the first step in STP operation?

The STP network convergence consists in three steps: elect a root bridge, elect root ports and elect designated and non-designated ports. When you enable STP, the first step in its convergence process is to elect a switch to act as a root bridge using the Spanning Tree Algorithm.

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Computer professionals known as software engineers, or Blank______, use the software development life cycle to create software required for information systems.

Answers

Answer:

Computer professionals known as software engineers, or programmers use the software development life cycle to create software required for information systems.

Explanation:

Computer professionals are called software engineers and programmers because they develop and program software. Some additional titles for computer professionals are hardware engineers and iOS/Android developers.

Output values below an amount Write a program that first gets a list of integers from input. The input begins with an integer indicating the number of integers that follow. Then, get the last value from the input, which indicates a threshold. Output all integers less than or equal to that last threshold value. Assume that the list will always contain fewer than 20 integers. java

Answers

The program that first gets a list of integers from input, gets the last value from the input, which indicates a threshold, and outputs all integers less than or equal to that last threshold value is:

import java.util.Scanner;

public class LabProgram {

 /* Define your methods here */

public static void main(String[] args) {

Scanner scnr = new Scanner(System.in);

int[] userValues = new int[20];

int upperThreshold;

int numVals;

numVals = scnr.nextInt();

GetUserValues(userValues, numVals, scnr);

upperThreshold = scnr.nextInt();

OutputIntsLessThanOrEqualToThreshold(userValues, numVals, upperThreshold);

}

}

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Define a function Output Value() that takes two integer parameters and outputs the sum of all negative integers starting with the first and ending with the second parameter. If no negative integers exist, sum is 0. End with a newline. The function does not return any value. Ex: If the input is -7 1, then the output is: -28 Note: Negative numbers are less than 0.

Answers

The function is written in C++ programming language and is be displayed below:

long OutputVal(int start, int end) {

 long result = 1;

 for (int num = start; num <= end; num++) {

   result *= num;

 }

 return result;

}

The program defines a function Output Value(), takes two integer parameters, and outputs the sum of all negative integers starting with the first and ending with the second parameter.

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When posting to a professional networking account, you should share stories and comments that _____.

Answers

When posting to a professional networking account, you should share stories and comments that  Offer valuable information to your target audience

What is meant by a professional networking account?

This is used to refer to an account that has a large number of audiences or of people who follow the account based on what the owner of the network offers. The reason for this may be due to the fact that account is a blog that talks about health or about lifestyle.

It is advised that the person who is behind the account keep the people that are his audiences in mind whenever he is sharing posts to the account. The information that would be most useful to the people has to be considered.

Hence we can say that When posting to a professional networking account, you should share stories and comments that  Offer valuable information to your target audience

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Javascript is an object-based programming language that involves working with the properties and methods associated with objects.
a) True
b) False

Answers

Answer:

True

Explanation:

You can set variables and make method functions.

In cell H5, create a formula to divide the value in cell F5 by cell F12 using relative cell references.

Answers

The Excel formula to enter in cell H5 using the relative style of cell referencing is = F5/F12

What are Excel formulas?

Excel formulas are expressions or equations used alongside Excel functions to perform arithmetic and logical formulas for computation.

How to create the Excel formula to enter in cell H5?

From the question, we understand that we are to make use of the relative style of referencing

This means that we make use of the cell name as it is, without adding the  "$" sign, as it is in absolute style of cell referencing and mixed style of cell referencing

So, we make use of cell F5 as F5 and we make use of cell F12 as F12

The value in cell F5 divided by cell F12 using relative cell references is represented as:

F5 divided by F12

Rewrite the above formula as follows:

F5/F12

Excel formulas begin with the "=' sign

So, the above formula becomes

= F5/F12

Hence, the Excel formula to enter in cell H5 using the relative style of cell referencing is = F5/F12

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Linux and Mac computers usually do not come with Python installed. PLEASE Help with question 16 The breaking strengthX[kg]of a certain type of plastic block is normally distributed with a mean of1250kgand a standard deviation of5.5kg. What is the maximum load such that we can expect no more than55% of the blocks to break? Calculate the monthly payment for a loan of $7,500 with an 11% interest rate compounded monthly over a period of 5 years. A. $128. 46 b. $163. 07 c. $858. 18 d. $1,541. 50 Please select the best answer from the choices provided A B C D. write out the first five terms of the sequence with, [ln(n)n 1]n=1[infinity], determine whether the sequence converges, and if so find its limit. Analysis Fabider love SHORT STORY ANALYSIS Author: Describe the themes of forbidden love by Can Themba The jet engine has angular acceleration of -2.5 rad/s2. Which one of the following statements is correct concerning this situation? 1. The direction of the angular acceleration is counterclockwise. 2. The direction of the angular velocity must be clockwise. 3. The angular velocity must be decreasing as time passes. 4. If the angular velocity is clockwise, then its magnitude must increase as time passes. 5. If the angular velocity is counterclockwise, then its magnitude must increase as time passes. When the earth revolves around the sun its axis always titles in the same direction if the axis is not tilted toward or away from the sun witch season could it be select all that apply 1.spring 2.fall 3.winter 4.summer TRUE/FALSE. (F) = 0. (Justify your answer by showing it is true or falsefor vector elds of the form F = Fi + Gj.) According to the SCOTUS, all rights are absolute with no exceptionsTrueFalse There are so many bird-cherries round me, great trees with branches sweeping the grass, and they are so wreathed just now with white blossoms and tenderest green that the garden looks like a wedding. I never saw such masses of them; they seem to fill the place. Even across a little stream that bounds the garden on the east, and right in the middle of the cornfield beyond, there is an immense one, a picture of grace and glory against the cold blue of the spring sky.My garden is surrounded by cornfields and meadows, and beyond are great stretches of sandy heath and pine-forests, and where the forests leave off the bare heath begins again; but the forests are beautiful in their lofty, pink-stemmed vastness, far overhead the crowns of softest grey-green, and underfoot a bright green whortleberry carpet, and everywhere the breathless silence; and the bare heaths are beautiful too, for one can see across them into eternity almost. For endangered species, like the Eastern Lowland Gorilla, one aspect that interests conservationists and zoologists is the survival time, in months, of the females upon reaching sexual maturity. Survival time, in this example, is the technical term for saying "how much longer will a female Eastern Lowland Gorilla live after reaching sexual maturity?" One statistical model used to model survival times is the exponential distribution. what is the longest-wavelength em radiation (in nm) that can eject a photoelectron from osmium, given that the binding energy is 5.93 ev? nm is this in the visible range? yes no