Is CO2 Polar or Nonpolar?

Answer: CO2 is a nonpolar molecule because the charges on either side of the molecule (180˚ apart) balance each other out. 

CO2 Ball and Stick Model
CO2 Ball and Stick Model. Created with Avagadro 1.2.

Although the bonds between carbon and oxygen are polar covalent (since the difference in electronegativity is greater than .5), the bonds cancel out the pull on carbons electrons due to the linear structure. Therefore there is no region of the electron that has either more positive or negative charge. If you are interested in learning more about the structure of CO2, feel free to check out this article on the lewis structure for CO2.

Why is CO2 so important?


Carbon Cycle
Source
Carbon participates in many critical processes such as photosynthesis, thereby traveling the globe mainly through the carbon cycle. By providing a source of carbon to autotrophs (i.e. photosynthesizing organisms), CO2 allows them to continue building organic material critical to the survival of all other ecosystems. 

ALIRA Unofficial Practice Test 2

Source: The Phormio of Terence

What relationship is portrayed here?
A.) Father - Son
B.) Young Man - Slave
C.) Old Man - Slave
D.) Merchant - Consumer

“Postquam Romani expulerunt Tarquinium helium habuerunt. Tarquinius enim Etruscus fuit. Ergo Etrusci venerunt ad bellum cum Romanis.”

Source: Latin by the Natural Method, William G. Most

Why did the Etruscan’s wage war with the Romans?
A.) Glory, Land and Honor
B.) Tarquinius became King of the Romans
C.) The Romans expelled Tarquinius 
D.) The Romans rebelled from colonial rule.

Source: Lingua Latīna Per Sē Illūstrāta Pars I: Familia Rōmāna

Which of these is a interiectio?
A.) Towards the castle
B.) Alas!
C.) Bob goes to the store
D.) Running through the hills

Source: Latin Wikipedia

To what position was Zoran Milanovic elected to?
A.) Prime Minister of Croatia 
B.) Chief of Interpol 
C.) President of Croatia 
D.) He was not elected to any position. 

Who owns the gladiators?
A.) The Lanista
B.) The Magister
C.) The Editor
D.) The Fame

“Philosophiae servias oportet, ut tibi contingat vera libertas. Haec sunt uerba Senecae, octaua epistola ad Lucillum: quia uocari philosophiam scientiam ueritatis recte se habet ex secundometaphysicae, et philosophia affert delectationes mirabiles firmitate et puritate, ex decimo Ethicorum.” - Thomas Aquinas, XPOSITIO IN BOETHII DE CONSOLATIONE PHILOSOPHIAE

Who said the words: “You must engage in philosophy to find true freedom”?
A.) Aquinas
B.) Seneca
C.) Lucillus
D.) Ethicorus

“Multos dies Titus in lecto iacebat. Primo convalescere videbatur; mox tamen fiebat infirmior, nam in febrem subito inciderat. In dies morbus ingravescebat”

What is happening to Titus?

A.) He is getting wealthier
B.) His illness is getting worse
C.) His fortunes are decreasing
D.) His chairs are getting less comfortable

Source: De Rerum Natura, Selected Passages

Hieronymus writes that Titus Lucretius killed himself in the year
A.) 66
B.) 46
C.) 44
D.) 64

Tum Mānlius ōrātor animōs populī ita cōnfīrmāvit:—“Magnam calamitātem accēpimus. Oppida nostra ā Cimbrīs Teutonibusque capiuntur, agricolae interficiuntur, agrī vāstantur, cōpiae barbarōrum Rōmae adpropinquant. Itaque, nisi novīs animīs proelium novum faciēmus et Germānōs ex patriā nostrā sine morā agēmus, erit nūlla salūs fēminīs nostrīs līberīsque. Servāte līberōs! Servāte patriam! Anteā superātī sumus quia imperātōrēs nostrī fuērunt īnfīrmī. Nunc Marius, clārus imperātor, quī iam multās aliās victōriās reportāvit, legiōnēs dūcet et animōs nostrōs terrōre Cimbricō līberāre mātūrābit.”

Source: Latin for Beginners by Benjamin L. D'Ooge

Who does the speaker recommend as a savior for the republic?
A.) Manlius
B.) The King
C.) The People
D.) Marius

“Postridie corpus Titi summo honore elatum est. Praecedebant tibicines, tubicines, cornicines. In pompa erant viri taedas tenentes, mulieres nenias cantantes, actores imagines et vestimenta maiorum gerentes, mimi, lictores, fasces ferentes, familiares, amici plorantes. “      

What was not present during the event?

A.) Grieving Family Members
B.) Actors in his likeness
C.) Mimes 
D.) Political Figures      

“Sed prior effigiem tribuit successus aënam, // oraque patricius nostra dicavit honos; // adnuit hic princeps titulum poscente senatu; // respice iudicium quam grave, Musa, subis! // ingenio minuit merces properata favorem: // carminibus veniam praemia tanta negant; // et magis intento studium censore laborat, // quod legimur medio conspicimurque foro.” - Claudian, De Bello Gothico

What is described in the passage?
A.) The consequences of a great honor being bestowed upon the poet
B.) The debates of the great fathers on the expediency of the Gothic Wars
C.) A religious ceremony involving prayer to the Muses before a battle scene
D.) The challenges present within the life of a lower-class Roman citizen

Answer Key (place your cursor over the text to highlight/reveal the key):
1.) B 2.) C 3.) B 4.) C 5.) A 6.) B 7.) B 8.) C 9.) D 10.) D 11.) A

Probability Distribution Example [w/ the NYC Tree Census]

Probability distributions take samples from a population, calculating the proportions of a certain item within each sample in order to estimate the parameter proportion. The parameter proportion is defined to be the actual proportion within the sample. The sample size of the amount of samples you take from the population for each collection of items (for your estimate) has a significant impact on your ability to predict the proportion. This can be demonstrated with a simple computer simulation.

London Planetree. Source

According to the 2015 NYC Tree Census, the most popular tree is the London planetree with 87014 member out of a total of 683788 total individual trees. This means our true parameter is 12.7%. In order to better estimate the figure from our proportion distribution, we will need to essentially make sure our probability distribution is normal.


This is accomplished via the normality test which states that: n*p >= 10 && n*(1-p) >= 10

where n is the sample size and p is the true proportion (parameter). If you aren't sure what p is, you will eventually reach a normal curve by increasing the sample size and re-running your simulation. You will also want to make sure that you are drawing samples from the same population each time you draw a sample (maintaining independence).

This principle is at work in the following example with the London planetrees:

Proportion of the London Planetree in the 2015 NYC Tree Census (n=5)

Since 5*.127 is not greater than ten, this simulation produces a graph that lacks normality.

Proportion of London Planetree in the 2015 NYC Tree Census (n=20)

Although 20*.127 is still not greater than ten, this simulation produces a graph that is closer to normal and less skewed than the previous example. This indicates that we are closer to achieving to our goal as we increase sample size. 

Proportion of London Planetree in the 2015 NYC Tree Census (n=200)

Since 200*.127>10, the condition for normality has been reached and we can form better estimates for the actual parameter proportion. 

Bonus Graphs (Sample Proportions for the 1995 and 2005 Census):

Proportion of London Planetree in the 2005 NYC Tree Census (n=200)

Proportion of London Planetree in the 1995 NYC Tree Census (n=200)
Feel free to remix the code with the three different datasets to try out these simulations for yourself (i.e. utilizing simulations for probability distributions).

Program Code


import pandas as pd
import matplotlib.pyplot as plt
from collections import Counter 
import numpy as np
from numpy.random import choice

def getKey(item):
    return item[1]

def main():
    treeStuff = pd.read_csv("new_york_tree_census_2015.csv")
    treeSpecies = list(treeStuff["spc_common"])
    treeSpeciesCombined = Counter(treeSpecies)
    j = sorted(treeSpeciesCombined.items(),key=getKey)
    treeSpecies2 = []
    treeCount = []
    for i in j:
        i = list(i)
        if (isinstance(i[0],float)):
            i[0] = "Unknown"
        treeSpecies2.append(i[0])
        treeCount.append(i[1])
    counts = []
    for k in range(0,1000):
        draw = choice(treeSpecies2, 200, p = [x / float(sum(treeCount)) for x in treeCount]) # where you set sample size
        count = sum(np.char.count(draw,sub="London planetree"))
        counts.append(count/float(len(draw)))
    probabilities = Counter(counts)
    l = sorted(probabilities.items())
    probCategories = []
    probValues = []
    for r in l:
        r = list(r)
        probCategories.append(r[0])
        probValues.append(r[1])
    x_pos = [e for e, _ in enumerate(probCategories)]
    plt.xticks(x_pos, probCategories,rotation='vertical')
    plt.xlabel("Proportion of London Planetree in a Sample")
    plt.ylabel("Number of Samples")
    plt.title("1000 Simple Random Sample's from 2015 NY Tree Census (n=200)")
    plt.bar(x_pos,probValues)
    plt.show()
    
main()

Data Source: See this file on Kaggle for the NYC Tree Census Data.