Preview
Rafael G. Nendel Flores, Esq., SBN 223358
Guillermo Tdllo, Esq., SBN 277896
Katie Sharpless, Esq., SBN 335463
Alejandro Rosa, Esq., SBN: 340410
CLARK HILL LLP
555 South Flower Street, 24" Floor
LosA! les, CA_ 90071
Telephone: (213) 891-9100
Facsimile: (213) 488-1178
mendelflores@ClarkHill.com
o@ClarkHill.com
ksharpless@ClarkHill.com
arosa@ClarkHill.com
Attol for Defendant
VARSITY TUTORS LLC
SUPERIOR COURT THE STATE OF CALIFORNIA
COUNTY OF SANTA CLARA.
ALEXANDER CHARLES and HENRY Case No.: 19CV347249
MULAK, as individuals,
[Assignedto Hon. Theodore C. Zayner,
Plaintiffs,
Department 19]
VS.
APPENDIX OF EXHIBITS IN SUPPORT
VARSITY TUTORS LLC, OF DEFENDANT'S OPPOSITIONTO
PLAINTIFF’ S MOTION FOR
Defendant. SUMMARY ADJUDICATION
October18, 2023
Time: 1:30pm
Dept:
Complaint Filed: May 1, 2019
FAC: 30, 2019
Trial Date: May 13, 2024
APPENDIX OF EXHIBITS IN SUPPORT OF DEFENDANT’ S OPPOSITION TO PLAINTIFF'S MOTION FOR SUMMARY ADJUDICATION
TO ALL PARTIES AND TO THEIR ATTORNEYS OF RECORD:
Defendant Varsity Tutors LLC hereby submits the following Appendix of Exhibits pursuant to
Califomia Rules of Court 3.1350(g) in support of its Opposition to Plaintiff's Motion for Summary
Adjudication:
_ Description
A Varsity’ s Statement of Information filed with the Califomia Secretary of State on August
31, 2015.
B. Varsity’ s Answerto Plaintiff’ s First Amended Complaint filed on September 15, 2019
Excerpts of deposition testimony from Plaintiff’ s deposition day one (05/30/23)
(“Charles Depo Day 1”)
Exhibit 37 to Charles Depo Day 1
10 Excerpts of deposition testimony from Plaintiff’ s deposition day two (06/23/23)
(“Charles Depo Day 2”)
11 Excerpts of deposition testimony from Chris Swenson’ s deposition (session one)
12 Excerpts of deposition testimony from Chris Swenson’ s deposition (session two)
Session Recording and Transcript for VARSITY 062081 (V.1)
13 Session Recording and Transcript for VARSITY 062081 (V.2)
14 CHARLES-VT_022725 (Comespondence between Plaintiff and his client Jayson Smith,
dated April 29, 2020)
15 CHARLES-VT 029195 (Comespondence between Plaintiff and his private client Diane
16 Salemo (“Salemo”), dated December 12, 2018)
CHARLES-VT_029208 (Comespondence between Plaintiff and his private client
17 Salemo, dated December 28, 2018)
18 CHARLES-VT_029216-029217 (Correspondence between Plaintiff and his private
client Salemo, dated January 2, 2019)
19 CHARLES-VT_029742 (Comespondence between Plaintiff and his private client
20 Salemo, dated March 11, 2019)
CHARLES-VT_029758 (Comespondence between Plaintiff and his private client
21 Salemo, dated March 13, 2019)
CHARLES-VT_029762 (Comespondence between Plaintiff and his private client
Salemo, dated March 13, 2019)
23 CHARLES-VT 032769 (Comespondence between Plaintiff and his client DeeEllen (last
24 name unknown), dated October 23, 2018)
CHARLES-VT_033271 (Comespondence between Plaintiff and his client Pristina Koon,
25 dated July 19, 2019).
26
27
APPENDIX OF EXHIBITS IN SUPPORT OF DEFENDANT’ S OPPOSITION TO PLAINTIFF'S MOTION FOR SUMMARY ADJUDICATION
Dated: September 13, 2023 CLARK HILL LLP
py. <2 ae
Rafael Nendel-Flores
Guillermo Tello
Katie Sharpless
Alejandro Rosa
Attol for Defendant
VARSITY TUTORS LLC
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APPENDIX OF EXHIBITS IN SUPPORT OF DEFENDANT’ S OPPOSITION TO PLAINTIFF'S MOTION FOR SUMMARY ADJUDICATION
EXHIBIT A
'
a State of California
ZN A Secretary of State
sia
6
AT
Se eROY STATEMENT OF INFORMATION
FILED
Secretary of State
(Limited Liability Company)
State of Califomia .
Filing Fee $20.00, If this is an amendment, see instructions,
IMPORTANT— READ INSTRUCTIONS BEFORE COMPLETING THIS FORM AUG3 1 205
1 LIMITED LIABILITY COMPANY NAME
VARSITY TUTORS LLC
This Space For Filing Use Only
File Number and State or Place of Organization
2 ‘SECRETARY OF STATE FILE NUMBER 3, STATE OR PLACE OF ORGANIZATION (If formed outside of California)
201120910030
No Change Statement
4 If there have been any changes to the information contained in the last Statement of Information filed with the California Secretary of
State, or no Statement of Information has been previously filed, this form must be completed in its entirety.
If there has been no change in any of the information contained in the last Statement of Information filed with the California Secretary of
State, check the box and proceed to Item 15.
Complete Addresses for the Following (Do not abbreviate the name of the city. Items 5 and 7 cannot be P.O, Boxes.)
5. STREET ADDRESS OF PRINCIPAL OFFICE city STATE 2IP CODE
%%o SOUANWood Ave Ste dE ot Louis Nap
STATE
GB10S
ZIP CODE
6 MAILING ADDRESS OF LLC, IF DIFFERENT THAN ITEM 5
7. ‘STREET ADDRESS OF CALIFORNIA OFFICE, city STATE ZIP CODE
CA
Name and Complete Address of the Chief Executive Officer, If Any
NAME . ADDRESS STATE, P CODE
Chacdis Cohn bo SOuthwoo da oF Louis Mo BIOS
Name and Complete Address of Any Manager or Managers, or if None Have Been Appointed or Elected, Provide the Name and
Address of Each Member (Attach additional pages, if necessary.)
, NAME RESS ITY STATE ZIP CODE
Charis Lon onADDRESS
3D Sousthwrod Ge dE
city
St Lows Mp
STATE
BIOs
ZIP CODE
10. NAME.
1. NAME ADDRESS: cry STATE 21P CODE
Agent for Service of Process Ifthe agent is an individual, the agent must reside in California and Item 13 must be completed with a California address, a
P.O, Box is not acceptable. If the agent is a corporation, the agent must have on file with the California Secretary of State a certificate pursuant to California
Corporations Code section 1505 and Item 13 must be left blank.
12, NAME OF AGENT FOR SERVIGE OF PROCESS
Anon! (Gist é ted Agtet Ine CIAVVNIDZS
13, STREET ADDRESS OF AGENT FOR SERVICE OF eee IN CALIFORNIA, IF AN INDIVIOUAL, city STATE ZIP CODE
C,
Type of Business
14. DESCRIBE THE TYPE OF BUSINESS OF THE LIMITED LIABILITY COMPANY
ELECTRONIC DIRECTORY PUBLISHERS, EXCLUSIVELY ON INTERNET
7
16. THE INFORMATION CONTAINED HEREIN, INCLUDING ANY ATTACHMENTS, IS TRUE AND CORRECT.
07/22/2015
‘DATE
PAMELA GOODWIN
TYPE OR PRINT NAME OF PERSON COMPLETING THE FORM
ACCOUNTANT.
TITLE
a ‘SIGNATURE
LLG-12 (REV 01/2014) - = “APPROVED'BY SECRETARY OF STATE
EXHIBIT B
Electronically Filed
Rafael Nendel-Flores (State Bar No. 223358)
Rafael.Nendel-Flores@leclairryan.com by Superior Court of CA,
Guillermo M. Tello (State Bar No. 277896) County of Santa Clara,
Guillermo.Tello@leclairryan.com on 7/15/2019 6:12 PM
Yesi Lagunas (State Bar No. 316008) Reviewed By: L Del Mundo
Yesi.Lagunas@leclairryan.com Case #19CV347249
LECLAIRRYAN, LLP Envelope: 3130123
725 South Figueroa Street, Suite 350
Los Angeles, CA 90017
Telephone: (213) 488-0503
Telefax: (213) 624-3755
Attorneys for Defendant
VARSITY TUTORS LLC.
10
SUPERIOR COURT FOR THE STATE OF CALIFORNIA
11
FOR THE COUNTY OF SANTA CLARA
12
ALEXANDER CHARLES and HENRY Case No.: 19CV347249
13 MULAK, as individuals,
14 Plaintiffs, DEFENDANT VARSITY TUTORS
LLC’S ANSWER AND AFFIRMATIVE
15 vs. DEFENSES TO PLAINTIFFS
ALEXANDER CHARLES AND HENRY
16 VARSITY TUTORS LLC, MULAK’S FIRST AMENDED
COMPLAINT
17 Defendant.
Complaint Filed: May 1, 2019
18 FAC: May 30, 2019
Trial Date: Not yet set
19
20
21 Defendant, VARSITY TUTORS LLC (“Defendant” or “Varsity”), for itself alone and no
22 other defendant, hereby answers the First Amended Complaint (““Complaint” or “FAC”) filed on
23 behalf of Plaintiffs ALEXANDER CHARLES and HENRY MULAK (collectively, “Plaintiffs”)
24 on file herein, and admits, denies, and alleges as follows:
25 GENERAL DENIAL
26 Pursuant to the provisions of California Code of Civil Procedure § 431.30(d), answering
27 Defendant denies, generally and specifically, each, every, and all of the allegations contained
28 therein and specifically denies that it did or failed to do anything which in any way caused or
1
DEFENDANT VARSITY TUTORS LLC’S ANSWER AND AFFIRMATIVE DEFENSES TO PLAINTIFFS’
FIRST AMENDED COMPLAINT
contributedto the accident, event, episode, injuries, if any, or damages, if any, eitheras alleged,
otherwise
or at all; and specifically denies that Plaintiffs have been or will be damaged in any sum.
orsums, either
as alleged otherwise or at all.
Without waiving or excusing each Plaintiffs own, and representative or collective,
burden(s) of proof and production of evidence, Defendant further alleges as and for its affirmative
defenses
to all causes of action asserted against it in the Complaint:
FIRST AFFIRMATIVE DEFENSE
1 The Complaint and each cause of action therein fails to state facts sufficient to
constitute a cause of action against this answering Defendant.
10 SECOND AFFIRMATIVE DEFENSE
11 2. The causes of action alleged in the Complaint, or some of them, are barred
by the
12 applicable statutes of limitation, including, without limitation, Code of Civil Procedure §§ 335.1,
13 338 and 343, and Business and Professions Code section 17208.
14 THIRD AFFIRMATIVE DEFENSE
15 3. The causes of action alleged in the Complaint, or some or parts of them, are barred
16 or outside the jurisdiction of this Court because each Plaintiff failed to timely exhaust the
17 administrative remedies available to hinythem before bringing those claims or filing this lawsuit,
18 as required
by law, and/or those causes of action, or some or parts of them, are not within
the
19 reasonable scope of any administrative charges allegedly filed by Plaintiffs against Defendant.
20 FOURTH AFFIRMATIVE DEFENSE
21 4. The Complaint fails because Plaintiffs were properly classified as independent
contractors under the applicable Califomia law. This proper classification
was confimmed by, inter
23 alia, a determination by the Califomia Employment Development Department that tutors who
24 utilized Defendant’
s platform to secure and provide tutoring services to their clients were properly
25 Classified as independent contractors.
26 FIFTH AFFIRMATIVE DEFENSE
27 5. Even assuming that Plaintiffs were employees—they were not—the Complaint fails
to properly state a claim for penalties under Labor Code section 203 et seq. or otherwise because
2
DEFENDANT VARSITY TUTORS LLC’S ANSWER AND AFFIRMATIVE DEFENSES TO PLAINTIFFS’
FIRST AMENDED COMPLAINT
there is a bona fide good faith dispute with respect to Defendant’ s obligation to pay any wages that
may be found
due.
SIXTH AFFIRMATIVE DEFENSE
6. Defendant did not employ Plaintiffs and therefore no employment relationship
existed with Plaintiffs.
SEVENTH AFFIRMATIVE DEFENSE
7. Even assuming that Plaintiffs were employees—they were not—Plaintiffs are
barred from collecting civil penalties for alleged meal and rest period violations because Plaintiffs
were the masters of their respective schedules and could have taken a meal/rest period at any time
10 and/or Defendant did not deny or prevent Plaintiffs the opportunity to take rest periods, to the
11 extent Plaintiffs were entitled to them.
12 EIGHTH AFFIRMATIVE DEFENSE
13 8. Plaintiffs’ claim for injunctive or declaratory relief are barred because they have
14 adequate remedies at law.
15 NINTHAFFIRMATIVE DEFENSE
16 9. Plaintiffs’ recovery in this action is barred in whole or in part by his/their waiver of
17 the rightto meal and/or
rest breaks in accordance with applicable law.
18 TENTH AFFIRMATIVE DEFENSE
19 10. Defendant alleges, on information and belief, that Plaintiffs’ recovery is barred by
20 the doctrine
of unclean hands.
21 ELEVENTH AFFIRMATIVE DEFENSE
11. Defendant alleges, on information and belief, that Plaintiffs are estopped to seek
23 recovery against Defendant.
24 TWELFTH AFFIRMATIVE DEFENSE
25 12. Defendant alleges, on information and belief, that Plaintiffs’ recovery is barred by
26 the doctrine
of laches.
27 ///
///
3
DEFENDANT VARSITY TUTORS LLC’S ANSWER AND AFFIRMATIVE DEFENSES TO PLAINTIFFS’
FIRST AMENDED COMPLAINT
THIRTEENTH AFFIRMATIVE DEFENSE
13. Plaintiffs’ claims are barred, in whole or in part, by the doctrine of consent insofar
as the conduct of which Plaintiffs complain was incident to the parties’ contractual relationship.
FOURTEENTH AFFIRMATIVE DEFENSE
14. The Complaint is barred because Plaintiffs failed to perform the necessary
conditions to give rise to an obligation by Defendantto pay any of the claimed wages, including
the obligations and pertinent duties pursuant to Califomia Labor Code sections 2856 and 2857.
FIFTEENTH AFFIRMATIVE DEFENSE
15. Even assuming that Plaintiffs were employees—they were not—to the extent that
10 Plaintiffs’ claims are based upon Labor Code section 2802, such claims are barred in whole orin
11 part because Plaintiffs failedto submitto Defendant
any proof or documents showing that any
12 alleged expenditures or losses were incurred by the Plaintiffs in the discharge of their duties.
13 SIXTEENTH AFFIRMATIVE DEFENSE
14 16. Even assuming that Plaintiffs were employees—they were not—to the extent that
15 Plaintiffs’ claims are based upon Labor Code section 2802, such claims are barred in whole orin
16 part because any alleged expenditures or losses were not necessary and/or were not the direct
17 consequence of the discharge of Plaintiffs’ employment duties, which Defendant denies ever
18 existed.
19 SEVENTEENTH AFFIRMATIVE DEFENSE
20 17. Defendant alleges that the imposition of any stabutory and/or civil penalties would
21 violate its rights, including
the right to due process and equal protection, under the Califomia and
United States Constitutions and other laws.
23 EIGHTEENTH AFFIRMATIVE DEFENSE
24 18. Plaintiffs are not entitled to recover any award of penalties as alleged in the
25 Complaintto the extent that such an award wouldbe unjust, arbitrary, oppressive, or confiscatory.
26 NINETEENTH AFFIRMATIVE DEFENSE
27 19. Plaintiffs, by the exercise of reasonable effort and/or care, could have mitigated
the amount of damages allegedto have been suffered, but Plaintiffs have failed, neglected, and
4
DEFENDANT VARSITY TUTORS LLC’S ANSWER AND AFFIRMATIVE DEFENSES TO PLAINTIFFS’
FIRST AMENDED COMPLAINT
refused, and continue
to fail, neglect, and refuse to exercise a reasonable effort to mitigate any
and all damages.
TWENTIETH AFFIRMATIVE DEFENSE
20. Plaintiffs’ claims are barred in whole or in part, to the extent that they are seeking
multiple penalties or remedies for the same conduct.
TWENTY-FIRST AFFIRMATIVE DEFENSE
21. If any damages have been sustained by Plaintiffs, although such is specifically
denied, Defendant is entitled under the equitable doctrine of setoff and recoupment to offset all
extra payments or overpayments and/or all obligations of Plaintiffs owed to Defendant against
10 any judgement that may be entered against Defendant.
11 TTWENTY-SECOND AFFIRMATIVE DEFENSE
12 22. Plaintiff’s claims are barred in whole or in partto the extent that each one of them.
13 controlled and created their own service schedules and Defendant did not have the right to control
14 Plaintiffs’ hours of service or tutoring locations.
15 TWENTY-THIRD AFFIRMATIVE DEFENSE
16 23. Even assuming Plaintiffs were employees - they were not - Plaintiffs’ claims for
17 pay for hours worked (including overtime) and for meal and rest periods civil penalties are barred
18 to the extent Defendant had no knowledge of or reason to know that Plaintiffs were working
19 uncompensated
hours and/or were not taking meal or rest breaks.
20 TWENTY-FOURTH AFFIRMATIVE DEFENSE
21 24. With the exception of the Complaint’s Labor Code Private Attomey General Act
(“PAGA”) claim, Plaintiffs’ claims are subject to an enforceable binding arbitration agreements.
23 Therefore, pursuant to the Califomia Arbitration Act (Code of Civil Procedure Section 1280 et
24 seq.) and the Federal Arbitration
Act (9 U.S.C. sections 1-14), Plaintiffs’ non-PAGA claims must
25 be compelled to individual arbitration.
26 ///
27 ///
///
5
DEFENDANT VARSITY TUTORS LLC’S ANSWER AND AFFIRMATIVE DEFENSES TO PLAINTIFFS’
FIRST AMENDED COMPLAINT
TWENTY-FIFTH AFFIRMATIVE DEFENSE
25. Plaintiffs’ PAGA claim cannot proceed on a representative basis because, inter alia,
their theories are unmanageable, too complex to be litigated, too numerous to be litigated, and
would require thousands of individualized liability assessments.
TWENTY-SIXTH AFFIRMATIVE DEFENSE
26. Plaintiffs lack standingto bring claims for civil penalties on behalf of others because
Plaintiffs are not “aggrieved employees” pursuant to PAGA.
TWENTY-SEVENTH AFFIRMATIVE DEFENSE
27. Plaintiffs’ PAGA claim fails because Plaintiffs failed to exhaust their administrative
10 remedies under PAGA, and Plaintiffs failed
to specify all facts and theoriesto support
the alleged
11 violations as required by PAGA.
12 TWENTY-EIGHTH AFFIRMATIVE DEFENSE
13 28. Plaintiffs failed to mitigate their damages.
14 RESERVATIONS OF RIGHTS
15 Defendant hereby gives notice that it intends to rely upon such other and further affirmative
16 defenses
as may become available
during discovery in this action and reserves
the right to amend
17 its Answerto assert any such defenses. The pleading of a defense as an affirmative defense is not
18 an admission or acknowledgement that Defendant bears the burden of proof on such defense, or
19 waiver of any argument that Plaintiff bears such burden.
20 //1
21 //1
//1
23 //1
24 //1
25 //1
26 //1
27 //1
//1
6
DEFENDANT VARSITY TUTORS LLC’S ANSWER AND AFFIRMATIVE DEFENSES TO PLAINTIFFS’
FIRST AMENDED COMPLAINT
WHEREFORE, this answering Defendant prays for relief as follows:
1 That Plaintiffs take nothing by way of this action;
2. That this actionbe dismissed in its entirety with prejudice;
3. That judgment be entered in favor of Defendant and against Plaintiffs;
4. For an award of Defendant's costs of suit and attomeys’ fees incurred herein; and
5. For such other and further relief as the Court deems just and proper.
DATED: July 15, 2019 LAIR YAN LLP
10
Geess
Rafael G. Nendel Flores
Guillermo M. Tello
11 Yesi
Attol for Defendant
12 VARSITY TUTORS LLC.
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DEFENDANT VARSITY TUTORS LLC’S ANSWER AND AFFIRMATIVE DEFENSES TO PLAINTIFFS’
FIRST AMENDED COMPLAINT
PROOF OF SERVICE
STATE OF CALIFORNIA )
SS.
COUNTY OF LOS ANGELES )
I declare that:
I am employed in the County of Los Angeles, State of California. I am over the age of 18
and not a party to the within action. My business address is: 725 South Figueroa Street, Suite 350,
Los Angeles, California 90017.
On July 15, 2019, I caused to be served the foregoing document described as
DEFENDANT VARSITY TUTORS LLC’S ANSWER AND AFFIRMATIVE DEFENSES
TO PLAINTIFFS ALEXANDER CHARLES AND HENRY MULAK’S FIRST AMENDED
COMPLAINT on the interested parties in this action by placing a true copy thereof enclosed in a
sealed envelope(s) addressed and served as follows:
10 Steven Tindall, Esq. Attorneys for Plaintiffs
Amanda M. Karl, Esq. ALEXANDER CHARLES and HENRY
11 Jeffrey Kosbie, Esq. MULAK
GIBBS LAW GROUP LLP
12 505 14th Street, Suite 1110
Oakland, CA 94612
13 Telephone: (510) 350-9700
Facsimile: (510) 350-9701
14 Email :smt@classlawgroup.com
amk@classlawgroup.com
15 jbk@classlawgroup.com
16
[Xx] BY MAIL: I caused such envelope to be deposited in the mail at Los Angeles, CA 90017.
17 The envelope was mailed with postage thereon fully prepaid. I am "readily familiar" with
the firm's practice of collection and processing correspondence for mailing. It is deposited
18 with the U.S. Postal Service on that same day in the ordinary course of business. I am
aware that on motion of party served, service is presumed invalid if postal cancellation date
19 or postage meter day is more than 1 day after date of expiration of deposit for mailing in
affidavit.
20
[xX] (STATE) I declare under penalty of perjury under the laws of the State of California that
21 the above is true and correct.
22 Executed on July 15, 2019, at Los Angeles, California.
23
24
Gpacitla proband
Gvaciela Anchante
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1
PROOF OF SERVICE
EXHIBIT C
ALEXANDER CHARLES etal. vs VARSITY TUTORS LLC
Alexander Charles on 05/30/2023
[ ceRTIFIED copy |
www.trustarray.com
949-521-1257
ALEXANDER CHARLES etal. vs VARSITY TUTORS LLC
Alexander Charles on 05/30/2023
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949-521-1257
ALEXANDER CHARLES etal. vs VARSITY TUTORS LLC
Alexander Charles on 05/30/2023
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ALEXANDER CHARLES etal. vs VARSITY TUTORS LLC
Alexander Charles on 05/30/2023
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ALEXANDER CHARLES etal. vs VARSITY TUTORS LLC
Alexander Charles on 05/30/2023
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ALEXANDER CHARLES et al. vs VARSITY TUTORS LLC
Alexander Charles on 05/30/2023
THE WITNESS: No. I never launched my own
tutoring business, and they didn't do anything to
prohibit me from attempting to do so.
MR. NENDEL-FLORES:
03 0 Pk
10 03 0 Pk
11
12
13
14
4
15 03 30 Ph
16
17
18
19
20 03 31 Pe
21
22
23
24
25 Tutors online platform? 03 1 Fk
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ALEXANDER CHARLES et al. vs VARSITY TUTORS LLC
Alexander Charles on 05/30/2023
03 31 Ph
Q. Was it less than five?
A. I think it was more than that.
Was it -- was it more than ten?
10 Maybe. 03 31 Ph
11 Q More than 15?
12 A I would be guessing. Maybe. I would be
13 guessing.
14 Q So you would agree with me that you utilized
15 this document which contains a logo for Alexander Charles 03 32 Ph
16 Tutor with respect to students that you obtained via
17 Varsity Tutors online platform, correct?
18 A Yes.
19 MR. NENDEL-FLORES: Do you guys mind if we take
20 a ten-minute break? 03 32 Ph
21 THE REPORTER: Thank you.
22 MR. KOSBIE: Fine.
23 THE VIDEOGRAPHER: The time is 3:32 p.m., and we
24 are going off the record.
25 (Break taken from 3:32 p.m. to 3:43 p.m.) 03 3 Ph
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ALEXANDER CHARLES etal. vs VARSITY TUTORS LLC
Alexander Charles on 05/30/2023
Celia A. Rarate
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EXHIBIT D
TOUTS Wal
CHARLES-VT_000182
i... Value Whole numbers are all “counting” numbers including zero
. Integers are positive and negative whole numbers
Rational numbers can be written as a ratio of integers
. 1.345, 3/7, “10
Irrational numbers cannot be written as a ratio of two
integers
. Ny2ze
Imaginary numbers are square roots of negative numbers.
. isV-a
Complex numbers are combinations of real and imaginary
numbers
CHARLES-VT_000183
Real Numbers
Whole
Integers
Rational
Irrational
CHARLES-VT_000184
BE sumbe
theory
Factors and multiples
Factors:A factor is an integer that divides evenly into
another number with NO remainders
— Integers have a finite set of factors
Multiples: The products of a given number created when
multiplied by another integer. Multiples are divisible by
the given number with NO remainders
- Every integer has an infinite set of multiples
<
CHARLES-VT_000185
Wace waive 123.456
a hundreds
2 tens
3 units/ones
4 tenths
5 hundredths
6 thousandths
<
CHARLES-VT_000186
a Multiples Which of the following expressions is the greatest
monomial factor of 125p?q3 + 450p7q
25p°q
<
CHARLES-VT_000187
a Prime and Prime factorization
— Allcomposite numbers are made up or composed of
composite prime numbers.
Divide until every integer is prime.
numbers Greatest Common Factor
— The largest factor that two or more numbers share
n — Select common primes to the lowest degree
Fe SS 36
Least Common Multiple
7™N 18 — The lowest number two numbers share
IN — Select common primes to the highest degree
e~
ve
CHARLES-VT_000188
a LCM and What two numbers have a GCF of 10 and LCM of 120?
A) 10820
GCF B) 20
& 60
9 30
& 40
D) 40&70
<
CHARLES-VT_000189
Fractions
For real numbers A and B:
[=A+B
and C _AD+BC
BD
reducing CAC
4A .fL
D BD
fractions 4,24c¢_ AD
DBC
What rational number is halfway between % and */,
A) 5/12
Tip: When dealing with fractions, set B) 1/6
denominators equal.
<
QC) 7/24
D) ”
CHARLES-VT_000190
C=?
A) 119
B) 420
C) 1008
D) 2940
CHARLES-VT_000191
BB sctoine for
X using When tk + wk = 1, what is the value of k ?
fractions A
B 12
Cc
D.
12
<
CHARLES-VT_000192
DD cercent Percents are a specific type of fraction.
means “for every one hundred.”
4,is what percent of 20?
The word literally
4. =x/100 * 20
or
4/20 = x/100 -> (100 * 4) / 20
What percent of 60 is 12?
<
CHARLES-VT_000193
DD cercent
change
When quantities change, percent change is found by
asking:
— The change is what percent of the original amount?
Find the difference between the original and new amount
Divide the difference of the two by the original amount
Actual increase
Percent increase =
riginal amount = (= * 100) %
A television that costs $50 now will cost $51.75 next year
due to inflation. What is the current rate of inflation per
year?
CHARLES-VT_000194
Ratios
Ratios are mathematical comparisons.
— Percents are ratios. Percents compare everything to 100
- xyisa ratio.
Given ratios the ratio of
A to the whole is os
$1000 will be given to three grandkids in the ratio of 3:4:5.
How much will 3 receive?
xy y:z what is x:z if 3:2 and 3:6?
CHARLES-VT_000195
conversion
factors
<
CHARLES-VT_000196
Rate
Rates are ratio and proportion applications.
If you travel 120 miles in 4 hours, how fast do you travel
ina hour?
120 miles _ x miles
x = 30 miles an hour
4hours — 1hour
CHARLES-VT_000197
a Basic stats Mean: Average
Median: Middle ofan odd number set; in set {2.2.3.4} 2+3
=2.5
Mode: Most
Range: Greatest
— least
desired
Probability = yutcome
Probability of a flipping a heads?
<
CHARLES-VT_000198
Be ctanitity Akoi pond normally has 1 koi fish and 15 goldfish. If 4 new
koi are added to the pond, what is the probability of
randomly selecting a koi?
A) 1/15
B) 5/15
C) 1/20
D) 5/20
E)15/20
<
CHARLES-VT_000199
Average What is the average of the following sum: 58 + 63 + 45 +
79?
formula Four distinct consecutive numbers have an average of
plus use 498. What are those four numbers?
algebra In Mr. X's Algebra class, a student’s average is calculated
by taking the average of their test scores. Michael has an
average of 86. His current test scores are 74, 76, and 100,
and X. What must his fourth test score, X, equal?
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CHARLES-VT_000200
dependent If two events have mutually exclusive, i.e. they both
cannot happen, then you add their probabilities.
events US — What is the chance of flipping a heads ora tails?
If two events can happen independently of each other,
mutually then you multiply their probabilities.
= What is the probability of flipping a heads twice ina row?
exclusive
events
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CHARLES-VT_000201
Combination: If there are X ways an event can occur and
then there areY ways that a different event can occur,
Combination then there are xy ways they can both happen.
Permutation: When the order of the arrange matters,
and then there are x! ways that event can occur.
X!=a*b*c..
Permutation
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CHARLES-VT_000202
At Mike's Friendly Restaurant, a person can chose among
3 entrees, 4 main courses, and 6 desserts. How many
Combination different combinations of meals can a person make?
and How many ways are there to arrange 6 plates on a drying
rack?
Permutation
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CHARLES-VT_000203
When you can only take a certain number of a given
ermutations organized set, you can use the formula
!
Formula for permutations: nPr : =r!)
If there are 16 different ingredients for pasta, but a chef
can only chose 11 at a time. In how many different ways
can the chef add the pasta ingredients?
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CHARLES-VT_000204
a Working
5<1-3X <10
5 <1-3X ----- >X<2
with 1-3X<10 wee eee >X>-3
inequalities
-3 3(2Xx -3)
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CHARLES-VT_000205
a Absolute Absolute value means the distance between two numbers
whether they are negative or positive.
value
What is the absolute value of |-5|?
What is the absolute value of ||-8-2|-|-10-12|| ?
What is the absolute value of 3 | 4-6]?
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CHARLES-VT_000206
Solving
The solutions of |al< b satisfy -b o two solutions
D=oone solution
equations D 0, then the parabola opens UP
For parabolas, when a <0 it opens down
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CHARLES-VT_000222
ompleting x? +bx + =(x+2p
Completing the square is taking any trinomial and creating a
the square binomial squared. Here’s a problem with explanation.
2x? +12x -16 =0
Ax? +Bx-C=0
1) Divide out the aterm so that a=2