Identify if the order triple (1, 2,3) is a solution of the given system of equations. 3x 5 y z 16 7 x y 3z 4 x 5 y 7 z 10 4. Identify if the system of equations given below has unique solution, infinitely many solutions, or no solution. 2 x 5 y 16 3x 7.5 y 24 5. Given is the augmented matrix of a system of equations: 1 5 6 2 7 1 3 5 1 5 7 13 Write the new form of the augmented matrix after the following row operations.
Problem 2. Find a recurrence relation for un , the number of bit strings of length n that do not contain two consecutive zeros, by (a): using the recurrence relation zn for the number of bit strings of length n that do contain two consecutive zeros. SOLUTION: We simply observe that all strings of length n either do or don’t have two consecutive zeros; mathematically, this means that zn +un = 2n . Hence, un = 2n −zn = 2n −(zn−1 +zn−2 +2n−2 ). (b): by reasoning from scratch.
4x 2 2 5 13. 12x 2 2 39x 1 9 14. 18x 2 2 9x 2 14 15. 20x 2 2 54x 1 36 16. 42x 2 1 35x 1 7 17.
The area of a circle is approximately 3.14 times the radius squared. Which of the following expressions is a correct way to write this, if the radius is r? a. r(3.14)2 b. 3.14r2 c. (3.14r)2 d. 2(3.14)r 3. Merrill bought m notebooks for $2.50 each and n pens for $1.25 each.
DATED: [ ] Respectfully submitted, By: [Attorney’s signature] Attorney for Appellant 17 CERTIFICATE OF COMPLIANCE Pursuant to ARCAP 14, I certify that the attached brief __X__ Uses proportionately spaced type of 14 points or more, is doublespaced using a roman font and contains 2,548 words or _____ Uses monospaced type of no more than 10.5 characters per inch and _____ Does not exceed 40 pages (opening and answering briefs) or 20 pages (reply briefs). ____________________________________________________ Date Signature of Attorney or Unrepresented Party 18 CERTIFICATE OF SERVICE I, Bonne Mullen, certify that on October 26, 2014, two copies of Appellant’s foregoing Answering Brief were sent via U.S. Mail, postage pre-paid, addressed to the following: Richard R. Thomas, Esq. Michael A. Schern, Esq. 1640 South Stapley Drive, Suite 205 Mesa, Arizona 85204 Counsel For Appellee DATED this 26th day of October, 2014 . By: __________________________ Bonne Mullen Attorney for Appellant
Daniel Jones NT1210 Lab 1.1 Review 1. Convert the decimal value 127 into binary. Explain the process of conversion that you used. 127 | 127 | 63 | 31 | 15 | 7 | 3 | 1 | 128 | - 64 | - 32 | - 16 | - 8 | - 4 | - 2 | - 1 | | = 63 | = 31 | = 15 | = 7 | = 3 | = 1 | = 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | The answer is: 01111111 If the decimal number is less than the greatest power of 2 than you must put a 0 for that number than carry that same decimal number over to the right one decimal place. For example.
ALGEBRA II Regents Review 1. Simplify: = 1 2. The expressionis equivalent to which of the following? a) b) c) d) 3. Solve for x: x = 5 4.
X100/201 NATIONAL QUALIFICATIONS 2010 FRIDAY, 21 MAY 1.00 PM – 1.45 PM MATHEMATICS INTERMEDIATE 2 Units 1, 2 and 3 Paper 1 (Non-calculator) Read carefully 1 You may NOT use a calculator. 2 Full credit will be given only where the solution contains appropriate working. 3 Square-ruled paper is provided. LI X100/201 6/27910 *X100/201* © FORMULAE LIST The roots of ax + bx + c = 0 are x = 2 −b ± (b 2 − 4ac ) 2a Sine rule: a = b = c sin A sin B sinC Cosine rule: 2 2 2 a2 = b2 + c2 − 2bc cos A or cos A = b + c − a 2bc Area of a triangle: 1 Area = 2 ab sin C Volume of a sphere: Volume = 4 π r 3 3 Volume of a cone: 1 Volume = 3 π r 2 h Volume of a cylinder: Volume = π r 2
If the sentence is geometric, find the common ratio r. If the sequence is arithmetic, find the common difference d. 3 3 3 3 3 , , , , ,... 2 4 8 16 32 A) arithmetic, d = C) geometric, r = 1 6 1 2 B) neither D) geometric, r = 2 28) 29) Determine whether the sequence is arithmetic, geometric, or neither. If the sequence is geometric, find the common ratio r. If the sequence is arithmetic, find the common difference d. 1 1 1 1 , , , 4 6 8 10 A) geometric, r = 1 2 B) geometric, r = 2 D) neither 1 2 29) C) arithmetic, d =
.. ... .... .. .. (b) Expand and simplify (x + 3)(x + 7) (2) .................................................. .. ... .... .. .. (c) Factorise fully 3pq – 12p2 (2) .................................................. .. ... .... .. .. (d) (i) Factorise 3 y 2 − 10 y + 3 (4) .................................................. .. ... .... .. .. Hence, or otherwise (ii) Factorise 3( x + 2) 2 − 10( x + 2) + 3 .................................................. .. ... .... .. .. (Total for Question 9 = 11 marks) Edexcel GCSE in Mathematics A Sample Assessment Materials Issue 2 © Edexcel Limited 2010 57 10 1 2 3 98 99 100 The diagram represents 100 cards. Each card has a whole number from 1 to 100 on it. No cards have the same number. Bill puts a red dot on every card which has a multiple of 6 on it.