math final
it is false that both this cat is cute and lazy cats do not listen
-(q^r)
this cat is not cute
-q
Find the first five terms in sequences with the following nth terms. 10 little n-9
1,91,991,9991,99991
1,2,4
100th=2 little 99 nth=2 little n-1
50,80,110
100th=3020 nth= 30n+20
A mathematician named Christian Goldbach (1690-1764) made a conjecture that has not been proven for over 300 years. Millions of examples have been found that support his conjecture, but no counterexample has ever been found. Until a counterexample is found or someone presents a logical proof, this will remain a conjuecture. Goldbach's Conjecture: Every even number greater than 2 can be written as the sum of two prime numbers. Test Goldbach's conjecture for various even numbers. Which two primes sum to 64? Select all that apply.
11 and 53
Cookies are sold singly or in packages of 13 or 39. With this packaging, how many ways can you buy 78 cookies?
12 ways
A designer has designed different tops, pants, and jackets to create outfits. How many different outfits can the models wear if she has designed the following pieces? -six tops, four pants, five jackets
120 outfits
As you leave Clark, the sign says Lutherville 115 miles, Otisburg 165 miles. If the Planet Diner is halfway between Lutherville and Otisburg, how far is it from Clark?
140
2+5+8+11+........296
14751
Joe's annual income has been increasing each year by the same dollar amount. The first year his income was $17,500 and the 4th year his income was $20,200. In which year was his income $29,200
14th year
Find the first five terms in sequences with the following nth terms. 4n-2
2,6,10,14,18
1+3+5+7+....+1003
252004
In each of the following, list three terms that continue the arithmetic or geometric sequences. Identify the sequences as arithmetic or geometric. 1,6,11,16,21
26,31,36 Arithmetic
One winter night the temperature fell 14 degrees between midnight and 5 A.M. By 9 A.M.the temperature had doubled from what it was at 5 A.M. By noon, it had risen another 8 degrees to 36 degrees. What was the temperature at midnight?
28
692+685+678+671+....+6
34551
1+2+3+4+.....+99
4950
In each of the following, list three terms that continue the arithmetic or geometric sequences. Identify the sequences as arithmetic or geometric. 14,22,30,38,46
54,62,70 arithmetic
A theater has 26 rows with 22 seats in each row. Estimate the number of seats in the theater
600
43+44+45+46+......+120
6357
In each of the following, list three terms that continue the arithmetic or geometric sequences. Identify the sequences as arithmetic or geometric. 2,4,8,16,32
64,128,256 geometric
Find the first five terms in sequences with the following nth terms. 6n+3
9,15,21,27,33
How are addition and subtraction related? Explain.
Addition and subtraction are inverses of each other; that is, they "undo" each other. That is, if the number 8 had the number 3 added to it, followed by the subtraction of the number 3, the addition and subtraction operations would cancel each other out.
A student says that if the hypothesis is false, an argument cannot be valid. How do you respond?
An argument is valid as long as the conclusion follows from the hypothesis. A valid argument does not have to contain true statements.
Choose the most general criteria for a counterexample of (n+4)little 2=n little 2 +16
Any natural number n can be used as a counterexample.
Choose the most general criteria for a counterexample of n+5/5=n+1
Any natural number n can be used as a counterexample.
Two students were asked to extend the sequence 2, 4, 8, and so on. The first student said the answer 2, 4, 8, 16, 32, 64, ... was the correct one. The second student, however, said the first student was wrong and that the correct answer is 2, 4, 8, 14, 22, 32, 44, and so on. Which student is correct?
Both students are correct. The first student is thinking of a geometric sequence. The second student is thinking of a different sequence where it starts with 2, then adds 2 to get the second term, then adds 4 to get the next term, then 6, then 8, then 10, then 12, and so on.
If a statement and its converse are both true, which of the other forms, inverse and contrapositive, are also true, if any?
Both the inverse and the contrapositive are true.
Explain why commands and questions are not statements.
Commands and questions are not statements because they can't be classified as true or false.
Describe Dr. No as completely as possible.
Dr. No is a male spy who is not poor and not tall.
Use quantifiers to make each of the following true, where n is a natural number. n+3=3+n
For all natural numbers n n+3=3+n
Use quantifiers to make each of the following true, where n is a natural number. 5n+6n=11n
For all natural numbers n, 5n+6n=11n
Analyze the following argument that was presented by a sixth-grade student. Alan said, "Mr. Jackson said that some of us could go to recess at 11:00 A.M., and all got to go but me. He lied." Describe circumstances in the situation where Mr. Jackson would have lied. In which circumstance would Mr. Jackson have lied?
He would have lied if no one was allowed to go to recess at 11:00 A.M.
Explain why in a drawer containing only two different colors of socks one must draw only three socks to find a matching pair
If there are only two colors of socks in the drawer, then of any 3 chosen, two must be the same color.
Joey said that 4, 24, 44, and 64 all have a remainder of 0 when divided by 4, so all numbers that end in 4 must have 0 remainder when divided by 4. How do you respond? Joey noticed a pattern that works for many numbers but must be careful when generalizing his pattern to all numbers, in case a counterexample proves his claim false. Is Joey correct?
Joey is not correct. The number 14 is a counterexample to his claim.
Do elementary students still have to learn their basic facts when the calculator is part of the curriculum? Explain.
Students need to know their basic facts to make estimates to judge if the calculator is correct.
Use quantifiers to make each of the following true, where n is a natural number. n little 2=9
There exists a natural number n such that n little 2=9
Use quantifiers to make each of the following true, where n is a natural number. n+8=16
There exists a natural number n such that n+8=16.
The first figure takes 5 matchstick squares to build, the second takes 11 to build, and the third takes 17 to build, as can be seen by clicking on the icon below. (a)How many matchstick squares will it take to build the 10th figure? (b)How many matchstick squares will it take to build the nth figure? (c)How many matchsticks will it take to build the nth figure?
a=59 b=6n-1 c=18n-2
Write the negation of the statement. Not all ostriches fly.
all ostriches fly
converse
if a quadrilateral has opposite sides that are congruent, then it is a parallelogram
contrapositive
if a quadrilateral has opposite sides that are not congruent, then its not a parallelogram
inverse
if a quadrilateral is not a parallelogram, then its opposite sides are not congruent
converse
if a rectamgle is not a quadrilateral, then it is a paralleogram
inverse
if a rectangle id not a parallelogram then it is a quadrilateral
contrapositive
if a rectangle is a quadrilateral, then it is not a parellelogram
converse
if an angle is a right angle,then it is not acute
inverse
if an angle is acute, then it is not a right angle
contrapositive
if an angle is not a right angle then it is acute
For each of the following, form a conclusion that follows logically from the given statements. Complete parts (a) through (c) below. -if i work on this project, I will get a good grade. If i get a good grade, then I will graduate college. If i graduate from college, then I will look for a job
if i work on this project, then I will look for a job
inverse
if you are awake , then you are in class
contrapositive
if you are in class then you are awake
converse
if you are not in class, then you are not awake
Brad, Joan,Gail, and Shana are in a horse race. Joan is the slowest. Gail is faster than Shana but slower than Brad. Name the finishing order of the horses. from last to first place
joan, shana, gail, brad
Audrey and Lauren began reading a novel on the same day. Audrey reads 10 pages a day and Lauren reads 5 pages a day. If Audrey is on page 30, on what page is Lauren?
lauren is on page 15 and audrey is on 30
1,5,9,13
nth term=4n-3 100th=397
Without computing each sum, find which is greater, O or E, and by how much.
o=1+3+5+7+......+97 e=2+4+6+8.....+98 e is greater than o by 49
If q stands for "This cat is cute" and r stands for "Lazy cats do not listen" write each of the following in symbolic form. -this cat is cute and lazy cats do not listen
qvr
lazy cats do not listen or this cat is not cute
rv-q
For each of the following, form a conclusion that follows logically from the given statements. Complete parts (a) through (c) below. -some employees are lazy. All lazy employees should be demoted
some employees should be demoted
Investigate the validity of the arguments shown on the right. -if a student is a sophomore, then the student takes physics. William is a junior. Conclustion william does not take physics
the conclusion is invalid
Investigate the validity of the arguments shown on the right. -All rhombuses are parallelograms. all parallelograms are quadrilaterals conclusion all rhombuses are quadrilaterals
the conclusion is valid by the chain rule (transitivity)
Find the first five terms in sequences with the following nth terms. 2n little 2+2
the first 5 terms are 4,10,20,34,52
Use a traditional clock face to determine the next three terms in the following sequence. 3,8,1,6,11.....
the next three terms are 4,9,2
For each of the following, form a conclusion that follows logically from the given statements. Complete parts (a) through (c) below. - every equilateral triangle is isosceles. There exist triangles that are equilateral
there exist triangles that are isosceles