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