Question

can anyone help me with this? Find the general term of the set. {8, 12, 16, 20, 24, . . .}

Answer 1

4

Answer 2

12-8=?
16-12=?
20-16=?
...........

Answer 3

I think it would be 4n+4... but I am unsure

Answer 4

you are correct, the nth term is 4n+4 (where n starts at n=1)

Answer 5

8n
4n + 4
3n + 5
5n + 3
out of these options

Answer 6

ok thank you so much, I hate math and i am taking an online class, my instructor seems to jump around the book so much as oppose to teaching one lesson at a time.

Answer 7

4(1)+4=?
4(2)+4=?
4(3)+4=?

Answer 8

online is pretty tough gdluck

Answer 9

thanks... and one more:

Let U = {5, 10, 15, 20, 25, 30, 35, 40}
A = {5, 10, 15, 20}
B = {25, 30, 35, 40}
C = {10, 20, 30, 40}.
Find A ⋂ B.

Answer 10

A ⋂ B = set of all things that are in BOTH set A and B

Answer 11

I have never seen the upside down "u" symbol before..
ahhh thanks

Answer 12

it's known as the intersection symbol

Answer 13

thank you i really appreciate this!

Answer 14

Jim, can you help with another one? I am pretty sure I figured it out but just to make sure...
Which sentence is not a statement?
2 x 4 = 7
8 + 2
Jan and Ella are neighbors.
Bill is a photographer

Answer 15

I said it was 8+2

Answer 16

8 + 2 is just an expression not a statement

Note: 2 x 4 = 7 is a statement even though it's false

Answer 17

good

Answer 18

a statement is something that is either true or false

Answer 19

I figured that it was because there wasnt an actual answer, false or not

Answer 20

but 8+2 is neither true or false

Answer 21

that's what I meant, because there wasn't an answer to make it either true or false

Answer 22

Select a counterexample to show that the statement is false. When an odd number is added to the product of two even numbers, the result will be even.
4•5 + 1 = 21. 21 is not even.
4•2 + 3 = 11. 11 is not even.
4•5 + 2 = 22. 22 is even.
3•5 + 4 = 19.19 is not even.

on this one I chose the second one, is that accurate?

Answer 23

good, you got it

Answer 24

I am also doing sets and subsets, can I give you another one?

Answer 25

sure

Answer 26

Which statement is false? (Points : 1)
a ∈ {a, b, c}
Ø ⊂ {a, b, c}
Ø ⊆ {a, b, c}
Ø ∈ {a, b, c}

I chose the last one, but I my book

Answer 27

does not seem to explain the set and subset stuff clearly

Answer 28

a ∈ {a,b,c} means "the element 'a' is in the set {a,b,c}" and this is true

Answer 29

I got that one, but which one is false? I don't really know what the other ones mean

Answer 30

the ⊂ means "is a proper subset of"

Answer 31

the ⊆ means "is a subset of"

Answer 32

what does \[\emptyset\] mean?

Answer 33

that's the empty set

Answer 34

since the empty set is a subset of every set, this means that choices 2 and 3 are also true

Answer 35

but choice 4 is not true because the empty set isn't listed in the set on the right side

Answer 36

ok, awesome! so I was accurate when I chose the last one?

Answer 37

yes

Answer 38

Which of the following phrases does not describe the number -¾? (Points : 1)
rational number
irrational number
real number
negative number

I chose irrational on this one,

Answer 39

good, it's not irrational since it's rational

Answer 40

how are you at explaining how to solve word problems?

Answer 41

show me the problem and we'll find out, it depends on the problem

Answer 42

Upon examining the contents of 38 backpacks, it was found that 23 contained a black pen, 27 contained a blue pen, and 21 contained a pencil, 15 contained both a black pen and a blue pen, 12 contained both a black pen and a pencil, 18 contained both a blue pen and a pencil, and 10 contained all three items. How many backpacks contained exactly two of the three writing instruments?
(Points : 1)
11
2
3
15

I am trying to write it out so it makes sense

Answer 43

Are you familiar with venn diagrams?

Answer 44

yeah and i tried to work out a problem from my book and eventually figured it out, but let me know if this is how I would start. My instructor gave us a study guide and i am trying to replace the figures from that one with these.

Answer 45

woud I start with this?
\[15-10=5\]
\[12-10=2\]
\[18-10=8\]

Answer 46

and those figures refer to what

Answer 47

eg: 5 refers to number of backpacks with black and blue pens only

Answer 48

the 15 is for black and blue pens, the 12 is for black and pencil, and the 18 is a blue pen and pencil

Answer 49

ok, so you would use that to fill in the diagram. These new numbers would go in between pairs of circles

Answer 50

subtracting the 10 because we are trying to find out how many have 2 items not three, so we take them out of the equation.
then we should just add up 5,2,and 8 and get 15

Answer 51

so 5 black and blue only, 2 black and pencil only, and 8 blue and pencil

Answer 52

is this a two or three circle diagram?

Answer 53

3 overlapping circles

Answer 54

now we need to find out how many backpacks there are with only one item, how do we do that

Answer 55

would it be:

\[23-10-5-2=7 for black pens only\]

Answer 56

good, there are 7 backpacks with black pens only

Answer 57

do the same for the other two items

Answer 58

ok, phew, I actually did the diagram right

Answer 59

so the question asks for the back packs with 2 items, so that is 15 right

Answer 60

that is correct

Answer 61

ok so for the other ones it would be 1 with pencil, and 4 with blue pens

Answer 62

oh wait I made a typo, there should be only 6 backpacks with black pens only

Answer 63

oh yeah, that was my fault

Answer 64

1 pencil, 4 blue, so your other numbers are correct

Answer 65

another question uses the same variables, but wants to know, . How many backpacks contained none of the three writing instruments?

Answer 66

ok you have the number of backpacks which have all 3, two items, or just one item right?

Answer 67

yeah

Answer 68

add up all of those individual numbers

Answer 69

what do you get when you do that?

Answer 70

37

Answer 71

I'm getting 36, what are your numbers

Answer 72

One item only 6, 1, 4

Two items 5, 2, 8

All three 10

Answer 73

oh I found my mistake

Answer 74

6 black pens and not 7

Answer 75

oh ok

Answer 76

so there are 36 items that have either a) one item only b) two items, or c) all three items

So subtract this from the total 38 to get 38-36 = 2

So there are two backpacks that have none of these items

Answer 77

ok, I got it! it is easier when you do the diagram

Answer 78

yeah it helps you see where everything goes

Answer 79

I have a question about subsets again.

Answer 80

ok

Answer 81

. Find the number of subsets the set has. {1, 2, 3, 4, 5, 6, 7, 8, 9}

Answer 82

what is the easiest way to figure this out?

Answer 83

If a set has 'n' elements, then the set will have \[2^n\] subsets

Answer 84

In this case, n=9, so there are \[2^9 = 512\] subsets

Answer 85

and it is always to the power of the number of elements?

Answer 86

yes

Answer 87

well 2 to that power

Answer 88

is it 2 because every set is a subset of itself?

Answer 89

it's 2 because each element is either in a subset or it's not in a subset (ie either a yes or a no)

Answer 90

ok...this is another one that confuses me: Which set is infinite?
{x | x ∈ N and x < 20}
{x | x is an improper fraction}
{3, 5, 7, . . ., 99}
Ø

Answer 91

{3, 5, 7, . . ., 99} is finite because it starts with 3 and counts by 2 until it hits 99

Answer 92

{x | x ∈ N and x < 20} is finite because this is the set of positive numbers from 1 to 19

Answer 93

i ruled that one out because of just that

Answer 94

Ø is finite because there are no elements in this set (and it's not infinite)

Answer 95

I would think it is the one about the improper fraction

Answer 96

{x | x is an improper fraction} is infinite because there are an infinite number of improper fractions

Answer 97

yes

Answer 98

Which property of real numbers does the following equation demonstrate?
4(x – 7) = 4x – 28
I said this is distributive property