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Let Z={a,c,{a,b}}. What is |Z|?What is the power set of Z?

Which of the following are true?

1. {a,c} ⊆ Z

2. a ∈ Z

3. {c} ⊆ Z

4. {c} ∈ Z

5. b ∈ Z

6. {a,b} ∈ Z

Answers

Answer 1
Answer:

Z=\{a,c,\{a,b\}\}

\boxed{|Z|=3} (treat \{a,b\} as one element of Z)

The power set of Z is

\boxed{2^Z=\bigg\{\{\},\{a\},\{c\},\big\{\{a,b\}\big\},\{a,c\},\big\{a,\{a,b\}\big\},\big\{c,\{a,b\}\big\},\big\{a,c,\{a,b\}\big\}\bigg\}}

1. \{a,c\}\subseteq Z is true because both a\in Z and c\in Z.

2. a\in Z is true.

3. \{c\}\subseteq Z is true (same reason as part 1).

4. \{c\}\in Z is false because Z does not contain the set \{c\}, rather just the element c itself.

5. b\in Z is false because the element b on its own simply is not in Z. That b\in\{a,b\} does not mean b\in Z, but that b belongs to a subset of Z.

6. \{a,b\}\in Z is true.

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Julio's dad owns a restaurant. He bought 9 dozen potatoes to make french fries. He needs 7 potatoes for a large order of fries. How many large orders of fires will he be able to make?I multiplied 9x12=108then divided 108/7 I got 15 with 3 left over. Is this right?
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Answers

Answer:

b=43 i think

Step-by-step explanation:

If this is a 1 attempt thing do not trust me but just know that is 180 degrees so a+b+c=180 will be your formula

There are 30 students in a class, including 16 boys. The ratio of girls to boys would be 7 over 8.

Answers

Answer:

i dont understand- theres 3 ways u can put them tho 7:8 , 7 to 8 , or 7/8

Step-by-step explanation:

Which of the following measurements issmallest?
a. 12 inches
b. 216 inches
c. 412 inches
d. 12/4 inches

Answers

I think it might be A

Which expressions are equivalent to the one below? Check all that apply.25^x
A. 5^x•5^x B. 5•5^x
C. 5^2•5^x
D. 5^2x
E. 5•5^2x F. (5•5)^x

Answers

Answer:

  A. 5^x•5^x

  D. 5^(2x)

  F. (5•5)^x

Step-by-step explanation:

25^x = (5•5)^x = (5^2)^x = 5^(2x) = (5^x)^2 = (5^x)•(5^x)

__

The applicable rules of exponents are ...

  (a^b)^c = a^(bc)

  a•a = a^2

You need to lay communications cable around the perimeter of three offices, each 8' by 10'. How much cable do you need?

Answers

Answer:

108 units

Step-by-step explanation:

We are given that

Length of each  office,l=10 units

Breadth of each office=b=8 units

Total number of office=3

We know that

Perimeter of rectangle=2(l+b)

Using the formula

Length of cable for 1 office=2(10+8)=36units

Length of cable required for 3 offices=36* 3=108units

Hence, the required length of cable=108 units

Who can answer this
(WITH AN EXPLANATION)
will mark brainlest

Answers

Answer:

Factors: (x²y+6)(y²-11)

Step-by-step explanation:

Here's the original equation.

x²y³ - 11x²y + 6y² - 66

Let's separate it into two groups to make it easier.

(x²y³ - 11x²y) + (6y² - 66)

Let's take a look at (x²y³ - 11x²y) first. Do we notice anything that can be removed from the parentheses?

Yes, x²y can be taken from both polynomials to simplify the contents of the parentheses.

Both polynomials have x² and both have at least one y. Combine that to get x²y. That means that within the parentheses y² and - 11 will be left.

So  (x²y³ - 11x²y) becomes x²y (y²-11)

This works because if we multiply x²y * (y² - 11) we get (x²y³ - 11x²)

Let's apply this same idea to (6y² - 66).

6 is the only thing in common between the two polynomials.

If we follow the same steps we get 6 (y²-11).

Notice how when we simplified both groups they each had something on the outside and (y² - 11) in the parentheses?

So lets combine the things that were on the outside of both (y² - 11).

What was on the outside of each? x²y was on the outside for the first one, and 6 for the outside of the second one.

This means that if we combine everything and simplify, the factors we have are (x²y+6)(y²-11).

If you want to confirm, work your way backwards using the distributive property. You'll find that when you multiply (x²y+6) * (y² -11) you'll get = x²y³ - 11x²y + 6y² - 66. That was the original equation, so we know that these are the factors.

Hope that helps!
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