Find the domain of this equation {-2

Beth wants to paint the four walls of her rectangular bedroom. Her room is 10 feet wide, 13 feet long, and 8 feet high. She will

Marat540 [252]

Answer:The answer is 1040

6 0

2 years ago

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The 65 students in a classical music lecture class were polled, with the following results: 37 like Wolfgang Amadeus Mozart 36 l

Anna35 [415]

Answer:

a) 25

b) 30

c) 10

d) Not Mozart, 6

e) 2

Step-by-step explanation:

We use a Venn Diagram to solve this question.

I am going to say that:

A are the students who like Mozart.

B are the students who like Beethoven

C are the students who like Haydn.

We have that:

$A = a + (A \cap B) + (A \cap C) + (A \cap B \cap C)$

In which a are those who only like Mozart, $(A \cap B)$ are those who like Mozart and Beethoven, $(A \cap C)$ are those who like Mozart and Haydn and $(A \cap B \cap C)$ are those who like all three of them.

By the same logic, we have that:

$B = b + (A \cap B) + (B \cap C) + (A \cap B \cap C)$

$C = c + (B \cap C) + (A \cap C) + (A \cap B \cap C)$

We start finding these values from the intersection:

8 like all three composers

This means that $A \cap B \cap C = 8$

14 like Beethoven and Haydn

This means that:

$(B \cap C) + (A \cap B \cap C) = 14$

So

$B \cap C = 6$

21 like Mozart and Haydn

This means that:

$(A \cap C) + (A \cap B \cap C) = 21$

Then

$A \cap C = 13$

14 like Mozart and Beethoven

This means that:

$(A \cap B) + (A \cap B \cap C) = 14$

$A \cap B = 6$

31 like Franz Joseph Haydn

This means that C = 31. So

$C = c + (B \cap C) + (A \cap C) + (A \cap B \cap C)$

$31 = c + 6 + 13 + 8$

$c = 4$

36 like Ludwig van Beethoven

This means that $B = 36$

So

$B = b + (A \cap B) + (B \cap C) + (A \cap B \cap C)$

$36 = b + 6 + 6 + 8$

$b = 16$

37 like Wolfgang Amadeus Mozart

This means that A = 37. Then

$A = a + (A \cap B) + (A \cap C) + (A \cap B \cap C)$

$37 = a + 6 + 13 + 8$

$a = 10$

a. exactly two of these composers?

$(A \cap B) + (A \cap C) + (B \cap C) = 6 + 13 + 6 = 25$

b. exactly one of these composers?

$a + b + c = 10 + 16 + 4 = 30$

c. like only Mozart?

$a = 10$

d. like Beethoven and Haydn, but not Beethoven?

I will use not Mozart.

So $B \cap C = 6$

Not Mozart, 6.

e. like none of these composers?

At least 1:

$(A \cup B \cup C) = a + b + c + (A \cap B) + (A \cap C) + (B \cap C) + (A \cap B \cap C) = 10 + 16 + 4 + 6 + 13 + 6 + 8 = 63$

The total is 65

So 65 - 63 = 2 like none of these composers

4 0

3 years ago

Find the side of a cube with surface area of 150cm square

vagabundo [1.1K]

Answer:

5cm for each side

4 0

3 years ago

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Write two expressions that have the same value as 36.8 divided by 2.3.

Svetllana [295]

Answer:

My examples, 4 x 4, 32/2

Step-by-step explanation:

36.8 / 2.3 = 16, so anything that equals 16 should work. Hope this helps!

3 0

3 years ago

Expand the logarithm.<br> ln((-3e^5)/(x^3))

Valentin [98]

Answer:

ln(3) + 5 - 3ln(x) or 6.0986 - 3ln(x)

Step-by-step explanation:

$ln(\frac{3e^{5} }{x^3} )$

$ln(\frac{3e^{5} }{x^3} )$ = $ln(3e^5)-ln(x^3)$ , since ln(x/y) = ln(x)-ln(y)

$ln(3e^5)$ = ln(3) + $ln(e^5)$ , since ln(xy) = ln(x) + ln(y)

$ln(\frac{3e^{5} }{x^3} )$ = ln(3) + $ln(e^5)-ln(x^3)$

$ln(\frac{3e^{5} }{x^3} )$ = $ln(3) + 5ln(e) -3ln(x)$ , since ln( $x^y$ ) = yln(x)

$ln(\frac{3e^{5} }{x^3} )$ = ln(3) + 5 -3ln(x) , since ln(e)=1

if needed further simplification,

ln(3) = 1.0986

ln(e) = 1

$ln(\frac{3e^{5} }{x^3} )$ = 6.0986 - 3ln(x)

7 0

2 years ago