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2 years ago

A hotel has 12 floors and 2,220 rooms. There are the same number of rooms on each floor of the hotel.

Mathematics

2 answers:

oee [108]2 years ago

8 0

Just simply divide 2,220 by 12 and you’ll get 185 rooms on each floor.

Naddik [55]2 years ago

5 0

185 on each floor

2220/12

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What is the binomial expansion of (x + 2)4? x4 + 4x3 + 6x2 + 4x + 1 8x3 + 24x2 + 32x x4 + 8x3 + 24x2 + 32x + 16 2x4 + 8x3 + 12x2

Margaret [11]

Answer-

$\boxed{\boxed{(x+2)^4=x^4+8x^3+24x^2+32x+16}}$

Solution-

Given expression is $(x+2)^4$

Applying Binomial Theorem

$\left(a+b\right)^n=\sum _{i=0}^n\binom{n}{i}a^{\left(n-i\right)}b^i$

Here,

a = x, b = 2 and n = 4

So,

$\left(x+2\right)^4=\sum _{i=0}^4\binom{4}{i}x^{\left(4-i\right)}\cdot \:2^i$

Expanding the summation

$=\dfrac{4!}{0!\left(4-0\right)!}x^4\cdot \:2^0+\dfrac{4!}{1!\left(4-1\right)!}x^3\cdot \:2^1+\dfrac{4!}{2!\left(4-2\right)!}x^2\cdot \:2^2+\dfrac{4!}{3!\left(4-3\right)!}x^1\cdot \:2^3+\dfrac{4!}{4!\left(4-4\right)!}x^0\cdot \:2^4$

$=\dfrac{4!}{0!\left(4\right)!}x^4\cdot \:2^0+\dfrac{4!}{1!\left(3\right)!}x^3\cdot \:2^1+\dfrac{4!}{2!\left(2\right)!}x^2\cdot \:2^2+\dfrac{4!}{3!\left(1\right)!}x^1\cdot \:2^3+\dfrac{4!}{4!\left(0\right)!}x^0\cdot \:2^4$

$=1\cdot x^4\cdot \:1+4\cdot x^3\cdot \:2+6x^2\cdot \:4+4\cdot x\cdot \:8+1\cdot 1\cdot \:16$

$=x^4+8x^3+24x^2+32x+16$

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2 years ago

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How do you Evaluate 3f(2)

kondor19780726 [428]

IT IS TWELVE............ 12

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2 years ago

Aaron, Blaine, and Cruz are solving the equation 4 7 (7 − n) = −1. Aaron started his solution by multiplying both sides of the e

hjlf

Answer:

D. All three chose a valid first step toward solving the equation.

Step-by-step explanation:

Aaron, Blaine, and Cruz are solving the equation 4/7 (7 − n) = −1. Aaron started his solution by multiplying both sides of the equation by 7/4 . Blaine started by using the distributive property to multiply 4/7 by both 7 and −n. Cruz started by dividing both sides of the equation by 4/7 .

Which of the following is true?

A. Blaine and Cruz made an error in picking their first steps.

B. Cruz made an error in picking his first step.

C. All three made an error because the right side equals -1.

D. All three chose a valid first step toward solving the equation.

Given:

4/7(7 - n) = -1

Aaron:

4/7(7 - n) = -1

Multiple both sides by 7/4

4/7(7 - n) * 7/4 = -1 * 7/4

7 - n = -7/4

- n = -7/4 - 7

- n = (-7-28)/4

- n = -35/4

n = 35/4

Blaine:

4/7(7 - n) = -1

4/7(7 - n) × 7 = -1 × 7

4(7 - n) = -7

28 - 4n = -7

-4n = -7 - 28

- 4n = - 35

n = -35/-4

n = 35/4

Cruz:

4/7(7 - n) = -1

Divide both sides by 4/7

4/7(7 - n) ÷ 4/7 = -1 ÷ 4/7

4/7(7 - n) × 7/4 = -1 × 7/4

7 - n = -7/4

- n = (-7-28)/4

- n = -35/4

n = 35/4

D. All three chose a valid first step toward solving the equation.

7 0

2 years ago

Allowance $10 Earn $18 Spend $3.28, $7.15, and $9.54 Save?

julsineya [31]

Answer:

8.03

Step-by-step explanation:

10+18 = 28

28 - 3.28 - 7.15 - 9.54 = 8.03

4 0

2 years ago

on monday, it took 3 builders 5 1/2 hours to build a wall. an identical wall needs to be built on tuesday and 5 builders are ava

castortr0y [4]

Answer:

£29.37

Step-by-step explanation:

→ First step is to find the amount of hours it takes for 5 builders

$\frac{3*\frac{11}{2} }{5} =\frac{33}{2} /5=\frac{33}{2} *\frac{1}{5} =\frac{33}{10} =3\frac{3}{10}$

→ Now we know how long 5 builder takes we need to multiply the hourly rate by their time worked

$3\frac{3}{10} *8.90=\frac{33}{10} *8.90=3.3*8.90 = 29.37$

5 0

2 years ago

Read 2 more answers