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DENIUS [597]
3 years ago
13

Henry wants to paint the ceilings and the walls of his living room. One gallon of paint covers 450 ft squared. The rooms is 24 f

t by 18 ft, and the walls are 9 ft high. How many gallons of paint will Henry need to paint his living room?
Mathematics
1 answer:
Mamont248 [21]3 years ago
6 0
If you would like to know how many gallons of paint will Henry need to paint his living room, you can calculate this using the following steps:

the ceiling: 24 ft * 18 ft = 432 ft squared
walls: 2 * 24 ft * 9 ft + 2 * 18 ft * 9 ft = 2 * 24 * 9 + 2 * 18 * 9 = 432 + 324 = 756 ft squared

432 ft squared + 756 ft squared = 1188 ft squared

1 gallon of paint ... 450 ft squared
x gallons of paint = ? ... 1188 ft squared

1 * 1188 = 450 * x
1188 = 450 * x    /450
x = 1188 / 450
x = 2.64 gallons of paint

The correct result would be 2.64 gallons of paint.
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Complete question:

Consider a class of 20 students consisting of 5 sophomores, 8 juniors, and 7 seniors. A math instructor assigns a group project in each of the scenarios below, the instructor selects 5 consecutive students from this class, keeping track (in order) of the level of the student that he gets.

1a. How many possible outcomes are in the sample space S? (An outcome is a 5- tuple of students.)

Let A2 denote the event that exactly 2 of the selected students are sophomore, A5 denote the event that exactly 5 of the selected students are the juniors, and A4 denote the event that exactly 4 of the selected students are seniors.

1b. Find the probabilities of each of these three events. A2, A5, A4

1c. Do the events A2, A5, A4 constitute a partition of the sample space?

Answer:

Given:

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a) The possible outcome in the sample space,S, =

ⁿCₓ = ²⁰C₅

= \frac{20!}{(20-5)! 5!)}

= \frac{20*19*18*17*16}{5*4*3*2*1}

= 15504

b) probabilities of A2, A5, A4

P(A2) = ⁵C₂ / ²⁰C₂

= \frac{20}{320} = \frac{1}{19}

P(A5) = ⁸C₅ / ²⁰C₅

= \frac{56}{15540} = \frac{7}{1938}

P(A4) = ⁷C₄ / ²⁰C₄

= \frac{35}{4845} = \frac{7}{969}

c) No,the events A2, A5, A4, do not comstitute a partition of the sample space. i.e P(A2)+P(A5)+P(A4) ≠ 1

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Answer:

Step-by-step explanation:

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