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2 years ago

The length of a room is 2 1/2 feet more than its width. If the perimeter of the room is 80 feet, find its width and length?

Mathematics

1 answer:

horsena [70]2 years ago

4 0

Answer:

The width is 20.625 and the length is 19.375

Step-by-step explanation:

Let 2 1/2 + w = length

Let w = width

Equation:

2 1/2 + w + w = 80 Combine liked terms

2 1/2 + 2w = 80

-2 1/2 -2 1/2 Subtract 2 1/2 from both sides

2w = 77.5

÷ 2 ÷ 2 Divide 2 from both sides

w = 41.25

Length:

2 1/2 + 41.25 = 165/4 or 38.75

Width:

41.25

41.25/2 = 20.625

38.75/2 = 19.375

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3 years ago

Find the inverse of the linear function y=1/2x+3.

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Answer:

2(x-3) = y

Step-by-step explanation:

y = 1/2 x +3

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3 years ago

Read 2 more answers

A food-packaging apparatus underfills 10% of the containers. Find the probability that for any particular 10 containers the numb

Maksim231197 [3]

Answer:

a) $P(X = 1) = 0.38742$

b) $P(X = 3) = 0.05740$

c) $P(X = 9) = 0.00000$

d) $P(X \geq 5) = 0.00163$

Step-by-step explanation:

For each container, there are only two possible outcomes. Either it is undefilled, or it is not. This means that we can solve this problem using the binomial probability distribution.

Binomial probability distribution:

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinatios of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

In this problem

There are 10 containers, so $n = 10$ .

A food-packaging apparatus underfills 10% of the containers, so $p = 0.1$ .

a) This is P(X = 1)

$P(X = 1) = C_{10,1}.(0.1)^{1}.(0.9)^{9} = 0.38742$

b) This is P(X = 3)

$P(X = 3) = C_{10,3}.(0.1)^{3}.(0.9)^{7} = 0.05740$

c) This is P(X = 9)

$P(X = 9) = C_{10,9}.(0.1)^{9}.(0.9)^{1} = 0.00000$

d) This is $P(X \geq 5)$ .

Either the number is lesser than five, or it is five or larger. The sum of the probabilities of each event is decimal 1. So:

$P(X < 5) + P(X \geq 5) = 1$

$P(X \geq 5) = 1 - P(X < 5)$

In which

$P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{10,0}.(0.1)^{0}.(0.9)^{10} = 0.34868$

$P(X = 1) = C_{10,1}.(0.1)^{1}.(0.9)^{9} = 0.38742$

$P(X = 2) = C_{10,2}.(0.1)^{2}.(0.9)^{8} = 0.1937$

$P(X = 3) = C_{10,3}.(0.1)^{3}.(0.9)^{7} = 0.05740$

$P(X = 4) = C_{10,4}.(0.1)^{1}.(0.9)^{9} = 0.38742$

$P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.34868 + 0.38742 + 0.19371 + 0.05740 + 0.01116 = 0.99837$

Finally

$P(X \geq 5) = 1 - P(X < 5) = 1 - 0.99837 = 0.00163$

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2 years ago

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weeeeeb [17]

Answer:

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3 years ago

Read 2 more answers

the length of a rectangle is 2 inches longer than twice its width. If the area of the rectangle is 24 square inches, what are th

gregori [183]

Answer:

The length is 8 inches and the width is 3 inches

Step-by-step explanation:

Let w represent the width.

The length can be represented by 2w + 2

Use the area formula, A = lw, and plug in the area and the expressions for the length and width:

A = lw

24 = (2w + 2)(w)

Simplify and solve for w:

24 = 2w² + 2w

2w² + 2w - 24

Divide everything by 2:

w² + w - 12

Factor:

(w + 4)(w - 3)

Set equal to 0 and solve for each factor:

w + 4 = 0

w = -4

w - 3 = 0

w = 3

Since the width cannot be negative, the width has to be 3.

Next, find the length by plugging in 3 as w:

2w + 2

2(3) + 2

= 8

So, the length is 8 inches and the width is 3 inches

7 0

2 years ago

The length of a room is 2 1/2 feet more than its width. If the perimeter of the room is 80 feet, find its width and length?​

The length of a room is 2 1/2 feet more than its width. If the perimeter of the room is 80 feet, find its width and length?