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2 years ago

15

A certain forest covers an area of 2.000 square kilometers Suppose that each year this area, decreases by 5%. What is the equati

on that best represents the area
of the forest each year?

1 answer:

const2013 [10]2 years ago

6 0

where n is the number of years

2000 x 0.95^n

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According to a 2018 survey by Bankrate, 20% of adults in the United States save nothing for retirement (CNBC website). Suppose t

nalin [4]

Answer:

0.5981 = 59.81% probability that three or less of the selected adults have saved nothing for retirement

Step-by-step explanation:

For each adult, there are only two possible outcomes. Either they save nothing for retirement, or they save something. The probability of an adult saving nothing for retirement is independent of any other adult. This means that the binomial probability distribution is used to solve this question.

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 combinations 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.

20% of adults in the United States save nothing for retirement (CNBC website).

This means that $p = 0.2$

Suppose that sixteen adults in the United States are selected randomly.

This means that $n = 16$

What is the probability that three or less of the selected adults have saved nothing for retirement?

This is:

$P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)$

In which

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

$P(X = 0) = C_{16,0}.(0.2)^{0}.(0.8)^{16} = 0.0281$

$P(X = 1) = C_{16,1}.(0.2)^{1}.(0.8)^{15} = 0.1126$

$P(X = 2) = C_{16,2}.(0.2)^{2}.(0.8)^{14} = 0.2111$

$P(X = 3) = C_{16,3}.(0.2)^{3}.(0.8)^{13} = 0.2463$

$P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0281 + 0.1126 + 0.2111 + 0.2463 = 0.5981$

0.5981 = 59.81% probability that three or less of the selected adults have saved nothing for retirement

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2 years ago

A rectangular sheet of paper has a perimeter of 60cm. When it is folded in half along its longer line of symmetry, the perimeter

Liula [17]

Answer:

Dimensions of the original rectangle:

Length = 19 cm

Width = 11 cm

Step-by-step explanation:

Let

Length = x

Width = y

Original rectangle:

2(Length + width) = 60

2x + 2y = 60

New rectangle has same length with original rectangle but half of the width of the original rectangle when folded

Length = x

Width = 1/2y

2(Length + 1/2width) = 49

2x + y = 49

2x + 2y = 60 (1)

2x + y = 49 (2)

Subtract (2) from (1) to eliminate x

2y - y = 60 - 49

y = 11

Substitute y = 11 into (2)

2x + y = 49

2x + 11 = 49

2x = 49 - 11

2x = 38

x = 38/2

x = 19

Dimensions of the original rectangle:

Length = 19 cm

Width = 11 cm

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2 years ago

A rectangular room is 3 times as long as it is wide, and its perimeter is 48 meters. Find the dimension of the room.

nekit [7.7K]

Length: 12

Width: 4 since 12x4=48 and length is 3 times as long as it is wide.

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3 years ago