A rectangle is removed from the right hand corner of a square board. What is the area of the remaining board in square feet?

Mathematics

2 answers:

alukav5142 [94]4 years ago

7 0

Answer:

Step-by-step explanation:

<h3>METHOD 1:</h3>

<em>(picture #1)</em>

$A_1=(12)(8)=96\ ft^2\\\\A_2=(2)(4)=8\ ft^2\\\\A=A_1+A_2\Rightarrow A=96+8=104\ ft^2$

<h3>METHOD 2:</h3>

<em>(picture #2)</em>

$A_1=(12)(12)=144\ ft^2\\\\A_2=(10)(4)=40\ ft^2\\\\A=A_1-A_2\Rightarrow A=144-40=104\ ft^2$

irinina [24]4 years ago

5 0

Answer:

104 ft²

Step-by-step explanation:

12² - 4 x (12-2) = 144 - 40 = 104

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Since 1851, exactly 119 hurricanes have hit Florida (this includes the years 1851 and 2019),—only direct hits by hurricanes are

alukav5142 [94]

Answer:

There is a 0.58% probability of Florida being struck by four or more hurricanes in the same year.

Step-by-step explanation:

Since we have only the mean during the interval, we can solve this problem using the Poisson probability distribution.

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

Poisson probability distribution

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

In which

x is the number of sucesses

$e = 2.71828$ is the Euler number

$\mu$ is the mean in the given time interval.

In this problem, we have that:

Since 1851, exactly 119 hurricanes have hit Florida (this includes the years 1851 and 2019). Counting 1851 and 2019, there are 169 years in this interval. This means that $\mu = \frac{119}{169} = 0.704$

If the probability of hurricane strikes has remained the same since 1851, what is the probability of Florida being struck by four or more hurricanes in the same year?

This is $P(X \geq 4)$ .