32 teams in 4 divisions
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<u>Given</u>:
The length of a rectangle is 5 less than its width.
The area of the rectangle is 84 square feet.
We need to determine the quadratic equation in standard form that represents the area of the rectangle.
<u>Dimensions of the rectangle:</u>
Let l denote the length of the rectangle.
Let w denote the width of the rectangle.
Since, it is given that the length is 5 less than its width, it can be written as,
and
<u>Area of the rectangle:</u>
The area of the rectangle can be determined using the formula,
Substituting A = 84, and
, we get
Adding both sides of the equation by w², we have;
Subtracting by 5w on both sides, we get;
Thus, the quadratic equation in standard form for the area of the rectangle is
Answer:
The probability that <em>X</em> is less than 42 is 0.1271.
Step-by-step explanation:
The random variable <em>X </em>follows a Normal distribution.
The mean and standard deviation are:
E (X) = <em>μ</em> = 50.
SD (X) = <em>σ</em> = 7.
A normal distribution is continuous probability distribution.
The Normal probability distribution with mean µ and standard deviation σ is given by,
To compute the probability of a Normal random variable we first standardize the raw score.
The raw scores are standardized using the formula:
These standardized scores are known as <em>z</em>-scores and they follow normal distribution with mean 0 and standard deviation 1.
Compute the probability of (X < 42) as follows:
*Use a <em>z</em>-table for the probability.
Thus, the probability that <em>X</em> is less than 42 is 0.1271.
The normal curve is shown below.
