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1 answer:
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The birth weight of elephants at the 85th percentile is 262.16 pounds
<h3>What is the standard deviation?</h3>Standard deviation is defined as the amount of variation or the deviation of the numbers from each other.
Given that:-
The average birth weight of elephants is 200 pounds = 200
The deviation of 60 pounds. = 60
The birth weight of elephants at the 85th percentile. z = 85%= 1.036
Now from the formula of z-score:-
Hence the birth weight of elephants at the 85th percentile is 262.16 pounds
To know more about standard deviation follow
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Answer:
The length of the diagonal = 3.6 feet
Step-by-step explanation:
* Lets change the story problem to equation to solve it
- Diagonal in a rectangle is the line which joining two
opposite vertices in it
- The diagonal , the length and the width formed together right
angle triangle where the diagonal is the hypotenuse of the
triangle and the length, the width are the two legs of the
right angle
- The length of the diagonal d is √(l² + w²) ⇒ Pythagoras theorem
∴ d² = l² + w²
- The diagonal is 2 feet more than the width
∴ d = w + 2
- The length is twice the width
∴ l = w
* Lets substitute the value of d and l in the equation of Pythagoras
∴ (w + 2)² = (2w)² + w² ⇒ solve the bracket
∴ w² + 4w + 4 = 4w² + w² ⇒ collect them in one side and add like term
∴ 4w² + w² - w² - 4w - 4 = 0 ⇒ add the like term
∴ 4w² - 4w - 4 = 0 ⇒ divide all term by 4
∴ w² - w - 1 = 0 ⇒ solve the quadratic using the formula
- In ax² + bx + c = 0
∵ a = 1 , b = -1 , c = -1
∴
-The value of the width is 1.6 feet
∴ The length = 1.6 × 2 = 3.2 feet
∴ The length of the diagonal = 2 + 1.6 = 3.6 feet