how do I set up this word problem: I have 88 pieces of gum, I gave 4 pieces each to all my class mates, I have 8 pieces left, ho
1 answer:
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Answer:
a. Check the attached image
b. The Pr(Y > 2) = ½
c. The mean is 2.4
d. The standard deviation is: 2.72
e. The exact value is 1 because it is certain from the given data that any probability will fall within that range.
Step-by-step explanation:
a. An image showing the step by step solution is attached.
b. P(Y > 2) = P(3) + P(4)
= 2/10 + 3/10 = 5/10 = ½
c. The mean is 2.4
d. The standard deviation is: 2.72
e. Check the attached image for the steps.
The solution to the equation x(x+4) = 6 is x = -2 + √10 or x = -2 - √10 after solving with the quadratic formula.
<h3>What is a quadratic equation?</h3>Any equation of the form where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.
As we know, the formula for the roots of the quadratic equation is given by:
We have an equation:
x(x + 4) = 6
By distributive property:
x² + 4x = 6
x² + 4x - 6 = 0
a = 1, b = 4, c = -6
Plugging all the values in the formula:
After calculating:
Thus, the solution to the equation x(x+4) = 6 is x = -2 + √10 or x = -2 - √10 after solving with the quadratic formula.
Learn more about quadratic equations here:
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Answer:
According to the Empirical Rule, 68% of the data should fall between 11.98 and 18.02
Step-by-step explanation:
We are given the following data in the question:
10, 11, 12, 13, 13, 13, 14, 15, 16, 16, 17, 18, 18, 19, 20
Formula:
where are data points,
is the mean and n is the number of observations.
Sum of squares of differences = 25 + 16 + 9 + 4 + 4+ 4 + 1 + 0+ 1+ 1 + 4 + 9 + 9+ 16 + 25 = 128
Empirical rule:
- According to this rule almost all the data lies within three standard deviation of the mean for a normal distribution.
- About 68% of data lies within one standard deviation of the mean.
- About 95% of data lies within two standard deviations of mean.
- Arround 99.7% of data lies within three standard deviation of mean.
Thus, by empirical rule,
According to the Empirical Rule, 68% of the data should fall between 11.98 and 18.02