If a function f(m) models the number of hours it take to hike m miles through the jungle, which describes the appropriate domain
2 answers:
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Answer:
(a) The expected value and standard deviation of the amount of ice cream served at the party are 54 ounces and 1.25 ounces respectively.
(b) The expected value and standard deviation of the amount of ice cream left in the box after scooping out one scoop are 46 ounces and 1.031 ounces respectively.
(c) Because the variance of each variable is dependent on the other.
Step-by-step explanation:
The random variable <em>X</em> and <em>Y</em> are defined as follows:
<em>X</em> = amount of ice cream in the box
<em>Y</em> = amount of ice cream scooped out
The information provided is:
E (X) = 48
SD (X) = 1
V (X) = 1
E (Y) = 2
SD (Y) = 0.25
V (Y) = 0.0625
(a)
The total amount of ice-cream served at the party can be expressed as:
<em>X</em> + 3<em>Y</em>.
Compute the expected value of (<em>X</em> + 3<em>Y</em>) as follows:
Compute the variance of (<em>X</em> + 3<em>Y</em>) as follows:
Then the standard deviation of (<em>X</em> + 3<em>Y</em>) is:
Thus, the expected value and standard deviation of the amount of ice cream served at the party are 54 ounces and 1.25 ounces respectively.
(b)
The amount of ice-cream left in the box after scooping out one scoop is represented as follows:
<em>X</em> - <em>Y</em>.
Compute the expected value of (<em>X</em> - <em>Y</em>) as follows:
Compute the variance of (<em>X</em> - <em>Y</em>) as follows:
Then the standard deviation of (<em>X</em> - <em>Y</em>) is:
Thus, the expected value and standard deviation of the amount of ice cream left in the box after scooping out one scoop are 46 ounces and 1.031 ounces respectively.
(c)
The variance of the sum or difference of two variables is computed by adding the individual variances. This is because the variance of each variable is dependent on the others.
The average speed of Joshua during that time is 2500 m/h.
Explanation:
It is given that Joshua started cycling at 5:15 pm. By 8:09 pm he has covered a distance of 7250 m.
The total time taken by Joshua from 5:15 pm to 8:09 pm is
Dividing we get,
Adding, we have,
Thus, the total time taken by Joshua is
To determine the average speed we use the formula,
where and
Hence, substituting the values we have,
Dividing, we get,
Thus, the average speed of Joshua during that time is 2500 m/h.