Answer:
a) 
b) 
Step-by-step explanation:
a) Lets denote 
the cumulative distribution function of X. Note that for any value a between 0 and I/2, we have that 
is the probability for the stick to be broken before the length a is reached following the stick from one starting point plus the probability for the stick to be broken after the length I-a from the same starting point. This means that 
b) Note that, as a consecuence of what we calculate in the previous item, X has a uniform distribution with parameter I/2, therefore, the probability density function f is
f(x) = 1/(I/2) = 2/I
Answer:
61 hours
Step-by-step explanation:
See the attached figure to better understand the problem
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form 
or 
To find out the constant of proportionality k , divide the variable y (total earned) by the variable x (number of hours)
<em>Kevin's wage</em>
Take any point from the table
I take the point (2,16.50)
The equation of the proportional relationship is equal to
substitute the value of k
For y=$500.00
substitute the value of y in the equation and solve for x
Divide by 8.25 both sides
Answer:
<em>147 toys</em>
Step-by-step explanation:
<em>for 1 person, 28toys/8hours = 3.5toys/ 1hour </em>
<em>for 42 people, 42 * 3.5toys/ 1hour = 147 toys/hour</em>
<em></em>
<em>~Hope it Helps!~</em>
Answer:
<em>Herlene has 8 dimes and 17 quarters</em>
Step-by-step explanation:
<u>System of Equations</u>
Let's call:
x = number of dimes Herlene has
y = number of quarters Herlene has
Since each dime has a value of $0.10 and each quarter has a value of $0.25, the total money Herlene has is 0.10x+0.25y.
We know this amount is $5.05, thus:
0.10x + 0.25y = 5.05 [1]
It's also given the number of quarters is one more than twice the number of dimes, i.e.:
y = 2x + 1 [2]
Substituting in [1]:
0.10x + 0.25(2x + 1) = 5.05
Operating:
0.10x + 0.5x + 0.25 = 5.05
0.6x = 5.05 - 0.25
0.6x = 4.8
x = 8
From [2]:
y = 2*8 + 1 = 17
y = 17
Herlene has 8 dimes and 17 quarters
When expanding number, we should separate the numbers according to the places like the number 275 written in expanded form 200+70+5. So, in this question we must likely done like this. The number is 39,005 the sum that is written on expanded form is 30,000+9,000+5.
