Answer: a) 1 / ⁴⁰C₅ b) 0.33
Step-by-step explanation:
a) The sample space consists of all numbers 1-40.
Since any of the number can be taken from the sample space so each of five 5 distinct numbers we take has equal probability of occurring. So probability of each 5 numbers set we take will be equal to 1 / ⁴⁰C₅
b)
If we pick exactly 3 even number then that means other 2 will be odd.
So, we have sample space of 40 numbers out of which 20 are even and 20 are odd.
Now we have to pick 3 even out of 20 and 2 odd out of 20.
Probability = ²⁰C₃ * ²⁰C₂ / ⁴⁰C₅
Probability= 0.33
Answer:
Richard used 
of fabric for his project.
Step-by-step explanation:
Given:
Total amount of fabric = 
Now To convert a mixed fraction to an improper fraction, Multiply the whole number part by the fraction's denominator, Add that to the numerator,Then write the result on top of the denominator.
can be Rewritten as 
Number of pieces fabric was cut = 4
Richard is given one of four pieces of equal-sized fabric.
Amount of fabric Richard was given = 
Amount of fabric left with Richard = 
We need to find the amount of fabric Richards used for his project.
Solution:
Now we can say that;
amount of fabric Richards used for his project is equal to Amount of fabric Richard was given minus Amount of fabric left with Richard.
framing in equation form we get;
amount of fabric Richards used for his project = 
Now we will make the denominator common using LCM we get;
amount of fabric Richards used for his project = 
Now Denominator is same so we will solve the numerator.
amount of fabric Richards used for his project = 
can be rewritten as
Hence Richard used of fabric for his project.
Answer:
- Library 2 charges more for each book loaned.
- Library 1 has a cheaper subscription fee.
Step-by-step explanation:
Based on the table, we can write the equation for the cost of borrowing from Library 2 using the two-point form of the equation of a line:
y = (y2 -y1)/(x2 -x1)(x -x1) +y1
for (x1, y1) = (2, 15.50) and (x2, y2) = (8, 26) this equation becomes ...
y = (26 -15.50)/(8 -2)(x -2) +15.50 . . . . . fill in the values
y = (10.50/6)(x -2) +15.50 . . . . . . . . . . . . simplify a bit
y = 1.75x -3.50 +15.50 . . . . . . simplify more
In the above, we have x = number of books; y = cost. We can use "n" and "C" for those, respectively, as in the equation for Library 1. Then the monthly cost for Library 2 is ...
C = 12 + 1.75n . . . . . . . arranged to the same form as for Library 1
_____
Now, we can answer the questions.
Library 2 charges more for each book loaned. (1.75 vs 1.50 for Library 1)
Library 1 has a cheaper subscription fee. (10 vs 12 for Library 2)
_____
The numbers in the cost equations are ...
C = (subscription fee) + (cost per book loaned)·n
When the "product" is used in math it means to multiply so.
0.13 x 2.07 = 0.2691
0.73 x 1.5 = 1.095
