Clearly, |S| = 50.
Count the multiples of 2 between 1 and 50:
⌊50/2⌋ = ⌊25⌋ = 25
(where ⌊x⌋ denotes the "floor of x", or the largest integer that is smaller than or equal to x; in other words, round <u>down</u> to the nearest integer)
Count the multiples of 3 between 1 and 50:
⌊50/3⌋ ≈ ⌊16.667⌋ = 16
Since LCM(2, 3) = 6, the sets of multiples of 2 and multiples of 3 have some overlap. Count the multiples of 6 between 1 and 50:
⌊50/6⌋ ≈ ⌊8.333⌋ = 8
Then by the inclusion/exclusion principle, we remove from S
25 + 16 - 8 = 33
elements, so that the new set S contains 50 - 33 = 17 elements.
9514 1404 393
Answer:
3.75 hours
Step-by-step explanation:
Travel time can be found using the relation ...
time = distance/speed
time = (2475 mi)/(660 mi/h) = 3.75 h
It will take 3 3/4 hours to travel that distance.
Answer:
H0: mu = 5
Ha: mu > 5
Step-by-step explanation:
A null hypothesis is a statement from a population parameter which is either rejected or accepted (fail to reject) upon testing.
It is expressed using the equality sign.
An alternate hypothesis is also a statement from a population parameter which negates the null hypothesis and is accepted if the null hypothesis is rejected.
It is expressed using any of the inequality signs.
Answer:
30 pounds of raspberries and 50 pounds of blueberries
Step-by-step explanation:
Let's use b to represent blueberries and r for raspberries. Each pound of raspberries costs $1, so to find the total cost of raspberries we use 1r, which is just r. For blueberries, we do 3.25b.
r+3.25b=192.5
We also know that we can combine the numbers for 80 total pounds.
r+b=80
We can subtract the two equations we have made to eliminate the r and solve for b.
2.25b=112.5
We divide both sides by 2.25.
b=50
We know that r+b=80, so if b is 50 then r must be 30.
Have a wonderful day! :D
