For example:
(4/9) x=8
Now can solve this equation multiplying each side by 9/4.
(9/4)(4/9)x=(9/4)8
x=18
To check:
(4/9)(18)=(4*18)/9=72/9=8
This is a simple problem based on combinatorics which can be easily tackled by using inclusion-exclusion principle.
We are asked to find number of positive integers less than 1,000,000 that are not divisible by 6 or 4.
let n be the number of positive integers.
∴ 1≤n≤999,999
Let c₁ be the set of numbers divisible by 6 and c₂ be the set of numbers divisible by 4.
Let N(c₁) be the number of elements in set c₁ and N(c₂) be the number of elements in set c₂.
∴N(c₁) =
N(c₂) =
∴N(c₁c₂) =
∴ Number of positive integers that are not divisible by 4 or 6,
N(c₁`c₂`) = 999,999 - (166666+250000) + 41667 = 625000
Therefore, 625000 integers are not divisible by 6 or 4
Answer:
168miles
Corrected question;
12. Raymond is reading a road map. On the map, 1/4- inch represents 12 miles. Approximately
how many miles apart are two cities that are 3 1/2 - inches apart on Raymond's map?
F. 12
G. 48
H. 96
J. 132
K .168
Step-by-step explanation:
Given;
1/4 inch = 12 miles
3 1/2 = 7/2 = 14/4 inch
number of 1/4 inch in 14/4 inch is;
14/4 ÷ 1/4 = 14
14/4 inch = 12×14 miles = 168miles
Answer:
Total time of the concert = 59.5 min = 59 minute 30 seconds
Explanation:
At a school concert the orchestra plays 8 songs that are 4.25 min and 3 songs that are twice as long as each of the others.
Total length of 8 songs = 4.25*8 = 34 min
Length of 3 songs = 2*4.25 = 8.5 min
Total length of 3 songs = 3* 8.5 = 25.5 min
Total time of the concert = 34 + 25.5 = 59.5 min = 59 minute 30 seconds