Average (mean) = (sum of all the data) / (# of data)
sum of all the data = (average)(# of data)
Thus for 100 students with an average of 93,
sum of all data = (93)(100) = 9300
and for 300 students with an average of 75,
sum of all data = (75)(300) = 22500
Therefore you would expect the overall average to be
(9300 + 22500) / (100 + 300) = 79.5 %
Now if there are x # of advanced students and y # of regular students, then
x + y = 90 (total # of students) and 93x + 75y = 87(x + y) (overall average)
The second equation can be simplified to x - 2y = 0
Subtracting the two equations yields
x = 60 and y = 90
Therefore you would need 60 advanced and 30 regular students.
First translate the English phrase "Four times the sum of a number and 15 is at least 120" into a mathematical inequality.
"Four times..." means we're multiplying something by 4.
"... the sum of a number and 15..." means we're adding an unknown and 15 and then multiplying the result by 4.
"... is at least 120" means when we substitute the unknown for a value, in order for that value to be in the solution set, it can only be less than or equal to 120.
So, the resulting inequality is 4(x + 15) ≤ 120.
Simplify the inequality.
4(x + 15) ≤ 120
4x + 60 ≤ 120 <-- Using the distributive property
4x ≤ 60 <-- Subtract both sides by 60
x ≤ 15 <-- Divide both sides by 4
Now that we have the inequality in a simplified form, we can easily see that in order to be in the solution set, the variable x can be no bigger than 15.
In interval notation it would look something like this:
[15, ∞)
In set builder notation it would look something like this:
{x | x ∈ R, x ≤ 15}
It is read as "the set of all x, such that x is a member of the real numbers and x is less than or equal to 15".
If the legs are legnth x, then the hyptonuse is x√2
x√2=7
divide both sides by √2
x=7/√2
times (√2)/(√2)
(7√2)/2
3.5√2
aprox 4.94974
round
4.95
Answer:
Number of catfish = 28
Step-by-step explanation:
Let the number of catfish = c
Number of angle fish = c + 6
Number of guppies = 4*(c + 6) = 4c + 4*6 = 4c + 24
Total fishes = 198
c + c + 6 + 4c + 24 = 198 {Combine like terms}
c + c +4c + 6 + 24 = 198
6c + 30 = 198 {Subtract 30 from both sides}
6c = 198 - 30
6c = 168
c = 168/6 {Divide both sides by 6}
c = 28
