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.
Let's just choose "x" as our variable for the length of a side of the triangle.
Two sides of a triangle are equal in length and double the length of the shortest side.
A triangle has 3 sides. Make the smallest side x then the two equal sides that are double the smallest side are both equal to 2x
The perimeter of the triangle is 35 inches. Perimeter is the sum of all sides.
x + 2x + 2x = 35
5x = 35
x = 7
So the smallest side is 7, and the other two sides are 14.
Answer: option d. the argument is valid by the law of detachment.
The law of detachment consists in make a conlcusion in this way:
Premise 1) a => b
Premise 2) a is true
Conclusion: Then, b is true
Note: the order of the premises 1 and 2 does not modifiy the argument.
IN this case:
Premise 1) angle > 90 => obtuse
Premise 2) angle = 102 [i.e. it is true that angle > 90]]
Conclusion: it is true that angle is obtuse
Answer:
$20.63 if you tip on the pre-tax amount
Step-by-step explanation:
You pay $12.99 for the pizza, plus the 8% tax on the pizza, plus the 20% tip of the cost of the pizza, so if you tip on the pre-tax amount, you pay
$12.99(0.08) = $1.04 in sales tax
$12.99(0.2) = $2.60 for the tip
and $4 delivery charge,
so you pay a total of
$12.99 + $1.04 + $2.60 + $4 = $20.63
A mixed number is a combination of a whole number and a fraction, so in this case we have 8 as the whole part and 0.45 as the fraction, 0.45 is equal to 45/100, and that fraction can be simplified as well, lets see:
8.45 = 8 45/100
= 8 9/20
