4 x = 36
Step-by-step explanation:
Because the groups have an equal number of students, we assume that each of the groups has <em>x </em>number of students.
Therefore since there is <em>x</em> number of students in each of the 4 groups, there is 4 * x number of total students in all groups combined.
Since the question already indicates that there are a total of 36 students in the class, then we can indicate that..
4x = 36
Cosine functions are positive in quadrant 4
Here is a helpful mnemonic All Students Take Calculus (might be helpful in the future)
Answer:
Step-by-step explanation:
Let the price for children and adults package be represented with x and y respectively.
For the first week the sum of the package will be as follows:
3x+8y = 126
For the two weeks after:
6x+4y= 108
So, we will be having two equations
3x+8y = 126..... (1)
6x+4y= 108.......(2)
These are simultaneous equations
From equation 1
3x+8y = 126
3x = 126-8y
X = 126-8y/3 ............. (3)
Put equation 3 into 2
6 ( 126-8y)/3 +4y = 108
756-48y/3 +4y = 108
756-48y+12y/3 = 108
Cross multiplying
756-48y+12y= 108×3
756-48y+ 12y = 324
Collecting like terms
756-324 = 48y-12y
432= 36y
Divide both sides by 36
432/36 = 36y/36
y= 12
Substituting y into equation 1
3x+8= 126
3x+96=126
3x= 126-96
3x= 30
Divide both sides by 3
3x/3 = 30/3
x = 10
Hence for each of the packages for children and adults. It will be 10 and 12 respectively.
Answer:
220 miles
Step-by-step explanation:
65 miles per hour for 2 hours — 65+ 65 = 130
60 miles per hour for 1.5 hours — 60 (for the 1 hour) + 30 (for the half hour) = 90
130 + 90 = 220
The equation described above can also be written as,
y = -x² + 100x + 4000
To get the number of notebooks that will give them the maximum profit, we derive the equation and equate to zero.
dy/dx = -2x + 100 = 0
The value of x from the equation is 50. Then, we substitute 50 to the original equation to get the profit.
y = -(50^2) + 100(50) + 4000 = 6500
Thus, the maximum profit that the company makes is $6,500/day.
