Answer:
52
Step-by-step explanation:
We can write this out as an equation. Let's say that the teacher's age is x. Triple the teachers age plus the students age is 163, which can be written out as:
We want to isolate the variable, so subtract 7 from both sides. This gives us:
Finally, we divide both sides by 3, giving:
So the teacher is 52 years old.
Hope this helps!
For the derivative tests method, assume that the sphere is centered at the origin, and consider the
circular projection of the sphere onto the xy-plane. An inscribed rectangular box is uniquely determined
1
by the xy-coordinate of its corner in the first octant, so we can compute the z coordinate of this corner
by
x2+y2+z2=r2 =⇒z= r2−(x2+y2).
Then the volume of a box with this coordinate for the corner is given by
V = (2x)(2y)(2z) = 8xy r2 − (x2 + y2),
and we need only maximize this on the domain x2 + y2 ≤ r2. Notice that the volume is zero on the
boundary of this domain, so we need only consider critical points contained inside the domain in order
to carry this optimization out.
For the method of Lagrange multipliers, we optimize V(x,y,z) = 8xyz subject to the constraint
x2 + y2 + z2 = r2<span>. </span>
To compare the two classes, the Coefficient of Variation (COV) can be used. The formula for COV is this:
C = s / x
where s is the standard deviation and x is the mean
For the first class:
C1 = 10.2 / 75.5
C1 = 0.1351 (13.51%)
For the second class:
C2 = 22.5 / 75.5
C2 = 0.2980 (29.80%)
The COV is a test of homogeneity. Looking at the values, the first class has more students having a grade closer to the average than the second class.
$20×.25=$5
$20-$5=$15
$15×.15=$2.25
$15+$2.25=$17.25
$17.25 is your answer
Answer: 3550
Step-by-step explanation:
1.6L equals 1600mL
8700-1600=7100 remaining
7100 divided by 2 = 3550
