Question

1. last semester, each of the 4 students listed below took 6 classes worth 1 credit each. in the 1st matrix, the row corresponding to each student gives the counts of the letter grades earned by that student. the second matrix gives the point value of each letter grade.

letter grades
points per letter grade
josé
a b c d f
a
5
dwayne
0 3 2 1 0
b
4
ann
2 3 1 0 0
c
3
maria
1 3 2 0 0
d
2
4 2 0 0 0
f
0
the grade point average of each student is the total number of grade points earned by that student divided by that students total number of class credits. to the nearest 0.01, what is anns grade point average?
a. 1.92
b. 2.00
c. 3.00
d. 3.83
e. 4.00

1. a circle with the equation x² + y² = 16 is graphed in the standard (x,y) coordinate plane. at what points does the circle intersect the x - axis?

f. (-2,0) and (2,0)
g. (-4,0) and (4,0)
h. (-8,0) and (8,0)
j. (-16,0) and (16,0)
k. (-32,0) and (32,0)

1. joanna drives a route that is exactly 450 miles from little rock, arkansas, to mobile, alabama. joanna has already driven 180 miles at an average speed of 60 miles per hour. what is the minimum average speed, in miles per hour, that joanna can drive for the remainder of the route and have a driving time of 9 hours for the entire trip?

a. 45
b. 50
c. 55
d. 60
e. cannot be determined from the given information

1. what is the least positive number that has a remainder of 3 when divided by 5 and a remainder of 4 when divided by 6?

f. 18
g. 23
h. 28
j. 30
k. 39

Explanation:

17.

Step1: Calculate Ann's total grade - points

Multiply grade - count by points per grade and sum. Ann's grade - count vector is $[1,3,2,0,0]$ and points per grade vector is $[5,4,3,2,0]$. Total points $=1\times5 + 3\times4+2\times3+0\times2 + 0\times0=5 + 12+6+0 + 0=23$.

Step2: Calculate Ann's grade - point average

Ann took 6 classes (total credits). Grade - point average $=\frac{23}{6}\approx3.83$.

Step1: Find intersection with x - axis

On the x - axis, $y = 0$. Substitute $y = 0$ into the circle equation $x^{2}+y^{2}=16$. We get $x^{2}+0^{2}=16$, so $x^{2}=16$, then $x=\pm4$.

Step1: Calculate time already driven

JoAnna has driven 180 miles at 60 miles per hour. Time already driven $t_1=\frac{180}{60}=3$ hours.

Step2: Calculate remaining distance and time

Remaining distance $d = 450 - 180=270$ miles. Total time allowed is 9 hours, so remaining time $t_2=9 - 3 = 6$ hours.

Step3: Calculate minimum average speed for the remaining part

Minimum average speed $v=\frac{270}{6}=45$ miles per hour.

Answer:

D. 3.83

18.