8. manish drove from chicago to baton rouge. at 8:00 a.m., he was 510 km from baton rouge. at 1:00 p.m., he was 105 km from baton rouge. which of the following values is closest to manishs average speed, in kilometers per hour, from 8:00 a.m. to 1:00 p.m.?
f. 58
g. 68
h. 81
j. 94
k. 102

9. in the figure shown below, e and g lie on (overline{ac}), d and f lie on (overline{ab}), (overline{de}) and (overline{fg}) are parallel to (overline{bc}), and the given lengths are in feet. what is the length of (overline{ac}), in feet?
a. 13
b. 26
c. 29
d. 42
e. 48

10. katerina runs 15 miles in (2\frac{1}{2}) hours. what is the average number of minutes it takes her to run 1 mile?
f. 6
g. 10
h. (12\frac{1}{2})
j. (16\frac{2}{3})
k. (17\frac{1}{2})

11. a bag contains 8 red marbles, 9 yellow marbles, and 7 green marbles. how many additional red marbles must be added to the 24 marbles already in the bag so that the probability of randomly drawing a red marble is (\frac{3}{5})?
a. 11
b. 16
c. 20
d. 24
e. 32

12. in the standard ((x,y)) coordinate plane, the point ((2,1)) is the mid - point of (overline{cd}). point c has coordinates ((6,8)). what are the coordinates of point d?
f. ((-2,-\frac{7}{2}))
g. ((-2,-6))
h. ((4,\frac{9}{2}))
j. ((10,10))
k. ((10,15))

13. at his job, the first 40 hours of each week that thomas works is regular time, and any additional time that he works is overtime. thomas gets paid $15 per hour during regular time. during overtime thomas gets paid 1.5 times as much as he gets paid during regular time. thomas works 46 hours in 1 week and gets $117 in deductions taken out of his pay for this week. after the deductions are taken out, how much of thomass pay for this week remains?
a. $492
b. $573
c. $609
d. $618
e. $735

14. at sweet stuff fresh produce the price of a bag of grapes depends on the total number of bags purchased at 1 time, as shown in the table below. in 2 trips to sweet stuff this week, janelle purchased 3 bags of grapes on monday and 4 bags of grapes on wednesday. how much money would janelle have saved if she had instead purchased 7 bags of grapes in 1 trip on monday?
| number of bags | price per bag |
|----|----|
| 1 - 3 | $3.00 |
| 4 - 6 | $2.80 |
| 7 - 9 | $2.60 |
| 10 or more | $2.50 |
f. $0.20
g. $1.00
h. $1.40
j. $2.00
k. $2.50

15. what is 3% of (4.14 imes10^{4})?
a. 1,242
b. 1,380
c. 12,420
d. 13,800
e. 124,200

Question

8. manish drove from chicago to baton rouge. at 8:00 a.m., he was 510 km from baton rouge. at 1:00 p.m., he was 105 km from baton rouge. which of the following values is closest to manishs average speed, in kilometers per hour, from 8:00 a.m. to 1:00 p.m.?
f. 58
g. 68
h. 81
j. 94
k. 102

9. in the figure shown below, e and g lie on (overline{ac}), d and f lie on (overline{ab}), (overline{de}) and (overline{fg}) are parallel to (overline{bc}), and the given lengths are in feet. what is the length of (overline{ac}), in feet?
a. 13
b. 26
c. 29
d. 42
e. 48

10. katerina runs 15 miles in (2\frac{1}{2}) hours. what is the average number of minutes it takes her to run 1 mile?
f. 6
g. 10
h. (12\frac{1}{2})
j. (16\frac{2}{3})
k. (17\frac{1}{2})

11. a bag contains 8 red marbles, 9 yellow marbles, and 7 green marbles. how many additional red marbles must be added to the 24 marbles already in the bag so that the probability of randomly drawing a red marble is (\frac{3}{5})?
a. 11
b. 16
c. 20
d. 24
e. 32

12. in the standard ((x,y)) coordinate plane, the point ((2,1)) is the mid - point of (overline{cd}). point c has coordinates ((6,8)). what are the coordinates of point d?
f. ((-2,-\frac{7}{2}))
g. ((-2,-6))
h. ((4,\frac{9}{2}))
j. ((10,10))
k. ((10,15))

13. at his job, the first 40 hours of each week that thomas works is regular time, and any additional time that he works is overtime. thomas gets paid $15 per hour during regular time. during overtime thomas gets paid 1.5 times as much as he gets paid during regular time. thomas works 46 hours in 1 week and gets $117 in deductions taken out of his pay for this week. after the deductions are taken out, how much of thomass pay for this week remains?
a. $492
b. $573
c. $609
d. $618
e. $735

14. at sweet stuff fresh produce the price of a bag of grapes depends on the total number of bags purchased at 1 time, as shown in the table below. in 2 trips to sweet stuff this week, janelle purchased 3 bags of grapes on monday and 4 bags of grapes on wednesday. how much money would janelle have saved if she had instead purchased 7 bags of grapes in 1 trip on monday?
| number of bags | price per bag |
|----|----|
| 1 - 3 | $3.00 |
| 4 - 6 | $2.80 |
| 7 - 9 | $2.60 |
| 10 or more | $2.50 |
f. $0.20
g. $1.00
h. $1.40
j. $2.00
k. $2.50

15. what is 3% of (4.14	imes10^{4})?
a. 1,242
b. 1,380
c. 12,420
d. 13,800
e. 124,200

Accepted Answer

### 8.
# Explanation:
## Step1: Calculate distance traveled
The distance at 8:00 a.m. is 510 km from Baton - Rouge and at 1:00 p.m. is 105 km from Baton - Rouge. So the distance traveled $d=510 - 105=405$ km.
## Step2: Calculate time elapsed
The time from 8:00 a.m. to 1:00 p.m. is $t = 5$ hours.
## Step3: Calculate average speed
The average speed $v=\frac{d}{t}=\frac{405}{5}=81$ km/h.
# Answer:
H. 81

### 9.
# Explanation:
## Step1: Use similar - triangles property
Since $DE\parallel BC$ and $FG\parallel BC$, we have similar triangles. Let $	riangle ADE\sim	riangle ABC$ and $	riangle AFG\sim	riangle ABC$.
We know that $\frac{AE}{AC}=\frac{AD}{AB}$. Let $AC = x$. From the similar - triangles formed by $DE\parallel BC$, we have $\frac{AE}{x}=\frac{AD}{AD + DF+FB}$. Given $AD = 8$, $DF = 7$, $FB = 6$, and $AE = 16$.
The ratio of the sides of similar triangles gives $\frac{16}{x}=\frac{8}{8 + 7+6}=\frac{8}{21}$.
## Step2: Solve for $x$
Cross - multiply: $8x=16	imes21$, then $x = 42$.
# Answer:
D. 42

### 10.
# Explanation:
## Step1: Convert hours to minutes
$2\frac{1}{2}$ hours is $2.5	imes60 = 150$ minutes.
## Step2: Calculate minutes per mile
The average number of minutes per mile is $\frac{150}{15}=10$ minutes per mile.
# Answer:
G. 10

### 11.
# Explanation:
## Step1: Let the number of additional red marbles be $x$
The total number of marbles after adding $x$ red marbles is $24 + x$, and the number of red marbles is $8 + x$.
## Step2: Set up the probability equation
We want $\frac{8 + x}{24 + x}=\frac{3}{5}$.
## Step3: Cross - multiply and solve
Cross - multiplying gives $5(8 + x)=3(24 + x)$.
Expand: $40+5x = 72+3x$.
Subtract $3x$ from both sides: $40 + 2x=72$.
Subtract 40 from both sides: $2x=32$.
Divide by 2: $x = 16$.
# Answer:
B. 16

### 12.
# Explanation:
## Step1: Use the mid - point formula
The mid - point formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Let the coordinates of point $D$ be $(x,y)$. Given the mid - point of $CD$ is $(2,1)$ and $C(6,8)$.
We have $\frac{6 + x}{2}=2$ and $\frac{8 + y}{2}=1$.
## Step2: Solve for $x$ and $y$
For $x$: $6 + x=4$, so $x=-2$.
For $y$: $8 + y = 2$, so $y=-6$.
# Answer:
G. $(-2,-6)$

### 13.
# Explanation:
## Step1: Calculate regular - time pay
Thomas works 40 regular hours at $15$ per hour, so the regular - time pay is $40	imes15 = 600$ dollars.
## Step2: Calculate overtime pay
He works $46-40 = 6$ overtime hours. The overtime pay rate is $15	imes1.5=22.5$ dollars per hour. So the overtime pay is $6	imes22.5 = 135$ dollars.
## Step3: Calculate total pay before deductions
The total pay before deductions is $600+135 = 735$ dollars.
## Step4: Calculate pay after deductions
After a $117$ - dollar deduction, the pay remaining is $735−117 = 618$ dollars.
# Answer:
D. $618

### 14.
# Explanation:
## Step1: Calculate the cost of two separate purchases
On Monday, Janelle bought 3 bags at $3$ per bag, so she spent $3	imes3 = 9$ dollars. On Wednesday, she bought 4 bags at $2.8$ per bag, so she spent $4	imes2.8 = 11.2$ dollars. The total cost of two separate purchases is $9 + 11.2=20.2$ dollars.
## Step2: Calculate the cost of one purchase
If she bought 7 bags in one trip, the price per bag is $2.6$ dollars, and the total cost is $7	imes2.6 = 18.2$ dollars.
## Step3: Calculate the savings
The savings is $20.2−18.2 = 2$ dollars.
# Answer:
J. $2.00

### 15.
# Explanation:
## Step1: Convert 3% to a decimal
$3\%=0.03$.
## Step2: Calculate 3% of $4.14	imes10^{4}$
$0.03	imes4.14	imes10^{4}=0.03	imes41400 = 1242$.
# Answer:
A. 1,242

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

8.

Step1: Calculate distance traveled

Step2: Calculate time elapsed

Step3: Calculate average speed

Step1: Use similar - triangles property

Step2: Solve for $x$

Step1: Convert hours to minutes

Step2: Calculate minutes per mile

Answer:

9.