Question

1. 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
2. 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
3. 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})
4. 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})?
5. in the standard ((x,y)) - coordinate plane, the mid - point of (overline{cd}). point c has coordinates ((-4,3)) and the mid - point of (overline{cd}) has coordinates ((3,\frac{13}{2})). 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)
6. at his job, the first 40 hours of each week thomas works is regular time, and any additional hours he works is overtime. thomas gets paid $12 per hour during regular time. during overtime, he gets paid 1.5 times as much as he gets paid during regular time. thomas works 46 hours in 1 week and has $128 in deductions taken out of his pay. after these deductions are taken out, how much money, in dollars, does thomas have remaining for this week? a. $492 b. $573 c. $609 d. $618 e. $735
7. at sweet stuff fresh produce, the price per pound of red grapes depends on the total number of pounds purchased at 1 time, as shown in the table below. sweet stuff this week purchased 10 pounds of red grapes on monday and 15 pounds of red grapes on friday. how much money would sweet stuff have saved if it had instead purchased 25 pounds of red grapes on monday?

Explanation:

Step1: Calculate distance traveled

Manish was 510 km from Baton Rouge at 8:00 a.m. and 105 km from Baton Rouge at 1:00 p.m. 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 formula is $v=\frac{d}{t}$. Substituting $d = 405$ km and $t = 5$ hours, we get $v=\frac{405}{5}=81$ km/h.

Step1: Use similar - triangles property

Since $DE\parallel BC$ and $FG\parallel BC$, we can use the property of similar triangles. Let $\triangle ADE\sim\triangle ABC$ and $\triangle AFG\sim\triangle ABC$.
We know that $\frac{AE}{AC}=\frac{AD}{AB}$ and $\frac{AG}{AC}=\frac{AF}{AB}$.
First, find the ratio of the sides of similar triangles. Consider the two - tiered similar - triangle situation.
The length of $AE = 14$ and $AG=14 + 12=26$. Let $AC=x$.
We can set up the proportion using the fact that the ratios of corresponding sides of similar triangles are equal.
Let's consider the first set of similar triangles $\triangle ADE$ and $\triangle ABC$. The ratio of the sides gives us a relationship.
We know that $\frac{AE}{AC}=\frac{AD}{AB}$. Also, from the figure, we can see that we can add up the segments along $AC$.
$AC=16 + 14+12=42$ feet.

Step1: Convert hours to minutes

Katerina runs 15 miles in $2.5$ hours. Since 1 hour = 60 minutes, $2.5$ hours is $2.5\times60 = 150$ minutes.

Step2: Calculate minutes per mile

To find the average number of minutes per mile, we use the formula $m=\frac{M}{n}$, where $M$ is the total number of minutes and $n$ is the number of miles. Substituting $M = 150$ minutes and $n = 15$ miles, we get $m=\frac{150}{15}=10$ minutes per mile.

Answer:

H. 81