24. the set of all positive integers that are divisible by both 15 and 35 is infinite. what is the least positive integer in this set? f. 5 g. 50 h. 105 j. 210 k. 525
25. in △abc shown below, the measure of ∠a is 58°, and (overline{ab}congoverline{ac}). what is the measure of ∠c? a. 32° b. 42° c. 58° d. 61° e. 62°
26. about (1.48 imes10^{8}) square kilometers of earths surface is land; the rest, about (3.63 imes10^{8}) square kilometers, is water. if a returning space capsule lands at a random point on earths surface, which of the following is the best estimate of the probability that the space capsule will land in water? f. 80% g. 71% h. 65% j. 41% k. 29%
27. on the first 7 statistics tests of the semester, jamal scored 61, 76, 79, 80, 80, 84, and 91. the mean, median, and mode of his scores were 79, 80, and 80, respectively. on the 8th statistics test, jamal scored 90. how do the mean, median, and mode of all 8 of his scores compare to the mean, median, and mode of his first 7 scores? mean median mode a. equal greater greater b. greater greater greater c. greater greater equal d. greater equal greater e. greater equal equal
28. the solid rectangular prism shown below was built by alternating congruent black cubes and white cubes such that 2 cubes of the same color have at most 1 edge touching. what is the total number of white cubes that were used to build the prism? f. 45 g. 102 h. 105 j. 140 k. 210
29. one side of square abcd has a length of 12 meters. a certain rectangle whose area is equal to the area of abcd has a width of 8 meters. what is the length, in meters, of the rectangle? a. 12 b. 16 c. 18 d. 20 e. 24
30. the average of a list of 4 numbers is 92.0. a new list of 4 numbers has the same first 3 numbers as the original list, but the fourth number in the original list is 40, and the fourth number in the new list is 48. what is the average of this new list of numbers? f. 81.0 g. 92.0 h. 94.0 j. 94.4 k. 96.6
31. the vector i represents 1 mile per hour east, and the vector j represents 1 mile per hour north. maria is jogging south at 12 miles per hour. one of the following vectors represents marias velocity, in miles per hour. which one? a. - 12i b. - 12j c. 12i d. 12j e. 12i + 12j

Question

24. the set of all positive integers that are divisible by both 15 and 35 is infinite. what is the least positive integer in this set? f. 5 g. 50 h. 105 j. 210 k. 525
25. in △abc shown below, the measure of ∠a is 58°, and (overline{ab}congoverline{ac}). what is the measure of ∠c? a. 32° b. 42° c. 58° d. 61° e. 62°
26. about (1.48	imes10^{8}) square kilometers of earths surface is land; the rest, about (3.63	imes10^{8}) square kilometers, is water. if a returning space capsule lands at a random point on earths surface, which of the following is the best estimate of the probability that the space capsule will land in water? f. 80% g. 71% h. 65% j. 41% k. 29%
27. on the first 7 statistics tests of the semester, jamal scored 61, 76, 79, 80, 80, 84, and 91. the mean, median, and mode of his scores were 79, 80, and 80, respectively. on the 8th statistics test, jamal scored 90. how do the mean, median, and mode of all 8 of his scores compare to the mean, median, and mode of his first 7 scores? mean median mode a. equal greater greater b. greater greater greater c. greater greater equal d. greater equal greater e. greater equal equal
28. the solid rectangular prism shown below was built by alternating congruent black cubes and white cubes such that 2 cubes of the same color have at most 1 edge touching. what is the total number of white cubes that were used to build the prism? f. 45 g. 102 h. 105 j. 140 k. 210
29. one side of square abcd has a length of 12 meters. a certain rectangle whose area is equal to the area of abcd has a width of 8 meters. what is the length, in meters, of the rectangle? a. 12 b. 16 c. 18 d. 20 e. 24
30. the average of a list of 4 numbers is 92.0. a new list of 4 numbers has the same first 3 numbers as the original list, but the fourth number in the original list is 40, and the fourth number in the new list is 48. what is the average of this new list of numbers? f. 81.0 g. 92.0 h. 94.0 j. 94.4 k. 96.6
31. the vector i represents 1 mile per hour east, and the vector j represents 1 mile per hour north. maria is jogging south at 12 miles per hour. one of the following vectors represents marias velocity, in miles per hour. which one? a. - 12i b. - 12j c. 12i d. 12j e. 12i + 12j

Accepted Answer

### 24.
# Explanation:
## Step1: Prime - factorize the numbers
$15 = 3	imes5$ and $35=5	imes7$.
## Step2: Find the LCM
The least - common multiple (LCM) is the product of the highest - power prime factors involved. So, $LCM(15,35)=3	imes5	imes7 = 105$. The least positive integer divisible by both 15 and 35 is the LCM.
# Answer:
H. 105

### 25.
# Explanation:
## Step1: Identify the triangle type
Since $\overline{AB}\cong\overline{AC}$, $	riangle ABC$ is an isosceles triangle. In an isosceles triangle, the base angles are equal.
## Step2: Calculate $\angle C$
The sum of the interior angles of a triangle is $180^{\circ}$. Let $\angle C=\angle B = x$. Then $x + x+58^{\circ}=180^{\circ}$, $2x=180^{\circ}-58^{\circ}=122^{\circ}$, and $x = 61^{\circ}$.
# Answer:
D. $61^{\circ}$

### 26.
# Explanation:
## Step1: Calculate the total surface area
The total surface area of the Earth is $1.48	imes 10^{8}+3.63	imes 10^{8}=(1.48 + 3.63)	imes10^{8}=5.11	imes 10^{8}$ square kilometers.
## Step2: Calculate the probability
The probability $P$ that the space capsule lands in water is $P=\frac{3.63	imes 10^{8}}{5.11	imes 10^{8}}\approx0.71$. As a percentage, $P\approx71\%$.
# Answer:
G. 71%

### 27.
# Explanation:
## Step1: Calculate the new mean
The sum of the first 7 scores is $61 + 76+79+80+80+84+91 = 551$. The sum of 8 scores is $551 + 90=641$. The new mean is $\frac{641}{8}=80.125>79$.
## Step2: Calculate the new median
The first 7 scores in ascending order are $61,76,79,80,80,84,91$. After adding 90, the 8 scores in ascending order are $61,76,79,80,80,84,90,91$. The median of 8 numbers is the average of the 4th and 5th numbers, which is $\frac{80 + 80}{2}=80$, same as the original median.
## Step3: Check the mode
The mode of the first 7 scores is 80, and the mode of the 8 - score set is also 80.
# Answer:
E. greater, equal, equal

### 28.
# Explanation:
## Step1: Analyze the pattern
Let the dimensions of the rectangular prism be $l	imes w	imes h$. Assume the prism has dimensions $7	imes5	imes6$. Since the cubes are alternating in color, we can consider the "checker - board" pattern.
## Step2: Calculate the number of white cubes
We can use the fact that if we consider the volume of the prism $V = lwh=7	imes5	imes6 = 210$. In an alternating - color pattern, half of the cubes (when the volume is even) or close to half are white. In this case, since the volume is 210, the number of white cubes is 105.
# Answer:
H. 105

### 29.
# Explanation:
## Step1: Calculate the area of the square
The area of square $ABCD$ with side length $s = 12$ meters is $A_{square}=s^{2}=12^{2}=144$ square meters.
## Step2: Calculate the length of the rectangle
The area of the rectangle $A_{rectangle}=l	imes w$, where $w = 8$ meters and $A_{rectangle}=A_{square}=144$ square meters. Then $l=\frac{A_{rectangle}}{w}=\frac{144}{8}=18$ meters.
# Answer:
C. 18

### 30.
# Explanation:
## Step1: Calculate the sum of the original 4 numbers
The sum of the original 4 numbers is $92.0	imes4 = 368$.
## Step2: Calculate the sum of the new 4 numbers
The sum of the first 3 numbers of the original list is $368 - 40=328$. The sum of the new 4 - number list is $328+48 = 376$.
## Step3: Calculate the new average
The new average is $\frac{376}{4}=94.0$.
# Answer:
H. 94.0

### 31.
# Explanation:
## Step1: Understand the vector directions
The vector $\mathbf{i}$ represents the east - direction and $\mathbf{j}$ represents the north - direction. Maria is jogging south, which is the opposite direction of the $\mathbf{j}$ vector.
## Step2: Determine the vector
Since her speed is 12 miles per hour in the south direction, her velocity vector is $- 12\mathbf{j}$.
# Answer:
B. $-12\mathbf{j}$

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QUESTION IMAGE

Question

Explanation:

24.

Step1: Prime - factorize the numbers

Step2: Find the LCM

Step1: Identify the triangle type

Step2: Calculate $\angle C$

Step1: Calculate the total surface area

Step2: Calculate the probability

Answer:

25.