Question

question 3 (multiple choice worth 2 points) (histograms and line plots mc) the line plot represents the age of pets owned by a group of students. line plot image which statement best describes the spread and distribution of the data? the data is symmetric with an approximate range of 5. this might mean that the age of the pets is commonly 5. the data is skewed with an approximate range of 5. this might mean that most of the students in the group rescued older dogs. the data is bimodal with an approximate range of 5. this might mean that most students are older and own a pet that is either 2 or 7 years old. the data is symmetric with an approximate range of 5. this might mean that the most frequent ages of pets were 2 or 7 years old. question 4 (multiple choice worth 2 points) (volume of rectangular prisms mc) a swimming pool in the shape of a rectangular prism has dimensions of 17.5 feet by 13 feet by 6 feet. what is the maximum amount of water that the pool can hold? 1,365 ft³

Explanation:

Question 3 (Histograms and Line Plots MC)

To determine the correct statement, we analyze the line plot:

• Symmetry Check: The data (dots) are balanced around the middle (ages 5 - 6), so symmetric.
• Range Calculation: Max age (7) - Min age (2) = \( 7 - 2 = 5 \), so range is 5.
• Mode Check: The most frequent ages are 2 (1 dot) vs. 3,4,5,6,7 (multiple dots). Wait, no—wait, the bimodal option says "most students are older and own a pet that is either 2 or 7 years old"—no, the symmetric with range 5 and most frequent ages 2 or 7? Wait, no, re - evaluate:

Wait, the line plot: age 2 has 1 dot, age 3 has 2 dots, age 4 has 2 dots, age 5 has 2 dots, age 6 has 3 dots, age 7 has 4 dots? Wait, no, the original plot (from the image) likely has: age 2: 1, age 3: 2, age 4: 2, age 5: 2, age 6: 3, age 7: 4? No, maybe I misread. Wait, the options:

• Option 1: Symmetric, range 5, common age 5? No.
• Option 2: Skewed, range 5, most rescued older dogs? No, data is symmetric.
• Option 3: Bimodal, range 5, most students older, pet 2 or 7? No.
• Option 4: Symmetric, range 5, most frequent ages 2 or 7? Wait, no—wait, the correct analysis:

The data is symmetric (mirror - like around the middle), range is \( 7 - 2 = 5 \), and the most frequent ages (peaks) are around 6 - 7 and 3 - 2? No, wait, the correct answer is the last option: "The data is symmetric with an approximate range of 5. This might mean that the most frequent ages of pets were 2 or 7 years old for most students." Wait, no—actually, when data is symmetric, the modes (most frequent) are at the ends if bimodal, but here, let's recast:

Range = max - min = 7 - 2 = 5. The data is symmetric (dots are evenly distributed around the center). The most frequent ages would be the ones with the most dots, but the option that fits is the last one: symmetric, range 5, and most frequent ages 2 or 7 (since it's bimodal symmetric). Wait, no, the first option says "common age 5"—no. The last option: "The data is symmetric with an approximate range of 5. This might mean that the most frequent ages of pets were 2 or 7 years old for most students." So the correct option is the fourth one (the last circle option).

Question 4 (Volume of Rectangular Prisms MC)

The volume \( V \) of a rectangular prism is \( V=l\times w\times h \). Given \( l = 17.5 \) ft, \( w = 13 \) ft, \( h = 6 \) ft.

Step 1: Recall the volume formula

\( V=l\times w\times h \)

Step 2: Substitute the values

\( V = 17.5\times13\times6 \)

Step 3: Calculate \( 17.5\times13 \) first

\( 17.5\times13=(17 + 0.5)\times13=17\times13+0.5\times13=221 + 6.5 = 227.5 \)

Step 4: Multiply by 6

\( 227.5\times6 = 1365 \)

Final Answers

Question 3

The correct option is the last one (the fourth circle): "The data is symmetric with an approximate range of 5. This might mean that the most frequent ages of pets were 2 or 7 years old for most students."

Question 4

The volume of the pool is \( \boldsymbol{1365} \) cubic feet.

Answer:

Question 3 (Histograms and Line Plots MC)

To determine the correct statement, we analyze the line plot:

• Symmetry Check: The data (dots) are balanced around the middle (ages 5 - 6), so symmetric.
• Range Calculation: Max age (7) - Min age (2) = \( 7 - 2 = 5 \), so range is 5.
• Mode Check: The most frequent ages are 2 (1 dot) vs. 3,4,5,6,7 (multiple dots). Wait, no—wait, the bimodal option says "most students are older and own a pet that is either 2 or 7 years old"—no, the symmetric with range 5 and most frequent ages 2 or 7? Wait, no, re - evaluate:

Wait, the line plot: age 2 has 1 dot, age 3 has 2 dots, age 4 has 2 dots, age 5 has 2 dots, age 6 has 3 dots, age 7 has 4 dots? Wait, no, the original plot (from the image) likely has: age 2: 1, age 3: 2, age 4: 2, age 5: 2, age 6: 3, age 7: 4? No, maybe I misread. Wait, the options:

• Option 1: Symmetric, range 5, common age 5? No.
• Option 2: Skewed, range 5, most rescued older dogs? No, data is symmetric.
• Option 3: Bimodal, range 5, most students older, pet 2 or 7? No.
• Option 4: Symmetric, range 5, most frequent ages 2 or 7? Wait, no—wait, the correct analysis:

The data is symmetric (mirror - like around the middle), range is \( 7 - 2 = 5 \), and the most frequent ages (peaks) are around 6 - 7 and 3 - 2? No, wait, the correct answer is the last option: "The data is symmetric with an approximate range of 5. This might mean that the most frequent ages of pets were 2 or 7 years old for most students." Wait, no—actually, when data is symmetric, the modes (most frequent) are at the ends if bimodal, but here, let's recast:

Range = max - min = 7 - 2 = 5. The data is symmetric (dots are evenly distributed around the center). The most frequent ages would be the ones with the most dots, but the option that fits is the last one: symmetric, range 5, and most frequent ages 2 or 7 (since it's bimodal symmetric). Wait, no, the first option says "common age 5"—no. The last option: "The data is symmetric with an approximate range of 5. This might mean that the most frequent ages of pets were 2 or 7 years old for most students." So the correct option is the fourth one (the last circle option).

Question 4 (Volume of Rectangular Prisms MC)

The volume \( V \) of a rectangular prism is \( V=l\times w\times h \). Given \( l = 17.5 \) ft, \( w = 13 \) ft, \( h = 6 \) ft.

Step 1: Recall the volume formula

\( V=l\times w\times h \)

Step 2: Substitute the values

\( V = 17.5\times13\times6 \)

Step 3: Calculate \( 17.5\times13 \) first

\( 17.5\times13=(17 + 0.5)\times13=17\times13+0.5\times13=221 + 6.5 = 227.5 \)

Step 4: Multiply by 6

\( 227.5\times6 = 1365 \)

Final Answers

Question 3

The correct option is the last one (the fourth circle): "The data is symmetric with an approximate range of 5. This might mean that the most frequent ages of pets were 2 or 7 years old for most students."

Question 4

The volume of the pool is \( \boldsymbol{1365} \) cubic feet.