Select all the times that are equivalent to 450 minutes. (A) 2,700 seconds (B) 27,000 seconds (C) 7 hours 30 minutes (D) \( 7 \frac{1}{3} \) hours (E) \( 7 \frac{1}{2} \) hours

To determine which options are equivalent to 450 minutes, we first need to convert 450 minutes into other time units. 1. **Convert 450 minutes to hours and minutes:** \[ 450 \text{ minutes} = 7 \text{ hours} + 30 \text{ minutes} = 7 \frac{1}{2} \text{ hours} \] 2. **Convert 450 minutes to seconds:** \[ 450 \text{ minutes} \times 60 \text{ seconds/minute} = 27,000 \text{ seconds} \] Now, let's evaluate each option: (A) **2,700 seconds** \[ 2,700 \text{ seconds} = \frac{2,700}{60} \text{ minutes} = 45 \text{ minutes} \quad \text{(not equivalent)} \] (B) **27,000 seconds** \[ 27,000 \text{ seconds} = \frac{27,000}{60} \text{ minutes} = 450 \text{ minutes} \quad \text{(equivalent)} \] (C) **7 hours 30 minutes** \[ 7 \text{ hours} + 30 \text{ minutes} = 450 \text{ minutes} \quad \text{(equivalent)} \] (D) **\( 7 \frac{1}{3} \) hours** \[ 7 \frac{1}{3} \text{ hours} = 7 \text{ hours} + \frac{1}{3} \text{ hour} = 7 \text{ hours} + 20 \text{ minutes} = 440 \text{ minutes} \quad \text{(not equivalent)} \] (E) **\( 7 \frac{1}{2} \) hours** \[ 7 \frac{1}{2} \text{ hours} = 7 \text{ hours} + 30 \text{ minutes} = 450 \text{ minutes} \quad \text{(equivalent)} \] Thus, the options that are equivalent to 450 minutes are: - (B) 27,000 seconds - (C) 7 hours 30 minutes - (E) \( 7 \frac{1}{2} \) hours Final answer: **(B), (C), (E)**.