A principal wants to know if students at a particular high school are in favor of a new dress code at their school. the principal is not to ask the opinion of every student at the school, so she needs to select an appropriate sample of the students to represent the high school.
Select which sample of students the principal should choose.
A
Students randomly selected from a list of all students at the school.
B
Students sitting at randomly selected tables in the library.
C
Students she selects from the hallway between classes.
D
Students selected by the teachers.
A - Students randomly selected from a list of all students at the school.
Emily leaves her house at exactly
a.m. to bike to her school, which is
miles away. When she passes the post office, which is
mile away from her home, she looks at her watch and sees that it is
seconds past
a.m.
If Emily's school starts at
8:50 a.m., can Emily make it to school on time without increasing her rate of speed? Show and/or explain the work necessary to support your answer.
To determine if Emily can make it to school on time without increasing her rate of speed, we need to calculate the time it will take her to get to school.
Let x be the time it takes for Emily to bike to school. The time it takes for Emily to bike from her house to the post office is x minutes since the post office is 1 mile away. Since it is also mentioned that Emily arrives at the post office at exactly a.m., she must have reached the post office at a; minutes.
After checking her watch at the post office, she continues to bike to school, which is 9 miles away from her house. The total distance traveled by Emily from the post office to her school is 9 miles. The total distance covered by Emily will be 10 miles, which includes the 1 mile from her house to the post office and the 9 miles from the post office to her school.
The time taken to travel a distance is given by the formula:
time = distance/speed
We know that the speed is constant and that Emily will not increase her speed. So we can set up the following equation:
10 = x(s)
where s is Emily's speed.
We also know that the time it takes for Emily to reach the post office is x minutes since it is 1 mile away and she passes the post office at , minutes past a.m. Therefore,
x = ax =
Using this equation, we can solve for x:
10 = (6 + + x)(s)
10 = (6 + + )(s)
10 = (360 + + )(s)
10 = ( + x)(s)
10 = (360 + x)(s)
Since x = , we can substitute in the equation:
10 = (360 + )(s)
10 = (360 + )s
10 = 360s + s
10 - 360 = s
s =
s =
Therefore, the constant speed at which Emily is traveling is mph.
Since the total distance is 10 miles and her speed is mph, the time taken will be hour = minutes. Adding this to the time at which she left her house (), we get:
a.m. + minutes = a.m.
This is earlier than the school start time of 8:50 a.m., so Emily will make it to school on time without increasing her speed.