Given:
The equations are
To find:
Which function is changing more quickly.
Solution:
The slope intercept form of a line is
Where m is slope and b is y-intercept.
On comparing with the slope intercept form, we get
On comparing with the slope intercept form, we get
Since, 
, it means the absolute rate of change of second function is greater than the first function.
Therefore, the second function is changing more quickly.
Answer: ∠B = 42° ∠A = 23° ∠F = 115°
Step-by-step explanation:
∠B≅∠C alternate interior angles 42°
∠CDF is supplementary to ∠CDE,
so m∠CDF = 23° and ∠FAB≅∠CDF so m∠FAB= 23°
<em>also ∠A ≅ CDE corresponding angles 157° ∠FAB is suplementary to ∠A </em>
<em>so 180 - 157 = 23 gives the m∠FAB</em>
The sum of the angles of a triangle is 180°, so m∠AFB = 180 -(23 +42)
180- 65 = 115 = m∠F
Option 1:
<span>Measuring the heights of every fiftieth person on the school roster to determine the average heights of the boys in the school
</span>
Comment: this might not be a good idea for fairness as we only wish to determine average height of the boys. Taking a group of 50 people randomly, might not give us the same number of boys every time.
Option 2:
<span>Calling every third person on the soccer team’s roster to determine how many of the team members have completed their fundraising assignment
Comment: The context doesn't seem to need a sampling. The number of players in a soccer team is considerably small. We can find exact data by asking in person.
Option 3:
</span><span>
Observing every person walking down Main Street at 5 p.m. one evening to determine the percentage of people who wear glasses
</span>
Comment: To get a more accurate result and fairer sampling, the period of observing could have been longer, for example, observing for 12 hours on that day, or an alternative is to observe at 5 pm for 7 days in a row. It could happen that no one walking down the Main street precisely at 5 pm wears glasses, or it could happen the other way around.
Option 4:
<span>Sending a confidential e-mail survey to every one-hundredth parent in the school district to determine the overall satisfaction of the residents of the town taking a poll in the lunch room (where all students currently have to eat lunch) to determine the number of students who want to be able to leave campus during lunch.
Comment: This sampling does fairly represent the population, although it might be an idea to scale down the sample population, i.e. every fiftieth parent.
Answer: Option 4</span>
Rate of change of profit for this period is $2750 per month
<em><u>Solution:</u></em>
Given that,
Profit of $6500 in January and $17,500 in May
<em><u>To find: Rate of change</u></em>
Since,
January is the first month of the year (1) while May is the fifth month (5)
<em><u>Therefore, we get two points</u></em>
(1, 6500) and (5, 17500)
Using these points we can find the rate of change in profit for this time period
<em><u>The rate of change using the following formula:</u></em>
Here from the points,
<em><u>Therefore, rate of change is given as:</u></em>
Thus rate of change of profit for this period = $2750 per month
