# Mathematics

Section 1

The following graph shows the fare rates for the Tortoise Taxi Co. and the Crash-up Cab Co.

https://hdsb.elearningontario.ca/content/enforced/13979006-EL_MAT_MAP4CJ-01_940968_1819Sem2/map4cpu01/map4cpu01a09/images/q2.jpg?_&d2lSessionVal=eSRUlMCNPVRYDF7gzcMyABVvU

Question 1 (3 points)

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What is the y-intercept of each line? What is the meaning of these values?

Question 2 (4 points)

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Determine the slope of each line(include calculations). What is the meaning of these values?

Question 3 (1 point)

A new species of bird is introduced into a sanctuary. Conservationists monitor the population of the birds for many years. The results are shown in the following graph.

Over what time period is the rate of change of population positive?

At what time is the population increasing fastest? Estimate the rate of change at this time(Include calculations).

When is the rate of change zero? What is the significance of this time in the context of the problem?

A manufacturer is testing the performance of insulating mugs in cold weather. They pour hot water into each mug and record the temperature over a period of time. The results are shown in the table below.

Question 6 (1 point)

Without creating a graph, how can you determine if the data is linear?

Question 7 (2 points)

After performing a regression analysis, the following was found:

Mug A: y = 75(0.9)x Mug B: y = 75(0.86)x

Use the equations above to predict the temperature of the water in each mug after 20 minutes(Show your work).

Question 8 (2 points)

The researchers test a third mug, and determine the following regression equation for its cooling data: y = 75(0.93)x

By comparing the regression equations, how well does the third mug insulate compared to mugs A and B?

Section 6 Include complete steps of calculations

Simplify each expression, then evaluate.

Question 14 (2 points)