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21 May 2018

[7,8), by 4. Prove that the interval A = [0,2) has the same cardinality as the set B = [5,6) constructing a bijection between the two sets. You can add a graph to support your argument.

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Jean Keeling
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24 May 2018
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2. (20 pts) An object begins moving along a vertical line at time t = Os and stops at time t = 6 s. Its height above the ground at time t is given by h(t) in the provided graph, where h is measured in meters. Use the graph to answer the following questions. on 0 (a) Compute the average velocity of the object on the time interval [0,6). Show your work. N 1 2 3 4 5 6 (b) Circle the choice that best describes the shape of the graph on the time interval (5,6). i. increasing and concave up ii. increasing and concave down iii. decreasing and concave up iv. decreasing and concave down (c) At what time is the object farthest away from the ground? What is the velocity at that time? time= velocity= (d) The maximum velocity attained on (0,6) occurs at one of the following times. Circle the correct choice. i. ls ii. 2 s iii. 3s iv. 4s v. 5s (e) Estimate the value of the maximum velocity attained. The value is an integer. (f) Let v(t) be the velocity at time t. Circle the greatest value amongst the following choices. i. v(2.5) ii. (2.6) ii. v(2.7) iv. v(2.8) V. (2.9) (8) List the time interval(s) on which the velocity is increasing. Use integer endpoints. (h) The maximum speed attained on (0,6) occurs at one of the following times. Circle the correct choice. i. ls ii. 2s iii. 35 iv. 4s v. 5s

The table shows the number of people per day who died from SARS in Singapore at two-week intervals beginning on March 1, 2003.

  1. By using an argument similar to that in Example 4, estimate the number of people who died of SARS in Singapore between March 1 and May 24, 2003, using both left endpoints and right endpoints.

  2. How would you interpret the number of SARS deaths as an area under a curve?

 

1.)  Some punch is made by mixing grape juice and bubbly water in a ratio of 4 to 3. Give at least five different pairs of quantities of grape juice and bubbly water that you could use to make the punch mixture in that ratio. Include at least two examples that involve fractions or mixed numberquantities. Show or explain why all the mixtures are in that same ratio of 5 to 2 using a method your choice (i.e. double-sided number line, strip diagram, batch table).

 

 

2.)  Using a ratio of 3 to 8;

 

a.)  Give two different ways of using this ratio with different ‘part-to-part’ perspectives.

 

 

b.)  Give two different ways of using this ratio with a ‘part-to-whole’ perspective.

 

 

3.)  A drink mixture is made by mixing cola and lemon-lime soda in a ratio of 5 to 3. How much cola and how much lemon-lime soda will you need to make 240 cups of the drink mixture?  Complete either (a) OR (b).

 

(a) Show how to solve the problem from the multiple-batches perspective by reasoning about multiplication and division with quantities. You can support your work with a table or double-sided number line.

 

(b) Show how to solve the problem from the variable-parts perspective by reasoning about multiplication and division with quantities. You can support your work with a strip diagram.

 

 

4.)  Traveling at a constant speed, a race car goes 15 miles every 6 minutes.  Use the unit rate method to solve the following:  (a) How far does the race car go in 15 minutes?  (b) How long does it take the race car to go 20 miles?

 

 

5.)  A type of fertilizer is made by mixing nitrogen and phosphate in an 8 to 3 ratio. For 35 kilograms of nitrogen, how many kilograms of phosphate are needed to make that type of fertilizer?

 

 

6.)  To make jewelry, jewelers often mix gold and copper in a 7 to 5 ratio. How much gold should a jeweler -mix with 42 grams of copper?​

 

 

7.)  You need 3 cups of grape juice for a recipe that makes 4 servings. How many cups of grape juice will you need if you want to make 10 servings of the same recipe?

8.)  Consider all ramps that could be built for which the ratio of height to length is 2 cm to 7 cm. Let x be the unspecified length of a ramp in feet, which can vary, and let y be the corresponding height of the ramp in feet. Derive and explain an equation of the form y = c•x for a suitable constant c (which you should find).

 

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