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  1. To divide multiple cells successively, type cell references separated by the division symbol. For example, to divide the number in A2 by the number in B2, and then divide the result by the number in C2, use this formula: =A2/B2/C2.

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In someone infected with measles, the virus level N (measured in number of infected cells per mL of blood plasma) reaches a peak density at aboutdays (when a rash appears) and then decreases fairly rapidly as a result of immune response. The area under the graph of fromto(as shown in the figure) is equal to the total amount of infection needed to develop symptoms (measured in density of infected cells time). The function N has been modeled by the function

Use this model with six subintervals and their midpoints to estimate the total amount of infection needed to develop the symptoms of measles.

 

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).

 

For this scenario, the manager at Shooters needs to know how advertising will effect customer turn out. In other words, how much should he spend each week in order to get the biggest return on his money. To that end, the manager at Shooters also recorded data relating how much he spent on weekly advertisements, such as fliers and commercials, with how many customers he had each week.

Week Ad $, a People, q Week Ad $, a People, q Week Ad $, a People, q
1  $          50 112 19  $           -   81 37  $       200 195
2  $       150 182 20  $       300 190 38  $       300 205
3  $       200 188 21  $       150 176 39  $       250 193
4  $       200 184 22  $          50 127 40  $       100 147
5  $       150 167 23  $       200 187 41  $          50 123
6  $           -   77 24  $       200 189 42  $       250 191
7  $       150 173 25  $       300 203 43  $          50 120
8  $           -   71 26  $       150 168 44  $           -   89
9  $       100 149 27  $       100 153 45  $       300 198
10  $       200 193 28  $       200 194 46  $       200 189
11  $       250 191 29  $       200 182 47  $           -   82
12  $       100 146 30  $       250 200 48  $           -   87
13  $       100 155 31  $          50 125 49  $           -   76
14  $       150 177 32  $       300 189 50  $       100 159
15  $          50 124 33  $       150 173 51  $          50 121
16  $       150 177 34  $       300 205 52  $          50 120
17  $       100 148 35  $       200 182      
18  $           -   76 36  $           -   80    

 

) Use this data to determine a model that describes the number of people q who come to Shooters as a quadratic function of the amount of money spent on ads.

Give a graph of the customer versus advertising data. Then state the formula that expresses how many customers he can expect based on advertising expenses, q(a).

2) Use the derivative of the quadratic function you found in question 1 to determine what amount should be spent on advertising each week in order for Shooters to achieve a maximum number of customers?  How many customers would come if the owner spent the maximum on advertising?

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