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A study was interested on the effect temperature (T) has on ants. In particular the top speed (s) of ants was recorded in centimeters per second. The following data was collected: Temperature â—¦C 9 15 18 23 29 30 34 Speed (cm per second) 1 2 2.5 3 4 4.5 5 A plot of the data (temperature versus speed) is illustrated below. 5 10 15 20 25 30 35 1 2 3 4 5 Temperature â—¦C Speed cm/s (a) What can be said about the collected data from the plot above? (b) Use Excel to determine the slope and intercept of the linear regression line for this data. (c) In the context of the data, interpret the meaning of the slope (if any) that you found in (b) above. (d) In the context of the data, interpret the meaning of the intercept (if any) that you found in (b) above. (e) What is the equation for the regression line for this data? (f) Use Excel to compute the correlation coefficient and comment what this means for the collected data. (g) If the temperature is 26 degrees Celsius, what is the expect top speed of an ant? (h) If the temperature is 43 degrees Celsius, what is the expect top speed of an ant? (i) Comment on the reliability of the predictions in (g) and (h). 3(j) On surveillance video an ant is observed with a measured top speed of 3.5 centimetres per second. What would a Crime Scene Investigators best guess be for the temperature when video was recorded? Question 2 (4 marks) Jenny wants to work out how many cane toads are living around the lake near her house. She carefully collects 25 toads and puts a pink stripe down their backs with a non toxic paint. She then releases these back to the lake and returns a week later. This time she collects another 25 cane toads, and two have a pink stripe down their back. Estimate how many toads are in the lake. Question 3 (4+2+4+4+(2+2)=18 marks) A proper fraction is any fraction where the numerator is less than the denominator, for example 3 7 or 10 11 . The other fractions, where the numerator is greater than or equal to the denominator are called improper fractions, for example 5 3 or 7 7 . The improper fractions resented the proper fractions because they were made to feel inferior. As a consequence many improper fractions would change their appearance. For example, as 5 3 = 3 + 2 3 = 1 + 2 3 = 1 2 3 , 5 3 would dress as 1 2 3 . Similarly as 43 19 = 2 5 19 , 43 19 would only allow herself to be seen as 2 5 19 when out in public. It made the improper fractions feel better about themselves, because in their minds they gained some air of respectability being made up in part by a proper fraction. The proper fractions wouldn’t stand for this though, and started calling these pretenders mixed numbers. It was a derogatory term, implying that they were not pure as the proper fractions were. The whole situation was making 43 19 feel depressed, making her feel unworthy dressed as herself or as 2 5 19 . Her girlfriend Goldie had an idea, she suggested 43 19 could dress as 43 19 = 2 + 5 19 = 2 + 1 19 5 . But old habits are hard to break, so when 43 19 noticed 19 5 in the mirror, she immediately realised 19 5 = 3 + 4 5 4and remodelled herself as 43 19 = 2 + 1 19 5 = 2 + 1 3 + 4 5 . Goldie liked the look, but said “Don’t validate the propers”, and adjusted 4 5 , so that now 43 19 = 2 + 1 3 + 1 5 4 . But 43 19 couldn’t help herself and upon noticing that 5 4 = 1 + 1 4 , refashioned herself again as 43 19 = 2 + 1 3 + 1 1+ 1 4 . “Wow, that is so cool! I love that pattern of ones” said Goldie as she pointed out the ones on her right side: 43 19 = 2 + 1 3 + 1 1+ 1 4 . They decided to go show their friend 70 29 , who immediately wanted a makeover too. The girls were amazed when they found 70 29 = 2 + 12 29 = 2 + 1 29 12 = 2 + 1 2 + 5 12 = 2 + 1 2 + 1 12 5 = 2 + 1 2 + 1 2+ 2 5 = 2 + 1 2 + 1 2+ 1 5 2 = 2 + 1 2 + 1 2+ 1 2+ 1 2 It was then that 70 29 decided that she was going to change her name to [2, 2, 2, 2, 2], saying “The name defines me, the ones on the right are always going to be there, but it is the 2’s, the five of them that make me me!” 43 19 agreed, and decided that from hence forth she wanted to be known as [2, 3, 1, 4]. (a) 43 19 ’s mother, or rather, we should say [2, 3, 1, 4]’s mother, namely 225 157 , had never been considered that attractive. So she asked the girls to give her a makeover too. She was very pleased with the results. What did 225 157 look like after her makeover, and what was her new name? 5(b) Three 8’s in a row is considered by some to be lucky, so what fraction is [8, 8, 8]? (c) The proper fractions felt left out, until one of them, 30 43 realised she could dress up this way too. What did she end up looking like and what was her new name? Hint: Zero is a number too. (d) Goldie was actually not a fraction, in fact, she was known to be irrational. Her and her little brother satisfied the quadratic equation x 2 − x − 1 = 0. Find out who Goldie is (to 5 decimal places), remembering her brother has always had a negative disposition, while Goldie has always been positive. Hint: Use the quadratic formula for finding roots. (e) The girls decided Goldie should have a makeover too, but Goldie didn’t think this possible, her not being a fraction. However [2, 3, 1, 4] observed that Goldie’s defining quadratic equation could be rearranged to x = 1 + 1 x . i) Carefully explain how this was done. ii) Armed with this new equation, [2, 3, 1, 4] said Goldie could undergo the same makeover transformation. She used the new equation to replace the x with 1+ 1 x on the right hand side of the new equation, and then kept repeating this idea. Goldie had always been considered attractive, but a new aspect of her beauty was then discovered. What ‘fraction’ did Goldie become, and what was her new named? Question 4 (4 marks) For a galvanic cell, the Nernst Equation relates the electrode potential E and its standard electrode potential Eâ—¦ as follows: E = E â—¦ + RT 2F ln Q where R is the gas constant, T is the temperature (Kevin), F is Faraday’s constant, and Q is the quotient of the concentration of Zn2+ to Cu2+ ions. Rearrange this formula to get an equation to find Q. Question 5 (6 marks) A magician randomly selects three audience members, Anna, Brock and Cassandra, and asks them to keep in mind the the last digit of their phone number. Using a giant calculator, which only the audience can see, he tells Anna to

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