need help to complete 30 and 31 ALGEBRA 1 Alternate Exam 5 continued Natalie per

Question

need help to complete 30 and 31

ALGEBRA 1 Alternate Exam 5 continued Natalie performs a chemistry experiment where she records the temperature of an ongoing reaction. The solution is 935 C after 3 minutes; 90° C after 5 minutes, 84.8 C after 9 minutes; 70.2 C after 18 minutes; 54.4° C after 30 minutes; 42.5° C after 37 minutes; and 24.9 C after 48 minutes. Perform a linear regression on this data to complete the following items. 28. What does the value of the correlation coefficient tell you about the correlation of the data? 29 Write the equation of the best-fitting line. (Round to the nearest l y 9353 30, On average how much does the temperature decrease every five minutes? 31. If Natalie's solution is expected to freeze at -7° C, how many minutes into the experiment should the solution freeze? (Show work that supports your prediction and round to the nearest minute.) FILL IN YOUR NAME AND THE OTHER REQUIRED INFORMATION ON EACH PAGE OF THE EXAM AND MAIL THE EXAM TO THE SCHOOL. A-(1096)-07/11-05 AMERICAN SCHOOL Lansing, IL

Explanation / Answer

Answer:

(30)

For solving it , let us assume here, time be x and temprature be y.

For this we will plot these values on x-y graph accordingly and calculate the slope using the formula below:

Slope, m = (y2 - y1)/(x2 - x1)

Here i am taking these two points for calculating the slope of line nd that are (9 min, 84.8) ; (48 min, 24.8)

So, m = (y2 - y1)/(x2 - x1) = (24.8 - 84.8) / (48 -9)= -1.54

Equation of line is given as y = m*x + c [where m = slope and c = y-intercept]

So, y = -1.54*x + c

Here we will use one point to find the c

So, 84.8 = -1.54*9 + c

Therefore, c = 98.66

So, we have best fit line, temprature(y) = -1.54*x(minutes) + 98.66

Clearly from the slope we can see, temprature decrease 1.54 degree per minute

So, an average the temprature decrease = 5*1.54 = 7.7 degrees in every 5 minutes

At last we are asked the minutes at which the solution freezes and given thetemprature = -7 degree

So using linear best fit curve equation solved above = temprature(y) = -1.54*x(minutes) + 98.66

So, we have -7 = -1.54*x +98.66

1.54 * x = 98.66+7

x= (106.36)/1.54

x = 68.61 minutes....................................................................................Answer

Minutes(x) 3 5 9 18 30 37 48 Degrees(y) 93..5 90 84.8 70.2 54.4 42.5 24.9

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