3.27

As concrete cures, it gains strength. The following data represent the 7-day, x 28-day 7-day, > 28-day, Y 7-day and 28-day strength (in pounds per square inch) of a certain type of 3120 5402 2820 5092 concrete. Complete parts (a) through (f) below. 2580 4668 3300 5480 2300 4380 3300 5400 3130 5343 3080 5178 2750 4795 2620 4572 (a) Draw a scatter diagram of the data, treating 7-day strength as the x variable. Choose the correct scatter diagram below. O B. O C. OD 6400 Q Q 320 6200 3200 a 2800- 4800 2400 2400 1000 2000 3000 2000- 2200 2800 4000 5200 6400 200 2600 3400 4000 5200 6400 (b) What type of relation appears to exist between the 7-day and 28-day strengths? There appears to be a relation between the 7-day and 28-day strengths. (c) Find an equation of the line containing the two given points. Find the equation of the line that passes through (2300,4380) and (3300,5480) in slope intercept form. y =_ (Simplify your answer. Use integers or decimals for any numbers in the expression. Do not round.) (d) Graph the line on the scatter diagram drawn in part (a). Choose the correct graph below. OA O B, O C. OD. 6400 a 6200 6200 5600 5400 a 5400 a 4600 4800 3800 3800 4000 4000 3000- 2200 2800 2200 2800 3400 7200 2600 2200 2800 3400 (e) Using the equation of the line found in part (c), predict the 28-day strength of a slab of concrete if its 7-day strength is 3000 psi. If the 7-day strength of a slab of concrete is 3000 psi, its 28-day strength is |psi. (Type an integer or a decimal. Do not round.) (f) Interpret the slope of the line found in part (c) as a rate of change in the context of the problem. Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal. Do not round.) O A. If the 7-day strength is increased by 1 psi, then the 20-day strength will decrease by|psi. O B. If the 7-day strength is increased by 1 psi, then the 28-day strength will increase by psi