Question

the data set represents a progression of hourly temperature measurements. use the regression equation $y \approx -0.875x^2 - 3.596x + 20.179$ to predict the temperature during the sixth hour.\
\

x	0	1	2	3	4	5	\
y	20	16	10	0	-7	-20	\

\
\
a. -24\
b. -15\
c. -25\
d. -32\
\
please select the best answer from the choices provided\
\
a\
b\
c\
d

Explanation:

Step1: Identify x for 6th hour

x = 6 (since x=0 is 1st hour, x=6 is 7th? Wait no—wait x values given: 0,1,2,3,4,5 correspond to hours 1-6? Wait no, problem says "predict the temperature during the sixth hour"—wait the x values: x=0 is first hour? Wait no, the regression equation is given, just plug x=5? Wait no, wait the table has x=0 to 5, y values for those. The sixth hour—wait if x=0 is hour 1, x=5 is hour 6? Wait no, problem says "use the regression equation to predict the sixth hour"—wait let's check the equation: y = -0.875x² - 3.596x + 20.179. Wait wait maybe the original equation was misread? Wait the user wrote "y = -0 875x² - 3 596x + 20 179"—probably decimal points: y = -0.875x² - 3.596x + 20.179. Let's plug x=5? Wait x=5 gives y=-0.875(25) -3.596(5)+20.179 = -21.875 -17.98 +20.179 ≈-19.676≈-20 (matches table). So sixth hour is x=6.

Step2: Plug x=6 into equation

Calculate each term:
-0.875(6²) = -0.87536 = -31.5
-3.596*6 = -21.576
Sum: -31.5 -21.576 +20.179 = (-53.076)+20.179≈-32.897≈-33? Wait no, wait maybe the equation was y = -0.875x² -3.596x +20.179? Wait wait the options have d. -32. That's closest. Wait wait maybe the original equation was different? Wait the user's input had "y = -0 875x² - 3 596x + 20 179"—probably typos in decimal separators (using space instead of dot). So assuming decimal points, x=6 gives ≈-32.897 which is closest to d. -32.

Answer:

d. -32