Theresa rolled a number cube, number 1 through 6, two times

4x+32

4 goes into 4 1 time. (4/4=1)
4 goes into 32 8 times. (32/4=8)
We can factor out 4 from both numbers. 

4(1x+8)
aka 4(x+8)

The digit 7 in 75390 is in the ten thousand position, 5 is in the thousand position, 3 is in the hundreds position, 9 is in the tens position, and 1 is located in the ones position.

C. No, because at least one of the sample sizes exceeds 10 percent of the population.

Answer: 470.85 gallons

Step-by-step explanation:

12.9 gal/min multiplied by 36.5 min equals 470.85 gal

Response:

Part A

The best choice is;

b. y = 128(0.989)x + 72

Part B

Ella can consume the tea post 7:22

Detailed clarification:

Here, we observe the temperature variation with time represented in an exponential equation as follows;

Let the temperature at time x (measured in minutes) be y

Thus, y = a × mˣ + b

Where:

b = Curve shift or the limiting value of the decreasing exponential function as x → ∞

When y = 200, x = 0

This leads to 200 = a × m⁰ + c = a + c

Here, c represents the graph's shift, which is the temperature increase = final temperature = 72°F

Thus, a = 200 - 72 = 128°F

When y = 197, at x = 2 minutes

Thus, 197 = 128·m² + 72 =

m² = (197 - 72)/128 = 125/128

m = √(125/128) = 0.98821

Therefore, the exponential cooling equation is given by;

y = 128 × (0.98821)ˣ + 72

Hence the best choice is b. y = 128(0.989)x + 72

Part B

When the tea's temperature reaches 172°F, we have;

172 = 128 × (0.989)ˣ + 72

Thus, (0.989)ˣ = (172 - 72)/128 = 100/128 = 25/32

log(0.989)ˣ = log(25/32)

x·log(0.989) = log(25/32)

x = log(25/32)/log(0.989) = 22.32 minutes

Thus, Ella can consume the tea post 7:22.