The rate of u. s. per capita sales of bottled water for the period 2007–2014 could be approximated by s(t) = 0.25t2 ? t + 29 gallons per year (0 ? t ? 7), where t is time in years since the start of 2007.† use a definite integral to estimate the total u. s. per capita sales of bottled water from the start of 2009 to the start of 2013. (round your answer to the nearest gallon.)

117 gallons

Step-by-step explanation:

The expression that describes the rate of U.S. per capita sales of bottled water for the period 2007–2014 is:

Since t=0 at 2007. At 2009 and 2013, t is:

The definite integral of the expression from t=2 to t=6 is:

Rounded to the nearest gallon, the estimated total U.S. per capita sales of bottled water from the start of 2009 to the start of 2013 is 117 gallons.

2 & 7

step-by-step explanation:

he climbs 300 ft/hr at a constant rate. the peak is at 1,500 ft.

when going up, he reaches 600 ft in 2 hours. remember, that he is going in a constant rate. divide 600 with 300:

600/300 = 2

assuming that he takes the same route back (meaning that it's a 1500 ft route back, you can solve.

note also that you are solving when he gets back to 600 ft after he reaches the peak.

first, find the amount of hours it takes to get up the peak. divide the total amount (1500), with the ft/her (300) to get the amount of hours (x):

1500/300 = x

x = 5

it takes jamie 5 hours to get up. now, he is returning down, and reaches 600 (his current destination). remember that he climbs at a constant 300 ft/hr. divide 600 with 300:

600/300 = x

x = 2

now add the two numbers together.

x = 5 + 2 = 7

jamie takes 7 hours to go up the mountain and reach his current position when descending.

(total amount/constant rate) = (time).

remember that it is a constant rate, so in total, when he gets back down the mountain, it will take the same amount of time as when he goes up. the total amount for the round trip is: 5 + 5 = 10.

~

d. 24+-0.114

step-by-step explanation:

the question requires us to calculate the approximate 95% confidence interval for the mean number of ounces of ketchup per bottle in the sample given the following statistics;

sample mean = 24

standard deviation, σ = 0.4

sample size , n = 49

the confidence interval for a population mean is calculated using the formula;

sample mean ± z-score*(σ/sqrt(n))

the z-score associated with a 95% confidence interval, from the standard normal tables, is;

1.96

substituting these values into the formula;

24 ± 1.96*(0.4/7)

= 24 ± 0.112

from the alternatives given, choice d is closest to the above expression;