A culture of bacteria has an initial population of 29000 bacteria and doubles every 5 hours. Using the formula P
t
=
P
0
⋅
2
t
d
P
t
​
=P
0
​
⋅2
d
t
​

, where
P
t
P
t
​
is the population after t hours,
P
0
P
0
​
is the initial population, t is the time in hours and d is the doubling time, what is the population of bacteria in the culture after 2 hours, to the nearest whole number

In the xy-plane, if the parabola with equation passes through the point (-1, -1), which of the following must be true?

Point r divides in the ratio 1 : 5. if the coordinates of e and f are (4, 8) and (11, 4), respectively, what are the coordinates of r to two decimal places?

According to a research study, parents with young children slept 6.4 hours each night last year, on average. a random sample of 18 parents with young children was surveyed and the mean amount of time per night each parent slept was 6.8. this data has a sample standard deviation of 0.9. (assume that the scores are normally distributed.) researchers conduct a one-mean hypothesis at the 5% significance level, to test if the mean amount of time parents with young children sleep per night is greater than the mean amount of time last year. the null and alternative hypotheses are h0: μ=6.4 and ha: μ> 6.4, which is a right-tailed test. the test statistic is determined to be t0=1.89 using the partial t-table below, determine the critical value(s). if there is only one critical value, leave the second answer box blank.