In the 2000 sydney olympics, a special program initiated by ioc president juan antonio samaranch allowed developing countries to send athletes to the olympics without the usual qualifying procedure. here are the 71 times for the first round of the 100 meter men’s swim (in seconds).60.39 49.93 53.40 51.82 50.46 51.36 50.28 50.19 52.1450.56 52.72 50.95 49.74 49.16 52.57 52.53 52.09 52.4049.75 54.06 53.50 50.63 51.93 51.62 52.58 53.55 51.0749.76 49.73 50.90 59.26 49.29 52.78 112.72 49.79 49.8352.43 51.28 52.22 49.76 49.70 52.90 50.19 54.33 62.4551.93 52.24 52.82 50.96 48.64 51.11 50.87 52.18 54.1250.49 49.84 52.91 52.52 50.32 51.52 52.00 52.85 52.2449.45 51.28 49.09 58.79 49.74 49.32 50.62 49.45calculate the sample mean and sample standard deviation(use excel functions).

The means for times for the first round of the 100 meter men’s swim is 52.64789 seconds

The satandar deviation for times for the first round of the 100 meter men’s swim is 7.60182 seconds

Step-by-step explanation:

The sample mean for a set of n data is given by:

In other words, the sample mean of the times for 71 times of the first round measured in seconds is:

seconds

The sample standard deviation for a set of n data is given by:

In other words, the sample standard deviation of the times for 71 times of the first round measured in seconds is:

seconds

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1