CASE STUDY: 10000 METER RACE AT THE 2016 RIO OLYMPICS
In 10000 meter race, runners complete over 25 laps or a 400 meter track. It is the longest track
running event held. The men's 10000 meter began at the 1912 Olympics. It was 1988 (over seventy
years later) before the women's 10000 meter was added to Olympic competition. The official world
records in the 10,000 meters are held by Kenenisa Bekele with 26:17.53 minutes for men and Almaz
Ayana from Ethiopia with 29:17.45 minutes for women.
In this project, we are going to take a look at the 2016 Rio Olympics men and women 10000 meter
competition. All the times for the participant's times are given to you in minutes. You should leave
the times in minutes and round to the nearest thousandth when needed. If the runner did not finish,
do not use their data.
1. Use the samples to find the mean completion time of the for the
a. male runners.
b. female runners.
2. Use the samples to find the sample standard deviation of the completion times for the
a. male runners.
b. female runners.
3. Find a point estimate for the mean completion time of the
a. male runners.
b. female runners.
4. Construct a 95% confidence interval for the population mean completion time of the
a. male runners.
b. female runners.
5. Interpret the results of number 4.
6. Use the samples to construct a 95% confidence interval for the population mean completion
time of all runners. How do your results differ from those in number 4? Explain.

a.   we have two

lines:   y = 4-x   and  

y = 8-x^-1

given two simultaneous equations that are both to be

true, then the solution is the points where the lines cross. the intersection is

where the two equations are equal. therefore the solution that works for both

equations is when

4-x = 8-x^-1

this is where the two lines will cross and that is the

common point that satisfies both equations.

b.   4-x = 8-x^-1

  x           4-x       8-x^-1

-3           7        

8.33

-2           6         8.5

-1           5         9

  0           4        

-

  1           3        

7

  2           2        

7.5

  3           1         7.67

the table shows that none of the x values from -3 to 3 is

the solution because in no case does

4-x = 8-x^-1

to find the solution we need to rearrange the equation to

find for x:

4-x = 8-x^-1

multiply both sides with x:

4x-x^2 = 8x-1

x^2+4x-1=0

x= -4.236, 0.236

therefore there are two points that satisfies the

equation.

find y:  

x=-4.236

y = 4-x   = 4 – (-4.236)

= 8.236

y = 8-x^-1 =   .236)^-1

= 8.236

x=0.236

  y = 4-x   = 4 – (0.236) = 3.764

y = 8-x^-1 =   8-(0.236)^-1

= 3.764

thus the two lines cross at 2 points:

(-4.236, 8.236) & (0.236, 3.764)

c.   to solve

graphically the equation 4-x = 8-x^-1

we would graph both lines: y = 4-x   and   y

= 8-x^-1

the point on the graph where the lines cross is the

solution to the system of equations.

just graph the points on part b on a cartesian coordinate

system and extend the two lines.   the

solution is, as stated, the point where the two lines cross on the graph.

step-by-step explanation:

mark brainliest!

14.29%

step-by-step explanation:

step-by-step explanation:

im not sure what the answer is