Todd is 30 years old. If his target heart rate during aerobic activity is 60-90 % of his maximum heart rate, how fast should his
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Answer:
So on this case the 95% confidence interval would be given by (563.997;741.203)
Step-by-step explanation:
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
represent the sample mean for the sample
population mean (variable of interest)
s=311.7 represent the sample standard deviation
n=50 represent the sample size
Soltuion to the problem
The confidence interval for the mean is given by the following formula:
(1)
In order to calculate the critical value we need to find first the degrees of freedom, given by:
Since the Confidence is 0.95 or 95%, the value of and
, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,49)".And we see that
Now we have everything in order to replace into formula (1):
So on this case the 95% confidence interval would be given by (563.997;741.203)
Answer:
This linear system has one solution.
Step-by-step explanation:
First equation: y = x + 2
Second equation: 6x - 4y = -10
Let's change the second equation in slope-intercept form y = mx + b.
<u>Slope-intercept form</u>
y = mx + b
m ... slope
b ... y-intercept
If two lines have the <em>same slope </em>but <em>different y-intercept</em>, they are parallel - <u>system has no solutions</u>.
If two lines have the <em>same slope</em> and the <em>same y-intercept</em>, they are the same line and are intersecting in infinite many points - <u>system has infinite many solutions</u>.
If two lines have <em>different slopes</em> then they intersect in one point - <u>system has one solution</u>.
We see that lines have different slopes. First line has slope 1 and the other line has slope . So the system has one solution.
You can also check this by solving the system.
Substitute y in second equation with y from first.
6x - 4y = -10
6x - 4(x + 2) = -10
Solve for x.
6x - 4x - 8 = -10
2x = -2
x = -1
y = x + 2
y = -1 + 2
y = 1
The lines intersect in point (-1, 1). <-- one solution