A study of king penguins looked for a relationship between how deep the penguins dive to seek food and how long they stay underw
1 answer:
Answer:
a) m = 0.0138
b) 0.0138 minutes
c) 6.057 minutes
Step-by-step explanation:
We are given the following in the question:
The relation of dive duration (DD) to depth (D) is given by the regression equation:
Duration DD is measured in minutes, and depth D is in meters.
Here, DD is the dependent variable and D is the independent variable.
Comparing the equation to a linear equation, we have,
where m is the slope of the equation and gives the rate of change and c is the y-intercept that is value of y when x is zero.
m = 0.0138
c = 2.69
a) slope of the regression line
The slope of the regression lines, m = 0.0138
b) increase in the diving duration, if the depth of the dive increases by one meter
Thus, On average, if the depth of the dive increases by one meter, 0.0138 minutes is the increase in the diving duration.
c) Duration of a typical dive to a depth of 244 meters
We put D = 244
It takes 6.057 minutes for a dive of 244 minutes.
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Answer:
1) The linear regression model is y = -0.0348·x + 13.989
2) The correlation coefficient is -0.0725
3) The strength of the model is strong - association
Step-by-step explanation:
1)
X Y XY X²
27 13 351 729
65 12 780 4225
83 11 913 6889
109 10 1090 11881
142 9 1278 20164
175 8 1400 30625
∑ 601 63 5812 74513
From y = ax + b, we have
b = 1/n(∑y -a∑x) = 1/6(63 - (0.0348)×601) = 13.989
Therefore, the linear regression model is y = -0.0348·x + 13.989
2)
3) The strength is - association.
<h2>Answer:</h2>
First of all let's write the slope-intercept form of the equation of a line, which is:
So we just need to find to solve this problem.
Moreover, this problem tells us that Amir drove from Jerusalem down to the lowest place on Earth, the Dead Sea, descending at a rate of 12 meters per minute. So this rate is the slope of the line, that is:
Negative slope because Amir is descending. So:
To find , we need to use the information that tells us that he was at sea level after 30 minutes of driving, so this can be written as the point
. Therefore, substituting this point into our equation:
Finally, the equation of Amir's altitude relative to sea level (in meters) and time (in minutes) is:
Whose graph is shown bellow.
To solve this, we are going to use the compound interest formula: 
where
is the final amount after 
years
is the initial investment
is the interest rate in decimal form
is the number of times the interest is compounded per year
For the first 4 years we know that:
, 
, 
, and since the problem is not specifying how often the interest is communed, we are going to assume it is compounded annually; therefore, 
. Lest replace those values in our formula:
Now, for the next 6 years the intial investment will be the final amount from our previous step, so
. We also know that: 
, 
, and . Lets replace those values in our formula one more time:
We can conclude that Collin will have <span>£3691.41 in his account after 10 years.</span>
where
For the first 4 years we know that:
Now, for the next 6 years the intial investment will be the final amount from our previous step, so
We can conclude that Collin will have <span>£3691.41 in his account after 10 years.</span>