Year 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 Temperature 44.45 43.29 43.61 43.35 46.66 45.71 45.53 47.53 45.86 46.23 CO2 316.9 320.0 325.7 331.1 338.7 345.9 354.2 360.6 369.4 379.7 Emissions Defining our variables: t = years after 1960, T = Temperature, and C = CO2 emissions.
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
![I.
Describe the Relationship with a Quadratic Functions in standard form
We will use the data from the years 1960, 1990, 2005, for our models.
That is, for t = 0, T = 44.45 and C = 316.9 and for t = 30, T = 45.53 and C = 354.2, etc.
3) Modeling Temperature
a) Use the data from 1960, 1990, and 2005 to find a quadratic function
T= at +bt+c that models the Temperature in terms of the years since 1960.
b) Use your quadratic function to predict the Temperature in 2020.
c) On graph paper, plot the entire set of temperature data from 1960 through 2020.
On the same axis, plot your function from part (a) with at least 4 actual points on
the graph to give it some adequate scale. Discuss the similarities and differences of
the graph and the data. How well does your function approximate the actual data
compared to the linear function you used in part 1 and the quadratic function in
vertex form in Part 2 #1?
4 Modeling CO2 emissions
d) Use the data from 1960, 1990, and 2005 to find a quadratic function
C= at+bt+c that models the CO2 emissions in terms of the years since 1960.
(Hint: Plug in each data point to get a system of equations. Solve the system to find
a, b, and c.)
e) Use your quadratic function to predict the CO2 emissions in 2020.
f) On graph paper, plot the entire set of CO2 emissions data from 1960 through 2005.
On the same axis, plot your function from part (a) with at least 4 actual points on
the graph to give it some adequate scale. Discuss the similarities and differences of
the graph and the data. How well does your function approximate the actual data
compared to the linear function you used in part 1 and the quadratic function in
vertex form in Part 2 #1?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F180e35fb-9b09-4fc5-8a6a-511bee286828%2Fbfe29de0-308a-41b3-b8d0-08833c690094%2Frtwsz2d_processed.jpeg&w=3840&q=75)
![Math 4b Class Project : Modeling Real World Relationships to Make Predictions
Part 3
Purpose: To use the concepts developed in Precalculus to model an actual real world relationship and
make a prediction. In this case we will model global warming
The data: The following table summarizes the average yearly temperature (F")and carbon dioxide
emissions in parts per million (ppm) measured at Mauna Loa, Hawaii
Year
1960
1965
1970
1975
1980
1985
1990
1995
2000
2005
Temperature 44.45
CO2
43.29 43.61
43.35
46.66 45.71
45.53
47.53
45.86
46.23
316.9
320.0 325.7 331.1
338.7 345.9 354.2
360.6
369.4
379.7
Emissions
Defining our variables: t = years after 1960, T = Temperature, and C = CO2 emissions.
%3D](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F180e35fb-9b09-4fc5-8a6a-511bee286828%2Fbfe29de0-308a-41b3-b8d0-08833c690094%2F0t4c50n_processed.jpeg&w=3840&q=75)
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