Make a horizontal line on the paper. You may draw arrows on the ends of the line to indicate it is a number line that continues past your data sample.
Put the label "X" to the right of the line to indicate the x axis.
Mark the center of the line with a vertical tick mark and label it 0. This is the origin of the graph.
Make equally spaced tick marks on the rest of the x axis. For this example you should label the tick marks from 1 to 10 on the right side of the 0.
Using the equation which models weight of cat in terms of amount of food fed, the weight of the cat will be : 151.11 ounces
<u>Given the equation</u> :
- <em>g = Amount of food in grams </em>
<u>Substituting g = 13 into the equation</u> :
W = 0.86(13)² - 0.01(13) +5.9
W = 0.86(169) - 0.13 + 5.9
W = 145.34 - 0.13 + 5.9
W = 151.11 ounces
Therefore, the weight of the cat will be 151.11 ounces
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This is an example of conditional probability because we are trying to find the probability of an event occurring GIVEN the occurrence of some other event. There is a formula for this (see image attached).
If we follow this formula, the numerator would be the probability of (A AND B) which in this case is "48% of the class passed BOTH exams." The denominator in the formula would be that "60% of the class passed ONLY THE SECOND exam."
Therefore, P(A and B) = 0.48, which is 48% expressed as a decimal and P(B)= 0.60, which is 60% expressed as a decimal. Then, you can figure out the answer by dividing.
There are 651.335 million cells in the petri dish after 11 hours and the cells will reach 1 billion cells after 14.068 hours
<h3>How to determine the number of cells after 11 hours?</h3>
The given parameters are:
At t = 0, Bacteria = 140 million
At t = 6, Bacteria = 320 million
This can be represented as:
f(0) = 140
f(6) = 320
An exponential function is represented as:
f(t) = f(0) * r^t
When t = 6, we have:
320 = 140 * r^6
Divide both sides by 140
r^6 = 2.28571428571
Take the 6th root of both sides
r = 1.15
So, we have:
f(t) = f(0) * 1.15^t
Substitute f(0) = 140
f(t) = 140 * 1.15^t
After 11 hours, we have:
f(11) = 140 * 1.15^11
Evaluate
f(11) = 651.33
Hence, there are 651.335 million cells in the petri dish after 11 hours
Time to reach 1 billion cells
This means that
f(t) = 1 billion i.e. 1000 million
So, we have:
1000 = 140 * 1.15^t
Divide by 140
1.15^t = 7.14285714286
Take the logarithm of both sides
t * log(1.15) = log(7.14285714286)
Divide both sides by log(1.15)
t = 14.068
Hence, the cells will reach 1 billion cells after 14.068 hours
Read more about exponential functions at:
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