A biologist is comparing the growth of a population of flies per week to the number of flies a lizard will consume per week. SHe
has devised an equation to solve for which day(x) the lizard would be able to eat the entire population. The equation is 3^x=5x-1
Explain the biologist how she can solve this on a graph using a system of equation
Explain the biologist how she can solve this on a graph using a system of equation
1 answer:
This equation can be solved graphically by plotting the equations
f(x) = 3^x
and
g(x) = 5x-1.
The x-coordinate of the point(s) of intersection is the solution.
_____
On my graphing calculator, I find it easier to locate x-intercepts, so I would rewrite the equation as
3^x -(5x -1) = 0
and plot the function
h(x) = 3^x -(5x -1)
The x-intercept(s) would be the solutions. (There are two: x≈0.577, x=2.)
f(x) = 3^x
and
g(x) = 5x-1.
The x-coordinate of the point(s) of intersection is the solution.
_____
On my graphing calculator, I find it easier to locate x-intercepts, so I would rewrite the equation as
3^x -(5x -1) = 0
and plot the function
h(x) = 3^x -(5x -1)
The x-intercept(s) would be the solutions. (There are two: x≈0.577, x=2.)
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Answer: kindly check explanation
Step-by-step explanation:
Given the data :
5 3 3 1 4 4 5 6 4 2 6 6 6 7 1 1 14 1 2 4 4 4 5 6 3 5 3 4 5 6 8 4 7 6 5 9 11 3 12 4 7 6 5 15 1 1 10 8 9 2 12
Frequency and relative frequency table can be found in the attachment below.
b. Where do the data tend to cluster?
3 up to 6
Answer:
75% confidence interval is 91.8±16.66. That is between 75.1 and 108.5 pounds.
Step-by-step explanation:
The question is missing. It is as follows:
Adult wild mountain lions (18 months or older) captured and released for the first time in the San Andres Mountains had the following weights (pounds): 69 104 125 129 60 64
Assume that the population of x values has an approximately normal distribution.
Find a 75% confidence interval for the population average weight μ of all adult mountain lions in the specified region. (Round your answers to one decimal place.)
75% Confidence Interval can be calculated using M±ME where
- M is the sample mean weight of the wild mountain lions (
)
- ME is the margin of error of the mean
And margin of error (ME) of the mean can be calculated using the formula
ME= where
- t is the corresponding statistic in the 75% confidence level and 5 degrees of freedom (1.30)
- s is the standard deviation of the sample(31.4)
- N is the sample size (6)
Thus, ME= ≈16.66
Then 75% confidence interval is 91.8±16.66. That is between 75.1 and 108.5