Pretend the greater than or equal to sign is an equal sign, we will substitute it back in later.
x/2 = -4
Multiply both sides by 2 to get x alone
x = -8
Substitute the greater than or equal to sign back in and voila!
x≥-8
The volume of a cone is 164 cubic feet. Its height is 12 feet. Ashlyn is finding the area of the base of the cone. Her work is
1 answer:
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Pretend the greater than or equal to sign is an equal sign, we will substitute it back in later.
x/2 = -4
Multiply both sides by 2 to get x alone
x = -8
Substitute the greater than or equal to sign back in and voila!
x≥-8
Answer:
And rounded up we have that n=421
Step-by-step explanation:
We know that the sample proportion have the following distribution:
In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 90% of confidence, our significance level would be given by and
. And the critical value would be given by:
The margin of error for the proportion interval is given by this formula:
(a)
And on this case we have that and we are interested in order to find the value of n, if we solve n from equation (a) we got:
(b)
We assume that a prior estimation for p would be since we don't have any other info provided. And replacing into equation (b) the values from part a we got:
And rounded up we have that n=421
The given exponential function can be used to determine the
population of the fish at different times.
Response:
1. 200
2. 0.05
3. Please find attached the graph of the exponential function and the table
4. Range; [0, ∞)
Domain: [200, ∞)
5. 346 fishes (approximate value)
<h3>How is the population of the fish obtained from the exponential function?</h3>The given function is f(x) = 200·(1.05)ˣ
1. The initial population is given by the value of the function when x = 0,
which is given as follows;
At x = 0, f(0) = 200·(1.05)⁰ = 200
- The initial population of the fish is <u>200</u>
2. The rate of growth of the fish from the exponential function is given as follows;
The growth factor = 1.05
- The growth rate =<u> 0.05</u>
3. Please find attached the graph of the exponential function created
with MS Excel.
The asymptote of the exponential function is the line, <u>y = 0</u>
The table of values is presented as follows;
4. The domain is the possible x-values which is; 0 ≤ x < ∞
The range is the possible y-values which is; 200 ≤ f(x) < ∞
Which gives;
- Domain; [0, ∞)
- Range: [200, ∞)
5. The population of the fish after 11 years is f(11) = 200·(1.05)¹¹
f(11) = 200 × (1.05)¹¹ ≈ 342
- The population of the fish after 11 years is <u>346 (fishes)</u>
Learn more about exponential function here:
