In a lab experiment, 2000 bacteria are placed in a petri dish. The conditions are such that the number of bacteria is able to do
1 answer:
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Answer:
And rounded up we have that n=115
Step-by-step explanation:
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:
Solution to the problem
The margin of error for the proportion interval is given by this formula:
(a)
The proportion of defectives is estimated as: . And on this case we have that the margin of error is
and we are interested in order to find the value of n, if we solve n from equation (a) we got:
(b)
And replacing into equation (b) the values from part a we got:
And rounded up we have that n=115
Answer:
A) t = 1 second to reach the highest point
B) h = 96 feet
C) t = 3.449 seconds to hit the ground
Step-by-step explanation:
We notice that the equation that describes the position of the object in terms of the time, is a parabola (quadratic) with negative leading coefficient. therefore this is a parabola with arms pointing down, and with vertex at the top. It is at that top vertex that the maximum altitude of the object is reached.
We need therefore to find the position of the vertex (time "t" is the horizontal coordinate and height "h" is the vertical coordinate).
We know that the vertex (maximum of a parabola of this type - normally described by ) is given by
. Therefore in our case, understanding that time "t" is equivalent to the variable "x", and eight "h" is equivalent to the variable "y", that "-16" is
, and "32" is
, we have that the maximum occurs for:
which means at one second from the launching.
We then can find the answer to part B by replacing t with "1" second in the formula for the height "h":
That is : a height of 96 feet.
To find the answer for part C: the time to hit the ground, we solve for the variable "t" in the given expression for the height, by setting the height to zero (object touching the ground) and using the quadratic formula:
which gives us two solutions: t = -1.449 seconds, and t = 3.449 seconds
Since the negative time does not have physical meaning in our case (time before the object was launched), we adopt the second answer: t = 3.449 seconds