What is the answer for x-5/9= -4?
2 answers:
You might be interested in
Answer:
And the 90% confidence interval would be given (0.0942;0.09978).
We are confident at 90% that the difference between the two proportions is between
Step-by-step explanation:
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
represent the real population proportion female for Biology
represent the estimated proportion female for biology
is the sample size for A
represent the real population proportion female for calculus AB
represent the estimated proportion female for Calculus AB
is the sample size required for B
represent the critical value for the margin of error
The population proportion have the following distribution
The confidence interval for the difference of two proportions would be given by this formula
For the 90% confidence interval the value of and
, with that value we can find the quantile required for the interval in the normal standard distribution.
And replacing into the confidence interval formula we got:
And the 90% confidence interval would be given (0.0942;0.09978).
We are confident at 90% that the difference between the two proportions is between
Step-by-step explanation:
The absolute value function is a well known piecewise function (a function defined by multiple subfunctions) that is described mathematically as
.
This definition of the absolute function can be explained geometrically to be similar to the straight line , however, when the value of x is negative, the range of the function remains positive. In other words, the segment of the line
where
(shown as the orange dotted line), the segment of the line is reflected across the <em>x</em>-axis.
First, we simplify the expression.
.
We, now, can simply visualise the straight line, , as a line having its y-intercept at the point
and its <em>x</em>-intercept at the point
. Then, imagine that the segment of the line where
to be reflected along the <em>x</em>-axis, and you get the graph of the absolute function
.
Consider the inequality
,
this statement can actually be conceptualise as the question
.
Algebraically, we can solve this inequality by breaking the function into two different subfunctions (according to the definition above).
- Case 1 (when
)
- Case 2 (when
)
*remember to flip the inequality sign when multiplying or dividing by
negative numbers on both sides of the statement.
Therefore, the values of <em>x</em> that satisfy this inequality lie within the interval
.
Similarly, on the real number line, the interval is shown below.
The use of open circles (as in the graph) indicates that the interval highlighted on the number line does not include its boundary value (-4 and 2) since the inequality is expressed as "less than", but not "less than or equal to". Contrastingly, close circles (circles that are coloured) show the inclusivity of the boundary values of the inequality.
