The margin of error of a given statistic is an amount that is allowed for in case of miscalculation or change of circumstances.
It is usually the radius or half of the width of the confidence interval of that statistic.
Given that a<span>
survey of the students in Lance’s school found that 58% of the
respondents want the school year lengthened, while 42% think it should
remain the same. The margin of error of the survey is ±10%.
This means that 58% </span><span>± 10% of the </span>respondents want the school year lengthened, while 42% <span><span>± 10% think it should
remain the same.</span>
Thus, from 48% to 68% </span><span><span>of the respondents want the school year lengthened, while from 32% to 52% <span>think it should
remain the same.</span> </span>
Therefore, according to
the survey data, at least 32% of students want the duration of the school
year to remain unchanged, and at least 48% want the school year to be
lengthened.</span>
Explanation:
It helps to understand the process of multiplying the binomials. Consider the simple case ...
(x +a)(x +b)
The product is ...
(x +a)(x +b) = x² +(a+b)x + ab
If the <em>constant</em> term (ab) is <em>negative</em>, the signs of (a) and (b) are <em>different</em>.
If the constant term (ab) is <em>positive</em>, the signs of (a) and (b) will both match the sign of the coefficient of the linear term (a+b).
___
Of course, the sum (a+b) will have the sign of the (a) or (b) value with the largest magnitude, so when the signs of (a) and (b) are different, the factor with the largest magnitude will have the sign of (a+b), the x-coefficient.
<u>Example</u>:
x² -x -6
-6 tells you the factors will have different signs. -x tells you the one with the largest magnitude will be negative.
-6 = -6×1 = -3×2 = ... (other factor pairs have a negative factor with a smaller magnitude)
The sums of these factor pairs are -5 and -1. We want the factor pair that has a sum of -1, the coefficient of x in the trinomial.
x² -x -6 = (x -3)(x +2)
Answer:
So the slope of this function is 
and the y-intercept is 
Step-by-step explanation:
A first order function has the following format:
In which a is the slope and b is the y-intercept, that is, the value of y when x = 0.
We have the following equation:
We just have to rewrite this equation
Which means that
So the slope of this function is and the y-intercept is
Answer:
Step-by-step explanation:
Area of the shaded region = area of the large rectangular - area of the small rectangle
Area of rectangle is given as l*w
Area of the large rectangle = 
Expand
Area of large rectangle 
Area of small rectangle = 
Area of small rectangle = 
Area of shaded region = 
Collect like terms
Hi!
<h3>Let's say you work 5 hours each day for 5 days. </h3>
<em>There are 300 minutes in 5 hours. </em>
- Monday: 300 - 20 = 280
- Tuesday: 280 - 20 = 260
- Wednesday: 260 - 20 = 240
- Thursday: 240 - 20 = 220
- Friday: 220 - 20 = 200
<u>It saves you 100 minutes, which is 1 hour and 40 minutes.</u>
Another way to solve this is 20 * 5 = 100.
<h2>The answer is: It will save you 1 hour and 40 minutes each week.</h2>
Hope this helps! :)
-Peredhel
