Answer:
![x\in [5.55,6.45]](https://tex.z-dn.net/?f=x%5Cin%20%5B5.55%2C6.45%5D)
Step-by-step explanation:
<u>Absolute Value Inequality</u>
Assume the actual width of a safety belt strap for a certain automobile is x. We know the ideal width of the strap is 6 cm. This means the variation from the ideal width is x-6.
Note if x is less than 6, then the variation is negative. We usually don't care about the sign of the variation, just the number. That is why we need to use the absolute value function.
The variation (unsigned) from the ideal width is:
The question requires that the variation is at most 0.45 cm. That poses the inequality:
That is the range of acceptable widths. Let's now solve the inequality.
To solve an inequality for an absolute value less than a positive number N, we write:
This is a double inequality than can be easily solved by adding 6 to all the sides.
Operating:
That is the solution in inequality form. Expressing in interval form:
![\boxed{x\in [5.55,6.45]}](https://tex.z-dn.net/?f=%5Cboxed%7Bx%5Cin%20%5B5.55%2C6.45%5D%7D)
Start at the given point. Draw a segment from that point through the center of the circle, and extend the segment until it intersects the circle. The new point of intersection of the segment and the circle is the image of the original point.
Because the parabola opens down and the vertex is at (0, 5), we conclude that the correct option is:
y = -(1/8)*x² + 5.
<h3>
Which is the equation of the parabola?</h3>
The relevant information is that we have the vertex at (0, 5), and that the parabola opens downwards.
Remember that the parabola only opens downwards if the leading coefficient is negative. Then we can discard the two middle options.
Now, because the parabola has the point (0, 5), we know that when we evaluate the parabola in x = 0, we should get y = 5.
Then the constant term must be 5.
So the correct option is the first one:
y = -(1/8)*x² + 5.
If you want to learn more about parabolas:
brainly.com/question/4061870
#SPJ1
Answer:
The 95% confidence interval estimate of the population proportion of managers who have caught salespeople cheating on an expense report is (0.5116, 0.6484).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of 
, and a confidence level of 
, we have the following confidence interval of proportions.
In which
z is the zscore that has a pvalue of 
.
In the survey on 200 managers, 58% of the managers have caught salespeople cheating on an expense report.
This means that 
95% confidence level
So 
, z is the value of Z that has a pvalue of 
, so 
.
The lower limit of this interval is:
The upper limit of this interval is:
The 95% confidence interval estimate of the population proportion of managers who have caught salespeople cheating on an expense report is (0.5116, 0.6484).
Answer:
60
Step-by-step explanation:
5 times 12
