Answer: 26.3 mm
Step-by-step explanation:
The two-standard deviations rule for outliers states that any value lying outside two standard deviations from the average is considered an outlier.
Given that the Mean is 23.5 millimeters (mm) and the standard deviation is 1.4 mm
The maximum thickness that should be reviewed = mean + 2 (standard deviation)
= 23.5 + 2(1.4)
= 23.5 + 2.8
= 26.3 mm
therefore, the maximum thickness warranting machine configuration review by the statistician = 26.3 mm.
Response: a) 0.9980, b) 0.0013, c) 0.0020, d) 0.00000026, e) 0.0318
Detailed explanation:
In Problem 8-4, the computer time-sharing system experiences teleport inquiries at an average rate of 0.1 per millisecond. We are tasked with determining the probabilities of the inquiries over a specific period of 50 milliseconds:
Given that
Applying the Poisson process, we find that
(a) at most 12
probability= 
(b) exactly 13
probability=
(c) more than 12
probability=
(d) exactly 20
probability=
(e) within the range of 10 to 15, inclusive
probability=
Thus, a) 0.9980, b) 0.0013, c) 0.0020, d) 0.00000026, e) 0.0318
The correct choice is option D. The given equations are:...[1]...[2] Multiply equation [1] by 5 on both sides; we have...[3]. By using the elimination method, we can add equations [2] and [3] to eliminate y and determine x, resulting in... Dividing both sides by 13 yields x = 3. Substituting x back into equation [1] results in 2(3) - y = -4, which simplifies to 6 - y = -4. After subtracting 6 from both sides, we find -y = -10. Dividing through by -1 gives y = 10. Hence, the solution is (3, 10). Consequently, a valid equation that can replace 3x + 5y = 59 in the original set while still yielding the same result is 13x = 39.
Response:
The fence's width is 6 feet.
Detailed explanation:
To start, let’s define some variables.
Let the width of the fence be denoted as w, and the length as l.
Next, determine the length: the width is 2 feet less than half of the length.
w = l/2 - 2
Alternatively, l/2 can be expressed as w + 2, leading to l = 2(w + 2).
The total perimeter of the fence is 44 feet. The perimeter for a rectangle can be calculated using the formula:
P = 2(l + w)
Inserting what we know:
P = 44 and l = 2(w + 2)
44 = 2(2(w+2) + w)
44 = 2(2w + 4 + w)
44 = 2(3w + 4)
44 = 6w + 8
6w = 36
w = 36/6
w = 6 feet
Response:
∠PQL=∠TRN [Angles corresponding]
Thus, PQ║RS and PQ=RS
Detailed explanation:
The side PQ has been drawn.
A second side QR is traced, forming an acute angle with side PQ.
Now side QR is extended to the left.
Create an arc from point Q such that it intersects QP at M and extends RQ at L. Without altering the compass width (i.e., the distance between the nib and pencil), draw an arc from R to intersect RQ at N. Now measure the distance LM with a compass. Position the compass at N and mark an arc cut from point R. Designate this intersection as T. Draw a line from point R through T. Then measure the length of PQ with the compass. Position your compass at R and create an arc on the produced line RT at S. Thus, we ascertain that PQ║RS and PQ=RS.
This occurs because
∠MQL=∠NRT [corresponding angles, with QR acting as the transversal]
∵PQ║RS and PQ=RS [This identifies PQRS as a parallelogram]
Out of the four students who illustrated their explanations
Student 2 presented a partially correct but valid explanation.
