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.
There is some information lacking in this question.
Response:
d. (63.9, 66.7)
This indicates that the 90% confidence interval is (a,b) = (63.9, 66.7)
Detailed explanation:
A confidence interval refers to a set of values within which there's a defined probability that a parameter’s value falls.
The formula for confidence interval in statistics can be represented as:
x +/- zr/√n
Here, we have;
Mean x = 65.3
Standard deviation r = 5.2
Sample size n = 36
Confidence interval level = 90%
z (for 90% confidence) = 1.645
Substituting our values gives us;
65.3 +/- 1.645(5.2/√36)
65.3 +/- 1.645(0.866667)
65.3 +/- 1.42567
65.3 +/- 1.4
Results in (63.9, 66.7)
This confirms that for a 90% confidence interval, (a,b) = (63.9, 66.7)
Answer:
The ratio of the perimeters is 3:1
Step-by-step explanation:
Given: The ratio of the sides of two squares is 3:1
To find: The ratio of their perimeters
Solution: Let the lengths of the sides be represented as 3:1 = 3x: x
Perimeter of a square = 4(side)
Using this formula,
Perimeter of square 1 = 4 × 3x = 12x
Perimeter of square 2 = 4 × x = 4x
The ratio of the perimeters of square 1 and square 2 is = 12x: 4x
= 3: 1
