Answer:
1. a. Q° = 95°
b. a = 20.3; b = 19.3
2. p = 36; q = 14.4
Step-by-step explanation:
Question 1:
Recall: The Exterior Angle Theorem of a Triangle states that the size of the exterior angle of a triangle equals the sum of the two sizes of the two opposite angles of the triangle.
a. Based on the theorem,
Q° = 41° + 54° = 95°
b.
✔️122° = 4a + 2a (exterior angle theorem)
122 = 6a
Divide both sides by 6
122/6 = a
a = 20.3
✔️122° + 3b = 180° (angles on a straight line)
3b = 180 - 122
3b = 58
b = 58/3
b = 19.3
Question 2:
Recall: Opposite angles of a parallelogram are equal while adjacent/consecutive angles are supplementary.
✔️2p + 3p = 180° (adjacent angles)
5p = 180
p = 180/5
p = 36
✔️2p = 5q (opposite angles)
Plug in the value of p
2(36) = 5q
72 = 5q
72/5 = q
q = 14.4
Answer:
The null hypothesis, H₀ is that the mean completion time for the TPS report remains at the duration of 6.3 hours
The alternative hypothesis, H₁ is that the mean completion time for the TPS report is less than 6.3 hours
Step-by-step explanation:
The given parameters are;
The average time spent on the TPS report = 6.3 hours
The number of workers in the sample used for the test = 48 office workers
The mean completion time of the TPS report for the sample = 5.7 hours
The test aim; To find out whether the mean time required to fill out the TPS report has been reduced
The null hypothesis, is H₀; μ = 6.3 hours
The alternative hypothesis, H₁; μ < 6.3 hours
Answer:
Answer is below
Step-by-step explanation:
I would use 2x + y = 5 to solve for y since there are no numbers attached to y. Then when I solve for y, I would plug that value into the other equation to solve for x.
If this answer is correct, please make me Brainliest!
Answer: The area of the square is 64 square inches and the area of the new rectangle is 60 square inches. The square's area is 4 inches larger than the rectangle.
Step-by-step explanation: If a side length of the square measures 8 inches, then its area can be calculated as follows;
Area = L x W
The length and the width both measure 8 inches (all sides of a square are equal in length).
Area = 8 x 8
Area = 64
Also, the the new rectangle is formed by increasing the width of the square by 2 inches (that is 8 + 2 = 10), and decreasing the length by 2 inches (that is 8 - 2 = 6). The area of the new rectangle is calculated as follows;
Area = L x W
Area = 10 x 6
Area = 60
Therefore the area of the square is 64 square inches and the area of the rectangle is 60 square inches. The area of the square is 4 inches larger than that of the rectangle.