Answer:
a. 61.92 in²
b. 21.396 ≈ 21.4%
c. $4.71
Step-by-step explanation:
a. Amount of waste = area of rectangular piece of stock - area of two identical circles cut out
Area of rectangular piece of stock = 24 in × 12 in = 288 in²
Area of the two circles = 2(πr²)
Use 3.14 as π
radius = ½*12 = 6
Area of two circles = 2(3.14*6²) = 226.08 in²
Amount of waste = 288 - 226.08 = 61.92 in²
b. % of the original stock wasted = amount of waste ÷ original stock × 100
= 61.92/288 × 100 = 6,162/288 = 21.396 ≈ 21.4%
c. 288 in² of the piece of stock costs $12.00,
Each cut-out circle of 113.04 in² (226.08/2) will cost = (12*113.04)/288
= 1,356.48/288 = $4.71.
Answer: The answer would be D. 64
Step-by-step explanation: Understanding that the question noted that the second rectangle was dilated from PQRS, which has a perimeter of 16. With the coordinates of point P for the first rectangle being (2,0.5) whilst the second rectangle has point P at (8,2). To figure out the perimeter, divide point P from the second rectangle with point P from the first. The result would be 4. Thus, the scale factor is 4, which you then multiply the perimeter of PQRS by, which was 16. 16 times 4 equals 64.
Answer: A.
Step-by-step explanation:
Null hypothesis
: A statement describing population parameters as per the objective of the study. It usually takes "≤,≥,=" signs.
Alternative hypothesis 
: A statement describing population parameters as per the objective of the study. It usually takes ">, <, ≠" signs.
Let p be the proportion of screens that will be rejected.
12 percent of the screens manufactured using a previous process were rejected at the final inspection.
(i.e. p= 0.12)
Objective of the study = whether the new process<em> reduces </em>the population proportion of screens that will be rejected
i.e. p< 0.12
So, the appropriate hypotheses to investigate whether the new process reduces the population proportion of screens that will be rejected:
Answer:
see below
Step-by-step explanation:
a bearing is the angle in degrees measured clockwise from north.
Triangle ABC is a right triangle
Tan C = opp side / hyp
tan C = AB / CA
tan C = 30/30
tan C = 1
taking the inverse tan
tan ^ -1 tan C = tan ^ -1 ( 1)
C = 45 degrees
This is 90+45 degrees from North
135 degrees from north
Tan B = opp side / hyp
tan B = AD/BA
tan B = 45/30
tan B = 3/2
taking the inverse tan
tan ^ -1 tan B = tan ^ -1 ( 3/2)
D = 56.30993247
Add 180 degrees
180+56.30993247
236.3099325 from north
9 inches
12+12+9+9+8+8+8+8=74
12+12=24
9+9=18
8+8+8+8=32
24+18+32=74
