Answer:
(12.1409, 14.0591
Step-by-step explanation:
Given that Tensile strength tests were performed on two different grades of aluminum spars used in manufacturing the wing of a commercial transport aircraft. From past experience with the spar manufacturing process and the testing procedure, the standard deviations of tensile strengths are assumed to be known.
Group Group One Group Two
Mean 87.600 74.500
SD 1.000 1.500
SEM 0.316 0.433
N 10 12
The mean of Group One minus Group Two equals 13.100
standard error of difference = 0.556
90% confidence interval of this difference:
t = 23.5520
df = 20
Answer:
- a rotation, followed by a translation
- a translation, followed by two reflections
Step-by-step explanation:
The rigid motions are the transformations that produce congruent images.
There are three main kinds of rigid motions :
- Reflections : Flips a figure across a line of reflection.
- Rotations : Rotates a figure about some degrees around a center point.
- Translations : Moves figure on a plane about some distance in a certain direction.
But dilation is not a rigid transformation because it may change the size of the image. It is usually used to shrink or enlarge a shape.
So, the options having dilation and term "stretch" cannot produce congruent figures.
Hence, the correct options are :
- a rotation, followed by a translation
- a translation, followed by two reflections
Answer:
First option: Square
with diagonals 
and 
.
Fifth option: Segment 
is parallel to segment 
.
Step-by-step explanation:
We know that a square is quadriteral whose sides are equal.
By definition, a square has the following properties:
1) Its four sides are congruent.
2) The diagonals are congruent.
3) The angles formed by the intersection of the diagonals measure 90 degrees.
4) The opposite sides are parallel.
5) Each internal angle measures 90 degrees.
Notice in the figure that:
- The diagonals of the square are: and .
- and are opposite sides, therefore, they are parallel.
When you have factors in shapes you must remember:
circumference and perimeter are in one unit measures
area is in squared units
volume is in cubed units
So, when the circumference of A is 4 times that of C there is a factor of 4.
Since we need to know the area the factor 4 will change to a factor of 4² since area is a squared unit.
The solution is 4²=16, the are of circle A is sixteen times the area of circle B.
Harry can rake the leaves in the yard 8 hours faster than his little brother Jimmy can.
<span>If they join to work together they can complete the job in 3 hours. </span>
<span>1/x + 1/(x - 8) = 1/3 </span>
<span>3(x - 8) + 3x = x(x - 8) </span>
<span>x^2 - 14x + 24 = 0 </span>
<span>(x - 12)(x - 2) = 0 </span>
<span>Solutions: </span>
<span>x = 2 </span>
<span>x = 12 </span>
<span>Jimmy can complete the job on his own in 12 hours.</span>
