Answer:
area of glass panel 39 inchea square
alice drew two triangles on the coordinate plane as shown. Which series of transformation proves the two triangles are congruent
1 answer:
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Answer: The correct options are
(A) Rotation 90° anticlockwise.
(D) (x, y) → (–y, x).
Step-by-step explanation: Given that ΔXYZ is rotated to create the image triangle ΔX'Y'Z'.
Triangle XYZ and its image triangle X'Y'Z' are shown in the attached figure.
The co-ordinates of the vertices of ΔXYZ are X(0, 0), Y(0, -2) and Z(-2, -2).
And the co-ordinates of the vertices ΔX'Y'Z' are X'(0, 0), Y'(2, 0) and Z'(2, -2).
<u>Option (A) Rotation 90°:</u>
We see from the figure that if we rotate ΔXYZ is rotated 90° anticlockwise, then it will coincide with ΔX'Y'Z'.
So, rotation of 90° anticlockwise is a correct option.
<u>Option (B) Rotation 180°:</u>
If we rotate ΔXYZ is rotated clockwise or anticlockwise 180°, then it will NOT coincide with ΔX'Y'Z'.
So, rotation of 180° is NOT a correct option.
<u>Option (C) Rotation 270°:</u>
If we rotate ΔXYZ is rotated clockwise 270°, then also it will not coincide with ΔX'Y'Z'.
So, rotation of 270° clockwise is also a correct option.
<u>Option (D) (x, y) → (–y, x):</u>
We see that the co-ordinates of both the triangle follow the transformation
X(0, 0) ⇒ X'(0, 0)
Y(0, -2) ⇒ Y'(2, 0)
Z(-2, -2) ⇒ Z'(2, -2).
So, the transformation is (x, y) ⇒ (-y, x).
Therefore, the transformation (x, y) → (–y, x) is a correct option.
<u>Option (E) (x, y) → (y, -x):</u>
We see that the co-ordinates of both the triangle does NOT follow this transformation
For example, suppose this transformation is correct. Then, we have
Y(0, -2) ⇒ (-2, 0), which are not the co-ordinates of Y'.
Therefore, the transformation (x, y) → (–y, x) is NOT a correct option.
Thus, the correct options are:
(A) Rotation 90° anticlockwise.
(D) (x, y) → (–y, x).
Complete Question
The complete question is shown on the first uploaded image
Answer:
a
The probability that he or she would choose the pair of socks in the center position is
The correct answer choice is
X has a binomial distribution with parameters n=100 and p=1/5
b
The mean is
The standard deviation is
c
The probability,
d
The correct answer is
The experiment supports the center stage effect. If participants were truly picking the socks at random, it would be highly unlikely for 34 or more to choose the center pair.
Using the R the probability
The probabilities
Step-by-step explanation:
Since the person selects his or her desired pair of socks at random , then the probability that the person would choose the pair of socks in the center position from all the five identical pair is mathematically evaluated as
The mean of this distribution is mathematical represented as
substituting the value
The standard deviation is mathematically represented as
substituting the value
Applying normal approximation the probability that 34 or more subjects would choose the item in the center if each subject were selecting his or her preferred pair of socks at random would be mathematically represented as
By standardizing the normal approximation we have that
Now z is mathematically evaluated as
Substituting values
So using the z table the is 0.0002
The probability P and Pe that 34 or more subject would choose the center pair is very small So
The correct answer is
The experiment supports the center stage effect. If participants were truly picking the socks at random, it would be highly unlikely for 34 or more to choose the center pair.
