Answer: 7 inches.
Given that there was a quadrilateral ABCD and it was reflected over a line y
Hence preimage = ABCD and image = TURS
When reflected we have new position of A = T
new position of B =U
new position of C = R and
new position of D = S
By transformation properties, for reflection the scale factor is 1 and hence AB will have the same length as TU
Since AB = 7 inches, TU = 7 inches.
Note:
A reflection in the coordinate plane is just like a reflection in a mirror. Any point or shape can be reflected across the x-axis, the y-axis, or any other line, invisible or visible. This line, about which the object is reflected, is called the “line of symmetry.” Here we have line of symmetry as line y.
Answer:
b
Step-by-step explanation:
I hope this helps
Answer:
would be the correct statement.
Step-by-step explanation:
As we know that
Average rate of change = Change in output / Change in input
= Δy / Δx
As the average rate of change of g(x) between x = 4 and x = 7 is 5/6.
so
Therefore, would be the correct statement.
Answer:
Options (A), (B)
Step-by-step explanation:
Option A.
Two sides of the given triangle are equal. Therefore, the given triangle is an isosceles triangle.
Option (B).
Given triangle has a right angle. Therefore, it's a right triangle.
Option (C).
Only two sides of the given triangle are equal. Therefore, it's not an equilateral triangle.
Option (D).
Although this triangle has two acute angles (less than 90°) but the third angle is 90°. Therefore, this triangle is not an acute triangle. It's a right triangle.
Option (E).
A scalene triangle is a triangle having all sides different in measure but the given triangle is an isosceles triangle. Therefore, it's not a scalene.
Option (F).
Any angle of this triangle is not more than 90°. Therefore, the given triangle is not an obtuse triangle.
Answer:
Kindly check explanation
Step-by-step explanation:
Given the data:
Number of Home alone movies (X)
Watched probability, p(x)
X : ___ 0 ____ 1 ____ 2 ____ 3 ___ 4 ___ 5
P(x) : _0.15 __ 0.42 __0.32 __? ___0.02 _0.01
a. Write the event "the student has seen 3 Home Alone movies" using probability notation. Then find this probability.
P(x = 3)
Since Σp(x) = 1
P(x =3) = 1 - (p(0)+p(1)+p(2)+p(4)+p(5))
P(x = 3) = 1 - (0.15 + 0.42 + 0.32 + 0.02 + 0.01)
P(x = 3) = 1 - 0.92
P(x = 3) = 0.08
b. Explain in words what P(X > 3) means. What is this probability?
P(x > 3) is the probability they a randomly chosen student has watched more than 3 home alone movies.
P(x > 3) = p(4) + p(5)
P( x > 3) = 0.02 + 0.01 = 0.04
d. Calculate and interpret the expected value of X.
E(X) = [Σ(X * p(x)]
(0*0.15) + (1*0.42) + (2*0.32) + (3*0.08) + (4*0.02) + (5*0.01) = 1.43
The avereage number of home alone movies watched is 1.43