Answer:
Mid- point =(-4+2/2, -2+8/2)
=(-2/2,6/2)
=(-1,3)
Given:
Mean, μ = 196
Std. dev., σ = 22
A sample size of 50 (> 30) is large enough to provide meaningful data.
The random variable is x = 200.
The z-score is
z = (x - μ)/σ = (200 - 196)/22 = 0.1818
From normal distribution tables, obtain
Prob(X < 200) = 0.572 = 57.2%
Answer: 57.2%
It definetly is congruent.
Have a Great Day!!!
Answer:
correct choice is 1st option
Step-by-step explanation:
Two given triangles have two pairs of congruent sides: one pair of length 7 units and second pair of length 8 units. The third side is common, i.e the lengths of third sides are equal too.
Use SSS theorem that states that if three sides of one triangle are congruent to three sides of another triangle, then these two triangles are congruent.
Thus, given triangles are congruent by SSS theorem.
Answer:
ΔEFG is an isosceles triangle.
Step-by-step explanation:
Given:
E (0, 0),
F (−7, 4),
G (0, 8)
ΔEFG
Solution:
Distance formula
Distance d = ![\sqrt{(x_2-x_1)^2 +( y_2-y_1)^2](https://tex.z-dn.net/?f=%5Csqrt%7B%28x_2-x_1%29%5E2%20%2B%28%20y_2-y_1%29%5E2)
Step 1: Finding the length of EF
By using distance formula,
![EF = \sqrt{(-7 - 0)^2 + (4-0)^2}](https://tex.z-dn.net/?f=EF%20%3D%20%5Csqrt%7B%28-7%20-%200%29%5E2%20%2B%20%284-0%29%5E2%7D)
![EF = \sqrt{(49) + (16)}](https://tex.z-dn.net/?f=EF%20%3D%20%5Csqrt%7B%2849%29%20%2B%20%2816%29%7D)
![EF = \sqrt{(49) + (16)}\\EF = \sqrt{65}\\](https://tex.z-dn.net/?f=EF%20%3D%20%5Csqrt%7B%2849%29%20%2B%20%2816%29%7D%5C%5CEF%20%3D%20%5Csqrt%7B65%7D%5C%5C)
Step 2: Finding the length of FG
By using distance formula,
![FG = \sqrt{(0-(-7))^2+(8-4)^2}\\FG = \sqrt{(7)^2 +(4)^2}\\FG = \sqrt{49 +16}\\FG = \sqrt{65}](https://tex.z-dn.net/?f=FG%20%3D%20%5Csqrt%7B%280-%28-7%29%29%5E2%2B%288-4%29%5E2%7D%5C%5CFG%20%3D%20%5Csqrt%7B%287%29%5E2%20%2B%284%29%5E2%7D%5C%5CFG%20%3D%20%5Csqrt%7B49%20%2B16%7D%5C%5CFG%20%3D%20%5Csqrt%7B65%7D)
Step 2: Finding the length of GE
![GE= \sqrt{(0-0)^2 + (0-8)^2}\\\\GE =\sqrt{(-8)^2}\\GE = \sqrt{64}\\GE = 8](https://tex.z-dn.net/?f=GE%3D%20%5Csqrt%7B%280-0%29%5E2%20%2B%20%280-8%29%5E2%7D%5C%5C%5C%5CGE%20%3D%5Csqrt%7B%28-8%29%5E2%7D%5C%5CGE%20%3D%20%5Csqrt%7B64%7D%5C%5CGE%20%3D%208)
Thus we could see that the sides EF = FG
So it is a isosceles triangle.