Answer:
Step-by-step explanation:On the given diagram you see two right triangles with equal hypotenuses and pair of equal angles.
Based only on the information given in the diagram you can conclude that triangles are congruent by HA theorem (the HA theorem states that "if the hypotenuse and an acute angle of one right triangle are congruent to the hypotenuse and an acute angle of another right triangle, then the two triangles are congruent").
Also you can conclude that triangles are congruent by AAS Postulate (the AAS Postulate states that "if two angles and a non-included side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent").
I hope this helps you
[2×4+1/4]×(-8)
[8+1/4]×(-8)
9×-8/4
9×-2
-18
: If all of the angles in both triangles are congruent then the triangles are SIMILAR not necessarily congruent. They can be congruent by using a theorem called ASA, SSS, or SAS. The "S" stands for Side and the "A" stands for angle.
Step-by-step explanation:
P(A) = 0.47
P(B) = 0.53
P(A|B) = 0.57
a. Probability that at least one stock will rise is equal to P(A u B)
= P(A) + p(B) - P(A n B)
= (O.47+0.53)-(0.53*0.57)
= 1-0.3021
= 0.6979
b. Events A and B are not mutually exclusive. This is because P(AnB)≠0
P(AnB) = p(B).P(A|B)
= 0.53x0.57
= 0.3021 and this value is not equal to 0
c. No, events A and B are not independent. This is because P(A|B) ≠ P(A)
Since we have
p(A) as 0.47
P(A|B) as 0.53
Answer:
y = 8
x = 8√5
z = 4√5
Step-by-step explanation:
Using the formula (which is a geometric mean):
a y
---- = -----
x a
Where a is the altitude (y), x is a projection (16), and y is the other projection (4):
y 4
---- = -----
16 y
Cross multiply:
y² = 16 (4)
y² = 64
√y² = √64
y = 8
To find x and z, use the Pythagorean Theorem:
16² + y² = x²
256 + 8² = x²
256 + 64 = x²
320 = x²
√320 = √x²
√64√5 = √x²
8√5 = x
x = 8√5
4² + y² = z²
16 + 64 = z²
80 = z²
√80 = √z²
√16√5 = √z²
4√5 = z
z = 4√5