Answer: BM = 21.4
Step-by-step explanation:
Considering the given triangle BMS, to determine angle BM, we would apply the sine rule. It is expressed as
m/SinM = s/SinS = b/SinB
Where m, s and b are the length of each side of the triangle and angle M, Angle S and angle B are the corresponding angles of the triangle.
From the information given,
Angle M = 102°
Angle B = 35°
Angle S = 180 - (102 + 35) = 43°
b = MS = 18
s = BM
Therefore
18/Sin 35 = BM/Sin 43
Cross multiplying, it becomes
BMSin35 = 18 × Sin 43
BM × 0.5736 = 18 × 0.6820
0.5736BM = 12.276
Dividing the left hand side and the right hand side of the equation by 0.5736, it becomes
0.5736BM/0.5736 = 12.276/0.5736
BM = 21.4
The vertex would be (5,-23)
If the relationship between two quantities is a proportional relationship, this relationship can be represented by the graph of a straight line through the origin with a slope equal to the unit rate.
Answer:
B. 90 + 90 √2
Step-by-step explanation:
From first base to the second base, it will travel 90 feet.
From the second base to the home plate, it will travel a longer distance. How much? Well, if you look at the layout of the field, you'll see that if you draw a line from second base to the home plate, you'll form two rectangular triangles, one with the 1st base, another one with the 3rd base.
The line from the 2nd base to home plate is the hypotenuse, which we can easily find by:
h²=90² + 90²
h = √(2 * 90²)
h = 90 √2
So, from second base to home plate, the ball has traveled 90 √2
Overall: 90 + 90 √2
Answer:
a) 0.1091
b) 0.9994
c) 0.5886
Step-by-step explanation:
X = the number of fish out of 20 that die after 24 hours
x = 0, 1, 2, . . . , 20
X~ Binomial (n= 20, p =0.20)
P(14 survive) = P(X = 6)
= 
=0.1091
Similarly we can find out
P(at least 10 survive) = P( X <= 10 ) = (Using technology) = 0.9994
P(at most 16 will survive) = P(X <= 16) = (Using technology) = 0.5886
