To subtract a number from another number, they must be the same type. 4 1/4 is a mixed number; 3/4 is a fraction. thus, 4 1/4 must be converted into fractional form go subract a fraction (3/4) from it.
Answer:
a) probability that is cracked=1/30 (3.33%)
b) probability that is discoloured = 29/600 (4.83%)
c) probability that is cracked and discoloured = 11/600 (1.83%)
Step-by-step explanation:
assuming that each stone is equally likely to be chosen then defining the events C= the stone is cracked , D= the stone is discoloured , N= the stone is neither cracked or discoloured, then
P(C)= number of favourable outcomes/total number of outcomes = 20 stones/600 stones = 1/30 (3.33%)
P(D)= number of favourable outcomes/total number of outcomes = 29 stones/600 stones = 29/600 (4.83%)
the probability that is discoloured and cracked is P(C∩D) , where
P(C∪D)=P(C) + P(D)-P(C∩D)
and
P(C∪D)= 1- P(N)
thus
1- P(N)=P(C) + P(D)-P(C∩D)
P(C∩D)= P(N)+P(C)+P(D) -1
replacing values
P(C∩D)= P(N)+P(C)+P(D)=562/600 + 20/600 + 29/600 -1= 611/600 -1 = 11/600
thus
P(C∩D)= 11/600 (1.83%)
Angle BAC
cosφ⁻¹ = (10² + 17² - 11²)/(2*10*17) = 37.9 ≈ 38°
Angle ACB
cosφ⁻¹ = (10² + 11² - 17²)/(2*10*11) = 108.0°
Angle ABC
cosφ⁻¹ = (11² + 17² - 10²)/(2*11*17) = 34.0°
See you !
B. Multiplied each side by 12