Answer:
about 117 times
Step-by-step explanation:
No. of possible outcomes of a cube: 6
2 out the 6 possible outcomes are less than 3,
and therefore, No. of favorable outcome: 2
P(less than 3)= No. of favorable outcome / No. of possible outcomes
=2/6 => 1/3
if you roll a standard number cube 350 times then,
Prediction= number of rolls x (P(less than 3))
=350 x 1/3
≈117 times.
{tan(60) + tan(10)}/{1 - tan(60)*tan(10)} - {tan(60) - tan(10)}/{1 + tan(10)*tan(60)}
<span>ii) Taking LCM & simplifying with applying tan(60) = √3, the above simplifies to: </span>
<span>= 8*tan(10)/{1 - 3*tan²(10)} </span>
<span>iii) So tan(70) - tan(50) + tan(10) = 8*tan(10)/{1 - 3*tan²(10)} + tan(10) </span>
<span>= [8*tan(10) + tan(10) - 3*tan³(10)]/{1 - 3*tan²(10)} </span>
<span>= [9*tan(10) - 3*tan³(10)]/{1 - 3*tan²(10)} </span>
<span>= 3 [3*tan(10) - tan³(10)]/{1 - 3*tan²(10)} </span>
<span>= 3*tan(30) = 3*(1/√3) = √3 [Proved] </span>
<span>[Since tan(3A) = {3*tan(A) - tan³(A)}/{1 - 3*tan²(A)}, </span>
<span>{3*tan(10) - tan³(10)}/{1 - 3*tan²(10)} = tan(3*10) = tan(30)]</span>
120, 90, 30 if you're going from the depths of the water to water level
Answer:
P = 8
Step-by-step explanation:
10 because 30 divided by 10 equals 3 and 50 divided by 10 equals 5 and 3 and 5 only have a GCF of 1 so 10 is your answer
