Answer:
Therefore the rate of growth of the tree is 33 cm/ yr.
Step-by-step explanation:
Given that,
The height of the tree is
H= 210 +33t
Here H represent the height of tree in cm and t is time in year.
The rate of growth is the first order derivative of the H with respect to time.
i.e The rate of growth
∴H= 210 +33t
Differentiating with respect to t
Therefore the rate of growth of the tree is 33 cm/ yr.
Answer:
Step-by-step explanation:
The total number of permutations of boys and girls on the team are:
¹⁶P₅*¹³P₄
1.
Bob will be one of the fixed boys to be picked. Hence, actually 4 boys are to be picked from 15. The permutations of girls being picked remains the same.
Probability = Permutations with Bob as one of the boys / Total permutations
Probability = (¹⁵P₄*¹³P₄) / (¹⁶P₅*¹³P₄) = ¹⁵P₄ / ¹⁶P₅
Probability = = 15! / 16! = 1/16
2.
Now, Bob is one of the fixed boys and Jane is one of the fixed girls. Hence, actually 4 boys are to be picked from 15 and 3 girls are to be picked from 12.
Probability = Permutations with bob as one of the boys and jane as one of the girls / Total permutations
Probability = (¹⁵P₄*¹²P₃) / (¹⁶P₅*¹³P₄) = (1/16)*(1/13) = 1/208
3.
Now, the probability that at least Jane or Bob will be picked has been asked. This probability is a combination of three probabilities:
Probability = (Probability that only Bob will be picked) + (Probability that only Jane will be picked) + (Probability that both will be picked)
Probability = 1/16 + 1/13 + 1/208 = 0.123
4.
Total teams possible = ¹⁶P₅*¹³P₄ = 8994585600 teams are possible