Step-by-step explanation:
Initially, there's only 1 letter.
Tania sends the letter to 4 friends.
Each friend sends a letter to 4 more friends (4 × 4 = 16).
Each of those friends sends to 4 more friends (16 × 4 = 64).
The pattern is 1, 4, 16, 64, etc.
This is a geometric sequence. The first term is 1 and each term is 4 times the previous term.
a₁ = 1
aₙ = 4 aₙ₋₁
The explicit formula is:
aₙ = 1 (4)ⁿ⁻¹
Let events
A=Nathan has allergy
~A=Nathan does not have allergy
T=Nathan tests positive
~T=Nathan does not test positive
We are given
P(A)=0.75 [ probability that Nathan is allergic ]
P(T|A)=0.98 [probability of testing positive given Nathan is allergic to Penicillin]
We want to calculate probability that Nathan is allergic AND tests positive
P(T n A)
From definition of conditional probability,
P(T|A)=P(T n A)/P(A)
substitute known values,
0.98 = P(T n A) / 0.75
solving for P(T n A)
P(T n A) = 0.75*0.98 = 0.735
Hope this helps!!
The center of mass is mathematically given as

<h3>What is the center of mass.?</h3>
Determine the center of mass in one dimension:
Represent the masses at the respective distances.

We calculate the total mass of the system.

Step 03: Calculate the moment of the system.

we calculate the center of mass.

Read more about the center of mass.
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Step-by-step explanation:
Two legs of the right triangle are 6 and 9. We can find its third side as follows :

The above is called Pythagoras theorem and it is applicable for a right angled triangle.
a,b and c are base, perpendicular and hypotenuse respectively
c is the third side
So,

Hence, Cade and Tyce both are correct. The length of the missing side is 10.82