Sum of geometric sequence
for the sum where the initial value is a₁ and the common ratio is r and the term is n
common ratio is -3
-5 times -3 is 15, -15 times -3=-45 etc
first term is -5
and we want the 8th term
the sum is 8200
Taking the 3 solutions as 3 different terms, we can create an equation as follows:
Solution 1 : 10mL with 20% acid
Solution 2 : 30mL with x% acid
Solution 3 : 40mL with 32% acid
Since solution 1 + solution 2 = solution 3, let us substitute the given values we have:
10(0.2) + 30(x) = 40(0.32)
2 + 30x = 12.8
To solve for the unknown concentration x, we subtract 2 from both sides:
2 + 30x - 2 = 12.8 - 2
30x = 10.8
Dividing both sides by 30:
30x/30 = 10.8/30
x = 0.36
Therefore the unknown solution is 36% acid.
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!!
Answer:
Step-by-step explanation:
we have
-----> equation A
-----> equation B
To find out (V of r)(t) substitute equation B in equation A
Answer:
The volume of the sphere is 1436 in³
The equation is
V = ⁴⁄₃ * 3.14 * (7ft)³
Step-by-step explanation:
radius = half of diameter
d = 14ft
r = 14ft / 2 = 7ft
To calculate the volume of a sphere we have to use the following formula:
V = volume
r = radius = 7ft
π = 3.14
V = ⁴⁄₃πr³
we replace with the known values
V = ⁴⁄₃ * 3.14 * (7ft)³
V = 4.187 * 343 in³
V = 1436 in³
The volume of the sphere is 1436 in³
