Answer:
3.9
Step-by-step explanation:
Given the data:
Payout ($) (x) : 0 2 4 8 10
Probability p(x) : 0.35 0.2 0.1 0.2 0.15
The expected winning ; E(X) = Σ(x * p(x))
Σ(x * p(x)) = (0*0.35)+(2*0.2)+(4*0.1)+(8*0.2)+(10*0.15)
= 0 + 0.4 + 0.4 + 1.6 + 1.5
= 3.9
The total volume of the 40 sphere shaped water balloons is 46032.38 cubic cm.
Radius of 1 sphere = 6.5 cm
We know that the volume of the sphere is given by 4/3 π r³
We will take the radius as 6.5 cm and π as 22/7
Now we will find the volume : 4/3 ×22/7×6.5³ = 1150.81 cubic cm.
Volume of 40 such spheres = 40 × 1150.81 = 46032.38 cubic cm.
The radius of all the spheres are 46032.38 cubic cm.
A sphere is a geometrical entity with three dimensions that resembles a two-dimensional circle. A sphere is a group of points in three dimensions that are all situated at the same r-distance from one another.
The supplied point is the sphere's center, while the letter r stands for the sphere's radius which is half the diameter. The earliest known allusions to spheres are found in the works of two ancient Greek mathematicians.
Therefore total volume of the 40 sphere shaped water balloons is 46032.38 cubic cm .
Disclaimer: The complete question is : Maggie and Amelia filled up 40 water balloons shaped like spheres. Each water balloon had a radius of 6.5 cm.Find the total volume of water required.
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F(13) means x equals 13.
Replace x in the equation with 13 and solve:
-13 + 3 = -10
F(13) = -10
The exponential equation of the model is A(t) = 2583 * 0.88^t and the multiplier means that the number of new cases in a week is 88% of the previous week
<h3>The function that models the data</h3>
The given parameters are:
New, A(t) = 2000
Rate, r = 12%
The function is represented as:
A(t) = A * (1 - r)^t
So, we have:
2000 = A * (1 - 12%)^t
This gives
2000 = A * (0.88)^t
2 weeks ago implies that;
t = 2
So, we have:
2000 = A * 0.88^2
Evaluate
2000 = A * 0.7744
Divide by 0.7744
A = 2583
Substitute A = 2583 in A(t) = A * 0.88^t
A(t) = 2583 * 0.88^t
Hence, the exponential equation of the model is A(t) = 2583 * 0.88^t
<h3>The interpretation of the multiplier</h3>
In this case, the multiplier is 88% or 0.88
This means that the number of new cases in a week is 88% of the previous week
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Answer: Average rates of change for Bird A is 0.045 and for Bird B is 3.816.
Step-by-step explanation: Through its graph, a function can be analyzed and be identified its attributes. Average Rate of Change is the ratio of change in the function values to the change of x-value, i.e., it is the slope of the function in a specific interval of x. With the Average it is possible to compare two function.
<u>Average Rate of Change</u>
<em><u>Bird A</u></em>:
For the interval [0,18]:
x₁ = 0 f(0) = 8.3
x₂ = 18 f(18) = 9.1
Average = 
Average = 
Average = 0.045
<em><u>Bird B</u></em>: y = 3.6(1.06)x
For the interval [0,18]:
x₁ = 0 y = 3.6(1.06)0 = 0
x₂ = 18 y = 3.6(1.06)18 = 68.7
Average =
Average = 
Average = 3.816
The Average Rate for Change for Bird A is 0.045 and for Bird B is 3.816. This means that the population of Bird B increase in rate faster than the population of Bird A.
