<h3>
Answer:</h3>
We know that,
- <u>Theoretical probability, when the probability is same no matter what the experiment says</u>.
Here, it is given 8 different names.
<u>Theoretical probability of highest choosing name</u>:
<u>Theoretical probability of Grace being chosen</u>:
<u>In sense of theoretical probability, if the number of names in the hat were different will change but then probability will not change</u>.
When x = 0, the value of f(x) is 2. You can see why below
f(x) = (2^x) + 1
f(0) = (2^0) + 1
f(0) = 1+1
f(0) = 2
So the point (0,2) is on the curve. This is visually shown as the y intercept (the location where the curve crosses the y axis)
When x = 2, the value of f(x) is 5
f(x) = (2^x) + 1
f(2) = (2^2) + 1
f(2) = (4) + 1
f(2) = 5
So (2,5) is another point on this curve
Find the slope of the line through these two points
m = (y2 - y1)/(x2 - x1)
m = (f(2) - f(0))/(2 - 0)
m = (5 - 2)/(2 - 0)
m = 3/2
m = 1.5
The slope as a fraction is 3/2
The slope as a decimal is 1.5
So the rate of change is 1.5
Answer:
C. 17.6
General Formulas and Concepts:
<u>Math</u>
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
- Multiplication Property of Equality
- Division Property of Equality
- Addition Property of Equality
- Subtraction Property of Equality<u>
</u>
<u>Trigonometry</u>
- [Right Triangles Only] SOHCAHTOA
- [Right Triangles Only] tanθ = opposite over adjacent
Step-by-step explanation:
<u>Step 1: Identify Variables</u>
Angle θ = 40°
Opposite Leg = <em>x</em>
Adjacent Leg = 21
<u>Step 2: Solve for </u><em><u>x</u></em>
- Substitute in variables [tangent]:
- [Multiplication Property of Equality] Isolate <em>x</em>:
- Rewrite:
- Evaluate:
- Round:
Answer:
B. The rate at which the number of people in the park is changing 4 hours after the gates open is 92 people per hour.
Step-by-step explanation:
Rate at which people enter:
e(x)=0.03x^3 + 2
Rate at which people leave:
L(x)=0.5x + 1
Rate at which the number of people in the park is changing:
(e - L)(x) = 0.03x^3 + 2 - (0.5x + 1) = 0.03x^3 - 0.5x + 1
4 hours after the gates open, the rate is:
(e - L)(4) = 0.03(4)^3 - 0.5(4) + 1 = 0.92 hundreds of people per hour or 0.92*100 = 92 people per hour