Outcome Bag of Gold Magic Wand
Relative frequency 0.32 0.68
The relative frequency of getting a bag of gold is .......... reasonably close
.32 is close to 30% so
Alison's claim about the theoretical probability is likely to be 2............true
Further, this means that the theoretical probability of getting a magic wand is most likely 3............1 - 30% = 70%
Answer:

Step-by-step explanation:
<u>Use the Pythagorean Theorem</u>
The equation for the Pythagorean Theorem is 
* a and b are the lengths of the legs, and c is the hypotenuse.*
(To know which side is the hypotenuse look at longest side which is across the right angle).
a= x, b=8, c=9

Let's Plug in the side lengths:

Evaluate 8^2 and 9^2:

Subtract 64 from both sides:


Take the square root of both sides:

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DANG $13,210,130 i would love to be this guy
I would personally take the number three and trow it out the window but that's not what we are talking about
Answer:
-2, 8/3
Step-by-step explanation:
You can consider the area to be that of a trapezoid with parallel bases f(a) and f(4), and width (4-a). The area of that trapezoid is ...
A = (1/2)(f(a) +f(4))(4 -a)
= (1/2)((3a -1) +(3·4 -1))(4 -a)
= (1/2)(3a +10)(4 -a)
We want this area to be 12, so we can substitute that value for A and solve for "a".
12 = (1/2)(3a +10)(4 -a)
24 = (3a +10)(4 -a) = -3a² +2a +40
3a² -2a -16 = 0 . . . . . . subtract the right side
(3a -8)(a +2) = 0 . . . . . factor
Values of "a" that make these factors zero are ...
a = 8/3, a = -2
The values of "a" that make the area under the curve equal to 12 are -2 and 8/3.
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<em>Alternate solution</em>
The attachment shows a solution using the numerical integration function of a graphing calculator. The area under the curve of function f(x) on the interval [a, 4] is the integral of f(x) on that interval. Perhaps confusingly, we have called that area f(a). As we have seen above, the area is a quadratic function of "a". I find it convenient to use a calculator's functions to solve problems like this where possible.