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.
The answer should be A. For example, if x = 1, and the ratio between x and y is y is 5 times greater than x, then y would equal 5, which is only true in A.
Or, use the number 5 as an example. If x = 5, and the ratio between x and y is y is 5 times greater than x, then y is 5.
And if you put that into A, y = 5x, it becomes 25 = 5(5)
Then 25 = 25, which is true!
Answer: Identify whether each scenario would be represented by a continuous or discrete graph
Step-by-step explanation:
Answer:
What is the probability both are math phobic? 0.49%
What is the probability at least one is math phobic? 9.31%
Step-by-step explanation:
In order to both be math phobic, both individuals has to be inside of the probability of 7%, that means 0.07*0.07 = 0.0049 = 0.49%
In order to at least one be math phobic there's some cases which satisfies the sentence:
Individual A is math phobic and B as well = 0.07*0.07 = 0.0049 = 0.49%
Individual A is math phobic, but B is not = 0.07*0.63 = 0.0441 = 4.41%
Individual A is not, but B is math phobic = 0.63*0.07 = 0.0441 = 4.41%
Suming the 3 possibles cases, the probability at least one is math phobic
= 9.31%
Answer:
The order of operations is Parenthesis, Exponents, Multiplication, Division, Addition, and Subtraction.
Step-by-step explanation:
The order of operations is PEMDAS.
P: Parenthesis
E: Exponents
M: Multiplication
D: Division
A: Addition
S: Subtraction
An easy way to remember PEMDAS is, please excuse my dear aunt sally.
Hope this helps!
If not, I am sorry.
