Answer:
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Step-by-step explanation:
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Add 3 to both sides so that the equation becomes -2x^2 + 5x + 5 = 0.
To find the solutions to this equation, we can apply the quadratic formula. This quadratic formula solves equations of the form ax^2 + bx + c = 0
x = [ -b ± √(b^2 - 4ac) ] / (2a)
x = [ -5 ± √(5^2 - 4(-2)(5)) ] / ( 2(-2) )
x = [-5 ± √(25 - (-40) ) ] / ( -4 )
x = [-5 ± √(65) ] / ( -4)
x = [-5 ± sqrt(65) ] / ( -4 )
x = 5/4 ± -sqrt(65)/4
The answers are 5/4 + sqrt(65)/4 and 5/4 - sqrt(65)/4..
Answer:
6 and 7
Step-by-step explanation:
To evaluate f(3), substitute x = 3 into f(x) , that is
f(3) = 2(3) = 6
To evaluate g(f(3)), substitute f(3) = 6 into g(x)
g(6) = 6 + 1 = 7
Answer:
Correct option: (a) 0.1452
Step-by-step explanation:
The new test designed for detecting TB is being analysed.
Denote the events as follows:
<em>D</em> = a person has the disease
<em>X</em> = the test is positive.
The information provided is:
Compute the probability that a person does not have the disease as follows:
The probability of a person not having the disease is 0.12.
Compute the probability that a randomly selected person is tested negative but does have the disease as follows:
Compute the probability that a randomly selected person is tested negative but does not have the disease as follows:
Compute the probability that a randomly selected person is tested negative as follows:
Thus, the probability of the test indicating that the person does not have the disease is 0.1452.
Simplifying
9 + -2x = 35
Solving
9 + -2x = 35
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-9' to each side of the equation.
9 + -9 + -2x = 35 + -9
Combine like terms: 9 + -9 = 0
0 + -2x = 35 + -9
-2x = 35 + -9
Combine like terms: 35 + -9 = 26
-2x = 26
Divide each side by '-2'.
x = -13
Simplifying
x = -13