Let's to the first example:
f(x) = x^2 + 9x + 20
Ussing the formula of basckara
a = 1
b = 9
c = 20
Delta = b^2 - 4ac
Delta = 9^2 - 4.(1).(20)
Delta = 81 - 80
Delta = 1
x = [ -b +/- √(Delta) ]/2a
Replacing the data:
x = [ -9 +/- √1 ]/2
x' = (-9 -1)/2 <=> - 5
Or
x" = (-9+1)/2 <=> - 4
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Already the second example:
f(x) = x^2 -4x -60
Ussing the formula of basckara again
a = 1
b = -4
c = -60
Delta = b^2 -4ac
Delta = (-4)^2 -4.(1).(-60)
Delta = 16 + 240
Delta = 256
Then, following:
x = [ -b +/- √(Delta)]/2a
Replacing the information
x = [ -(-4) +/- √256 ]/2
x = [ 4 +/- 16]/2
x' = (4-16)/2 <=> -6
Or
x" = (4+16)/2 <=> 10
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Now we are going to the 3 example
x^2 + 24 = 14x
Isolating 14x , but changing the sinal positive to negative
x^2 - 14x + 24 = 0
Now we can to apply the formula of basckara
a = 1
b = -14
c = 24
Delta = b^2 -4ac
Delta = (-14)^2 -4.(1).(24)
Delta = 196 - 96
Delta = 100
Then we stayed with:
x = [ -b +/- √Delta ]/2a
x = [ -(-14) +/- √100 ]/2
We wiil have two possibilities
x' = ( 14 -10)/2 <=> 2
Or
x" = (14 +10)/2 <=> 12
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To the last example will be the same thing.
f(x) = x^2 - x -72
a = 1
b = -1
c = -72
Delta = b^2 -4ac
Delta = (-1)^2 -4(1).(-72)
Delta = 1 + 288
Delta = 289
Then we are going to stay:
x = [ -b +/- √Delta]/2a
x = [ -(-1) +/- √289]/2
x = ( 1 +/- 17)/2
We will have two roots
That's :
x = (1 - 17)/2 <=> -8
Or
x = (1+17)/2 <=> 9
Well, this would be your answers.
Answer: 0.206
Step-by-step explanation: the probability of employees that needs corrective shoes are =8%= 8/100 = 0.08
Probability of employees that needs major dental work = 15% = 15/100 = 0.15
Probability of employees that needs both corrective shoes and dental work = 3% = 3/100 = 0.03
The probability that an employee will need either corrective shoes or major dental work = (Probability an employee will need correct shoes and not need dental work) or (probability that an employee will need dental work or not corrective shoes)
Probability of employee not needing corrective shoes = 1 - 0.08 = 0.92
Probability of employee not needing dental work = 1 - 0.15 = 0.85
The probability that an employee will need either corrective shoes or major dental work = (0.08×0.85) + (0.15×0.92) = 0.068 + 0.138 = 0.206 = 20.6%
The probability that an employee will need either corrective shoes or dental work = 0.206.
Please note that the word "either" implies that we must choose one of the two options (corrective shoes or dental work) and not both.
The volume of soup in the cylindrical can is 100.48 inches cube.
<h3>How to find the volume of a cylindrical can?</h3>
We have to find the volume of the soup in a cylindrical can of height 8 inches and 4 inches across the lid.
The volume of the soup is the volume of the cylindrical can.
Therefore,
volume of the cylindrical can = πr²h
where
- r = radius of the cylinder
- h = height of the cylinder
Therefore,
h = 8 inches
r = 4 / 2 = 2 inches
volume of the soup in the cylindrical can = πr²h
volume of the soup in the cylindrical can = π × 2² × 8
volume of the soup in the cylindrical can = π × 4 × 8
volume of the soup in the cylindrical can = 32π
Therefore,
volume of the soup in the cylindrical can = 32 × 3.14
volume of the soup in the cylindrical can = 100.48 inches³
learn more on volume here:brainly.com/question/23207959
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