Solve the system of equations.
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The zero product property tells us that if we multiply two quantities together and get zero, then one or both of these is equal to zero.
In symbols this means that if ab = 0 then a = 0, b = 0 or both.
This means that if we have a product equal to zero one of both of the factors (the things we are multiplying together) is equal to zero.
Of the equations given, the only one that has product (a few terms multiplied together) equal to zero is -(x-1)(x+9)=0 so this is the one that can most appropriately be solved by the zero product property.
We can re-write -(x-1)(x+9) = 0 as (-1)(x-1)(x+9) = 0 which means (x-1) or (x+9) or both equal zero. It should be clear that -1 cannot equal zero.
To solve we set x - 1 = 0 and obtain x = 1.
Next we set x + 9 = 0 and obtain x = -9
The solutions to the equation are x = -9 and x = 1.
We are, however, asked for two equations. Though none of the remaining equations has a product set equal to zero, we can re-write the equation
by factoring 3x from each term on the left-hand side. Doing so gives us 
. Now we have a product equal to zero which means that one or both of the factors on the left-hand side equals zero.
That is, 3x equals 0, or x-2 equals 0 or both do. If 3x = 0 then x = 0. If x-2=0 then x=2. As such the solution to the equation is x = 0, x = 2.
In symbols this means that if ab = 0 then a = 0, b = 0 or both.
This means that if we have a product equal to zero one of both of the factors (the things we are multiplying together) is equal to zero.
Of the equations given, the only one that has product (a few terms multiplied together) equal to zero is -(x-1)(x+9)=0 so this is the one that can most appropriately be solved by the zero product property.
We can re-write -(x-1)(x+9) = 0 as (-1)(x-1)(x+9) = 0 which means (x-1) or (x+9) or both equal zero. It should be clear that -1 cannot equal zero.
To solve we set x - 1 = 0 and obtain x = 1.
Next we set x + 9 = 0 and obtain x = -9
The solutions to the equation are x = -9 and x = 1.
We are, however, asked for two equations. Though none of the remaining equations has a product set equal to zero, we can re-write the equation
That is, 3x equals 0, or x-2 equals 0 or both do. If 3x = 0 then x = 0. If x-2=0 then x=2. As such the solution to the equation is x = 0, x = 2.
The 97% confidence interval for the proportion of adults is 0.801<P<0.851.
Given that 867 adults are randomly selected from 1050 who always wear seat belts.
A confidence interval refers to the probability that a population parameter will fall between a set of values for a certain proportion of times.
Let's assume n=1050 and x=867
Find the sample proportion by dividing the given proportion with sample size as,
Find the α by subtracting the given confidence interval that is 97% from 1 as
α=1-(97÷100)
α=1-0.97
α=0.03
To find the critical value that is by dividing alpha with 2,
From this table which is shown in the figure it says that the critical value is
Use this formula to find the confidence interval
Substitute the values in the formula,
Hence, a 97% confidence interval for the proportion of adults who always wear seat belts is 0.801<P<0.851.
Learn more about confidence interval from here brainly.com/question/13929861
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