The answer to the question
Two numbers have prime factorizations of 2^ 2 • 3 • 5 and 2 • 3^ 2 • 5.
2 answers:
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Answer: 49x^2=-21x-2 quadratic functions -1/7and -2/7
Step-by-step explanation:
Quadratic function:
In elementary algebra, the quadratic formula is a formula that provides the solution to a quadratic equation. There are other ways of solving a quadratic equation instead of using the quadratic formula, such as factoring, completing the square, graphing and others.
Move terms to the left side
49 =-21x-2
49 -(-21x-2) =0
Distribute
49 -(-21x-2) =0
49+21x+2=0
Use the quadratic formula
x=(-b±√ -4ac ) / 2a
Once in standard form, identify a, b, and c from the original equation and plug them into the quadratic formula.
49+21x+2=0
let, a=49
b=21
c=2
Replace with values in this equation
X=(-b±√ -4ac ) / 2a
Simplify
Evaluate the exponent
Multiply the numbers
Subtract the numbers
Evaluate the square root
Multiply the numbers
x=(-21±7) /98
Separate the equations
To solve for the unknown variable, separate into two equations: one with a plus and the other with a minus.Separate
x=(-21+7) /98
x=(-21-7) /98
Solve
Rearrange and isolate the variable to find each solution
x=-1/7
x=-2/7
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Answer:
The probability that the assembly line will be shut down is 0.00617.
Step-by-step explanation:
We are given that a soda bottling company’s manufacturing process is calibrated so that 99% of bottles are filled to within specifications, while 1% is not within specification.
Every hour, 12 random bottles are taken from the assembly line and tested. If 2 or more bottles in the sample are not within specification, the assembly line is shut down for recalibration.
Let X = <u><em>Number of bottles in the sample that are not within specification</em></u>.
The above situation can be represented through binomial distribution;
where, n = number of trials (samples) taken = 12 bottles
x = number of success = 2 or more bottles
p = probabilitiy of success which in our question is probability that
bottles are not within specification, i.e. p = 0.01
So, X ~ Binom (n = 12, p = 0.01)
Now, the probability that the assembly line will be shut down is given by = P(X 2)
P(X 2) = 1 - P(X = 0) - P(X = 1)
=
=
= <u>0.00617</u>