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The odds against an event are 19 to 12 find the probability that The event will occur
1 answer:
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Answer:
Step-by-step explanation:
1. Swap sides
Swap sides:
2. Isolate the y
Multiply to both sides by 18:
Group like terms:
Simplify the fraction:
Multiply the fractions:
Simplify the arithmetic:
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Why learn this:
- Linear equations cannot tell you the future, but they can give you a good idea of what to expect so you can plan ahead. How long will it take you to fill your swimming pool? How much money will you earn during summer break? What are the quantities you need for your favorite recipe to make enough for all your friends?
- Linear equations explain some of the relationships between what we know and what we want to know and can help us solve a wide range of problems we might encounter in our everyday lives.
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Terms and topics
- Linear equations with one unknown
The main application of linear equations is solving problems in which an unknown variable, usually (but not always) x, is dependent on a known constant.
We solve linear equations by isolating the unknown variable on one side of the equation and simplifying the rest of the equation. When simplifying, anything that is done to one side of the equation must also be done to the other.
An equation of:
in which and
are the constants and
is the unknown variable, is a typical linear equation with one unknown. To solve for
in this example, we would first isolate it by subtracting
from both sides of the equation. We would then divide both sides of the equation by
resulting in an answer of:
Answer:
The confidence interval for the mean is given by the following formula:
(1)
Or equivalently:
For this case we have the interval given (3.9, 7.7) and we want to find the margin of error. Using the property of symmetry for a confidence interval we can estimate the margin of error with this formula:
Step-by-step explanation:
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
represent the sample mean for the sample
population mean (variable of interest)
Solution to the problem
The confidence interval for the mean is given by the following formula:
(1)
Or equivalently:
For this case we have the interval given (3.9, 7.7) and we want to find the margin of error. Using the property of symmetry for a confidence interval we can estimate the margin of error with this formula: