Solve the rational equation 4/x=3x+2/x^2, and check for extraneous solutions.
1 answer:
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Answer:
The approximate volume of a stack of 40 nickels is 25132.741 cubic milimeters.
Step-by-step explanation:
A nickel can be modelled by the formula of a right cylinder, the approximate volume of the stack of nickels (), measured in cubic milimeters, is the product of the number of elements (
), no unit, and the volume of each element (
), measured in cubic milimeters. That is:
(1)
By volume equation of right cylinder, we have the following formula:
(2)
Where:
- Amount of nickels, no unit.
- Diameter of nickel, measured in milimeters.
- Thickness of nickel, measured in milimeters.
If we know that ,
and
, then the net volume of the stack of nickels is:
The approximate volume of a stack of 40 nickels is 25132.741 cubic milimeters.
Answer: 2172
Step-by-step explanation:
Formula to find the sample size n , if the prior estimate of the population proportion(p) is known:
, where E= margin of error and z* = Critical z-value.
Let p be the population proportion of adults have consulted fortune tellers.
As per given , we have
p= 0.20
E= 0.02
From z-table , the z-value corresponding to 98% confidence interval = z*=2.33
Then, the required sample size will be :
Hence, the required sample size = 2172
<h2>Translating Word Equations into Numerical Equations</h2>
To change words into equations, we can recognize keywords that translate into operations and/or numbers:
- <em>quotient</em> = divide
- <em>a number/the number/two numbers</em> = variables
- <em>sum</em> = add
Let the two numbers be <em>a</em> and <em>b</em>.
We're given:
- quotient of <em>a</em> and <em>b</em> is 3
⇒ - sum of <em>a</em> and <em>b</em> is 8
⇒
First, isolate <em>a</em> in the first equation and substitute it in the second equation to solve for <em>b</em>:
Therefore, one of the numbers is 2. Substitute this into one of our equations to solve for <em>a</em>:
Therefore, the other number is 6.
<h2>Answer</h2>The two numbers are 2 and 6.