"Rationalizing the denominator" of a number is exactly what its title implies: turning its denominator into a rational number.
For an example, let's take the fraction 1/√2. We call √2 <em>irrational</em> because it cannot be expressed as a <em>ratio </em>of two integers. Oftentimes when we have irrational numbers like √2 in the denominator, it helps to perform a little bit of algebraic manipulation on them to make the denominator rational. Here's where that "form of 1" comes in. Remember that, as a rational number, 1 can be expressed as n/n, where n is any number. We can use this fact to rationalize the denominator of 1/√2 <em />by multiplying it by √2/√2, which is equivalent to 1.
When we multiply the two together, we get:
Crucially, multiplying by 1 in the form of √2/√2 <em>keeps the fraction's value the same</em>, since 1 times any number just equals that same number. If we weren't multiplying but some form of 1, we'd change the number entirely, making the whole attempt at rationalizing the denominator pointless.
Umm tis is a really old question are you sure you want me to answer this
Answer:
Option B) Fail to reject the null hypothesis that the true population mean annual salary of full-time college professors in the region is equal to $127,000.
Step-by-step explanation:
We are given the following in the question:
Population mean, μ = $127,000
Sample mean, = $126,092
Sample size, n = 160
Alpha, α = 0.10
Sample standard deviation, σ = $8,509
First, we design the null and the alternate hypothesis
We use Two-tailed t test to perform this hypothesis.
Formula:
Now,
Since,
The calculated t-statistic lies in the acceptance region, we fail to reject and accept the null hypothesis.
Option B) Fail to reject the null hypothesis that the true population mean annual salary of full-time college professors in the region is equal to $127,000.
Answer:
2 in a half 6 player games and 6 and half 2 player games. hope this helps
Step-by-step explanation:
Answer: A number with the same absolute value of 23 is -23.
Explanation: The absolute value of a number is how far it is from zero, and the absolute value of a number is always positive, unless the number is 0, in which case the absolute value is neutral, and the absolute value is 0.
Examples: 6 is 6 away from zero, so the absolute value of 6 is 6.
−6 is 6 away from zero, so the absolute value of −6 is 6.