Simplify v20
align="absmiddle" class="latex-formula">
1 answer:
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9514 1404 393
Answer:
(a) -(x+7)/y
(b) (x+7)/-y
Step-by-step explanation:
There are several ways you can show expressions are equivalent. Perhaps the easiest and best is to put them in the same form. For an expression such as this, I prefer the form of answer (a), where the minus sign is factored out and the numerator and denominator have positive coefficients.
The given expression with -1 factored out is ...
Likewise, the expression of (b) with the minus sign factored out is ...
On the other hand, simplifying expression (c) gives something different.
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Another way you can write the expression is term-by-term with the terms in alpha-numeric sequence (so they're more easily compared).
Given: (-x-7)/y = (-x/y) +(-7/y)
(a) -(x+7)/y = (-x/y) +(-7/y)
(b) (x+7)/(-y) = (-x/y) +(-7/y)
(c) (-x-7)/(-y) = (x/y) +(7/y) . . . . not the same.
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Of course, you need to know the use of the distributive property and the rules of signs.
a(b+c) = ab +ac
-a/b = a/(-b) = -(a/b)
-a/(-b) = a/b
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<u>Summary</u>: The given expression matches (a) and (b).
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<em>Additional comments</em>
Sometimes, when I'm really stuck trying to see if two expressions are equal, I subtract one from the other. If the difference is zero, then I know they are the same. Looking at (b), we could compute ...
Yet another way to check is to substitute numbers for the variables. It is a good idea to use (at least) one more set of numbers than there are variables, just to make sure you didn't accidentally find a solution where the expressions happen to be equal. We can use (x, y) = (1, 2), (2, 3), and (3, 5) for example.
The given expression evaluates to (-1-7)/2 = -4, (-2-7)/3 = -3, and (-3-7)/5 = -2.
(a) evaluates to -(1+7)/2 = -4, -(2+7)/3 = -3, -(3+7)/5 = -2, same as given
(b) evaluates to (1+7)/-2 = -4, (2+7)/-3 = -3, (3+7)/-5 = -2, same as given
(c) evaluates to (-1-7)/-2 = 4, different from given
Answer:
a)
Using the symmetrical property we can write this like this:
We can solve for the probability like this:
And we can find the value using the following excel code: "=T.INV(0.05,7)"
So on this case the answer would be
b) For this case we can use the complement rule and we got:
We can solve for the probability and we got:
And we can use the following excel code to find the value"=T.INV(0.95;7)"
And the answer would be
Step-by-step explanation:
Previous concepts
The t distribution (Student’s t-distribution) is a "probability distribution that is used to estimate population parameters when the sample size is small (n<30) or when the population variance is unknown".
The shape of the t distribution is determined by its degrees of freedom and when the degrees of freedom increase the t distirbution becomes a normal distribution approximately.
The degrees of freedom represent "the number of independent observations in a set of data. For example if we estimate a mean score from a single sample, the number of independent observations would be equal to the sample size minus one."
Solution to the problem
For this case we know that
And we want to find:
Part a
We can rewrite the expression using properties for the absolute value like this:
Using the symmetrical property we can write this like this:
We can solve for the probability like this:
And we can find the value using the following excel code: "=T.INV(0.05,7)"
So on this case the answer would be
Part b
For this case we can use the complement rule and we got:
We can solve for the probability and we got:
And we can use the following excel code to find the value"=T.INV(0.95;7)"
And the answer would be