I need help with #'s 59, 63, 67, and 71 PLEASE!!!I need to find the domain!!
1 answer:
9514 1404 393
Answer:
59. t ≥ -1
63. x ≤ -1/2
67. (x ≤ 0) ∪ (x ≥ 6)
71. x > 1/2
Step-by-step explanation:
The domain is the set of values of x where the function is defined. In rational functions it excludes any values of x that make the denominator zero. When even-index roots are involved, it excludes values of x that make the argument of the root function negative.
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59. t+1 ≥ 0 ⇒ t ≥ -1
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63. 1 -2x ≥ 0 ⇒ x ≤ -1/2
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67. x² -6x ≥ 0 ⇒ x(x -6) ≥ 0 ⇒ (x ≤ 0) ∪ (x ≥ 6)
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71. 2x -1 > 0 ⇒ x > 1/2 . . . . note we left off the =0 case for this one
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The attachment is a plot of the g(x) in 67. You can see that it is undefined for 0 < x < 6.
As you can see, a graphing calculator can be helpful in identifying the domain. Of course, any vertical asymptotes are excluded, as are any "holes" in a function.
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Answer:
The probability that the sample proportion will differ from the population proportion by greater than 0.03 is 0.009.
Step-by-step explanation:
According to the Central limit theorem, if from an unknown population large samples of sizes n > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.
The mean of this sampling distribution of sample proportion is:
The standard deviation of this sampling distribution of sample proportion is:
As the sample size is large, i.e. <em>n</em> = 492 > 30, the central limit theorem can be used to approximate the sampling distribution of sample proportion by the normal distribution.
The mean and standard deviation of the sampling distribution of sample proportion are:
Compute the probability that the sample proportion will differ from the population proportion by greater than 0.03 as follows:
Thus, the probability that the sample proportion will differ from the population proportion by greater than 0.03 is 0.009.
The answer is: " f ⁻¹(x) = 
+ 5 " .
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Explanation:
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Given the function: " f(x) = 2x <span>− 10 " ; Find the "inverse function" .
Let "f(x)" be represented by "y" ; and rewrite:
y = 2x </span><span>− 10 ;
Change the "y" to an "x" ; and change to "x" to a "y" ; as follows:
___________________________________________________
x = 2y </span><span>− 10 ;
Now, rewrite this equation, in "slope-intercept form"; that is; "y = mx + b" ;
To do this, start by solving THIS equation for "y"; in terms of "x" ; with "y" as an "isolated variable" on the "left-hand side" of the equation;
___________________________________________________
We have:
___________________________________________________
" x = 2y </span><span>− 10 " ;
Add "10" to each side of the equation; as follows:
x + 10 = 2y </span><span>− 10 + 10 ;
to get:
x + 10 = 2y ;
</span>↔ 2y = x + 10 ;
<span>
Now, divide each side of the equation by "2" ;
to isolate "y" on one side of the equation (as a single variable);
& to solve for "y" ;
</span>→ 2y / 2 = (x + 10) / 2 ;
<span>
to get:
</span>→ y = (x/2) + (10/2) ;
→ y = (x/2) + 5 ;
<span>
Now, rewrite the equation, by substituting: " f </span>⁻¹(x) " ; in place of the "y" ; to indicate that this function is an "inverse function; as follows:
→ " f ⁻¹(x) = + 5 " .
______________________________________________________
The answer is: " f ⁻¹(x) = + 5 " .
_______________________________________________________
____________________________________________________
Explanation:
____________________________________________________
Given the function: " f(x) = 2x <span>− 10 " ; Find the "inverse function" .
Let "f(x)" be represented by "y" ; and rewrite:
y = 2x </span><span>− 10 ;
Change the "y" to an "x" ; and change to "x" to a "y" ; as follows:
___________________________________________________
x = 2y </span><span>− 10 ;
Now, rewrite this equation, in "slope-intercept form"; that is; "y = mx + b" ;
To do this, start by solving THIS equation for "y"; in terms of "x" ; with "y" as an "isolated variable" on the "left-hand side" of the equation;
___________________________________________________
We have:
___________________________________________________
" x = 2y </span><span>− 10 " ;
Add "10" to each side of the equation; as follows:
x + 10 = 2y </span><span>− 10 + 10 ;
to get:
x + 10 = 2y ;
</span>↔ 2y = x + 10 ;
<span>
Now, divide each side of the equation by "2" ;
to isolate "y" on one side of the equation (as a single variable);
& to solve for "y" ;
</span>→ 2y / 2 = (x + 10) / 2 ;
<span>
to get:
</span>→ y = (x/2) + (10/2) ;
→ y = (x/2) + 5 ;
<span>
Now, rewrite the equation, by substituting: " f </span>⁻¹(x) " ; in place of the "y" ; to indicate that this function is an "inverse function; as follows:
→ " f ⁻¹(x) =
______________________________________________________
The answer is: " f ⁻¹(x) =
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