Answer:
![\huge\boxed{\bf\:1}](https://tex.z-dn.net/?f=%5Chuge%5Cboxed%7B%5Cbf%5C%3A1%7D)
Step-by-step explanation:
![\frac{ x ^ { 2 } -4x+3 }{ x ^ { 2 } -7x+12 } \times \frac{ x ^ { 2 } +2x-24 }{ x ^ { 2 } +5x-6 } ^ { }](https://tex.z-dn.net/?f=%5Cfrac%7B%20x%20%20%5E%20%7B%202%20%20%7D%20%20-4x%2B3%20%20%7D%7B%20x%20%20%5E%20%7B%202%20%20%7D%20%20-7x%2B12%20%20%7D%20%20%20%5Ctimes%20%20%20%5Cfrac%7B%20x%20%20%5E%20%7B%202%20%20%7D%20%20%2B2x-24%20%20%7D%7B%20x%20%20%5E%20%7B%202%20%20%7D%20%20%2B5x-6%20%20%7D%20%20%20%20%5E%20%7B%20%20%20%7D)
Take
& factorise it at first.
![\frac{ x ^ { 2 } -4x+3 }{ x ^ { 2 } -7x+12 } \\= \frac{\left(x-3\right)\left(x-1\right)}{\left(x-4\right)\left(x-3\right)}\\= \frac{x-1}{x-4}](https://tex.z-dn.net/?f=%5Cfrac%7B%20x%20%20%5E%20%7B%202%20%20%7D%20%20-4x%2B3%20%20%7D%7B%20x%20%20%5E%20%7B%202%20%20%7D%20%20-7x%2B12%20%20%7D%20%20%20%5C%5C%3D%20%5Cfrac%7B%5Cleft%28x-3%5Cright%29%5Cleft%28x-1%5Cright%29%7D%7B%5Cleft%28x-4%5Cright%29%5Cleft%28x-3%5Cright%29%7D%5C%5C%3D%20%5Cfrac%7Bx-1%7D%7Bx-4%7D)
Now factorise the next set :
.
![\frac{ x ^ { 2 } +2x-24 }{ x ^ { 2 } +5x-6 } ^ { }\\= \frac{\left(x-4\right)\left(x+6\right)}{\left(x-1\right)\left(x+6\right)}\\= \frac{x-4}{x-1}](https://tex.z-dn.net/?f=%5Cfrac%7B%20x%20%20%5E%20%7B%202%20%20%7D%20%20%2B2x-24%20%20%7D%7B%20x%20%20%5E%20%7B%202%20%20%7D%20%20%2B5x-6%20%20%7D%20%20%20%20%5E%20%7B%20%20%20%7D%5C%5C%3D%20%5Cfrac%7B%5Cleft%28x-4%5Cright%29%5Cleft%28x%2B6%5Cright%29%7D%7B%5Cleft%28x-1%5Cright%29%5Cleft%28x%2B6%5Cright%29%7D%5C%5C%3D%20%20%5Cfrac%7Bx-4%7D%7Bx-1%7D)
Now, multiply the two simplified results.
![\frac{ x ^ { 2 } -4x+3 }{ x ^ { 2 } -7x+12 } \times \frac{ x ^ { 2 } +2x-24 }{ x ^ { 2 } +5x-6 } ^ { }\\= \frac{x-1}{x-4}\times \frac{x-4}{x-1} \\= \frac{\left(x-1\right)\left(x-4\right)}{\left(x-4\right)\left(x-1\right)} \\= \boxed{\bf\: 1}](https://tex.z-dn.net/?f=%5Cfrac%7B%20x%20%20%5E%20%7B%202%20%20%7D%20%20-4x%2B3%20%20%7D%7B%20x%20%20%5E%20%7B%202%20%20%7D%20%20-7x%2B12%20%20%7D%20%20%20%5Ctimes%20%20%20%5Cfrac%7B%20x%20%20%5E%20%7B%202%20%20%7D%20%20%2B2x-24%20%20%7D%7B%20x%20%20%5E%20%7B%202%20%20%7D%20%20%2B5x-6%20%20%7D%20%20%20%20%5E%20%7B%20%20%20%7D%5C%5C%3D%20%5Cfrac%7Bx-1%7D%7Bx-4%7D%5Ctimes%20%5Cfrac%7Bx-4%7D%7Bx-1%7D%20%5C%5C%3D%20%5Cfrac%7B%5Cleft%28x-1%5Cright%29%5Cleft%28x-4%5Cright%29%7D%7B%5Cleft%28x-4%5Cright%29%5Cleft%28x-1%5Cright%29%7D%20%5C%5C%3D%20%5Cboxed%7B%5Cbf%5C%3A%201%7D)
![\rule{150pt}{2pt}](https://tex.z-dn.net/?f=%5Crule%7B150pt%7D%7B2pt%7D)
1 is not. 2 is. 3 is not. 4 is. 5 is. 6 is. 7 is not. 8 is.
Answer:
Step-by-step explanation:
Previous concepts
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".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the scores of a population, and for this case we know the distribution for X is given by:
Where
and
We are interested on this probability
And the best way to solve this problem is using the normal standard distribution and the z score given by:
If we apply this formula to our probability we got this:
And we can find this probability using the normal standard table or excel and we got:
Compound inequality combines multiple single inequalities.
The solution and interpretation of the inequality is:
<em />
<em> and </em>
<em>. Ryan needs to consume more than 50 grams of carbohydrates, but less than 150 grams of carbohydrates.</em>
<em />
We have:
and ![2x + 10< 310](https://tex.z-dn.net/?f=2x%20%2B%2010%3C%20310)
Solve for x in both inequalities
![110 < 2x + 10](https://tex.z-dn.net/?f=110%20%3C%202x%20%2B%2010)
![110 -10 < 2x](https://tex.z-dn.net/?f=110%20-10%20%3C%202x)
![100 < 2x](https://tex.z-dn.net/?f=100%20%3C%202x)
Divide both sides by 2
![50 < x](https://tex.z-dn.net/?f=50%20%3C%20x)
Rewrite as:
![x > 50](https://tex.z-dn.net/?f=x%20%3E%2050)
Also, we have:
![2x + 10< 310](https://tex.z-dn.net/?f=2x%20%2B%2010%3C%20310)
![2x< 310 - 10](https://tex.z-dn.net/?f=2x%3C%20310%20-%2010)
![2x< 300](https://tex.z-dn.net/?f=2x%3C%20300)
Divide by 2
![x < 150](https://tex.z-dn.net/?f=x%20%3C%20150)
So, the solutions to the inequalities are:
and ![x < 150](https://tex.z-dn.net/?f=x%20%3C%20150)
This means that Ryan needs to consume more than 50 but less than 150 grams of carbohydrates.
Hence, (a) is correct
Read more about compound inequalities at:
brainly.com/question/13290962
Answer:
1623623
Step-by-step explanation:
i just got this question on deltamath lol