![\bf \begin{array}{lccclll} &\stackrel{lb}{amount}&\stackrel{lb}{price}&\stackrel{total}{price}\\ &------&------&------\\ \textit{plain popcorn}&p&3&3p\\ \textit{caramel popcorn}&c&2.2&2.2c\\ -------&------&------&------\\ mixture&10&2.5&25 \end{array}](https://tex.z-dn.net/?f=%5Cbf%20%5Cbegin%7Barray%7D%7Blccclll%7D%0A%26%5Cstackrel%7Blb%7D%7Bamount%7D%26%5Cstackrel%7Blb%7D%7Bprice%7D%26%5Cstackrel%7Btotal%7D%7Bprice%7D%5C%5C%0A%26------%26------%26------%5C%5C%0A%5Ctextit%7Bplain%20popcorn%7D%26p%263%263p%5C%5C%0A%5Ctextit%7Bcaramel%20popcorn%7D%26c%262.2%262.2c%5C%5C%0A-------%26------%26------%26------%5C%5C%0Amixture%2610%262.5%2625%0A%5Cend%7Barray%7D)
so hmm whatever "p" and "c" are, we know that
p + c = 10.
and we also know that
3p + 2.2c = 25thus
![\bf \begin{cases} p+c=10\implies \boxed{c}=10-p\\ 3p+2.2c=25\\ ----------\\ 3p+2.2\left(\boxed{10-p} \right)=25 \end{cases} \\\\\\ 3p+22-2.2p=25\implies 3p-2.2p=25-22\implies 0.8p=3 \\\\\\ p=\cfrac{3}{0.8}\implies p=\cfrac{15}{4}\implies p=3.75](https://tex.z-dn.net/?f=%5Cbf%20%5Cbegin%7Bcases%7D%0Ap%2Bc%3D10%5Cimplies%20%5Cboxed%7Bc%7D%3D10-p%5C%5C%0A3p%2B2.2c%3D25%5C%5C%0A----------%5C%5C%0A3p%2B2.2%5Cleft%28%5Cboxed%7B10-p%7D%20%20%5Cright%29%3D25%0A%5Cend%7Bcases%7D%0A%5C%5C%5C%5C%5C%5C%0A3p%2B22-2.2p%3D25%5Cimplies%203p-2.2p%3D25-22%5Cimplies%200.8p%3D3%0A%5C%5C%5C%5C%5C%5C%0Ap%3D%5Ccfrac%7B3%7D%7B0.8%7D%5Cimplies%20p%3D%5Ccfrac%7B15%7D%7B4%7D%5Cimplies%20p%3D3.75)
how much will it be needed for caramel popcorn? well, c = 10 - p.
Answer: Divide both parts of equation by 25. The answer is 92%
Step-by-step explanation:
Answer:
And using a calculator, excel or the normal standard table we have that:
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 weights of a population, and for this case we know the distribution for X is given by:
Where
and
They select a sample size of n=9 people.The distribution for the sample mean
is given by:
And we want to find this probability:
![P(\bar X](https://tex.z-dn.net/?f=%20P%28%5Cbar%20X%20%3C200%29)
In order to the helicopter can safely lift off. We can use the z score formula given by:
![z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}](https://tex.z-dn.net/?f=%20z%20%3D%20%5Cfrac%7B%5Cbar%20X%20-%5Cmu%7D%7B%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D%7D)
And using a calculator, excel or the normal standard table we have that:
Answer:
<em>The length of RS is 47 units</em>
Step-by-step explanation:
<u>Midsegment Theorem</u>
The midsegment of a trapezoid is a line segment that connects the midpoints of the non-parallel sides.
The length of the midsegment of a trapezoid is the average of the lengths of the bases.
The midsegment of the given trapezoid is VW, and the bases are RS and UT.
According to the midsegment theorem:
![\displaystyle VW=\frac{RS+UT}{2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20VW%3D%5Cfrac%7BRS%2BUT%7D%7B2%7D)
Substituting the variable lengths of the sides:
![\displaystyle 3x+5=\frac{2x+15+6x-37}{2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%203x%2B5%3D%5Cfrac%7B2x%2B15%2B6x-37%7D%7B2%7D)
Operating:
![\displaystyle 3x+5=\frac{8x-22}{2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%203x%2B5%3D%5Cfrac%7B8x-22%7D%7B2%7D)
Dividing the fraction:
![3x+5=4x-11](https://tex.z-dn.net/?f=3x%2B5%3D4x-11)
Rearranging:
![4x-3x=5+11](https://tex.z-dn.net/?f=4x-3x%3D5%2B11)
Operating:
x=16
The length of RS is:
![RS=2x+15=2*16+15=32+15=47](https://tex.z-dn.net/?f=RS%3D2x%2B15%3D2%2A16%2B15%3D32%2B15%3D47)
The lenght of RS is 47 units