Hello,
I am not doing that with sin, cos and pythagorean theorem.
DEFINITION: we call TAN x=sin x / cos x
This means that in a right triangle the tangent of an angle is the ration of opposed side by adjacent side.
11: tan 8°=12.5/d
==>d=12.5/tan 8°=12.5/0.14054...=88.942121...m≈88.9 (m)
12:
tan 28°=h/420
==>h=420*tan 28°=420*0.5317...=223.3179...≈223.3 (m)
The percentage of the total cost of 23 separate tickets that George saves by buying a season ticket is 23%.
<h3>What are percentages?</h3>
A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.
To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.
As the cost of the separate ticket is £24, and there are a total of 23 games, therefore, the total cost of the 23 games separate ticket can be written as,
= £24 × 23
= £552
Now, the cost of the season ticket is £425, therefore, the percentage of the total cost of 23 separate tickets that George saves by buying a season ticket can be written as,
![\rm Percentage = \dfrac{\text{Total cost of 23 seperate ticket}-\text{Cost of season ticket}}{\text{Total cost of 23 seperate ticket}} \times 100\%](https://tex.z-dn.net/?f=%5Crm%20Percentage%20%3D%20%5Cdfrac%7B%5Ctext%7BTotal%20cost%20of%2023%20seperate%20ticket%7D-%5Ctext%7BCost%20of%20season%20ticket%7D%7D%7B%5Ctext%7BTotal%20cost%20of%2023%20seperate%20ticket%7D%7D%20%5Ctimes%20100%5C%25)
![\rm Percentage = \dfrac{552-425}{552} \times 100\% = \dfrac{127}{552} \times 100\% = 23\%](https://tex.z-dn.net/?f=%5Crm%20Percentage%20%3D%20%5Cdfrac%7B552-425%7D%7B552%7D%20%5Ctimes%20100%5C%25%20%3D%20%5Cdfrac%7B127%7D%7B552%7D%20%5Ctimes%20100%5C%25%20%3D%2023%5C%25)
Hence, the percentage of the total cost of 23 separate tickets that George saves by buying a season ticket is 23%.
Learn more about Percentages:
brainly.com/question/6972121
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Answer:
Tasha should mix 25 liters of 20% solution and 50 liters of 50%.
Step-by-step explanation:
Let x liters be the amount of 20% solution and y liters be the amount of 50% solution Tasha takes.
1. Tasha needs 75 liters of a 40% solution of alcohol. Then
x + y = 75
2. There are
liters of alcohol in x l of 20% solution
liters of alcohol in 50% solution
liters of alcohol in 75 liters of 40% solution
In total,
of alcohol that is 30 l, so
0.2x + 0.5y = 30
3. Solve the system of two equations:
![\left\{\begin{array}{l}x+y=75\\ \\0.2x+0.5y=30\end{array}\right.](https://tex.z-dn.net/?f=%5Cleft%5C%7B%5Cbegin%7Barray%7D%7Bl%7Dx%2By%3D75%5C%5C%20%5C%5C0.2x%2B0.5y%3D30%5Cend%7Barray%7D%5Cright.)
From the first equation:
![x=75-y](https://tex.z-dn.net/?f=x%3D75-y)
Substitute it into the second equation
![0.2(75-y)+0.5y=30\\ \\15-0.2y+0.5y=30\\ \\0.3y=30-15\\ \\0.3y=15\\ \\3y=150\\ \\y=50\\ \\x=75-50=25](https://tex.z-dn.net/?f=0.2%2875-y%29%2B0.5y%3D30%5C%5C%20%5C%5C15-0.2y%2B0.5y%3D30%5C%5C%20%5C%5C0.3y%3D30-15%5C%5C%20%5C%5C0.3y%3D15%5C%5C%20%5C%5C3y%3D150%5C%5C%20%5C%5Cy%3D50%5C%5C%20%5C%5Cx%3D75-50%3D25)
Tasha should mix 25 liters of 20% solution and 50 liters of 50%.
819 as a decimal is
<em> 819.00000</em>
with as many zeros as you want after the decimal point.
If you do anything else to it, then it's a different number,
and it's not 819 anymore.
(7 + 7)² = 14² = 196
(7 + 6)² = 13² = 169
196 > 169
Therefore (7 + 7)² > (7 + 6)²
Could've deducted without the math but might as well show the work.