The first thing we must do is calculate the circumeference:
![\begin{gathered} c=2\cdot\pi\cdot r \\ c=2\cdot3.14\cdot7.9 \\ c=49.612 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20c%3D2%5Ccdot%5Cpi%5Ccdot%20r%20%5C%5C%20c%3D2%5Ccdot3.14%5Ccdot7.9%20%5C%5C%20c%3D49.612%20%5Cend%7Bgathered%7D)
now, calculate the angle of arc
360° = 49.612
360° - 66.4° - 180° = x
x = 113.6°
now, to calculate the arc length it would be:
<h2>|| <u>Question</u> ||</h2>
John purchased 24 chocolates for Rs.96. How many chocolates can be purchased for Rs.72?
<h2>|| <u>Answer</u> ||</h2>
John purchased 24 chocolates = Rs.96.
Chocolates can be purchased for Rs.72 = x
<h3>
![\frac{24}{96} = \frac{x}{72}](https://tex.z-dn.net/?f=%20%5Cfrac%7B24%7D%7B96%7D%20%20%3D%20%20%5Cfrac%7Bx%7D%7B72%7D%20)
</h3>
24:96 = x:72
Means = Extreams
96 × x = 24 × 72
<h3>
![x = \frac{24 \times 72}{96}](https://tex.z-dn.net/?f=x%20%3D%20%20%5Cfrac%7B24%20%5Ctimes%2072%7D%7B96%7D%20)
</h3>
( 12 × 2 = 24, 12 × 8 = 96 )
<h3>
![x = \frac{2 \times 72}{8}](https://tex.z-dn.net/?f=x%20%3D%20%20%5Cfrac%7B2%20%5Ctimes%2072%7D%7B8%7D%20)
</h3>
(8 × 1 = 8, 8 × 9 = 72)
<h3>
![x = \frac{2 \times 9}{1}](https://tex.z-dn.net/?f=x%20%3D%20%20%5Cfrac%7B2%20%5Ctimes%209%7D%7B1%7D%20)
</h3><h3>
![x = 2 \times 9](https://tex.z-dn.net/?f=x%20%3D%202%20%5Ctimes%209)
</h3><h3>
![x = 18](https://tex.z-dn.net/?f=x%20%3D%2018)
</h3>
Therefore, 18 chocolates can be purchased for Rs.72
Answer:
In mathematics, an algebraic expression is an expression built up from integer constants, variables, and the algebraic operations. For example, 3x² − 2xy + c is an algebraic expression.
Answer: lower bound = 0.7404; upper bound = 0.8596
Step-by-step explanation:
The proportion p for this population:
p = ![\frac{240}{300}](https://tex.z-dn.net/?f=%5Cfrac%7B240%7D%7B300%7D)
p = 0.8
Confidence interval for proportion is calculated as:
p ± z-score.![\sqrt{\frac{p(1-p)}{n} }](https://tex.z-dn.net/?f=%5Csqrt%7B%5Cfrac%7Bp%281-p%29%7D%7Bn%7D%20%7D)
Z-score for a 99% confidence interval is: z = 2.58
Calculating:
0.8 ± 2.58.![\sqrt{\frac{0.8(0.2)}{300} }](https://tex.z-dn.net/?f=%5Csqrt%7B%5Cfrac%7B0.8%280.2%29%7D%7B300%7D%20%7D)
0.8 ± 2.58.![\sqrt{0.00053}](https://tex.z-dn.net/?f=%5Csqrt%7B0.00053%7D)
0.8 ± 2.58(0.0231)
0.8 ± 0.0596
This means that the lower limit of this interval is 0.7404 and upper bound is 0.8596