1. First, put the range in order and then divide the set into quarters. In this case, quartiles are between numbers.
<span>83, 85, 89, l 91, 95, 104, l 112, 118, 118, l 125, 134, 138
Q</span>₁ = (89 + 91)/2 = 90
Q₂ = (104 + 112)/2 =108
Q₃ = (118 + 125)/2 = 121.5
Interquartile range (IQR) = Q₃ - Q₁
= 121.5 - 90
IQR = 31.5
2. To find the standard deviation follow the simple steps.
Formula in finding the standard deviation: (see attached file)
Step 1. Work out the simple average of the numbers (mean)
<span><span><u>212 + 249 + 212 + 248 + 239 + 212 + 216 + 234 + 248</u>
</span> 9
= <span><u>2070</u>
</span> 9
mean (</span>μ) = 230
Step 2. Subtract the mean on each number and square the result.
212 - 230 = (-18)² = 324<span>
249 </span>- 230 = ( 19)² = 361<span>
212 </span>- 230 = (-18)² = 324<span>
248 </span>- 230 = (18)² = 324<span>
239 </span>- 230 = (9)² = 81<span>
212 </span>- 230 = (-18)² =324<span>
216 </span>- 230 = (-14)² =196<span>
234 </span>- 230 = (4)² =16<span>
248 </span>- 230 = (18)² =324
Step 3. Add all the squared results and get the mean.
<span><u>2274</u>
</span> 9
Variance = 252.6666667
Step 4. Get the square root of the variance.
√252.6666667
= 15.89549202
a = amount invested at 7%
b = amount invested at 9%
we know the amount invested was ₹36000, thus we know that whatever "a" and "b" are, a + b = 36000. We can also say that
since we know the interest earned from the invested was ₹2920, then we say that 0.07a + 0.09b = 2920.
![\begin{cases} a + b = 36000\\\\ 0.07a+0.09b=2920 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{using the 1st equation}}{a + b = 36000\implies \underline{b = 36000-a}}~\hfill \stackrel{\textit{substituting on the 2nd equation}}{0.07a~~ + ~~0.09(\underline{36000-a})~~ = ~~2920} \\\\\\ 0.07a+3240-0.09a=2920\implies 3240-0.02a=2920\implies -0.02a=-320 \\\\\\ a=\cfrac{-320}{-0.02}\implies \boxed{a=16000}~\hfill \boxed{\stackrel{36000~~ - ~~16000}{20000=b}}](https://tex.z-dn.net/?f=%5Cbegin%7Bcases%7D%20a%20%2B%20b%20%3D%2036000%5C%5C%5C%5C%200.07a%2B0.09b%3D2920%20%5Cend%7Bcases%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Cstackrel%7B%5Ctextit%7Busing%20the%201st%20equation%7D%7D%7Ba%20%2B%20b%20%3D%2036000%5Cimplies%20%5Cunderline%7Bb%20%3D%2036000-a%7D%7D~%5Chfill%20%5Cstackrel%7B%5Ctextit%7Bsubstituting%20on%20the%202nd%20equation%7D%7D%7B0.07a~~%20%2B%20~~0.09%28%5Cunderline%7B36000-a%7D%29~~%20%3D%20~~2920%7D%20%5C%5C%5C%5C%5C%5C%200.07a%2B3240-0.09a%3D2920%5Cimplies%203240-0.02a%3D2920%5Cimplies%20-0.02a%3D-320%20%5C%5C%5C%5C%5C%5C%20a%3D%5Ccfrac%7B-320%7D%7B-0.02%7D%5Cimplies%20%5Cboxed%7Ba%3D16000%7D~%5Chfill%20%5Cboxed%7B%5Cstackrel%7B36000~~%20-%20~~16000%7D%7B20000%3Db%7D%7D)
Multiply both parts of this relationship by four, to get 40 pages in one hour. Done (40 pg/hr).
Answer:
40) D
41) -56.33
Step-by-step explanation:
40)
Equation #1) 1 centimeter = 2.5 meters on the drawing
Equation #2) Length of the cafeteria on the drawing = 12.25 cm
Actual length:
Multiply both sides of equation #1 by 12.25 to get the actual length of the cafeteria
1(12.25) = 2.5(12.25)
12.25 cm = 30.625 meters
D
41)
Start with multiplication inside the parenthesis
Add/Subtract
Simplify
<h2>
</h2>
Hope this helps ツ
Answer:
4, 5, 6, 7
Step-by-step explanation:
