1) quels sont les quartiles de cette distribu...
1) quels sont les quartiles de cette distribution? 8, 11, 20, 10, 2, 17, 15, 5, 16, 15, 25, 6 a. q1 = 15,q2 = 16,q3 = 15.5 b. q1 = 7,q2 = 13,q3 = 16.5 c. q1 = 6,q2 = 13,q3 = 17 d. q1 = 8,q2 = 13,q3 = 16 2) quelle est létendue interquartile de cette distribution? 4,5,6,8,9,11,13,16,16,18,20,21,25,30,31,33,36,37,40 a. 20 b. 22 c. 36 d. 24 3) quelle expression algébrique correspond au résultat de la division suivante? (14r^4s^10t^3 - 21r^8s^8t^4)÷ - 7r^2s^2t a. - 2r^2s^8t^2 + 3r^6s^6t^3 b. - 2r^2s^5t^3 - 3r^4s^4t^4 c. - 2r^2s^6t^3 + 3r^4s^3t^4 d. 2r^2s^8t^2 - 3r^6s^6t^3 4) sous la forme dun intervalle, quelles sont les valeurs que peuvent prendre le rayon dans un cylindre base circulaire dont la circonférence est de moins de 34π cm? a. - ∞,17 b. 0,17 c. 17,∞ d. 0,17
Answer
# Explanation:
## Step1: Arrange data for quartiles in 1)
Arrange 2, 5, 6, 8, 10, 11, 15, 15, 16, 17, 20, 25 in ascending - order. There are \(n = 12\) data points.
The first - quartile \(Q1\) position is \(\frac{n + 1}{4}=\frac{12+1}{4}=3.25\). So \(Q1=6+(0.25)\times(8 - 6)=6 + 0.5 = 6.5\approx6\) (using interpolation). The median \(Q2\) position is \(\frac{n + 1}{2}=\frac{12 + 1}{2}=6.5\), so \(Q2=\frac{11 + 15}{2}=13\). The third - quartile \(Q3\) position is \(\frac{3(n + 1)}{4}=\frac{3\times(12 + 1)}{4}=9.75\), so \(Q3=16+(0.75)\times(17 - 16)=16.75\approx17\).
## Step2: Calculate inter - quartile range in 2)
Arrange 4, 5, 6, 8, 9, 11, 13, 16, 16, 18, 20, 21, 25, 30, 31, 33, 36, 37, 40 in ascending - order. There are \(n = 19\) data points. \(Q1\) position is \(\frac{n + 1}{4}=\frac{19+1}{4}=5\), so \(Q1 = 9\). \(Q3\) position is \(\frac{3(n + 1)}{4}=\frac{3\times(19 + 1)}{4}=15\), so \(Q3 = 31\). The inter - quartile range \(IQR=Q3 - Q1=31 - 9 = 22\).
## Step3: Simplify algebraic division in 3)
\[
\begin{align*}
\frac{14r^{4}s^{10}t^{3}-21r^{8}s^{8}t^{4}}{-7r^{2}s^{2}t}&=\frac{14r^{4}s^{10}t^{3}}{-7r^{2}s^{2}t}-\frac{21r^{8}s^{8}t^{4}}{-7r^{2}s^{2}t}\\
&=- 2r^{4 - 2}s^{10 - 2}t^{3 - 1}+3r^{8 - 2}s^{8 - 2}t^{4 - 1}\\
&=-2r^{2}s^{8}t^{2}+3r^{6}s^{6}t^{3}
\end{align*}
\]
## Step4: Solve for radius range in 4)
The formula for the circumference of a circle is \(C = 2\pi r\). Given \(C\lt34\pi\), then \(2\pi r\lt34\pi\). Divide both sides by \(2\pi\) (since \(2\pi\gt0\)), we get \(r\lt17\). Also, the radius \(r\gt0\) (a non - negative quantity for a real - world circle). So the interval is \((0,17)\) or \([0,17]\) in French notation \([0,17]\) (open - closed interval where \(0\) is not included and \(17\) is not included in the strict sense of the problem context, but the closest option is \([0,17]\)).
# Answer:
1. C. Q1 = 6, Q2 = 13, Q3 = 17
2. B. 22
3. A. \(-2r^{2}s^{8}t^{2}+3r^{6}s^{6}t^{3}\)
4. B. \([0,17]\)