Answer:
The sample standard deviation is 15.3.
Step-by-step explanation:
Given data items,
84, 85, 83, 63, 61, 100, 98,
Number of data items, N = 7,
Let x represents the data item,
Mean of the data points,


Hence, sample standard deviation would be,






Answer:
Given:
Body mass index values:
17.7
29.4
19.2
27.5
33.5
25.6
22.1
44.9
26.5
18.3
22.4
32.4
24.9
28.6
37.7
26.1
21.8
21.2
30.7
21.4
Constructing a frequency distribution beginning with a lower class limit of 15.0 and use a class width of 6.0.
we have:
Body Mass Index____ Frequency
15.0 - 20.9__________3( values of 17.7, 18.3, & 19.2 are within this range)
21.0 to 26.9__________8 values are within this range)
27.0 - 32.9____________ 5 values
33.0 - 38.9____________ 2 values
39.0 - 44.9 _____________2 values
The frequency distribution is not a normal distribution. Here, although the frequencies start from the lowest, increases afterwards and then a decrease is recorded again, it is not normally distributed because it is not symmetric.
a. We're looking for
such that




b. Integrating with respect to
will make things easier.

(where we take the positive square root because we know
)
Now we want to find
such that




Answer:
Given: A triangle ABC and a line DE parallel to BC.
To prove: A line parallel to one side of a triangle divides the other two sides proportionally.
Proof: Consider ΔABC and DE be the line parallel to Bc, then from ΔABC and ΔADE, we have
∠A=∠A (Common)
∠ADE=∠ABC (Corresponding angles)
Thus, by AA similarity, ΔABC is similar to ΔADE, therefore
AB/AD= AC/AE
⇒AD+DB/AD = AE+EC/AE
⇒1+DB/AD = 1+ EC/AE
⇒DB/AD = EC/AE
Therefore, a line parallel to one side of a triangle divides the other two sides proportionally.
⇒Therefore Proved
Hope this helps!!!
QR =12 because you set up a proportion 21/14=x/8 then cross multiply and get 14x=168 then you divide and get 12