A set of elementary school student heights are normally distributed with a mean of 105105105 centimeters and a standard deviatio
2 answers:
Answer:
The proportion of student heights that are between 94.5 and 115.5 is 86.64%
Step-by-step explanation:
We have a mean and a standard deviation
. For a value x we compute the z-score as
, so, for x = 94.5 the z-score is (94.5-105)/7 = -1.5, and for x = 115.5 the z-score is (115.5-105)/7 = 1.5. We are looking for P(-1.5 < z < 1.5) = P(z < 1.5) - P(z < -1.5) = 0.9332 - 0.0668 = 0.8664. Therefore, the proportion of student heights that are between 94.5 and 115.5 is 86.64%
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If you look at the figure, triangles XVW and ZYW are similar. So, you can use ratio and proportion to solve this problem. Notice that there are tick marks on th other two sides of the bigger triangles. That indicates that the like signs of ticks are equal. For example, that means XZ = ZW and that XW = 2XZ = 2ZW.
24.4/YZ = XW/ZW
24.4/YZ = 2ZW/ZW
24.4/YZ = 2
Solving for YZ,
<em>YZ = 12.2</em>
24.4/YZ = XW/ZW
24.4/YZ = 2ZW/ZW
24.4/YZ = 2
Solving for YZ,
<em>YZ = 12.2</em>
Answer:
Option C and E are correct.
The sequences which are arithmetic:
18, 5.5, -7, -19.5, -32,....
16, 32, 48, 64, 80
Step-by-step explanation:
Arithmetic sequence states that a sequence in which a common difference between each consecutive term is constant.
Common difference(d) = for every natural number n.
Option A:
-5, 5, -5, 5, -5, .....
5-(-5) = 5+5 = 10 ,
-5 -5 = -10 .....
Since, the common difference for the given sequence is not constant.
Option B:
96, 48, 24, 12, 6
48 -96 = -48
24-48 = -24 ....
Common difference for the given sequence is not constant.
Option C:
18, 5.5, -7, -19.5, -32,....
5.5-18 = -12.5
-7 -5.5 = -12.5 ....
∴Common difference for the sequence is constant.
Option D:
-1, -3, -9, -27, -81 ,....
-3 -(-1) = -3+1 = -2
-9-(-3) = -9+3 = -6 ....
∴Common difference for the sequence is not constant.
Option E:
16, 32, 48, 64, 80
32-16 = 16
48 - 32 = 16 and so on...
∴Common difference for the sequence is constant.
Therefore, the sequences which are arithmetic are:
18, 5.5, -7, -19.5, -32,....
16, 32, 48, 64, 80