Answer:
<h3>C. They are both perfect squares and perfect cubes.</h3>
Step-by-step explanation:
Perfect squares are numbers that their square root can be found easily without any remainder.
Given the following patterns;
1*1 = 1 and 1*1*1 = 1
It can be seen that 1 is 1 perfect square since 1*1 = 1² = 1
Also 1 is perfect cube since 1*1*1 = 1³ = 1 (cube of the value gives 1)
Similarly for the expression;
8*8 = 64
8² = 64 (since the square of 8 gives 64, then 64 is known to be a perfect square)
Also 4*4*4 = 64
i.e 4³ = 64 (This shows that the cube root of 64 is 4 making it a perfect cube since we can get a whole number for the cube root of 64)
The same is applicable for other expressions 729 = 27 × 27, and 9 × 9 × 9, 4,096 = 64 × 64, and 16 × 16 × 16
This values are easily expressed as a constant multiple of a number showing that they are both perfect squares and perfect cubes.
Answer:
a
Step-by-step explanation:
Answer:
1191.4 ; 34.5
Step-by-step explanation:
Given the data:
29; 37; 38; 40; 58; 67; 68; 69; 76; 86; 87; 95; 96; 96; 99; 106; 112; 127; 145; 150
The sample variance and standard deviation can be obtained thus :
Σ(X - m)² / (n - 1)
Where, m = mean of the sample
n = sample size
The standard deviation equals, sqrt(variance )
Using a calculator:
The variance, σ² ;
Mean = Σx / n = 1681 / 20 = 84.05
(x -m)^2
[(29-84.05)^2 + (37-84.05)^2 + (38-84.05)^2 + (40-84.05)^2 + (58-84.05)^2 + (67-84.05)^2 + (68-84.05)^2 + (69-84.05)^2 + (76-84.05)^2 + (86-84.05)^2 + (87-84.05)^2 + (95-84.05)^2 + (96-84.05)^2 + (96-84.05)^2 + (99-84.05)^2 + (106-84.05)^2 + (112-84.05)^2 + (127-84.05)^2 + (145-84.05)^2 + (150-84.05)^2] / 19
22636.95 / 19
= 1191.4184 = 1191.42
Standard deviation = sqrt( Variance)
Standard deviation = sqrt(1191.4184)
Standard deviation = 34.516929 = 34.52