Answer:
Option (d)
Step-by-step explanation:
Let's work by the process of elimination.
Option (a):
The population as well as the aim of study is not defined. Hence, it is incorrect.
Option (b):
As the girls belong to soccer team, the views towards their favourite sport would likely be biased and they will probably chose soccer as their favourite sport. This is incorrect.
Option (c):
The nature of data is not described. Also we don't know whether the sample drawn was random or biased. Hence, this option is also incorrect.
Option (d):
In this scenario, the sample is drawn randomly. The aim of the study is also clearly defined. Hence, this option is correct.
I used mental math and it took a long time, but I got the answer of 2,499.
Answer:
Least value of the smaller number is -8.
Step-by-step explanation:
Let the smaller number be x and the higher one y.
So y = x + 12 and
xy = -32
Substitute for y in the second equation:
x(x + 12) = -32
x^2 + 12x + 32 = 0
(x + 8)(x + 4) = 0
x = -4, -8.
So the least value of the smaller number x is -8.
Step-by-step explanation:
cos(3x) − 3 cos x = cos(2x) + 1
Use triple and double angle formulas.
(4 cos³x − 3 cos x) − 3 cos x = (2 cos²x − 1) + 1
Simplify.
4 cos³x − 6 cos x = 2 cos²x
4 cos³x − 2 cos²x − 6 cos x = 0
2 cos³x − cos²x − 3 cos x = 0
Factor.
cos x (2 cos²x − cos x − 3) = 0
cos x (cos x + 1) (2 cos x − 3) = 0
Solve.
cos x = 0 → x = 90°, 270°
cos x + 1 = 0 → x = 180°
2 cos x − 3 = 0 → no solution