Find the mean deviation of a set of numbers: 14, 15, 16, 17, 18, and 19.
2.5
1.7
1.5
3.5
Correct answer is C
x̄ = 14+15+16+17+18+196=996 = 16.5
M . D = (14−16.5)+(15−16.5)+(16−16.5)+(17−16.5)+(18−16.5)+(19−16.5)6
M.D = (−2.5)+(−1.5)+(−0.5)+(0.5)+(1.5)+(2.5)6
Taking the absolute value of the deviations
M.D = 2.5+1.5+0.5+0.5+1.5+2.56
M.D = 96 = 1.5
The diagonals of a rhombus are 16 cm and 12 cm find the length of the side.
20cm
8cm
14cm
10cm
Correct answer is D
In a rhombus, the diagonals are perpendicular bisectors of each other, and they bisect the angles of the rhombus. This means that a rhombus is essentially made up of four congruent right-angled triangles.
We can use the Pythagorean theorem to find the length of one side of the rhombus (s)
s2=82+62
s2=64+36
s2=100
s = √100
s =10 cm
So, the length of each side of the rhombus is 10 cm.
If 2x - 3y = -11 and 3x + 2y = 3, evaluate (y−x)2
16
25
9
4
Correct answer is A
2x - 3y = -11 --- (i)
3x + 2y = 3 --- (ii)
Multiply equation (i) by 3 and equation (ii) by 2
6x - 9y = -33 --- (iii)
6x + 4y = 6 --- (iv)
Subtract equation (iii) from (iv)
13y = 39
y = 3913 = 3
substitute (3) for y in equation (ii)
3x + 2(3) = 3
3x + 6 = 3
3x = 3 - 6
3x = -3
x = −33 = - 1
Now,
(y−x)2=(3−(−1))2
= (3+1)2
= 42
= 16