Find the median of each set:-
Median is middle number of a data set. If a data set has an odd number of numbers then the median is the middle number when ordered form least to greatest but if its an even number you have to find the mean for the middle 2 numbers when ordered for least to greatest.
A.
1.2, 2.4, 3.2, 3.2, 3.6, 4.0, 4.1, 4.7
Even numbers = 8
3.2 + 3.6 = 6.8
6.8 ÷ 2 =
Median = 3.4
So this shows that A isn't the answer because the median of A is 3.4, not 3.2.
B.
1.6, 2.8, 2.9, 3.1, 3.3, 3.6, 4.2, 4.5
Even numbers = 8
3.1 + 3.3 = 6.4
6.4 ÷ 2 = 3.2
Median = 3.2
<span>So this shows that B is the answer because the median of B is 3.2.
C.
1.8, 2.0, 2.0, 2.2, 3.2, 4.7, 4.8, 4.9
</span>
Even numbers = 8
2.2 + 3.2 = 5.4
5.4 ÷ 2 = 2.7
Median = 2.7
<span>So this shows that C isn't the answer because the median of C is 2.7, not 3.2.
</span>
D.
1.4, 1.7, 2.9, 3.0, 3.1, 3.2, 3.2, 3.2, 4
Odd numbers = 9
Median = 3.1
<span>So this shows that D isn't the answer because the median of D is 3.1, not 3.2.
</span>
The stem and leaf plot which median is 3.2 is B.
Answer:
a. v.v' = v₁v₂ - v₁v₂ = 0 b. (20, -21)/29 and (-20,21)/29
Step-by-step explanation:
a. For two vectors a, b to be orthogonal, their dot product is zero. That is a.b = 0.
Given v = (v₁, v₂) = v₁i + v₂j and v' = (v₂, -v₁) = v₂i - v₁j, we need to show that v.v' = 0
So, v.v' = (v₁i + v₂j).(v₂i - v₁j)
= v₁i.v₂i + v₁i.(- v₁j) + v₂j.v₂i + v₂j.(- v₁j)
= v₁v₂i.i - v₁v₁i.j + v₂v₂j.i - v₂v₁j.j
i.i = 1, i.j = 0, j.i = 0 and j.j = 1
So, v.v' = v₁v₂i.i - v₁v₁i.j + v₂v₂j.i - v₂v₁j.j
= v₁v₂ × 1 - v₁v₁ × 0 + v₂v₂ × 0 - v₂v₁ × 1
= v₁v₂ - v₂v₁
= v₁v₂ - v₁v₂ = 0
So, v.v' = 0
b. Now a vector orthogonal to the vector v = (21,20) is v' = (20,-21).
So the first unit vector is thus a = v'/║v'║ = (20, -21)/√[20² + (-21)²] = (20, -21)/√[400 + 441] = (20, -21)/√841 = (20, -21)/29.
A unit vector perpendicular to a and parallel to v is b = (-21, -20)/29. Another unit vector perpendicular to b, parallel to a and perpendicular to v is thus a' = (-20,-(-21))/29 = (-20,21)/29
Answer:
$49,893.6
Step-by-step explanation:
$555.26/mo(30yr)(12 mo/yr) - $150000 = $49,893.6
