Answer: Choice D)
The angle between the two vectors is approximately 71.6 degrees
----------------------------------------------
----------------------------------------------
Work Shown:
Each time I write the word "dot" I mean "dot product".
|u| = length of vector u
|u| = sqrt(u dot u)
|u| = sqrt(<8,4> dot <8,4>)
|u| = sqrt(8*8 + 4*4)
|u| = sqrt(64 + 16)
|u| = sqrt(80)
|u| = sqrt(16*5)
|u| = sqrt(16)*sqrt(5)
|u| = 4*sqrt(5)
-----------------------
|v| = length of vector v
|v| = sqrt(v dot v)
|v| = sqrt(<9,-9> dot <9,-9>)
|v| = sqrt(9*9 + (-9)*(-9))
|v| = sqrt(81+81)
|v| = sqrt(2*81)
|v| = sqrt(2)*sqrt(81)
|v| = sqrt(2)*9
|v| = 9*sqrt(2)
-----------------------
u dot v = <8,4> dot <9,-9>
u dot v = 8*9 + 4*(-9)
u dot v = 72-36
u dot v = 36
-----------------------
cos(theta) = (u dot v)/(|u|*|v|)
cos(theta) = (36)/(4*sqrt(5)*9*sqrt(2))
cos(theta) = (36)/(36*sqrt(10))
cos(theta) = 1/(sqrt(10))
cos(theta) = sqrt(10)/10
theta = arccos(sqrt(10)/10)
theta = 71.56505
which rounds to 71.6 when rounding to one decimal place (nearest tenth)
That's why the approximate answer is roughly 71.6 degrees
You need to subtract 638 and 62 and that will give 576
Answer:
a.
Probability of Diet Cola = 19/28
Probability of Lemonade = 4/28
Probability of Root Beer = 5/28
b. Theoretical Probability
Step-by-step explanation:
Given
Diet Cola = 19
Lemonade = 4
Root Beer = 5
Required
Probability the her next drink will be
- Diet Cola
- Lemonade
- Root beer
To calculate the probability of each of the above, first we need to calculate the total number of drinks she's had
Total = Diet Cola + Lemonade + Root Beer
Total = 19 + 4 + 5
Total = 28
The probability that her next drink can be any of the above can then be calculated.
This is calculated by dividing each outcome by the total; as follows;
Probability of Diet Cola = 19/28
Probability of Lemonade = 4/28
Probability of Root Beer = 5/28
This type of probability is referred to as theoretical probability because it makes predictions base on previous occurrence of events.
Answer:
B. 50°
Step-by-step explanation:
∠PLM+ ∠PML =60+70 =130°
So, ∠MPL = 180°-130°=50°
According to the opposite angle theorem,
∠ KPN = ∠MPL which is 50°
