Answer:
p = (2k + 1)i + j
q = 25i + (k + 4)j
p . q = 11
Find the dot product of p and q
(2k + 1)(25) + (k + 4) = 11
50k + 25 + k + 4 = 11
51k = -18
k = - 18/51 = –6/17.✅
b) p.q = |p||q|cos∅
p= (2k + 1)i + j = [2(-6/17) + 1)i + j ]= 5/17i + j
|p| = √ (5/17)² + 1²
|p| = √314/ 17 ( The square root doesn't cover the 17) = 1.0424
q = 25i + (k + 4)j = 25i + ( -6/17 + 4)j
q = 25i + 62/17 j
|q| = √ 25² + (62/17)²
= 25.2646
Now applying them to the formula above
We already have p.q = 11 from the question.
11 = (1.0424)(25.2646)Cos∅
11 = 26.3358Cos∅
Cos∅ = 11/26.3358
Cos∅ = 0.4177
∅ = 65.31°.
This should be it.
Hope it helps
Answer:
c. 60.9%
Step-by-step explanation:
Given:
The probability P that a person responds to an advertisement can be modeled by the function:
![P=1-e^{-0.047t}](https://tex.z-dn.net/?f=P%3D1-e%5E%7B-0.047t%7D)
where
represents number of days since the advertisement first appeared.
To find the probability that a person has responded after 20 days.
Solution:
In order to find the probability that a person has responded after 20 days, we will plugin
in the formula given.
We have:
![P(t)=1-e^{-0.047t}](https://tex.z-dn.net/?f=P%28t%29%3D1-e%5E%7B-0.047t%7D)
Plugging in ![t=20](https://tex.z-dn.net/?f=t%3D20)
![P(20)=1-e^{-0.047(20)}](https://tex.z-dn.net/?f=P%2820%29%3D1-e%5E%7B-0.047%2820%29%7D)
![P=1-e^{-0.94}](https://tex.z-dn.net/?f=P%3D1-e%5E%7B-0.94%7D)
![P=1-e^{-0.047t}](https://tex.z-dn.net/?f=P%3D1-e%5E%7B-0.047t%7D)
![P=1-0.3906](https://tex.z-dn.net/?f=P%3D1-0.3906)
![P=0.6094](https://tex.z-dn.net/?f=P%3D0.6094)
Thus, probability
after 20 days = 0.6094
The probability in percentage can be given =
= 60.9%
Answer:
3/10
Step-by-step explanation:
You have to make them the same fraction.
2/5 = 4/10
3/10 =3/10
3/10 + 4/10 = 7/10
10/10 - 10/10 =3/10
3/10 is the amount of tigers.
Answer:
F 904.32in ^3
Step-by-step explanation:
first use find the radius, which is always half the diameter, in this case 6.
then use the formula, knowing the radius is 6
![v = 4 \div 3 \pi {r}^{3}](https://tex.z-dn.net/?f=v%20%3D%204%20%5Cdiv%203%20%5Cpi%20%7Br%7D%5E%7B3%7D%20)
the cube the radius
![{6}^{3} = 216](https://tex.z-dn.net/?f=%20%20%7B6%7D%5E%7B3%7D%20%20%3D%20216)
multiple radius by 4/3
![(4 \div 3)216 = 288](https://tex.z-dn.net/?f=%284%20%5Cdiv%203%29216%20%3D%20288)
then multiply by pi
![\pi \times 288 = 904](https://tex.z-dn.net/?f=%5Cpi%20%5Ctimes%20288%20%20%3D%20904)