Answer: 0.8413
Step-by-step explanation:
Given : Henry has collected data to find that the typing speeds for the students in a typing class has a normal distribution.
Mean : 
Standard deviation : 
Let x be the random variable that represents the typing speeds for the students.
The z-score :-
For x= 51
Using the standard normal distribution table ,the probability that a randomly selected student has a typing speed of less than 51 words per minute :-
Hence, the probability that a randomly selected student has a typing speed of less than 51 words per minute = 0.8413
Answer:
7234.56 in³
Step-by-step explanation:
4/3πr³
4/3 (3.14)(12)³
7234.56 in³
Given that
, then
The slope of a tangent line in the polar coordinate is given by:
Thus, we have:
Part A:
For horizontal tangent lines, m = 0.
Thus, we have:
Therefore, the <span>values of θ on the polar curve r = θ, with 0 ≤ θ ≤ 2π, such that the tangent lines are horizontal are:
</span><span>θ = 0
</span>θ = <span>2.02875783811043
</span>
θ = <span>4.91318043943488
Part B:
For vertical tangent lines,
Thus, we have:
</span>Therefore, the <span>values of θ on the polar curve r = θ, with 0 ≤ θ ≤ 2π, such that the tangent lines are vertical are:
</span>θ = <span>4.91718592528713</span>
Answer:
t=-6
Step-by-step explanation:
The coordinates of the image point are given to be B(4, -8). We are to find the coordinates of pre-image that is the coordinates before the translation.
The translation made was (x-2, y+3)
This means, the x coordinate was moved 2 units to left and y coordinate was moved 3 units above.
So, the coordinates of original point will be, 2 units to right of B and 3 units down of B.
So the coordinates will be (6, -11)
