Answer:
D. π/30 + n(π/15)
Step-by-step explanation:
The given equation can be solved by isolating the cosine function and using the inverse function to find the angles.
<h3>Solution</h3>
30cos(30x) +14 = -16
30cos(30x) = -30 . . . . . . subtract 14
cos(30x) = -1
This is an extreme value of the cosine function that first occurs where the argument is π, and repeats every 2π after that:
30x = π +2nπ
x = π/30 +n(π/15) . . . . . odd multiples of π/30
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<em>Additional comment</em>
The answer choices other than D include <em>all</em> multiples of π/30, or <em>only even</em> multiples of π/30. Either way, they are not part of the correct answer.
Answer:
P(x < 5) = 0.70
Step-by-step explanation:
Note: The area under a probability "curve" must be = to 1.
Finding the sub-area representing x < 5 immediately yields the desired probability.
Draw a dashed, vertical line through x = 5. The resulting area, on the left, is a trapezoid. The area of a trapezoid is equal to:
(average length)·(width, which here is:
2 + 5
----------- · 0.02 = (7/2)(0.2) = 0.70
2
Thus, P(x < 5) = 0.70
5.207 rounded to the nearest tenth is 5.2 if the hundredth is 4 or lower you keep the tenth the same, if it's 5 or above you bump it up
Answer: x=-1 and y=0 .
Step-by-step explanation:
The given linear equations:
![10y + 9x = -9\ ...(i)\\\\10y + 5x= -5\ ...(ii)](https://tex.z-dn.net/?f=10y%20%2B%209x%20%3D%20-9%5C%20...%28i%29%5C%5C%5C%5C10y%20%2B%205x%3D%20-5%5C%20...%28ii%29)
Subtract (ii) from (i) , we get
![10y+9x-(10y+5x)=-9-(-5)\\\\\Rightarrow\ 10y+9x-10y-5x=-9+5\\\\\Rightarrow\ 4x=-4\\\\\Rightarrow\ x=-1](https://tex.z-dn.net/?f=10y%2B9x-%2810y%2B5x%29%3D-9-%28-5%29%5C%5C%5C%5C%5CRightarrow%5C%2010y%2B9x-10y-5x%3D-9%2B5%5C%5C%5C%5C%5CRightarrow%5C%204x%3D-4%5C%5C%5C%5C%5CRightarrow%5C%20x%3D-1)
Put value of x in (i), we get
![10y+9(-1)=-9\\\\\Rightarrow\ 10y-9=-9\\\\\Rightarrow\ 10y=-9+9=0\\\\\Rightarrow\ y=0](https://tex.z-dn.net/?f=10y%2B9%28-1%29%3D-9%5C%5C%5C%5C%5CRightarrow%5C%2010y-9%3D-9%5C%5C%5C%5C%5CRightarrow%5C%2010y%3D-9%2B9%3D0%5C%5C%5C%5C%5CRightarrow%5C%20y%3D0)
Hence, x=-1 and y=0 .
Answer:
Step-by-step explanation:
In each option you need to find the number of outcomes of a single event and then multiply that by the number of times that event takes place.
1. 2 outcomes (heads and tails)
2. 6 outcomes (2 outcomes * 3 tosses)
3. 60 outcomes (6 outcomes per die * 10 rolls)
4. 12 outcomes (6 outcomes per die * 2 rolls)
5. 10 outcomes (10 numbers on the pad)
6. 52 outcomes (52 cards in a regular deck)
7. 32 outcomes (32 letters in the alphabet)
8. 7 outcomes (7 letters to choose from)
9. 10 outcomes (10 letters to choose from)
10. 36 outcomes (36 crayons to choose from)