Solve the equation
12E − 4 = 0

Answers

Answer 1
Answer: This could get complicated.  Please try to follow my steps carefully:

Begin by writing the equation to be solved:    12E - 4 = 0

Add 4 to each side of the equation:  12E = 4

Divide each side by 12:                      E = 4/12 = 1/3 .

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Find an exact value cos(19pi/12)

Answers

cos\left ( (9\pi)/(12)\right )=\frac{\sqrt{2-√(3)}}{2}

Step-by-step explanation:

We know that

          cos 2x = 2cos²x - 1

So we have

          cosx=\sqrt{(1+cos2x)/(2)}

Substituting x=(19\pi)/(12)

         cos\left ( (19\pi)/(12)\right )=\sqrt{(1+cos2\left ( (19\pi)/(12)\right ))/(2)}\n\ncos\left ( (19\pi)/(12)\right )=\sqrt{(1+cos\left ( (19\pi)/(6)\right ))/(2)}\n\ncos\left ( (9\pi)/(12)\right )=\sqrt{(1+cos570)/(2)}\n\ncos\left ( (9\pi)/(12)\right )=\sqrt{(1-(√(3))/(2))/(2)}\n\ncos\left ( (9\pi)/(12)\right )=\sqrt{(2-√(3))/(4)}\n\ncos\left ( (9\pi)/(12)\right )=\frac{\sqrt{2-√(3)}}{2}

   cos\left ( (9\pi)/(12)\right )=\frac{\sqrt{2-√(3)}}{2}

19 π / 12 = 19 * 180° / 12 = 285 °
cos ( 19 π / 12 ) = cos 285° = cos ( - 75° ) = cos 75°
cos 75° = cos ( 45° + 30° ) = cos 45° cos 30° - sin 45° sin 30° =
= ( √2 / 2 · √3/2 ) - ( √2 / 2 · 1/2 ) = √6/4  - √2/4 =
= ( √6 - √2 )/ 4

Copy and complete the table for the sequence 3n-1 Term number Term 3n-1
1
2
3.

Answers

3n-1

where n = 1 ; n = 2 ; n = 3

3(n) - 1 = 3(1) - 1 = 3 - 1 = 2
3(n) - 1 = 3(2) - 1 = 6 - 1 = 5
3(n) - 1 = 3(3) - 1 = 9 - 1 = 8

A person playing a game of chance has a 0.25 probability of winning. If the person plays the game 20 times and wins half of that number of times, what is the difference between the theoretical probability and the experimental probability of that person winning ?

Answers

The theoretical probability is what is expected to happen which is 0.25 or 25%. The experimental probability is the actual or observed during the play. Since the person won half of 20 games, the experimental probability is 10/20 or 50%.

The difference between the theoretical and experimental probability is then

50%-25%=25% or 0.25

We note that the experimental probability is higher than the theoretical. However, as more games are played, the fraction of games won becomes closer and closer to the theoretical probability.

In a refrigerator, there are 6 bottles of soft drinks (each a different brand) and 8 cans of juice (each a different type). How many combinations can be made with one soft drink and one fruit drink?a. 1
c. 36
b. 14
d. 48

Answers

The number of ways of choosing 1 soft drink from 6 soft drinks is 6C1 = 6!/((6-1)! * 1!) = 6!/(5!) = (6*5*4*3*2*1)/(5*4*3*2*1) = 6.

Similarly, the number of ways of choosing 1 fruit juice from 8 cans of juice is 8C1 = 8!/((8-1)! * 1!) = 8!/7! = 8

number of combinations of 1 soft drink AND 1 fruit drink = 6 x 8 = 48

Answer: D [48]

Standing in your tree house, 50 feet off the ground, you look down at a 60° angle and notice a
Frisbee. Approximately how many feet from the base of the tree is the
Frisbee?

Answers

\alpha = 60^o , \ b= 50 \ feet \n \n tan\alpha =(b)/(a)\n \ntan60^o = (b)/(50)\n \n√(3)=(b)/(50)\ \ / \cdot 50\n \nb=50√(3) \approx 50\cdot 1.73 = 86.5 \ feet \n \nAnswer : \ Frisbee \ is \ about \ 50 \ feet \ from \ the\ base \ of \ the \ tree

Real fourth roots of 256

Answers

I'd solved in pic. Please see the pic.