CPhill

124°18' 30"

We can  use  this "fraction"  system....keep the degrees....divide the minutes by 60....divide the seconds by 3600

124  +  18 / 60  +  30/3600  =   124.3083°

Think you can do 2  based on this, Manuel??.....

 y = 1/3x + 8 and 2x - y = 2

Rearrange the second as    y = 2x  - 2

Set these y's equal and we have that

(1/3)x  +  8  = 2x - 2         add 2  to both sides, subtract  (1/3)x from both sides

10 =  2x  - (1/3) x

10 = 6/3 x  - 1/3 x

10 =  5/3 x      multiply both sides by  (3/5)

10 (3/5)  = x   =  30 / 5    = 6

First Problem:

log N=1.3

This says that   10^1.3  = N   =  19.9526

Second Problem:

In N=2.2

This says that    e^2.2  = N  =  9.0250

Third Problem:

antilog 0.8

This says  that

10^x  = 0.8

Take the log of each side

log 10^x  = log 0.8

And we can write

x  log 10  = log0.8     {log 10  = 1}  

x(1) = log 0.8

x  = log 0.8  =  -0.0969

A)

We have 4  10s......so  if we have replacement....the probability of  drawing a 10 on each draw is the same  =  4/52

So....

P (Two 10s with replacement)   =   4/52  * 4/52   =    1/13  * 1/13      = 1/169

B )  Without replacement we have   4/52  of drawing a 10 on the first draw and  (3/51)  of drawing a 10 on the second draw

So.....this probability  =  4/52  *  3/51    =   (1/13) * (1/17)  =    1/ 221 

C) The second event is dependent.  If we   don't draw a 10 on the first draw, the probability of drawing a 10  on the second draw is different  = 4/ 51.   In the first scenario, the probability of drawing a 10 is the same on both draws. Thus, it is independent  - one draw does not affect the other.

Note that the  intersection of the lines is the solution....this  is  (2,-2)

So....the x coordinate is   2

Not that great at this either, RP...but...I think I can do a few

We have  6 * 4  = 24 possible outcomes.....here is the sample space :

Sum  = (a, b)  =  (result of 4-sided die, result of 6-sided die )

2 = (1,1)

3 =(1,2) (2,1)

4 = (1,3) (3,1) (2,2)

5 = (1,4) (4,1) (2,3) (3,2) 

6 = (2,4) (4,2) (3,3) (1,5)

7 = (2,5) (1,6) (3,4) (4,3)

8 = (4, 4)  (3,5) (2,6)

9 = (4,5) (3,6)

10 = (4,6)

P(A)=   the six-sided die is 3  ....

We have the following possibilities  ......    (1,3) (2,3) (3,3) (4,3)

So P(A)  =  4/24   = 1/6

P(B)=  sum of the dice is 5  or less  = 10 possibilities

So  P(B)  =  10/24  = 5/12

P (A  l B)  =  Probability the six-sided die is 3, given that the sum of the die is 5 or less

If we let  the first number represent the result of the 4 sided die  and the second number the result of the 6-sided die, we have the following possibilites  (1,3)  and (2,3)  = 2 possibilities

And the number of results l of 5 or less = 10 possibilities  

So  P (A l  B)  =     2/10   = 1/5

P(B l A)  =  Probability that the sum of the dice  is 5, given that the six-sided is 3

We have the following possibilites for the six-sided die  = 3

(1,3) (2,3)  (3,3)  (4,3) = 4 possibilities

Notice that  there's only one thing that sums to 5  ⇒  (2,3)

So  P(B l A)  =  1 / 4

P (A and B )  = Probabilitiy  that six-sided die is 3 and the sum of the die  is 5 or less

Note : P(A  and B)   = P(A) * P(B)  = (1/6)  * (5/12)   =   5 / 72

P(A)  * P (B l A)  =  (1/6) * (1/4)  =  1/24

P (B) * P( A l B)  =  (5/12) * (1/5)  =  1/12

All of these are solve using exactly the same procedure

I'll do the first one....you should be able to do the rest based on this....

If we have two sides of a triangle and an included angle between these sides, which is is exactly the case in every one of these....the area of the triangle =

(1/2)  (product of the sides)*sin (included angle)

So....for the first one we have

Area  = (1/2) (2.7 * 3.4) sin (40°)   = (1/2) (9.18) sin (40° )  ≈   2.95 ft^2

Let us know if you run into trouble....but.....I think you can solve every one of these if you follow my example....

This isn't much, tertre....more...."draw a pic and see what makes sense "......

Look at this.....

The triangle ABC  is a right isosceles triangle....note the rectangle DEFG....GF  = 25    and DG  = 10

So...their ratio  is  25/10  = 5/ 2

So....the sides of the rectangle are  25  and 10

The right angle at the bottom right sets up the following relationship

4 / y = y / 16     cross-multiply

16 * 4  =  y^2

64  = y^2     take the square root of both sides

8  = y

So....using the Pythagorean Theorem, we have that

z^2  = 4^2 + y^2

z^2  = 16  + 8^2

z^2  =  16  + 64

z^2  = 80       take the square root of both sides

z  = √80

If you want to simplify this :

z  = √ [16 * 5 ]

z = √16   * √5

z = 4√5

e^3.8  = x

Log form :

ln_e x = 3.8

b  = e

x  = 3.8

n  = x