CPhill

We have

11/8 = x/3      cross-multiply

33 = 8x          divide by 8 on both sides

33/8 = x = 4.125 = 4.1 (rounded)

cross multiply

13(x - 9) = 15

13x - 117 = 15        add 117 to each side

13x = 132               divide by 13 on both sides

x = 132/13

1/sin(49) = sin(20)/sin(r)    cross multiplying, we have

sin(r) = sin(49)*sin(20)

sin(r) = 0.2581258787973758     and using the sine inverse, we have

sin^-1(0.2581258787973758) = r =  about 14.96°

Let the time Carlos drove = x  ....then the time that Maria drove = (5-x)

And Rate * Time = Distance   ....so we have

53x + 51(5-x) = 258    simplify

53x + 255 - 51x = 258

2x + 255 = 258      subtract 255 from both sides

2x = 3         divide both sides by 2

x = 3/2        and Maria drove (5 - x)   =  5 - 3/2   = 3.5 hs.

We can use the tangent function for this...let x be the opposite side...so we have

tan(20) = x / 18   multiply both sides by 18

18* tan (20) = x = about 6.55 units

Yeah...you're correct!!!

I have to think about that, geno....but you're probably correct......my brain is too tired !!! (LOL!!!)

There are 24 possiible arrangements.......

Let's look at the possible arrangements with  cheque 1 going into envelope 1.

So we have

1 2 3 4

1 2 4 3

1 3 2 4

1 3 4 2

1 4 2 3

1 4 3 2

Note that only 2 of these have cheque 1 going into  envelope 1 and all the others the wrong ones. These would be 1 3 4 2  and 1 4 2 3. So, that is 1/3 of the possible arrangements where  cheque 1 goes into envelope 1.

And every other arrangement (2nd check in 2nd envelope, etc.) would have the sme probabilty.

So, the answer - I think - is 1/3.......

This one seems difficult...but it's not that hard.....

If we unroll the cylinder we have a rectangle that is 48cm high and 16cm wide. And the string would extend from one bottom edge of the rectangle to the opposite top corner. Thus, the string is the hypoteneuse of a right triangle with legs of 48 and 16. And the string's length is given by.....

√(48^2 + 16^2) = √2560 ≈ 50.6 cm

I think that's it ......???

If you key in a decimal...it will give you a fraction.....