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                                    .02   (accident)

.90 (not distracted) 

                                    .98(no accident)

                                     .30(accident)

.10 (distracted)

                                     .70 (no accident)

a.  P(accident) =  P ( not distracted and accident)  + P ( distracted and  accident)  =

                                   (.90) (.02)  +  (.10) (.30)  =

                                         0.048  = 

                                          4.8%

b. P ( distracted and accident)  =   (.30)(.10)  = 0.03  = 3%

"Anchor"  April and May  in any two seats with a seat between them

We can seat them in 2 ways

For the person between them we have  C (6,1)   = 6  possibilities

And the other 5 people can  be seated in 5!  =120 ways

So.....the total possible arrangements  =

2 * 6 * 120  = 

12 * 120  = 

1440

thanks

-3 ( a - 7)  +  4a

-3a  + 21  + 4a

a + 21

We have   C(5,3)   = 10   possible sets

These are

(1, 2, 3)     (2, 3, 4)   (3, 4, 5)

(1, 2, 4)     (2, 3, 5)

(1, 2, 5)     (2, 4, 5)

(1, 3, 4)

(1, 3, 5)

(1, 4, 5)

Thank you very much, Alan!

A water tank in the form of an inverted frustum of a right cone has an altitude of 38 ft., and a slant height of 46 ft. The ratio of the upper and lower radii is 5:4. Compute for the measurement of the shorter radius.

Height =>      h = 38 ft

Slant height => H = 46 ft

Upper radius  R = ?                         R = D * 5 

Lower radius   r = ?                          r = D * 4     

Ratio    R : r = 5 : 4

Let the defference of R - r be  D

D = sqrt(H² - h²)  = sqrt (672)

    (1 - r^2)                                          (1 - r^6) 

a*_______  =  7          and      a  *  _________  =  91

        1 - r                                            (1   - r)

a * (1  -r^2) =  7 (1 - r)                a ( 1 -r^6)  =  91 ( 1 - r)

13 a ( 1 - r^2) = 91 (1 - r)          a ( 1 - r^6)  = 91 ( 1 - r)

So

13a ( 1 -r^2)  =  a ( 1 - r^6)

13 ( 1 - r^2)  = ( 1 -r^6)

13 - 13r^2 = 1 - r^6

r^6  - 13r^2  + 12  =   0

Note that   r = 1   and  r  = -1  are roots   

So  (r + 1) ( r -1)  =  r^2  - 1

Dividing we have

                 r^4  + r^2  - 12

r^2  -1   [  r^6  - 13r^2 +  12]

                r^6                          - 1r^4

              _____________________________________

                                      r^4  -13r^2 + 12

                                      r^4 -  r^2

                                   _______________

                                              -12r^2  + 12

                                              -12r^2  +  12

                                             ____________

                                                                  0

The remaining polynomial  =   r^4  + r^2  - 12

Set to 0  and factor

(r^2 + 4) ( r^2 - 3)   = 0

Since the  sum of the  first n terms increases, then  √3  is the only possible value  for  r

So

7 =  a ( 1 - 3) / ( 1  -√3)

7 = -2a / (1 - √3)

7=  2a / (√3 - 1)

a = (7/2)(√3 - 1)

And the sum of the 1st  4 terms   =

(7/2) (√3 -1)  ( 1 - 9) / ( 1 - √3)  =

(7/2) (√3  -1) (-8) / ( 1 - √3)   =

(7/2) (√3 -1) (8) / ( √3 - 1)  =

(7/2) (8)  =

28

6 / (1/2) =12 mph - his cycling speed
5 / 12 mph x 60 =25 minutes to get to Minnie's house.
45 - 25 = 20 minutes to walk to school.
1 mile / (1/3) hours = 1 x 3 =3 mph - walking speed to school.

Ah, thank you!

Yeah  because  notice  that

(-7x -  ___)  (-x + ___)    is really the same as

(-1) *(7x +  ___)  * ( -1) *  (x - ___)   =

(-1) (-1) ( 7x +  ___) ( x - ___)  =

(1) (7x + ____)  ( x -  ___) =

(7x + ___ )  ( x  - ___)

Hello Guest!

Have you tried 4320?

Let x be the smaller number  and y  the larger....so.....

x = (1/5)y     (1)

y - x  = 260    (2)

Sub (1) into (2)

y - (1/5)y =  260    simplify

(4/5)y  = 260

y =260 (5/4)

y = 325

x = (1/5)(325)   = 65 

Thanks! But what if it were (-7x-_)(-x+_) as well? Would the polynomials follow the same pattern?

Let   the time that  Welch travels  = H hours

Let the time  that Gwen travels  ( H + 1) hours

So

Welch's Rate  * Time traveled   +  Gwen's Rate * Time traveled =  Total Combined Distance

60 H  +  40 (H + 1)  =  115    simplify

60 H + 40H + 40   =115

100H  = 115 - 40

100 H =  75     divide both sides by  100

H = 75/100   = 3/4  hr

They meet  at  10 AM  + (3/4)hr =   10:45 AM

You could try using a Venn diagram, maybe that'll help. 

7x^2  + nx  -  11

We  have these possiibilities

(7x  - 11) ( x + 1)  →  7x^2 - 11x + 7x - 11  → n = -4

(7x  + 1) ( x - 11) →  7x^2 -77x + 1x - 11 →  n = -76

(7x + 11) ( x - 1)   →  7x^2  + 11x - 7x - 11 →  n  = 4

(7x - 1) ( x + 11) →  7x^2 + 77x - 1x - 11 →  n = 76

Rate of riding his bike =    6mi / (1/2)hr =  12miles/hr

Call his walking rate  =  W mph

And Distance / Rate  = Time....so

5 miles / 12mph  +   1mile / Wmph  =  45 min               {45 min  = 3/4 hr}

5/12 (hrs)  +  ( 1 / W ) hrs =  ( 3/4) hrs 

1/W =  3/4 -5/12

1/W  = 9/12 - 5/12

1/W=  4/12

W / 1=  12/ 4

W = 3 mph

I will give this a try!!

a - The first integer can be any integer between 0 and 12                      =13 / 13

      The probability that the 2nd number is different from the first           =12 / 13

      The probability that the 3rd number is different from the first two     =11 / 13

       The probability that the 4th number is different from the first three =10 / 13

Then, the overall probability that all four numbers are different from each other =13 /13  x  12 / 13  x  11 / 13  x  10 / 13 =17,160 / 13^4 =1,320 / 2,197 =60.08 %

b - [13 C 2  x  13^11] / 13^13 =6 / 13 =46.15 %

Note: Somebody should check this,please. Thanks.

Very nice, heureka  !!!!

Let the radius of the lower  base   =  R

Using the Pythagorean Theorem.....the  length of the radius of the upper base =

R + √ [46^2 - 38^2]  =  R + √672

So

R + √672           5

_______  =     ____            cross-multiply

     R                  4

4 [ R + √672 ]   = 5R

4R  + 4√672  = 5R

4√672  =  R

4 (4√42)  = R

16√42  = R  = length of shorter radius (in feet)

Right triangle ABC is on a coordinate plane. Segment AB is on the line y = 2 and is 3 units long. Point C is on the line x = −1. If the area of ΔABC is 12.5 square units, then find a possible y-coordinate of point C.

14.88 / kg  x   kg /  1000g  x  250 g   =

14.88 / 1000  * 250

14.88 ( 250/1000) 

14.88 (1/4)  = 

3.72

Let the two smallest  integers =  x  and x + 2

Let the two largest  =  x + 4 , x + 6

So

x(x + 2) + 72  = (x + 4) ( x + 6)       simplify

x^2 + 2x  + 72 =  x^2  + 4x + 6x  + 24      subtract x^2 from both sides and simplify

2x + 72  =  10x  + 24     subtract  24, 2x from both sides

8x  =  48   divide both sides by 8

x = 6

x + 2  =8

x + 4  =10 

x + 6  = 12

We have

.30 (x)  + .04 (8)  =  .14 (x + 8)    simplify

.30x  + .32  = .14x  + 1.12         subtract .32 , .14x  from  both sides

.16x  = .80       divide both sides by  .16

x = 5   (gallons of 30% butterfat cream)