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4.

The number of ways that you can have 5 cards where three are 4s and the other two are not 4 is

4C3*48C2 = 4*1128= 4512

The number of ways you can choose 5 cards from 52 cards is   52C5 = 2598960

so the prob you want is    4512/2598960 = 

factor(4512) = 2^5*3*47

factor(2598960) = 2^4*3*5*7^2*13*17

\(\dfrac{4512}{2598960} = \dfrac{2*47}{5*49*13*17}=\dfrac{94}{54145}​\)

Sorry, hectictar....I didn't see your answer when I posted....!!!

I get  99

9 + 9  =  18

99 / 18   =  5.5

The sum of the digits for each of the first ten multiples of 9  is  9 .

So the first 10 positive multiples of 9 must be lucky integers.

etc.

But....

9 * 11  =  99     and     99/( 9 + 9 )  =  5.5

So

99  is the least positive multiple of  9  that is not a lucky integer.

If PQ  is 6 times the length of QR, then  PR  can be divided  into (6 + 1)  =  7 equal parts

So....each equal part  is   98 / 7  =   14 cm

So..... QR  is  one of these equal parts  = 14 cm

And PQ is six of the equal parts  =  6 * 14   =   84 cm

1. A board USB cut into 20 equal pieces so that each piece is 6 1/2 cm in length. How long was the board before it was cut?

20  *  (6 + 1/2)   =   20*6  + 20* (1/2)  =  120 + 10  =  130 cm

2. Mr. Phillips served 1/2 of a chicken for dinner. 2/3 of the chicken served was eaten. What fraction of the roast served was eaten?

Well.....this could be construed as a" trick " question...if 2/3 of what was served was eaten, then 2/3 must be the answer

However...if we are talking about the fraction of the total roast eaten, we have

(1/2) (2/3)  =  2/6  =   1/3  of the whole roast was eaten

3. Mario completed 3/5 of his homework. One fourth of the completed homework was in geography. What franctional part of the homework was in geography?

(3/5) (1/4)  =  3/20   

yup that helps, thank ya 

The scale factor  from   ABC  to RQR  is      6/4  =  3/2  =  1.5

So....each dimension  of  PQR  is 1.5 times that of ABC

Now....just for the heck of it,if we let the base of ABC  = 4 cm...so.... its altitude must be 10 cm

Proof  ..area ABC  =   (1/2) base * altitude  =  (1/2) (4) (10)  =  20  cm^2

So....since each dimension of PQR  is 1.5 times that of ABC, its altitude must be 10 * 1.5  = 15 cm

And let its base  = 6cm

So...it's area is just  (1/2) (6) ( 15)  =  45 cm^2

Note that  we could obtain the same result  by taking the area of ABC  and multiplyng this by the square of the scale factor

Proof :   20 (1.5)^2   =  20 (3/2)^2  =  20 * 9 / 4  =  180  / 4   = 45  cm^2

Hope that helps  !!!

Since AB  = AC  ....the angles opposite these sides are also equal...

So   y   =    [ 180 - 24 ] / 2   =  156 /  2    =   78°

b^2  - 4ac   =    the discriminant....correct....!!!!

If ZAX  is equilateral  and has a perimeter of 30, then  XA  must  = 10

So...ZA  must also  = 10

Note that angle ZAX  = 60...so angle LAZ  = 90 - 60  = 30

And we can find LA   thusly :

cos LAZ   = LA / ZA

cos (30)  = LA / 10

10 cos (30 )  = LA

10 √3/2  = LA   =  5√3

So....the area of FLAX  =    XA  *  LA   =   10 * 5√3   =  50√3  units^2  

Thanks now I remember use the future value formula!

We have the following ratio

25 / 15  = [7x - 40 ] / 18     cross-multiply

18 * 25  =    15 * [ 7x - 40]     simplify

450  =  105x - 600     add  600 to both sides

1050  = 105x       divide both sides by 105

10  = x

1 

P (Red  or Blue)  =  P(Red) + P (Blue) - P (Red and Blue)  =

                                     6/16   +   4/16   -  0 / 16  =

                                      10/16  =

                                        5/8

2  Don't know the answer, NSS

3

The numbers   12    36    and  24    are multiples of 3 and 4

And we have 8 total numbers....so the probability  is    3/8

circle :

"Produced by the equation x^2 + y^2  =  16  "

4.  Don't know the answer here, NSS

5.   Probability  =  area of smaller circle  / area of larger circle  =

pi * (3)^2  /  [ pi * (12)^2 ]   =   9 / 144    =   1 / 16

This is the formula you would use to calculate that:

FV=P{[1 + R]^N - 1/ R}, Where R=Interest rate per period, N=number of periods, P=periodic payment,  FV=Future value.

FV = 150 x {[1 + 0.048/12]^(3*12) -1 / 0.004}

FV = 150 x {[1 + 0.004]^36 - 1 / 0.004} 

FV = 150 x     1.004^36 - 1 / 0.004}

FV = 150 x      38.638108459.....

FV = $5,795.72 - this is how much you will have at the end of 3 years @ 4.8% comp.monthly.

From that drop down list choose the meaning that matches the term

I don't see any question, Manuel....

Correct....!!!

We can use the Law of Cosines, here

JK   =  sqrt [ 3^2 + 5^2 - 2(3)(5)cos (62) ] 

JK =  sqrt  [ 34 - 30cos(62) ] ≈ 4.46 mm  ≈  4.5 mm 

OK....!!!

Note that since AB  = AC....then angles ABC  and ACB  are  equal.....

So ACB  =  (180 - 24) / 2  =   156 / 2  =  78°

And ACD  is supplemental to ACB...so ACD  = 180 - 78  =  102°

And since AC  = CD....then angles ADC  and CAD are equal

So.... ADC  =  (180 - 102) / 2  =  78/2   =  39°  =  "x"

I uploaded a link to the image

Can you just upload the image  ???