first is a king: 4 kings out of 52 cards means 4/52=1/13
second not a king: 48 cards are not kings out of 52 cards (with replacement) means 48/52=12/13
(1/13)(12/13)=12/169
first is a king: 4/52=1/13
second is not a king: 48/51=16/17 (without replacement)
(1/...

p=2l+2w
w=width
w+10=length
100=2l+2w
50=l+w
50=w+10+w
50=2w+10
50-10=2w
40=2w
w=40/2
w=20 yards
l=20+10=30 yards

P=2l+2w
2400=2l+2w
1200=l+w
1200-l=w
A=lw
A=l(1200-l)
A=1200l-l2
use -b/2a
-1200/-2=600 yards on a side will maximize the area; therefore you have a square 600 by 600
simply speaking, the maximum area will always be a square
(before showing your...

17 feet 8 inches=17 2/3 feet
11 feet 8 inches=11 2/3 feet
17 2/3 times 11 2/3
53/3 * 35/3=1855/9=206.111... square feet rounded up to 207 square feet
207*$2.89=$598.23

mean: add the numbers together and divide by the number of numbers
the sum of the numbers is 247
247/15=16.4666... is the mean (round accordingly)
mode: the most frequently occurring number which is 16 which occurs 3 times
median: the number in the middle when there is an odd number...

log75=log(52*3)=log(52)+log(3)
log(52)+log(3)
2log(5)+log(3)
2*0.6989+0.4771 log(5)=0.6989
1.3978+0.4771
1.8749
log(75)=1.8749

let log(0.6)(9/25)=x
therefore (0.6)^x=(9/25)
(0.6)^x=(3/5)^2
0.6=6/10=3/5
(3/5)^x=(3/5)^2
if the bases are equal then the exponents must be equal
x=2 so log(0.6)(9/25)=2
or,...
log(0.6)(9/25)=log(0.6)(3/5)^2=log(0.6)(0.6)^2=2log(0.6)(0.6)=2*1=2 again

no three consecutive even numbers sum to 56
16+18+20=54
18+20+22=60
no three consecutive odd numbers sum to 56 either
no three consecutive numbers sum to 56
is there a typo ?

the length, width, and diagonal form a right triangle with the diagonal being the hypotenuse
the length squared plus the width squared equals the diagonal squared
the square of √101 is 101
101 is the sum of two perfect squares according to the Pythagorean Theorem
101 can be written...

1 7/16 as a decimal is 1.4375
one solution is to divide 16 into 7.0000 to get .4375
another solution is the following...
7/16=7/(2*2*2*2)=(7*5*5*5*5)/(2*2*2*2*5*5*5*5)=4375/10,000=0.4375
put the whole number 1 with the decimal part to get 1.4375

distance=rate*time
d=r*t
d=r*20 for the car
d=(r+10)*16 for the bus
equate the two right sides because they are both equal to d
20r=16(r+10)
20r=16r+160
20r-16r=160
4r=160
r=160/4
r=40 mph for the car
r+10=50 mph for the bus
distance=40*20=800...

use the Pythagorean Theorem
a2+b2=c2
let a=the distance from A to B which is the unknown
let b=the distance from B to Sam which is 1300
let c=the distance from A to Sam which is 1700
(1700)2=(1300)2+a2
2,890,000=1,690,000+a2
2,890,000-1,690,000=a2
1,200,000=a2
take...

n=# of nickels
q=# of quarters
$12 is 1200 cents
5n+25q=1200
n=q
substitute q for n or n for q
5q+25q=1200
30q=1200
q=1200/30
q=40 quarters and therefore n=40 nickels
40 quarters is $10 and 40 nickels is $2, therefore you have $12

n=the number
n-5
3(n-5)
2n
2n+3
3(n-5)=2n+3
3n-15=2n+3
3n-2n=15+3
n=18 (answer)

the sample space is as follows for the 2 dice
11,12,13,14,15,16
21,22,23,24,25,26
31,32,33,34,35,36
41,42,43,44,45,46
51,52,53,54,55,56
61,62,63,64,65,66
double 5's occur only once in the sample space of 36 outcomes
the probability is 1/36
36 rolls 1 double 5
72...

d=rt
1096=(r+w)*2
948=(r-w)*2
divide both sides by 2 in both equations
548=r+w
474=r-w
add
1022=2r
r=1022/2
r=511 mph (speed of the plane)
548=511+w
548-511=w
w=37 mph (speed of the wind)

use the quadratic formula where a=1, b=-1, and c=1
x^2-x+1
[1±√(1-4)]/2
[1±√-3]/2
[1+i√3]/2 and [1-i√3]/2, two imaginary roots

1*1=1
2*2=4
3*3=9
4*4=16
5*5=25
6*6=36
7*7=49
8*8=64 (8 feet is the answer)
A=s^2
64=s^2
s=√64
s=8 feet

x+(x+2)+(x+4)-25=2(x+2)
3x+6-25=2x+4
3x-19=2x+4
3x-2x=19+4
x=23
x+2=25
x+4=27