Given:
Let x be the whole amount inherited.
1/2 * x - invested with Bernie Madoff
1/3 * x - lost due to identity theft
1/8 * x - lost in casino
40,000 - remainder
x - x/2 - x/3 - x/8 = 40,000
LCM:
2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24
3: 3, 6, 9, 12, 15, 18, 21, 24
8: 8, 16, 24,
x * 24/24 = 24x / 24
x/2 * 12/12 = 12x / 24
x/3 * 8/8 = 8x / 24
x/8 * 3/3 = 3x / 24
40,000 * 24/24 = 960,000 / 24
24x/24 - 12x/24 - 8x/24 - 3x/24 = 960,000/24
(24x - 12x - 8x - 3x)/24 = 960,000/24
x/24 = 960,000/24
24 * x/24 = 24 * 960,000/24
x = 960,000
x = 960,000 initial inheritance
x/2 = 960,000/2 = 480,000 invested with Bernie Madoff
x/3 = 960,000/3 = 320,000 lost due to identity theft
x/8 = 960,000/8 = 120,000 lost in the casino
40,000 - remaining amount.
960k - 480k - 320k - 120k = 40k
40k = 40k
Answer: z _> -10
Step-by-step explanation:
1st) reflection over the point G
2nd) a dilation of 1/2 with fixed point G
3rd) a traslation 2 units left and 4 units up
Answer:
A translation of 2 units at right and 5 units down
Step-by-step explanation:
we have
(x,y) -----> (x+2,y-5)
This transformation represent a translation
Remember that
A translation is a type of transformation that moves each point in a figure the same distance in the same direction
That means ----->The translation is 2 units at right and 5 units down
Answer: 34.965%
Step-by-step explanation:
Number of ways of selecting 8 songs from 14 songs = = 14! / [ 8! × (14-8)! ]
= 14! / (8! × 6!)
= 3003
If you listended to exactly four country songs, then you should listen to four pop songs because you listened to 8 songs
Number of ways of selecting 4 country songs from total 8 country songs
= 8! / [ 4! × (8-4)! ]
= 8! / (4! × 4!)
= 70
Number of ways of selecting 4 pop songs from total 6 pop songs
= 6! / [ 4! × (6-4)! ]
= 6! / (4! × 2!)
= 15
Number of ways of playing 4 country songs and 4 pop songs in total 8 songs = 70 × 15
= 1050
So Probability that you listened to exactly four country songs =1050/3003
= 0.34965
= 34.965%
