All Questions
Lê Quốc Trần Anh Coodinator
04/03/2018 at 04:25
Jacob 05/03/2018 at 02:19
1,
2,
3,
1 + 2 + 3 = 6,
2 + 3 + 6 = 11,
3 + 6 + 11 = 20,
6 + 11 + 20 = 35,
11 + 20 + 35 = 66.
20 + 35 + 66 = 121,
35 + 66 + 121 = 222,
66 + 121 + 222 = 409
The 11th is 409
Lê Quốc Trần Anh selected this answer.
Lê Quốc Trần Anh Coodinator
04/03/2018 at 04:24The first four stages of a dot pattern are shown. How many more dots are in the figure at Stage 47 than in the figure at Stage 27?
Stage 1  1 
Stage 2  4 
Stage 3  9 
Stage 4  16 

Jacob 05/03/2018 at 02:22
The stage ith is \(i^2\)
So the number of dots at stage 47 is more than at the stage 27 is:
\(47^227^2=\left(4727\right)\left(47+27\right)=20.74=1480\)
Lê Quốc Trần Anh selected this answer.
Lê Quốc Trần Anh Coodinator
04/03/2018 at 04:21
ANSWER:
Recall that a number is divisible by 4 if the twodigit number formed by the tens and ones digits is divisible by 4. Using the digits 1, 2, 3, 4 and 5, the following twodigit multiples of four can be formed: 12, 24, 32 and 52. There are 5 × 4 = 20 permutations of two digits chosen from the digits 1, 2, 3, 4 and 5. Therefore, the probability that the fivedigit number is divisible by 4 is 4/20 = 1/5.
Lê Quốc Trần Anh Coodinator
04/03/2018 at 04:19
ANSWER:
Multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, … . It appears that every fifth multiple of 3 is also a multiple of 5. The percent probability that a randomly selected multiple of 3 is also a multiple of 5 is 1/5 = 20%.
Lê Quốc Trần Anh Coodinator
04/03/2018 at 04:09
ANSWER:
After that circuit is turned on, lights A and B will blink together every 55 seconds. Lindsey sees light A blink alone. Because light B blinks once every 11 seconds, and it did not blink this time, it will blink in one of the 10 following seconds, with equal lihood. In 5 of those cases, it will blink before or at the same time as light A; and in the other 5 cases, light A will blink alone first. Therefore the probability that the next light to blink will be light A blinking alone is 5/10 = 0.50 = 50%. Alternative solution: Whether or not light B blinks with A, A will always blink alone twice before the next time light B blinks. When she sees light A blink alone, it could be either the first or the second time, so the probability that it’s the first time is 50%.
Lê Quốc Trần Anh Coodinator
04/03/2018 at 04:09
ANSWER:
The probability that the nickel comes up heads is 1/2. The probability that one or more of the other two coins comes up heads is 3/4. The probability that at least two heads come up, with one of them being the nickel, is 1/2 × 3/4 = 3/8.
Lê Quốc Trần Anh Coodinator
04/03/2018 at 04:08
ANSWER:
The probability of pulling out two green socks is 2/5 × 1/4 = 1/10. The probability of pulling out two blue socks is 3/5 × 2/4 = 3/10. The probability, therefore, of randomly pulling out a matching pair of socks is 1/10 + 3/10 = 4/10 = 2/5.
Lê Quốc Trần Anh Coodinator
04/03/2018 at 04:08
ANSWER:
Danya can get a total of 10 with two or three chips if the first two chips drawn are 4 and 6, which can occur in 2 ways, or if the first three chips drawn are 2, 3 and 5, which can occur in 6 ways. There are 5 × 4 = 20 ways to randomly select two chips, and there are 5 × 4 × 3 = 60 ways to randomly select three chips. The probability that Danya’s total will equal 10 at some point is 2/20 + 6/60 = 1/10 + 1/10 = 2/10 = 0.2
Lê Quốc Trần Anh Coodinator
04/03/2018 at 04:07
ANSWER:
There are 8 situations of the cup. Only two of the cups contain three or more dimes. Therefore, the probability that Max randomly selects one of these cups is 2/8 = 1/4.
Lê Quốc Trần Anh Coodinator
04/03/2018 at 04:07
ANSWER:
In a standard deck of 52 playing cards, the red number cards greater than 6 are the 7, 8, 9 and 10 in the suits of diamonds and hearts. That’s a total of 8 cards. The percent probability that Perta randomly selects one of these 8 cards, then, is 8/52 ≈ 15.38%.