Answer:
Step-by-step explanation:
First what we must do is rewrite the table to find a solution:
0.25^x −0.75x+1
64 3.25
16 2.5
4 1.75
1 1
0.25 0.25
0.0625 −0.5
0.015625 −1.25
We see where the values of the function are the same:
x = 0 (1)
x = 1 (0.25)
answer:
x = 0
x = 1
107 m
Step-by-step explanation:
Step 1:
Here the microscope magnifies by 10 times.
The initial length is 10.7 m
Step 2:
Let the object be magnified by 10 times . Then, 10 × 10.7 = 107
Answer:
132
Step-by-step explanation:
Let x represent the amount of silk-screened shirts Joel sold:
176 = x + 3x
176/4 = x
44 = x
tie dyed shirts = 3x
= 3 * 44
= 132
Answer:
The probability of winning directly is, as you calculated, 8/36, and the probability of losing directly is (1+2+1)/36=4/36.
For the remaining cases, you need to sum over all remaining rolls. Let p be the probability of rolling your initial roll, and q=6/36=1/6 the probability of rolling a 7. Then the probability of rolling your initial roll before rolling a 7 is p/(p+q), and the probability of rolling a 7 before rolling your initial roll is q/(p+q). Thus, taking into account the probability of initially rolling that roll, each roll that doesn't win or lose directly yields a contribution p2/(p+q) to your winning probability.
For p=5/36, that's
(536)25+636=2511⋅36,
and likewise 16/(10⋅36) and 9/(9⋅36) for p=4/36 and p=3/36, respectively. Each of those cases occurs twice (once above 7 and once below), so your overall winning probability is
836+236(2511+1610+99)=244495=12−7990≈12−0.007.
Step-by-step explanation:
Suppose you throw a 4 and let p(4) your winning probability. At your next roll you have a probability 3/36 of winning (you throw a 4), a probability 6/36 of losing (you throw a 7) and a probability 27/36 of repeating the whole process anew (you throw any other number). Then:
p(4)=336+2736p(4),so thatp(4)=13.
Repeat this reasoning for the other outcomes and then compute the total probability of winning as:
ptot=836+336p(4)+436p(5)+…
