Response:
Detailed explanation:
The final result is 3 /8/33.
step by step breakdown
Initially, we write:
x
=
3
.
¯¯¯¯
24
After that, we will multiply each side by
100
leading to:
100
x
=
324
.
¯¯¯¯
24
Subsequently, we will subtract the first equation from the second equation:
100
x
−
x
=
324
.
¯¯¯¯
24
−
3
.
¯¯¯¯
24
We can then solve for
x
in the following manner:
100
x
−
1
x
=
(
324
+
0
.
¯¯¯¯
24
)
−
(
3
+
0
.
¯¯¯¯
24
)
(
100
−
1
)
x
=
324
+
0
.
¯¯¯¯
24
−
3
−
0
.
¯¯¯¯
24
99
x
=
(
324
−
3
)
+
(
0
.
¯¯¯¯
24
−
0
.
¯¯¯¯
24
)
99
x
=
321
+
0
99
x
=
321
99
x
99
=
321
99
99
x
99
=
3
×
107
3
×
33
x
=
3
×
107
3
×
33
x
=
107
33
Next, we convert this improper fraction to a mixed numeral:
x
=
107
33
=
99
+
8
33
=
99
33
+
8
33
=
3
+
8
33
=
3
8
33
3
.
¯¯¯¯
=
3
8
33
Answer:
a) Ann has a 1/3 chance of winning in the first round
b) The chance of Ann winning for the first time in the fourth round is 8/81
c) The probability that Ann's first win occurs after the fourth round is 16/81
Step-by-step explanation:
a) Each strategy is played with a probability of 1/3. Given any strategy, there’s a 1/3 chance that Bill will choose the strategy that allows Ann to win. Consequently, the probability of Ann securing a victory in the first round (or any round) is
1/3 * 1/3 + 1/3 * 1/3 + 1/3 * 1/3 = 1/9 + 1/9 + 1/9 = 1/3.
Thus, the likelihood of Ann winning the initial round is 1/3.
b) The chances of Ann winning a round stand at 1/3; therefore, her chances of not winning are 2/3. This must happen three times before her first victory. Thus, the probability that Ann's first win occurs in the fourth round is
(2/3)³ * 1/3 = 8/81.
c) The first victory happens after the fourth round if she remains unsuccessful in the first four rounds, translating to a possibility of (2/3)⁴ = 16/81.
Answer:
Detailed steps:
y – 4 = –1 (x – 2)
y – 7 = –1 (x + 1)
y = –x + 6
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137 paquetes de vasos, aunque el último solo tiene 7 vasos, es necesario para asegurar que no queden sin empacar.
Answer:
The solution yields a number equal to -136.
Step-by-step explanation:
Let x represent the number, leading to the following equation:
x + 2 = 7/8 x - 15
Rearranging gives:
x - 7/8 x = -15 - 2
1/8 x = -17
x = -17 * 8 resulting in -136.
