Part A:
The probability that all three strangers have their birthdays on a Wednesday is calculated as
Part B:
The probability that the birthdays of the three individuals fall on distinct days throughout the week is calculated as
Part C:
The probability that none of the three have their birthdays on a Saturday is determined by
The likelihood that at least one trip occurs before Isabella's birth is 0.7627.
Step-by-step explanation:
In this scenario, Isabella has invented a time machine, but she lacks control over where she travels. Each use of the device holds a 0.25 probability of leading her to a time preceding her birth. Over the initial year of trials, she operates her machine 5 times. If we assume every journey has an equal chance of going back in time, we can calculate the odds that at least one of these trips occurs before she was born. Here's the calculation:
The probability of traveling to a time prior to her birth is 0.25.
The chance of not traveling back in time, given that the machine is used 5 times:
⇒ 
⇒ 
⇒ 
The probability that at least one trip goes before Isabella's birth is equal to 1 minus the probability of not traveling back to that period:
⇒ 
⇒ 
Consequently, the chance that at least one trip travels before Isabella's birth is 0.7627.
It includes the procedures to reach that specific point.
Some of them are arranged incorrectly.
I will label them with letters.
The sequence is:
A: 2x+5=19
B: 2x+5-5=19-5
C: 2x=14
D: 2x/2=14/2
E: x=7
A: initial condition
B: we subtracted 5 from both sides based on the subtraction property of equality
C: perform the subtraction
D: applying the division property of equality (dividing both sides by 2)
E: result of the division
To tackle the problem, the general approach is to convert all measurements into the smallest unit possible.
a. 3 km 9 hm 9 dam 19 m + 7 km 7 dam
3,000 m 900 m 90 m 19 m + 7,000 m 70 m = 4,009 + 7,070 = 11,079 m
b. 5 sq.km 95 ha 8,994 sq.m + 11 sq. km. 11 ha 9,010 sq. m.
5,000,000 sq m 95,0000 sq m 8,994 sq m + 11,000,000 sq m 110,000 sq
9,010 sq m
5,103,994 sq m + 11,119,010 sq m = 16,223,004 sq m
c. 44 m - 5 dm
44 m - 0.5 m = 43.5 m
d. 73 km 47 hm 2 dam - 11 km 55 hm
73,000 m 4,700 m 20 m - 11,000 m 5,500 m
77,720 m - 16,500 m = 61,220 m
