1
Step-by-step explanation:
Step 1:
Let a coin is flipped. My choice is Heads and my unfavorable becomes Tails.
Here the probability of getting heads is (1/2) and getting tails is (1/2).
Step 2:
Hence, If we add both of it we will get the resultant sum as 1 only.
(1/2) + (1/2) = 1
Answer:
You should graph the lines (0, 0) to (2, 120), (2, 120) to (2.5, 120), and (2.5, 120) to (3.5, 150).
Step-by-step explanation:
If we see, for the first part, she drive 60 miles an hour and drives for 2 hours. This means that after 2 hours, she has driven 60 * 2 = 120 miles in 2 hours. Then she spends 30 minutes, or half an hour, no moving forward as she changes the tire. Finally, she drives at 30 miles an hour for an hour. This means she has driven 120 + 30 = 150 miles in total after 3 and a half hours.
Our first line goes from (0, 0) to (2, 120), as thats how far we drove in 2 hours. The next line goes from (2, 120) to (2.5, 120), as she was changing a tire and made no progress. Finally, the last line goes from (2.5, 120) to (3.5, 150), as she drives for another hour at 30 miles an hour.
Answer: the speed of the boat on the lake is 9 mph
Step-by-step explanation:
Let x represent the speed of the boat on the lake or in still water.
The speed of the current in a river is 6 mph. This means that if the boat goes upstream against the speed of the current, its total speed would be (x - 6)mph. If the boat goes downstream against the speed of the current, its total speed would be (x + 6)mph.
Time = distance/ speed
Every day, his route takes him 22.5 miles each way against the current and back to his dock, and he needs to make this trip in a total of 9 hours. This means that the time taken to travel upstream is
22.5/(x - 6). The time taken to travel downstream is
22.5/(x + 6)
Since the total time is 9 hours, it means that
22.5/(x - 6) = 22.5/(x + 6)
Cross multiplying, it becomes
22.5(x + 6) + 22.5(x - 6) = 9
Multiplying through by (x + 6)(x - 6), it becomes
22.5(x - 6) + 22.5(x + 6) = 9[(x + 6)(x - 6)]
22.5x - 135 + 22.5x + 135 = 9(x² - 6x + 6x - 36)
22.5x + 22.5x = 9x² - 324
9x² - 45x - 324 = 0
Dividing through by 9, it becomes
x² - 5x - 36 = 0
x² + 4x - 9x - 36 = 0
x(x + 4) - 9(x + 4) = 0
x - 9 = 0 or x + 4 = 0
x = 9 or x = - 4
Since the speed cannot be negative, then x = 9
bearing in mind that
standard form for a linear equation means
• all coefficients must be integers, no fractions
• only the constant on the right-hand-side
• all variables on the left-hand-side, sorted
• "x" must not have a negative coefficient
so, let's multiply both sides by the LCD of 7 to do away with the denominators
Answer:
27
Step-by-step explanation:
add 5+5+7+6+4
