9514 1404 393
Answer:
- kayak: 12 mph
- current: 2 mph
Step-by-step explanation:
Bunny's rate downstream is ...
(70 mi)/(5 h) = 14 mi/h = k + c
Bunny's rate upstream is ...
(70 mi)/(7 h) = 10 mi/h = k -c
The kayak speed is the average of these:
(14 mi/h +10 mi/h)/2 = ((k +c) +(k -c))/2
(24 mi/h)/2 = 2k/2
12 mi/h = k
Then the current speed is ...
c = k -10 = 12 -10 = 2 . . . . mi/h
The still-water speed of the kayak is 12 mi/h; the speed of the current is 2 mi/h.
_____
<em>Additional comment</em>
World-class kayak paddlers will not maintain a speed more than 8 mi/h for that distance and/or time (140 miles in 12 hours). Bunny is exceptional.
Answer: See explanation
Step-by-step explanation:
Your question isn't complete but let's help out by giving some values to the question.
Let's say there are 230 students in a school. This number is 15% more than it was last year. Calculate the number of students last year.
Let the number of students last year be x.
Since there's a 15% increase, this implies that (100% + 15%) = 115% of x equals to 230. This will be:
115% of x = 230
115% × x = 230
115/100 × x = 230
1.15x = 230
x = 230/1.15
x = 200
There were 200 students last year.
Just assign the missing values and use the above method and you'll get your answer.
Answer: No, the events are not mutually exclusive
Work Shown:
P(A and B) = P(A) + P(B) - P(A or B)
P(A and B) = 0.51 + 0.79 - 0.66
P(A and B) = 0.64
Since the result is not zero, this means the events are not mutually exclusive.
Mutually exclusive events are ones that cannot happen at the same time. Example: getting a "2" and a "3" on the same roll of a number cube.
Answer:
2(x+5)
Step-by-step explanation:
2 ln 8 + 2 ln y
The first thing we could do is use the distributive property and "take out" the 2.
After we do that, we get
2( ln 8 + ln y)
Here's a cool property of logarithms of any base.
log a + log b = log ab
Note: The bases of the logarithms must be the same for this to work.
Let's apply that property
2 (ln 8 + ln y)
= 2 ln 8y
That could be your answer. If you want to remove the 2, we can use the following property:
a log b = log (a^b)
2 ln (8y)
= ln (8y)^2
= ln (64y^2)
That could be another answer.
Have an awesome day! :)
