Answer:
I kinda did a lil of this in my head so i might not be 100% correct, but i would say the bigger group is 20 and the smaller group is 10
Answers:
- Total equation: x+y = 80
- Legs equation: 2x+4y = 248
- How many ducks? 36
- How many cows? 44
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Further explanation:
- x = number of ducks
- y = number of cows
x+y = 80 is the total equation (ie the head count equation) since we assume each animal has 1 head, and there are 80 heads total.
That equation can be solved to y = 80-x after subtracting x from both sides.
The legs equation is 2x+4y = 248 because...
- 2x = number of legs from all the ducks only
- 4y = number of legs from all the cows only
- 2x+4y = total number of legs from both types of animals combined
We're told there are 248 legs overall, so that's how we ended up with 2x+4y = 248
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Let's plug y = 80-x into the second equation and solve for x.
2x+4y = 248
2x+4( y ) = 248
2x+4( 80-x ) = 248
2x+320-4x = 248
-2x+320 = 248
-2x = 248-320
-2x = -72
x = -72/(-2)
x = 36
There are 36 ducks
Now use this x value to find y
y = 80-x
y = 80-36
y = 44
There are 44 cows.
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Check:
36 ducks + 44 cows = 80 animals total
36*2 + 44*4 = 72 + 176 = 248 legs total
The answers are confirmed.
Answer: She cycles 25% of the time
Step-by-step explanation:
From the question, Sally walks 15% of the time.
She drives 3/5 of the time.
We then convert 3/5 to percentage.
Converting to percentage means multiplying by a factor of 100.
Hence, Sally drives 3/5*100 = 60% of the time.
If Sally walks 15% of the time and drives 60% of the time, adding up the percentage time used by these two media of transportation will give us
60% + 15% = 75%
Hence if she cycles for the remainder of the time, expressing it as percentage would mean subtracting the time used in other means by 100%
Hence it will be 100% - 75% = 25%
5% of 200 is 10, after six months, so total of $60? not sure though.
Answer:
D) Yes. The five trials are independent, have only two outcomes, and have the same P(success); n = 5, r = 2, p = 1/6.
Step-by-step explanation:
The Number of boxes = 6
Box containing a prize = 1
Probability of success, p = box containing a price / number of boxes = 1 /6
Number of trials = 5
Probability of success on exactly 2 trials, r = 2
Hence,
P(r = 2) = nCr * p^r * (1-p)^(n-r)
n = 5 ; r = 2 ; p = 1/6
Using a binomial probability calculator :
P(r = 2) = 0.1608
