Answer:
The speed of the current is 2 miles per hours
Step-by-step explanation:
Given as :
The speed of motorboat = x = 15 miles per hour
The time taken by motorboat trip upstream = 51 minutes
The time taken by motorboat trip downstream = 39 minutes
Let The speed of the current = y miles per hour
Let The total distance cover = A miles
So ,
Speed = 
So, x - y = 
I.e 15 - y =
And x + y = 
I.e 15 + y =
= 
I.e = 
Or, 17 × (x - y) = 13 × (x + y)
Or, 17 x - 17 y = 13 x + 13 y
Or, 17 x - 13 x = 13 y + 17 y
Or, 4 x = 30 y
Now, ∵ x = 15 miles per hour
So, 4 × 15 = 30 y
Or, y = 
∴ y = 2 miles per hour
Hence The speed of the current is 2 miles per hours Answer
Answer:
0.024
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean 
and standard deviation 
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean and standard deviation 
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean 
and standard deviation 
Suppose the true proportion of high school juniors who skateboard is 0.18.
This means that 
Samples of 250 high school juniors are taken
This means that 
By how much would their sample proportions typically vary from the true proportion?
This is the standard error, so:
So 0.024 is the answer.
Area is equal to length times width. The perimeter (the amount of rope) has to equal twice the length added to twice the width so we're left with:
A = l * w
200 = 2l + 2w
solve for either l or w
l = 100 - w
plug into the area equation to get one equation with two variables
A = w(100 - w)
A = -w^2 + 100w
take the derivative
A' = -2w + 100
set the derivative equal to zero
0 = -2w + 100
2w = 100
w = 50
This is the width that maximizes the area
with a width of 50, the length must also be 50 to have a perimeter of 200
therefore, they can rope up to 50 * 50 = 2500 ft^2
This has infinitely many solutions if that is all that the question asked...
2x+3y=12
3y=-2x+12
y=(-2x+12)/3
So for any value of x you choose it will give you the corresponding y value that makes your original equation true.
Let's say x = 15% copper and y = 75% copper
We need 120 kg of a 51% copper alloy.
A) x + y = 120
B) .15x + .75y = 61.2 (which is 120*.51%)
Multiplying A by -.15
A) -.15x -.15y = -18 Then add this to B
.60y = 43.2
y = 72
x = 48
I'd suggest you look at this web page
http://www.1728.org/mixture.htm
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Double Check
48 kilograms of .15% copper = 7.2 kg copper
72 kilograms of .75% copper = 54 kg kg copper
So we have 61.2 kg of copper in 120 kg
61.2 / 120 = .51 = 51%
