Answer:
2.0%
Step-by-step explanation:
The probability of two events happening in the sequence is calculated by multiplying the probability of each event happening separately by one another. Since there are a total of 7 letters in this word then the probability of choosing one letter correctly is 
. Since the first letter is replaced before choosing the second letter the probability remains the same. Therefore, the sequence would be the following...
= 0.020164 or 2.0%
This is an independent scenario because it does not depend on any external factors and under these circumstances the percentage will remain the same.
Let the lengths of the east and west sides be x and the lengths of the north and south sides be y. the dimensions you want are therefore x and y.
The cost of the east and west fencing is $4*2*x; the cost of the north and south fencing is $2*2*y. We have to put in that "2" because there are 2 sides that run from east to west and 2 sides that run from north to south.
The total cost of all this fencing is $4(2)(x) + $2(2)(y) = $128. Let's reduce this by dividing all three terms by 4: 2x + y = 32.
Now we are to maximize the area of the vegetable patch, subject to the constraint that 2x + y = 32. The formula for area is A = L * W. Solving 2x + y = 32 for y, we get y = -2x + 32.
We can now eliminate y. The area of the patch is (x)(-2x+32) = A. We want to maximize A.
If you're in algebra, find the x-coordinate of the vertex of this quadratic equation. Remember the formula x = -b/(2a)? Once you have calculated this x, subst. your value into the formula for y: y= -2x + 32.
Now multiply together your x and y values to obtain the max area of the patch.
If you're in calculus, differentiate A = x(-2x+32) with respect to x and set the derivative equal to zero. This approach should give you the same x value as before; the corresponding y value will be the same; y=-2x+32.
Multiply x and y together. That'll give you the maximum possible area of the garden patch.
Simplify by dividing a common factor (5). 15/24. Check to see if it can be simplified. Repeat (using 3). 5/8. Check to see if it can be simplified. It can't, so the answer is 5/8
All you have to do is plug in the given x values. your first equations would read:
f(-3) = 2^(-3)
f(-2) = 2^(-2)
f(-1) = 2^(-1)
these can be solved by moving decimal points or entering them into a calculator. regardless of the method, your answers are:
f(-3) = 0.002
f(-2) = 0.02
f(-1) = 0.2
so just repeat that process to fill in the rest of your table. to graph it, you'll use them as normal (x, y) points:
(-3, 0.002)
(-2, 0.02)
(-1, 0.2)
the graph might be a little difficult, working with such small values, but precision isn't totally important--0.002 will be super close to 0, 0.02 will be slightly further, 0.2 will be slightly further. the smaller values don't matter as much graphically and you'll recognize the graph of a growing exponential as you graph more of the table.
