<h3>
Answer: f(x) = x + 13 </h3>
This is the same as y = x+13
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Explanation:
Let's find the slope
I'll use the first two rows as the (x1,y1) and (x2,y2) points
m = (y2-y1)/(x2-x1)
m = (19-18)/(6-5)
m = 1/1
m = 1
The slope is 1.
Now apply the point slope formula and solve for y
y - y1 = m(x - x1)
y - 18 = 1(x - 5)
y - 18 = x - 5
y = x-5 + 18
y = x + 13
f(x) = x + 13 is the final answer
As a check, note how something like x = 5 leads to...
f(x) = x+13
f(5) = 5+13 ... replace x with 5
f(5) = 18
We see that x = 5 leads to f(x) = 18. That verifies the first row. I'll let you check the remaining three rows.
The equation y = x+13 has slope 1 and y intercept 13.
For the answer to the question above,
1. If we let x as the side of the square cut-out, the formula for the capacity (volume) of the food dish is:
V = (12 - 2x)(8 - 2x)(x)
V = 96x - 40x^2 + 4x^3
To find the zeros, we equate the equation to 0, so, the values of x that would result to zero would be:
x = 0, 6, 4
2. To get the value of x to obtain the maximum capacity, we differentiate the equation, equate it to zero, and solve for x.
dV/dx = 96 - 80x + 12x^2 = 0
x = 5.10, 1.57
The value of x that would give the maximum capacity is x = 1.57
3. If the volume of the box is 12, then the value of x can be solved using:
12 = 96x - 40x^2 + 4x^3
x = 0.13, 6.22, 3.65
The permissible value of x is 0.13 and 3.65
4. Increasing the cutout of the box increases the volume until its dimension reaches 1.57. After that, the value of the volume decreases it reaches 4.
5. V = (q -2x) (p - 2x) (x)
Answer:
Step-by-step explanation:
x is the cherries eaten
Answer:
144
Step-by-step explanation:
Answer:
A) The relative frequencies in the table are reasonably close; C) The relative frequency of rolling an even number is 0.51.
Step-by-step explanation:
The relative frequencies given are at most 0.02 apart. This means they are reasonably close.
The theoretical probability for each outcome would be 1/4, or 0.25; this means the theoretical probability of rolling an even number would be 0.50, not 0.51.
However, the relative frequency of rolling an even number would be 0.24+0.27 = 0.51.
Since the relative frequencies are reasonably close, the number cube is likely to be fair.
