Answer:
The 'constant of proportionality k' DOES NOT remain constant for all the points in the table.
Therefore, the table DOES NOT represent a proportional relationship between X and Y.
Step-by-step explanation:
We know that when y varies directly with x, we get
y ∝ x
y = kx
k = y/x
where k is called the 'constant of proportionality'.
Given the table
x 0 5 10 15
y 2 17 32 47
Let us calculate the k value for all the points
FOR (0, 2)
k = y/x
substitute x = 0, and y = 2
k = 2 / 0 = ∞
FOR (5, 17)
k = y/x
substitute x = 5, and y = 17
k = 17/5
k = 3.4
FOR (10, 32)
k = y/x
substitute x = 10, and y = 32
k = 32/10
k = 16/5
k = 3.2
FOR (15, 47)
k = y/x
substitute x = 15, and y = 47
k = 47/15
k = 3.1
It is clear that the 'constant of proportionality k' DOES NOT remain constant for all the points in the table.
Therefore, the table DOES NOT represent a proportional relationship between X and Y.
The solution to the binomial expression by using Pascal's triangle is:



<h3>How can we use Pascal's triangle to expand a binomial expression?</h3>
Pascal's triangle can be used to calculate the coefficients of the expansion of (a+b)ⁿ by taking the exponent (n) and adding the value of 1 to it. The coefficients will correspond with the line (n+1) of the triangle.
We can have the Pascal tree triangle expressed as follows:
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
--- --- --- --- --- --- --- --- --- --- --- --- --- --- ---
From the given information:
The expansion of (3x-4y)^11 will correspond to line 11.
Using the general formula for the Pascal triangle:

The solution to the expansion of the binomial (3x-4y)^11 can be computed as:



Learn more about Pascal's triangle here:
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36 -81.9 - 45.9 I keep getting -45.9
Answer:
Ben
Step-by-step explanation:
Ben has an absolute advantage in making of pizza because he can make five pizzas in one hour which is a greater quantity compared to Sam that makes four pizzas in one hour.
Answer:
C
Step-by-step explanation:
write an equation for the costs:
if x is the number of sodas
and y is the number of waters
2.75x + 2y <= 15
(<= is less than or equal to)
if we substitute 3 for y
we get 2.75x + 2(3) <= 15
2.75x + 6 <= 15
2.75x <= 9
9 / 2.75 = 3.2727
however, you cannot buy part of a soda
so, round to 3
you also cannot buy negative sodas
so, the answer is C