Answer:
It will take 11 robots to do the same job as the 15 humans
Explanation:
Given:
<em>Workers in use = 15</em>
<em>Each worker can move an average of 15 boxes per minute.</em>
<em>A robot has been built that can move an average of 21 boxes per minute</em>
15 worker would move:
15 * 15 boxes = 225 boxes per minute.
The number of robots it will take to move 225 boxes is:
225/21 = 10.7
It will take 11 robots to do the same job as the 15 humans
Answer:
The average number of tornado's in December is 22 and the average number of tornado's in June is 226
Step-by-step explanation:
<u><em>The complete question is</em></u>
The average number of tornado's in June is 16 less than 11 times the average number of tornado's in December. If the difference between the average number of tornado's in June and December is 204,determine the average number of tornado's in December and June.
Let
x ----> the average number of tornado's in June
y ----> the average number of tornado's in December
we know that
---> equation A
----> equation B
solve the system by substitution
substitute equation A in equation B
solve for y
Find the value of x
---->
therefore
The average number of tornado's in December is 22 and the average number of tornado's in June is 226
Algebraic properties can be applied in any mathematical equation.
<h3>How to explain the algebraic property?</h3>
There are several algebraic properties; they include:
- Distributive property
- Additive property
- Inverse property
- Commutative property
- And so on
All these properties can be applied in a mathematical equation.
An instance is as follows:
3(x + 2) = 18
<u>Method 1</u>
Apply the distributive property
3x + 6 = 18
Apply the subtraction property of equality
3x = 12
Apply the division property of equality
x = 4
<u>Method 2</u>
Apply the division property of equality
x + 2 = 6
Apply the subtraction property of equality
x = 4
Read more about mathematical properties at:
brainly.com/question/723406
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Answer:
Step-by-step explanation:
Answer: The min value of Q is Q = 84 and it happens when x = 4 and y = 3
===========================================================
Explanation:
x+y = 7 turns into y = 7-x after subtracting x from both sides
Replace y with 7-x in the other equation to get
Q = 3x^2 + 4y^2
Q = 3x^2 + 4( y )^2
Q = 3x^2 + 4(7-x)^2
Q = 3x^2 + 4(49 - 14x + x^2)
Q = 3x^2 + 196 - 56x + 4x^2
Q = 7x^2 - 56x + 196
We have a function with one variable. Graphing 7x^2-56x+196 produces a parabola in which the vertex point is what we're after
Anything in the form p(x) = ax^2+bx+c will have a vertex (h,k) such that
h = -b/(2a)
k = p(h)
Let's find the x coordinate of the vertex
h = -(-56)/(2*7)
h = 4
Use this to find the y coordinate of the vertex
k = p(h)
p(x) = 7x^2-56x+196
p(h) = 7h^2-56h+196
p(4) = 7(4)^2-56(4)+196
p(4) = 84
The vertex is the lowest point in this case (since a = 7 is positive) and the vertex is (4,84)
Therefore, the minimum value of Q is Q = 84 and this happens when x = 4 and y = 3. Recall that y = 7-x.
We can see that,
Q = 3x^2 + 4y^2
Q = 3(4)^2 + 4(3)^2
Q = 3(16) + 4(9)
Q = 48 + 36
Q = 84
Which helps us verify we have the right Q value.