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Anon25 [30]
3 years ago
14

The box shown is used to ship miniature dice with side lengths of

Mathematics
2 answers:
My name is Ann [436]3 years ago
7 0
The answer to this is b
yawa3891 [41]3 years ago
7 0

Answer:

the answer is c i just took the test .

Step-by-step explanation:

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How many solutions does the equation have, x1 + x2 + x3 = 10 , where x1 , x2, and x3 are non-negative integers?
MAVERICK [17]

Non-negative integers are positive integers or zero.

1. When x_1=0, then there are such possible cases for x_2 and x_3:

  • x_2=0,\ x_3=10;
  • x_2=1,\ x_3=9;
  • x_2=2,\ x_3=8;
  • x_2=3,\ x_3=7;
  • x_2=4,\ x_3=6;
  • x_2=5,\ x_3=5;
  • x_2=6,\ x_3=4;
  • x_2=7,\ x_3=3;
  • x_2=8,\ x_3=2;
  • x_2=9,\ x_3=1;
  • x_2=10,\ x_3=0.

In total 11 solutions for x_1=0.

2. For x_1=1, there are such possible cases for x_2 and x_3:

  • x_2=0,\ x_3=9;
  • x_2=1,\ x_3=8;
  • x_2=2,\ x_3=7;
  • x_2=3,\ x_3=6;
  • x_2=4,\ x_3=5;
  • x_2=5,\ x_3=4;
  • x_2=6,\ x_3=3;
  • x_2=7,\ x_3=2;
  • x_2=8,\ x_3=1;
  • x_2=9,\ x_3=0.

In total 10 solutions for x_1=1.

3. This process gives you

  • for x_1=2 - 9 solutions;
  • for x_1=3 - 8 solutions;
  • for x_1=4 - 7 solutions;
  • for x_1=5 - 6 solutions;
  • for x_1=6 - 5 solutions;
  • for x_1=7 - 4 solutions;
  • for x_1=8 - 3 solutions;
  • for x_1=9 - 2 solutions;
  • for x_1=10 - 1 solution.

4. Add all numbers of solutions:

11+10+9+8+7+6+5+4+3+2+1=66.

Answer: there are 66 possible solutions (with non-negative integer variables)

8 0
3 years ago
Read 2 more answers
If i graduated high school in 1990 what year was it when i was in 4th grade
Tems11 [23]
The school year would be 1981-1982
8 0
3 years ago
Please help meeeee!!!!!!! complete the equation below. 5x+5x=10x____
saul85 [17]
5x5 - 10x = 0


5x5 - 10x = 5x • (x4 - 2)
5 0
3 years ago
Given the trinomial 5x2 − 2x − 3, predict the type of solutions.
Contact [7]
5x^2 - 2x - 3 

5x^2+3x-5x-3 

x(5x+3)-(5x+3) 

(5x+3)(x-1) 

Factoring is the only solution.
5 0
3 years ago
The radius of the cone is 1.25 inches, and its height is 2.75 inches. If the diameter of the bubble gum ball is 0.5 inches, what
nasty-shy [4]
<h2>Explanation:</h2><h2></h2>

The volume of a cone can be found as:

V=\frac{1}{3}\pi r^2 h \\ \\ \\ Where: \\ \\ V:Volume \\ \\ r:radius \ of \ base \\ \\ h:height

Given the radius and height, we can find the volume of the cone:

V=\frac{1}{3}\pi r^2 h \\ \\ V=\frac{1}{3}\pi (1.25)^2(2.75) \\ \\ V=\frac{1}{3}\pi(1.5625)(2.75) \\ \\ V\approx 4.5in^3

The volume of a sphere is:

V=\frac{4}{3}\pi r^3 \\ \\ \text{Each gum ball has a diameter of 0.5in, so the radius is:} \\ \\ r=\frac{0.5}{2}=0.25in

So, for each gum ball the volume is:

V=\frac{4}{3}\pi r^3 \\ \\ V=\frac{4}{3}\pi (0.25)^3 \\ \\ V=0.065in^3

Therefore, the he closest approximation of the volume of the cone that can be filled with flavored ice is:

4.5-0.065=4.43in^3

Conclusion: The volume of the cone that can be filled with flavored ice is 4.43 cubic inches.

3 0
3 years ago
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