We try to represent the data in segments from 0 to 20.
<span>The length of the line segment along the number line from 0 to 5 is 5 - 0 = 5 units. The length of the line segment along the number line from 20 to 5 is 20 - 5 = 15 units. If you were to randomly throw a dart on this number line, then the probability of landing in the shaded region is 15/20 = 3/4 or 75%</span>
Answer:
The distance between the two given complex numbers = 9
Step-by-step explanation:
<u><em>Explanation</em></u>:-
<u><em>Step(i):</em></u>-
Given Z₁ = 9 - 9 i and Z₂ = 10 -9 i
Let A and B represent complex numbers Z₁ and Z₂ respectively on the argand plane
⇒ A = Z₁ = x₁ +i y₁ = 9 - 9 i and
B = Z₂ = x₂+ i y₂ = 10 -9 i
Let (x₁ , y₁) = ( 9, -9)
(x₂, y₂) = (10, -9)
<u>Step(ii)</u>:-
<em>The distance between the two points are </em>
A B = 
A B = 
AB = 
<em> AB = √81 = 9</em>
<u><em>Conclusion:-</em></u>
The distance between the two given complex numbers = 9
<u><em></em></u>
Answer:
The volume of the solution with 20% acid is 27 gallons and the one with 10% acid is 18 gallons
Step-by-step explanation:
Myra needs to mix "x" gallons of the solution with 20% and "y" gallons of the solution with 10%. The volume of the final solution must be 45 gallons, therefore:
x + y = 45
The concentration of acid of the final solution is:
0.2*x + 0.1*y = 45*0.16
0.2*x + 0.1*y = 7.2
Therefore we have a system of equation:
x + y = 45
0.2*x + 0.1*y = 7.2
We need to multiply the first equation by -0.1:
-0.1*x -0.1*y = -4.5
0.2*x + 0.1*y = 7.2
We now sum both equation:
0.1*x = 2.7
x = 2.7/0.1 = 27 gallons
y = 45 - 27 = 18 gallons
You would have eaten 1/6 of the serving.
45. 3/5 is nearer to 1/2
46. 1 2/6 is nearer to 1 1/2. 1 2/6 can be simplified to 1 1/3
47. 12/10 is nearer to 1 1/2. 12/10 can be simplified to 1 2/10 and further simplified to 1 1/5.
48. 2/18 is nearer to 0. 2/18 can be simplified to 1/9 or 0.11
49. 1 8/10 is nearer to 1 1/2. 1 8/10 can be simplified to 1 4/5
50. 1 12/15 is nearer to 1 1/2. 1 12/15 can be simplified to 1 4/5.
