The probability of picking a green marble the first time is 3/20 and the probability of picking a yellow marble the second time is 8/20.
probabilities are heavily related to percents so it would make sense that the probability of picking a color would be the number of that color divided by the total number.
note that it is really important that the problem said that the marble was replaced. If the marble was not replaced, the probability of picking a yellow marble the second time would be 8/19 if the first marble picked was not a yellow one.
I hope this helps.
9514 1404 393
Answer:
x = 3
Step-by-step explanation:
It is convenient to remember the ratios of side lengths of these "special triangles."
The side ratios of ΔABC are 1 : 1 : √2, so BC = AC/√2 = 6.
The side ratios of ΔBCD are 1 : √3 : 2, so BD = BC/2 = 6/2 = 3.
The value of x is 3.
9514 1404 393
Answer:
- Translate P to E; rotate ∆PQR about E until Q is coincident with F; reflect ∆PQR across EF
- Reflect ∆PQR across line PR; translate R to G; rotate ∆PQR about G until P is coincident with E
Step-by-step explanation:
The orientations of the triangles are opposite, so a reflection is involved. The various segments are not at right angles to each other, so a rotation other than some multiple of 90° is involved. A translation is needed in order to align the vertices on top of one another.
The rotation is more easily defined if one of the ∆PQR vertices is already on top of its corresponding ∆EFG vertex, so that translation should precede the rotation. The reflection can come anywhere in the sequence.
__
<em>Additional comment</em>
The mapping can be done in two transformations: translate a ∆PQR vertex to its corresponding ∆EFG point; reflect across the line that bisects the angle made at that vertex by corresponding sides.
Answer:
The estimated distance is 8.1cm.
The actual distance is 8.106cm.
Step-by-step explanation:
Given that the Pythogorean Theorem, c² = a² + b². Then substitute the following values into the formula :
Let a = 5.1cm,
Let b = 6.3cm,
So, 4/3 - 2i
4/3 - 2i = 12/13 + i8/13
multiply by the conjugate:
3 + 2i/3 + 2i
= 4(3 + 2i)/(3 - 2i) (3 + 2i)
(3 - 2i) (3 + 2i) = 13
(3 - 2i) (3 + 2i)
apply complex arithmetic rule: (a + bi) (a - bi) = a^2 + b^2
a = 3, b = - 2
= 3^2 + (- 2)^2
refine: = 13
= 4(3 + 2i)/13
distribute parentheses:
a(b + c) = ab + ac
a = 4, b = 3, c = 2i
= 4(3) + 4(2i)
Simplify:
4(3) + 4(2i)
12 + 8i
4(3) + 4(2i)
Multiply the numbers: 4(3) = 12
= 12 + 2(4i)
Multiply the numbers: 4(2) = 8
= 12 + 8i
12 + 8i
= 12 + 8i/13
Group the real par, and the imaginary part of the complex numbers:
Your answer is: 12/13 + 8i/13
Hope that helps!!!
