Answer:
[ry, yr, gy, yg, rg, gr]-Any three picks from this sample space.
Step-by-step explanation:
-The bag contains exactly
marbles.
-He picks one ball without looking, and chooses a second ball without replacing the first:
- If the first is red, the the second is either yellow or green,
- If the first is a yellow, then the second can be red or green,
- If the first is green, then the second can be a red or yellow.
The sample space of the second pick is therefore:
[ry, yr, gy, yg, rg, gr]
Hence, any three picks from the sample space are correct possible outcomes.
<span> f(x)=4x^8+7x^7+1x^6+
</span>∴<span> f(-2)=4(-2)^8+7(-2)^7+1(-2)^6+1
</span>∴ <span>f(-2)=(4x256) + (7x-128) + (1x64) +1
</span>∴ <span>f(-2)=1024 - 896 + 64 +1
</span>∴ <span>f(-2)= 193</span>
(1) y² + x² = 53
(2) y - x = 5 ⇒ y = x + 5
subtitute (2) to (1)
(x + 5)² + x² = 53 |use (a + b)² = a² + 2ab + b²
x² + 2x·5 + 5² + x² = 53
2x² + 10x + 25 = 53 |subtract 53 from both sides
2x² + 10x - 28 =0 |divide both sides by 2
x² + 5x - 14 = 0
x² - 2x+ 7x - 14 = 0
x(x - 2) + 7(x - 2) = 0
(x - 2)(x + 7) = 0 ⇔ x - 2 = 0 or x + 7 = 0 ⇔ x = 2 or x = -7
subtitute the values of y to (2)
for x = 2, y = 5 + 2 = 7
for x = -7, y = 5 + (-7) = 5 - 2 = 3
Answer: x = 2 and y = 7 or x = -7 and y = 3