Answer:
9p⁸ + 12p⁴q⁴ + 4q⁸
Step-by-step explanation:
(3p⁴ + 2q⁴)² ⇒ The square of (3p⁴ + 2q⁴)
Squares are such bases that multiply itself two times.
⇒ (3p⁴ + 2q⁴)(3p⁴ + 2q⁴)
<u>Simplifying the expression using (a + b)(a + b) = (a x a) + (ab) + (ab) + (b²)</u>
⇒ (9p⁸ + 6p⁴q⁴ + 6p⁴q⁴ + 4q⁸)
⇒ (9p⁸ + 12p⁴q⁴ + 4q⁸) = 9p⁸ + 12p⁴q⁴ + 4q⁸
Since we have that the slope is m = 7/9 and the y-intercept is b = 12, we can write the equation of the line in slope-intercept form:
to find three coordinate points, we can use arbitrary values on x to get the y-coordinate. To make things easier, let's use x = 9, 18 and 27:
therefore, the line with slope m = 7/9 and y-intercept 12 passes through the three points (9,19), (18,26) and (27,33)
For all probability exercises, the probability is always
(the number of possible 'successful' results)
divided by
(the total possible number of results).
1). Number of diamonds in the deck = 13
Total cards in the deck = 52.
Probability = (13/52) = 1/4 = 25%
2). Probability of the first one being a diamond = 1/4 .
Now there are 51 cards left, and 12 of them are diamonds.
Probability of the second one being a diamond = 12/51
Probability of both events =
(1/4) x (12/51) = 3/51 = about 5.88% (rounded)
3). First one is a diamond: 13/52
Now there are 51 cards left, and 13 of them are clubs.
Second one is a club: 13/51.
Probability of both events = (13/52) x (13/51)
= 169/2652 = about 6.37% (rounded)
4). Same logic, same solution, as #3.
5). 6.37% chance that it happens with the diamond coming up first,
6.37% chance that it happens with the club coming up first.
Probability of either one happening = 12.74% (rounded).
Sorry I dont know this answer