Answer:
Step-by-step explanation:
P(green) is asking what are the chances that if your stuck your hand into the bag and grabbed a marble that it would be green. There are 3 green, 2 blue, 1 red, and 1 white marble for a total of 7 marbles. If you pull out a marble without looking you have 3 chances of 7 that it will be green. So
10. 3/7 or 3:7
Do we even have any yellow marbles? Not that I can see, so if there isn't a yellow to pull out, your chances of pulling one out is 0. So
11. 0/7 or 0
Since there are 3 green and 1 red, which is a total of 4 marbles, we have 4 out of 7 chances that the marble we pull is red or green. So
12. 4/7 or 4:7
SinФ=-12/13
cosФ=Base/hypotenus
(hy)^2-(perpendicular)^2=(base)^2=13^2-12^2=5
cosФ=-5/13
Answer/Step-by-step explanation:
1. (7j³ - 2) + (5j³ - j - 3)
Open the parentheses
7j³ - 2 + 5j³ - j - 3
Collect like terms. Like terms are terms that have the same degree.
7j³ + 5j³ - j - 2 - 3 (7j³ and 5j³, have the same degree, 2 and 3 are if the same degree)
12j³ - j - 5 (this already in descending order)
2. (8a⁵ - 4) + (3a⁵ + a - 2)
Open parentheses
8a⁵ - 4 + 3a⁵ + a - 2
Collect like terms
8a⁵ + 3a⁵ + a - 4 - 2
12a⁵ + a - 6 (in ascending order from largest to smallest degree)
3. (6m² + 1) + (3a⁵ + a - 2)
6m² + 1 + 3a⁵ + a - 2
Collect like terms
6m² + 3a⁵ + a + 1 - 2
6m² + 3a⁵ + a - 1
Rearrange from largest to smallest degree
3a⁵ + 6m² + a - 1
4. (3m⁵ + 1) + (9m⁵ + 3m - 2)
3m⁵ + 1 + 9m⁵ + 3m - 2
Collect like terms
3m⁵ + 9m⁵ + 3m + 1 - 2
12m⁵ + 3m - 1
5. (- 5x² - x + 4) + (- 3x² - 5x + 2)
Open parentheses
-5x² - x + 4 - 3x² - 5x + 2
Collect like terms
-5x² - 3x² - x - 5x + 4 + 2
-8x² - 6x + 6
21 students will receive the award.
Hope this helps.
