<span>Carly needs to deposit $350 into the savings account per month over the next 3 years to be able to pay for her first year of college</span>
Answer:
x = 4
Step-by-step explanation:
Using cosine triangle formula, we know that;
c² = a² + b² - 2ac(cos C)
From our diagram;
a = 2x
b = x + 1
c = 7
C = 60°
Thus;
7² = (2x)² + (x + 1)² - 2(2x)(x + 1)cos 60
49 = 4x² + (x² + 2x + 1) - (4x² + 4x)(0.5)
49 = 5x² + 2x + 1 - 2x² - 2x
3x² + 1 - 49 = 0
3x² - 48 = 0
3x² = 48
x² = 48/3
x² = 16
x = √16
x = 4
Answer:
1/3
Step-by-step explanation:
Lets start with the red ball because it is easier. You have 1/10 chances to pick the same number that is drawn randomly. Thus your base probability is .1
Now going to the white balls, you need atleast 2 numbers picked as the numbers drawn. Let's say we pick numbers 1-3. In order to win, the numbers 1 and 2, 2 and 3, 1 and 3, or 1 2 and 3 must be drawn. You can calculate the probability for each of these cases. In the case only 2 are drawn, the probability for each is 0.075. Since there are three cases that this could happen, you multiply this probability by 3, becoming 1/4. However, there is also the chance that you get all three. The probability of this is 3/10*2/9*1/8.
.225 + .1 + 0.008333 = 33.333...% or 1/3
Answer:
The number of different combinations of three students that are possible is 35.
Step-by-step explanation:
Given that three out of seven students in the cafeteria line are chosen to answer a survey question.
The number of different combinations of three students that are possible is given as:
7C3 (read as 7 Combination 3)
xCy (x Combination y) is defines as
x!/(x-y)!y!
Where x! is read as x - factorial or factorial-x, and is defined as
x(x-1)(x-2)(x-3)...2×1.
Now,
7C3 = 7!/(7 - 3)!3!
= 7!/4!3!
= (7×6×5×4×3×2×1)/(4×3×2×1)(3×2×1)
= (7×6×5)/(3×2×1)
= 7×5
= 35
Therefore, the number of different combinations of three students that are possible is 35.