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Ymorist [56]
3 years ago
14

A little boy is placing 20 oh his marbles in a row. If 12 are red and 8 are blue and he decides not to place 2 blue marbles next

to each other, how many arrangements of the marbles are possible? Expert Answer
Mathematics
1 answer:
aleksandr82 [10.1K]3 years ago
6 0

Answer:

Consider lining up all the blue marbles and placing one red marble in between them. Let that arrangement be fixed. The remaining red marbles will be 5 red marbles. Note that the arrangement will be:

x BR x BR x BR x BR x BR x BR x BR x B x

Note that this is the same even if our arrangement is

x B x RB x  RB x RB x RB x RB x RB x RB x

Note that there are 9 spots, denoted by x, where we can put the 5 remaining red marbles. To find the number of ways of putting the remaining 5 red marbles to x, it is similar in finding the number of non-negative solution for the equation

a_1 + a_2 + a_3 + a_4 + a_5 + a_6 + a_7 + a_8 + a_9 = 5

which is given by

(^{5+9-1}_{9-1}) = 1287

Hence, there are 1287 ways of arranging 8 blue marbles and 12 red marbles without placing 2 blue marbles next to each other.

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There are 4 red marbles and 3 blue marbles in a bag. Once a marble is drawn it is not replaced. Find the probability of drawing
Goshia [24]

Answer:

2/7

Step-by-step explanation:

4 red marbles and 3 blue marbles in a bag = 7 marbles

P(red) = red/total = 4/7

No replacement

3 red marbles and 3 blue marbles in a bag = 6 marbles

P(red) = red/total = 3/6 = 1/2

P(red, no replacement, red) = 4/7 * 1/2 = 2/7

5 0
4 years ago
Find the percent of each number:<br> 0.55% of 220=
Sphinxa [80]
1.21 because of means multiply and .55% is .0055 so 220*0.0055 is 1.21.
6 0
3 years ago
Read 2 more answers
Two arrows are launched at the same time with the same speed. arrow a at an angle greater than 45 degrees, and arrow b at an ang
valentina_108 [34]
Let V = the launch velocity
Let θ =  the launch angle
Let d =  the horizontal distance traveled

Ignore air resistance.

The horizontal component of velocity is
u = V cos θ
The time of flight is
t = d/(V cosθ) = (d/V) secθ

Create a table of θ versus t as shown below.
   θ    t/(d/V)
----   ----------
45    1.4142
40    1.3054
35    1.2208
30    1.1547

The graph shows that as the launch angle decreases below 45°, the time of flight decreases.
Therefore arrow b (θ < 45°) arrives first.

Answer: Arrow b arrives first.
6 0
3 years ago
What is the equation of a line that is perpendicular to y=0.25x-7 and passes through the point -6,8
Olenka [21]

Answer:

The equation ls: y = -4x - 16

Step-by-step explanation:

Given the point (-6, 8)

Given the line y = .25x - 7

Use a fraction:

y = 1/4x - 7

The slope is 1/4 (or .25)

The slope of a perpendicular line is the negative inverse or -4.

Use the point slope form and substitute:

y - y1 = m(x - x1)

y - 8 = -4(x - (-6))

y - 8 = -4x - 24

y = -4x - 16

Proof:

f(-6) = -4(-6) - 16

= 24 - 16

= 8, giving (-6, 8)

7 0
3 years ago
Help please. <br> Give the slope of y - 3 = 4(x + 8) and a point on the line
Sauron [17]
-----------------------------------------------------------
Make y the subject :
-----------------------------------------------------------
y - 3 = 4(x + 8)      
y - 3 = 4x + 32           // Apply distributive property
y = 4x + 35                // Add 3 to both sides

-----------------------------------------------------------
Identify Slope : 
-----------------------------------------------------------
Slope = 4

-----------------------------------------------------------
Find a point on the line :
-----------------------------------------------------------
When x = 0, 
y = 4(0) + 35              // Sub x = 0 into the equation 
y = 35                         // Combine like terms
Point = (0, 35)

-----------------------------------------------------------
Answers :
(a) Slope = 4
(b) One point on the line is (0, 35)
-----------------------------------------------------------
4 0
4 years ago
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