How many distinct signals can be made with 8 flags displayed at the same time in a vertical array if 3 flags are white, 2 flags are red, 1 flag is checkered and the rest of the flags are yellow?1,680
3,360
6,720

Answers

Answer 1

Answer:

Answer:

Option 1 - 1680 distinct signals can be made with 8 flags displayed at the same time in a vertical array.

Step-by-step explanation:

Given : 8 flags displayed at the same time in a vertical array if 3 flags are white, 2 flags are red, 1 flag is checkered and the rest of the flags are yellow.

To find : How many distinct signals can be made with 8 flags ?

Solution :

The total number of flags is 8

White flag = 3

Red flag = 2

Checkered flag = 1

Yellow flag = 8-3-2-1=2

Applying the Fundamental Counting Principle which state that the multiplication of the events together to get the total number of outcomes.

The distinct signals can be made with 8 flags is

$T=(8!)/(3!* 2!* 1!* 2!)$

$T=(8* 7* 6* 5* 4* 3!)/(3!* 2* 1* 1* 2* 1)$

$T=1680$

Therefore,Option 1 - 1680 distinct signals can be made with 8 flags displayed at the same time in a vertical array.

Answer 2

Answer: The answer is a.
1,680 distinct signals can be made.

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Write an explicit formula for each sequence.
3, 7, 11, 15, ...

Answers

Answer:

f(n)= f(1)+d(n-1)

Step-by-step explanation:

the aerithmetric explict formula is the one above, but im not sure what the question is asking, your difference is 4 btw

The table below shows the number of cars Jing sold each month last year.What is the median of the data in the table.
13
16
19
20.5
23.5
Other:

Answers

Answer:

The median of the data in the table is 19.

Step-by-step explanation:

We are given the following data that shows the number of cars Jing sold each month last year below;

Number of cars Jing sold: 13, 16, 19, 20.5, 23.5

For calculating the median, firstly we have to observe that the number of observations (n) in our data is even or odd because;

If n is odd, then the formula for calculating median is given by;

Median = $((n+1)/(2) )^(th) \text{ obs.}$

If n is even, then the formula for calculating median is given by;

Median = $\frac{((n)/(2) )^(th) \text{ obs.} + ((n)/(2)+1 )^(th) \text{ obs.} }{2}$

Here, the number of observations in our data is odd, i.e. n = 5.

So, Median = $((n+1)/(2) )^(th) \text{ obs.}$

= $((5+1)/(2) )^(th) \text{ obs.}$

= $((6)/(2) )^(th) \text{ obs.}$

= 3rd obs. = 19

Hence, the median of the data in the table is 19.

1/2x +31/2y=
Please help I have only till 3 pm

Answers

Answer: $(x)/(2)$ + $(31y)/(2)$

Step-by-step explanation:

1) Combine multiplied terms into a single fraction.

$(1)/(2)$ x + $(31)/(2)$ ⋅ y

2) Multiply the equation by 1.

1x/2+ 31/2 ⋅ y

x/2 + 31/2 ⋅ y

3) Combine multiplied terms into a single fraction.

x/2 + 31/2 y

x/2 + 31y/2

4) Solution

x/2 + 31y/2

2. The height of a triangle is 5 m less than its base. The area of the triangle is 42 m2. Find the length of the base.(Points : 1)

Answers

Let's start with what we know

Area:
$42 = (1)/(2)bh$ where 42 is the area, b = base, and h = height

Height:
Since we know the height is 5 less than the base, we can write that as an equation.
$h = b - 5$

Now let's go and plug $h = b - 5$ into $42 = (1)/(2)bh$

$42 = (b)/(2)(b-5)$
Let's distribute b over (b-5)

$42 = ( b^(2) - 5b )/(2)$
Let's move 42 over to the right side to make a quadratic formula

$0 = (1)/(2) b^(2) - (5)/(2)b - 42$

Let's plug that into the quadratic equation, which is:

$\frac{-b +/- \sqrt{ b^(2) - 4ac } }{2a}$
And we can now plug the pieces in to calculate b

$\frac{- (-(5)/(2)) +/- \sqrt{ (-(5)/(2))^(2) - 4 ((1)/(2))(-42) } }{2 ((1)/(2)) }$
$\frac{(5)/(2) +/- \sqrt{ (25)/(4) +84 } }{1 }$
${(5)/(2) +/- \sqrt{ (361)/(4) } }$
${(5)/(2) +/- { (19)/(2) }$
Since we can't have a negative value for b (a base can't be negative meters), let's add:

${(5)/(2) + { (19)/(2) }$
${ (24)/(2) }$
$12 = b$

So the base of the triangle is 12m

Answer:

took the quiz and it is correct the answer is 12

Look at the image of the table of values below. Over which interval of x is the average rate of change the largest?