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3 years ago

In how many ways can six people sit in a six-passenger car?

Mathematics

1 answer:

nekit [7.7K]3 years ago

5 0

Answer:

number of ways = 720

Step-by-step explanation:

The number of ways six people sit in a six-passenger car is given by the number of permutations of 6 elements in 6 different positions ( seats), then

number of ways = number of permutations of 6 elements = 6! = 6 * 5 * 4 *3 * 2 * 1 = 720

Since the first person that sits can be on any of the seats , but then the second person that sits can choose any of 5 seats (since the first person had already occupied one) , the third can choose 4 ... and so on.

You might be interested in

If f(x)=7x+4x and g(x) =1/2x what is the value of (f/g)(5)

Aliun [14]

Answer:

(f/g)(5) = 22

Step-by-step explanation:

All we need to do is plug in 5 for x in both f(x) and g(x) then divide the result of f(x) and g(x) to find our final answer.

Step 1: Plug in 5 for x

f(x) = 7(5) + 4(5) = 55

g(x) = 1/2(5) = 2.5

Step 2: Divide f(x) by g(x)

f(5)/g(5) = 55/2.5 = 22

And we have our final answer!

4 0

3 years ago

Determine whether the lines are parallel, intersect, or coincide. x-5y=0, y+1=1/5(x+5)

MAXImum [283]

Answer-

The lines are two coinciding lines or the same lines.

Solution-

The given line equations are

the first one,

$\Rightarrow x-5y=0$

the second one,

$\Rightarrow y+1=\dfrac{1}{5}(x+5)\\\\\Rightarrow 5y+5=x+5\\\\\Rightarrow 5y=x\\\\\Rightarrow x-5y=0$

As we know two line equations $A_1x+B_1y+C_1=0$ and $A_2x+B_2y+C_2=0$ will be,

Parallel if, $\dfrac{A_1}{A_2}=\dfrac{B_1}{B_2}$
Coincide if, $\dfrac{A_1}{A_2}=\dfrac{B_1}{B_2}=\dfrac{C_1}{C_2}$
Intersect if, $\dfrac{A_1}{A_2}\neq \dfrac{B_1}{B_2}$

As here,

$\Rightarrow \dfrac{A_1}{A_2}=\dfrac{B_1}{B_2}=\dfrac{C_1}{C_2}$

$\Rightarrow \dfrac{1}{1}=\dfrac{-5}{-5}$

(C₁ and C₂ aren't considered as they are 0)

Therefore, the lines are two coinciding lines or the same lines.

4 0

3 years ago

Katie is selling a camera online. She bought the camera at a wholesale cost of $125 and will mark the camera up 60% to make a pr

Bond [772]

Answer:

$200

Step-by-step explanation:

To find the retail price, multiply the wholesale cost by 1.6

125(1.6)

= 200

So, the retail price will be $200

3 0

2 years ago

Please help me asap i will give brainiest and all my points

Alinara [238K]

Answer:

a. Not Divisible

b. Divisible

c. Divisible

d. Divisible

e. Divisible

Step-by-step explanation:

To find the divisibility we need to follow the PEMDAS rule and check if the total value can be divided by the selected numbers without returning a remainder.

Let's begin with a:

$16^{5}+215$ by 33

$1,048,576 + 215$

$1,048,791$

We now then divide the total amount with 33.

$\dfrac{1,048,576}{33}$

= 31,781.5454

We can see that the value has a decimal point indicating that the total value divided by 33 will return a remainder. So it is NOT Divisible by 33.

Now let's continue on with the others.

$51^{7}-51^{6}$ by 25

$897,410,677,851 - 17,596,287,801$

$879,814,390,050$

We now then divide the total amount with 25.

$\dfrac{879,814,390,050}{25}$

= 35,192,575,602

The total value did NOT return a decimal point, therefore making the equation true. $51^{7}-51^{6}$ IS divisible by 25.

Next on we have:

$5^{5}-5^{4} +5^{3}$ by 7

$3,125 - 625 + 125$

As we know in the PEMDAS rule, that addition comes first. In this situation we have to read the equation from left to right and solve which ever comes first.

$2,500 + 125$