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4 years ago

In how many ways can Joseph, Michael, Chris, Katherine, Rebecca and Kyle stand in a line?

Mathematics

1 answer:

Andrews [41]4 years ago

6 0

Answer:

720

Step-by-step explanation:

I got it from Quora

We can use 6 people without repetition, which means we simply have to use counting principle 1.

A number of n objects can be arranged in n! ways.

Total number of combinations possibles = 6! =720

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The system when solved is:

Karolina [17]

Answer:

1,-4

its the right answer

3 0

3 years ago

Find the first term and the common ratio <br>third term =6 and seventh term= 96

mamaluj [8]

Answer:

First term a₁ = 3/2 and common ratio r = 2

Step-by-step explanation:

We need to find the first term and common ratio while we are given third term = 6 and seventh term = 96

Since common ratio is required so, the sequence is geometric sequence

The formula used is: $a_n= a_1r^{n-1}$

We are given: third term = 6 i,e

$a_3=a_1r(3-1)\\6=a_1r^2----eq(1)$

Seventh term = 96

$a_7=a_1r(7-1)\\96=a_1r^6----eq(2)$

Dividing eq(2) and eq(3)

$\frac{96}{6}=\frac{a_1r^6}{a1r2}\\16=\frac{r^6}{r^2}\\16=r^{6-2}\\=> r^4=16\\Taking \ fourth \ root\\ r=2,-2,2i,-2i\\ \ We \ will \ consider \ only \ positive \ value \ of \ r \ i.e \ \textbf{ r= 2}$

So, Common Ratio r = 2

Finding First term using eq(1)

$a_3=a_1r^2\\6=a_1(2)^2\\6=a_1(4)\\a_1= \frac{6}{4}\\a_1= \frac{3}{2}$

So, First term a₁ = 3/2 and common ratio r = 2

6 0

3 years ago

Which has more liquid ,1 gallon of milk or a 12 pack of mountain Dew? how much more?

tatuchka [14]

It depends on the size of Mountain Dew bottles! It differs whether it is a 12 oz or a 16 oz bottle. I need more information to solve it.

7 0

3 years ago

Apply the commutative property to 13 × 7 × 21 to rearrange the terms and still get the same solution.

Andru [333]

Hey there!!
The answer is (13)(21)(7).

Hope this is what ur looking for.

~ TRUE BOSS

7 0

3 years ago

Mrs. Sloan draws two figures on the board.

Trava [24]

A dilated shape will either be enlarged or compressed.

<em>Allen did not make any mistake, and the scale factor is 3.</em>

The dimension of the smaller rectangle (figure Z) is:

3 units by 4 units

The corresponding dimension of the bigger rectangle (figure Z') is:

9 units by 12 units

The scale factor (k) is calculated by dividing the dimensions of Z' by Z.

So, we have:

$k = \frac{9}{3}$

$k = 3$

$k = \frac{12}{4}$

$k = 3$

Notice that both values of k are the same (i.e. 3)

This means that the scale factor is 3

Also figure Z and Z' share the same center of origin at point X

This means that the center of dilation from Z to Z' is X

Hence,

Allen made no mistake, and she is correct about the scale factor.