a. The first part asks for how many ways they can be seated together in a row. Therefore we want the permutations of the set of 6 people, or 6 factorial,
6! = 6 
5
= 30 4
= 360 2 = 720 possible ways to order 6 people in a row
b. There are two cases to consider here. If the doctor were to sit in the left - most seat, or the right - most seat. In either case there would be 5 people remaining, and hence 5! possible ways to arrange themselves.
5! = 5 4
= 20 3
= 120 1 = 120 possible ways to arrange themselves if the doctor were to sit in either the left - most or right - most seat.
In either case there are 120 ways, so 120 + 120 = Total of 240 arrangements among the 6 people if the doctor sits in the aisle seat ( leftmost or rightmost seat )
c. With each husband on the left, there are 3 people left, all women, that we have to consider here.
3! = 3 2 6 ways to arrange 3 couples in a row, the husband always to the left
Answer:
x= 72
Step-by-step explanation:
simplify 1.2 × 60 will equal 72 so therefore x will be 72
Your answer is xy-1<span><span>
</span></span><span>=<span><span><span><span>4<span>x2</span></span><span>y2</span></span>−<span><span>4x</span>y/</span></span><span><span>4x</span>y
</span></span></span><span>=<span><span><span><span>4x</span>y</span>−4/</span>4
</span></span><span>=<span><span>xy</span>−<span>1
</span></span></span>Hope this helps!
The two numbers are 41 & 37.
The way to solve this is by setting up an equation. We know that 2 numbers are going to equal 78, so here would be the general equation (let x represent the number we don't know):
(x) + (x + 4) = 78
Now, we need to simplify it (combine like terms):
2x + 4 = 78
Then you can solve it like any other equation. Subtract 4 on both sides:
2x = 74
Divide by 2 on both sides:
x = 37.
So, now you know one number is equal to 37 and that the other is 37 + 4.
That's how you get 37 & 41.
Area of a rectangle is length x width.
Let the width = x
The length would be x +7. ( 7 inches longer than the width)
Area = 20
Set up the formula:
20 = x * x+7
Simplify the right side:
20 = x^2 + 7x
Subtract 29 from both sides:
X^2 + 7x -20 = 0
Solve using the quadratic equation
X = -b + sqrt(b^2 -4ac) / 2a
X = -7 + sqrt(7^2-4(1)(-20) / 2(1) (exact answer)
X = 2.178908 ( as a decimal)
The width is 2.178907 inches (round as needed)
The length would be 9.178907 inches ( round as needed.)
Depending on how you round, when you multiply them together you get approximately 20 square inches.
