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3 years ago

Four friends are waiting in line. how many different ways can they arrange themselves in that line?

Mathematics

2 answers:

Serhud [2]3 years ago

4 0

Answer:

Step-by-step explanation:

Say their names are A,B,C,and D.

You can put A,B,C,D.

D,C,B,A

C,D,B,A

C,D,A,B

C,A,D,B

C,A,B,D

mixer [17]3 years ago

3 0

Answer:

(5)(4)(3)(2)(1)= <u>120. </u>your answer will be 120

Step-by-step explanation:

You might be interested in

Greetings. As a beginner, I'm struggling a bit to learn calculus. May I know what is the derivative of x to the power 4 step by

elena-14-01-66 [18.8K]

If you're just starting calculus, perhaps you're asking about using the definition of the derivative to differentiate $x^4$ .

We have

$\dfrac{d}{dx} x^4 = \displaystyle \lim_{h\to0} \frac{(x+h)^4 - x^4}h$

Expand the numerator using the binomial theorem, then simplify and compute the limit.

$\dfrac{d}{dx} x^4 = \displaystyle \lim_{h\to0} \frac{(x^4+4hx^3 + 6h^2x^2 + 4h^3x + h^4) - x^4}h \\\\ ~~~~~~~~ = \lim_{h\to0} \frac{4hx^3 + 6h^2x^2 + 4h^3x + h^4}h \\\\ ~~~~~~~~ = \lim_{h\to0} (4x^3 + 6hx^2 + 4h^2x + h^3) = \boxed{4x^3}$

In general, the derivative of a power function $f(x) = x^n$ is $\frac{df}{dx} = nx^{n-1}$ . (This is the aptly-named "power rule" for differentiation.)

3 0

2 years ago

Farmer Emmet used to own 2,300 acres of farmland. However, he recently sold 28% of his farm to a residential developer.

kap26 [50]

9514 1404 393

Answer:

1656 acres left
644 acres sold
$32,200,000

Step-by-step explanation:

1. The number of acres sold is ...

28% × 2300 = 0.28 × 2300 = 644

Then the number of acres Emmet has left will be ...

2300 -644 = 1656 . . . acres left

2. Emmet sold 644 acres.

3. At $50,000 per acre, the value of the land sold was ...

$50,000 × 644 = $32,200,000 . . . . paid by the developer

5 0

2 years ago

Diego has 3 times as many comic books as Han.

Sloan [31]

Answer:

Han has 9 books

Step-by-step explanation:

If diego has 27 comic books than that means that all you have to do is divide 27/3. then that equals to 9

5 0

3 years ago

PLEASE HELP (30 POINTS) Solve the rational equation x/3 = x^2/x + 5 , and check for extraneous solutions.

anygoal [31]

Option C: $x=0$ and $x=\frac{5}{2}$ are the solutions.

Explanation:

The equation is $\frac{x}{3} =\frac{x^{2} }{x+5}$

We shall determine the value of x, by simplifying the equation.

$\begin{aligned} x(x+5) &=3 x^{2} \\ x^{2}+5 x &=3 x^{2} \\ 2 x^{2}-5 x &=0 \\ x(2 x-5) &=0 \end{aligned}$

Thus, $x=0$ and $x=\frac{5}{2}$ are the solutions.

Now, let us check whether the solutions are extraneous solutions.

Let us substitute $x=0$ in the original equation to check whether both sides of the equation are equal.

$\begin{aligned}&\frac{0}{3}=\frac{0^{2}}{0+5}\\&0=\frac{0}{5}\\&0=0\end{aligned}$

Thus, both sides of the equation are equal.

Hence $x=0$ is a true solution.

Now, Let us substitute $x=\frac{5}{2}$ in the original equation to check whether both sides of the equation are equal.

$\begin{aligned}\frac{\left(\frac{5}{2}\right)}{3} &=\frac{\left(\frac{5}{2}\right)^{2}}{\left(\frac{5}{2}\right)+5} \\\frac{5}{6} &=\frac{\left(\frac{25}{4}\right)}{\left(\frac{15}{2}\right)} \\\frac{5}{6} &=\frac{5}{6}\end{aligned}$