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Studentka2010 [4]
3 years ago
12

How many ways can six kids line up in a single row to have their picture taken?

Mathematics
1 answer:
Elina [12.6K]3 years ago
4 0
Slot method aka permuations
6 slots
1st slot: 6 options
2nd slot: 5 options (1 went to first slot)
3rd slot: 4
4th slot:3
5th slot:2
6th slot:1

multiply
6*5*4*3*2*1=720

720 ways
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Write 107% as a decimal. Pls with solutions
otez555 [7]

Answer:

1.07

Step-by-step explanation:

1 To convert to a decimal, divide the percent number by 100.

<h3>107÷100=1.07</h3>

2 Therefore, the decimal form is 1.07

<h3>1.07</h3>

5 0
2 years ago
Read 2 more answers
2. Find the length of segment JK with endpoints J(4,8) and K(-1,-2). Leave answer as a
yuradex [85]

Answer:

Distance of JK = 15 unit

Step-by-step explanation:

Given:

J(4,8)

K(-1,-2)

Find:

Distance of JK

Computation:

Distance = √(x₂-x₁)² + (y₂-y₁)²

Distance of JK = √(-1-4)² + (-2-8)²

Distance of JK = √25 + 100

Distance of JK = √125

Distance of JK = 15 unit

3 0
3 years ago
Helps pls help pls thank you so much
Juliette [100K]

Answer:

Increases, same, increases, decreases

Step-by-step explanation:

I mean just look at the graph

7 0
3 years ago
For what values of x is f(x) = |x + 1| differentiable? I'm struggling my butt off for this course
pav-90 [236]

By definition of absolute value, you have

f(x) = |x+1| = \begin{cases}x+1&\text{if }x+1\ge0 \\ -(x+1)&\text{if }x+1

or more simply,

f(x) = \begin{cases}x+1&\text{if }x\ge-1\\-x-1&\text{if }x

On their own, each piece is differentiable over their respective domains, except at the point where they split off.

For <em>x</em> > -1, we have

(<em>x</em> + 1)<em>'</em> = 1

while for <em>x</em> < -1,

(-<em>x</em> - 1)<em>'</em> = -1

More concisely,

f'(x) = \begin{cases}1&\text{if }x>-1\\-1&\text{if }x

Note the strict inequalities in the definition of <em>f '(x)</em>.

In order for <em>f(x)</em> to be differentiable at <em>x</em> = -1, the derivative <em>f '(x)</em> must be continuous at <em>x</em> = -1. But this is not the case, because the limits from either side of <em>x</em> = -1 for the derivative do not match:

\displaystyle \lim_{x\to-1^-}f'(x) = \lim_{x\to-1}(-1) = -1

\displaystyle \lim_{x\to-1^+}f'(x) = \lim_{x\to-1}1 = 1

All this to say that <em>f(x)</em> is differentiable everywhere on its domain, <em>except</em> at the point <em>x</em> = -1.

4 0
3 years ago
Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely many solutions. If
pav-90 [236]

Answer:

Second option: One solution. Independent.

Step-by-step explanation:

The equation of the line in Slope-Intercept form is:

y=mx+b

Where "m" is the slope and "b" is the y-intercept.

Since the equations of the system have this form, we know that they are lines.

We can identify that the y-intercept of the first equation y=-5x+1 is:

b=1

Now we need to find the x-intercept. Substitute y=0 and solve for "x":

0=-5x+1\\\\5x=1\\\\x=\frac{1}{5}=0.2

Then, we can graph the first line which passess through the points (0,1) and (0.2,0). Observe the graph attached.

The y-intercept of the second equation y=-2x-2 is:

b=-2

Now we need to find the x-intercept. Substitute y=0 and solve for "x":

0=-2x-2\\\\2x=-2\\\\x=\frac{-2}{2}=-1

Then, we can graph the second line, which passess through the points (0,-2) and (-1,0).

You can observe in the graph that the lines intersect at the point (1,-4). Therefore, that point is the solution of the system of equations.

Since the lines intersect, then there is one solution that is true for both equations. It is independent

4 0
2 years ago
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