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3241004551 [841]

3 years ago

5

Two n-digit sequences of digits 0,1,. . . ,9 are said to be of the same type if the digits of one are a permutation of the digit

s of the other. For n = 8, for example, the sequences 03088929 and 00238899 are the same type. How many types of n-digit sequences are there?

1 answer:

Stells [14]3 years ago

6 0

Answer:

(n+9)!/(n!9!)

Step-by-step explanation:

A combination is a selection of items from a collection, such that (unlike permutations) the order of selection does not matter.

This is a case of combination with repetition because any n-digit sequence can have numbers repeated. For example in the sequence 00238899 there are 2 zeros.

The formula to find the number of combinations when repetition is allowed is:

(n+N-1)!/[n!(N-1)!]

where

N is the number of elements of the set we can choose from

n is the number of elements we choose

In this case, the set {0,1,2,3,4,5,6,7,8,9} has 10 elements, N=10

The number of n-digit sequences is given by

(n+10-1)!/[n!(10-1)!]=(n+9)!/(n!9!)

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Consider the parabola given by the equation: f(x) = 4x² - 6x - 8 Find the following for this parabola: A) The vertex: Preview B)

jeyben [28]

Answer:

The vertex: $(\frac{3}{4},-\frac{41}{4} )$

The vertical intercept is: $y=-8$

The coordinates of the two intercepts of the parabola are $(\frac{3+\sqrt{41} }{4} , 0)$ and $(\frac{3-\sqrt{41} }{4} , 0)$

Step-by-step explanation:

To find the vertex of the parabola $4x^2-6x-8$ you need to:

1. Find the coefficients <em>a</em>, <em>b</em>, and <em>c </em>of the parabola equation

<em> $a=4, b=-6, \:and \:c=-8$ </em>

2. You can apply this formula to find x-coordinate of the vertex

$x=-\frac{b}{2a}$ , so

$x=-\frac{-6}{2\cdot 4}\\x=\frac{3}{4}$

3. To find the y-coordinate of the vertex you use the parabola equation and x-coordinate of the vertex ( $f(-\frac{b}{2a})=a(-\frac{b}{2a})^2+b(-\frac{b}{2a})+c$ )

$f(-\frac{b}{2a})=a(-\frac{b}{2a})^2+b(-\frac{b}{2a})+c\\f(\frac{3}{4})=4\cdot (\frac{3}{4})^2-6\cdot (\frac{3}{4})-8\\y=\frac{-41}{4}$

To find the vertical intercept you need to evaluate x = 0 into the parabola equation

$f(x)=4x^2-6x-8\\f(0)=4(0)^2-6\cdot 0-0\\f(0)=-8$

To find the coordinates of the two intercepts of the parabola you need to solve the parabola by completing the square

$\mathrm{Add\:}8\mathrm{\:to\:both\:sides}$

$x^2-6x-8+8=0+8$

$\mathrm{Simplify}$

$4x^2-6x=8$

$\mathrm{Divide\:both\:sides\:by\:}4$

$\frac{4x^2-6x}{4}=\frac{8}{4}\\x^2-\frac{3x}{2}=2$

$\mathrm{Write\:equation\:in\:the\:form:\:\:}x^2+2ax+a^2=\left(x+a\right)^2$

$x^2-\frac{3x}{2}+\left(-\frac{3}{4}\right)^2=2+\left(-\frac{3}{4}\right)^2\\x^2-\frac{3x}{2}+\left(-\frac{3}{4}\right)^2=\frac{41}{16}$

$\left(x-\frac{3}{4}\right)^2=\frac{41}{16}$

$\mathrm{For\:}f^2\left(x\right)=a\mathrm{\:the\:solutions\:are\:}f\left(x\right)=\sqrt{a},\:-\sqrt{a}$

$x_1=\frac{\sqrt{41}+3}{4},\:x_2=\frac{-\sqrt{41}+3}{4}$

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A copy machine can print 480 copies every 4 minutes.

Elenna [48]

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It took the Selby family hours round -trip to drive from their house to their beach house 154 miles away . Find their average sp

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Step-by-step explanation:

Distance = 154 miles .

Time = 5 ½ hrs .

We know ,

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v = 154 mi/ 5.5 hrs = 28 mi / hr

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Examine the following table. Determine whether the rate of change is constant or variable. If it is constant, state the rate of

xenn [34]

Answer:

Variable rate of change.

Step-by-step explanation:

Plot the points and you'll see that the graph is not a straight line, therefore the rate of change is variable.

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2 years ago

HELP ILL GIVE U BRAINLESS I NEED THIS ANSWER FAST! I’ll make u art tol

lapo4ka [179]

1: 80% The reason why is because if you do 4/5, you get .80, move the decimals to places to the right, and you get 80%

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<em>I hope this helps, and Happy Holidays! :)</em>

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