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3 years ago

7

You have 12 balls, numbered 1 through 12, which you want to place into 4 boxes, numbered 1 through 4. If boxes can remain empty,

in how many ways can the 12 balls be distributed among 4 boxes

1 answer:

Feliz [49]3 years ago

4 0

Answer:

48 DIFFERENT WAYS

Step-by-step explanation:

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Find all real and complex roots of the equation below x^4-81=0

Pepsi [2]

$x^4-81=0 \\ (x^2-9)(x^2+9)=0\\ (x-3)(x+3)(x^2+9)=0\\ x=3 \vee x=-3 \vee x=3i \vee x=-3i$

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3 years ago

which of the functions have a range of real numbers greater than or equal to 1 or less than or equal to-1

lilavasa [31]

The question is incomplete. Here is the complete question:

Which of the functions have a range of all real numbers greater than or equal to 1 or less than or equal to -1? check all that apply.

A. $y=\sec x$

B. $y= \tan x$

C. $y= \cot x$

D. $y= \csc x$

Answer:

A. $y=\sec x$

D. $y=\csc x$

Step-by-step explanation:

Given:

The range is greater than or equal to 1 or less than or equal to -1.

The given choices are:

Choice A: $y=\sec x$

We know that, the $\sec x=\frac{1}{\cos x}$

The range of $\cos x$ is from -1 to 1 given as [-1, 1]. So,

$|\cos x|\leq 1\\\textrm{Taking reciprocal, the inequality sign changes}\\\frac{1}{|\cos x|}\geq 1\\|\sec x|\geq 1$

Therefore, on removing the absolute sign, we rewrite the secant function as:

$\sec x\leq -1\ or\ \sec x\geq 1\\$

Therefore, the range of $y=\sec x$ is all real numbers greater than or equal to 1 or less than or equal to-1.

Choice B: $y= \tan x$

We know that, the range of tangent function is all real numbers. So, choice B is incorrect.

Choice C: $y= \cot x$

We know that, the range of cotangent function is all real numbers. So, choice C is incorrect.

Choice D: $y=\csc x$

We know that, the $\csc x=\frac{1}{\sin x}$

The range of $\sin x$ is from -1 to 1 given as [-1, 1]. So,

$|\sin x|\leq 1\\\textrm{Taking reciprocal, the inequality sign changes}\\\frac{1}{|\sin x|}\geq 1\\|\csc x|\geq 1$

Therefore, on removing the absolute sign, we rewrite the cosecant function as:

$\csc x\leq -1\ or\ \csc x\geq 1\\$

Therefore, the range of $y=\csc x$ is all real numbers greater than or equal to 1 or less than or equal to-1.

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3 years ago

A number has more tens than ones. the value of the ones digit is 8. what are the possible numbers?

natulia [17]

-----98 with any quantity of any digits before the 9 .

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2 years ago

Read 2 more answers

Rationalize the denominator √7x/75

Leokris [45]

Do what the problum ids telling you than apply it to the math and you will always get the right answer

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3 years ago

Fill in the blank 43_ _ _54

Oksana_A [137]

Answer:

The answer is add 4.

Step-by-step explanation:

I know this because if you add 4 to 43 that's 47 so that's 1 of the blanks. Add another 4 that's 51. that's another 1. and that's last one is add 4 which makes 54.

Hope this helps.

6 0

2 years ago