Linear function help

Determine whether the congruence is true or false.<br> 12 ≡ 10 mod 5

dolphi86 [110]

Answer:

The given congruence is false.

Step-by-step explanation:

Given : Expression $12 \equiv 10 \mod 5$

To find : Determine whether the congruence is true or false ?

Solution :

The congruence is in the form $x\mod y\equiv r$

where, x is the dividend

y is divisor

r is the remainder

So, We find $10 \mod 5$

We know, 10 is completely divide by 5 and we get quotient is 2 and remainder is 0.

$10 \mod 5=0$

As $0\neq 12$

Therefore, The given congruence is false.

8 0

3 years ago

The lines 3y + 1 = 6x + 4 and 2y + 1 = x - 9 are ?

harkovskaia [24]

Answer:

lines are not perpendicular or parallel

6 0

2 years ago

Translate the verbal statements into a system of linear equations: Fatima invested a total of $1000 in two simple-interest bank

mixas84 [53]

Answer:

Step-by-step explanation:

Translate the verbal statements into a system of linear equations: Fatima invested a total of $1000 in two simple-interest bank accounts. One account paid 5% annual interest; the other paid 6% annual interest. The total amount of interest she earned after 1 year was $56

Simple interest formula =

I = PRT

We are to find the Amount = Principal invested

For Account 1

I1 = P × 5% × 1

= 0.05P

Account 2

I2 = P × 6% × 1

= 0.06P

Therefore:

0.05P + 0.06P = $56

6 0

2 years ago

QuizBIGPOINT

lianna [129]

The number of permutations of the problem is

This = 24
Outfit = 360

<h2>Combination</h2>

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Combinations are the number of ways to choose members from a certain number, namely from members of a set, combinations can also be interpreted as many ways to make subsets, namely with a certain number of members, namely from members of a set, if a set has n members then the selection of r members, and the combination of n is where r is less than n.

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<h3>The Formula : </h3>

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<h2>Permutation</h2>

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Permutations are a way to determine the number of arrangements that occur by paying attention to the order. So in permutations, position/order is very important, namely AB is considered different from BA (AB ≠ BA). Permutation formula

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<h3>The Formula :</h3>

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$\frac {n!}{k!}$ (With Double Elements)

n! (Without Double Elements)

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<h2>Factorial</h2>

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The factorial of a natural number is the successive multiplication of a natural number that begins with the number one and arrives at the natural number, the factorial is used in calculating combinations, probabilities, and permutations.

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<h3>For example</h3>

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》2! = 1 × 2
》3! = 1 x 2 x 3
》4! = 1 x 2 x 3 x 4
》5! = 1 x 2 x 3 x 4 x 5
》6! = 1 × 2 × 3 × 4 × 5 × 6
》7! = 1 × 2 × 3 × 4 × 5 × 6 × 7
》8! = 1 × 2 × 3 × 4 × 5 × 6 × 7 × 8
》9! = 1 × 2 × 3 × 4 × 5 × 6 × 7 × 8 × 9
》10! = 1 × 2 × 3 × 4 × 5 × 6 × 7 × 8 × 9 × 10

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The following is an example of a factorial that does not involve mixed arithmetic operations, so if you want to add it up we just need to calculate it like a normal number, a factorial number that only multiplies the difference between a factorial number that is added up by addition, subtraction, multiplication, division, for example see below.

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6! x2! - 3! : 4!

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The example above is a mixed arithmetic operation that contains multiplication, subtraction, and division. Remember that in mixed arithmetic operations, multiplication/division must be completed before addition/subtraction.

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<h3>The Formula : </h3>

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n! (Combined Multiplication)

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<h2>Place Filling Rules</h2>

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The Place Fill Rule is a method or method that can be used to determine the number of ways an object occupies its place. The filling slots rule is a method of calculating how many possible ways there are in an experiment or event. If a first event can be done in m different ways and the second event can be done in a different way and so on until the last event in k.

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<h3>The formula</h3>

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n1 × n2 × n3 × ... × nr

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<h2><u>Question</u></h2>

Find the number of permutations of letters of the word

- this

- outfit

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<h2><u>Answer</u></h2>

"Number One"

=》This = Four Letters ( 4! )

P = 4!

P = 1 × 2 × 3 × 4

P = 2 × 3 × 4

P = 6 × 4

P = 24

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"Number Two"

=》Outfit = Six Letters ( 6! )

=》Outfit = Two Letters The Same ( "T" ) = 2!

P = $\frac {1×2×3×4×5×6}{2×1}$

P = $\frac {2×3×4×5×6}{2}$

P = $\frac {6×4×5×6}{2}$

P = $\frac {24×5×6}{2}$

P = $\frac {120×6}{2}$

P = $\frac {720}{2}$

P = 360

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<h2><u>Conclusion</u></h2>

So, the number of permutations of the problem is

This = 24
Outfit = 360

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<h2>Learn More</h2>

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<h2>Answer Detail</h2>

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➽ Subject: Mathematics
➽ Class : 12
➽ Chapter : 7 - The Rule of Counting:
➽ Maple Code
➽ Categorization code : 12.2.7
➽ Keywords : This, Outfit

5 0

3 years ago

How many 1/3 cm by 1/3 cm by 1/3 cm cubes will fit in a 1 cm by 1 cm by 1 cm box? Explain how you know.

Tems11 [23]

1/3^3=0.037 recurring. 1^3= 1. 1/0.37=27.027. That rounds to 27 so you can fit 27 cubes into the box.

8 0

3 years ago