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Digiron [165]
3 years ago
7

Evaluate 10^C6 and 4^P3

Mathematics
2 answers:
Rus_ich [418]3 years ago
5 0

Answers

Part 1: 210

Part 2: 24


Explanation



Part 1

This is called combination. 

ⁿCm means, the number of different combinations of m objects out of n objects. 

¹⁰C₆ = 10!/10!(10-6)!

        = 10!/(6!×4!)

        =210


Part 2

This is called permutation.

If you have nPm, this means the number of permutations of m objects out of n.

It's solve as follows;


nPm = n!/(n-m)!

⁴P₃ =4!/(4-3)!

      = 4!/1!

       = 24




Nata [24]3 years ago
4 0

\bf \stackrel{combination}{_nC_r=\cfrac{n!}{r!(n-r)!}\qquad\qquad \qquad\qquad \qquad   _{10}C_6=\cfrac{10!}{6!(10-6)!}} \\\\\\ \stackrel{permutation}{_nP_r=\cfrac{n!}{(n-r)!}\qquad\qquad \qquad\qquad \qquad   _4P_3=\cfrac{4!}{(4-3)!}}


yes, check your calculator for the [ ! ] factorial button.


one note that your calculator also has a [ ₙCᵣ ] and [ ₙPᵣ ] buttons for combinations and permutations.

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On 1st January 2020, Laurie invests P dollars in an account that pays a nominal annual interest rate of 5.5%, compounded quarter
andrezito [222]

Answer:

1) The common ratio =  1.055

2) The year in which the amount of money in Laurie's account will become double is the year 2032

Step-by-step explanation:

1) The given information are;

The date Laurie made the investment = 1st, January, 2020

The annual interest rate of the investment = 5.5%

Type of interest rate = Compound interest

Therefore, we have;

The value, amount, of the investment after a given number of year, given as follows;

Amount in her account = a, a × (1 + i), a × (1 + i)², a × (1 + i)³, a × (1 + i)ⁿ

Which is in the form of the sum of a geometric progression, Sₙ given as follows;

Sₙ = a + a × r + a × r² + a × r³ + ... + a × rⁿ

Where;

n = The number of years

Therefore, the common ratio = 1 + i = r = 1 + 0.055 = 1.055

The common ratio =  1.055

2) When the money doubles, we have;

2·a = a × rⁿ = a × 1.055ⁿ

2·a = a × 1.055ⁿ

2·a/a = 2 = 1.055ⁿ

2 = 1.055ⁿ

Taking log of both sides gives;

㏒2 = ㏒(1.055ⁿ) = n × ㏒(1.055)

㏒2 = n × ㏒(1.055)

n = ㏒2/(㏒(1.055)) ≈ 12.95

The number of years it will take for the amount of money in Laurie's account to double = n = 12.95 years

Therefore, the year in which the amount of money in Laurie's account will become double = 2020 + 12..95 = 2032.95 which is the year 2032

The year in which the amount of money in Laurie's account will become double = year 2032.

3 0
3 years ago
. Which ordered pairs in the form (x, y) are solutions to the equation 7x – 5y = 28?
Brut [27]

we know that

If a ordered pair (x,y) is a solution of the equation, then the ordered pair must satisfy the equation

we have the equation

7x-5y=28

Let's verify all the cases to determine the solution to the problem.

<u>case A)</u> point (-6,-14)

Substitute the values of x and y in the equation

x=-6\\y=-14

7(-6)-5(-14)=28

-42+70=28

28=28 -------> is  true

therefore

The point  (-6,-14) is a solution of the equation

<u>case B)</u> point (-1,-7)

Substitute the values of x and y in the equation

x=-1\\y=-7

7(-1)-5(-7)=28

-7+35=28

28=28 -------> is  true

therefore

The point  (-1,-7) is  a solution of the equation

<u>case C)</u> point (4,10)

Substitute the values of x and y in the equation

x=4\\y=10

7(4)-5(10)=28

28-50=28

-22=28 -------> is not true

therefore

The point (4,10) is not a solution of the equation

<u>case D)</u> point (7,9)

Substitute the values of x and y in the equation

x=7\\y=9

7(7)-5(9)=28

49-45=28

4=28 -------> is not true

therefore

The point  (7,9) is not a solution of the equation

therefore

<u>the answer is </u>

(-6,-14)

(-1,-7)

8 0
3 years ago
Read 2 more answers
Please help! this is hard for me!
weqwewe [10]

Answer:

$12.31

Step-by-step explanation:

Think of the original rate of pay as being 100%.

If your rate is increasing by 7%, it will now be 107% of the original rate (since 100% + 7% = 107%)

To find 107% of $11.50, convert 107% into a decimal

⇒ 107% = 107/100 = 1.07

then multiply this by the original rate to get the new increased rate:

⇒ $11.50 × 1.07 = $12.305

Rounding this to the nearest hundred = $12.31

Alternatively, you can find 7% of $11.50 and then add this to $11.50.

⇒ 7% = 7/100 = 0.07

Therefore, 7% of $11.50 = 0.07 × $11.50 = $0.805

Add this to the original rate:

$11.50 + $0.805 = $12.305

Rounding this to the nearest hundred = $12.31

8 0
2 years ago
Pls help im really bad at math no links pls​
lawyer [7]

Answer:

-\frac{1}{2}

Step-by-step explanation:

-\frac{5}{6} +\frac{6}{18}

-\frac{5}{6} +\frac{2}{6}        reduced

\frac{-5+2}{6}            transformed the expression to make it easier

-\frac{3}{6}               add

-\frac{1}{2}               reduce

8 0
2 years ago
8 Select the correct answer from each drop-down menu. Some of the images in the diagram are images of polygon 1 from similarity
makkiz [27]

It should be noted that Polygon 3 and polygon 4 are similar to polygon 1.

<h3>What exactly is polygon?</h3>

In geometry, it should be noted that a polygon is a plane figure which is described by a finite number of straight line segments that are connected in order to form a closed polygonal chain.

In this case, the bounded plane region, the bounding circuit, may be called a polygon. Also, a similarity transformation is the conformal mapping whose transformation matrix are identical.

In this case, it should be noted that Polygon 3 and polygon 4 are similar to polygon 1.

Learn more about polygon on:

brainly.com/question/24966296

#SPJ1

8 0
2 years ago
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