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3 years ago

Among the following, a perfect number a) 6 b)28 c) 625 d) 100

Mathematics

2 answers:

Gnesinka [82]3 years ago

8 0

<h3>Answer: A) 6 and B) 28</h3>

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Explanation:

By definition, a perfect number is one where the factors smaller than itself add to the number in question.

The factors of 6, smaller than 6, are {1,2,3}. We can see that 1+2+3 = 6. Therefore, 6 is a perfect number.

Similarly, 1+2+4+7+14 = 28 showing that 28 is also a perfect number.

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The factors of 625, that are smaller than 625, are 1,5,25,125. They add to 1+5+25+125 = 156. This isn't equal to 625, so 625 isn't a perfect number.

A similar issue happens with 100 as well. The smaller factors are 1,2,4,5,10,20,25,50, meaning we get a sum of 1+2+4+5+10+20+25+50 = 117, which is too large.

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The first four perfect numbers are: {6, 28, 496, 8128}

Verdich [7]3 years ago

6 0

Answer:

28 and 6

Step-by-step explanation:

List the factors (excluding itself):

6: 1, 2, 3,

28: 1, 2, 4, 7, 14

Add them up!

1+2+3=6

1+2+4+7+14=28

if they add up to the original number then the number is perfect.

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If 6000 dollars is invested in a bank account at an interest rate of 9 per cent per

Volgvan

Answer:

(1) $11955.38

(2) $12228.62

(3) $12293.527

(4) $12326.6

Step-by-step explanation:

Compound interest is given by

A= P( 1 + r/n)^n*t

A= Final amount

P = initial amount = 6000

r = interest rate = 9% = 0.09

n = number of times interest applied per time period

t = number of time periods elapsed

(1) Compounded annually

n = 1 , t = 8

A = 6000( 1+ 0.09/1) ^1*8

A = 6000( 1.09) ^8 = $11955.38

(2) compounded quarterly

n = 4 , t = 8

A = 6000( 1+ 0.09/4) ^4*8

= 6000( 1.0225)^32 = $12228.62

(3) compounded monthly

n = 12 , t = 8

A = 6000( 1+0.09/12)^12*8 = $12293.527

(4) compounded continuously

A = P* e^rt

r = 0.09 , t = 8

= 6000* e^0.09*8

= 6000* e^0.72 = $12326.6

5 0

3 years ago

Read 2 more answers

The area of a rectangle garden is 38 1/4 Square meters the width of the garden is 4 1/2 meters. Find the length of the garden

maxonik [38]

Area of rectangle it's the width multiply by the lenth.

A=W*L

A=38 1/4 m²
W=4 1/2 m²

So:       38 1/4 = 4 1/2 * L
Dividing both sides by 4 1/2: : 4 1/2         :4 1/2
      $38\frac14\ :\ 4\frac12\ =\ L\\\\L=\frac{153}4\ :\ \frac{9}2\\\\L=\frac{153}4\ \cdot\ \frac2{9}\\\\L=\frac{17}{2}\cdot\ \frac1{1}\\\\L=8\frac12$

Answer: T<span>he length of the garden is 8 1/2 meters</span>

3 0

3 years ago

xP(x)00.2510.0520.1530.55Find the standard deviation of this probability distribution. Give your answer to at least 2 decimal pl

Nookie1986 [14]

The Solution:

Given:

Required:

Find the standard deviation of the probability distribution.

Step 1:

Find the expected value of the probability distribution.

$E(x)=\mu=\sum_{i\mathop{=}0}^3x_iP_(x_i)$ $\begin{gathered} \mu=(0\times0.25)+(1\times0.05)+(2\times0.15)+(3\times0.55) \\ \\ \mu=0+0.05+0.30+1.65=2.0 \end{gathered}$

Step 2:

Find the standard deviation.

$Standard\text{ Deviation}=\sqrt{\sum_{i\mathop{=}0}^3(x_i-\mu)^2P_(x_i)}$ $=(0-2)^2(0.25)+(1-2)^2(0.05)+(2-2)^2(0.15)+(3-2)^2(0.55)$ $=4(0.25)+1(0.05)+0(0.15)+1(0.55)$ $=1+0.05+0+0.55=1.60$

Thus, the standard deviation is 1.60

Answer:

1.60

8 0

1 year ago

What do we call financial assistance for a student who meets academic, athletic, or talent requirements to help pay for college

sladkih [1.3K]

This is a scholarship.

Student loans must be repaid; grants are given usually without those types of restrictions; and student work involves a student having an on-campus job.

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3 years ago

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rewona [7]

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3 years ago

Among the following, a perfect number a) 6 b)28 c) 625 d) 100​

Among the following, a perfect number a) 6 b)28 c) 625 d) 100