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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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Assume the general population gets an average of 7 hours of sleep per night. You randomly select 45 college students and survey

tekilochka [14]

Answer:

a) ii. This is a left-tailed test.

b) -1.59

c) -1.301

d) i. reject null hypothesis

e) Option i) The data supports the claim that college students get less sleep than the general population.

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 7 hours

Sample mean, $\bar{x}$ = 6.87 hours

Sample size, n = 45

Alpha, α = 0.10

Sample standard deviation, s = 0.55 hours

First, we design the null and the alternate hypothesis

$H_{0}: \mu = 7\text{ hours}\\H_A: \mu < 7\text{ hours}$

a) We use one-tailed(left) t test to perform this hypothesis.

b) Formula:

$t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}} }$

Putting all the values, we have

$t_{stat} = \displaystyle\frac{6.87 - 7}{\frac{0.55}{\sqrt{45}} } =-1.59$

c) Now,

$t_{critical} \text{ at 0.10 level of significance, 44 degree of freedom } = -1.301$

Since,

$t_{stat} < t_{critical}$

d) We fail to accept the null hypothesis and reject it.

We accept the alternate hypothesis and conclude that mean number of hours of sleep for all college students is less than 7 hours.

e) Option i) The data supports the claim that college students get less sleep than the general population.

8 0

3 years ago

Please answer correctly !!!!! Will mark Brianliest !!!!!!!!!!!!!!

expeople1 [14]

Answer:

PT and SQ

Step-by-step explanation:

IF two segments are perpendicular then they will create 90 degree angles

segment PR and segment SQ cross over each other and create 90 degree angles therefore segment PR is perpendicular to segment SQ

4 0

3 years ago

Read 2 more answers

Y=x+ 5 <br>y = 6<br>HELP!!<br>Solve this system of equation algerbraically.

kati45 [8]

Answer:

x = 1

Step-by-step explanation:

plug y = 6 on to the equation y =x + 5

=> 6 = x +5

=> x = 1

5 0

3 years ago

Read 2 more answers

The circles are identical. What is the circumference of each circle? Circle 1: radius of 2x; Circle 2: diameter of 2x+3. A. 3/2

Delicious77 [7]

Answer:

C=6π

Step-by-step explanation:

It is given that, two circles are identical. The radius of first circle is 2x and the diameter of other circle is 2x+3.

If identical, it means that the radius of both circles are same i.e.

$2x=\dfrac{2x+3}{2}\ \ (\because\ r=\dfrac{D}{2}, d=\text{diameter})\\\\4x=2x+3\\\\2x=3\\\\x=1.5$

Radius of both circles is 2(1.5)=3

The circumference of a circle is given by :

$C=2\pi r\\\\C=2\pi (3)\\\\C=6\pi$

So, the circumference of each circle is 6π.

7 0

3 years ago

Anyone know this answer?

damaskus [11]

La of sine:

sinC/c = sinB/b==> sin 37°/8 = sin B/12 ==> sin B = 0.903

arcsinB or sin⁻¹ B = 64.5°, & sin (B°) = sin (180° - B°), then

sin(64.5) = sin(180°-64.5°) ==> B = 64.5° or 115.5°

6 0

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