the sum of the prime divisors of 2001 is a) 55, b) 56, c) 670, d) 671, e) 2001

Answers

Answer 1

Answer:

Option  A

Step-by-step explanation:

2001 can be divided by 3, 23, and 29 without remainders. This means that the three numbers are prime divisors of 2001.

2001/3 = 667

2001/23 = 87

2001/29 = 69

The sum of the prime divisors is 55.

3 + 23 + 29 = 55

Option A should be the correct answer.

Hope this helps.


Related Questions

Please help!

Explain how changes in the dimensions of a cube dimensions affect the volume of a cube. Be specific, explaining how much the volume will change with each increase of 1 unit on the side lengths.

Answers

Answer:

when each side length of a cube increases by 1 unit, the volume increases by 3x² + 3x + 1 (units)³

Step-by-step explanation:

Let the initial length of the sides of the cube = x unit

when the length of the cube = x ;  volume of the cube = length × breadth × height = x × x × x = x³ (unit)³

when the length increased by 1 unit,

new length = (x + 1) unit

New volume = (x + 1) × (x + 1) × (x + 1)

multiplying the first two brackets

New volume = (x² + 2x + 1 ) (x + 1)

espanding the brackets

New volume = x³ + 2x² + x + x² + 2x + 1

New volume = x³ + 3x² + 3x + 1 (unit)³

Change in volume:

(New volume) - (old volume)

(x³ + 3x² + 3x + 1) - (x³)

x³ + 3x² + 3x + 1 - x³

collecting like terms:

(x³ - x³) + 3x² + 3x + 1

0 + 3x² + 3x + 1

change in volume = 3x² + 3x + 1

Therefore, when each side length of a cube increases by 1 unit, the volume increases by 3x² + 3x + 1 (units)³

To paint his apartment, Alex but 6 gallons of paint to cover 1440 ft.². What is the ratio of square feet to gallons of paint?

Answers

Answer & Step-by-step explanation:

The ratio of square feet to gallons of paint:

[tex]1440:6[/tex]

This can also be written as:

[tex]\frac{1440}{6}[/tex]

This fraction can be simplified by dividing the numerator and denominator by 6:

[tex]\frac{1440}{6}=\frac{240}{1}[/tex]

So, the ratio of square feet to gallons of paint is:

1 gallon for every 240 ft².

:Done

somebody please help

Answers

Answer: 3

Explanation:

x^2 + 6x + 9
= (x + 3)^2

Can some body write a word problem using these numbers

Answers

Answer:

Mr Singh was travelling from England to Punjab, India. He arrived 5 hours after 0:00. When he was on the plane, there was a delay which caused the whole flight to be pushed 4 hours ahead. This would mean that he would arrive 9 hours after 0:00. Mr Singh was also with his son and he had some homework to do. He had to order the numbers   [tex]-4,-2\frac{1}{3} ,0, \frac{3}{4} ,\sqrt{5},5[/tex]  from lowest to highest.

Translate and solve: 54 greater than x is greater than 216

Answers

Answer:

x >162

Step-by-step explanation:

x+54 > 216

Subtract 54 from each side

x+54-54 > 216 - 54

x >162

Answer:

[tex]\huge \boxed{{x>162}}[/tex]

Step-by-step explanation:

[tex]x+54 > 216[/tex]

[tex]\sf Subtract \ 54 \ from \ both \ parts.[/tex]

[tex]x+54 -54> 216-54[/tex]

[tex]x>162[/tex]

Find the fourth roots of 16(cos 200° + i sin 200°).

Answers

Answer:

See below.

Step-by-step explanation:

To find roots of an equation, we use this formula:

[tex]z^{\frac{1}{n}}=r^{\frac{1}{n}}(cos(\frac{\theta}{n}+\frac{2k\pi}{n} )+\mathfrak{i}(sin(\frac{\theta}{n}+\frac{2k\pi}{n})),[/tex] where k = 0, 1, 2, 3... (n = root; equal to n - 1; dependent on the amount of roots needed - 0 is included).

In this case, n = 4.

Therefore, we adjust the polar equation we are given and modify it to be solved for the roots.

Part 2: Solving for root #1

To solve for root #1, make k = 0 and substitute all values into the equation. On the second step, convert the measure in degrees to the measure in radians by multiplying the degrees measurement by [tex]\frac{\pi}{180}[/tex] and simplify.

[tex]z^{\frac{1}{4}}=16^{\frac{1}{4}}(cos(\frac{200}{4}+\frac{2(0)\pi}{4}))+\mathfrak{i}(sin(\frac{200}{4}+\frac{2(0)\pi}{4}))[/tex]

[tex]z^{\frac{1}{4}}=2(cos(\frac{5\pi}{18}+\frac{\pi}{4}))+\mathfrak{i}(sin(\frac{5\pi}{18}+\frac{\pi}{4}))[/tex]

[tex]z^{\frac{1}{4}} = 2(sin(\frac{5\pi}{18}+\frac{\pi}{4}))+\mathfrak{i}(sin(\frac{5\pi}{18}+\frac{\pi}{4}))[/tex]

Root #1:

[tex]\large\boxed{z^\frac{1}{4}=2(cos(\frac{19\pi}{36}))+\mathfrack{i}(sin(\frac{19\pi}{38}))}[/tex]

Part 3: Solving for root #2

To solve for root #2, follow the same simplifying steps above but change k  to k = 1.

[tex]z^{\frac{1}{4}}=16^{\frac{1}{4}}(cos(\frac{200}{4}+\frac{2(1)\pi}{4}))+\mathfrak{i}(sin(\frac{200}{4}+\frac{2(1)\pi}{4}))[/tex]

[tex]z^{\frac{1}{4}}=2(cos(\frac{5\pi}{18}+\frac{2\pi}{4}))+\mathfrak{i}(sin(\frac{5\pi}{18}+\frac{2\pi}{4}))\\[/tex]

[tex]z^{\frac{1}{4}}=2(cos(\frac{5\pi}{18}+\frac{\pi}{2}))+\mathfrak{i}(sin(\frac{5\pi}{18}+\frac{\pi}{2}))\\[/tex]

Root #2:

[tex]\large\boxed{z^{\frac{1}{4}}=2(cos(\frac{7\pi}{9}))+\mathfrak{i}(sin(\frac{7\pi}{9}))}[/tex]

Part 4: Solving for root #3

To solve for root #3, follow the same simplifying steps above but change k to k = 2.

[tex]z^{\frac{1}{4}}=16^{\frac{1}{4}}(cos(\frac{200}{4}+\frac{2(2)\pi}{4}))+\mathfrak{i}(sin(\frac{200}{4}+\frac{2(2)\pi}{4}))[/tex]

[tex]z^{\frac{1}{4}}=2(cos(\frac{5\pi}{18}+\frac{4\pi}{4}))+\mathfrak{i}(sin(\frac{5\pi}{18}+\frac{4\pi}{4}))\\[/tex]

[tex]z^{\frac{1}{4}}=2(cos(\frac{5\pi}{18}+\pi))+\mathfrak{i}(sin(\frac{5\pi}{18}+\pi))\\[/tex]

Root #3:

[tex]\large\boxed{z^{\frac{1}{4}}=2(cos(\frac{23\pi}{18}))+\mathfrak{i}(sin(\frac{23\pi}{18}))}[/tex]

Part 4: Solving for root #4

To solve for root #4, follow the same simplifying steps above but change k to k = 3.

[tex]z^{\frac{1}{4}}=16^{\frac{1}{4}}(cos(\frac{200}{4}+\frac{2(3)\pi}{4}))+\mathfrak{i}(sin(\frac{200}{4}+\frac{2(3)\pi}{4}))[/tex]

[tex]z^{\frac{1}{4}}=2(cos(\frac{5\pi}{18}+\frac{6\pi}{4}))+\mathfrak{i}(sin(\frac{5\pi}{18}+\frac{6\pi}{4}))\\[/tex]

[tex]z^{\frac{1}{4}}=2(cos(\frac{5\pi}{18}+\frac{3\pi}{2}))+\mathfrak{i}(sin(\frac{5\pi}{18}+\frac{3\pi}{2}))\\[/tex]

Root #4:

[tex]\large\boxed{z^{\frac{1}{4}}=2(cos(\frac{16\pi}{9}))+\mathfrak{i}(sin(\frac{16\pi}{19}))}[/tex]

The fourth roots of 16(cos 200° + i(sin 200°) are listed above.

g Which of the following is equivalent to P( A|B)? a. P(A and B) b. P(B|A) c. P(A)/P(B) d. None of these choices.

Answers

Answer:

The correct option is D.

But option B is correct if P(A) = P(B).

Step-by-step explanation:

P(A|B) is read as "The probability of A given B".

It is different from the options A, B, and C.

It is equal to option B only if the probability of A is equal to the probability of B. That is P(A|B) = P(B|A) if P(A) = P(B).

Find the measure of A.
A. 50
B. 70
C. 100
D. 90

Answers

Answer:

D

Step-by-step explanation:

I don't know how to eliminate the wrong answers.

Two line segments which have one end at a diameter and the other end meeting at a common point, make a 90 degree angle.

A is made that way, so A is 90 degrees.

Answer:

Step-by-step explanation:

I believe it is 90

evaluate the expression for -c-12=

Answers

Answer:

-10

Step-by-step explanation:

We can substitute c into the equation as -2.

[tex]-(-2) - 12[/tex]

Two negatives make a positive:

[tex]2-12[/tex]

And [tex]2 - 12 = -10[/tex].

Hope this helped!

Which of the following units is incommensurable with kilograms

Answers

Answer:

All units of measurement that are not based on or do not measure mass or weight and volume are incommensurable with kilograms.

Step-by-step explanation:

A measure unit is said to be incommensurable with another if it does not have the same measurement basis with the other measure unit.  For example, a measure in time cannot be measured in kilograms because time is measured in hours, minutes, seconds, days, etc.  But, if a measurement base can be applied to two or more measurement units, then the measurement units are commensurable with the measurement base.

You want to construct a pool that will hold 3496 ft. of water if the pool is to be 23 feet long and 19 wide how deep will it need to be

Answers

Answer:

8 feet deep

Step-by-step explanation:

volume = length x width x depth

3496 = 23 x 19 x d

3496 = 437 x d

divide both sides by 437

d = 8

(16 points) Find the radius of convergence and the interval of convergence of the power series. g

Answers

Answer:

The equation to be solved is missing in the question.

I will explain power series and ways to find the radius and interval of convergence of a powers series in the attached image.

Step-by-step explanation:

Understand the power seriesFind radius of convergenceDetermine interval of convergence

Find y using the Angle Sum Theorem

Answers

Step-by-step explanation:

Hey, there!!

Look this figure, simply we find that;

In triangle ABC,

angle CBD is an exterior angle of a triangle.

and its measure is 90°

Then,

angle CBD= y +48° {sum of interior opposite angle is equal to exterior angle or from theorem}.

or, 90°= y + 48°

Shifting, 48° in left side,

90°-48°= y

Therefore, the value of y is 42°.

Hope it helps...

What is the correct standard form of the equation of the parabola? Enter your answer below. Be sure to show each step of your work.

Answers

Answer:

Step-by-step explanation:

eq. of directrix is y=4 or y-4=0

perpendicular distance of (x,y) from directrix =distance of (x,y) from focus (-3,2)

[tex]| \frac{y-4}{1}|=\sqrt{(x+3)^2+(y-2)^2} \\squaring~both~sides\\y^2-8y+16=(x+3)^2+(y-2)2\\(x+3)^2=y^2-8y+16-(y-2)^2\\(x+3)^2=y^2-8y+16-(y^2-4y+4)\\(x+3)^2=y^2-8y+16-y^2+4y-4\\(x+3)^2=-4y+12\\(x+3)^2=-4(y-3)[/tex]

You calculate the correlation between height and weight for a simple random sample of 50 students from your college. Another student does the same for a simple random sample of 200 students from the college. The other student should get:_________.
A. a correlation greater than 1.
B. a higher value for the correlation.
C. about the same value for the correlation.
D. a lower value for the correlation.
E. a correlation less than-1.

Answers

Answer:

B

Step-by-step explanation:

What is the value of x to the nearest tenth?

Answers

Step-by-step explanation:

Hello!!!

Let's workout with this figure.

BC is a chord, O is the centre and OA is the perpendicular bisector.

AB = 1/2 of BC (according to circle's theorem)

so, A B = 1/2 × 25.6

Therefore, the measure of AB is 12.8.

now, let's have a small work with triangle AOB.

as it is a Right angled triangle, taking angle B as refrence angle we get,

p=x

b=12.8

h= OB = 16 (it is also a radius.)

now,

by Pythagoras relation we get,

[tex]p = \sqrt{ {h}^{2} - {b}^{2} } [/tex]

or, x = root 16^2- 12.8 ^2

by simplification, we get;

the measure of x is 9.6.

Therefore, the value of x is 9.6.

Hope it helps...

how many hours are there from 10:30 on Monday to 11:30 on Tuesday​

Answers

Answer:

25 hours.

Step-by-step explanation:

We are to find the number of hours from:

Monday at  10:30

to

Tuesday at 11:30

Since the question does not state whether the times are in A.M / P.M ,

There are 24 hours upto 10:30 on Tuesday.

Adding 1 hour gives 11:30

So the answer = 24 + 1 = 25 hrs

Answer:

25 hours

Step-by-step explanation:

1 day=24 hours

11.30-10.30=1 hour

----------------------------

add the total 25 hours

PLEASE ANSWER ASAP!!


How many cubic centimeters (
[tex] {cm}^{3} [/tex]
) are there in a 5 gallon jug of water?

Must show your work!!!




any unrelated answer will be reported​

Answers

Answer:

[tex]\boxed{\sf A}[/tex]

Step-by-step explanation:

[tex]\sf 1 \ gallon = 3785.41 \ cm^3[/tex]

[tex]\sf 5 \ gallon = \ ? \ cm^3[/tex]

[tex]\sf Multiply \ the \ gallon \ value \ by \ 3785.41.[/tex]

[tex]5 \times 3785.41 = 18927.1[/tex]

[tex]\sf Approximate \ the \ value.[/tex]

[tex]18927.1 \approx 19000[/tex]

Was is a macroeconomics

Answers

Answer:

Macroeconomics is a study that deals with the whole economy and everything pertaining to it.

Step-by-step explanation:

when we talk about Macroeconomics, we mean the whole economy. It can be related to a country's import or export, governance, how resources are accurately allocated to people in the country and the like.

Hi i need help on this im not that smart sorry, what is the x-intercept of the graph that is shown below

Answers

Answer:

(3, 0)

Step-by-step explanation:

x-intercept is where the line touches the x-axis

It is the point on the line where y=0

Answer:

3,0

Step-by-step explanation:

the point where the line cuts the x axis is the x-intecept

What is a categorical variable

Answers

It's a variable that deals with various labels, rather than the usual type of numeric variable you may be used to.

One example of a categorical variable is color. You could have red, green, blue, yellow, and orange as the five choices for your categorical variable. Each color is a label or category.

This is an example of a qualitative variable. We don't have any numeric data attached to color. They're simply names or labels. In contrast, a quantitative variable is something like a person's height since a number is attached here (more specifically its a continuous quantitative variable).

HELP ME ILL GIV ROBUX Identify the property shown by the equation. 14 × 6 = 6 × 14 A. Commutative Property B. Associative Property C. Identity Property D. Distributive Property PLEASE HELP ME

Answers

Answer:

A. Commutative Property

Step-by-step explanation:

Hello!

This is the Commutative property which is when you can change the order of the numbers and the result does not change.

Hope this helps!

Can someone help I would really appreciate

Answers

Answer:

18/a

Step-by-step explanation:

quotient means divide

18/a

(01.01 MC) Monica earned $60 from a bonus plus $8.50 per hour (h) she worked this week. Which of the following expressions best represents Monica's income for the week? 8.50h + 60 8.50 + 60 8.50 + 60h 8.50 + h + 60

Answers

Answer:

Option (1)

Step-by-step explanation:

Monica earned a bonus = $60

Per hour earning in addition to bonus = $8.50

Let she worked for 'h' hours this week.

Then total earning from the hourly rate = $8.50h

Total earning for the week = Earning of 'h' hours + Bonus earned

                                             = $(8.50h + 60)

Therefore, Option (1) will represent Monica's earnings for the week.

Answer:

8.50h + 60

Step-by-step explanation:

Help me please thank y’all

Answers

x= 30 degrees

Step-by-step explanation:

there's 180 degrees in a triangle. You can see 60 degrees right there. Theres a 90 degree angle right next to it. 180-150=30

confidence interavls for a population proportion. suppose that a random sample of 1000 mortgage loans that were defaulted within the first year reveals 410 of these loans were approved on hte basis of falsified applications. what is point estiamte of and a 95% confidence interval for p, the proportion of all first year defaults that are approved on the basis of flsified application

Answers

Answer:

The 95% confidence interval is  [tex]0.3795 < p < 0.4405[/tex]

Step-by-step explanation:

From the question we are told that

     The sample size is  [tex]n = 1000[/tex]

      The  number of approved loan is  k =  410

       

Generally the sample proportion is mathematically represented as

       [tex]\r p = \frac{k}{n}[/tex]

substituting values

      [tex]\r p = \frac{410}{1000}[/tex]

       [tex]\r p = 0.41[/tex]

Given that the confidence level is  95% then the level of significance is mathematically represented as

       [tex]\alpha = 100 - 95[/tex]

        [tex]\alpha = 5\%[/tex]

       [tex]\alpha = 0.05[/tex]

Next we obtain the critical value of  [tex]\frac{\alpha }{2}[/tex] from the normal distribution table,the value is  

         [tex]Z_{\frac{\alpha }{2} } =Z_{\frac{0.05 }{2} }= 1.96[/tex]

Generally the margin of error is mathematically represented as

        [tex]E = Z_{\frac{\alpha }{2} } * \sqrt{\frac{\r p(1- \r p)}{n} }[/tex]

substituting values

        [tex]E = 1.96 * \sqrt{\frac{ 0.41(1- 0.41)}{1000} }[/tex]

        [tex]E = 0.03048[/tex]

The 95% confidence interval for p is mathematically represented  as

     [tex]\r p - E < p < \r p + E[/tex]

substituting values

     [tex]0.41 - 0.03048 < p < 0.41 + 0.03048[/tex]

    [tex]0.3795 < p < 0.4405[/tex]

Word phrase for algebraic expression 15-1.5/d

Answers

Answer: 1.5 less than 15 is divided by a number d.

Step-by-step explanation:

Please help with this

Answers

Answer:

B) x=80°

Step-by-step explanation:

This is a hexagon, so it has interior angles equaling 720°.  (N-2)*180

So the equation would be

78+134+136+132+2x+x=720

480+3x=720

3x=720-480

3x=240

x=80°

Jesse bought 3 T-shirts for $6 each and 4 T-shirts for $5 each. What expression can you use to describe what Jesse bought?

Answers

(3x6) + (4x5). Is your answer for this question

What is the volume of a rectangular prism with a length, width,
2
1
5
and height of
cm, -
cm, and
cm, respectively?
3
4
6

Answers

Step-by-step explanation:

Hey, there!!

It's so simple,

Given,

length (l)= 2/3cm

Breadth (b) = 1/4cm

and height (h)=5/6cm

now, we use the formula for volume of rectangular prism is,

v = l× b× h

or, v= (2/3 × 1/4 × 5/6)^3

By simplifying it we get,

The volume is 5/36cm^3.

Hope it helps...

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