(1 point) Find how many positive integers with exactly four decimal digits, that is, positive integers between 1000 and 9999 inclusive, have the following properties: (a) are divisible by 5 and by 7. 257 (b) are divisible by 5 but not by 7. (c) are divisible by 5. (d) are divisible by 7.

Answers

Answer 1

Using arithmetic sequences, it is found that there are:

a) 257 numbers that are are divisible by 5 and by 7.

b) 1543 numbers that are divisible by 5 but not by 7.

c) 1800 numbers that are divisible by 5.

d) 1286 numbers that are divisible by 7.

In an arithmetic sequence, the difference between consecutive terms is always the same, called common difference d.

The nth term of an arithmetic sequence is given by:

[tex]a_n = a_1 + (n-1)d[/tex]

In which [tex]a_1[/tex] is the first term.

Item a:

Numbers that are divisible by 5 and 7 are multiples of 35, as the least common multiple of 5 and 7 are 35, thus we have an arithmetic sequence with [tex]d = 35[/tex].The first multiple of 35 in this interval is 1015, so [tex]a_1 = 1015[/tex].The last multiple of 35 in this interval is 9975, so [tex]a_n = 9975[/tex].

We apply the general formula and solve for n, thus:

[tex]a_n = a_1 + (n-1)d[/tex]

[tex]9975 = 1015 + 35(n-1)[/tex]

[tex]35n - 35 = 8960[/tex]

[tex]35n = 8995[/tex]

[tex]n = \frac{8995}{35}[/tex]

[tex]n = 257[/tex]

There are 257 numbers that are are divisible by 5 and by 7.

Item b:

First, we find the number of multiples of 5, with [tex]a_1 = 1000, a_n = 9995, d = 5[/tex]. Thus:

[tex]a_n = a_1 + (n-1)d[/tex]

[tex]9995 = 1000 + 5(n-1)[/tex]

[tex]5n - 5 = 8995[/tex]

[tex]5n = 9000[/tex]

[tex]n = \frac{9000}{5}[/tex]

[tex]n = 1800[/tex]

Of those numbers, 257 are multiples of 35, which means that they also are multiplies of 7, thus they are removed.

1800 - 257 = 1543.

There are 1543 numbers that are divisible by 5 but not by 7.

Item c:

From the previous item, there are 1800 numbers that are divisible by 5.

Item d:

We find the number of multiples of 7, with [tex]a_1 = 1001, a_n = 9996, d = 7[/tex]. Thus:

[tex]a_n = a_1 + (n-1)d[/tex]

[tex]9996 = 1001 + 7(n-1)[/tex]

[tex]7n - 7 = 8995[/tex]

[tex]7n = 9002[/tex]

[tex]n = \frac{9002}{7}[/tex]

[tex]n = 1286[/tex]

There are 1286 numbers that are divisible by 7.

A similar problem is given at https://brainly.com/question/23901992


Related Questions

100 POINTS FOR THE CORRECT ANSWER
(03.03 MC)

A marine biologist is studying the growth of a particular species of fish. She writes the following equation to show the length of the fish, f(m), in cm, after m months:

f(m) = 3(1.09)m

Part A: When the marine biologist concluded her study, the length of the fish was approximately 5.98 cm. What is a reasonable domain to plot the growth function? (4 points)

Part B: What does the y-intercept of the graph of the function f(m) represent? (2 points)

Part C: What is the average rate of change of the function f(m) from m = 2 to m = 8, and what does it represent? (4 points)

Answers

Answer:

I hope this helped. Look throught the pictures

Step-by-step explanation:

Answer:

Part A: 0<x<9

Part B: The y-intercept 3 represents how big the fish was when she first started her study.

Part C: The average rate of change from m=2 to m=8 is 2.09, and it represents the growth of the species of fish.

I don't know about Part C, but I hope this helps!

algebra ii question!

Answers

It’s the first answer because it’s greatest value is 6.

solve the inequality 2x + 3 < 7
A. x < 2
B. x > -2
C. x < -2
D. x > 2​

Answers

Answer:

A. x < 2

Step-by-step explanation:

solution:

=2x<7-3

=2x<4

=x<2


[tex]f(a) = {a}^{ \frac{1}{2} } + 3a + {a}^{2} [/tex]
[tex]f(x) = \frac{9}{17} {x}^{83} + \sqrt{54 {x}^{97} } + \pi[/tex]
[tex]g(x) = (x - \frac{2}{3} )(x + \frac{3}{4} )[/tex]
which one of the following is a polynomial and which is not, and why?​

Answers

Step-by-step explanation:

g(x) is a polynomial. It doesn't contain a rational degree with the variable as the denominator, negative eexponents, or irrational coeffecienfs, and no rational exponents as a degree.

f(x) and f(a) isn't a polynomial. It contain a irrational coeffceint like pi. So it not a polynomial. And they both have a rational exponet as a degree

Point C is located at ( -6,5). Point D is located at (-2, y). The
* distance between points C and D is 5 units. Find a possible y
value for point D.
Select all possible answers.
Pick up to 0 answers.
А
1
B. 2
C. 5
D. 8
E 9

Answers

Answer:

Step-by-step explanation:

yes cdrj

ejkfkj

ennejw

NEED HELP ASAP WILL GIVE BRAINLIEST
Find the quotient: 11.28 divided by 4.7

Answers

Answer:

11.28 Divided by 4.7 equals 2.4.

Step-by-step explanation:

It's just simple division. Glad I could help though!

Answer:

2.4

Step-by-step explanation:

What are your realizations after watching the video about Nature By Numbers By Cristobal Vila

Answers

Bacchae be cccdhjkgg here at the end of your life if

what is the product of 2 x 2 x 3 x 3 using an exponent?

Answers

Answer:

2^2 * 3^2

Step-by-step explanation:

2 * 2 * 3 * 3

We are multiplying 2 twos and we are multiplying 2 threes 3^2

The base is the number and the exponent is the number of the times

2^2 * 3^2

10
What is the volume of the rectangular prism,
if the length of one cube is 1 cm?

Answers

Answer:

60 cubic centimetres

which quanity is proportional to 5/25

Answers

Answer:

1/5

Step-by-step explanation:

A cube shaped block of ice has a mass of 59 kg. The density of ice is 917 kg per cubic meter. The mass of an object is the product of its density and its volume. Write a cubic function to model the mass of a block of ice in terms of its edge length x (in meters).

Answers

Using the density formula, the cubic function that models the mass of of a block of ice in terms of its edge length x is:

m = 917x³.

Using the function, the edge length of the block of ice is of 0.4 m.

What is the formula for the density of an object?

The density of an object is given by the mass of the object divided by it's volume, as follows:

d = m/v.

Hence the mass of the object is given by the following equation:

m = dv.

For this problem, we have that:

The density of ice is 917 kg per cubic meter, hence d = 917.The block of ice has a cubic format, meaning that v = x³, in which x is the edge length.

Hence the cubic function that models the mass of of a block of ice in terms of its edge length x is:

m = 917x³.

Considering the mass of the block of ice, the length is found as follows:

59 = 917x³

x = cubic root(59/917) -> (59/917)^(1/3) in any calculator

x = 0.4 m.

Using the function, the edge length of the block of ice is of 0.4 m.

More can be learned about the density formula at https://brainly.com/question/11836799

#SPJ1

What is 5.521 rounded to the nearest whole number?

Answers

Answer:

6

Step-by-step explanation:

If the first number (in this case, behind the decimal) is 5 or more, you round up. If it is 4 or less, you round down. since 2 and 1 are less than 4, you round down making them both 0. Then, you round up making the answer 6. I hope this makes sense! I wasn't entirely sure how to explain this.

f(x) = 3x + 6 please help quickly!!!!!!!

Answers

Given the function, f(x) = 3x + 6, we can solve for f(a), f(a + h) and [tex]\frac{(f(a + h) - f(a)) }{h}[/tex] by substituting their values into f(x) = 3x + 6. We will have the following:

[tex]\mathbf{f(a) = 3a + 6}\\\\\mathbf{f(a + h) = 3a + 3h + 6}\\\\\mathbf{\frac{(f(a + h) - f(a)) }{h} = 6}[/tex]

Given:

f(x) = 3x + 6

We are told to find:

f(a)f(a + h), and[tex]\frac{(f(a + h) - f(a)) }{h}[/tex]

1. Find f(a):

Substitute x = a into f(x) = 3x + 6

f(a) = 3(a) + 6

f(a) = 3a + 6

2. Find f(a + h):

Substitute x = a + h into f(x) = 3x + 6

f(a + h) = 3(a + h) + 6

f(a + h) = 3a + 3h + 6

3. Find [tex]\frac{(f(a + h) - f(a)) }{h}[/tex]:

Plug in the values of f(a + h) and f(a) into [tex]\frac{(f(a + h) - f(a)) }{h}[/tex]

Thus:

[tex]\frac{((3a + 3h + 6) - (3a + 6)) }{h}\\\\\frac{(3a + 3h + 6 - 3a - 6) }{h}\\\\[/tex]

Add like terms

[tex]\frac{(3a - 3a + 3h + 6 - 6) }{h}\\\\= \frac{3h }{h}\\\\\mathbf{= 3}[/tex]

Therefore, given the function, f(x) = 3x + 6, we can solve for f(a), f(a + h) and [tex]\frac{(f(a + h) - f(a)) }{h}[/tex] by substituting their values into f(x) = 3x + 6. We will have the following:

[tex]\mathbf{f(a) = 3a + 6}\\\\\mathbf{f(a + h) = 3a + 3h + 6}\\\\\mathbf{\frac{(f(a + h) - f(a)) }{h} = 6}[/tex]

Learn more here:

https://brainly.com/question/8161429

[tex]-3\frac{1}{3} * -3\frac{2}{5}[/tex]

Answers

Answer: 4

Step-by-step explanation:

First create numbers into an improper fraction.

-10/3 * (-3) 2/5

Then solve it using pemdas, resulting into the answer #4

Answer:

11 1/3

Step-by-step explanation:

Identify the sampling designs that use voluntary response sampling. Check all that apply.

Mrs. O’Neill asks all her seventh-period students about their study habits.
Each customer of a fitness club is interviewed about their health as they exit.
An online poll about voter opinion of political issues is posted on social media.
A student organization interviews students in the drama club about the spring play.
A doctor’s office sends email surveys to all its patients.
A department store includes a link to an online survey on customers’ receipts.

Answers

Answer: C, E, F

Step-by-step explanation:Got it right

y"+y'-6y = 12e^3t+12e^-2t

Answers

Answer

yc(T)=y"+y'-6y=0

Step-by-step explanation:

What is length of Ef?

Answers

Choice e) radical 300

Step-by-step explanation:

Using Pythagoras ;

[tex]20=\sqrt{10^{2}+x^{2} } \\20^{2}=10^{2}+ x^{2}\\400 = 100 +x^{2} \\300 = x^{2} \\x =\sqrt{300}[/tex]

Please give me a brainliest answer

can you help please i beg you guys

Answers

Answer:

Mr. Pandya's class has 12 boys and 18 girls.

Mr. Chapman's class has 5 girls and 25 boys.

Step-by-step explanation:

What is the answer X=-2(6+4)

Answers

Answer:

X = -20

Step-by-step explanation:

X = -2(6+4)

            ^ add 6 and 4 together first because they are in parentheses

-2(10)

   ^ this parenthesis means you want to multiply -2 and 10

because 2 x 10 = 20

that must mean -2 x 10 = -20

therefore, the value of X is -20

X= -20

Select the two statements that are true about the equation y − 10 = 60(x − 40).

A. The slope of the line is 10.
B. The slope of the line is 60.
C. One point on the line is (40, 10).
D. One point on the line is (10, 60).

Answers

Answer:

The answer for this question is B and C

The answer is B and C

The equation above is in point slope form

y-y1=m(x-x1)

Using the form, you can see that m represents the slope which is 60, y1 is 10 and x1 is 40. (40,10)

So thats why B and C is the answer!

brianlist me?

Blaine subtracted 340,139 from 601,800 Is Blaine's answer correct? If not, explain why and write the correct answers.​

Answers

Answer:

fsuu vvv

Step-by-step explanation:

gdcytzvnvdezcghiyyk for giving biscuits vicbeddings vicbeddings vicbeddings

Mr. Braun has $75.00 to spend on pizzas and soda pop for a picnic. Pizzas cost $9.00 each and the drinks cost $0.75 each. Five times as many drinks as pizzas are needed. What is the maximum
number of pizzas that Mr. Braun can buy?

Answers

The maximum  number of pizzas that Mr. Braun can buy is 5.

The equation that can be used to represent the total amount spent on soda pop and pizzas is:

$75 = 5x($0.75) + x($9)

Where:

x = number of pizzas that can be bought5x = total number of drinks that can be bought

In order to determine the number of pizzas that can be bought, we have to solve for x

$75 = 3.75x + 9x

$75 = $12.75x

x = $75 / 12.75

x = 5.88

If 6 pizzas are bought, 30 drinks would be bought, the total cost would be:

6($9) + 30(0.75) = $76.50

If 5 pizzas are bought, 25 drinks would be bought, the total cost would be:

5($9) + 25(0.75) = $63.75

A similar question was answered here: https://brainly.com/question/13965560

Write the equation of the line passing through the points (-7,8) and (7,2) The equation of the line is [ ]Can someone please help me!!!

Answers

Answer:

y = -3/7x + 5

Step-by-step explanation:

y2 - y1 / x2 - x1

2 - 8 / 7 - (-7)

-6/14

= -3/7

y = -3/7x + b

2 = -3/7(7) + b

2 = -3 + b

5 = b

Who can help me with this entire page?

Answers

Answer:

I'm not entirely sure what the question is but every thing under 12.5 is closer to 12, everything 12.5 and upwards like 12.87 would be closer to 13

a 2) Choose the correct name for the set of numbers. . {4 4. 256, 0.888, 26, – 4.0, 81 1.0, 781 4 O natural numbers O irrational numbers integers O whole numbers real numbers O rational numbers​

Answers

Answer:

irrational numbers integers

Consider the equation as shown:
(x-a)(y-b) = (x-2a)(y- b/2)

x(x + 1/2b) + y(y + a/2) -2xy = 5+(x-y)²

On comparing the coefficient, a student says these pairs of equations is consistent. Is he/she correct? Which of these explains why?
(a) Yes; because they are parallel lines.
(b) No; because they are interesting lines.
(c) Yes; because they are parallel lines.
(d) No; because they are interesting lines.​

Answers

[tex]\large\underline{\sf{Solution-}}[/tex]

First equation is

[tex]\rm \longmapsto\:(x - a)(y - b) = (x - 2a)\bigg(y -\dfrac{b}{2}\bigg) [/tex]

can be further simplified to

[tex]\rm \longmapsto\:xy - bx - ay + ab = xy - \dfrac{bx}{2} - 2ay + ab[/tex]

[tex]\rm \longmapsto\: - bx - ay = - \dfrac{bx}{2} - 2ay [/tex]

[tex]\rm \longmapsto\: - bx + \dfrac{bx}{2} = - 2ay + ay[/tex]

[tex]\rm \longmapsto\: - \dfrac{bx}{2} = - ay[/tex]

[tex]\rm \longmapsto\: \dfrac{bx}{2} = ay[/tex]

[tex]\rm \longmapsto\:bx = 2ay[/tex]

[tex]\rm:\longmapsto \:\boxed{\tt{ bx - 2ay = 0}} - - - - (1)[/tex]

Second equation is

[tex]\rm \longmapsto\:x\bigg(x + \dfrac{1}{2b} \bigg) + y \bigg(y + \dfrac{a}{2}\bigg) - 2xy = 5 + {(x - y)}^{2} [/tex]

[tex]\rm \longmapsto\: {x}^{2} + \dfrac{x}{2b} + {y}^{2} + \dfrac{ay}{2} - 2xy = 5 + {x}^{2} + {y}^{2} - 2xy[/tex]

[tex]\rm \longmapsto\: \dfrac{x}{2b} + \dfrac{ay}{2} = 5[/tex]

[tex]\rm \longmapsto\: \dfrac{x + aby}{2b} = 5[/tex]

[tex]\rm :\longmapsto\:\boxed{\tt{ x + aby = 10b}} - - - (2)[/tex]

So, we have two equations in simplest form as

[tex]\rm \longmapsto\:bx - 2ay = 0 [/tex]

and

[tex]\rm \longmapsto\:x + aby = 10b[/tex]

Now, Consider

[tex]\rm \longmapsto\:\dfrac{a_1}{a_2} = \dfrac{b}{1} = b[/tex]

[tex]\rm \longmapsto\:\dfrac{b_1}{b_2} = \dfrac{ - 2a}{ab} = - \dfrac{2}{b} [/tex]

[tex]\bf\implies \:\dfrac{a_1}{a_2} \: \ne \: \dfrac{b_1}{b_2} [/tex]

This implies, System of equations is consistent having unique solution.

So, The student is correct as lines are intersecting.

So, option (b) is correct.

A fair 20-sided die is tossed. What is the probability that the numbers 15 or 4 or 18 are tossed?

Answers

The probability of 1 number showing up out of 20 is 1/20

The probability of 3 different numbers showing up would be 3/20

Answer: 3/20

Find the value of a
1)3a=9
2)5a=20
3)7a=28

Find the value of p
4)p/2=5
5)p/5=4
6)p/9=6​

Answers

Answer:

Please do every single answer by transposition method..

Step-by-step explanation:

1) 3a=9

=a=9/3

=3

2) 5a=20

=a=20/5

=4

3) 7a=28

=a=28/7

= 4

4) p/2=5

=p=5×2

10

5) p/5=4

=p=4×5

=20

6) p/9=6

=p=6×9

=54

Divide. 3/5 divided by 4 =. 12/5 5/20 3/20 6/30

Answers

Answer:

3/20

Step-by-step explanation:

3/5 ÷ 4

Copy dot flip

3/5 * 1/4

Multiply

3/20

C. 3/20 is answer for that question

1. Brady had 432 Legos. Owen has
three times as many. How many Legos
does Owen have?
How
many do
they have all together?

Answers

Total legos = Brady’s legos + Owen’s legos. Brady has 432 legos and Owen has three times that amount. This means Owen has 432 X 3 legos: this will give you the answer that Owen has 1296 legos. To find the number of legos they have all together, use the equation in the beginning (Brady’s legos + owens legos). 432 + 1296 = 1728(the total number of legos they have altogether)
They have 1296 legos all together
Other Questions
Please help with story idea! (I will give brainliest, I just want ideas)I have a story idea where a group of maybe 8 year olds or so sneaks out one night to find some sort of artifact> I'm trying to figure out what that should do. Why do they want it? The story is going to start in a small town where everyone knows eachother, and this one group of kids try to go find this thing - I'm thinking the story will be somewhat like the Monkey's paw, with the three wishes, but I don't know. Does anyone have any ideas? This is supposed to be a horror story for class, but it doesnt have to be too scary, and it has to answer the question What are humans most afraid of? en la feria del condado, la calabaza con la cinta roja pesaba 108 libras menos que la calabaza con la cinta azul. cuanto pesaba la calabaza con la cinta azul? why did the national government pass the land ordinance of 1785? how can Jacey best present a professional image to her supervisor during the meeting (step 2, prompt 3)? Escriban la forma correcta del verbo Ser:Mi amiga y yo ...Group of answer choicessoyeressomoses A theme park has a Ferris wheel that takes 2 minutes to go around its 450-foot circumference. The equation (130) = 450 relates the speed of the Ferris wheel to its circumference. What exactly does represent? On a piece of paper, graph y-3 > 2x + 2. Then determine which answerchoice matches the graph you drew.ABD56(0.556(0.5)56(0,5)5(0,5-5 (-3,-1)5-5 (-3,-1)55 (-3,-1)56 (-3,-1)5-5A. Graph AB. Graph Bc. Graph CD. Graph D Thit k biu thc th lin kt v tp lc c s d liu quan h cho cc bi ton qun l sau:Bi ton 1. Bn cn mt c s d liu qun l thng tin v cc tp ch. Vi mi tp ch bn cn qun l tn tp ch, s ISSN (m s cng b ca tp ch), s pht hnh v nm pht hnh. D liu v cc bi bo trong tp ch bao gm: tiu bi bo, trang bt u v trang kt thc ca bi bo trong tp ch (ngha l bi bo bt u t trang no, v kt thc trang no trong tp ch). Gi thit rng khng c hai bi bo no c cng tiu . Mi bi bo c vit bi mt vi tc gi. Mi tc gi bn s lu cc thng tin v tn, a ch email v a ch c quan. in American Born Chinese, which characters serve as round characters? The Moon is about 240,000, or x _____ 10 miles from earth Can someone pls help me PLSSS HELP ME OUTTT!! what is the prefix of 10^10PLEASE BE FAST :) what do all craniates have that earlier chordates did not have? How quickly did tie Black Death kill people? Historians have recently discovered a historical journal published In the early twentleth century. The journal contalns facts based on originalsources about the downfall of the early Byzantium Empire. Historians consider this long-lost Journal to be a breakthrough In their understandingof the Byzantium Empire. Based on this Information, the journal Is asource. How does the initial mass of the candle compare with the final mass? Does this violate the Law of Conservation of Mass? Explain your reasoning. A/ Choose the underlined word or phrase that needs correcting.1. Yoga helps us learn what to co-ordinate breathing and movement.2. When should children do yoga too?3. Life in a small town is much peaceful than that in a big city.4. Today Ba gets up more earlier than he did yesterday.5.Among the ethnic minorities, the Tay have a largest population.6. How is more colourful, the Nungs or the Hoas costume?7. A: How long do Thai hold ceremonies to worship their ancestors? - B: Every year.8. When you play game online, be careful when you make friends to strangers.9. A: Look at this dish, Nick. It has five colours. - B: Sounds bad.10. A: Lets go to the local open-air market. - B: Yes, of course11. For many ethnic groups in the mountains, the horse is still the more convenient means of transport. I NEED A 100% ACCURATE ANSWER FOR THIS QUESTION ASAP NO LINKS !!!What describes the pressure in a contained fluid? 1: unknown as long as the fluid is contained2: the same throughout the fluid3: higher in some places and lower in other places Helpp i have 12 minutes