Ana escribe conjuntos de cinco enteros positivos consecutivos con la siguiente propiedad: La suma de tres de los números es tan grande como la suma de los otros dos. ¿Cuántos conjuntos con esta propiedad ha escrito Ana?


Seleccione una:

a. 1

b. 2

c. 0

d. 3

e. Mas de 3

Answers

Answer 1

Answer:

a) 1.

Step-by-step explanation:

Supongamos que el primer número entero positivo es a tal que a ∈ Z⁺.

Luego, el conjunto de los cinco enteros positivos se puede expresar como

A = {a; a+1; a+2; a+3; a+4}

Dada la condición del problema, se debe cumplir que

a + (a+1) + (a+2) = (a+3) + (a+4)

⇒  3a + 3 = 2a + 7

Resolviendo la ecuación resulta

a = 4

Luego, el conjunto A nos resulta

A = {4; 5; 6; 7; 8}

Puede concluirse que sólo un conjunto cumple con esta condición.


Related Questions

What single transformation was applied to triangle A to get Triangle B?​

Answers

Answer: can u help me with an equation then I will help you?

Step-by-step explanation:

Answer:

Dilation

Step-by-step explanation:

Dialation-A dilation is a transformation that produces an image that is the same shape as the original, but is a different size

Suppose a city with population 800 comma 000 has been growing at a rate of 5​% per year. If this rate​ continues, find the population of this city in 17 years.

Answers

Answer: 1,833,615

Step-by-step explanation:

Hi, to answer this question we have to apply an exponential growth function:

A = P (1 + r) t  

Where:

p = original population

r = growing rate (decimal form)

t= years

A = population after t years

Replacing with the values given:

A = 800,000 (1+ 5/100)^17

A = 1,833,615  

Feel free to ask for more if needed or if you did not understand something.

Find the area of the parrallelogram

Answers

Answer:

I believe it is about 47.63 meters squared

Leave a comment if you'd like a step-by-step explanation

A grocery store has advertised a sale on ice cream. Each carton of any flavor of ice cream costs $3.79. a.) It is asking us to give an expression that represents the Millie's total of buying one carton of strawberry ice cream and one carton of chocolate ice cream. First, we will need variables to represent each flavor of ice cream Millie is will buy: S: represents Strawberry ice cream C: represents chocolate ice cream Now, let make our expression... We know that EACH cost of a carton of ice cream is $3.79. Expression: 3.79 (S + C) <—- answer for A b.) Give another way to write 3.79 (S + C) Hint: Distributive property c.) You used distributive property on b to find the equivalent expression.

Answers

Answer:

$7.58

Step-by-step explanation:

Think about it, (S+C), each flavor costs $3.97 per carton, and there's 2 cartons. $3.79 x 2 = $7.58

What is the ratio of white shirts to all other colored shirts?
Favorite T-Shirt Colors of Teen-Aged Girls Surveyed
Red
Blue
Green
White
Pink
Orange
Yellow
Type your answer here
Back
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OPTIONS Options​

Answers

Answer:

1:12

Step-by-step explanation:

Please help me!!! -50 + 2a if a = 2.5 write the meaning of each algebraic expression then evaluate it for the given value I have no idea what this means please help

Answers

Answer:

-45

Step-by-step explanation:

I think it means that you just solve it.

What is the complete factorization of 12x^2+36x+27

Answers

Answer:

Those numbers are factored to

3(2x+3)2 <-------- the last 2 is squared

Answer:

Have a great rest of your day ;)

Step-by-step explanation:

On Monday, Mr. Roberts drove 42 miles. On Tuesday, he drove 5 miles more than half the distance he drove on Monday. Which expression shows how you could find the distance, in miles, Mr. Roberts drove on Tuesday? A.(42-5)*2 B. 42-(5*2) C. (42/2)-5 D.(42/2)+5

Answers

Answer:

D

Step-by-step explanation:

If it is half the distance, it would be divided by 2. plus 5 miles more would be added after the division.

Ella has a box of chocolate candies. She gives 1/3 of the candies to her sister, 4 to her brother, and eats the remaining 12 candies. How many chocolate candies were in the box originally?

Answers

Answer:

24 candies originally

Step-by-step explanation:

Add the 4 to how many you had left, then think about that number, 16, and what goes into 16 evenly 2 times? 8 and originally she gave away 1/3 of the box and if you were to add another 8 to the box it would be 24 divided by 1/3, -,-4,= 12.

does anyone have the rest of the test? Surface Area and Volume Unit Test????

Answers

Answer:

B) 112 cm²; 336 cm²

Step-by-step explanation:

The lateral area would be without the bases. In this case, the bases are the top and the bottom

Lateral Area

(2)(2.54)(8) = 40.64

(2)(2.54)(14) = 71.12

Add together and get 111.76 cm²

Surface Area

LA + Bases

Bases

(2)(14)(8) = 224

Add with lateral area and get 335.76 cm²

A rotating light is located 20 feet from a wall. The light completes one rotation every 3 seconds. Find the rate at which the light projected onto the wall is moving along the wall when the light's angle is 10 degrees from perpendicular to the wall.

Answers

Answer:

43.17 ft/s

Step-by-step explanation:

Let the height of the wall is y.

distance of wall from light is 20 feet.

[tex]tan\theta =\frac{y}{20}[/tex]    

y = 20 tanθ    .... (1)

time period, T = 3 second

[tex]\frac{d\theta}{dt}=\frac{2\pi}{3}[/tex]

Differentiate equation (1) with respect to t.

[tex]\frac{dy}{dt}=20sec^{2}\theta\times \frac{d\theta}{dt}[/tex]

[tex]\frac{dy}{dt}=20sec^{2}10\times \frac{2\pi}{3}[/tex]

dy/dt = 20 x 2.16

dy/dt = 43.17 ft/s

SOMEBODY PLEASE PLEASE PLEASE HELP ASAP ASAP ASAP I WILL MARK THE BRAINLIEST FOR WHOEVER ASNWERS RIGHT PEASE HURRRRRRYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY!!!!!!!!!!!!!!!!!!!!!!!!!! wow ok cuz this app is really making me mad nobody frickin answers when needed but then 500 days later they wanna answer honey by then imma be a grown women wit 5 kids a husband and dog f outta here man

Answers

Answer:

13

Step-by-step explanation:

√(12-0)^2+(5-10)^2√12^2+(-5)^2√144+25√16913

The half-life of a drug is 4 hours. A patient has been taking the drug on a regular basis for a few months and then discontinues taking it. The concentration of the drug in a patient's system is 120 ng/mL when the patient stops taking the medication. Complete the table, rounded to the nearest tenth of a ng.

Answers

After 4 hours: 60 ng/mL, After 8 hours: 30 ng/mL, After 12 hours: 15 ng/mL, After 16 hours: 7.5 ng/mL.

The half-life of a drug is the time it takes for the concentration of the drug in the body to reduce by half. In this case, the half-life of the drug is 4 hours. When a patient discontinues taking the medication, the concentration of the drug decreases exponentially over time.

The initial concentration is given as 120 ng/mL. After the first 4 hours, which is one half-life, the concentration reduces to 60 ng/mL. Subsequent half-lives continue to halve the concentration. After 8 hours, it becomes 30 ng/mL, after 12 hours it's 15 ng/mL, after 16 hours it's 7.5 ng/mL.

This exponential decrease reflects the nature of drug elimination from the body, with each half-life reducing the concentration by half. The rounded values in the table represent the decreasing drug concentrations at different time intervals after the patient stops taking the medication.

The base area of a triangular pyramid is 22 square yards and the height of the pyramid is 15 yards. What is the volume of the triangular pyramid?

V = 1
3
Bh

Answers

Answer:

110 yd cubed

Step-by-step explanation:

The volume of a triangular pyramid is denoted by: [tex]V=\frac{1}{3} Bh[/tex] , where B is the base area and h is the height. We already know here that B = 22 and h = 15, so we can just plug in these values:

[tex]V=\frac{1}{3} *22*15=110[/tex]

Thus, the volume is 110 yards cubed.

Hope this helps!

Answer:

330

Step-by-step explanation:

Because the formula for volume is Base time height (BH) so the base was 22 and the height was 15 so you just multiply them

What is the product? StartFraction 2 y Over y minus 3 EndFraction divided by StartFraction 4 y minus 12 Over 2 y + 6 EndFraction

Answers

Answer:

  [tex]\dfrac{y^2+3y}{y^2-6y+9}[/tex]

Step-by-step explanation:

When we write this using appropriate math symbols, it is easier to see the solution. To evaluate this, we multiply by the inverse of the denominator fraction.

  [tex]\dfrac{2y}{y - 3}\div \dfrac{ 4 y - 12}{2 y + 6}=\dfrac{2y}{y-3}\cdot\dfrac{2y+6}{4y-12}\\\\=\dfrac{4y(y+3)}{4(y-3)^2}}=\boxed{\dfrac{y^2+3y}{y^2-6y+9}}[/tex]

Answer:

d

Step-by-step explanation:

Do most students walk, bike, or bus to school?
Most students to school.
If 100 students were surveyed, how many students
walk to school each day?
students

Answers

Answer:

Most students ride the bus since the pie chart section is biggest at the bus section.

23 people walking / 100 people is 23% and 23% of 100 is 23 people.

Step-by-step explanation:

Answer:

Do most students walk, bike, or bus to school?

Most students

✔ bus to school.

If 100 students were surveyed, how many students walk to school each day?

✔ 23 students

Step-by-step explanation: I just did it, it's 100% correct!

the measures of angles of a hexagon 4x,5x,6x,7x,8x,9x.calculate the size of the largest angle.

Answers

Answer:

166 2/13 deg

Step-by-step explanation:

The sum of the measures of the interior angles of a convex polygon of n sides is 180(n - 2).

A hexagon has 6 sides, so n = 6.

sum of measures of angles = 180(n - 2) = 180(6 - 2) = 180(4) = 720

4x + 5x + 6x + 7x + 8x + 9x = 720

39x = 720

x = 720/39

x = 240/13

The largest angle has measure 9x.

9x = 9 * 240/13 = 2160/13

2160/13 = 166 2/13

Answer: 166 2/13 deg

I need help ASAP on this math question first one to answer get marked brainliest

Answers

Answer and Step-by-step explanation:

First, you want to graph the line of x = -1. This line is simply a vertical line running through (-1, 0).

The coordinates of each of the points are:

G(5, 9)

F(8, 9)

D(5, 6)

E(8, 6)

When we reflect point G over the line x = -1, we will get a point with the same y-coordinate, but with a different x-coordinate. Since 5 is 6 units away from -1, when you reflect G, the new x-coordinate will be -1 - 6 = -7. So, the new point for G is (-7, 9).

By similar reasoning for all the other points, we have:

F'(-10, 9)

D'(-7, 6)

E'(-10, 6)

Finally, just graph the points G'(-7, 9), F'(-10, 9), D'(-7, 6), and E'(-10, 6), and that's your new shape.

Hope this helps!

Answer:

D': (-7,6)

E': (-10,6)

F': (-10,9)

G': (-7,9)

Step-by-step explanation:

D: (5,6)

E: (8,6)

F: (8,9)

G: (5,9)

After reflection in x = -1

D': (-1-6,6)

E': (-1-9,6)

F': (-1-9,9)

G': (-1-6,9)

D': (-7,6)

E': (-10,6)

F': (-10,9)

G': (-7,9)

What is the slope of the line represented by the table below?

x y
-2 0
0 2
1 3
3 5
7 9
whats the slope

Answers

Answer:

The slope is 1 and the y-intercept is 2

HELP!!! I can't figure out what do do or how to solve the last part!!

Answers

Answer:

Use what you used for the first one and you should get the right answer.

Step-by-step explanation:

(PLEASE HELP) A red die is tossed and then a green die is tossed. What is the probability that the red die shows a number larger than three or the green die shows a number less than three? Make sure your answer is reduced.

Answers

Answer:

2/3

Step-by-step explanation:

Well, it supplied the formula, so let's start from there.

    P(A or B) = P(A) + P(B) - P(A and B)

Let A = the probability that the red die shows a number larger than three

Let B = the probability that the green die shows a number less than three

I'm assuming they both have 6 numbers on them, like a regular die.

    So there are 3 possibilities that are larger than 3 (4, 5, and 6) and 6 total possibilities, so A = 3/6.

    There are 2 possibilities that are less than 3 (1 and 2) and 6 total possibilities, so B = 2/6.

Plug that into the formula.

    P(A or B) = 3/6 + 2/6 - P(A and B)

Now we have to subtract the probability that both A and B happen, which is 3/6 * 2/6 = 6/36 = 1/6.

    P(A or B) = 3/6 + 2/6 - 1/6

    P(A or B) = 4/6 = 2/3

The volume of a cube is found by using the formula Alta third power where else side length if the side length is 4X to the third power what is the volume of the cube

Answers

Answer:

Volume of the cube is [tex]64x^9[/tex].

Step-by-step explanation:

Given:

Volume of the cube [tex]V = L^3[/tex]

where [tex]L[/tex] ⇒ side length

side length [tex]L =4x^3[/tex]

We need to find the Volume of the cube.

Solution:

Now we know that;

Volume of the cube [tex]V = L^3[/tex]

But side length [tex]L =4x^3[/tex]

So we will substitute the value of L in above equation we get;

Volume of the cube [tex]V = L^3=(4x^3)^3[/tex]

Now by using Law of indices which states [tex](a^m)^n=a^{mn}[/tex]

So we can say that;

Volume of the cube [tex]V = L^3=(4x^3)^3=4^3x^{3\times3}=64x^9[/tex]

Hence Volume of the cube is [tex]64x^9[/tex].

In circle A shown, secant DE and tangent DG are drawn. It ir know that m BAC = 63 and mBE = 96.

Answers

Answer:

Givens

[tex]m \angle BAC=63\°[/tex]

[tex]m(BE)=96\°[/tex]

[tex]DE[/tex] is secant.

[tex]DG[/tex] is tangent.

(A)

Remember that the arc subtended by a central angle is equal to it. That means

[tex]m(BC)=m\angle BAC = 63\°[/tex]

(B)

Now, by sum of arcs, we know

[tex]m(EBC)=m(EB)+m(BC)=96\° +63\°=159\°[/tex]

(C)

By definition, the total arc of a circle is 360°, so

[tex]m(EFC)=360\°-m(EBC)=360\° - 159\°=201\°[/tex]

(D)

We know that the external angle formed by a secant and a tanget is one half of the difference between the intercepted arcs, so

[tex]\angle D=\frac{1}{2}(m(EFC)-m(BC))=\frac{1}{2} (201\° - 63\°)=\frac{1}{2} (138\°)=69\°[/tex]

So, the angle D is 69°.

How many unit cubes are in one layer??

Answers

Final answer:

The number of unit cubes in one layer may vary depending on the type of cubic lattice structure. In a simple cubic lattice, there is one atom per unit cell. However, without specific dimensions or the exact structure type, the exact number of cubes per layer cannot be determined.

Explanation:

When we talk about the number of unit cubes in one layer, we must understand the geometry of the structure we are discussing. In a simple cubic lattice, each layer is made up of unit cubes that sit next to each other on each side. If the structure is in fact a simple cubic unit cell, then according to Figure 10.49 which describes this as having an atom at each of its eight corners and being shared by eight unit cells, there would be a total of one atom per unit cell.

In the context of a body-centered cubic structure mentioned, which is depicted in Figure 10.51, atoms in a specific layer do not touch each other, making the calculation of unit cubes in a single layer less straightforward; the cubes in the layers above and below touch the atom at the center.

Without specific dimensions or the type of cubic structure (simple cubic, face-centered cubic, or body-centered cubic), the exact number of unit cubes per layer cannot be determined. If we consider a cube made up of smaller unit cubes with a known side length, such as the polystyrene cube measuring 10 cm per side as mentioned, the number of unit cubes per layer would simply be the area of the cube's face divided by the area of one unit cube face. For a 10 cm cube, if each unit cube is 1 cm3, then there would be 10 x 10 = 100 unit cubes per layer.

4n+ 0.24 = 15.76
contains decimals
step by step please

Answers

Answer:

3.88

1. Subtract both sides by 0.24:

4n + 0.24 = 15.76

     - 0.24   - 0.24

______________

4n            = 15.52

2. Divide by 4 on both sides to isolate 'n':

4n = 15.52

__    ____

4         4  

n = 3.88

What is the image of (6,−3) after a dilation by a scale factor of 1/3 centered at the origin?

Answers

Answer:

(2,-1)

Step-by-step explanation:

Multiply everything by 1/3:

6*1/3=2

-3*1/3=-1

This makes it smaller, so you know what the dilation is.

Answer:

first person is correct

Step-by-step explanation:

Wayne exercised for 5/6 of an hour in the morning and 1/3 of an hour in the evening. How much more of an hour did Wayne spend exercising in the morning than in the evening?

Answers

Answer:

[tex]\frac{1}{2}[/tex] of an hour

Step-by-step explanation:

Given:

Wayne exercised for 5/6 of an hour in the morning and 1/3 of an hour in the evening

To find:

Additional hours spent by Wayne exercising in the morning than in the evening.

Solution:

Time spent by Wayne in the morning = [tex]\frac{5}{6}[/tex] of an hour

Time spent by Wayne in the evening = [tex]\frac{1}{3}[/tex] of an hour = [tex]\frac{2}{6}[/tex] of an hour

So, Wayne spends [tex]\frac{5}{6}-\frac{2}{6}=\frac{3}{6}=\frac{1}{2}[/tex] more in the morning than in the evening.

TRUE or FALSE: In the quarter circle, the radius is 4 cm and the diameter is 8 cm.

Answers

Answer: False.

Step-by-step explanation:

There does not exist a "quarter circle" as a circle with a radius of 4 units, the only notable circle that does exist is the unit circle, that is the circle where the radius is equal to 1, represented by the equatin x^2 + y^2 = 1

The term "quarter circle" actually does refer to a fourth part of a circle, not to a circle of radius 4.

So the statement is false

Suppose you flip a coin and spin a spinner that is divided into 8 equal regions. Of the 8 equal regions, 3 are red, 4 are black and 1 green. What is the probability of "tails" on the coin, and the spinner landing on red?
 (Hint: How many spaces are on the spinner total?)Immersive Reader
(5 Points)

Answers

Answer:

18.75%

Step-by-step explanation:

The probability of the coin is 1/2, because it only has two options (tail or head).

Now, in the case of roulette, it has a total of 8 options, and the red region has 3 parts, that is, of the 8 options, roulette 3 is red, therefore the probability is 3/8

Now the final probability is the multiplication of the probability of both events:

(1/2) * (3/8) = 0.1875 s 18.75%

In other words, the probability of these two events happening, that the tail comes out and is red, i

In the circle below, F is the center, GI is a diameter, and m

Answers

Answer:uh look up a video?

Step-by-step explanation:

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To investigate whether this result applies to its own product, the manufacturer of a national name-brand ketchup asked a sample of shoppers whether they believed that supermarket ketchup was as good as the national brand ketchup.a. Formulate the hypotheses that could be used to determine whether the percentage of supermarket shoppers who believe that the supermarket ketchup was as good as the national brand ketchup differed from 64%.b. If a sample of 100 shoppers showed 52 stating that the supermarket brand was as good as the national brand, what is the p-value (to 4 decimals)?c. At = = 0.05, what is your conclusion?d. Should the national brand ketchup manufacturer be pleased with this conclusion? How did American gothic literature differ from American romantic literature?