He conseguido ahorrar 510 euros en billetes de 50 y de 20 euros. Si en total tengo 15 billetes, ¿cuántos billetes de cada tipo tengo?

Answer:

Step-by-step explanation:

Common ratios are found by either multiplying the same number in to get to the next number in the sequence, or by dividing out the same number in to go the next number in the sequence. Multiply or divide, NOT add or subtract! Be careful! Obiviously, our numbers are going down, so we are dividing out a specific number as opposed to multiplying one in. To get from 18 to 6, we have to divide by 3; however, the 6 is negative, so we have to divide by -3. To determine if we are correct, divide -6 by -3 and see if that result is the next one in line. -6 divided by -3 is 2. So we are correct, and the common ratio is -3.

To prove that the group g is cyclic, we analyze the possible values of the order |g|. We consider the cases for each possible value and demonstrate that in all cases, g is either cyclic or leads to a contradiction.

For |g| = 1, 2, 3, 5, or 7, the groups of these orders are always cyclic.

If |g| = 4, 6, 8, 9, 10, 12, or 15, we show that g cannot have the required subgroups. Assuming g is not cyclic, we find an element x of order 2 and additional elements y, z, w, etc., also of order 2. This contradicts the given conditions since g would be isomorphic to Z₂ × Z₂ or have more than one subgroup of order 3 or 5.

For composite orders |g| = pq, where p and q are prime, we generalize the analysis. By Cauchy's theorem, g has elements of order p and q, and since there is only one subgroup of each order, they are cyclic. We show that the intersection of these subgroups cannot have an order of pq, leading to a contradiction. Hence, g is cyclic.

Therefore, in all cases, g is proved to be cyclic. QED.

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We have to find the probability of selecting a white ball on the second draw given that the first ball drawn was green.

We know that probability of selecting a green ball and then a white ball without replacement is 0.15, so we can write:

We also know that the probability of selecting a green ball in the first draw is 0.65:

Then, we can use this to find the conditional probability of selecting a white ball on the second draw given that the first ball drawn was green can be calculated as:

Answer: the probability is 0.231.

Some sources of initial funding when starting business are:

These are those sources that provide funds for a business to start-up at initial stages.

They include bank loans as banks are able to loan you money to start a business if they see you have a good business plan. Then there are personal savings that you can accumulate to invest in your business.

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A federal study reported that 7.5% of the u.s. workforce has a drug problem

a-1. You would expect 1.5 of the 20 employed workers in the sample to have a drug problem.

a-2. The standard deviation for this problem would be 1.1180.

b. The likelihood that none of the workers sampled has a drug problem is 0.3679.

c. The likelihood that at least one of the workers sampled has a drug problem is 1 - 0.3679 = 0.6321.

Using drugs may result in dependency and addiction, as well as physical and mental health concerns, difficulties sleeping, and other negative outcomes. Your usage of drugs has an effect not just on you but also on the people around you.

a-1. It is reasonable to anticipate that 1.5 of the 20 employed people in the sample will have a problem with drugs.

a-2: The value of 1.1180 would be used to represent the standard deviation for this situation.

a. The probability that any of the employees who were surveyed struggle with substance abuse is 0.3679.

c. The probability that at least one of the employees who have sampled struggles with substance abuse is 1 less than 0.3679, which equals 0.6321.

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Answer:

The answer is D!!!

Step-by-step explanation:

x=-7/5,=8/5 or (x=-1 2/5,y= 1 3/5) D one -7/5 = 1 2/5. 8/5 = 1 3/5

D IS THE CORRECT ANSWER

Answer:

x=3/2

Step-by-step explanation:

i think?

Hii :))

\( \tt(2x - 3) ^{2} \\ = \tt( 2 {x})^{2} - 2 \times 2x \times 3 + 3 ^{2} \\ = \boxed{ \tt 4 {x}^{2} - 12x + 9}\)

Just use the (a - b)² algebraic identity which is equal to a² - 2ab + b².

__________________

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ᴛʜᴇᴇxᴛʀᴀᴛᴇʀᴇꜱᴛʀɪᴀʟ

Answer:

One Solution

Step-by-step explanation:

Trust me

Given that at a toll plaza, vehicles arrive following an exponential distribution and departures are also exponential with one departure channel. The mean arrival rate is one vehicle every 20 seconds and the departure rate is 4 vehicles per minute. To find the average wait time (in seconds)

Solution:

We know that:

Average Wait Time = [µ^2 / (µ - λ)] * (1 + Cρ / (1 - ρ))

Where,µ = Service rate (departures), λ = Arrival rate, C = Number of serversρ = λ/µ.

First, we need to find the value of ρ.ρ = λ/µ= (1/20) / (4/60)= (3/2) * (1/20) = 0.075

Now, we need to find the value of Cρ:Cρ = 1 * 0.075 = 0.075

Next, we can find the value of 1 - ρ:1 - ρ = 1 - 0.075 = 0.925

Now, we can find the value of µ^2 / (µ - λ)µ^2 / (µ - λ) = (1/4)^2 / ((1/4) - (1/20))= 1/16 / (3/20)= 5/12

So, the Average Wait Time = [µ^2 / (µ - λ)] * (1 + Cρ / (1 - ρ))= (5/12) * (1 + 0.075 / 0.925)= (5/12) * 1.0811= 0.4482 minutes= 26.89 seconds

Therefore, the average wait time (in seconds) is 26.89 seconds.

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Step-by-step explanation:

20n 20394848484848575

The impulse on the body is 20 kg-m/s, the final speed of the body is 2m/s, and the distance covered within the time interval is 0.5m.

Force is the strength applied on an object with mass to change its state of motion.

The mass of the body is 10kg.

The force applied on the object is 40N.

The time for which the force is applied is 0.5 sec.

The impulse on the body is calculated by,

Impulse =  Force * Time

Impulse = 40 * 0.5

Impulse = 20 kg-m/s

The final speed of the body is given by

v = u + at

Assuming the initial speed = 0

v = at

Acceleration =  Force / mass

Acceleration = 40/10

a = 4 m/s²

v = 4 * 0.5

v = 2 m/s

The distance covered within the time interval is given by,

s = ut + (1/2) at²

s = (1/2) at²

s = (1/2) 4 * 0.5 *0.5

s = 0.5 m

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Answer:

10s+24

Step-by-step explanation:

2(5s+12)=2(5s)+2(12)=10s+24

The population variance is closest to 67.43, hence option C: 67.00, by referring the formula for population variance where N plays the number of data points.

The following gives the formula for population variance:

σ2 = (1 /N) ∑ (xi – μ) 2

Where:

σ2 refers to the population variance.

N refers to the total number of data points

∑ (xi – μ) 2 is the sum of the squared differences between each data point and the mean of the population.

For example, consider a population with data values of 12, 8, 28, 22, 12, 30, 14. The mean of this population is:

12+8+28+22+12+30+14)/7 = 18.

The population variance is calculated as follows:

σ2 = (1/7) [(12-18)2 + (8-18)2 + (28-18)2 + (22-18)2 + (12-18)2 + (30-18)2 + (14-18)2]

= 67.43

Therefore, the population variance is closest to 67.43.

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Complete question is:

Consider a population with data values of 12 8 28 22 12 30 14. The population variance is the closest to:

A. 8.00

B. 8.64

C. 67.00

D. 74.67

Answer:

They are congruent because GH ≅ GF, JF ≅ JH, and FH ≅ FH.

Step-by-step explanation:

On solving the provided question, w can say that - by distance here we can say that the distance are    \(d = sqrt ((20 - 80)^2 + (60 - 20)^2) = 72.11 = > d = sqrt ((110 - 20)^2 + (85 - 60)^2) = 93.41\)

Distance is a quantitative and occasionally qualitative indicator of how far away two objects or points are. Distance in physics or common use can refer to estimates based on physical length or other factors. formula for determining distance. a formula in algebra that uses coordinates to represent the distance between two places (see Coordinate Systems). The Cartesian point distance formula is based on the Pythagorean theorem in both 2-D and 3-D Euclidean space.

The distance formula given two points is,

\(d = sqrt ((x_2 - x_1)^2 + (y_2 - y_1)^2)\\ d = sqrt ((12 - 0)^2 + (3 - 5)^2) = 12.17\)                        

now to calculate the distance

\(d = sqrt ((20 - 80)^2 + (60 - 20)^2) = 72.11\\ d = sqrt ((110 - 20)^2 + (85 - 60)^2) = 93.41\)

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Answer:

7.01

7.02

7.03

7.04

and on and on till

7.99

or 7 1/100 7 2/100 and on and on

Step-by-step explanation:

Answer:

Difference in the lengths of the polygons is (x + 7) units.

Step-by-step explanation:

Lengths of the given polygon = (7x + 2) units and (6x - 5) units

Therefore, difference in the given lengths = (7x + 2) - (6x - 5)

                                                                      = (7x - 6x) + (2 + 5)

                                                                      = x + 7

Therefore, difference in the lengths of the polygons is (x + 7) units.

The number of definite integrals required to represent the area of the region enclosed by the curves y = cos^2(x)sin(x) and y = 0.03x^2, without using the absolute value function, would be n + 1, where n is the number of points of intersection between the curves.

To determine the number of definite integrals required to represent the area of the region enclosed by the curves y = cos^2(x)sin(x) and y = 0.03x^2, we need to identify the points of intersection between the two curves. The area can then be divided into separate regions, each requiring a separate definite integral.

To find the points of intersection, we set the two equations equal to each other:

cos^2(x)sin(x) = 0.03x^2

Solving this equation is a bit complex and requires numerical methods or approximation techniques. Once we find the points of intersection, let's say there are n points, we can divide the area into n + 1 regions, each requiring a separate definite integral.

For each region, we need to set up the integral to find the area between the two curves within that region. This involves integrating the difference between the upper and lower curves over the appropriate interval.

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a) the dimension of its column space is also 2. b) the rank of A is 2. c) the nullity of matrix A is 1. d) the dimension of the solution space of the homogeneous system \(A_x = 0\) is also 1.

(a) The dimension of the row space of a matrix is equal to the dimension of its column space. So, if the dimension of the row space of matrix A is 2, then the dimension of its column space is also 2.

(b) The rank of a matrix is defined as the maximum number of linearly independent rows or columns in the matrix. Since the dimension of the row space of matrix A is 2, the rank of A is also 2.

(c) The nullity of a matrix is defined as the dimension of the null space, which is the set of all solutions to the homogeneous equation Ax = 0. In this case, the matrix A is a 3 x 3 matrix, so the nullity can be calculated using the formula:

nullity = number of columns - rank

nullity = 3 - 2 = 1

Therefore, the nullity of matrix A is 1.

(d) The dimension of the solution space of the homogeneous system Ax = 0 is equal to the nullity of the matrix A. In this case, we have already determined that the nullity of matrix A is 1. Therefore, the dimension of the solution space of the homogeneous system \(A_x = 0\) is also 1.

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Answer:

1 1/3.

Step-by-step explanation:

Multiply the smaller triangle's amounts by 1 1/3, you get the corresponding bigger triangle's amount for that side.

Answer:

(-6 , 0)

Step-by-step explanation:

Given,

T.V = (-4)

( 5)

Now,

T.V = (-4)

(5)

<ABC (-2 , -7) ---------------> <ABC' (-2 + (-4) , -7+ 7)

<ABC (-2 , -7) ---------------> <ABC' (-2 -4) , -7+ 7)

<ABC (-2 , -7) ---------------> <ABC' (-6 , 0)

Explanation:

The translator vector is added to the co-ordinates.

Answer:

D. 25.12 feet

Step-by-step explanation: C= r(pi)^2

Answer:

Null hypothesis: Policy B remains more effective than policy A.

Alternate hypothesis: Policy A is more effective than policy B.

Step-by-step explanation:

Remember, a hypothesis is a  usually tentative (temporary until tested) assumption about two variables– independent and the dependent variable.

We have two types of hypothesis errors:

1. A type I error occurs when the null hypothesis (H0) is wrongly rejected.

That is, rejecting the assumption that policy B remains more effective than policy A when it is actually true.

2. A type II error occurs when the null hypothesis H0, is not rejected when it is actually false. That is, accepting the assumption that policy B remains more effective than policy A when it is actually false.

The number of different combinations to pay 10p with British coins is given as follows:

6.

The British coins are defined as follows:

Hence the different combinations to pay 10p with British coins are given as follows:

Which means that the number of combinations is of six, and the six combinations are the ones listed by the bullet points, above.

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Answer:

92

Step-by-step explanation:

\(M=1/2(78+106)\\M=1/2(184)\\M=92\)

Hope this helped! Have a good day.

The direction of Beatriz relative to the starting point of her trip is approximately \(278.806^{\circ}\).

After a careful reading of the statement, we find that final position (\(\vec r\)) by the end of the second day is found by means of this vector sum:

\(\vec r = \vec r_{1} + \vec r_{2}\) (1)

Where:

If we know that \(\vec r_{1} = (200\,km \cdot \cos 300^{\circ}, 200\,km\cdot \sin 300^{\circ})\) and \(\vec r_{2} = (150\,km\cdot \cos 250^{\circ}, 150\,km\cdot \sin 250^{\circ})\), then final position of Beatriz relative to origin is:

\(\vec r = (200\,km\cdot \cos 300^{\circ}, 200\,km\cdot \sin 300^{\circ})+(150\,km \cdot \cos 250^{\circ}, 150\,km\cdot \sin 250^{\circ})\)

\(\vec r = (48.670, -314.159)\,[km]\)

And the direction relative to the starting point (\(\theta\)), in degrees, is found by following inverse trigonometric relation:

\(\theta = \tan^{-1} \frac{r_{y}}{r_{x}}\) (2)

If we know that \(r_{x} = 48.670\,km\) and \(r_{y} = -314.159\,km\), then the direction of Beatriz relative to the starting point of her trip is:

\(\theta = \tan^{-1} \left(\frac{-314.159\,km}{48.670\,km} \right)\)

\(\theta \approx 278.806^{\circ}\)

The direction of Beatriz relative to the starting point of her trip is approximately \(278.806^{\circ}\). \(\blacksquare\)

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The two binomials for the expression x(x − 8) − 9(x − 8) are (x - 8) and (x - 9).

What are the binomials expression ?

The expression x(x − 8) − 9(x − 8) can be simplified as follows:

x(x − 8) − 9(x − 8) = x² - 8x - 9x + 72

= x² - 17x + 72

To find the two binomials, we need to factor the expression \(x^2 - 17x + 72\). We can do this by finding two numbers that multiply to 72 and add to -17. Those numbers are -8 and -9. Therefore, we can write:

\(x^2 - 17x + 72 = (x - 8)(x - 9)\)

Hence, the two binomials for the expression x(x − 8) − 9(x − 8) are (x - 8) and (x - 9).

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Answer: Polynomial

Step-by-step explanation:

If a typical somatic cell has 64 chromosomes, each gamete of that organism is expected to have 32 chromosomes.

In sexually reproducing organisms, somatic cells are the cells that make up the body and contain a full set of chromosomes, which includes both sets of homologous chromosomes. Gametes, on the other hand, are the reproductive cells (sperm and egg) that contain half the number of chromosomes as somatic cells.

During the process of gamete formation, called meiosis, the number of chromosomes is halved. This reduction occurs in two stages: meiosis I and meiosis II. In meiosis I, the homologous chromosomes pair up and undergo crossing over, resulting in the shuffling of genetic material. Then, the homologous chromosomes separate, reducing the chromosome number by half. In meiosis II, similar to mitosis, the sister chromatids of each chromosome separate, resulting in the formation of four haploid daughter cells, which are the gametes.

Since a typical somatic cell has 64 chromosomes, the gametes produced through meiosis will have half that number, which is 32 chromosomes. These gametes, with 32 chromosomes, will combine during fertilization to restore the full set of chromosomes in the offspring, creating a diploid zygote with 64 chromosomes.

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