Se presentaron entre 50 y 80 participantes del Nivel 1. Para trabajar durante el certamen se pudieron agrupar en forma exacta si lo hacían de a cuatro; pero si lo hacían de a cinco, faltaba una persona. ¿Cuántos participantes del Nivel 1 se postularon?

Answer:

5s

Step-by-step explanation:

Algebraic rule

s is a variable and it is an unspoken rule to multiply them if they are next to one another without a mathematical sign

The value of 3BC - 2AB is a matrix obtained by performing scalar multiplication and matrix addition/subtraction. The solution to the given system of simultaneous equations is x = 2, y = -1, and z = -2.

A matrix multiplication is performed by multiplying the entries of one matrix by the corresponding entries of the other matrix and summing the results. To find the value of 3BC - 2AB, we first calculate the products 3BC and 2AB, and then subtract 2AB from 3BC.

The matrix BC is obtained by multiplying the matrix B by the matrix C:

BC =

[(−2)(−2) + (2)(−1) (−2)(1) + (2)(1) ]

[(1)(−2) + (3)(−1) (1)(1) + (3)(1) ]

Simplifying this expression gives us:

BC =

[2 0]

[-5 4]

Next, we calculate the product AB by multiplying the matrix A by the matrix B:

AB =

[(0)(−2) + (2)(1) (0)(2) + (2)(3) ]

[(1)(−2) + (−3)(1) (1)(2) + (−3)(3) ]

Simplifying this expression gives us:

AB =

[2 6]

[-5 -7]

Finally, we subtract 2AB from 3BC:

3BC - 2AB =

[3(2) - 2(2) 3(0) - 2(6) ]

[3(-5) - 2(-5) 3(4) - 2(-7) ]

Simplifying this expression gives us the final result:

3BC - 2AB =

[2 -12]

[-5 34]

Moving on to the second part of the question, to solve the given system of simultaneous equations, we can use the matrix method or any other appropriate method such as Gaussian elimination. Here, we'll use the matrix method.

We can represent the system of equations as a matrix equation AX = B, where:

A =

[1 2 -1]

[3 5 -1]

[-2 -1 -2]

X =

[x]

[y]

[z]

B =

[6]

[2]

[4]

To find X, we can solve the equation AX = B by multiplying both sides of the equation by the inverse of matrix A:

X =\(A^(-1) * B\)

Calculating the inverse of matrix A and multiplying it by B, we obtain:

X =

[2]

[-1]

[-2]

Therefore, the solution to the given system of simultaneous equations is x = 2, y = -1, and z = -2

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The mileage rating that the upper 11% of cars achieve is approximately 40.568 (approx).

Automobile mileage ratings is normally distributed with a mean of 38 mpg and a standard deviation of 1.6 mpg. We need to find the probability of P(X <37), P(3541), P(X>37) and mileage rating that the upper 11% of cars achieve.

Let X be the mileage rating of automobile. Then, X ~ N (38, 1.6^2)The z - score for any value x can be calculated using the formula :\( z = \frac{x-\mu}{\sigma} \)a) P(X < 37)We need to find the probability that the mileage rating is less than 37. Hence, we need to find P(X < 37).\(P(X < 37) = P \left( z < \frac{37-38}{1.6} \right) = P(z < -0.625) \)

From the standard normal distribution table, the probability of getting z < -0.625 is 0.2643.Therefore, P(X < 37) = 0.2643 (approx)Hence, the correct option is Incorrect.b) P(X > 41)We need to find the probability that the mileage rating is greater than 41. Hence, we need to find P(X > 41).\(P(X > 41) = P \left( z > \frac{41-38}{1.6} \right) = P(z > 1.875) \)

From the standard normal distribution table, the probability of getting z > 1.875 is 0.0304.Therefore, P(X > 41) = 0.0304 (approx)Hence, the correct option is 0.0304. c) P(X > 37)We need to find the probability that the mileage rating is greater than 37. Hence, we need to find P(X > 37).\(P(X > 37) = P \left( z > \frac{37-38}{1.6} \right) = P(z > -0.625) \)

From the standard normal distribution table, the probability of getting z > -0.625 is 0.7340.Therefore, P(X > 37) = 0.7340 (approx)Hence, the correct option is 0.7340. d) The mileage rating that the upper 11% of cars achieveLet X be the mileage rating of the automobile.Then, X ~ N(38, 1.6^2)

The probability that the mileage rating is greater than any value x can be given as,\( P(X > x) = 1 - P(X < x) \)

The probability that the mileage rating is greater than x = 38 can be calculated as follows :\(P(X > 38) = 1 - P(X < 38) = 1- P \left( z < \frac{38-38}{1.6} \right) = 1- P(z < 0) = 1- 0.5000 = 0.5000\)

Now, let 'a' be the mileage rating that the upper 11% of cars achieve. Then, P(X > a) = 0.11

This can be written as,\( P(X < a) = 1- P(X > a) = 1 - 0.11 = 0.89 \)

We need to find the value of 'a' such that P(X < a) = 0.89 i.e. 89th percentile from the normal distribution table.

By looking into the normal distribution table, we get the z-value that corresponds to the area 0.89 to be 1.23.Then, the mileage rating a can be calculated as,\( z = \frac{a - \mu}{\sigma} \Rightarrow 1.23 = \frac{a - 38}{1.6} \)

Simplifying the above equation, we get the mileage rating a as, a = 40.568Therefore, the mileage rating that the upper 11% of cars achieve is approximately 40.568 (approx).Hence, the correct option is 40.568.

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The proof of every positive integer k that divides the order of g, there exists a subgroup h of g of order k is shown below:

A subgroup is a group nested inside another group. The subgroup test is used on subsets of a group to determine if they are subgroups. A proper subgroup is a subgroup that does not contain all of the original group, while a trivial subgroup contains only the identity.

Suppose k ∣ g ⟹n=dk:

If h(g)=⟨g⟩ is cyclic then

clearly K:=|⟨g^d⟩|=k .

Suppose now we have

1≠H≤h(g),

|H|=k and

let r>0 be the minimal natural number s.t.

g^r ∈ H , then

1=(g ^ r)^k = g^(r k)

⟹n ∣ r k ⟹ r k=ns =d ks ⟹ r= ds ⟹ s ∣ d

and from here we have

g^ r=(g^ d)^ s ∈K

Also,  |H|=||K|

we get equality and thus uniqueness of K.

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Answer:

56

Step-by-step explanation:

they are same side interior angles so both add up to 180 so just subtract 124 from 180 to get 56

Answer:

Step-by-step explanation:

6y - y = y(6 - 1) = y * 5

The answer is 5y.

Answer:

blue

Step-by-step explanation:

If \(MU_{x}/P_{x}\)=30 and \(MU_{y} /P_{y}\)=40 then the consumer should buy the commodity y to maximise utility.

Given that \(MU_{x}/P_{x}\)=30 and \(MU_{y} /P_{y}\)=40 of commodities x and y.

Marginal utility is the additional utility that a consumer gets from consuming additional units of commodity. For maximising the utility of the consumer,the ratio of marginal utilities must be equal to the ratio of the products.

There can be two situations in our case:

Because \(MU_{x}/P_{x}\)<\(MU_{y} /P_{y}\)

So to equalise the ratio we need to reduce \(MU_{y} /P_{y}\). To reduce the utility of y the consumer needs to increase the consumption of y because as the consumption of commodity y increase it decreases the utility of commodity y.

Hence if \(MU_{x}/P_{x}\)=30 and \(MU_{y} /P_{y}\)=40 then the consumer should buy the commodity y to maximise utility.

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The equations show a directly proportionate relationship will be y = 4x. Option A is correct.

It is defined as the relationship between two variables when the first variable increases, the second variable also increases according to the constant factor.

When two quantities are directly proportional, this implies that if one quantity increases by a specific percentage, the other quantity also increases by the same percentage.

The equations show a directly proportionate relationship is,

y = 4x

Here 4 is taken as the constant, In order to eradicate the constant we have to apply the proportionality sign.

y ∝ x

Thus, the equations show a directly proportionate relationship will be y = 4x. Option A is correct.

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Answer:

5 boys

Step-by-step explanation:

boys to girls in math class = 3/12

3/12 can be reduced to 1/4

In the science class, the ratio is the same but there is a total of 20 girls.

Multiply the fraction 1/4 by 2/2, 3/3, 4/4, 5/5, etc. until you get x/20. Then you have 20 girls. x is the number of boys.

1/4 = 2/8 = 3/12 = 4/16 = 5/20

In science the ratio of 1/4 is the same as 5/20, so there are 5 boys.

Answer: 5 boys

Answer:

11 - 6√3

Step-by-step explanation:

Given the expression;

5+2√3/7+4√3

Rationalize

5+2√3/7+4√3 * 7-4√3/7-4√3

= 35 - 20√3+14√3 - 24/49 - 16(3)

= 35 - 20√3+14√3 - 24/49 - 48

= 35 - 20√3+14√3 - 24

= 35 - 6√3- 24

= 35 - 24 -  6√3

= 11 - 6√3

This gives the required solution

Answer: y = 5x + 26

Step-by-step explanation:

To find the equation of a line that is perpendicular to the given line y = -1/5x + 1 and passes through the point (-5, 1), we need to determine the slope of the perpendicular line. The given line has a slope of -1/5. Perpendicular lines have slopes that are negative reciprocals of each other. So, the slope of the perpendicular line will be the negative reciprocal of -1/5, which is 5/1 or simply 5. Now, we have the slope (m = 5) and a point (-5, 1) that the perpendicular line passes through.

We can use the point-slope form of a linear equation to find the equation of the line:

y - y1 = m(x - x1)

Substituting the values, we get:

y - 1 = 5(x - (-5))

Simplifying further:

y - 1 = 5(x + 5)

Expanding the brackets:

y - 1 = 5x + 25

Rearranging the equation to the slope-intercept form (y = mx + b):

y = 5x + 26

Therefore, the equation of the perpendicular line that passes through the point (-5, 1) is y = 5x + 26.

a. The probability of success (hitting the target) is constant for each trial (88% or 0.88).

b. The probability of hitting the 6th target is:

P(X = 1) = C(1, 1) * 0.88^1 * (1 - 0.88)^(1 - 1) = 0.88

c. Using the binomial probability formula as before, with p = 0.88 and n = 3:

P(X = 1) = C(3, 1) * 0.88^1 * (1 - 0.88)^(3 - 1)

P(X = 2) = C(3, 2) * 0.88^2 * (1 - 0.88)^(3 - 2)

P(X = 3) = C(3, 3) * 0.88^3 * (1 - 0.88)^(3 - 3)

a) The three characteristics of this scenario that indicate we are working with Bernoulli trials are:

The experiment consists of a fixed number of trials (eight shots).

Each trial (shot) has two possible outcomes: hitting the target or missing the target.

The probability of success (hitting the target) is constant for each trial (88% or 0.88).

b) To find the probability of hitting the 6th target (considered as a single trial), we can use the binomial probability formula:

P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)

where:

P(X = k) is the probability of getting exactly k successes,

C(n, k) is the binomial coefficient or number of ways to choose k successes out of n trials,

p is the probability of success in a single trial, and

n is the total number of trials.

In this case, k = 1 (hitting the target once), p = 0.88, and n = 1. Therefore, the probability of hitting the 6th target is:

P(X = 1) = C(1, 1) * 0.88^1 * (1 - 0.88)^(1 - 1) = 0.88

c) To find the probability that the first time hitting the target is not until the 4th shot, we need to consider the complementary event. The complementary event is hitting the target before the 4th shot.

P(not hitting until the 4th shot) = P(hitting on the 4th shot or later) = 1 - P(hitting on or before the 3rd shot)

The probability of hitting on or before the 3rd shot is the sum of the probabilities of hitting on the 1st, 2nd, and 3rd shots:

P(hitting on or before the 3rd shot) = P(X ≤ 3) = P(X = 1) + P(X = 2) + P(X = 3)

Using the binomial probability formula as before, with p = 0.88 and n = 3:

P(X = 1) = C(3, 1) * 0.88^1 * (1 - 0.88)^(3 - 1)

P(X = 2) = C(3, 2) * 0.88^2 * (1 - 0.88)^(3 - 2)

P(X = 3) = C(3, 3) * 0.88^3 * (1 - 0.88)^(3 - 3)

Calculate these probabilities and sum them up to find P(hitting on or before the 3rd shot), and then subtract from 1 to find the desired probability.

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Answer:

(1, -2)

Step-by-step explanation:

hope this helps :)

Least to greatest slope, the segments are B, C, A.

What is the segment's slope ?

The slope of a line segment indicates how steep the line segment is. It is the ratio of rise (the change in vertical height between the endpoints) to run (the change in horizontal length between the endpoints).

The segment's slope provides information about how quickly the water level is rising. In relation to the angle the segment makes with the +x axis, the slope is defined as the rise to run ratio.

Greater slope can be found in segments that have more ascent for a given run. With respect to the +x axis, segments with a greater reference angle have a steeper slope.

Segment B has the least slope in this case, followed by segment C, and then segment A, which has the greatest slope.

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Answer:

The answer is 24

just multiply 6 and 4 together

The statement that is true on the bowling alley charges and the additional cost for renting bowling shoes is The description shows a linear relationship, but not a proportional relationship.

In a linear relationship, the values of the two variables can be drawn on a graph such that they form a line. There would often be a y-intercept and then a slope or a constant rate of change. In this case the constant rate of change is the $15 per game and the additional cost to rent bowling shoes is the y-intercept. This is therefore a linear relationship.

A proportional relationship would have a constant rate of change but there would be no y - intercept. As there is a y - intercept in this scenario, this is not proportional.

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Answer: A: The description shows a linear relationship, but not a proportional relationship.

Answer:

isnfdytsafksjd

Step-by-step explanation:

ryref w4trfd ws 3wqrs

To complete the square for the equation \(x^2 + 8x + 32 = (x - h)^2 + 16\),

we need to choose h = -2.

To complete the square for the given equation

\(x^2 + 8x + 32 = (x - h)^2 + 16\),

we need to express the left-hand side of the equation in the form

\((x - p)^2 + q\), where p and q are constants.

We can start by expanding the right-hand side of the equation:

\((x - h)^2 + 16 = x^2 - 2hx + h^2 + 16\)

Now we can compare the coefficients of \(x^2\), x, and the constant term on both sides of the equation:

\(x^2 + 8x + 32 = (x - p)^2 + q\)

=> \(p^2 = 0\) (since the coefficient of \(x^2\) is 1 on both sides)

=> -2hp = 8 (since the coefficient of x is 8 on the left-hand side)

=> h = -2 (solving for h)

=> q = \(h^2 + 16\) = 20 (since the constant term on the right-hand side is 16)

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The complete question may be:

What value of h is needed to complete the square for the equation \(x^2+8 x+32=(x-h)^2+16\) ?

The polar equation \( r = 32/(8 - 5 sin θ)\)  the simplified rectangular equation with all terms on the left side and 0 on the right side

\(8(sqrt(x^2 + y^2)) - 5y - 32 = 0\)

To convert the polar equation to a rectangular equation, we'll use the following relations:
\(x = r cos θ and y = r sin θ\)
First, let's solve for r in the given polar equation:
\(r = 32/(8 - 5 sin θ)\)
Now, multiply both sides by (8 - 5 sin θ) to get rid of the denominator:
\(r(8 - 5 sin θ) = 32\)
Replace r with its rectangular equivalent \((sqrt(x^2 + y^2))\):
\((sqrt(x^2 + y^2))(8 - 5 sin θ) = 32\)
Next, replace sin θ with its rectangular equivalent \((y/r or y/sqrt(x^2 + y^2))\):
\((sqrt(x^2 + y^2))(8 - 5(y/sqrt(x^2 + y^2))) = 32\)
Now, distribute the sqrt(x^2 + y^2) into the parentheses:
\(8(sqrt(x^2 + y^2)) - 5y = 32\)
To simplify the equation, move all terms to the left side:
\(8(sqrt(x^2 + y^2)) - 5y - 32 = 0\)
This is the simplified rectangular equation with all terms on the left side and 0 on the right side.

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Answer: B. XIX

Step-by-step explanation: If Sarah is 3 years older than Ben, she is 3 years older than 16. That means she is 19 years old. In Roman numerals, we need to think of it as she is 10+9 years old.

X represents 10.

IX represents 9 Because...

... in order to represent a number less than ten, we need to think about how much less than ten it is. Since 9 is one less than 10, you write it as IX since a smaller numeral in front of X represents subtraction.

So you combine the 10 and 9 to get XIX.

Answer:

6 Apples

Step-by-step explanation:

There would be six apples and 2 oranges left over.

Hope this Helps!

:D

Answer:

I was kind of confused on this one but is it 15 apples?

Step-by-step explanation:

3, 6, 9, 12, 15

4, 8, 12, 16, 20

I think the answer is 15 apples.

The quotient of the division x - 3 | 4x^2 + 3x + 2 is 4x + 15

From the question, we have the following parameters that can be used in our computation:

x - 3 | 4x^2 + 3x + 2

Using the long division method of quotient, we have

x - 3 | 4x^2 + 3x + 2

The division steps are as follows

          4x + 15

x - 3 | 4x^2 + 3x + 2

          4x^2 - 12x

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

              15x + 2

              15x - 45

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

                        47

Hence, the quotient is 4x + 15

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Answer:

x=2

Step-by-step explanation:

plz mark as brainliest

Answer:

\(y=-5x+2\)

Step-by-step explanation:

\(y-y_{1} =m(x-x_{1} )\\y-2=-5(x)\\y-2=-5x\\y=-5x+2\)

The ball traveled approximately \(26.27\) units in total.

To calculate the distance the ball traveled, we can use the distance formula between two points in a Cartesian coordinate system.

Distance = \(\sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1} )^{2} }\)

Let's calculate the distance between Player A and Player B first:

Distance_AB =

\(\sqrt{((16-2)^{2}+(9-4)^{2}) }\)

\(= \sqrt{(14^{2}+5^{2} ) } \\= \sqrt{(196 +25)} \\= \sqrt{221} \\= 14.87\)

Now, let's calculate the distance between Player B and Player C:

Distance_BC =

\(\sqrt{ ((25 - 16)^2 + (16 - 9)^2)}\\= \sqrt{ (9^2 + 7^2)}\\= \sqrt{(81 + 49)}\\= \sqrt{130}\\=11.40\)

Finally, we can calculate the total distance traveled by adding the distances AB and BC:

Total distance = Distance_AB + Distance_BC

\(= 14.87 + 11.40 \\= 26.27\)

Starting from Player A at \((2, 4),\) it was thrown to Player B at \((16, 9),\) covering a distance of about \(14.87\) units. From Player B, the ball was then thrown to Player C at \((25, 16),\) covering an additional distance of approximately \(11.40\) units.

Combining these distances, the total distance the ball traveled was approximately \(26.27\) units.

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The probability that the first two electric toothbrushes sold are defective is 0.016.

The probability of an event, say E occurring is:

\(P(E)=\frac{n(E)}{N}\)

Here,

n (E) = favorable outcomes

N = total number of outcomes

Let X = the number of defective electric toothbrushes sold.

The number of electric toothbrushes that were delivered to a store is n = 20.

The number of defective electric toothbrushes is x = 3.

The number of ways to select two toothbrushes to sell from the 20 toothbrushes is:

\((\left {{20} \atop {2}} \right. )\)\(=\frac{20!}{2!(20-2)!} =\frac{20!}{2!18!} =\frac{20*19*18!}{2!*18!} = 190\)

The number of ways to select two defective toothbrushes to sell from the 3 defective toothbrushes is:

\((\left {{3} \atop {2}} \right. )\)\(=\frac{3!}{2!(3-2)!} =\frac{3!}{2!1!} =\frac{3*2!}{1!2!} =3\)

Compute the probability that the first two electric toothbrushes sold are defective as follows:

P (Selling 2 defective toothbrushes) = Favorable outcomes ÷ Total no. of outcomes

\(\frac{3}{190}\\ =0.01579\\=0.016\)

Thus, the probability that the first two electric toothbrushes sold are defective is 0.016.

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Answer:

A. I and II, only

Step-by-step explanation:

y = x

Switch variables.

x = y

y = 1/x

Switch variables.

x = 1/y

1/x = y

y = x²

Switch variables.

x = y²

±√x = y

y = x³

Switch variables.

x = y³

∛x = y

The inverse of the function f(x) = 12x + 4 is y = (x - 4) / 12.

An inverse function or an anti function is defined as a function, which can reverse into another function.

The given function is,

f(x) = 12x + 4

Now, to find inverse function

Let y =  f(x) = 12x + 4

⇒ y = 12x + 4

Switch x and y we get,

x = 12y + 4

Solve for y

12y = x - 4

⇒ y = (x - 4) / 12

this is the required inverse function.

Thus, the inverse of the function f(x) = 12x + 4 is y = (x - 4) / 12.

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