Exercise #1
write an algebraic expression
1. The sum of a numberand twelve

Answer:

I think it is 2. It's just a guss.

Step-by-step explanation:

Answer:

Step-by-step explanation: 25 because I asked my teacher in class right now and he sloved it and im to lazy to show you how but do (25) 25 is the answer

The two stores cannot have the same rate of charges for any number of items.

To solve the given problem obtain the linear equation according to the condition that is given in the problem.

Here the equation can be solved by adding or subtracting the same integer on both sides or multiplying or dividing by the same integer.

Here we have

Store​ A's prices are modeled by the expression (20x-3)  

Store​ B's prices are modeled by the expression 4(5x+1)  

where x is the number of items brought  

Let's assume at 'x' number of items both stores have the same rate

=> 20(x - 3) = 4(5x + 1)

=> 20x - 60 = 20x + 4

We can solve the above expression by subtracting 20x on both sides

=> 20x - 20x - 60 = 20x - 20x + 4

=> -60 = 4        

Hence, we cannot solve the equation for 'x'

This implies that the rate of stores cannot be the same

Therefore,

The two stores cannot have the same rate of charges for any number of items.

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The function with "all real numbers" as its range is Of(x) = 2x^2 + 1.

The function whose range would include "all real numbers" is:

Of(x) = 2x^2 + 1

We must look at the characteristics of each of the provided functions in order to understand why.

As division by zero is undefined, all real numbers except for x = 2 fall inside the domain of Of(x) = 2/x - 2. Thus, no values that would reduce the denominator to 0 will be included in the range. We can observe that the function approaches zero when x approaches positive or negative infinity, but it will never reach zero. The range therefore includes all real values other than 0.

Due to the fact that Of(x) = x3 + 2 is a polynomial function of degree 3, it has an infinite range. The range therefore only contains real numbers.

Due to the fact that the square root of a negative number is undefined, the domain of the function For(x) = x - 2 is x >= 2. As the function returns the square root of x minus 2, which is always non-negative, the range of this function includes all non-negative real integers.

Of(x) = 2x2 + 1 is the function with "all real numbers" as its range.

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Among the given matrices, only the matrix A with entries -9 3 8 1 -12 3 has columns that span R2.

To check whether the columns of the matrix span R2 or not, we put the matrix into row echelon form. This step reduces the matrix to the simplest possible form, and allows us to see the structure of the column space.

To put the matrix into row echelon form, we perform a sequence of elementary row operations that do not change the column space. We start by performing the row operation R2 = R2 + 9R1. Then we perform the row operation R3 = R3 - 8R1. After these row operations, the matrix takes the form -9 3 8 1 -12 3 0 -3 -61 -12 -17 -5Now the matrix is in row echelon form.

The pivots are in the first and second columns, so the column space consists of all linear combinations of the first and second columns. This is the set of all vectors of the form (x, y, z) where x and y are arbitrary and z = -3x - 4y. Thus the columns of the matrix span R2. Among the given matrices, only the matrix A with entries -9 3 8 1 -12 3 has columns that span R2.

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Using the work completed in Excel for the Exponential Growth, the mass of the bacterial population after 116 hours is option E: 6.49 x 10^38 grams.

What is Exponential growth?

Exponential growth is a type of growth in which the growth rate of a population is proportional to its current size. The bigger the population, the faster it grows, and the faster it grows, the bigger it gets. This is represented by a curve that increases rapidly as it goes up. The bacterial population has been studied here.

What is the formula for exponential growth?

The formula for exponential growth is as follows: N = N0e^(rt), where N is the size of the current population, N0 is the size of the initial population, e is the constant of natural logarithms (about 2.718), r is the rate of growth, and t is the length of time. For bacterial population, you can replace N with the mass of the population.

What is the mass of the bacterial population after 116 hours?

After 116 hours, the size of the population (mass of the population) can be calculated using the formula mentioned above. The initial population size is not given. Using the given data for the rate of growth (r) and the length of time (t), the mass of the population can be calculated.

The rate of growth is given in the Excel file, which is 0.055 per hour (rounded to 3 decimal places). Therefore, r = 0.055. The time (t) is given as 116 hours. So, t = 116.

Substituting the values in the formula, we get:

N = N0e^(rt)

N = N0e^(0.055 × 116)

N = N0e^6.38

N = N0 × 6.49 × 10^2 (e^6.38 is approximately 6.49 × 10^2)

The initial size of the population (N0) is not given. Therefore, we cannot find the exact mass of the bacterial population. We can only find it in terms of the initial mass. We can assume that the initial mass was 1 gram (N0 = 1), which will give us the mass of the bacterial population after 116 hours.

N = N0 × 6.49 × 10^2

N = 1 × 6.49 × 10^2

N = 6.49 × 10^2 grams

Therefore, the mass of the bacterial population after 116 hours is option E: 6.49 x 10^38 grams.

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The value of Manny's investment after 1 year is approximately $9,906.72.

We can use the formula for compound interest to find the value of Manny's investment after 1 year:

A = P(1 + r/n)^(nt)

Where

In this case, P = $9,600, r = 0.03 (since the annual rate is 3%), n = 12 (since the interest is compounded monthly), and t = 1 (since we want to find the value after 1 year). Substituting these values into the formula:

A = $9,600(1 + 0.03/12)^(12*1)

A = $9,600(1.0025)^12

A = $9,600(1.03145)

A = $9,906.72

Therefore, the value of Manny's investment after 1 year is approximately $9,906.72.

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To solve this equation, we need to use the formula y = mx + b, where m is the slope and b is the y-intercept.

The equation y = 3x + 1 is in slope-intercept form, which is a linear equation in the form y = mx + b, where m is the slope and b is the y-intercept. In this case, the slope is 3 and the y-intercept is 1.

In this case, we have m = 3 and b = 1, so we can rearrange the equation as follows:

y = 3x + 1

Since (0) = 1, we can set y = 1 and solve for x:

1 = 3x + 1

0 = 3x

x = 0

Therefore, the solution to the given equation with y = 1 is x = 0. This means that when y is equal to 1, x must be equal to 0 in order to satisfy the equation y = 3x + 1.

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The length of the water slide is 30 meters.

Let's denote the length of the slide as x.

According to the problem statement, Tarzan climbs a 20-meter tower and then rides a straight water slide of length x. After landing in the splash pool, he walks 10 meters back to the base of the tower. This means that the total distance he travels is

20 meters (climbing the tower) + x meters (riding the slide) + 10 meters (walking back to the tower base) = 30 + x meters

Since the total distance he travels is equal to the length of the slide plus the distance he walks back to the base of the tower, we can set up the following equation

30 + x = length of the slide

Solving for x, we get

x = length of the slide - 30

Substituting this expression for x into the equation we derived earlier, we get

20 + (length of the slide - 30) + 10 = length of the slide

Simplifying this equation, we get

length of the slide - 30 + 30 = 20 + 10 + length of the slide

Simplifying further, we get

length of the slide = 30 meters

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The consumer price index of the raincoat by using the todays and the 1983 costs of raincoat is given by option b 151.

Todays cost of raincoat = $79.25

Cost of raincoat in 1983 = $52.48

Calculate the CPI (Consumer Price Index) in 1983,

Use the formula we have,

CPI = (Cost of the raincoat today / Cost of the raincoat in 1983) x 100

Plugging in the values given in the problem, we get,

⇒ CPI = ($79.25 / $52.48) x 100

⇒ CPI = 1.51009 x 100

⇒ CPI = 151.009

Rounding this to the nearest whole number gives a CPI of $151.

Therefore, the best answer to represent the consumer price index of the raincoat is equals to option  (b) 151.

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Answer:

The Triangle Postulate states that if three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.

If the three sides of one triangle are known to be congruent to the three sides of another triangle, the Triangle Postulate can be used to prove that the two triangles are congruent. For example, if two triangles have sides of length a, b, and c, then if the sides of the first triangle are congruent to the sides of the second triangle, the two triangles must be congruent. This can be proven using the Triangle Postulate.To prove the congruence of two triangles using the Triangle Postulate, first the lengths of the sides of each triangle must be known. Once the lengths are known, the two triangles can then be compared side-by-side. If the lengths of the three sides of the first triangle are equal to the lengths of the three sides of the second triangle, the two triangles are congruent. This can be proven using the Triangle Postulate, which states that if three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.

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Answer:

2769.592cm³

Step-by-step explanation:

Calculate the volume of the cuboid below and add to the volume of the rectangular pyramid above

Volume of cuboid = Lenght x width x height

V = 26.6 x 11.4 x 7.2

V =2183.328cm³

Volume of rectangular pyramid 1/3lwh or 1/3Bh

V = 1/3 x 26.6 x 11.4 x 5.8

V = 1758.792/3

V = 586.264

Add both volumes 2183.328 + 586.264

The interest earned by Maria after 6 years would be $368.10 .

What is simple interest?

Simple interest is a calculation of interest that doesn’t take into account the effect of compounding.  In many cases, interest compounds with each designated period of a loan, but in the case of simple interest, it does not.  The calculation of simple interest is equal to the principal amount multiplied by the interest rate, multiplied by the number of periods.  

The formula for calculating simple interest is:

I = P x r x t

where I is the interest earned, P is the principal (the amount invested), r is the interest rate, and t is the time period in years.

Plugging in the values given, we get:

I = 1500 x 0.0409 x 6

I = $368.10

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The null space of A is given by $\begin{pmatrix} 3t\\3t\\0\\t\\0\\ \end{pmatrix} = t\begin{pmatrix} 3\\3\\0\\1\\0\\ \end{pmatrix}$This is the explicit description of the null space. A spanning set for null space is $\left\{3\begin{pmatrix} 1\\1\\0\\0\\0\\ \end{pmatrix},\begin{pmatrix} 0\\0\\1\\0\\0\\ \end{pmatrix}\right\}$.

Find an explicit description of Nul A by listing vectors that span the null space. [1 0 0 -3 0 0 0 1 0 -3 4 0] A spanning set for Nul A isGiven matrix [1 0 0 -3 0 0 0 1 0 -3 4 0] is equivalent to the matrix $\begin{pmatrix} 1&0&0&-3\\0&0&0&0\\0&0&0&0\\0&1&0&-3\\0&0&4&0\\ \end{pmatrix}$As we know NulA denotes the null space of matrix A. A null space of a matrix is a vector space that contains the set of all solutions to the homogeneous equation Ax = 0.Find a solution to homogeneous equation $\begin{pmatrix}

1&0&0&-3\\0&0&0&0\\0&0&0&0\\0&1&0&-3\\0&0&4&0\\ \end{pmatrix}$ $\begin{pmatrix} x_1\\x_2\\x_3\\x_4\\ \end{pmatrix}$ = $\begin{pmatrix} 0\\0\\0\\0\\0\\ \end{pmatrix}$Thus the equation set is: $1x_1-3x_4 = 0$$1x_2-3x_4=0$$4x_3=0$

Hence the solutions to the equation set can be written as: $x_4=t,x_3=0,x_2=3t,x_1=3t$Therefore null space of A is given by $\begin{pmatrix} 3t\\3t\\0\\t\\0\\ \end{pmatrix} = t\begin{pmatrix} 3\\3\\0\\1\\0\\ \end{pmatrix}$This is the explicit description of the null space. A spanning set for null space is $\left\{3\begin{pmatrix} 1\\1\\0\\0\\0\\ \end{pmatrix},\begin{pmatrix} 0\\0\\1\\0\\0\\ \end{pmatrix}\right\}$.

As we know the null space is a subspace of $\mathbb{R}^n$, so a subspace of $\mathbb{R}^n$ is defined by the set of solutions of a homogeneous linear system of equations.In order to find the explicit description of the null space, find a basis for the null space (the vectors that span it). Afterward, to define the null space, you simply need to write the linear combination of that basis.

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The examples of algebra skills that you have previously learned are explained.

Addition and subtraction: If we start with an equation like x+5=10, we can use subtraction to isolate the variable x. We can subtract 5 from both sides of the equation to get:

[tex]$\begin{align*}x+5-5 &= 10-5 &\\=x= 5\end{align*}[/tex]

Then;

In this case, the initial action was adding 5 to x, and we reversed it by subtracting 5 from both sides of the equation.

Multiplication and division: Another example is when we have an equation like 4y=12 and we want to solve for y. We can use division to isolate y. We can divide both sides of the equation by 4 to get:

[tex]$\frac{4y}{4} &= \frac{12}{4} \\=y= 3\end{align*}[/tex]

In this case, the initial action was multiplying y by 4, and we reversed it by dividing both sides of the equation by 4.

In both of these examples, we used the  to undo the initial operation and isolate the variable we were solving for.

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Answer:   83  

Step-by-step explanation:

200*2.5=83

Answer:

x = 36

Step-by-step explanation:

We are given the value of y, so we just plug it into our equation.

[tex]2=\frac{x}{4}- 7[/tex]

Lets switch sides so its a little easier

[tex]\frac{x}{4}-7=2[/tex]

Add 7 to both sides

[tex]\frac{x}{4}=9[/tex]

Multiply 4

[tex]x=36[/tex]

Answer:

Step-by-step explanation:

Let the numbers be [tex]x,y[/tex]:

[tex]xy=-48[/tex]     [tex](a)[/tex]

[tex]x+y=13[/tex]    [tex](b)[/tex]

Solve [tex](a),(b)[/tex] simultaneously:

  from [tex](b)[/tex],  [tex]y=13-x[/tex]. Sub this into [tex](a)[/tex] to get

     [tex]x(13-x)=-48[/tex]

     [tex]13x-x^2=-48[/tex]

     [tex]x^2-13x-48=0[/tex]

     [tex](x-16)(x+3)=0[/tex]

     [tex]x=-3,16[/tex]

  When [tex]x=-3, y=16[/tex] and when [tex]x=16, y=-3[/tex]

SOLUTIONS: -3,16  

The sketch of the vector equation r(t) = (sin(6t), t) is illustrated below.

In this case, the vector equation r(t) = (sin(6t), t) describes a curve in two dimensions. The x-coordinate is given by sin(6t) and the y-coordinate is given by t. As t varies, the point on the curve moves along the path described by the vector equation.

To sketch the curve, we can plot a series of points on the coordinate plane by choosing different values of t and evaluating the vector equation at each value.

As t increases, the point on the curve moves in the direction determined by the vector equation. To indicate this direction, we can draw an arrow on the curve pointing in the direction of increasing t. In this case, the arrow would point in the positive y-direction, since t is increasing while the x-coordinate remains constant.

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According to the information an example of a math lesson plan for 3rd grade would be: Topic: Multiplication, Material: board, markers and learning guides, lesson focus and goal: Know how to multiply, Structure activity: Explanation, practice activity and feedback /corrections, Learning objectives: Know how to multiply with one and two digits Assessment: You can multiply the following values.

To create a lesson plan we must take into account different aspects so that our class is effective and the students learn with our lessons. In accordance with the above, we must take into account the following aspects:

In accordance with the above, we can establish that the correct way to complete these requirements would be:

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An inequality represents two unequal variables, two or more inequalities are system of inequalities, a restricting condition is a constraint and divider of the coordinate plane is called boundary.

When two or more mathematical expressions are compared to one another or weighed against one another and it is discovered that they are not equal, an inequality usually results.

An inequality is a claim that links two variables using the inequality symbol.

Constraints are limitations or restrictions on a problem's solution or solutions.

Systems of Linear Inequalities are two or more linear inequalities involving the same variables.

The boundary is a line that divides the coordinate plane into three sets of points.

The open half-plane is one of the two areas where a boundary line divides the coordinate plane.

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The coordinates of the point on the plane z = 4x + 2y + 3 that  is closest to the origin  (x, y, z) = (0, 0, 3) can be determined using the Method of Lagrange Multipliers. We must find the values of x, y, and z that minimize the distance from the origin, given the constraint that z = 4x + 2y + 3.

Lagrange multiplier equation:

Let L(x,y,z) = x^2 + y^2 + z^2 and f(x, y, z) = 4x + 2y + 3.

The Lagrange multiplier equation is then:
L(x, y, z) = λf(x, y, z)

Partial derivatives:

Taking the partial derivatives of L(x, y, z)  concerning  x, y, and z, and setting them equal to zero yields:
2x = 4λ
2y = 2λ
2z = 3λ

Solution:

Solving the above equations for x, y, and z yields

x = 2λ/4, y = λ/2, and z = 3λ/2.

Substituting this into the equation

f(x, y, z) = 4x + 2y + 3 yields 0 = λ/2, which has no solutions.

Therefore, the coordinates of the point on the plane z = 4x + 2y + 3 that is closest to the origin is (x, y, z) = (0, 0, 3).

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A) The point of intersection of the lines L1 and L2 is (5, 7, -2).

B) The equation in the form ax + by + cz = d for the plane containing both the lines L1 and L2 is x - 6y - 8z = -20.

The given L1 is the line given by the symmetric equations:

x - 12 = x - 13 = z + 5

6x - 12 = 6x - 13 = 6z + 30

And L2 is the line given by:

x - 4 = y - 11/5 = z - 11/2

2x - 8 = 5y - 11 = 10z - 55

Solving these equations by the elimination method gives the point of intersection of the lines L1 and L2 as (5, 7, -2).

The vector equation of a line passing through a point P with the direction vector d is given by:

r = P + td.

So, the vector equations of lines L1 and L2 are given by:

L1: r = [2i + 3j + 6k] + t[3i + 2j + 6k]

L2: r = [4i + 11j/5 + 11k/2] + s[-4i + 5j + 11k/2]

Now, let's find the normal vector of the plane containing L1 and L2 using the direction vectors of L1 and L2.

The cross-product of the direction vectors of the two lines L1 and L2 gives the normal vector of the plane containing both lines:

L1: d1 = 3i + 2j + 6k

L2: d2 = -4i + 5j + 11k/2

The normal vector, n = d1 × d2 = (22i - 33j - 23k).

Now, we can use this normal vector and any point on the plane, say (5, 7, -2), which is the point of intersection of the two lines L1 and L2, to form the required plane equation of the form ax + by + cz = d.

Here, a = 22, b = -33, c = -23, and d = -20.

The equation of the plane containing both of the lines L1 and L2 is 22x - 33y - 23z = -20, which when simplified gives the required equation in the form of ax + by + cz = d, as x - 6y - 8z = -20.

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To prove,

Span (S1 ∪ S2)  = Span (S1) + Span (S2)

Given,

S1 and S2 are arbitrary subsets of a vector space V .

Let S1 and S2 be any subsets of vector space V .

We know that, for any set S1, S2

S1⊆S1⊆S2 and S2 ⊆ S1 ⊆ S2

According to the result,

A⊆B ⇒ Span (A) ⊆ Span (B)

There for by applying the result we get,

span(S1) ⊆ span(S1 ∪ S2),

span(S2)⊆ Span(S1 ∪S2) .

Hence span(S1) + span (S2) ⊆ Span (S1 ∪ S2)

Now,

let s∈ span(S1∪S2)

Then s will be the linear combination of both S1 and S2 .

So,

s ∈ span (S1) + span (S2)

Hence,

span(S1) + span (S2) ⊆ Span (S1 ∪ S2)

Combining ,

Span (S1 ) + Span (S2) ⊆ span (S1 ∪ S2)

span (S1 ∪ S2) ⊆ Span (S1 ) + Span (S2)

Thus,

Span (S1 ∪ S2)  = Span (S1) + Span (S2)

Hence proved.

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Answer:

To substitute the equation for y in the second equation, we need to solve for y in the first equation and then substitute that expression for y in the second equation.

Starting with the first equation:

-24x + 6y = 12

We can isolate y by adding 24x to both sides:

6y = 24x + 12

Then, we can divide both sides by 6 to solve for y:

y = 4x + 2

Now that we have an expression for y in terms of x, we can substitute it into the second equation:

4x + 7y = 13

4x + 7(4x + 2) = 13

Simplifying and solving for x:

4x + 28x + 14 = 13

32x = -1

x = -1/32

Finally, we can substitute x back into either equation to solve for y:

-24(-1/32) + 6y = 12

3/4 + 6y = 12

6y = 11 1/4

y = 1 7/8

Therefore, the solution to the system of equations is (x,y) = (-1/32, 1 7/8).

Step-by-step explanation:

The area of the triangle with the given vertices is 19.5 square units.

To find the area of a triangle with the given vertices, we can use the formula A = (1/2)abs[(x1y2 + x2y3 + x3y1) - (x2y1 + x3y2 + x1y3)], where (x1, y1), (x2, y2), and (x3, y3) are the coordinates of the vertices.

Plugging in the given coordinates, we have:

A = (1/2)abs[(0*1 + 6*7 + 3*0) - (6*0 + 3*1 + 0*7)]

A = (1/2)abs[(42) - (3)]

A = (1/2)abs[39]

A = (1/2)(39)

A = 19.5

Therefore, the area of the triangle with the given vertices is 19.5 square units.

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Answer: The margin of error for a confidence interval depends on the sample size and the level of confidence. For a sample of 4,000 people, a margin of error of 1% implies that the sample proportion is within 1% of the true proportion with a certain level of confidence.

Let's denote the true proportion of unemployed people in the city by p. Then the margin of error can be expressed as:

z*sqrt((p(1-p))/n) = 0.01

where z* is the critical value of the standard normal distribution corresponding to the level of confidence.

Since we don't know the value of p, we'll use the worst-case scenario where p = 0.5, which gives us the maximum possible margin of error. Then we have:

z*sqrt((0.5(1-0.5))/4000) = 0.01

Simplifying and solving for z*, we get:

z* = 2.576

The critical value of 2.576 corresponds to a level of confidence of approximately 99%. Therefore, the confidence level that the newspaper used in their report is 99%.

Step-by-step explanation:

D) Submit a Mailing Permit Application and Customer Profile is the last step in the application process for bulk mailings.

Mailings must include at least 200 addressed items to be eligible for Standard Mail (bulk) rates (or 50 pounds). be constructed from printed components that are all the same in terms of their composition, dimensions, and weight. be under 1 pound in weight (each piece).

From organisations like InfoUSA, BBDirect, and USAData, business owners can purchase mailing lists online. In a list, providers frequently sell a minimum of 1,000 to 5,000 names. The type of list and the country of origin affect the cost.

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Answer:

10 girls

Step-by-step explanation:

We can show our ratio as a fraction: [tex]\frac{2}{5}[/tex]

Since the denominator of 5 is the total number of participants and the numberator is the # of girls in the competition, we can write another proportional ratio.

It would be: [tex]\frac{x}{25}[/tex]

 [tex]\frac{2}{5}[/tex]and      [tex]\frac{x}{25}[/tex] would be proportional. To solve this, we can find a number that can be multiplied, by both the numerator and the denominator, which gives a value of 25 for the denominator.

This number would be 5.

If we multiply the denomitator of [tex]\frac{2}{5}[/tex] by 5, we get 25, which is the value of the other fraction. Now, if we multiply the numerator by 5, we get 10, which is the number of girls in the competition.