There are 10 horses in a race. In how many ways can thre first three positions of the order of the finsih occur assuming noties

The recursively defined function has a first term equal to 10 and a common difference of 4 is f(n) = 6 + 4n.

When a recursive procedure gets repeated, it's called recursion. A recursive is a type of function or expression stating some conception or property of one or further variables, which is specified by a procedure that yields values or cases of that function by constantly applying a given relation or routine operation to known values of the function.

We have first term = a = 10

And the common difference of d = 4

We have the formula for the t terms of a as 10 and d as 4

f(n) = a + (n - 1)d

f(n) = 10 + (n-1) x 4

f(n) = 10 + 4n - 4

f(n) = 6 + 4n

So, the defined function is f(n) = 6 + 4n.

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The average rate of change of the function as x varies from 2 to 5 is 22.

Given function: g(x) = 1 – 2x + [tex]3x^2[/tex]

To find the average rate of change of the function as x varies from 2 to 5.

Solution: We are given a function: g(x) = 1 – 2x + [tex]3x^2[/tex]

The average rate of change of the function as x varies from a to b is given by:

Average rate of change = f(b) - f(a) / b - a

Let a = 2 and b = 5

We have to find the average rate of change of g(x) as x varies from 2 to 5.

So, the average rate of change of g(x) is given by:

Average rate of change = g(5) - g(2) / 5 - 2

= [1 - 2(5) + 3([tex]5^2[/tex])] - [1 - 2(2) + 3([tex]2^2[/tex])] / 3

= [1 - 10 + 75] - [1 - 4 + 12] / 3= 66 / 3= 22

Therefore, the average rate of change of the function as x varies from 2 to 5 is 22.

An average rate of change is the amount that the function changes on average over a specified interval.

The formula for average rate of change is given as the change in the function value divided by the change in x value for two distinct points on the function.

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Since the triangles are similar, the value of x is equal to: C. 18 units.

In Mathematics, two (2) triangles are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.

By applying the properties of similar triangles, we have the following ratio of corresponding side lengths;

AC/RS = AB/RT

By substituting the given side lengths into the above equation, we have the following:

x/24 = 24/32

By cross-multiplying, we have the following;

32x = 24(24)

32x = 576

x = 576/32

x = 18 units.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

30 feet

Step-by-step explanation:

Coordinates of Ann: (-4,3)

Coordinates of bottle caps: (4,-10)

Distance from Ann to bottle caps can be found out using the distance formula:
[tex]x_2=4, x_1=-4\\y_2=-3,y_1=-10\\Distance=\sqrt{(x_{2}-x_{1})^2 + (y_{2}-y_{1})^2 } \\=\sqrt{(4-(-4))^2 + ((-10)-3)^2} \\=15.26\\15\text{ is the answer}[/tex]

Answer:

x [tex]\geq[/tex]2

Step-by-step explanation:

Since the arrow is pointing to the right, we know that it is greater than two. We also know that it could be equal to 2 because the dot is filled in on the number line. So, the answer is x is greater than or equal to 2.

Answer: what do you mean? I need more info-

Step-by-step explanation:

I can answer it with more info :)

Answer:

The possible coordinates of point A are (−8,1) or (8,1).

Using the area formula for the rectangle, we can find that 2752 in² of plastic is needed to line the trough.

To determine the area a rectangle occupies within its perimeter, apply the formula for calculating a rectangle's area. Multiplying the length by the width yields the area of a rectangle (breadth).

As a result, the area of a rectangle with the length and breadth l and w, respectively, is calculated as follows. L × W = the rectangle's area. Hence, the area of a rectangle is equal to (length width).

Now in the given question,

We have 5 faces of the cuboid.

Now to find the total area of the required space we have to find the area of all the rectangles.

Area of rectangle with dimensions, l = 40inches and b = 14 inches.

Area = l × b

= 40 × 14

= 560in²

Now there are 2 rectangles with the same dimensions, so the total area = 560 + 560 = 1120in².

Now area of rectangles with dimensions, l = 14 inches and b = 24 inches.

Area = l × b

= 14 × 24

= 336in².

There are 2 rectangles with the same dimensions, so area = 336 + 336 = 672in².

Area of the final rectangle = l × b

= 40 × 24

= 960in².

So, the total required area = 1120 + 672 + 960 = 2752in².

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The required length of YZ is [tex]\frac{145}{16}$[/tex]  units.

To find the length of YZ, we can use the fact that the length of XZ is the sum of the lengths of XY and YZ. We are given that XZ is [tex]12 \frac{11}{16}$[/tex]units and XY is [tex]3 \frac{5}{8}$[/tex] units. Let's convert these mixed numbers to improper fractions so that we can add them:

[tex]$XZ = 12 \frac{11}{16} = \frac{12 \times 16 + 11}{16} = \frac{203}{16}$[/tex]

[tex]$XY = 3 \frac{5}{8} = \frac{3 \times 8 + 5}{8} = \frac{29}{8}$[/tex]

Now we can use the formula:

XZ = XY + YZ

to solve for YZ. Rearranging the equation, we get:

YZ = XZ - XY

Plugging in the values we calculated, we get:

[tex]$YZ = \frac{203}{16} - \frac{29}{8}$[/tex]

To subtract these fractions, we need to find a common denominator. The smallest number that both 16 and 8 divide into evenly is [tex]16 \times 2 = 32$[/tex], so we can rewrite the fractions with a denominator of 32:

[tex]$YZ = \frac{203}{16} \times \frac{2}{2} - \frac{29}{8} \times \frac{4}{4} = \frac{406}{32} - \frac{116}{32}$[/tex]

Now we can subtract:

[tex]$YZ = \frac{406 - 116}{32} = \frac{290}{32}$[/tex]

We can simplify this fraction by dividing both the numerator and denominator by the greatest common factor, which is 2:

[tex]$YZ = \frac{145}{16}$[/tex]

Therefore, the length of YZ is [tex]\frac{145}{16}$[/tex]  units.

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Complete question:

XY is a line, Z is a point on this line such that  XZ is 12 11/16 units XY is 3 5/8 units find YZ​.

The probability that a randomly chosen college student will spend between $300 and $400 on clothing in a year is approximately 0.6645 or 66.45%.

To solve this problem, we need to standardize the given range of values using the z-score formula:

z = (x - μ) / σ

where x is the value of interest, μ is the mean, and σ is the standard deviation. For x = 300:

z = (300 - 310) / 50 = -0.2

For x = 400:

z = (400 - 310) / 50 = 1.8

Using a standard normal distribution table or calculator, we can find the probability of the z-score being between -0.2 and 1.8:

P(-0.2 ≤ z ≤ 1.8) = 0.6645

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The school can purchase 91 adult tickets and 41 children tickets, allowing for a total of 132 teachers and students to go on the trip within the budget of $12000.

Let's start by defining some variables to represent the quantities we're interested in: Let A be the number of adult tickets purchased. Let C be the number of children tickets purchased. Let T be the total number of teachers and students who go on the trip. To maximize the number of teachers and students while staying within budget, we can use linear programming. The objective function is N = T - A - C, where N is the number of teachers and students. The inequalities are 68A + 47C ≤ 12000 and T ≤ 225. Solving this linear program, we find that the school can purchase 91 adult tickets and 41 children tickets, allowing for a total of 132 teachers and students to go on the trip within the budget of $12000.

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the complete question :

A middle school wants to take students and teachers on a field trip to Six Flags Great America for spring break. The school has a budget of spending at most $12,000. They can also only take no more than 225 teachers and students. The adult tickets cost $68 each, and children tickets cost $47 each. How many adults and children can the school take to Six Flags within the given budget and attendance limit?

The following conditions must be met to conduct a two-proportion significance test:

the populations are independent, the probabilities of success multiplied by the sample sizes are greater than or equal to 10 and the probabilities of failure multiplied by the sample sizes are greater than or equal to 10 for each population, and the sample sizes are greater than 30.

The two-proportion significance test is a hypothesis test that compares the proportions of two independent populations.

To conduct the two-proportion significance test, the following conditions must be met:

Populations must be independent.

Sample sizes are greater than 30.

The probabilities of success multiplied by the sample sizes are greater than or equal to 10 and the probabilities of failure multiplied by the sample sizes are greater than or equal to 10 for each population.

The sample size should be large enough so that the sampling distribution of the sample proportion is nearly normal. The sample sizes should be large enough so that the central limit theorem can be applied.

In short, to conduct a two-proportion significance test, the populations must be independent, the probabilities of success multiplied by the sample sizes are greater than or equal to 10 and the probabilities of failure multiplied by the sample sizes are greater than or equal to 10 for each population, and the sample sizes are greater than 30.


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Answer:

a quarter of an hour, or 15 minutes is equal to 15 minutes × 60 = 90 seconds a quarter of an hour, or 15 minutes is equal to 15 minutes × 60 = 90 seconds

Answer:

90 seconds

Step-by-step explanation: We know that,

A quarter of an hour= 60×1/4 =15 mins

15 minutes is equal to 15 minutes × 60 = 90 seconds.

Answer:

Paper clip, Mobile phone, S​, Tennis racket, Car, Football pitch.

Step-by-step explanation:

Area of circle =   pi r^2

10 inch = pi (5)^2 = 25 pi

12 inch = pi (6)^2 = 36 pi

12 inch is 11pi bigger

    percentage:  11 pi is what percentage of 25 pi ?

        11 pi / 25 pi x 100%  = 44 % bigger

The area of a pizza increases with the square of the diameter. Therefore, a 10-inch pizza has an area of [tex]π*(10/2)^2= 78.54[/tex]  square inches, and a 12-inch pizza has an area of [tex]π*(12/2)^2 = 113.10[/tex] square inches. This is an increase of 113.10 - 78.54 = 34.56 square inches, or an increase of 44.2%.

To explain further, the diameter of a pizza is measured from one side to the other through the center of the pizza. As the diameter of the pizza increases, the area of the pizza increases. This is because the area of a pizza is calculated as [tex]π*(d/2)^2[/tex], where d is the diameter. So, if the diameter increases, the area increases as well.

For example, if a 10-inch pizza has an area of 78.54 square inches, a 12-inch pizza would have an area of 113.10 square inches. This is an increase of 113.10 - 78.54 = 34.56 square inches, or an increase of 44.2%. This is because the diameter of the pizza has increased by 2 inches (10 inches to 12 inches), and the area has increased by 44.2%.

It is important to note that increasing the diameter of the pizza does not just increase the circumference of the pizza, but also the area. The increase in area is directly related to the increase in diameter, and can be calculated by taking the difference between the areas of the two pizzas.

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it will take approximately 22.56 years for the amount to triple.

The given information for this problem is that there is an initial investment of $600 in an account with an annual interest rate of 4%. The task is to determine after how many years the amount will triple.Using the compound interest formula, we can find the amount in the account after t years:A = P(1 + r/n)nt Where,A = final amount in the account, P = initial amount in the account r = annual interest rate ,n = number of times the interest is compounded per year ,t = time in years.

From the problem statement, we know that the initial amount, P, is $600 and the annual interest rate, r, is 4%. Let's assume that the interest is compounded annually, i.e., n = 1.Substituting these values in the formula, we get:A = $600(1 + 0.04/1)1t Simplifying this expression,A = $600(1.04)t.

Taking the ratio of the final amount to the initial amount, we get: 3P = $600 × 3 = $1800. Therefore,A/P = 3 = (1.04)t.Dividing both sides by P, we get:3 = (1.04)t ln(3) = ln(1.04)t. Using the logarithmic property, we can bring down the exponent to the front:ln(3) / ln(1.04) = t Using a calculator, we get ≈ 22.56. Therefore, it will take approximately 22.56 years for the amount to triple.

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There are 107 multiples of 2 between 176 and 389.

The first multiple of 2 within the range is the smallest multiple of 2 that is greater than or equal to the lower endpoint, which is 176. To find this, we divide 176 by 2:

176 ÷ 2 = 88

So the first multiple of 2 within the range is 88.

The last multiple of 2 within the range is the largest multiple of 2 that is less than or equal to the upper endpoint, which is 389. To find this, we divide 389 by 2:

389 ÷ 2 = 194.5

Since we are only interested in whole numbers, we round 194.5 down to the nearest integer, which is 194.

So the last multiple of 2 within the range is 194.

Now that we know the first and last multiples of 2 within the range, we can count how many multiples of 2 exist between them. To do this, we subtract the first multiple from the last multiple and add 1:

194 - 88 + 1 = 107

Therefore, there are 107 multiples of 2 between 176 and 389.

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, Doug Bernard would profit $4,014.97 from this arbitrage opportunity.

Explanation:

Yes, Doug Bernard has an arbitrage opportunity based on these quotes. To make an arbitrage profit, he can follow these steps:

1. Convert $1,000,000 to Swiss francs using the Swiss franc/dollar rate: $1,000,000 * (SFr1.5995/$) = SFr1,599,500.
2. Convert the Swiss francs to Australian dollars using the Australian dollar/Swiss franc rate: SFr1,599,500 * (A$1.1458/SFr) = A$1,831,604.90.
3. Convert the Australian dollars back to U.S. dollars using the Australian dollar/U.S. dollar rate: A$1,831,604.90 / (A$1.8242/$) = $1,004,014.97.

The arbitrage profit would be the difference between the initial amount and the final amount

: $1,004,014.97 - $1,000,000 = $4,014.97.

Therefore, Doug Bernard would profit $4,014.97 from this arbitrage opportunity

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Two plus x divided by twelve equals one divided by three

Case 1 :

Rewrite into numbers : 2 + x /12 = 1/3

-> x/12 = 1/3 - 2 = -5/3

-> x = -5/3 x 12 = -20

Case 2 :

Rewrite into numbers : (2 + x)/12 = 1/3

-> 2 + x = 1/3 x 12 = 4

-> x = 4 - 2 = 2

i dont know if you meant it the right way or the wrong way but ill just put them both

x=2

Step-by-step explanation:

(2+x)/12=1/3

3(2+x)=12

2+x=4

x=4-2

x=2

We can solve the system by elimination without multiplying first only when, [tex]$a = 8$[/tex].

To solve the system by elimination, we want to eliminate one of the variables, either x or y, from one of the equations. To do this, we need to find a multiple of one equation that cancels out one of the variables in the other equation.

We can eliminate x by multiplying the first equation by -4 and adding it to the second equation:

[tex]-4(ax+3y) + (4x+5y) &=\\ -4(7) + 15\(-4a+4)x + (5-12)y &=\\ -13\ (4-4a)x - 7y &= -13[/tex]

By adding the first equation to the second equation and multiplying it by -4, we can get rid of x:

[tex](4-4a)x-7y=13\\4x+5y=15[/tex]

We can eliminate y by multiplying the second equation by 7 and subtracting it from the first equation:

[tex](4-4a)x - 7y &=\\ -13-28x - 35y &=\\ -105[/tex]

Simplifying this last equation, we get:

[tex](4a-4)x &= 28x\\4a &= 32\\a &= 8[/tex]

Therefore, we can solve the system by elimination without multiplying first only when, [tex]$a = 8$[/tex].

For any other value of a, we need to multiply one or both equations by a constant before we can eliminate a variable.

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Therefore, the expression that would give the total number of elements in the array list is n*m.

The Student question is given below :Assume that Item is some class available to the code below and that n and m are two integer variables correctly initialized. Consider the following array declaration and initialization.

[tex]Item[][] list= new Item[n][m];[/tex]

What expression would give the total number of elements in the array list?

The expression that would give the total number of elements in the array list is n*m. The given array declaration and initialization is Item[][] list= new Item[n][m]; This declaration and initialization signify that the array list is a 2D array with n rows and m columns. The total number of elements in this array can be determined by computing the product of the total number of rows (n) and the total number of columns (m).

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The rectangular prism is 3 inches by 4.75 inches by 20.5 inches, has a total surface area of 346.25 in².

We need to find the surface area of an object, the surface area of a solid three-dimensional object is the area of the boundary surface of the object and its surroundings, therefore:

The dimensions of the rectangular prism will be as follows:

Let the length of the rectangular prism = 3 inches

Let the width of the prism = 4.75 inches

Let the height of the prism = 20.5 inches

Therefore, the surface area, A, of a rectangular prism can be found using the formula:

A = 2 × Length × Width + 2 × Length × Height + 2 × Height × Width

Therefore, the surface area of the rectangular prism in the question is found as follows:

Area, A = 2 × 3 × 4.75 + 2 × 3 × 20.5 + 2 × 20.5 × 4.75 = 346.25

The total surface area of the rectangular prism is 346.25 in².

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Answer:

346.25

Step-by-step explanation:

took the test :)

In the following question, among the conditions given, The greatest value in the data set is 21, the mean is 13.4, the mode is 12, and the median is 12.

The greatest value is the highest number in the set, 21.
The mean is the average of the set, and is calculated by adding all the numbers together and dividing by the number of values, which in this case is 11.  11 + 11 + 12 + 12 + 12 + 12 + 13 + 15 + 17 + 21 + 21 + 21 = 163, and 163 / 11 = 13.4.
The mode is the number that appears the most often, which is 12 in this set.
The median is the middle number when all the numbers are put in order from least to greatest, which is also 12 in this set.

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The least common multiple (LCM) of two or more integers is the smallest positive integer that is a multiple of all of them. In other words, it is the smallest number that is divisible by each of the given numbers without leaving a remainder. [tex]3(5/8) + 2(3/8) = 6.[/tex]

To add the mixed numbers 5 3/8 and 3 2/8, we need to convert them to fractions with a common denominator. Since both have a denominator of 8, we can add the whole numbers to the fractions to get:

[tex]5 3/8 = 5 + 3/8 = 40/8 + 3/8 = 43/8[/tex]

[tex]3 2/8 = 3 + 2/8 = 24/8 + 2/8 = 26/8[/tex]

Now we can add these fractions:

[tex]5 3/8 + 3 2/8 = 43/8 + 26/8 = 69/8[/tex]

So the sum of  [tex]5 3/8[/tex] and [tex]3 2/8[/tex]  as a fraction is [tex]69/8[/tex]  .

The LCM is often used when adding or subtracting fractions with different denominators, since we need to find a common denominator to perform the operation. To do this, we can find the LCM of the denominators and use it as the common denominator.

To write equivalent fractions with a common denominator, we need to find the least common multiple of the denominators, which in this case is 8.

For [tex]3(5/8)[/tex]  :

[tex]3(8/8) + 5/8 = 24/8 + 5/8 = 29/8[/tex]

For [tex]2(3/8):[/tex]

[tex]2(8/8) + 3/8 = 16/8 + 3/8 = 19/8[/tex]

To add these fractions, we simply add their numerators:

[tex]3(5/8) + 2(3/8) = 29/8 + 19/8 = 48/8 = 6[/tex]

Therefore, [tex]3(5/8) + 2(3/8) = 6.[/tex]

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Answer:

it is a triangle bc it has angles of points

Step-by-step explanation:

The statement "Hazardous chemicals are only found in industrial settings, so school employees do have responsibilities regarding them" is False.

What are hazardous chemicals?

Hazardous chemicals are substances that can cause harm to living beings when exposed to them. They are also known as hazardous substances, and they are found in various forms such as solids, liquids, gases, and dust. Hazardous chemicals pose a significant danger to human health and the environment, and they are found in both industrial and non-industrial settings.

What is the role of school employees regarding hazardous chemicals?

School employees have a responsibility to ensure that students and staff are safe from hazardous chemicals.

School laboratories and art rooms are examples of locations where hazardous chemicals may be found.

School employees must ensure that hazardous chemicals are properly labeled and stored, and they must provide safety training and equipment to students and staff who work with hazardous chemicals.

Therefore, it is not true that school employees do not have any responsibilities regarding hazardous chemicals, even though they are not found exclusively in industrial settings.

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