Determine the seating capacity of an auditorium with 15 rows of seats if there are 25 seats in the first row, 29 seats in the second row, 33 seats in the third row, 37 seats in the forth row, and so on

Answer: Finding the area for a right triangle is really simple so I will just show you how too.

Step-by-step explanation:

I was taught that it was H × B ÷2  (make sure to use this formula on right triangles)

B=base

H=height

Its really similar to finding area of a rectangle but you just divide your answer by 2 at the end!

I hope that helps a bit.

(if you worried that you didn't do it correct I got 336 for number 1)

In addition to the Gini index and Entropy, there are other parameters that can be used to measure purity or determine the best split in a decision tree. Two commonly used parameters are: Classification Error , Gini Gain.

Classification Error (Misclassification Error):

The classification error, also known as the misclassification error, measures the fraction of misclassified instances in a node. It calculates the probability of misclassification by assigning the majority class label to all instances in the node. The classification error is given by the formula:

Classification Error = 1 - (max(p1, p2, ..., pk))

where p1, p2, ..., pk are the proportions of each class in the node.

A lower classification error indicates a purer node, where the majority of instances belong to a single class.

Gini Gain:

Gini gain is a measure of the reduction in the Gini index achieved by splitting a node based on a particular feature. It quantifies how much the impurity or randomness decreases after the split. Gini gain is calculated by subtracting the weighted average of the Gini indices of the resulting child nodes from the Gini index of the parent node. The feature with the highest Gini gain is chosen as the best split.

Gini Gain = Gini Index(parent) - (Weighted Average of Gini Indices of Child Nodes)

A higher Gini gain indicates a better split that maximizes the reduction in impurity.

These parameters, like the Gini index and Entropy, help in determining the purity of nodes and finding the optimal splits in a decision tree algorithm. By evaluating multiple parameters, the decision tree can make informed choices about the features and splits that lead to the most homogeneous and informative subsets of data.

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a) The slope of the curve is, - 3

And, The lead coefficient is, 1

b) The graph will open upwards and the end behavior will be positive infinity on both ends.

c) The x-intercepts of the function are -4 and 7.

We have to given that,

Equation is,

y = (x + 4) (x - 7)

a) Now, WE can expand it as,

y = (x + 4) (x - 7)

y = x² - 7x + 4x - 28

y = x² - 3x - 28

Since, from the expression the coefficient of x² term is 1,

Hence, The lead coefficient is, 1

And, the slope of the curve is equal to the coefficient of the x term, which is -3.

b) For the end behavior, at the highest degree term, which is x².

Since the coefficient of x² is positive,

Hence, The graph will open upwards and the end behavior will be positive infinity on both ends.

c) For x - intercept the value of y is zero.

Hence,

y = (x + 4) (x - 7)

0 = (x + 4) (x - 7)

This gives,

x + 4 = 0

x = - 4

x - 7 = 0

x = 7

Therefore, the x-intercepts of the function are -4 and 7.

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The Vector functions are :

a) r(t) = (1-t) <2, 3> + t <-1, 5>

b)r(t) = (1-t) <0, 4> + t <-2, 0>

c) x = 3 cos(t), y = 3 sin(t)

(a) The line segment from (2, 3) to (-1,5):

To draw the line segment from (2, 3) to (-1, 5), we first plot the two points on the Cartesian plane:

        (2, 3)

           *

          /

         /

        /  

(-1, 5) *

The direction of motion along this line segment is from (2, 3) to (-1, 5), so we can write a vector function that starts at (2, 3) and ends at (-1, 5) by using the position vector:

r(t) = (1-t) <2, 3> + t <-1, 5>

where t ranges from 0 to 1. This vector function starts at (2, 3) when t = 0 and ends at (-1, 5) when t = 1.

(b) The part of y=4 – x^2 from (0,4) to (-2,0):

To draw the part of y = 4 - x^2 from (0, 4) to (-2, 0), we first plot the two points on the Cartesian plane:

   (0, 4)    *

             / \

            /   \

           /     \

(-2, 0) *  /       \

          *--------*

The direction of motion along this curve is from (0, 4) to (-2, 0), so we can write a vector function that starts at (0, 4) and ends at (-2, 0) by using the position vector:

r(t) = (1-t) <0, 4> + t <-2, 0>

where t ranges from 0 to 1. This vector function starts at (0, 4) when t = 0 and ends at (-2, 0) when t = 1.

(c) The part of the circle x^2 + y^2 = 9 from (3, 0) to (0, -3), moving counter-clockwise:

To draw the part of the circle x^2 + y^2 = 9 from (3, 0) to (0, -3), moving counter-clockwise, we first plot the two points on the Cartesian plane:

markdown

         * (3, 0)

       / | \

     /   |   \

    *----*----*

(0, -3)

We know that the equation of the circle is x^2 + y^2 = 9, so we can parameterize this curve by writing x and y in terms of cos(t) and sin(t):

x = 3 cos(t)

y = 3 sin(t)

where t ranges from π/2 to π. This vector function starts at (3, 0) when t = π/2 and ends at (0, -3) when t = π. Since we want to move counter-clockwise along the circle, we start at the point (3, 0) and move towards (0, -3) as t increases.

In mathematics, we use vector functions to describe curves in two- or three-dimensional space. Vector functions are functions that map a parameter t to a vector in space, allowing us to describe the position and movement of an object over time.

In this problem, we are asked to draw three different curves in the plane and write vector functions that describe each curve.

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Answer:

18.84cm

Step-by-step explanation:

circumference is diameter × π

to find the diameter we double the radius

3×2= 6 so 6 is the diameter

6×3.14=18.84

Solving the inequalities is similar to solving equations.

Isolate the variable be doing basic operations on both sides and check the solution.

e.g.

5x + 9 < 4

subtracting 9 from both sides:

5x + 9 - 9 < 4 -9

5x < -5

dividing by 5 on both sides:

x < -1

Here , -1 is excluded,

So at number line draw open circle at -1,

then using below table we find solution on number line:

When graphing an inequality , you need to determine if the value that was solved for is in the solution set or not and which way to shade. If the sign is < or >, the value is not in the solution set and has an open circle to indicate that.  

If the sign is <= or >=, the value is included and will have a closed, or filled in, circle. See the table for guidelines.

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There is a 1 in 16 chance that Jose will guess all four questions correctly on the true or false quiz.

The probability that Jose gets all of the questions correct depends on the number of answer choices for each question.

Assuming each question has two answer choices (true or false), we can calculate the probability of getting all four questions correct.

Since Jose guesses at each answer, the probability of guessing the correct answer for each question is 1/2. As the questions are independent events, we can multiply the probabilities together. Therefore, the probability of getting all four questions correct is (1/2) * (1/2) * (1/2) * (1/2) = 1/16.

In other words, there is a 1 in 16 chance that Jose will guess all four questions correctly on the true or false quiz.

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Therefore, the circumference of the triangle is 2r, which is equal to the diameter of the circle.

To find the circumference of the triangle, we need to first find the lengths of its sides. Let the three sides be x, y, and z, such that x:y:z is the given ratio. Without loss of generality, we can assume that x is the shortest side.

Let k be a constant such that y = kx and z = lx, where k and l are constants. Then, we have:

x + kx + lx = 2r

Simplifying this equation, we get:

x(1 + k + l) = 2r

So, we have:

x = (2r)/(1 + k + l)

y = kx = k(2r)/(1 + k + l)

z = lx = l(2r)/(1 + k + l)

The circumference of the triangle is the sum of its three sides:

C = x + y + z

Substituting the expressions for x, y, and z, we get:

C = (2r)/(1 + k + l) + k(2r)/(1 + k + l) + l(2r)/(1 + k + l)

Simplifying this expression, we get:

C = (2r(1 + k + l))/(1 + k + l)

C = 2r

Therefore, the circumference of the triangle is 2r, which is equal to the diameter of the circle.

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The area of the triangle is equal to A) 8.64. The Correct option is A) 8.64.

Let the lengths of the triangle be, 3x,4x,5x

Square of largest side = \(25x^{2}\)

Sum of square of other sides = \(3x^{2} + 4x^{2} = 25x^{2}\)

It is a right-angled triangle because the square of the greatest side equals the sum of the squares of the other sides.

The circumference of a right-angled triangle has a diameter equal to its hypotenuse.

hence, 5x=6 or x= \(\frac{6}{5}\)

Now, two perpendicular sides are then,  \(\frac{18 }{5} , \frac{24}{5}\)

\(Area = \frac{1}{2} \times \frac{18}{5} \times \frac{24}{5} = 8.64\)

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Question

A triangle with side lengths in the ratio 3 : 4 : 5 is inscribed in a circle of radius 3. The area of the triangle is equal to

A. 8.64

B. 12

C. 6

D. 10.5

Answer:

7+(5 3/10+ 2 2/10) = 12 5/10

The mathematical expression will be;

⇒ 7 + (5 3/10 + 2 2/10)

⇒ 145/10

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The algebraic expression is,

''Seven plus the sum of five and three tenths and two and two tenths​.''

Now,

Since, The algebraic expression is,

''Seven plus the sum of five and three tenths and two and two tenths​.''

Hence, We can formulate;

The mathematical expression as;

⇒ 7 + (5 3/10 + 2 2/10)

⇒ 7 + (53/10 + 22/10)

⇒ 7 + (75/10)

⇒ (70 + 75) / 10

⇒ 145/10

Thus, The value of the expression is,

⇒ 145/10

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Answer:

1/3

Step-by-step explanation:

(number of favoured outcomes)/(total possible outcomes)

here number of favoured choices is 1 and the total number of choices is 3

The \(PROBABILITY\) of drawing a \(BLUE\) counter is

\(\frac{1}{3}\) because we have 3 counters, and only 1 of them is blue.

Hope it helps!

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◦    Comment:               ◦

◦     Please                    ◦

◦          Mark                   ◦

◦          Brainliest           ◦

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Answer:

15

Step-by-step explanation:

the range is the largest number take away the smallest number

56-41=15

The first five terms of the geometric sequence with a first term of 2 and a common ratio of 3 are 2, 6, 18, 54, 162.

A geometric sequence is a sequence of numbers in which each term is found by multiplying the previous term by a constant called the common ratio (r).

The general form of a geometric sequence is:

a, ar, ar^2, ar^3, ar^4, ...

Where:

- a is the first term,

- r is the common ratio.

To find the first five terms of a geometric sequence, you need the values of the first term (a) and the common ratio (r).

For example, let's assume the first term (a) is 2 and the common ratio (r) is 3.

The first five terms of this geometric sequence would be:

2, 2 * 3, 2 * 3^2, 2 * 3^3, 2 * 3^4

Calculating these terms, we get:

2, 6, 18, 54, 162

So, the first five terms of the geometric sequence with a first term of 2 and a common ratio of 3 are 2, 6, 18, 54, 162.

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The amount that Jamal makes is given as follows:

$403.2.

The amount is obtained applying the proportions in the context of the problem.

Jamal is painting a house of 24 ft width and 14 ft length, hence the area is given as follows:

A = 24 x 14

A = 336 ft².

It takes 2 hours for every 50 square feet they paint, hence the time needed is given as follows:

336/50 x 2 = 13.44 hours.

The paint company charges 30$ a hour, hence the total cost is given as follows:

13.44 x 30 = $403.2.

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Control limits are based on multiples of the sample statistic's standard deviation, hence the assertion is false that "control limits are based on multiples of the process standard deviation".

A control chart is made up of many different parts. There are two control limitations. The top dashed line represents the upper control limit (UCL), and the bottom dashed line represents the lower control limit (LCL).The solid middle line denotes the statistic's average for the plot.

The horizontal lines known as control limits in a control chart show the upper and lower limits of the acceptable range of results for a process. When plotted data goes over a control limit, a process is out of control and requires management action. The control limits are defined as three standard deviations on either side of the mean.

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The value of x is 3 in a right triangle for the u side angle having equation u = 9x+6.

Angle v = 57

Angle u =9x+6

The right angle triangle follows a rule that the sum of the two acute angles is 90 degrees. That means the angles u + v must be equal to 90 degrees.

v + u = 90

From the given angle equations, we can write

57 + 9x + 6 = 90

9x + 63 = 90

9x = 90-63

9x = 27

x = 27 ÷ 3

x = 3

Therefore we can conclude that the value of x is 3.

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Answer:

Katelynn has $285 already saved. The bike she likes starts at 475. It starts at, it's not exactly. However, we are looking for the least amount she needs to save. Therefore, we need to subtract what she has saved from the least amount she is trying to save or reach. least amount needed $475 minus-saved $285 this equals $190.

Step-by-step explanation:

Answer:

no

Step-by-step explanation:

unu

Step-by-step explanation:

do you have the answer now I need it please

Answer:

The house will be worth $287,163 in 5 years.

Step-by-step explanation:

To solve this problem, we can use the formula for compound interest:

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

Where:

A = the final amount (the value of the house in 5 years)

P = the initial amount (the value of the house when it was bought)

r = the annual interest rate (5%)

n = the number of times the interest is compounded in a year (we will assume it is compounded annually, so n = 1)

t = the number of years (5)

Plugging in the values, we get:

A = 225,000(1 + 0.05/1)^(1*5)

A = 225,000(1.05)^5

A = 225,000(1.27628)

A = $287,163.00

Therefore, the house will be worth approximately $287,163 in 5 years, rounded to the nearest dollar.

Answer:

$287.2 (After I round it)

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The total distance traveled for KLM is 61 meters.

To solve KLM, we need to find the total distance traveled by each segment and then add them up.

Given:

k = 12

l = 9m

m = 20m

We know that "m" is a unit of distance, so we don't need to convert it.

Distance traveled for segment K = k = 12

Distance traveled for segment L = l = 9m

Distance traveled for segment M = m + m = 20m + 20m = 40m

Total distance traveled = K + L + M

= 12 + 9 + 40

= 61 meters.

Therefore, the total distance traveled for KLM is 61 meters.

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This suggests that the translation vector \($\mathbf{t}$\) has a component of -1 in the y-direction. Therefore, we have:

t=(3,−1)

To find the translation vector that maps quadrilateral ABCD to quadrilateral $A"B"C"D"$, we can subtract the coordinates of corresponding vertices. Let $\mathbf{t}$ be the translation vector. Then:

\($$ \begin{align*}\\\mathbf{A}" - \mathbf{A} &= \langle -3 - t_x, -3 - t_y \rangle - \langle -3, -2 \rangle \\\&= \langle -3 - t_x + 3, -3 - t_y + 3 \rangle \\\&= \langle -t_x, -t_y \rangle\end{align*} $$\)

Similarly, we have:

Since \($\mathbf{D}"$\) is not given, we cannot use it to solve for the components of \($\mathbf{t}$\). However, note that the x-coordinate of \($\mathbf{A}"$\) is -3, which is 3 less than the x-coordinate of \($\mathbf{A}$\). This suggests that the translation vector \($\mathbf{t}$\) has a component of 3 in the x-direction. Similarly, the y-coordinate of \($\mathbf{B}"$\) is -1, which is 1 more than the y-coordinate of \($\mathbf{B}$\). This suggests that the translation vector \($\mathbf{t}$\) has a component of -1 in the y-direction. Therefore, we have:

t=(3,−1)

which means that the correct answer is \($\boxed{\langle 3, -1 \rangle}$\)

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Answer:

D.

Step-by-step explanation:

Answer:

<Q, <R, <P

Step-by-step explanation:

The measures of the angles are in the same order of size as the length of the opposite side.

shortest side: RP = 2; opposite angle: Q

middle side: PQ = 5; opposite angle: R

longest side: QR = 6; opposite angle: P

Answer: <Q, <R, <P

Biggest angle has biggest side and vice versa.

Orde of sides

Order of angles

Answer:

3 hours

Step-by-step explanation:

but it can be a cent off, so it might be wrong.

Based on the information, Arnie ate 1/6 unit of the bar.

First, let's assume that the bar is equal to 1 unit. So, Yolanda ate 1/3 of the bar, which is 1/3 * 1 = 1/3 unit.

Next, Zeb ate 3/4 of what Yolanda left, which is 3/4 * (1 - 1/3) = 3/4 * 2/3 = 1/2 unit.

Finally, Arnie ate the rest, which is 1 - 1/3 - 1/2 = 1 - 5/6 = 1/6 unit.

So, Yolanda ate 1/3 unit of the bar, Zeb ate 1/2 unit of the bar, and Arnie ate 1/6 unit of the bar.

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We are given a matrix A and a scalar λ and asked to show that λ is an eigenvalue of the matrix and determine a basis for its eigenspace.

To determine if λ is an eigenvalue of matrix A, we need to check if there exists a non-zero vector v such that Av = λv. In other words, if multiplying matrix A by vector v results in a scaled version of v. Given the matrix A = [6, 9; -10, 63] and scalar λ = 5, we can find the eigenvectors by solving the equation (A - λI)v = 0, where I is the identity matrix. Substituting the values, we have: [6-5, 9; -10, 63-5]v = 0. Simplifying the equation, we get: [1, 9; -10, 58]v = 0. Solving the system of linear equations, we can find the eigenvectors v corresponding to the eigenvalue λ = 5.

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The maximum profit is 6 and it is obtained when we mix 0.6 kg of type A, 0 kg of type B, and 0.4 kg of type C.

The optimal mix for the maximum profit can be found as follows:

The company mixes three types of toffees, A, B, and C. Let the weights of type A, B, and C be a, b, and c kg, respectively. Let us assume that we are making 1kg of toffee pack. Therefore, the weight of type C should be 1 - (a + b) kg. Also, the mixture must contain at least 300 gms of type A i.e a >= 0.3 kg

Also, the weight of the first two types (A and B) must be at least equal to the weight of type C, i.e a + b >= c. This condition can also be written as a + b - c >= 0

Let us now calculate the total cost of making 1kg of toffee pack.

Cost = 20a + 10b + 5c

If the pack is sold at Rs. 17, then the profit per 1kg of toffee pack is by

Profit = Selling Price - Cost = 17 - (20a + 10b + 5c)

Now we have the following linear programming problem:

Maximize P = 17 - (20a + 10b + 5c)

Subject to constraints: a + b + c = 1 (since we are making 1kg of toffee pack)

a >= 0.3a + b - c >= 0a, b, c >= 0

We can use the simplex method to solve this linear programming problem. However, to save time, we can solve it graphically. The feasible region is as follows:

We can see that the corner points of the feasible region are: (0.3, 0, 0.7), (0.6, 0, 0.4), (0, 0.5, 0.5), and (0, 1, 0).

Let us calculate the profit at each of these corner points. For example, at the point (0.3, 0, 0.7), we have a = 0.3, b = 0, and c = 0.7. Therefore, the profit is

P = 17 - (20(0.3) + 10(0) + 5(0.7)) = 3.5

Similarly, we can calculate the profit at the other corner points as well. The corner point (0.3, 0, 0.7) gives a profit of 3.5

Corner point (0.6, 0, 0.4) result in a profit of 6

Corner point (0, 0.5, 0.5) results in a profit of 5

Corner point (0, 1, 0) gives a profit of 3

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It is false, that the margin of error of a confidence interval is the error from biased sampling methods.

The margin of error of a confidence interval is the amount of accuracy in a sample with respect to the population. It is calculated by taking the sample standard deviation and dividing it by the square root of the sample size. The margin of error helps to quantify the reliability of estimates and provides a range within which the population parameter is likely to fall. It does not refer to errors in sampling methods, which are typically a result of bias. Bias is a systematic error that arises from the sampling procedure, resulting in estimates that are not an accurate representation of the population.

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