There are eight boys in a pre-school class. Their mean height is 33 inches and their median height is 33 inches. The tallest boy whose height is 38 inches moves away and is replaced by a boy whose height is 39 inches. How does this affect the median

Answer:

62/100 multiplied by 650 which is 403 fruits left

count the number of triangles,calculate the area then multiply by the no of triangles and again back to rectangle

The function has a vertical asymptote at x = -6 and a hole at x = -5.

To find the points of discontinuity, we need to look for values of x that make the denominator of the fraction equal to zero. We can factor the denominator of the rational function as follows:

x² + 11x + 30 = (x + 6)(x + 5)

So the function is undefined for x = -6 and x = -5, since these values make the denominator equal to zero.

These are the points of discontinuity for the rational function.

At x = -6, the function has a vertical asymptote. To see this, we can examine the behavior of the function as x approaches -6 from the left and right:

As x approaches -6 from the left (i.e., x < -6), the denominator becomes a large negative number, while the numerator is a small negative number. So the fraction becomes a large negative number. As x approaches -6 from the right (i.e., x > -6), the denominator becomes a large positive number, while the numerator is a small positive number. So the fraction becomes a large positive number. Therefore, the function has a vertical asymptote at x = -6.

At x = -5, the function has a hole.

To see this, we can factor out the common factor (x + 6) from the numerator and denominator of the fraction:

y = (x + 6)/(x + 6)(x + 5) = 1/(x + 5)

So the function is undefined at x = -5, but we can see that the numerator and denominator have a common factor of (x + 5), which cancels out. Therefore, the function has a hole at x = -5, and can be defined at this point by the limit as x approaches -5:

lim (x -> -5) y = lim (x -> -5) 1/(x + 5) = -∞

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QUESTION 1: Class boundary before 1st and 2nd class

The first class limit is given as

and the second class limit is given as

The class boundary can be gotten by adding 0.5 to the upper-class limit and subtracting 0.5 to the lower-class limit.

Hence, the class boundaries are

The coordinates of the point on the directed line segment from (-7, 9) to (3, -1) that partitions the segment into a ratio of 2 to 3 are (-3, 5).

To find the coordinates of the point that divides the directed line segment from (-7, 9) to (3, -1) into a ratio of 2 to 3, we can use the section formula.

Let's label the coordinates of the desired point as (x, y). According to the section formula, the x-coordinate of the point is given by:

x = (2 * 3 + 3 * (-7)) / (2 + 3) = (6 - 21) / 5 = -15 / 5 = -3

Similarly, the y-coordinate of the point is given by:

y = (2 * (-1) + 3 * 9) / (2 + 3) = (-2 + 27) / 5 = 25 / 5 = 5

Therefore, the coordinates of the point that divides the line segment in a ratio of 2 to 3 are (-3, 5).

To understand this conceptually, consider the line segment as a distance from the starting point (-7, 9) to the ending point (3, -1). The ratio of 2 to 3 means that the desired point is two-thirds of the way from the starting point and one-third of the way from the ending point. By calculating the x and y coordinates using the section formula, we find that the desired point is located at (-3, 5).

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Answer:

Line ZL and line LZ.

Step-by-step explanation:

Since it is a line (because a line needs to have two or more points to be able to graph), it can be represented in two ways. The first being ZL, and the second being LZ.

Brainliest please.

Answer:

Step-by-step explanation

Oh

When a person places $48,800 in an investment account at an annual rate of 3.1% compounded continuously, using the formula, V = \(Pe^rt\), the amount of money (future value) after 13 years is $73,019.78.

Compounding refers to the process or interest system that computes periodic or continuous interest on both the principal and accumulated interest.

We can solve for the future value of an investment under continuous compounding using an online finance calculator as follows:

Using the formula V = \(Pe^rt\)

Principal (P) = $48,800.00

Annual Rate (R) = 3.1%

Compound (n) = Compounding Continuously

Time (t in years) = 13 years

Result:

V = $73,019.78

V = P + I where

P (principal) = $48,800.00

I (interest) = $24,219.78

Calculation Steps:

First, convert R as a percent to r as a decimal

r = R/100

r = 3.1/100

r = 0.031 rate per year,

Solving the equation for V:

V = \(Pe^rt\)

V = \(48,800.00(2.71828)^(0.031)(13)\)

V = $73,019.78

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Answer:

10x+5y=1500

Step-by-step explanation:

I don't know how to explain this but i think this is right.

Answer:

Option 4

Step-by-step explanation:

The domain of this function is the possible values of n that are suitable for this function. Since n represents a number of vehicles, the domain of n should be a whole number (since you cannot have a negative number of vehicles or half of a vehicle).

hope this helps :)

Answer:

-9/7

Step-by-step explanation:

\(slope \: of \: line \\ \\ = \frac{12 - 3}{3 - 10} \\ \\ = \frac{9}{ - 7} \\ \\ = - \frac{9}{7} \)

Answer:

It should be 15 c

Step-by-step explanation:

Basically you would move down the number line until you get to -8c and count how much you moved.

Answer:

C

Step-by-step explanation:

-3+7=4

Answer:

The question is not complete

Answer:

10 guests

Step-by-step explanation:

5 guests= $15

If the most he can spend is $30 that means he can only spend $15 more dollars!

10 guests=$30

____________________________________________________________

Hope this helps!

An algorithm for navigating or searching through tree or graph data structures is called depth-first search. The algorithm begins at the root node (choosing an arbitrary node to serve as the root node in the case of a graph) and proceeds to investigate each branch as far as it can go before turning around.

Thus, the basic concept is to begin at the root or any other random node, mark that node, then advance to the next nearby node that is not marked. This process is repeated until there are no more adjacent nodes that are unmarked. Then go back and look for more unmarked nodes to cross. Print the path's nodes lastly.

To solve the issue, adhere to the instructions listed below:

Make a recursive function that accepts a visited array and the node's index.

STEP -1

// C++ program to print DFS traversal from

// a given vertex in a given graph

#include <bits/stdc++.h>

using namespace std;

// Graph class represents a directed graph

// using adjacency list representation

class Graph {

public:

map<int, bool> visited;

map<int, list<int> > adj;

// function to add an edge to graph

void addEdge(int v, int w);

// DFS traversal of the vertices

// reachable from v

void DFS(int v);

};

void Graph::addEdge(int v, int w){

adj[v].push_back(w); // Add w to v’s list.}

void Graph::DFS(int v)

{

// Mark the current node as visited and

// print it

visited[v] = true;

cout << v << " ";

// Recur for all the vertices adjacent

// to this vertex

list<int>::iterator i;

for (i = adj[v].begin(); i != adj[v].end(); ++i)

if (!visited[*i])

DFS(*i);

}

// Driver's code

int main()

{

// Create a graph given in the above diagram

Graph g;

g.addEdge(0, 1);

g.addEdge(0, 2);

g.addEdge(1, 2);

g.addEdge(2, 0);

g.addEdge(2, 3);

g.addEdge(3, 3);

cout << "Following is Depth First Traversal"

" (starting from vertex 2) \n";

// Function call

g.DFS(2);

return 0;

STEP- 2

Time complexity: O(V + E), where V is the number of vertices and E is the number of edges in the graph.

Auxiliary Space: O(V), since an extra visited array of size V is required.

Pseudocode:

Depth_First_Search(matrix[ ][ ] ,source_node, visited, value)

{

If ( sourcce_node == value)                

return true // we found the value

visited[source_node] = True

for node in matrix[source_node]:

  If visited [ node ] == false

  Depth_first_search ( matrix, node, visited)

  end if

end for

return false //If it gets to this point, it means that all nodes have been explored.

                   //And we haven't located the value yet.

}

final answer-

A tree data structure or a graph's vertices can be searched using a recursive technique called t. Beginning with the first node of graph G, the depth-first search (DFS) algorithm digs down until it reaches the target node, also known as the node with no children.

The DFS method can be implemented using a stack data structure due to its recursive nature. The DFS algorithm implementation procedure is comparable to that of the BFS algorithm.

The following describes how to implement DFS traversal step-by-step. -

Create a stack with all of the graph's vertices in it first.

Select whatever vertex you want to use as the first vertex in the traverse, and add it to the stack.

uses for the DFS algorithm

The following list of uses for the DFS algorithm includes:

The topological sorting can be implemented using the DFS algorithm.

It can be applied to determine the routes connecting two vertices.

It can also be used to find graph cycles.

DFS technique is also applied to puzzles with a single solution.

If a graph is bipartite or not, it can be determined using DFS.

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Answer:

Question 1 : Pierre is right

Question 2 : 0.85 (because 1 - 0.15 = 0.85)

Question 3 : Less than 1

Step-by-step explanation:

Answer:

22.5

Step-by-step explanation:

If you divide y/x each ticket costs $2.5, so multiply 2.5x9 and that's your answer. :)

A graph of the given piecewise-defined function is shown in the image below.

In Mathematics and Geometry, a piecewise-defined function simply refers to a type of function that is defined by two (2) or more mathematical expressions over a specific domain.

Generally speaking, the domain of any piecewise-defined function simply refers to the union of all of its sub-domains. By critically observing the graph of this piecewise-defined function, we can reasonably infer and logically deduce that it is constant over several intervals or domains such as x > 2 and x < -2.

In conclusion, this piecewise-defined function has a removable discontinuity.

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2 by 7 + – is equals to 1 so we can say that x.

x=1-2/7

x=7/7-2/7

x=5/7

Answer:

the value of a - b is 4.

Step-by-step explanation:

We have been given the following two equations:

a + b = 10 ------------(1)

a² - b² = 40 -------(2)

We can factor the left-hand side of equation (2) using the difference of squares identity:

(a + b)(a - b) = 40

Substituting equation (1) into this equation, we get:

10(a - b) = 40

Dividing both sides by 10, we get:

a - b = 4

Therefore, the value of a - b is 4.

Step-by-step explanation:

if I understand this correctly :

a + b = 10

a² - b² = 40

(a² - b²) = (a + b)(a - b) = 40

10(a - b) = 40

(a - b) = 4

The characteristics of the function graphed are given as follows:

As the function is increasing, the graph represents exponential growth.

The y-intercept is the value of y at which the graph crosses the y-axis, hence:

y = 2, point (0,2).

Which is also the horizontal asymptote, as it is the lowest value assumed by the function.

The domain and range are given as follows:

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Answer:

10%

40inches=100%

44inches=??

44×100 11×10= 110%

----------- =

40

110%-100%= 10%

Answer:

0

Step-by-step explanation:

x < 4 means all numbers less than 4, excluding 4 itself.

4.5 > 4.

5 > 4.

so 0 is the solution

Answer:

4

Step-by-step explanation:

interval notation ( negative infinity, 4)

Answer:

Add 89 to both sides

Step-by-step explanation:

This is because the goal is to isolate x, which means get x by itself. To do that, we need to get rid of the -89 on that side. We can get rid of it by using its inverse operation, addition, and adding 89 to both sides. Now, x = 91.

The simplified form of the expression is   \(\frac{2a-1}{a(a-1)}$.\)

What is expression ?

An expression is a mathematical phrase that can contain numbers, variables, and operators. It can represent a value, a quantity, or a mathematical relationship between two or more values. Expressions can be simple, such as 3 + 4 or 5x, or more complex, such as (3x + 5y)/(2z - 1). In general, expressions can be evaluated to produce a single value or simplified to make them easier to work with.

To simplify the expression a/a-1 - (a-1)/a, we can start by finding a common denominator, which is (a-1)a.

So, we have:

\(\frac{a}{a-1} - \frac{a-1}{a} \\&\\=\frac{a^2}{a(a-1)} - \frac{(a-1)(a-1)}{(a-1)a} \\\&\\= \frac{a^2}{a(a-1)} - \frac{a^2 - 2a + 1}{a(a-1)} \&\\ \\= \frac{a^2}{a(a-1)} - \frac{a^2}{a(a-1)} + \frac{2a-1}{a(a-1)} \&\\ \\= \frac{2a-1}{a(a-1)}\end{aligned}\)

Therefore, the simplified form of the expression is \(\frac{2a-1}{a(a-1)}$.\)

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Answer:

690 square ft

Step-by-step explanation:

2,070 cubic ft ÷ 3 ft = 690 ft squared

1) The probability distribution of the average weekly earnings for employees in general automotive repair shops is the sampling distribution of the sample mean. According to the Central Limit Theorem, if the sample size is large enough, the sampling distribution of the sample mean is approximately normal, with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

2) To find the probability that the average weekly earnings is less than $445, we can standardize the sample mean and use a z-table. The z-score for $445 is calculated as follows: z = (445 - 450) / (50 / sqrt(100)) = -1. Using a z-table, we find that the probability that the average weekly earnings is less than $445 is approximately 0.1587.

3) Since we are dealing with a continuous distribution, the probability that the average weekly earnings is exactly equal to any specific value is zero.

4) To find the probability that the average weekly earnings is between $445 and $455, we can subtract the probability that it is less than $445 from the probability that it is less than $455. The z-score for $455 is calculated as follows: z = (455 - 450) / (50 / sqrt(100)) = 1. Using a z-table, we find that the probability that the average weekly earnings is less than $455 is approximately 0.8413. Therefore, the probability that it is between $445 and $455 is approximately 0.8413 - 0.1587 = 0.6826.

5) In answering questions 2-4, we made an assumption about the population distribution based on the Central Limit Theorem. We assumed that since our sample size was large enough (n=100), our sampling distribution would be approximately normal.

6) If we assume that weekly earnings for employees in all general automotive repair shops are normally distributed with a mean of $450 and a standard deviation of $50, then we can calculate the z-score for an employee earning more than $480 in a given week as follows: z = (480 - 450) / 50 = 0.6. Using a z-table, we find that the probability that an employee will earn more than $480 in a given week is approximately 1 - 0.7257 = 0.2743.

Answer:

1. 17.8 cm

2. 32.0 cm

3. 15.9 m

Step-by-step explanation:

1. Determination of the length of the arc.

Radius (r) = 6 cm

Angle at the centre (θ) = 170°

Pi (π) = 3.14

Length of arc (L) = ?

L = θ/360 × 2πr

L = 170/360 × 2 × 3.14 × 6

L = 17/36 × 37.68

L = 17.8 cm

2. Determination of the length of the arc.

Diameter (d) = 13 cm

Angle at the centre (θ) = 282°

Pi (π) = 3.14

Length of arc (L) = ?

Next, we shall determine the radius. This can be obtained as follow:

Diameter (d) = 13 cm

Radius (r) =?

r = d/2

r = 13/2

r = 6.5 cm

Finally, we shall determine the length of the arc. This can be obtained as follow:

Radius (r) = 6.5 cm

Angle at the centre (θ) = 282°

Pi (π) = 3.14

Length of arc (L) = ?

L = θ/360 × 2πr

L = 282/360 × 2 × 3.14 × 6.5

L = 282/360 × 40.82

L = 32.0 cm

3. Determination of the length of the arc.

Radius (r) = 11 m

Angle at the centre (θ) = 83°

Pi (π) = 3.14

Length of arc (L) = ?

L = θ/360 × 2πr

L = 83/360 × 2 × 3.14 × 11

L = 83/360 × 69.08

L = 15.9 m