The possible locations for the start of the trail are given as follows:
3 units west: (-2,-4).3 units east: (4,-4).How to obtain the coordinates of the start of the trail?The current coordinates for Alexis position are given as follows:
(1,-4).
Meaning that:
The x-coordinate is of 1.The y-coordinate is of -4.East/West movements are horizontal, hence the x-coordinate is changed and the y-coordinate remains constant.
The changes are given as follows:
Movement to the west: subtracts the x-coordinate.Movement to the east: adds to the x-coordinate.If the start of the trail is 3 miles west of the point (1,-4), 3 is subtracted from the x-coordinate, hence the coordinates are given as follows:
(1 - 3, -4) = (-2,-4).
If the start of the trail is 3 miles east of the point (1,-4), 3 is added to the x-coordinate, hence the coordinates are given as follows:
(1 + 3, -4) = (4,-4).
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PLEASE HELP WILL GIVE BRAINLIEST
Solve the equation.
log base (3) of (81) = 3x+5
there you go i think
Question In △XYZ, A is the midpoint of XY¯¯¯¯¯¯¯¯, B is the midpoint of YZ¯¯¯¯¯¯¯, and C is the midpoint of XZ¯¯¯¯¯¯¯¯. AC = 7, AB = 5, and XY = 24. What is the perimeter of △XYZ? Enter your answer in the box. Perimeter = units
The perimeter of triangle XYZ is 48 units
What is the perimeter of a triangle?
The total of a triangle's sides equals the triangle's perimeter. The space encircled by a triangle's three sides is known as its area.
Here, we have
In The triangle XYZ
A is the midpoint of XY
B is the midpoint of YZ
AB = 1/2 XZ
AB = 5 units
Substitute the value of XZ in AB
5 = 1/2 × XZ
XZ = 10 units
B is the midpoint of YZ
C is the midpoint of XZ
BC = 1/2 XY
XY = 24 units
BC = 1/2 × 24 = 12 units
A is the midpoint of XY
C is the midpoint of XZ
AC = 1/2 YZ
AC = 7
7 = 1/2 YZ
YZ = 14
The perimeter of a triangle = the sum of the lengths of its sides
Perimeter ΔXYZ = XY + YZ + ZX
Perimeter ΔXYZ = 24 + 14 + 10
Hence, the perimeter of triangle XYZ is 48 units
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use the following information to determine the value of river gardens' common stock: a. expected dividend payout ratio is 45%. b. expected dividend growth rate is 6.5%. c. river gardens' required return is 12.4%. d. expected earnings per share next year are $3.25.
The value of river garden's common stock is $24.79.
What is the value of the common stock?In order to determine the value of the common stock, the constant dividend model would be used.
According to this model, the value of a common stock is determined by its dividend, the growth rate and the required return.
Value of the stock = Dividend / (required return - growth rate)
The first step is to determine the dividend of the common stock.
Dividend = pay out ratio x expected earnings
Dividend = 0.45 x $3.25
Dividend = $1.46250
Value of the stock = $1.46250 / (0.124 - 0.065)
Value of the stock = $24.79
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A person's body mass index, B, is directly proportional their weight, w, and inversely proportional to the square of their height, h. a. (6 points) Write a single equation to express the proportionality relationship, using k as the constant of proportionality. b. (6 points) A 70 inch tall person who weighs 198 pounds has a body mass index of 28.4
The proportionality constant, k, in this case is 0.00043.
a. The proportionality relationship between body mass index (B), weight (w), and height (h) can be expressed as follows:
B ∝ w * [tex]h^{-2[/tex]
where k is the constant of proportionality.
b. To find the value of the constant of proportionality, k, we can substitute the known values into the equation and solve for k.
28.4 = k * 198 * [tex]70^{-2[/tex]
Solving for k gives:
k = 0.00043
Therefore, the proportionality constant, k, in this case is 0.00043.
A proportionality constant is a number that is used to indicate the ratio of two different variables that are proportional to each other. It is also known as a scaling factor or a constant of proportionality. It is usually represented by the letter k.
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The triangle and the rectangle below have the same area.
Calculate the value of w.
Show your working.
Answer:5 cm
Step-by-step explanation:
Answer: w=2.5cm
Step-by-step explanation:
when solving for a right triangle, you need to to the length multiplied by the width and then divided by two. You then get (6*5)/2=30/2=15.
When solving for a rectangle, it’s the same, but without dividing by two. But you need them to be equal, and you already have the measure six.
So 5/2=2.5 therefore w=2.5cm.
se the following information for questions 31-34: The average GPA for all college students in the United States as of 2006 was 3.11. We want to test to see if the GPA of students at Texas A&M is higher than the national average. Suppose we survey 47 randomly selected students at Texas A&M and the average GPA is 3.27, with a standard deviation of 0.54. Assuming all conditions are met, conduct a hypothesis test at the 0.01 significance level.
Which of the following below best describes the p-value?
a. p value = 0.0424
b. 0.02 < p-value < 0.025
c. p-value = 0.9788
d. 0.04 < p-value < 0.05
e. p-value = 0.0212
The best option which describes the p-value is 0.02 < p-value < 0.025.
We know that for the p-value method,
Z = (Sample Mean - Population Mean) / (standard deviation/sqrt (number of selections))
The average GPA for all the college students in the United States as of 2006 = 3.11 (Sample Mean)
The average GPA of randomly selected students at Texas A&M
= 3.27 (Population Mean)
Number of students randomly selected = 47
Standard deviation of them = 0.54
Therefore, Z = (3.27-3.11)/ (0.54/ sqrt(47)) = 2.031
Hence, by right tailed test,
p = 0.024
which implies, 0.02 < p-value < 0.025.
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in three to five sentences explain your understanding of the algorithm express the algorithm in either detailed pseudocode or in program code establish the running time complexity of the algorithm by explaining how you arrived at it.
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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What is the slope of a line that is perpendicular to a line whose equation is 3y=-4x+2?
The slope of a line that is perpendicular to a line whose equation is; 3y = -4x + 2 is; 3 / 4.
What is the slope of a line that is perpendicular to a line whose equation is; 3y = -4x + 2?As evident in the task content is; the given equation is; 3y = -4x + 2.
To determine the slope of the given line; the equation can be expressed in slope-intercept form by dividing through by; 3.
y = -4/3x + 2/3
On this note, by comparison with the slope-intercept form of a linear equation; the slope, m is; -4/3.
Therefore, since the product of the slopes of perpendicular lines equal; -1;
The slope of the required line which is perpendicular to the given line can be determined as follows;
Slope of perpendicular; m = -1 ÷ (-4/3)
= -1 × 3 / -4
= -3 / -4
= 3/4.
On this note, the slope of the line perpendicular to the given line is; 3 / 4.
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A
college student takes out a $7,500 loan from a bank. What will the balance of the loan
not made any payments yet) if the bank
be after one year (assuming the student has not made
charges 3.8% interest each year?
The balance of the loan (not made any payments yet) of the bank
be after one year charges 3.8% interest each year is; $7785
How to calculate the interest amount with a given rate and time?There are mainly two types of interest. One which works only on principal(or say initial) amount, and one which works on amount plus interest to be paid till date.
For 1 year case, if interest is applied annually, both interests are same since there is no interest before first year.
For 1 year, interest with R% rate for principal amount P is just R% of P which is; (P/100) * R
We are given that R = 3.8% each year
Since P = $7500, thus, interest for 1 year is 3.8% of $7500 is;
I = 7500/100 * 3.8
I = $285
Thus, total payable amount = Principal amount + interest
Total amount = $7500 + $285 = $7785
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David says that a triangle with side measures 9 cm, 12 cm, and 17 cm is a right triangle. Susie says it is not. Who is correct? Explain
your reasoning.
12 cm
17 cm
9 cm
Susie is correct as it is not a right triangle
How to prove the nature of the triangle?According to Pythagoras theorem, In a right triangle ,the square of the hypotenuse side in a right-angled triangle equals the sum of the squares of the other two sides.Here let the hypotenuse side = 17 (longest )
Square of the hypotenuse side = 289
Squares of the other two sides = 12 * 12 = 144
=9 * 9 = 81
Sum of the squares of the other two sides = 144 + 81
= 225
So, here 225 ≠ 289
The square of the hypotenuse side of this triangle does not equal the sum of the squares of the other two sides. So this is not a right triangleThus, Susie is correct as it is not a right triangle.To learn more about Pythagoras theorem, refer:
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5. You use a line of best fit for a set of data to make a prediction about an unknown value. The
correlation coefficient for your data set is -0.993. How confident can you be that your
predicted value will be reasonably close to the actual value?
Answer: The correlation coefficient is a measure of the strength and direction of the relationship between two variables. A correlation coefficient of -0.993 indicates a very strong negative relationship, which means that as one variable increases, the other variable decreases. This suggests that you can be quite confident that your predicted value will be reasonably close to the actual value.
Given figure below as well as the fact that a is parallel to b what is the value of x?
Answer:
17
Step-by-step explanation:
The value of x from the angles between given parallel line is 17.
What are consecutive angles in between two parallel lines?Consecutive angles lie along the transversal, both angles will always be on one side of the transversal, and they'll either both be inside the parallel lines or outside the parallel lines (interior or exterior angles, respectively). Consecutive angles are always supplementary if the transversal crosses parallel lines.
From the given figure, we have two angles 2x+5 and 8x+5.
As we know, sum of consecutive angles is 180°
Now, 2x+5+8x+5=180
10x+10=180
10x=170
x=17
So, 2x+5=39° and 8x+5=141°
Therefore, the value of x from the angles between given parallel line is 17.
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In the gymnastics competition, Jill earned nine and six-sevenths points. Alice earned eight and two-thirds points. How many more points did Jill earn than Alice?
Answer:
[tex]\boxed{1.1914285714285713}[/tex]
Step-by-step explanation:
Jill earned a total of 9 + 6/7 = <<9+6/7=9.857142857142857>>9.857142857142857 points.
Alice earned a total of 8 + 2/3 = <<8+2/3=8.666666666666666>>8.666666666666666 points.
Therefore, Jill earned 9.857142857142857 - 8.666666666666666 = <<9.857142857142857-8.666666666666666=1.1914285714285713>>1.1914285714285713 more points than Alice. Answer: \boxed{1.1914285714285713}.
Alice earned approximately 1.19 points more than Jill.
To find the difference between the number of points earned by Jill and the number of points earned by Alice, we need to first convert both amounts to a common denominator.
Since the denominators of the fractions representing the number of points earned by Jill and Alice are different, we will need to find a common denominator. To do this, we can find the least common multiple (LCM) of 7 and 3, which is 21.
We can then rewrite the fraction representing the number of points earned by Jill as 9 + 6/7 = (9 * 3 + 6)/21 = 27/21 + 6/21 = 33/21, and the fraction representing the number of points earned by Alice as 8 + 2/3 = (8 * 7 + 2)/21 = 56/21 + 2/21 = 58/21.
To find the difference between the number of points earned by Jill and the number of points earned by Alice, we can subtract the number of points earned by Alice from the number of points earned by Jill:
33/21 - 58/21
We can simplify this expression by combining like terms:
(33 - 58)/21 = -25/21
This represents a difference of -25/21 points, or approximately -1.19 points. Since a negative difference represents a smaller quantity, this means that Alice earned approximately 1.19 points more than Jill.
if there are too many categories of statistics to present clearly on a graph, what is the next best option?
If there are too many categories of statistics to present clearly on a graph, then the next best option is a Chart.
Hence, option (a) is the correct choice.
A chart displays data that can be shown as a table, graph, or diagram. It includes a variety of information presentation techniques.
Various Graph and Chart Formats for Data are the following:
Bar Graph: When one data label is lengthy or if there are more than ten things to compare, a bar graph should be used to reduce clutter.
Column Chart.
Line Graph.
Dual Axis Chart.
Area Chart.
Stacked Bar Chart.
Mekko Chart.
Pie Chart.
The chart is one of the most effective ways to categorise the data.
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May be the complete questions should be as follow:
if there are too many categories of statistics to present clearly on a graph, what is the next best option?
Bar graph
Column Chart.
Line Graph.
Stacked Bar Chart.
Mekko Chart.
Two angles form a linear pair, the sum of one angle plus 27 is equal to two times the sum of the other angle
The pair of Linear angles are 51° and 129°.
What are Linear Angles:When two lines intersect at a point then they will form two linear angles. The sum of angles of a linear pair is always equal to 180°. Such angles are also known as supplementary angles.
In other words, if the sum of two adjacent angles is 180° then the pair of angles are said to be Linear Angles.
Here we have
Two angles form linear angles
Let x and y be the two angles
=> x + y = 180 ------ (1) [ since both are linear angles ]
Given that the sum of one angle plus 27 is equal to two times the sum of the other angle
=> x + 27 = 2y
=> x = (2y - 27) ---- (2)
Substitute (2) in (1)
=> 2y - 27 + y = 180
=> 3y = 153
=> y = 153/3
=> y = 51
Now substitute y = 51 in (1)
=> x + 51 = 180
=> x = 180 - 51
=> x = 129
The pair of Linear angles are 51° and 129°.
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What is the image of (10,-6) after a dilation by a scale factor of 1/2 centered at the origin?
The image of (10,-6) after dilation by a scale factor of 1/2 centered at the origin is (-5,-3).
What is dilation?
A dilation is a function f from a metric space M into itself that, for any points x, y in M, fulfills the identity d=rd, where d is the distance between x and y and r is a positive real number. Such a dilatation is a resemblance of the space in Euclidean space.
Here, we have
Given
The image of (10,-6) after dilation by a scale factor of 1/2 centered at the origin.
We have to find the image after dilation.
The coordinates of an image (-10,-6), dilating the coordinate by 1/2 means reducing the image by multiplying each coordinate by the factor of 1/2.
Image = (1/2(-10), 1/2(-6))
Image = (-5,-3)
Hence, the image of (10,-6) after dilation by a scale factor of 1/2 centered at the origin is (-5,-3).
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Suppose that the supply of x units of a product at price p dollars per unit is given by the following. 30 +90 In(4x +5) p (a) Find the rate of change of supply price with respect to the number of units supplied. dp dx (b) Find the rate of change of supply price when the number of units is 30. $ (c) Approximate the price increase associated with the number of units supplied changing from 30 to 31. $ Need Help? Talk to a Tutor Rea Watch It Read It
For part (a), we need to find the derivative of the supply equation with respect to the number of units, x.
The supply equation is given by:
S(x) = 30 + 90p * In(4x + 5)
To find the derivative of S(x) with respect to x, we can use the chain rule:
[tex]\frac{dS(x)}{dx} =\frac{dS(x)}{dp}*\frac{dp}{dx}[/tex]
Since the derivative of S(x) with respect to p is 90 * In(4x + 5), we can substitute this into the equation above:
[tex]\frac{dS}{dx}=(90*ln(4x+5))*(\frac{dp}{dx} )[/tex]
This gives us the expression for the rate of change of supply price with respect to the number of units supplied.
For part (b), we need to find the rate of change of supply price when the number of units is 30. Substituting x = 30 into the equation above gives us:
[tex]\frac{Ds(30)}{dx} = (90*ln(4*30+5))*\frac{dp}{dx}[/tex]
For part (c), we need to approximate the price increase associated with the number of units supplied changing from 30 to 31. To do this, we can use the equation from part (a) to find the rate of change of supply price with respect to the number of units supplied and then multiply this rate by the change in the number of units (from 30 to 31).
The approximate price increase is given by:
[tex]\frac{dS(x)}{dx} *(x2-x1)=\frac{dS(x)}{dx}*(31-30)[/tex]
Substituting the appropriate values into this equation will give us the approximate price increase associated with the number of units changing from 30 to 31.
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slope of a line perpendicular to y=-4x-7
Because the slope of the supplied line is -4, the needed slope of a line perpendicular to y=-4x-7 is 1/4.
What is slope of line?The slope of a line indicates its steepness. Slope is computed mathematically as "rise over run" (change in y divided by change in x). The slope of a line is its steepness as it goes from LEFT to RIGHT. Slope is the ratio of a line's rise, or vertical change, to its run, or horizontal change. The slope of a line is always constant (it never changes) no matter what 2 locations on the line you select. The slope-intercept form of an equation occurs when the equation of a line is stated in the form y = mx + b.
Here,
y=mx+c
m=-4
slope of a line perpendicular to y=-4x-7,
m1=1/4
The required slope of a line perpendicular to y=-4x-7 will be 1/4 as the slope of given line is -4.
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i don’t who’s reporting this question but stop, this question isn’t even my question i’m trying to help someone else out by posting it for them. can someone answer this and the two other questions i posted today too?
Answer:
a) 1 degree above
b) 4 degrees below
c) 12 degrees above
d) 7 degrees above
Step-by-step explanation:
Five standard (six-sided) dice are rolled, one at a time. What is the probability that
a. the first two dice show aces, and the next three do not?
b. two of the five dice show aces, and the other three do not?
The values of the probability in both scenarios are 0
How to determine the probabilitiesFirst two dice show aces, and the next three do not
From the question, we have the following parameters that can be used in our computation:
Experiment = rolling of dice
The outcome of an ace is not in the sample space of rolling a die
This means that the probability is 0.
Two of the five dice show aces, and the other three do not
Here, we have
Experiment = rolling of dice
The outcome of an ace is not in the sample space of rolling a die
This means that the probability is 0.
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What is the greatest common factor of 18, 24, and 40?
2
3
4
8
Answer:
(a) 2
Step-by-step explanation:
You want the greatest common factor of 18, 24, 40.
FactorsThe prime factorization of these numbers is ...
18 = 2 · 3²24 = 2³ · 340 = 2³ · 5The only common factor is 2.
2 is the greatest common factor of 18, 24, and 40.
solve the equation 1/3(x+6) = 1/2 (x-3) Show work pleaseee i need this now please help meeeee!!!!!!!!!!
Answer:
x = –24
[tex] \frac{1}{3(x + 6)} = \frac{1}{2(x - 3)} \\ \\ ⇒ \frac{1}{3x + 18} = \frac{1}{2x - 6} \\ \\ ⇒3x + 18 = 2x - 6 \: \\ \\ ⇒3x - 2x = - 6 - 18 \\ \\ ⇒x = - 24 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:[/tex]
Hope it helps you
Answer:
21.
Step-by-step explanation:
[tex]\frac{1}{3} (x+6)=\frac{1}{2} (x-3);\\\\6*\frac{1}{3} (x+6)=6*\frac{1}{2} (x-3);\\2(x+6)=3(x-3);\\2x+12=3x-9;\\x=21.[/tex]
North Pole 3. Write an equation of a line that is parallel to the line y = 4x + 7 and
passes through point (3, 2)
Solve for x in the triangle. Round your answer to the nearest tenth.
Answer: 2.795
Step-by-step explanation:
[tex]cos 56= \frac{x}{5}[/tex]
evaluate f(x)=(3x-1)(2x+10), what is f(2)=
Thee value of the function f(2) is 70
What is a function?A function can be defined as an expression, law or rule that stands to explain the comparison between two variables.
These are namely;
The independent variableThe dependent variableFrom the information given, we have the function as;
f(x)=(3x-1)(2x+10)
To determine the value of the function when x = 2, we have to substitute the value of x as
Now, substitute the value into the function, we have;
f(2) = (3(2) - 1 )(2(2) + 10)
expand the bracket
f(2) = (6 -1)(4 + 10)
Add or subtract the values
f(2) = (5)(14)
Multiply the values, we have
f(2) = 70
Hence, the value is 70
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Question 1
Two months ago, a car dealership sold 30 red cars and 120 cars that were not red. Last
month the car dealership sold a total of 200 cars. Tarik predicts that the dealership sold
45 red cars last month. Do you think this is a reasonable prediction? Explain.
Answer:
Yes this is a resendable prediction
Step-by-step explanation:
barttleby rework problem 17 from section 5.1 of your text, involving the production of basketballs. assume that the number of defective basketballs produced is related by a linear equation to the total number produced. suppose that 7 defective balls are produced in a lot of 275, and 14 defective balls are produced in a lot of 375. find the number of defective balls produced in a lot of 600 balls.
the number of defective balls produced in a lot of 500 balls is 26 when 7 defective balls are produced in a lot of 275, and 14 defective balls are produced in a lot of 375
what is linear equation ?A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.
calculation
let y be the number of defective basket balls
x be the total number of basketball produced
let y1 = 12 , x2 = 200
y2 = 19 , x2 = 350
since its given that no. of defective basketballs produced is related by a linear equation to the total no. of produced we have
y = mx +c
m = 19 - 12 / 350 - 200 = 7/150
y = 7x/150 + c
put x = 200 , y = 12
12 - 7 * 200/ 150 = c
c = 8/3
y = 7x /150 + 8 /3 ...........1
no. of defective balls produced in a lot of 500 balls
y (500) = 7*500/150 + 8/3
= 70/3 + 8 /3 = 78/3 = 26
the number of defective balls produced in a lot of 500 balls is 26 when 7 defective balls are produced in a lot of 275, and 14 defective balls are produced in a lot of 375
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A salesperson works at a car dealership and earns $20 per hour plus a $100 bonus for each car sold. The salesperson sells 8 cars and earns a minimum of $1,400 this week.
Which inequality represents the possible number of hours, x, the salesperson works this week?
Responses
100x+20≥1,400, where x≥13.8
100 x + 20 ≥ ≥ 1 , 400 , where x ≥ ≥ 13.8
100x+20≤1,400, where x≤13.8
100 x + 20 ≤ ≤ 1 , 400 , where x ≤ ≤ 13.8
20x+800≥1,400, where x≥30
20 x + 800 ≥ ≥ 1 , 400 , where x ≥ ≥ 30
20x+800≤1,400, where x≤30
The inequality which represents the possible number of hours , x, the salesperson works this week is 20x + 800 ≥ 1400 where x ≥ 30,
using equation formation steps.
What is an equation ?
In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.
For instance, 3x + 5 = 14 is an equation.
Equations and inequalities are both mathematical sentences formed by relating two expressions to each other. In an equation, the two expressions are deemed equal which is shown by the symbol =. Where as in an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.
In given que,
minimum earning = $1400
The possible number of hours = x
No. of cars sold = 8
Price earned by sold cars = $800
Price earned per hour =$20
Price earned for x hours = $20x
So, the total amount = 20x + 800
The equation become 20x + 800 ≥ 1400
Solving inequality que,
20x >= 600
x ≥ 30
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7. Multiply the
polynomials.
(2x³ + 4x² − 5x)(x³ + 2x - 1)
2x⁶ + 4x⁵ - x⁴ + 6x² - 5x is the product of multiplying the polynomials (2x³ + 4x² − 5x)(x³ + 2x - 1).
Define multiplication.Multiplication in elementary algebra is the process of figuring out what happens when a number is multiplied by itself. Each of the numbers and is referred to as a factor of the product, which is the outcome of a multiplication.
Given
Polynomial
(2x³ + 4x² − 5x)(x³ + 2x - 1)
Multiplying by distributive method,
2x³(x³ + 2x - 1) + 4x²(x³ + 2x - 1) - 5x(x³ + 2x -1)
2x⁶ + 4x⁴ - 2x³ + 4x⁵ + 2x³ - 4x² - 5x⁴ + 10x² - 5x
Adding polynomials with same powers
2x⁶ + 4x⁵ + 4x⁴ - 5x⁴ - 2x³ + 2x³ - 4x² + 10x² - 5x
2x⁶ + 4x⁵ - x⁴ + 6x² - 5x
2x⁶ + 4x⁵ - x⁴ + 6x² - 5x is the product of multiplying the polynomials (2x³ + 4x² − 5x)(x³ + 2x - 1).
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Please, someone, help me?
The equation that represents the total amount is y = 50(4+x).
What is Equation:The mathematical statement that shows two mathematical terms have equal values is known as an equation. An equation simply states that two things are equal.
Equations contain both constant terms and algebraic terms which are combined by operations like Adding and subtraction etc.
Here we have
An electrician charges a callout fee of $ 200 and $ 50 per hour
Given that the total amount charged is y for x hours
As we know the electrician charges $ 50 per hour
=> The charge per x hours = 50x
And callout fee = $ 200
The equation that represents the above situation is
=> y = 200 + 50x
=> y = 50(4+x)
Therefore,
The equation that represents the total amount is y = 50(4+x)
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