Answer: Since the sample size is large (n > 30) and the population standard deviation is known, we can use the normal distribution to approximate the sampling distribution of the mean.
The standard error of the mean is the standard deviation of the sampling distribution of the mean, and it can be calculated as follows:
standard error of the mean = standard deviation / sqrt(n)
Plugging in the given values, we get:
standard error of the mean = 7 inches / sqrt(51) = 1.17 inches
The probability that x is within 0.5 inches of the claimed population mean (15 inches) is equal to the probability that x is between 14.5 inches and 15.5 inches. We can use the normal distribution to find this probability by standardizing the range 14.5 inches to 15.5 inches and using a z-table or a calculator to find the corresponding probability.
The standardized value for 14.5 inches is (14.5 - 15) / 1.17 = -0.43, and the standardized value for 15.5 inches is (15.5 - 15) / 1.17 = 0.43.
The probability that x is between -0.43 and 0.43 is equal to the area under the standard normal curve between these two values. Using a z-table or a calculator, we can find that this probability is 0.6915.
Therefore, the probability that x is within 0.5 inches of the claimed population mean is approximately 0.6915, which is the final answer.
Average Bloxyy
Which is not an equation of the line going through (3, -6) and (1, 2)?
A. y=-4x+6
B. y+ 6 = -4(x- 3)
C. y- 1=-4(x-2)
D. y - 2 = -4(x-1)
An equation of the line going through two points (x1, y1) and (x2, y2) can be written in the form y - y1 = m(x - x1), where m is the slope of the line. The slope of the line can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)
Plugging in the values for (x1, y1) and (x2, y2) from the problem, we get:
m = (2 - (-6)) / (1 - 3) = 8/ -2 = -4
Therefore, an equation of the line going through (3, -6) and (1, 2) is of the form y - (-6) = -4(x - 3).
Option B is of this form, so it is an equation of the line going through (3, -6) and (1, 2). The other options are not of this form, so they are not equations of the line going through (3, -6) and
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:
14=6+z over -2 whats the answer please i need help
Answer:
Hi!
If you're trying to solve for z, the answer would be -34.
I hope this helps you :)
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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Your friend asks for help on the following question:
Solve the system of equations using substitution:
x+7 y=0
2 x-8 y=22
Your friend says they want to rearrange the first equation for x and get x=-7 y, but now they are stuck. What needs to be done next?________
After doing this, you will now have______________
You tell your friend to remember that substitution means to replace. So we are replacing _____ with_________
Final answer is________
Answer:
(7,-1)
Step-by-step explanation:
x + 7y = 0
x = -7y Substitute -7y for x
2x -8y = 22
2(-7y) - 8y = 22
-14y - 8y = 22
-22y = 22 Divide both sides by -1
y = -1
Solve for x:
x - -7y
x = -7(-1)
x = 7
(7,-1)
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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25%498.60 how much in total
Cathy is planning to take the Certified Public Accountant Examination (CPA exam). Records kept by the college of business from which she graduated indicate that 56% of students who graduated pass the CPA exam. Assume that the exam is changed each time it is given. Let n = 1, 2, 3, ... represent the number of times a person takes the CPA exam until the first pass.
(Assume the trials are independent.)
(a) What is the probability that Cathy passes the CPA on the first try? (Use 2 decimal places.)
(b) What is the probability that Cathy passes the CPA exam on the second or third try? (Use 4 decimal places.)
a) The probability that Cathy passes the CPA on the first try is of: 0.56 = 56%.
b) The probability that Cathy passes the CPA exam on the second or third try is of: 0.3548 = 35.48%.
How to calculate the probabilities?A probability is the division of the number of desired outcomes by the number of total outcomes.
56% of students who graduated pass the CPA exam, hence the probability of passing on each test, including the first, is of:
0.56 = 56%.
Then the probabilities for the second or the third test are given as follows:
Second: fails with 0.44 probability then passes with 0.56 probability.Third: fails the first two, each with 0.44 probability, then passes with 0.56 probability.Then the probability that Cathy passes the CPA exam on the second or third try is calculated as follows:
p = 0.44 x 0.56 + 0.44² x 0.56 = 0.3548 = 35.48%.
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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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in the equation y = 75 - 6x, what is the slope and what is the y-intercept ?
The slope and y intercept of the equation are -6 and 75 respectively.
What is slope?The slope of a line is a number that describes both the direction and the steepness of the line.
Given that, the equation of a line is y = 75 - 6x
Comparing to the standard equation of the line, y = mx+c
m = slope and c is the y intercept.
In the equation, we can see,
The slope (m) = -6
The y intercept (put x = 0) = y = 75 - 6x0
y = 75
Hence, the slope is -6 and y intercept is 75.
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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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Please help me with this and show work!! I’ll give brainliest
Answer:
The original price of the tie was 20 dollars
Step-by-step explanation:
The price of the t-shirt was originally 24, but because he bought it on sale, he would have payed 12 because 24x.5=12. This means we can subtract the value payed for the shirt from the total money payed. 22(total)-12(shirt)=. 10 (tie). However, 10 is the price he payed for the tie, not its original value. We can find this by multiplying 10x2, which gives us our answer.
Answer:
20 dollars is the original price
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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Find x to the nearest tenth.
After using trigonometric function the value of to the nearest tenth digit is 11.11
What is Trigonometric function ?
Trigonometric functions are mathematical functions that are used to describe relationships between certain angles and lengths in a triangle. They are based on the ratios of the sides of a right triangle and are used in a variety of applications including surveying, navigation, engineering, and physics. Trigonometric functions are commonly referred to as sine, cosine, tangent, cotangent, secant, and cosecant. Each of these functions can be used to calculate the angle of a triangle, the length of the sides, or the area of the triangle.
Function of Sine
The ratio of the opposing side's length to the hypotenuse is known as an angle's sine function.
Sin a =Opp/Hypot = CB/CA
Cos Function
The cosine of an angle is the ratio of the neighbouring side's length to the hypotenuse's length.
Adjacent/Hypotenuse = AB/CA is the cosine of.
Functional Tan
The ratio of the lengths of the adjacent and opposing sides is known as the tangent function. It should be noted that the ratio of sine and cosine to the tan may also be used to express the tan.
Tan a = Opposite/Adjacent = CB/BA
In terms of sine and cos, tan is also equivalent to:
Tan = cos a/sin a
Sin 46° = 8/x
x = 8/Sin 46°
x= 8/0.72
x=11.11
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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.
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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P1.Suppose that the US population is growing by 0.94% each year and continues to grow at this rate everyyear.a. What is the overall growth factor for 30 years of population growth? (Round to 4 decimalplaces.) By what overall percentage will the US population grow over the next 30 years? (Roundto 2 decimal places.)
Answer:
Below
Step-by-step explanation:
.94 % is .0094 in decimal
this exponential growth is like a bank account compounded yearly
factor = ( 1+.0094)^30 = 1.3240
which would represent 32.40% growth
A line passes through point (-6, 1) and has a slope of 4/3 write an equation in Ax+By=C
The equation in the form Ax+ By=C is 4x-3y=27 if the line passes through the point (-6, 1) and slope is 4/3.
What is meant by an equation?A mathematical formula that connects two expressions with the equals sign (=) expresses the equality of the two expressions. The word equation and its translations in several languages might have slightly different meanings. For instance, in French, an equation is defined as including one or more variables, whereas in English, an equation is defined as any properly expressed formula that consists of two expressions joined by the equals sign.
The values of the variables that must fulfill the equality to make up the solution are referred to as the unknowns, together with the variables for which the equation must be solved.
Given point is (-6, 1)
Slope m=4/3
The equation of the line is:
y-y₁=m(x-x₁)
y-1=(4/3)(x+6)
3y-3=4x+24
4x-3y=27
Therefore, the equation in the form Ax+ By=C is 4x-3y=27
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North Pole 3. Write an equation of a line that is parallel to the line y = 4x + 7 and
passes through point (3, 2)
PLEASE HELP WILL GIVE BRAINLIEST
Solve the equation.
log base (3) of (81) = 3x+5
there you go i think
A battery producer claimed that the mean lifetime of a battery produced by his factory was 30 hours. A competitor thought that the figure was too high and took 8 batteries at random and the lifetime of each is as follows:
a) Can the claim by the battery producer be accepted at the 5% significant level? b) Can the claim by the battery producer be accepted at the 20% significant level?
The claim of the producer can be accepted at 5% significant level since the 30 hours is within 21.8118 < X < 30.932
The claim of the producer cannot be accepted at 20% significant level since the 30 hours is not within 23.648 < X < 29.102
How to check the claim of the producerThe claim is done using t score as the sample is less than 30. the formula for t scores is as follows
= x-bar ± t(s/√n)
from the given data the mean is calculated
sample mean, x-bar = (15 + 28 + 33 + 24 + 28 + 25 + 31 + 27) / 8
= 211/8
= 26.375
sample standard deviation, s
variance = (15 - 26.375)² + (28 - 26.375)² + (33 - 26.375)² + (24 - 26.375)² + (28 - 26.375)² + (25 - 26.375)² + (31 - 26.375)² + (27 - 26.375)²) / (8 - 1)
= 207.875 / 7
= 29.696
standard deviation = √variance
= √29.6964
= 5.45
Definition of variables
mean, x-bar = 26.375
standard deviation, s = 5.45
sample size, n = 8
significance level = 5%
confidence level = 1 - significance level = 1 - 0.05 = 0.95 = 95%
z score, z
For sample size less than 30, n < 30. t scores are used
degree of freedom, df = n - 1 = 8 - 1 =7
t score for 95% confidence level and df of 7 = 2.365
substituting into the formula
= x-bar ± t(s/√n)
= 26.375 ± 2.365 (5.45 / √8)
= 26.375 ± 4.557
= 21.8118 < X < 30.932
t score for 20% significant level and df of 7 = 1.415
substituting into the formula
= x-bar ± t(s/√n)
= 26.375 ± 1.415 (5.45 / √8)
= 26.375 ± 2.727
= 23.648 < X < 29.102
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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 population grows exponential. if it was 3190 initially and after 4 years grew to 3605 what is formula?
The exponential formula that shows population is y = y₀ (1.031)ˣ.
What is an exponential function?An exponential function is a function which can be defined as y = y₀ aˣ, Where 'x' is a variable and 'a' is a constant.
Given that,
The growth of population is exponential.
Also,
The initial population y₀ = 3190.
And after 4 year the population y = 3605.
Use exponential formula
y = y₀ aˣ (1)
Where x = time
Substitute the values in the formula,
3605 = 3190 a⁴
3605/3190 = a⁴
1.13009 = a⁴
a = 1.031
Substitute the value of a in equation (1),
y = y₀ (1.031)ˣ
The required formula is y = y₀ (1.031)ˣ.
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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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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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I need the answer
2x+3y+7x+4y
Answer:
The correct answer to this expression is 9x + 7y. To find this answer, you need to combine like terms. This means that you need to add together any terms that have the same variable and coefficient. In this case, the expression has two terms with the variable x and two terms with the variable y. The coefficients of the x terms are 2 and 7, and the coefficients of the y terms are 3 and 4. To combine these terms, you need to add the coefficients of the x terms together to get 9, and add the coefficients of the y terms together to get 7. Therefore, the combined expression is 9x + 7y.
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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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.
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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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]
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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