Therefore, the probability of this event is 3/6 or 1/2.
What is Probability?Probability is a measure of the likelihood of an event occurring, expressed as a number between 0 and 1. It is used to quantify the uncertainty or risk associated with a particular event or situation.
given by the question.
Event: Rolling a standard die and landing on either 1, 2, or 3.
A standard die has six faces, numbered from 1 to 6. Rolling the die is a random experiment that can result in any of the six possible outcomes with equal probability. The event described in the statement only includes three of the six possible outcomes, namely 1, 2, and 3
To learn more about probability:
https://brainly.com/question/14210034
#SPJ1
tan(11pi/12)
Find the exact value of the following trig expression using
trig identities and the special points on the unit circle.
The exact value of the following trig expression tan(11pi/12) is (18sqrt(3) + 18sqrt(2-sqrt(2)))/(8-9sqrt(3)*sqrt(2-sqrt(2))).
The exact value of the following trig expression tan(11pi/12) can be found using trig identities and the special points on the unit circle.
First, we can use the double angle formula for tangent:
tan(2x) = 2tan(x)/(1-tan^2(x))
We can then use this formula to rewrite the given expression:
tan(11pi/12) = tan(2*11pi/24) = 2tan(11pi/24)/(1-tan^2(11pi/24))
Next, we can use the sum formula for tangent to rewrite the expression in the numerator:
tan(11pi/24) = tan(7pi/24 + 4pi/24) = (tan(7pi/24) + tan(4pi/24))/(1-tan(7pi/24)*tan(4pi/24))
We can then use the special points on the unit circle to find the exact values of these expressions:
tan(7pi/24) = tan(pi/3 + pi/8) = (tan(pi/3) + tan(pi/8))/(1-tan(pi/3)*tan(pi/8)) = (sqrt(3) + sqrt(2-sqrt(2)))/(1-sqrt(3)*sqrt(2-sqrt(2)))
tan(4pi/24) = tan(pi/6) = sqrt(3)/3
Plugging these values back into the original expression, we get:
tan(11pi/12) = 2(sqrt(3) + sqrt(2-sqrt(2)))/(1-sqrt(3)*sqrt(2-sqrt(2)))/(1-(sqrt(3)/3)^2) = 2(sqrt(3) + sqrt(2-sqrt(2)))/(1-sqrt(3)*sqrt(2-sqrt(2)))/(8/9) = (2(sqrt(3) + sqrt(2-sqrt(2))))*(9/(8-9sqrt(3)*sqrt(2-sqrt(2))))
Simplifying further, we get:
tan(11pi/12) = (18sqrt(3) + 18sqrt(2-sqrt(2)))/(8-9sqrt(3)*sqrt(2-sqrt(2)))
Therefore, the exact value of the following trig expression tan(11pi/12) is (18sqrt(3) + 18sqrt(2-sqrt(2)))/(8-9sqrt(3)*sqrt(2-sqrt(2))).
Learn more about identities
brainly.com/question/6971003
#SPJ11
u think u guys can help with this?
The IQR is the difference between Q3 and Q1: IQR = Q3 - Q1 = 4 - 1 = 3 hours.
The presented graph displays a line or dot plot of a data set that indicates the average daily activity time of a group of individuals over the previous week.
We must locate the data set's middle value in order to get the median. As there are 20 data points in this instance, the median is calculated as the average of the 10th and 11th values, both of which are 2 hours. As a result, 2 hours is the median amount of exercise per day.
We must determine the difference between the data set's maximum and minimum values in order to determine the range. The ranges are 0 hours for the minimum and 5 hours for the highest. The range is therefore 5 - 0 = 5 hours.
Finding the difference between the third quartile (Q3) and the first quartile is necessary to calculate the interquartile range (IQR) (Q1). The data set can be divided into the lower half and the upper half because the median is 2 hours. 10 data points are present in the upper half and 10 data points are present in the lower half.
The median of the lower half of the data set must be located in order to determine Q1. The median is the average of the fifth and sixth values, both of which are one hour because there are ten data points in the lower half. Q1 is therefore 1 hour.
We must determine the median of the upper half of the data set in order to determine Q3. The median is the average of the fifth and sixth values, which are both 4 hours, as there are 10 data points in the upper half. Q3 is therefore 4 hours.
The IQR represents the variation between Q3 and Q1: IQR is equal to Q3 - Q1 (4 - 1 = 3 hours).
To know more about interquartile visit:
https://brainly.com/question/30425767
#SPJ1
Select all the correct answers. Which equations represent functions? 2x + 3y = 10 4x = 16 2x − 3 = 14 3y = 18 14.6 = 2x
The equations that represent functions are:
1) 2x + 3y = 10
2) 3y = 18
What is a function?Functions are relations which give a particular output for each input. The characteristic that every input is associated with exactly one output defines a function as a relationship between a set of inputs and a set of allowable outputs. Specific input is supplied to a function in order to produce a specific result. To determine if a curve is a function or not, apply the vertical line test. Any curve that intersects a vertical line at more than one point is not a function.
Let us look into each equation.
1) 2x + 3y = 10
Here for each input of x, we get only one output y.
So this is a function.
2) 4x = 16
This is not a function because there can be multiple values of y for a single value of x.
3) 2x − 3 = 14
This is also not a function because there can be multiple values of y for a single value of x.
4) 3y = 18
This is a function because there is only one value of y for exactly one value of x. Also, considering the vertical line test, the curve is a straight horizontal line which intersects with a given vertical line only once. So it is a function.
5)14.6 = 2x
This is also not a function because there can be multiple values of y for a single value of x.
Therefore the equations that represent functions are:
1) 2x + 3y = 10
2) 3y = 18
To learn more about functions, follow the link.
https://brainly.com/question/11624077
#SPJ1
What is the set of x-intercepts of this graphed function?
-3, -1, 3
Step-by-step explanation:X-intercepts are also known as the roots or zeros of a function.
Finding Intercepts From Graphs
In the problem, we are given a basic polynomial graph. The x-intercepts are where the graphs intersect with the x-axis. Remember that the x-axis is the horizontal axis. Finding x-intercepts when given a graph is as simple as just looking to see where the line crosses over. We can see that the graph crosses the axis in three points. The x-intercepts are x = -3, -1, and 3.
Finding Intercepts From Equations
In this question, we are not given an equation, but if we were there is another possible way to solve it. The x-intercepts occur when y = 0. So, to find x-intercepts from an equation, all you need to do is plug 0 in for y and solve.
help!!!!!!!!!! quick
Step-by-step explanation:
Refer to pic...........
The diameter of a quarter is about 1
in.
You trace around the edge of the quarter on a sheet of paper.
What is the area of the circle on the paper?
Use 3.14
as an approximation for π
. Round your answer to the nearest tenth.
The area of the circle which is drawn by tracing around the edge of the quarter on a sheet of paper is 0.78 in.²
What is meant by a quarter of a circle?All points in a plane that are at a specific distance from a specific point, the centre, form a circle. In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.
Each of the four equally sized pieces that make up a circle is known as a quarter of a circle. The quadrant of the circle is the name given to each quarter. One-fourth of the total area of the circle is represented by the area of a quarter circle.
Given,
the diameter of the quarter = 1 in.
When we trace around the edge of the quarter on a sheet of paper, we get a circle of diameter 1 in.
So the radius of the circle r = 1/2 = 0.5 inches
Area of the circle on the paper = πr² = 3.14 × 0.5² = 0.78 in.²
Therefore the area of the circle which is drawn by tracing around the edge of the quarter on a sheet of paper is 0.78 in.²
To learn more about the quarter, follow the link.
https://brainly.com/question/28982779
#SPJ1
The Sugar Sweet Company will choose from two companies to transport its sugar to market. The first company charges $2804 to rent trucks plus an additional
fee of $100.50 for each ton of sugar. The second company does not charge to rent trucks but charges $275.75 for each ton of sugar.
For what amount of sugar do the two companies charge
the same?
What is the cost when the two companies charge the
same?
Answer:
16 tons$4412Step-by-step explanation:
We can rewrite the situation using cost equations for the two companies
If c1 and c2 represent the total costs for companies 1 and 2 respectively and w the weight of sugar transported
For the first company we have
c1 = 2804 + 100.50w
For the second company
c2 = 275.75w
Costs are the same when c1 = c2
or
2804 + 100.50w = 275.75w
To Solve:
Subtract 100.50w from both sidesAt 16 tons of sugar, the costs will be the same for both companies
At this tonnage, the cost is
275.75 x 16 = $4412
A) The priestess at Horus’ temple has to go up a flight of 5 steps each day.The high priest has decreed that she will ascend the steps one or two at a time. She wants to know if she can do this a different way each day for a week.Is it possible?How many ways are there of ascending the steps?
B) The grand staircase has 13 steps. The priest wants to know if he can climb this a different way each day for a year using the same rules as the priestess.
Is it possible?
How many ways are there of ascending the grand staircase?
Explain why your answer is correct.
please answer this pleaase
There are a total of 32 possible sequences because there are two alternatives for each stage. Since there are more than seven distinct ways to mount the stairs, the priestess can do so every day for a week.
How many ways are there of ascending the steps?(a) Every day, the priestess at the temple of Horus must climb a flight of five stairs, which she can do by taking one or two steps at a time. The amount of ways she can up the stairs on any given day can be represented by a binary digit, where 1 denotes a two-step ascent and 0 denotes a one-step ascent. For each of the five steps, for instance, 00101 reflects the order of her one- and two-step climbs.
How many ways are there of ascending the grand staircase?(b) The same regulations apply. The entire number of potential sequences, using the same binary digit format, is 213 = 8,192. There are therefore more than 365 possible ways to mount the grand staircase, allowing the priest to do so every day for a whole year.
In conclusion, the number of alternative binary sequences, where each digit denotes a one- or two-step climb, may be used to determine the number of ways the priestess can ascend the five-step flight of stairs and the number of ways the priest can ascend the thirteen-step grand staircase.
Learn more about Permutation here:
brainly.com/question/30649574
#SPJ1
name the property the statement illustrates
Answer:
1. Transitive
2. Reflexive
3. Symmetric
4. Reflexive
5. Symmetric
6. Transitive
Three baby penguins and their father were sitting on an iceberg
0.5
0.50, point, 5 meters above the surface of the water. The father dove down
4.7
4.74, point, 7 meters from the iceberg into the water to catch dinner for his kids.
What is the father penguin's position relative to the surface of the water?
Answer:The father's position relative to the surface of the water is 4.2 meters below the surface of the water.
Step-by-step explanation:
What is an expression?
Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
The height relative to the water surface is calculated as:-
Height from iceberg to water surface = 0.5 meters
The height from iceberg to deep inside the water is = 4.7 meters
Father's height relative to the water surface is,
H= 4.7 - 0.5 = 4.2 meters.
The image of the condition is also attached with the answer below.
To know more about Expression follow
brainly.com/question/723406
What is the shortest distance from the point (6,5) to the line 2x+3y=1 ? (A) √13 (B) 2√13 (C) 4√13 (D) 6√13 (E) None of these
The shortest distance from a point to a line can be found by using the formula:
d = |Ax + By + C| / √(A² + B²)
where A, B, and C are the coefficients of the line equation and x and y are the coordinates of the point.
In this case, A = 2, B = 3, C = -1, x = 6, and y = 5.
Plugging these values into the formula, we get:
d = |(2)(6) + (3)(5) - 1| / √(2² + 3²)
d = |17| / √(13)
d = 17 / √(13)
d = √(13) * 17 / 13
d = √(13) * √(13) / √(13)
d = √(13)
Therefore, the shortest distance from the point (6,5) to the line 2x+3y=1 is √(13).
To know more about shortest distance refer here:
https://brainly.com/question/15172156
#SPJ11
increase 72 in the ratio 3:5
Answer:
75:77
Step-by-step explanation:
5 is 2 more than 3
3+72=75
5+72=77
therefore: 3:5 = 75:77
If that's not what you meant, then I don't understand the question
Of the following parent functions, which one has an infinite number of zeroes? (Select all that apply) linear o quadratic exponential o reciprocal absolute value 0 square root sine cosine This is a re
The parent functions that have an infinite number of zeroes are sine and cosine. A zero of a function is a value of x for which the function equals zero. For example, the function f(x) = x has a zero at x = 0, because f(0) = 0.
The parent functions sine and cosine have an infinite number of zeroes because they are periodic functions, meaning they repeat their values at regular intervals.
The sine function has zeroes at every multiple of π, or 0, π, 2π, 3π, etc. The cosine function has zeroes at every odd multiple of π/2, or π/2, 3π/2, 5π/2, etc.
In contrast, the other parent functions listed have a finite number of zeroes. The linear function has one zero, the quadratic function has at most two zeroes, the exponential function has at most one zero, the reciprocal function has no zeroes, the absolute value function has at most one zero, and the square root function has at most one zero.
To learn more about number of zeroes here:
https://brainly.com/question/17954695#
#SPJ11
In a popular online role playing game, players can create detailed designs for their character's "costumes," or appearance. Camden sets up a website where players can buy and sell these costumes online. Information about the number of people who visited the website and the number of costumes purchased in a single day is listed below. 93 visitors purchased no costume. 94 visitors purchased exactly one costume. 10 visitors purchased more than one costume. If next week, he is expecting 1200 visitors, about how many would you expect to buy no costume? Round your answer to the nearest whole number.
Rounding to the nearest whole number, we can estimate that about 566.49 visitors would be expected to buy no costume when there are 1200 visitors to the website.
What constitutes the basic unit of a number?The first 10 integers are known as the fundamental numbers in mathematics. These fundamental integers are given from 0 to 9. Basic integers in the 0 to 9 range include 0 through 1, 2, 3, 4, 5, 6, 7 and 8.
According to the information given, 93 visitors purchased no costume, 94 visitors purchased one costume, and 10 visitors purchased more than one costume. Let's calculate the total number of costumes purchased:
Total number of costumes purchased = 1(94) + 2(10) = 114
Next, let's calculate the total number of visitors to the website:
Total number of visitors = 93 + 94 + 10 = 197
To estimate the number of visitors who are likely to purchase no costume when there are 1200 visitors to the website, we can use a proportion:
93/197 = x/1200
x = (93/197) * 1200 ≈ 566.49
Rounding to the nearest whole number, we can estimate that about 566.49 visitors would be expected to buy no costume when there are 1200 visitors to the website.
To know more about number visit:
https://brainly.com/question/17429689
#SPJ1
Use the function value to find the indicated trigonometric value in the specified quadrant. \[ \mathrm{Fu} \] cc
The function value and the indicated trigonometric value are not specified in the question. Additionally, the specified quadrant is not mentioned. Therefore, it is not possible to provide an accurate answer to this question.
However, generally speaking, to find the indicated trigonometric value in a specified quadrant using a function value, you can use the following steps:
1. Identify the function and the quadrant in which the value is to be found.
2. Use the function value to find the reference angle in the first quadrant.
3. Use the reference angle and the specified quadrant to find the indicated trigonometric value.
For example, if the function value is sin(θ) = 1/2 and the specified quadrant is II, you can use the following steps to find the indicated trigonometric value:
1. Identify the function and the quadrant: sin(θ) and II.
2. Find the reference angle in the first quadrant: θ = 30°.
3. Use the reference angle and the specified quadrant to find the indicated trigonometric value: sin(150°) = 1/2.
Learn more about trigonometric value
brainly.com/question/14434745
#SPJ11
Correct tion for the circle with the following properties. Center (4,8), passes through (-10,-5)
The equation of a circle with center at (4, 8) and passing through (-10, -5) is [tex](x-4)^2 + (y-8)^2 = (6)^2.[/tex]
To find this equation, we need to use the distance formula: [tex]d = sqrt((x2-x1)^2 + (y2-y1)^2).[/tex]
We can substitute in the coordinates of the center of the circle and the point it passes through:
[tex]d = sqrt((-10-4)^2 + (-5-8)^2)[/tex]
[tex]d = sqrt( (6)^2 + (13)^2 )[/tex]
d = sqrt(36 + 169)
d = sqrt(205)
d = 14.2
Now, we have the radius of the circle. We can use this to form the equation of the circle:
[tex](x-4)^2 + (y-8)^2 = (14.2)^2[/tex]
[tex](x-4)^2 + (y-8)^2 = (6)^2[/tex]
To know more about circle refer to-
brainly.com/question/29142813#
#SPJ11
Zoe's bank is offering a low nominal rate of 3.9% om loans. If the nominal rate is compounded monthly, use r=100(1+in)n−1
to determine the effective rate. Round your answer to the nearest hundredth.
Responses
3.9%
3.9%
3.97%
3.97%
39.70%
39.70%
58.27%
Answer: To determine the effective rate of Zoe's loan, we can use the formula:
Effective rate = (1 + (nominal rate/number of compounding periods))^number of compounding periods - 1
Since the nominal rate is compounded monthly, the number of compounding periods is 12.
Plugging in the values, we get:
Effective rate = (1 + (0.039/12))^12 - 1
Effective rate = 0.0407 or 4.07%
Therefore, the effective rate of Zoe's loan is 4.07%, rounded to the nearest hundredth. The correct response is 3.97%.
Step-by-step explanation:
Find X (the missing variable)
14
33
19
27
pls, I really need this!
In the triangle the value οf x is D) 27.
What is triangle?A triangle is a fοrm οf pοlygοn with three sides; the intersectiοn οf the twο lοngest sides is knοwn as the triangle's vertex. There is an angle created between twο sides. One οf the crucial elements οf geοmetry is this.
Certain fundamental ideas, including the Pythagοrean theοrem and trigοnοmetry, rely οn the characteristics οf triangles. The angles and sides οf a triangle determine its kind.
Here in the given triangle, using ratiο then
=> [tex]\frac{x+8}{10}=\frac{2x-5}{14}[/tex]
=> [tex]14\times(x+8)=10(2x-5)[/tex]
=> 14x+112=20x-50
=> 20x-14x=112+50
=> 6x = 162
=> x =[tex]\frac{162}{6}[/tex]
=> x = 27
Hence the cοrrect οption is D)27.
To learn mοre about triangle refer the below link
https://brainly.com/question/17335144
#SPJ1
browns books are 2 for $11 and noble books are 5 for $31 who’s is cheaper
Therefore , the solution of the given problem of unitary method comes out to be Browns books are less expensive than Noble books at $5.50 each.
What is unitary method ?Take the lengths of this minute subsection and split the sum by two to complete a task using a unitary variable technique. The unit technique, in a nutshell, removes a wanted item both from the specific sets and color subsets. For instance, 40 pencils will cost Rs/kg ($1.01). It's possible that one country will have total influence over the approach taken to accomplish this. Almost every living creature has a distinctive quality. There are unanswered questions and changes (mathematics, algebra).
Here,
We must ascertain the price per book for each retailer in order to evaluate the costs of Browns and Noble books.
Two of Brown's books cost $11, so each volume costs $5.50 (11/2 = 5.50).
Five novels from Barnes & Noble cost $31, making each book $6.20 (31/5 = 6.20).
Browns books are less expensive than Noble books, which cost $6.20 per volume, at $5.50 each.
To know more about unitary method visit:
https://brainly.com/question/28276953
#SPJ1
Mark drove to the mall on a busy shopping day. He got to the mall parking lot at 6:46, but he didn't find a parking spot until 19 minutes later. What time was it when Mark finally parked the car?
Answer:
Step-by-step explanation:
1000
Hi due today pls help! Ty!
red counter to blue
There are 15 blue counters in the bag.
What are ratios and proportions?
Two quantities are compared to form a ratio. An equality of two ratios is a proportion.
We know that the initial ratio of red counters to blue counters was 4:5. Therefore, we can write:
4x : 5x
We also know that 10 more red counters were added to the bag. Therefore, the new number of red counters in the bag is:
4x + 10
The ratio of red counters to blue counters then became 6:5. Therefore, we can write:
(4x + 10) : y = 6 : 5
We can simplify this equation by cross-multiplying:
5(4x + 10) = 6y
20x + 50 = 6y
Dividing both sides by 6, we get:
y = (20x + 50)/6
Simplifying, we get:
y = (10x + 25)/3
Since y has to be a whole number, 10x + 25 has to be divisible by 3. The only value of x that satisfies this condition is x = 2.
Therefore, the initial number of red counters was 4x = 8, and the initial number of blue counters was 5x = 10.
After adding 10 more red counters, the new number of red counters was 18, and the new ratio of red counters to blue counters was 6:5.
To find the new number of blue counters, we can use the equation we derived earlier:
y = (10x + 25)/3
Substituting x = 2, we get:
y = (10(2) + 25)/3 = 15
Therefore, there are 15 blue counters in the bag.
To know more about ratios and proportions follow
https://brainly.com/question/12024093
#SPJ1
!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Please help!
Answer:
Step-by-step explanation:
So first you have to divide the monkey by the + sign then when you did that you take the exponent and turn it into a ratio. When you are done doing that you have to multiply and divide and then you have your answer.
Using composition, determine if the functions are inverses: f(x)=(2)/(3)x-8 and g(x)=(3)/(2)x+12
Both f(g(x)) and g(f(x)) equal x, we can determine that the functions f(x) and g(x) are inverses.
To determine if the functions f(x) and g(x) are inverses using composition, we need to find f(g(x)) and g(f(x)) and see if they both equal x.
First, let's find f(g(x)):
f(g(x)) = f((3)/(2)x+12)
= (2)/(3)((3)/(2)x+12)-8
= (2)/(3)(3)/(2)x + (2)/(3)(12) - 8
= x + 8 - 8
= x
Now, let's find g(f(x)):
g(f(x)) = g((2)/(3)x-8)
= (3)/(2)((2)/(3)x-8) + 12
= (3)/(2)(2)/(3)x - (3)/(2)(8) + 12
= x - 12 + 12
= x
Since both f(g(x)) and g(f(x)) equal x, we can determine that the functions f(x) and g(x) are inverses.
Learn about Composition
brainly.com/question/13808296
#SPJ11
Write a program to take a positive whole number from user and do the following task: a. Sperate all digits in the number and save them in a vector array named "Info". b. Check every digit you saved in "Info" is even or odd. For odd digit use "O" and for Even digit use "E" to create another vector (named Odd_Even) of the same size of "Info". c. Check every digit you saved in "Info" is a prime or not a prime number. For the prime digit, use "P" and for the Not Prime digit use "NP" to create another vector (named Prime_info) of the same size of "Info". d. For number with more than 4 digits, find the minimum, maximum, mean, median, and standard deviation of all digits saved in Info array. Create a vector with the same size of "Info" vector. Store the value of the calculated minimum, maximum, mean, median, and standard deviation in the first five indices and fill the rest of the vector by zeros. e. Combine vectors in Part A, B, C, and D (if it exists!) to define a data frame (Name: Number_Information). Export the data frame as an excel file (You may install some Packages!)
vectors Info, Odd_Even, Prime_info, and the vector containing the statistical values.
This program can be written in R using the following steps:
1. Create a function number_info() that takes an input of a positive whole number and saves all the digits of that number in a vector array named Info.
2. Create a loop to check each number in the Info array and use an if-else statement to assign either "O" for odd numbers and "E" for even numbers to another vector array named Odd_Even.
3. Create a second loop to check each number in the Info array and use an if-else statement to assign either "P" for prime numbers and "NP" for non-prime numbers to another vector array named Prime_info.
4. If the Info array contains more than four digits, use R functions to calculate the minimum, maximum, mean, median, and standard deviation of the numbers in Info and save them in a new vector array. Fill the remaining indices of this vector with zeros.
5. Create a data frame called Number_Information using the vectors Info, Odd_Even, Prime_info, and the vector containing the statistical values.
6. Export the data frame as an excel file using the write.xlsx() function.
Learn more about prime number
brainly.com/question/30358834
#SPJ11
If log_x y = 4 which of the following is true?
Please
The equation log_x y = 4 can be written as y = x⁴ and the true, correct option is 1.
What is logarithmic rule?A base must be raised to a certain exponent or power, or logarithm, in order to produce a specific number. that is, b raised to x = n, in which case one writes x = log base b n. Scientists embraced logarithms immediately because of a number of advantageous characteristics that made complicated, time-consuming computations simpler. In specifically, by searching up each number's logarithm in a special database, adding the logarithms together, and then rechecking the table to discover the number with that computed logarithm, scientists could find the product of two integers m and n.
Given that, log_x y = 4 .
Using the logarithmic rule we have:
log_x y = 4
y = x⁴
Hence, the equation log_x y = 4 can be written as y = x⁴ and the correct option is 1.
Learn more about logarithm here:
https://brainly.com/question/27389970
#SPJ1
Ayudaaaa porfa ):porfavor
The vertices of the dilated image are given.
What is Dilation?Dilation is a type of transformation where the figure is enlarged or made smaller such that it preserves the shape but not size.
Every dilated image are similar figures to the original figure.
The point (x, y) with the scale factor of k will dilate to the vertex (kx, ky) if the center of dilation is origin.
1) Given for ΔQRS, Q(-1, 0), R(-1, 2) and S(-2, 1).
Scale factor = 2
Q'(2×-1, 2×0) = Q'(-2, 0)
R'(2×-1, 2×2) = R'(-2, 4)
S'(2×-2, 2×1) = S'(-4, 2)
2) Given for ΔTRK, T(-1, -2), R(1, 0) AND K(0, 1).
Scale factor = 3
T'(-3, -6), R'(3, 0) and K'(0, 3)
3) Given for ΔXYZ, X(-4, 0), Y(-4, 4) and Z(-2, -2).
Scale factor = 1/2
X'(-2, 0), Y'(-2, 2) and Z'(-1, -1)
4) If the center of dilation is not origin, then,
P'(x, y) = O(x, y) + k [P(x, y) - O(x, y)]
where, P'(x, y) is the dilated point, O(x, y) is the center of dilation, k is the scale factor and P(x, y) is the original point.
Given for ΔHAT, H(-1, -1), A(1, 0) and T(-1, 2).
Scale factor = 2
Center of dilation = (-1, 2)
H'(x, y) = (-1, 2) + 2 [(-1, -1) - (-1, 2)]
= (-1, 2) + 2 (-1+1, -1-2)
= (-1, 2) + 2 (0, -3)
= (-1, 2) + (0, -6)
= (-1, -4)
A'(x, y) = (-1, 2) + 2 [(1, 0) - (-1, 2)]
= (-1, 2) + 2 (2, -2)
= (3, -2)
T'(x, y) = (-1, 2) + 2 [(-1, 2) - (-1, 2)]
= (-1, 2) + 2 (0, 0)
= (-1, 2)
Hence the vertices of the dilated image are found.
Learn more about Dilation here :
https://brainly.com/question/13176891
#SPJ1
Marquis and Yolanda plan to sell T-shirts at their school’s Community Day. They make 25 shirts and each costs $15 to make. If they would like to make $320 in profit, how much should they sell each T-shirt for?
They should sell each T-shirt for $27.80 to make a profit of $320.
Describe Profit?Profit is the financial gain that a company or individual makes after deducting all the expenses from the revenue earned. It is the positive difference between the total revenue generated from the sale of goods or services and the total cost of producing and selling those goods or services.
Profit is one of the key indicators of a company's financial performance, and it is calculated by subtracting the total expenses from the total revenue. The expenses include the cost of raw materials, labor, rent, taxes, and other overhead costs associated with producing and selling the goods or services.
To make a profit of $320, they need to sell all 25 shirts for a total of $320 + ($15 x 25) = $695.
Therefore, the price they need to sell each T-shirt for is $695 ÷ 25 = $27.80 (rounded to the nearest cent).
So they should sell each T-shirt for $27.80 to make a profit of $320.
To know more about price visit:
https://brainly.com/question/15779608
#SPJ1
Express the difference in medians as a multiple of the irq for each data set
Difference in the medians as a multiple of the IQR = 5.
Define IQR?The Interquartile Range (IQR) formula computes the median of a set of data. One of the smallest statistical measurements of dispersion is the interquartile range. The interquartile range refers to the spread between the upper and lower quartiles.
The interquartile range is defined as Upper Quartile - Lower Quartile.
According to the question,
Data set of Mount Vernon= 55, 60, 65, 70, 75, 80, 85, 90
Data set of Lakewood= 65, 70, 75, 80, 85
Data sets are already in ascending order.
Median for Mount Vernon = 70+75/2 = 77.5
Median for lower half of set= 55+60+65+70/4 = 62.5
Median for upper half of set= 75+80+85+90/4 = 82.5
IRQ for Mount Vernon = 82.5-62.5 = 20
Now similarly in case of Lakewood,
Median= 75.
Median for lower half of set = 65+70/2 = 67.5
Median for upper half of set = 80+85/2 = 82.5
IRQ = 82.5 - 67.5 = 15.
Hence, difference in IRQ = 20-15 = 5.
To know more about IQR, visit:
https://brainly.com/question/29198800
#SPJ1
Data was collected on the weight, in ounces, of kittens for the first three months after birth. A line of fit was drawn through the scatter plot and had the equation w = 2.75 + 0.2d, where w is the weight of the kitten in ounces and d is the age of the kitten in days.
What is the w-intercept of the line of fit and its meaning in terms of the scenario?
0.2; a kitten who is just born is predicted to weigh 0.2 ounces
0.2; for each additional day after the kitten is born, its weight is predicted to increase by 0.2 ounces
2.75; a kitten who is just born is predicted to weigh 2.75 ounces
2.75; for each additional day after the kitten is born, its weight is predicted to increase by 2.75 ounces
2.75; a kitten who is just born is predicted to weigh 2.75 ounces.
What is Statistics?
Statistics is a branch of mathematics that involves collecting, analyzing, interpreting, presenting, and organizing data. It enables the identification of trends, patterns, and relationships within the data. The goal of statistics is to make meaningful inferences and predictions based on the data.
It is used in a wide range of fields, including business, economics, social sciences, healthcare, and engineering. The main tools of statistics include probability theory, statistical inference, and statistical modeling.
2.75; a kitten who is just born is predicted to weigh 2.75 ounces.
The w-intercept of the line of fit represents the weight of a kitten at birth, which is the value of w when d equals zero. In this case, the intercept is 2.75, which means that a kitten who is just born is predicted to weigh 2.75 ounces.
To learn more about Statistics from the given link
https://brainly.com/question/15525560
#SPJ1
the permulation [[1,2,3,4,5,6],[6,5,4,3,2,1]]can be written as a product of disjoint cycles as
The permutation [[1,2,3,4,5,6],[6,5,4,3,2,1]] can be written as a product of disjoint cycles as (1,6)(2,5)(3,4).
A permutation can be represented as a product of disjoint cycles. A cycle is a sequence of numbers that are permuted in a circular fashion. For example, the cycle (1,2,3) means that 1 is permuted to 2, 2 is permuted to 3, and 3 is permuted to 1.
To write the given permutation as a product of disjoint cycles, we can start with the first number in the first row, 1, and see where it is permuted to in the second row. In this case, 1 is permuted to 6. Then we look at where 6 is permuted to, which is 1, completing the cycle (1,6).
Next, we move on to the next number in the first row that has not been included in a cycle, which is 2. We see that 2 is permuted to 5, and 5 is permuted to 2, completing the cycle (2,5).
Finally, we move on to the next number in the first row that has not been included in a cycle, which is 3. We see that 3 is permuted to 4, and 4 is permuted to 3, completing the cycle (3,4).
Therefore, the given permutation can be written as a product of disjoint cycles as (1,6)(2,5)(3,4).
Learn more about permutation at brainly.com/question/17045948
#SPJ11
