If ∆AFD, m ∠F = 90° AD = 14, m ∠D = 30° .The Area of ∆AFD is 49 square units.
What is area?To find the area of triangle AFD, we can use the formula for the area of a triangle given its base and height. In this case, the base is AD, and the height can be found by constructing an altitude from F to AD.
First, we will find the length of FD. Since m ∠D = 30°, we can use the trigonometric function sine to find the length of FD. Using the sine formula:
FD = AD * sin(∠D) = 14 * sin(30°) = 14 * 1/2 = 7
Next, we will find the length of A.F. Since m ∠F = 90°, FD is the height of the triangle. So, the area of triangle AFD is given by:
Area = (AD * FD) / 2 = (14 * 7) / 2 = 49 square units
Therefore the area of ∆AFD is 49 square units.
Learn more about area here:https://brainly.com/question/25292087
#SPJ1
what is the probability that the first card you draw is a heart, the second card is a jack, and you roll the same number twice?
The probability of drawing a heart as the first card is 1/52.
The probability of drawing a jack as the second card given that the first card is a heart is 4/51 (since there are 4 jacks and 51 remaining cards after one heart is drawn). The probability of rolling the same number twice with a fair six-sided die is 1/6. The total probability is (1/52) * (4/51) * (1/6) = 1/1098.
Assume that there are a finite number of elementary events that are all equally likely to occur in the sample space of the experiment under consideration.
Where total cases equal the extent of the sample space, and favorable instances are those elementary occurrences that belong to E.
To learn more about probability, refer:-
https://brainly.com/question/11234923
#SPJ4
debate team has ten members. five members must be chosen for a particular debate. a.) in how many ways can the five be chosen if no positions are assigned to the members? b.) in how many ways can the five be chosen if each member is assigned a position from one to five? the positions signify the order in which each member will participate in the debate. c.) suppose of the ten debate team members there are only two members who may be assigned position five in the debate. any member may be assigned positions one through four. in how many ways can the five members be chosen?
In total, there are 252 ways to choose five members without assigning positions, 5 ways to choose five members with assigned positions, and 56 ways to choose five members with two members assigned to a particular position.
a.) The number of ways that the five team members can be chosen without assigning them positions is 10C5 = 252. This is calculated using the formula for combinations, which is n!/(r!(n-r)!), where n is the total number of members and r is the number to choose. In this case, n=10 and r=5, so 10!/(5!(10-5)!) = 252.
b.) The number of ways that the five team members can be chosen with assigned positions is 5!. This is because there are five positions, and each team member must occupy one of the positions. The order of the positions is irrelevant, so there is only one possible combination.
c.) The number of ways that the five team members can be chosen with the two members assigned to position five is 8C5 = 56. This is calculated using the same formula as in part a, but with n=8 since two members are already assigned to position five. 8!/(5!(8-5)!) = 56.
In total, there are 252 ways to choose five members without assigning positions, 5 ways to choose five members with assigned positions, and 56 ways to choose five members with two members assigned to a particular position.
Learn more about combinations here:
https://brainly.com/question/20211959
#SPJ4
if the zero vector is a solution of the system , then the system is homogeneous. group of answer choices true false
True, If the zero vector is a solution of the system , then the system is homogeneous.
A system of linear equations is considered homogeneous if the zero vector (i.e., the vector with all components equal to 0) is a solution. This means that the system of equations only has the trivial solution of all variables equal to zero, but no non-trivial solutions.
A homogeneous system of linear equations is a system where all the equations have the same form and all the coefficients are proportional to each other. This means that if one equation is multiplied by a constant, the same constant must be multiplied by all the other equations in the system to maintain the homogeneous property.
The zero vector is a solution of a homogeneous system because if all the variables are equal to zero, all the coefficients in the equations are also equal to zero and the equations are satisfied. This is why the presence of the zero vector as a solution is a defining characteristic of homogeneous systems.
In contrast, a non-homogeneous system is a system where the zero vector is not a solution and there are both trivial (zero) and non-trivial (non-zero) solutions. Non-homogeneous systems are solved using different methods compared to homogeneous systems.
Learn more about homogeneous systems here:
https://brainly.com/question/14934034
#SPJ4
Find the solution to the system of equations.
The solution to the system of equation is (4, 1).
How to solve system of equation?System of equation can be solved using different method such as elimination method, substitution method and graphical method. Therefore, the system of equations have been solved using graphical method.
Therefore, the point where the lines or graph intersect is the solution of the system of equation.
Hence, let's find the coordinates where the lines intersect as follows:
The lines intersect at (4, 1)
learn more on system of equation here: https://brainly.com/question/10524752
#SPJ1
okok pls help it’s important the question is “Write a multiplication equation and a division equation to represent each question, statement, or diagram.” “ There are 6 thirds in 2.”
The multiplication and division of the numbers 2 and 2 will be 4 and 1, respectively.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
The numbers are given below.
6/3 and 2
2 and 2
Then the multiplication of the numbers 2 and 2 is given as,
⇒ 2 x 2
⇒ 4
Then the division of the numbers 2 and 2 is given as,
⇒ 2 / 2
⇒ 1
The multiplication and division of the numbers 2 and 2 will be 4 and 1, respectively.
More about the Algebra link is given below.
https://brainly.com/question/953809
#SPJ1
Find the inverse of this function f(x)=(x-2)^4 (if x ≥ 2)
Answer:
[tex]f^{-1}(x)=\sqrt[4]{x}+2 \qquad \textsf{for $x \geq 0$}[/tex]
Step-by-step explanation:
Given function:
[tex]f(x)=(x-2)^4[/tex]
The domain of the given function is restricted:
{x : x ≥ 2}Therefore, the range of the given function is also restricted:
{f(x) : f(x) ≥ 0}To find the inverse of a function, swap x and y:
[tex]\implies x=(y-2)^4[/tex]
Rearrange the equation to make y the subject:
[tex]\implies \sqrt[4]{x}=y-2[/tex]
[tex]\implies y=\sqrt[4]{x}+2[/tex]
Replace y with f⁻¹(x):
[tex]\implies f^{-1}(x)=\sqrt[4]{x}+2[/tex]
The domain of the inverse of a function is the same as the range of the original function. Therefore, the domain of the inverse function is restricted to {x : x ≥ 0}.
Therefore, the inverse of the given function is:
[tex]f^{-1}(x)=\sqrt[4]{x}+2 \qquad \textsf{for $x \geq 0$}[/tex]
ou go to the doctor and he gives you 11 milligrams of radioactive dye. after 20 minutes, 5.5 milligrams of dye remain in your system. to leave the doctor's office, you must pass through a radiation detector without sounding the alarm. suppose the detector will sound the alarm if more than 2 milligrams of the dye are in your system. how long will your visit to the doctor take, assuming you were given the dye as soon as you arrived? give your answer to the nearest minute.
Suppose the detector will sound the alarm if more than 2 milligrams of the dye are in your system. It will take 56 minutes for the visit of the doctor
The amount of radioactive dye remaining in your system after t minutes can be modeled as:
A(t) = 11 * (1/2)^(t/20)
where A(t) is the amount of dye remaining after t minutes. We want to find the time t when A(t) = 2 milligrams.
A(t) = 11 * (1/2)^(t/20) = 2
Solving for t:
(1/2)^(t/20) = 2/11
Taking the natural logarithm of both sides:
(t/20) = ln(2/11) / ln(1/2)
Multiplying both sides by 20:
t = 20 * ln(2/11) / ln(1/2)
Using a calculator or logarithm tables, we can estimate t to be approximately 56 minutes. So, your visit to the doctor would take about 56 minutes.
To learn more about logarithm click on,
https://brainly.com/question/28081645
#SPJ4
use rguroo to solve for the proportions (probabilities). a normal population has a mean and standard deviation . round answers up to four decimal places. a) the proportion of the population that is less than 18 is 0.3085 . b) the probability that a randomly chosen value is greater than 25 is 2.6667
a) The proportion of the population that is less than 18 is 0.3085.
b) The probability that a randomly chosen value is greater than 25 is 15.39%, which is not equal to 2.6667 as stated in the question.
a) To find the z-score corresponding to the value of 18, we can use the standard normal formula:
z = (18 - mu) / sigma
Where mu is the mean and sigma is the standard deviation of the population.
To find the proportion of the population that is less than 18, we can use the cumulative distribution function (CDF) of the standard normal distribution.
The CDF gives us the proportion of the population that is less than a given value.
For a standard normal distribution, we can use a standard normal table or a calculator to find the CDF.
Using the standard normal table, or a standard normal calculator,
we find that the CDF of the standard normal distribution at z = -0.6309 is 0.3085.
So, the proportion of the population that is less than 18 is 0.3085.
b) To find the z-score corresponding to the value of 25, we can use the standard normal formula:
z = (25 - mu) / sigma
Using a standard normal calculator or table,
we find that the z-score for 25 is 1.0538.
The proportion of the population that is greater than 25 is 1 - the CDF of the standard normal distribution at z = 1.0538.
Using a standard normal calculator or table, we find that the CDF of the standard normal distribution at z = 1.0538 is 0.8461.
So, the proportion of the population that is greater than 25 is 1 - 0.8461 = 0.1539.
To find the probability that a randomly chosen value is greater than 25, we can multiply 0.1539 by 100% to get 15.39%.
Therefore, the probability that a randomly chosen value is greater than 25 is 15.39%, which is not equal to 2.6667 as stated in the question.
For more questions on standard normal distribution
https://brainly.com/question/26822684
#SPJ4
Example 4: Find the length of AC? D A 65° 12cm 7cm B
topic: trigonometry
Step-by-step explanation:
hope you can see the awful green
Answer:
13.14cm
Step-by-step explanation:
lets start by finding the length of AD
90 + 65=155...........180-155= 25
x/sin 25= 7/sin 90
xsin90=7sin 25
x= 2.96cm=AD
Now lets find DC
we shall find DB first;
x/sin65=7/sin90
xsin90=7sin65
x=6.34cm...=DB
Now lets use Pythagoras theorem to find DC
12²-6.34²=√103.80
DC=10.18cm
Add AD and DC
2.96+10.18= 13.14cm
AC=13.14cm
Which graph represents the linear equation y = −5x − 3?
a graph of a line that passes through the points negative 4 comma 0 and 0 comma negative 3
a graph of a line that passes through the points negative 1 comma 2 and 0 comma negative 3
a graph of a line that passes through the points negative 1 comma 0 and 0 comma negative 5
a graph of a line that passes through the points negative 1 comma 4 and 0 comma negative 2
Answer: a graph of a line that passes through the points negative 1 comma 2 and 0 comma negative 3.
Step-by-step explanation: the y-intercept is where the line meets the y line which in this case is -3. I used slope formula to find the m of the equation ( slope ) take a look at the attached image to see how I solved it.
Answer:
a graph of a line that passes through the points negative 1 comma 2 and 0 comma negative 3.
Step-by-step explanation:
in convex hexagon , all six sides are congruent, and are right angles, and , , , and are congruent. the area of the hexagonal region is . find .
In a convex hexagon, if the area of the hexagonal region is 2116 (√2 + 1), then the value of AB is 46.
What is a convex hexagon?A convex hexagon is a hexagon in which all of the inner angles and all of the vertices have to be smaller than 180 degrees. There are both regular and irregular convex hexagons. Inside a convex hexagon, there are no angles. More specifically, no internal angle will exceed 180 degrees. Any internal angle which exceeds 180 degrees is concave.
Let the side length be x.
So, the diagonal BF = √(AB^2 + A F^2) = √(x^2 + x^2) = x√2.
Then, the areas of the triangles AFB and CDE in total equals (x^2 / 2) * 2, and the area of the rectangle BCEF equals x * x√2 = x^2 √2.
Now, let the equation be:
2116 (√2 + 1) = x^2√2 + x^2
And by simplifying the above equation, we will get:
2116 (√2 + 1) = x^2 (√2 + 1)
2116 = x^2
By taking root both sides, then it will be:
x = 46
Hence, the value of AB is 46.
Learn more convex hexagon at: https://brainly.com/question/16615236
#SPJ4
Although part of your question is missing, you might be referring to this full question: In a convex hexagon ABCDEF, all six sides are congruent, ∠A and ∠D are right angles. And ∠B, ∠C, ∠E and ∠F are congruent. The area of the hexagonal region is 2116 (√2 + 1). Find AB.
the assembly time for a product is uniformly distributed between 6 and 10 minutes. the standard deviation of assembly time (in minutes) is approximately . a. .33 b. .13 c. 16 d. 1.15
The standard deviation of assembly time (in minutes) is approximately .33.
The standard deviation of a uniform distribution of assembly time is calculated using the following formula:
σ = √((b-a)^2 / 12),
where a is the lower boundary of the range of assembly time (6 minutes) and b is the upper boundary of the range of assembly time (10 minutes).
Substituting a = 6 and b = 10 into the formula yields:
σ = √((10-6)^2 / 12)
σ = √(16/12)
σ = √(1.33)
σ = .33
Therefore, the standard deviation of assembly time (in minutes) is approximately .33.
Learn more about standard deviation here:
https://brainly.com/question/23907081
#SPJ4
Help with thisss pleasseeeee
Answer: The last one; is the one closest to the keyboard.
Step-by-step explanation: Its D because after I looked at the range, I looked at the median, which is 22, and D is the only one that had that as its median. I hope this helped!
What’s next in the sequence
1/3, 7/15, 3/5, 11/15…
Answer:
The next number in the sequence is 17/15.
Step-by-step explanation:
if a car travals for 105km in 1hr 45 min ,how many minutes will the car spend to cover 18km
The car will spend 18 minutes to cover 18 km.
What is Proportion?Proportions are defined as the concept where two or more ratios are set to be equal to each other.
Suppose we have two ratio p : q and r : s. If both these ratios are proportional, then we can write it as p : q = r : s or p/q = r/s
Given that,
Time taken to travel 105 km = 1 hr 45 min = 60 min + 45 min = 105 minutes
Time taken to travel 18 km = x
Using the concept of proportion,
105 / 105 = 18 / x
Cross multiplying,
105 x = 18 × 105
x = 18
Hence the time taken to travel 18 km is 18 minutes.
Learn more about Proportion here :
https://brainly.com/question/165414
#SPJ1
What is the slope of the line please help ASSP!!
the graph below shows the growth of three samples of the different bacteria on petri dishes incubated over 24 hours as temperature was increased 10 degrees every eight hours: graph of bacteria counts at different temperatures shows 5 bacteria per cm squared at 20, 30 and 40 degrees celsius for sample 1; shows 2 bacteria per cm squared at 20, 4 bacteria per cm squared at 30 degrees celsius, and 7 bacteria per cm squared for at 40 degrees celsius for sample 2; shows 3 bacteria per cm squared at 20, 8 bacteria per cm squared at 30 degrees celsius, and 12 bacteria per cm squared for at 40 degrees celsius sample 3. which statement best explains the data trend observed in the bacteria samples?
The correct answer is option b) Bacteria in samples 2 and 3 mutated quickly to adjust to temperature change.
From the given graph it is seen that sample 1 is not showing any growth or decline despite of the temperature change. One cannot ascertain its gene expression. On the other hand, Sample 2 shows a slight change from 4cm² to 7cm² bacteria count and Sample 3 shows a wide change as per temperature change from 8cm² to 12cm². Hence it can be said that samples 2 and 3 mutated to adjust to the temperature compared to sample 1 which showed no changes.
To learn more about gene expression click here
brainly.com/question/21217992
#SPJ4
Complete Question
the graph below shows the growth of three samples of the different bacteria on Petri dishes incubated over 24 hours as the temperature was increased 10 degrees every eight hours: (Graph in the figure attachment) which statement best explains the data trend observed in the bacteria samples?
a) All bacteria samples grow better at higher temperatures.
b) Bacteria in samples 2 and 3 mutated quickly to adjust to temperature change.
c) Temperature changes do not affect gene expression for growth in sample 1.
d) Bacteria in sample 1 will eventually die out at higher temperatures.
3. Six square-based pyramids fit exactly onto the six faces of a cube of side 4 cm. If the volume of the object formed is 256 cm³, find the height of each of the pyramids.
The height of the pyramid is 6cm
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
Given that Six square-based pyramids fit exactly onto the six faces of a cube of side 4 cm.
The volume of the object formed is 256 cm³.
We need to find the height of each of the pyramids.
The total volume can be calculated as
Total volume= cube volume+6 one pyramid volume
cube volume=4³=64
pyramid volume=1/3.4²h=16/3h
64+6.16h/3=256
64+32h=256
Subtract 64 on both sides
32h=256-64
32h=192
Divide both sides by 32
h=6
Hence, the height of the pyramid is 6cm
To learn more on Three dimensional figure click:
https://brainly.com/question/2400003
#SPJ1
Due to a study linking a food dye to cancer, M&Ms packages did not include which color from 1976 to 1987?
a. Yellow
b. Red
c. Green
d. Brown
From 1976 until 1987, red M&Ms were removed from packets owing to a research associating the food dye used to color them to cancer.
What is arithmetic?Arithmetic is defined as working with numbers through addition, subtraction, multiplication, and division. Adding two and two to produce four is an example of arithmetic. Arithmetic is a fundamental branch of mathematics that studies the characteristics of classical operations on numbers such as addition, subtraction, multiplication, division, exponentiation, and root extraction. Arithmetic (derived from the Greek word arithmos, "number") relates to the fundamental components of number theory, arts of mensuration (measuring), and numerical computing (that is, the processes of addition, subtraction, multiplication, division, raising to powers, and extraction of roots).
To know more about arithmetic,
https://brainly.com/question/29259404
#SPJ4
Six less than the product of a number n and 1/4 is no more than 96
Answer:
1/4n - 6 < 96
Step-by-step explanation:
Im a tutor but the way it is worded hurts my brain
kristin spent $131 on shirts. fancy shirts cost $28 and plain shirts cost $15. if she bouahgt a total of 7 then how many of each did she buy
Kristin bought 4 fancy shirts and 3 plain shirts.
Let's assume Kristin bought "x" fancy shirts and "y" plain shirts.
We know that:
x + y = 7 (the total number of shirts Kristin bought)
28x + 15y = 131 (the total amount of money she spent)
We can use the first equation to solve for one of the variables in terms of the other.
For example: y = 7 - x
Substituting this into the second equation:
28x + 15(7 - x) = 131
28x + 105 - 15x = 131
13x = -74
x = -5.692307692 (approximately)
Since x must be a positive integer (the number of fancy shirts cannot be negative or a fraction), this solution is not valid.
However, we can see that the equation does have a solution by trying a larger value for x:
x = 1
y = 6
This gives us:
28 * 1 + 15 * 6 = 131
28 + 90 = 131
118 = 131
This solution is not valid either, since the total amount spent cannot be less than the cost of the shirts.
By repeating this process, we can find that the solution is x = 4 and y = 3.
For more questions on Linear Equation
https://brainly.com/question/2030026
#SPJ4
Which statement best describes the function?
A. The function is never negative.
B. The function is negative when x < 0.
C. The function is negative when x > 0.
D. The function is negative when x < 0 and when x > 0.
The statement which best describes the function is The function is negative when x < 0, the correct option is B.
How to know if a point lies in the graph of a function?All the points (and only those points) which lie on the graph of the function satisfy its equation.
Thus, if a point lies on the graph of a function, then it must also satisfy the function.
Given;
The graph of the function
Now
We can say that the graph is negative when x<0
The function is never negative is false
The function is negative when x > 0 false
The function is negative when x < 0 and when x > 0 false
Therefore, the function will be negative when x<0.
Learn more about points lying on graph of a function here:
brainly.com/question/1979522
#SPJ1
shannon is traveling from new york city to washington, d.c. she wants to go by train so she can see the views. since she will be driving home with a family member, she only priced the cost of a one-way ticket on amtrak for any time of day on february 15. below is an ordered listing of all fares that were available for selection on that day. a. find the percentile rank for a fare of $119. b. find the percentile rank for a fare of $272. c. based on your first two answers, which train fare would have a percentile rank of approximately 82%?
a. The percentile rank for a fare of $119 is 30%.
b. The percentile rank for a fare of $227 is 91.11%.
c. Based on your first two answers, for $173 train fare would have a percentile rank of approximately 82%.
a. We have to determine the percentile rank for a fare of $119.
Total number of fare below and at the fare $119 = 27
Total fare = 90
The percentile rank for a fare of $119 = Total number of fare below and at the fare $119/Total fare × 100
The percentile rank for a fare of $119 = 27/90 × 100
The percentile rank for a fare of $119 = 0.3 × 100
The percentile rank for a fare of $119 = 30%
b. We have to determine the percentile rank for a fare of $272.
Total number of fare below and at the fare $272= 82
Total fare = 90
The percentile rank for a fare of $272 = Total number of fare below and at the fare $272/Total fare × 100
The percentile rank for a fare of $272 = 82/90 × 100
The percentile rank for a fare of $272 = 0.911 × 100
The percentile rank for a fare of $272 = 91.11%
c. Based on your first two answers, We have to determine which train fare would have a percentile rank of approximately 82%.
The percentile rank for a fare of $119 is 30%.
The percentile rank for a fare of $272 is 91.11.
There are three pricing ranging from $119 to $272. The percentile rank of 82% for the $272 response to section B is closer to 91.11%. $173 is the cost next to $272. Therefore, it makes the most sense that $173 would have a percentile rank of about 82%. Determine how many fares there are
= 12 × 6 + 2
= 72 + 2
= 74 fares
The percentile rank = 74/90 × 100%
The percentile rank = 82.22%
To learn more about percentile rank link is here
brainly.com/question/10684835
#SPJ4
The complete question is:
Shannon is traveling from New York City to Washington, D.C. She wants to go by train so she can see the views. Since she will be driving home with a family member, she only priced the cost of a one-way ticket on Amtrak for any time of day on February 15. Below is an ordered listing of all fares that were available for selection on that day.
49 88 88 88 119 133 133 133 161 171 173 173 173 272 284
49 88 88 88 119 133 133 161 161 173 173 173 173 272 284
88 88 88 119 119 133 133 161 161 173 173 173 272 272 284
88 88 88 119 133 133 133 161 171 173 173 173 272 272 284
88 88 88 119 133 133 133 161 171 173 173 173 272 284 284
88 88 88 119 133 133 133 161 171 173 173 173 272 284 284
a. Find the percentile rank for a fare of $119.
b. Find the percentile rank for a fare of $272.
c. Based on your first two answers, which train fare would have a percentile rank of approximately 82%?
When using the elimination method to solve, what would be a possible first step in the process?
4x - 2y = -4
2x+y=4
When using the elimination method to solve, what would be a possible first step in the process is to write the equations in standard forms.
What is the elimination method?The elimination method is a method used in solving a pair of simultaneous linear equations by reducing one equation to one that has only a single variable.
This method is called the Gaussian elimination method.
The steps in the Gaussian elimination method are;
Write both equations in standard formsThe make the coefficients of one variable oppositeNow, add the equations that results from Step 2 to eliminate one variable from the equationSolve for the other variableSubstitute the solution from Step 4 into one of the original equations and then determine the valueHence, the step is writing the equations in standard forms.
Learn about elimination method on:
https://brainly.com/question/25427192
#SPJ1
The first step in solving this equation by using elimination is to multiply
(4x – 2y = -4) *2
(2x + y = 4)*4
8x – 4y = -8
8x + 4y = 16
An art class is making a mural for their school which has a triangle drawn in the middle. The length of the bottom of the triangle is . Another side is more than times the length of the bottom of the triangle. The last side is more than the bottom of the triangle. Write and simplify an expression for the perimeter of the triangle.
Let x be the length of the bottom of the triangle. Then, the second side has a length of more than x * k, where k is some number greater than 1. And the third side has a length of more than x.
The perimeter of the triangle can be represented by the expression:
P = x + (x * k) + (x + y), where y is a positive number that represents the difference between the length of the third side and the length of the bottom of the triangle.
Simplifying the expression:
P = x * (1 + k) + (x + y) = x * (k + 1) + y.
This expression represents the perimeter of the triangle in terms of the length of the bottom of the triangle and the unknown values
A. Solve the following initial value problem:
(t2−16t+60)dy/dt=y
with y(8)=1. (Find y as a function of t.)
y= .
B. On what interval is the solution valid?
Answer: It is valid for ?
C. Find the limit of the solution as t approaches the left end of the interval.
(Your answer should be a number or the word "infinite".)
Answer: .
D. Similar to C, but for the right end.
Answer: .
Refer to the images attached (answers are circled). Let me know if you have any questions.
a moving average can be used to smooth question 2 options: 1) cyclical variation 2) seasonal variation 3) irregular variation 4) all responses are correct
A moving average is used to smooth the option 2) seasonal variation .
Moving averages represents a series of averages which calculates sequential segments using data points over a series of given values. They calculate a length, also defines the number of data points and include in each average.Moving average is used to smooth the seasonal variation.Seasonal variation fluctuate as per the different seasons. Set the length in such a way of moving average to equal the pattern’s of the length.Longer the lengths more will produce the smoother lines.
Therefore, a moving average which is used to smooth the seasonal variation.
The above question is incomplete , the complete question is:
A moving average can be used to smooth which of the following options?
1) cyclical variation 2) seasonal variation
3) irregular variation 4) all responses are correct
Learn more about moving average here
brainly.com/question/15572913
#SPJ4
Brenda wants to make scrapbooks with old family photos. An online scrapbooking company charges $12 for a basic book and $2 per page. Meanwhile, a family friend is willing to make a scrapbook for $47 plus $1 per page. For a certain number of pages, the price would be equal. How many pages would that be? How much would that cost?
For a 35 number of pages, the price would be equal. & it would cost $82.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. 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, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
here, we have,
An online scrapbooking company charges $12 for a basic book and $2 per page.
Meanwhile, a family friend is willing to make a scrapbook for $47 plus $1 per page.
let, the number of page = x, the price would be equal.
so, we get,
12 + 2x = 47+x
i.e. x = 35
Hence, For a 35 number of pages, the price would be equal. & it would cost $82.
To learn more on equation click:
brainly.com/question/24169758
#SPJ1
3. Decide whether the polygons are similar, not similar, or not enough information is given. If similar, write a similarity statement. If not, explain why.
The solution is the given triangles are similar to each other due to S-S-S rule.
What is triangle?A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.
here, we have,
From the given figure we get,
triangle ABC & HIJ
we get,
AC = 2* HI
AB= 2*IJ
BC = 2* HJ
so, the scale factor = 2
Hence, The solution is the given triangles are similar to each other due to S-S-S rule.
To learn more on triangle click:
brainly.com/question/29126067
#SPJ1
On a coordinate plane, 2 triangles are shown. Triangle J K L has points (2, negative 4), (5, negative 4), (2, negative 2). Triangle J double-prime K double-prime L double-prime has points (2, 2), (2, 5), (0, 2).
Which rule describes the composition of transformations that maps ΔJKL to ΔJ"K"L"?
90 degree rotation about point 0 composition translation of 0 units x, negative 2 units y
Translation of 0 units x, negative 2 units y composition 90 degree rotation about point 0
90 degree rotation about point 0 composition translation of negative 2 units x, 0 units y
Translation of negative 2 units x, 0 units y composition 90 degree rotation about point 0
The triangle JLK is transformed to J''K''L'' by a rotation of 90° anticlockwise and a translation of -2 units
What is Rotation?The measure of the amount a figure is rotated about the center of rotation is called the angle of rotation. The angle of rotation is usually measured in degrees. We specify the degree measure and direction of a rotation.
90° clockwise rotation: (x,y) becomes (y,-x)
90° counterclockwise rotation: (x,y) becomes (-y,x)
180° clockwise and counterclockwise rotation: (x, y) becomes (-x,-y)
270° clockwise rotation: (x,y) becomes (-y,x)
270° counterclockwise rotation: (x,y) becomes (y,-x)
Given data ,
Let the triangle be represented as ΔJKL
Now , the coordinates of the triangle JKL is
J ( 2 , -4 ) , K ( 5 , -4 ) and L ( 2 , -2 )
And , the transformed triangle be represented as Δ J''K''L
Now , the coordinates of the triangle J''K''L'' is
J'' ( 2 , 2 ) , K'' ( 2 , 5 ) and L'' ( 0 , 2 )
The triangle JKL is first rotated by an angle of 90° counterclockwise rotation: (x,y) becomes (-y,x) to form J'K'L'
So , substituting the values in the equation , we get
The coordinates of the triangle J'K'L' is
J' ( 4 , 2 ) , K' ( 4 , 5 ) and L' ( 2 , 2 )
Now , when the triangle is translated -2 units to up , we get
So , the coordinates of the triangle J''K''L'' is
J'' ( 2 , 2 ) , K'' ( 2 , 5 ) and L'' ( 0 , 2 )
Hence , the transformed triangle is going through a rotation of 90° counterclockwise and a translation of -2 units
To learn more about rotation click :
https://brainly.com/question/3956347
#SPJ1
Answer:
Either
90 degree rotation about point 0 composition translation of 0 units x, negative 2 units y
or
90 degree rotation about point 0 composition translation of negative 2 units x, 0 units y
Step-by-step explanation:
The answer above is correct.