Step-by-step explanation:
g(-4) = 3(-4)-12
= -24
f(g(-4)) = f(-24)
f(-24) = 2(-24)+7
= -41
i don't know it is true i'm just trying:)
i could really use some help please
The coordinate of the circumcentre of ΔABC is (-1, 0.15).
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
Triangle ABC.
A = (-5, -4)
B = (3, -4)
C = (-1, 6)
The circumcentre of a triangle is the point where the perpendicular bisectors of the sides of the triangle intersect.
Now,
Let the circumcentre be M = (x, y).
The length from each side of the triangle to the circumcentre is equal.
So,
AO² = BO² = CO²
Now,
AO² = BO²
(x + 5)² + (y + 4)² = (x - 3)² + (y + 4)²
x² + 10x + 25 + y² + 8y + 16 = x² - 6x + 9 + y² + 8y + 16
10x + 25 = -6x + 9
16x + 16 = 0
x + 1 = 0
x = -1
BO² = CO²
(x - 3)² + (y + 4)² = (x + 1)² + (y - 6)²
x² - 6x + 9 + y² + 8y + 16 = x² + 2x + 1 + y² - 12y + 36
-6x + 9 + 8y + 16 = 2x + 1 - 12y + 36
20y - 8x + 25 - 36 = 0
20y - 8x - 11 = 0
20y = 11 + 8x
y = (11 + 8x)/20
y = (11 - 8)/20
y = 3/20
y = 0.15
Thus,
Circumcentre M = (-1, 0.15)
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Rotate this image 90° counter-clockwise around the point (1, 1):
The coordinates of the rotated image are:
A' = (1, 1)
B' = (1, 3)
C' = (-2, 1)
Option A is the correct answer.
What is translation?It is the movement of the shape in the left, right, up, and down directions.
The translated shape will have the same shape and shape.
There is a positive value when translated to the right and up.
There is a negative value when translated to the left and down.
We have,
Triangle ABC.
A = (1, 1)
B = (3, 1)
C = (1, 4)
When rotated 90 degrees counterclockwise around (1, 1).
A = (1, 1) will stay the same.
B = (3, 1) will change into B' = (1, 3)
C = (1, 4) will change into C' = (-2, 1)
Now,
The coordinates of the image after reflection are:
A' = (1, 1)
B' = (1, 3)
C' = (-2, 1)
This image is found in option A.
Thus,
The rotated image of the triangle is in option A.
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In Problems 13 through 16, substitute y = e^rx into the given differential equation to determine all values of the constant r for which y = e^rx is a solution of the equation. 13. 3y' = 2y 14. 4y" = y 15. y" + y' - 2y = 0 16. 3y" + 3y' - 4y = 0
The values of given differential equation constant r are = 1/5 and -3.
A differential equation is an equation which contains one or more terms and the derivatives of one variable (i.e., dependent variable) with respect to the other variable (i.e., independent variable) dy/dx = f(x)
Here “x” is an independent variable and “y” is a dependent variable.
For example, dy/dx = 5x A differential equation contains derivatives which are either partial derivatives or ordinary derivatives.
The derivative represents a rate of change, and the differential equation describes a relationship between the quantity that is continuously varying with respect to the change in another quantity.
There are a lot of differential equations formulas to find the solution of the derivatives.
As y = e power rx
y¹= dy/dx= re power rx
and y'' = r²e power rx
Hence 5y'' +14y' – 3y = 0 can be written as
5r²e - 14re** - 3e¹² - 0
or 5r2 + 14r - 3 - 0
or 5r2 + 15r - r - 3 - 0
or (5r − 1)(r + 3) = 0
r=1/5 or r= -3
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The total average monthly expenditure in 2010 was £1200.
What was it in 2020?
The total average monthly expenditure in 2020 was £2400.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
The expenditure in 2020 will be calculated as:-
Average monthly expenditure in 2020 = 600 + 500 + 400 + 300 + 200 + 100 = £2400
So, the total average monthly expenditure in 2020 was £2400.
The complete question is given below:-
Average monthly expenditure (£)
600
500
400
300
200
100
The total average monthly expenditure in 2010 was £1200. What was it in 2020?
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Kara needs to pick a pair of matching socks from a drawer consisting of 4 black socks, 11 blue socks, 3 white socks, and 5 brown socks. If the first sock that Kara draws is blue, what is the probability that she will get a matching sock on her second draw?
A. 0.22
B. 0.78
c. 0.93
d. 0.07
Find Y if the slope between (8, y) and (14, -13) is -2/3
Answer: The slope between two points (x1, y1) and (x2, y2) is given by the formula:
m = (y2 - y1) / (x2 - x1)
We are given that the slope between (8, y) and (14, -13) is -2/3. So we can use this information to set up the equation:
-2/3 = (-13 - y) / (14 - 8)
To find y, we can solve for y:
-2/3 = (-13 - y) / 6
-2 = -13 - y
y = 11
So the value of y is 11.
Step-by-step explanation:
jeremy is looking for a good auto loan in his city. He is willing to pay no more than an effective rate of 7.000% annually. which if any of the following loans meet jermeys criteria?
loan A : 6.785% normal rate compounded semi annually
loan B : 6.795% nominal rate compounded, manually
loan C : 6.659% nominal rate, compounded weekly.
Answer: To determine which loan(s) meet Jeremy's criteria of no more than an effective rate of 7.000% annually, we need to calculate the effective rate for each loan.
The effective rate is the true annual interest rate that a borrower will pay on a loan, taking into account the frequency of compounding.
Loan A: 6.785% normal rate compounded semi-annually
To calculate the effective rate, we can use the formula:
(1+ (nominal rate/2))^2 - 1
Effective rate = (1+ (6.785/2))^2 - 1 = 6.897%
Loan B: 6.795% nominal rate compounded, manually
Since the loan is compounded manually, the effective rate is the same as the nominal rate.
Effective rate = 6.795%
Loan C: 6.659% nominal rate, compounded weekly
To calculate the effective rate, we can use the formula:
(1+ (nominal rate/number of compounding periods per year))^(number of compounding periods per year) - 1
Effective rate = (1+ (6.659/52))^52 - 1 = 6.759%
Since 6.897% > 7.000% and 6.795% > 7.000% and 6.759% < 7.000%. So Loan C with 6.659% nominal rate, compounded weekly meets Jeremy's criteria.
Step-by-step explanation:
1) The table below shows a future estimated population and the number of hospitals in
2009 in the United States and the three states - Texas, California, and Florida. Use
the data to answer each question.
Estimated Future Population and Number of Hospitals by State (2009)
Number of
hospitals in
2009
5,008
428
343
210
United States
Texas
California
Florida
Projected
Population
316 million
26.4 million
38.3 million
19.5 million
Patients Admitted in
2009 (in Thousands)
35,527
2,621
3,433
2,453
Assume Florida has the same number of hospitals per million people as Texas.
Estimate the number of hospitals in Florida. Is this estimate close to the actual
number of hospitals in Florida in 2009?
In 2009, Florida would have 558 hospitals if it had the same hospital beds per million residents as Texas. This is a little more than what Florida's real number of hospitals was in 2009. (343).
What is logical proportionality?A mathematical technique called proportional reasoning is used to compare the ratios of two or more identical quantities.
The proportionate reasoning theory is being used in this query.
In this instance, we're contrasting Florida's hospital density per million residents with Texas' hospital density per million residents.
We may predict the number of hospitals in Florida given the same ratio as Texas by comparing these two ratios.
1. Determine Texas's hospital density per million residents: 428 hospitals divided by 26.4 million residents equals 16.2 hospitals per million residents.
2. Determine Florida's hospital density per million residents: 343 hospitals / 19.5 million residents = 17.6 hospitals per million residents.
3. Multiply the population of Florida (19.5 million) by the number of hospitals per million of the population of Texas (16.2) to arrive at 315.3 hospitals: 19.5 million people x 16.2 hospitals per million of the population.
The result should be rounded to the next whole number: 315 hospitals are equal to 315.3 hospitals.
5. Contrast Florida's actual hospital count in 2009 with the expected number of hospitals there (315). (343).
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2. Amir's community center has an evening art class. He pays $5 every time he goes to the class. His cost, C(a), is given by C(a) = 5a, where a is the number of art classes Amir attends.
a. Identify the independent variable and tell what it represents.
b. Identify the dependent variable and tell what it represents.
Answer: a. The independent variable in the equation C(a) = 5a is a. It represents the number of art classes Amir attends.
b. The dependent variable in the equation C(a) = 5a is C(a). It represents the cost Amir incurs as he attends art classes. The dependent variable is dependent on the independent variable because the cost will change as the number of classes attended changes.
(1 point) A company received a shipment of 42 laser printers, including 8 that are defective. 2 of these printers are selected to be used in the copy room. (a) How many selections can be made? (b) How many of these selections will contain no defective printers?
The number of selections that will contain no defective printers can be found using the nCr formula as well, but with n being the number of non-defective printers (34) and r being the number of items selected (2). So nCr = 34!/(2!(34-2)!) = 34!/(2!32!) = 5,832.
(a) There are 6,632 selections that can be made.
(b) There are 5,832 selections that will contain no defective printers.
(a)The number of selections can be found using the nCr formula: nCr = n!/(r!(n-r)!), where n is the total number of items (42) and r is the number of items selected (2). So nCr = 42!/(2!(42-2)!) = 42!/(2!40!) = 6,632.
(b) The number of selections that will contain no defective printers can be found using the nCr formula as well, but with n being the number of non-defective printers (34) and r being the number of items selected (2). So nCr = 34!/(2!(34-2)!) = 34!/(2!32!) = 5,832.
There are 6,632 selections that can be made when two printers are chosen from a shipment of 42, including 8 that are defective. Out of these selections, 5,832 will contain no defective printers.
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A The numbers 4, 2, 5, ( ) have a mean of 4. What is the missing number?
B The numbers 4, 2, 7, ( ) have a mode of 2. What is the missing number?
C The numbers 8, 4, 6, ( ) have a median of 5. Write down a possible value of c
D The numbers 20, 70, 10, ( ) have a range of 80. What is the missing number? the missing number.
Based on given data, Mean is 4, missing number can be 4,2,7., So the arrangement is c,4,6,8.
a) What is meant by mean?The mean of numbers is the average value of given numbers.
Given numbers are 4,2,5
Mean is 4
Mean = sum of numbers/ total number of values given
4 = (4+2+5+x) /4
16 = 11 +x
x = 5
Therefore the missing number is 5.
b) What is mode?Mode is the number which is most frequently repeated in a list of numbers.
Given numbers are 4,2,7 and x
Mode is given as 2
So x can be any number from the given values since any number can be repeated twice.
Therefore missing number can be 4,2,7.
c) What is the median?The median of the set is the middle number after the numbers are arranged from least to greatest.
There are four numbers given. So the median is the average of middle numbers.
To get the median of 5 the middle numbers should be 4 and 6.
So the arrangement is c,4,6,8
Therefore the missing number can be any number less than or equal to 4.
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why did the authors ain the 2nd matrix article the authors argue that cypher should not have made the choice to go back into the matrix because he would betray his friends.rgue that
The authors argue that Cypher's decision to go back into the Matrix was a betrayal of his friends because it showed that he was willing to abandon his beliefs and betray those closest to him in order to return to a life of comfort and ease within the Matrix.
By doing so, he effectively gave up his freedom and became a tool of the machines once again, thereby betraying the ideals of the rebellion and those who had fought alongside him to achieve it. Hence, The authors argue that Cypher's decision to go back into the Matrix was a betrayal of his friends.
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the mean of an iq test are normally distributed with a mean of 100 points and a standard deviaiton of 15. calculate the following probability in r using the pnorm() function. what is the probability a student taking the exam scores below 125 points?
The percentage of scores below 112 is equal to 78.81.
Let X represent a test's score. X is regularly distributed, hence
P(X < 112)
= P[(X - 100)/15 < (112 - 100)/15]
= P[ SNV < 0.8] .8]
SNV stands for Standard Normal Variable,
A normal distribution with a mean of 0 and a standard deviation of 1 is the standard normal distribution. When referring to a random variable that has this typical normal distribution, the letter Z is frequently employed.
z = (X – μ) / σ
If X is a normal random variable, represents its mean, and represents its standard deviation. The normal distribution formula is also available here.
and the value is 0.7881.
Thus, the percentage of scores below 112 is equal to 78.81.
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The full question
If the scores for a test have a mean of 100 and a standard deviation of 15, what is the percentage of scores that will fall below 112? Assuming a normal distribution
Pqrs is a rhombus. The length of the shorter diagonal pr is 12cm and the m angle pqr =60.
Find the length of a side of the rhombus
The required length of a side of the rhombus is 10 cm.
What is Rhombus?A parallelogram is a particular instance of a rhombus. The opposing sides and angles in a rhombus are parallel and equal. A rhombus also has equal-length sides on each side, and its diagonals meet at right angles to form its shape. The rhombus is also referred to as a diamond or rhombus.
According to question:Let diagonals intersect each other at o,
In ΔROQ
RQ = [tex]\sqrt{OR^{2}+OQ^{2}}[/tex]
RQ =[tex]\sqrt{36+64} =\sqrt{100}[/tex]
RQ = 10 cm
Thus, required length of the side of rhombus is 10 cm.
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Complete question:
PQRS is a rhombus. The shorter diagonal PR measures 12 units and QS = 16 units. The measure of angle PQR = 60°. Find the length of a side of the rhombus.
Housing prices in a small town are normally distributed with a mean of
$157,000 and a standard deviation of $8,000. Use the empirical rule to
complete the following statement.
Approximately 99.7% of housing prices are between a low price of
$ and a high price of $
Answer: The empirical rule states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, approximately 95% falls within two standard deviations, and approximately 99.7% falls within three standard deviations.
So, using the empirical rule, we can say that approximately 99.7% of housing prices in this small town fall within 3 standard deviations of the mean.
To find the range of prices that this corresponds to, we can use the following formula:
(mean - (3 x standard deviation), mean + (3 x standard deviation))
Plugging in the given values:
(157,000 - (3 x 8,000), 157,000 + (3 x 8,000))
(141,000, 173,000)
So, approximately 99.7% of housing prices in this small town are between $141,000 and $173,000.
Step-by-step explanation:
Christian is making a circular pizza. The diameter of the pizza is 12 inches. Approximately, how many inches of the pizza will be the outer
edge crust?
Christian is making a circular pizza. The diameter of the pizza is 12 inches. The pizza crust on the outside will be about 12 inches thick.
How is the pizza's circumference determined using this formula?The formula for determining a pizza's circumference is C = 2πr, where C is the circumference, pi is a constant that is roughly equivalent to 3.14, and r is the pizza's radius.
We must determine the pizza's circumference in order to locate the crust on the pizza's outer edge. C = 2πr is the formula for a circle's circumference, where C is the circumference, pi is a constant that is roughly equivalent to 3.14, and r is the circle's radius.
The pizza has a diameter of 12 inches, so the radius, or 6 inches, is half of that. Thus, the pizza's circumference is:
C= 2π6 = 12π
The pizza's circumference represents the crust's outer edge. C = 26 inches = 12 inches As a result, the pizza's crust on the outside measures about 12 inches.
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What would need to be used to show the triangles are congruent by AAS?
A: Nothing as the triangles can not be proved congruent by AAS.
B: Angles are congruent by vertical
angles.
C: Sides are congruent by the
reflexive property.
D: Angles are congruent by the
reflexive property.
Triangles are shown to be congruent by the statement that "Angles are congruent by vertical angles."
What is the congruent triangle?Triangles are said to be congruent if, under a correspondence, two of a triangle's sides and the angle that connects them are equal to two of another triangle's sides and the angle that connects them.
Given two triangles, Where the base of these triangles are same
And also given that the two angles are the same.
Since,
Two intersecting lines form a pair of vertical angles. The vertical angles are opposite angles with a common vertex (which is the point of intersection).
Thus, the third angle is also equal
From AAS:
AAS stands for Angle-Angle-Side. When two angles and a non-included side of a triangle are equal to the corresponding angles and sides of another triangle, then the triangles are said to be congruent
Therefore. "Angles are congruent by vertical angles" is used to show the triangles are congruent by AAS,
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"Dondarrion's Wood," Galshore said to herself as she approached the dense growth of trees. She spied all kinds of trees and shrubs. Galshore prided herself on her knowledge of plant life, but there were three trees that she did not recognize. She regarded the strange trees for a moment then turned to the trees she knew. She saw ten sprightly maple trees eager to catch the sun. She saw four ancient and venerable oaks placidly lording over the wood. She saw two cedars, four pines, a birch and seven sycamores. A crow quorked. Galshore looked up searching. She spotted the crow perched at the top of one of the maple trees hidden behind the sycamores. The crow quorked again. Galshore was a little afraid. The wood was dark. She felt a coolness linger and caress her face. Galshore concentrated on listening and noticed other sounds coming from the wood. They were strange sounds. She wondered what sort of animals made such sounds and shivered. Galshore turned and sat on a boulder.
She stared into the wood for fifteen minutes wondering about the strangeness of the wood and trying to peer through the shadows of leaf and branch to discover what awaited her in the wood. "It is the only way to Ten Alders," she said under her breath.
A light breeze shimmered through the cedars. Galshore smelled oak and pine and remembered.
"Father, what will we do when the Kargs come to Oranea?" Galshore asked.
The stout merchant sat down by the fire with a book. "Galshore dear child, fear not for our safety." He leaned forward in his high backed chair. "The walls of our city are strong. We are well protected by stone and metal."
"What about food?" Galshore asked. "Do we have enough food to survive if the Kargs stay outside our walls for a long time?"
Galshore's father took a sip of Merasha tea. "We have been storing grain for quite some time. I have calculated that we have enough grain to give each of the 2200 inhabitants of Oranea one and one half pounds of grain each week. Never fear, you shall continue to enjoy cakes and cookies even if the Kargs come." He folded his hands and looked down at Galshore. "We shall not be troubled by mindless Kargs.
Our hard work will not be undone by savages and brutes. The beauty we have created here will be protected. We are safe. asked.
"What about your Merasha? Maybe we should give it to the Kargs," Galshore Galshore's father hooked his thumbs under his belt and smiled. "So you would invite the Kargs to tea my little dear? Even if they could learn to precisely measure the proper proportions of 5 parts black lion's fennel leaf to two parts greebe root and seven parts prisic, they don't believe in medicines of any kind. They have some sort of superstition that medicines weaken the body and rob the true warrior of his strength and turn him into a zombie or some such nonsense."
Galshore's father picked up his book.
Galshore was curious, "Why do the Kargs want to attack us?"
Galshore's father sighed. "The Kargs are not nice. They do not build and work.
They plant no crops. They only know how to destroy, so they have nothing of their own. They steal from others. They know nothing of peace or beauty. They know only the violence and disorder they bring wherever they go."
Galshore clasped her knees. "Why don't we give them some food if they have none of their own? I want to give them half of my one and a half pounds of grain I am to receive each week."
Galshore's father smiled. "I am afraid my dear that would only insult the
Kargs. There is no reasoning with them. They must destroy or be destroyed. Misery is like a comfortable warm blanket for them."
The crow left its tree and perched on a rock in front of Galshore and cawed loudly. Galshore started. The crow regarded her curiously. "I wish you had been right father," Galshore whispered into the darkness of the wood. "I wish you had been right." She stepped into a green unknown world of shade and shadows.
QUESTIONS:
1. What percentage of the trees were oaks?
2. If over the span of one year the number of pines were increased by 3, cedars by 2, sycamores by 1 , oaks by 5 and birches by 4; by what fraction would the total number of trees have increased?(don’t forget the unknown trees)**
3. Make a table of the propagation of the trees in Dondarrion’s Wood over a year. The table should include information about the fractional changes in tree proliferation over the year. (use all the info at your disposal including the info from question 2 -and don’t forget the unknown trees)**
4. What percentage of the trees were unknown to Galshore?(first year)
5. How much grain would it take to feed the inhabitants of Oranea for one year?
6. If Galshore gave 24% of her grain to the Kargs for one week, how much grain would she have left for that week?
7. How much prisic would be contained in 13 pounds of Merasha Tea?. **
8. How much greebe root would be contained in 13 pounds of Merasha Tea?**
In reality, only 55% of the calories produced by crops around the world are consumed directly by humans. Animal feed accounts for an additional 36% of usage.
How much grain is used for animal feed?The percentage of crops grown for human consumption compared to all crops farmed for animal feed or biofuels is fascinatingly depicted on this National Geographic map:In reality, only 55% of the calories produced by crops around the world are consumed directly by humans. Animal feed accounts for an additional 36% of usage. The remaining 9% is used for biofuels and other industrial applications. (Those numbers are from a study by Emily Cassidy and colleagues at the Institute on the Environment at the University of Minnesota.)Just 27% of crop calories in the US are directly ingested, such as wheat or Californian fruits and vegetables. In the US, these figures are even more startling.As opposed to this, animal feed accounts for almost 67 percent of all crops, especially the soy farmed in the Midwest. Ethanol and other biofuels receive a part of the remaining funds.Of course, some of that feed for animals does eventually end up as food, but the process is a lot, lot more deceptive. Just 12 calories of chicken or 3 calories of beef, for example, are made from grain, which requires roughly 100 calories.The Complete Question.
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14.3 percentage of the trees were oaks, The total number of trees have increased by: 15/28.
How to solve the following?There were 4 ancient oaks and a total of ten sprightly maple trees, four ancient oaks, two cedars, four pines, a birch, and seven sycamores, so the percentage of oaks would be 4/(10+4+2+4+1+7) = 4/28 = 14.3%.The total number of trees was 10+4+2+4+1+7 = 28, and the increase over one year was 3+2+1+5+4 = 15. The fractional increase would be 15/28 = 0.5357.The fractional change in tree proliferation for each type of tree over the year is not specified in the text.The total number of trees was 28, and Galshore did not recognize three of the trees, so the percentage of unknown trees would be 3/28 = 10.7%.2200 people would each receive one and a half pounds of grain per week for 52 weeks in a year, so the total amount of grain required would be 2200 x 1.5 x 52 = 183,400 pounds.If Galshore received 1.5 pounds of grain each week, and gave away 24% of it, she would have 1.5 x (1 - 0.24) = 1.5 x 0.76 = 1.14 pounds left for the week.The proper proportions of 5 parts black lion's fennel leaf to two parts greebe root and seven parts prisic are not specified.The amount of prisic contained in 13 pounds of Merasha Tea is not specified, so this question cannot be answered.To know more about percentage visit:
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Amelia grabbed 50% of the M&M's from a bowl. Then, Jess took 50% of what was left. Dominick takes 50% of the remaining M&M's. There were 3 left. How many M&M's were in the bowl before Amelia arrived.
The number of M&M's that were in the bowl before Amelia arrived is; 12
How to solve Percentage problems?Let the original amount in the bowl be x. Thus;
If Amelia grabbed 50%, then amount left = (100% - 50%)x = 50%x = 0.5x
Now, we are told that domicick took 50% of what was keft after amelia. Thus; New amount left = 100%x - (0.5x + 0.25x) = 0.25x
Now, we are told that there were finally 3 left after all the deductions. Thus;
0.25x = 3
x = 3/0.25
x = 12
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please help will mark BRAINLIEST
The composite translation for this problem is represented as follows:
<3, -9>
What are the translation rules?The four translation rules are defined as follows:
Left a units: x -> x - a.Right a units: x -> x + a.Up a units: y -> y + a.Down a units: y -> y - a.Another notation is the <x,y> notation, in which:
x is the horizontal movement.y is the vertical movement.For the composition of translations, we add the movements, hence:
6 - 3 = 3.-4 - 5 = -9.Meaning that the first option is the correct option.
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The distributions shown, state the mean and standard deviation for each. Hint: The vertical lines are I standard deviation apart. Part: 0/2 Part 1 of 2 (a) 164.3 173.5 182.7 191.9 2011 210.3 219.5 Mean = Standard deviation
The mean is 120 and the standard deviation is 20.
How to find the mean and standard deviation?
We must calculate the mean and standard deviation from the curve in the preceding graph.
As we can see from the normal distribution curve that the center is at 120.
As a result, 120 is the distribution's mean.
From the above curve:
Mean + Standard deviation = 140
We know that the Mean = 120.
120 + Standard Deviation = 140
Standard Deviation = 20
Therefore, 20 is the standard deviation.
Therefore, from the given data we can find that the Mean is 120 and the Standard deviation is 20.
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SOLVE FOR Y 32=16Y+64X
Answer: y = 2-4x
Step-by-step explanation:
a company produces a product for which the variable cost is $12.13 per unit, and the fixed costs are $92,000. the product sells for $17.10. let x be the number of units produced and sold.(A). The total cost for a business is the sum of the variable cost and the fixed costs. Write the total cost C as a function of the number of units produced. C = _____(B). Write the revenue ft as a function of the number of units sold. R = _____(C). Write the profit P as a function of the number of units sold. P = _____
a. The total cost C as a function of the number of units produced is C = $12.13x + $92,000
b. The revenue R as a function of the number of units sold is R = $17.10x
c. The profit P as a function of the number of units sold is P = $5.97x - $92,000
(A) The total cost for a business is the sum of the variable cost and the fixed costs.
The variable cost per unit is $12.13, so the total variable cost for x units produced is $12.13x.
The fixed costs are $92,000 and do not change with the number of units produced, so the total cost C as a function of the number of units produced is given by -
C = $12.13x + $92,000
(B) The revenue is the total amount of money earned from selling the product. The product sells for $17.10 per unit, so the revenue R as a function of the number of units sold is given by -
R = $17.10x
(C) The profit is the difference between the revenue and the total cost. Using the equations from (A) and (B), the profit P as a function of the number of units sold is given by -
P = R - C = $17.10x - ($12.13x + $92,000) = $5.97x - $92,000
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The perimeter of a triangle is 100cm and the angles are in the ratio: 1:3:5 find the length of each side triangle
By applying the rule of sin, it can be concluded that the length of the sides of the triangle is 15.48 cm, 39.68 cm, and 44.84 cm.
Triangle is a 2D shape that is bounded by three sides and has three vertices. The perimeter of a triangle is the sum of the lengths of the three sides of the triangle.
Perimeter = a + b + c, where a, b, and c are the sides of the triangle
One of the most important properties of a triangle is that the sum of the angles in a triangle equals 180°.
The rule of sin describes the ratio of the angles corresponding to the side lengths of the sine function.
a / sin A = b / sin B = c / sin C, where A, B, and C are the angles of the triangle
If the ratio of the angles is 1 : 3 : 5 and let x be the smallest angle, then we can put this information into the following equation:
Total angle = A + B + C
180° = x + 3x + 5x
180° = 9x
x = 20°
Then we can calculate the other angles:
A = 20°
B = 3x = 3 * 20° = 60°
C = 5x = 5 * 20° = 100°
Now we put the value of A, B, and C into the rule of sin equation:
a / sin A = b / sin B
a / sin 20° = b / sin 60°
a / 0.34 = b / 0.87
a = 0.34 * b / 0.87
a = 0.39b
c / sin C = b / sin B
c / sin 100° = b / sin 60°
c / 0.98 = b / 0.87
c = 0.98 * b / 0.87
c = 1.13b
Then we go back to the perimeter formula:
perimeter = a + b + c
100 = 0.39b + b + 1.13b
100 = 2.52b
b = 39.68 cm
Then we can calculate the length of the other sides, a and c:
a = 0.39b
= 0.39 * 39.68
= 15.48 cm
c = 1.13b
= 1.13 * 39.68
= 44.84 cm
Thus, the length of the sides of the triangle is 15.48 cm, 39.68 cm, and 44.84 cm.
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4 more the quotient of 24 and number n
Answer:
Step-by-step explanation:
PLEASE HELP ITS MY BDAY TOMORROW
Zachary measures the area of a glacier at
the start of every year.
2
At the start of this year, the glacier had an
area of exactly 56.20 km. This is 0.2%
less than it was at the start of last year.
Work out what the area of the glacier was
at the start of last year.
2
Give your answer in km² to 2 d.p.
The area of the glacier at the beginning of the last year is given as follows:
56.31 km².
How to obtain the area of the glacier?The area of the glacier is obtained applying the proportions in the context of this problem.
The current area is given as follows:
56.20 km².
The percentage of this area relative to the area at the beginning of the last year is given as follows:
100 - 0.2 = 99.8% = 0.998.
Hence the area at the beginning of the last year is obtained as follows:
0.998x = 56.20
x = 56.20/0.998
x = 56.31 km².
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Michelle has 4 1/5 feet of yarn. She cuts the yarn into pieces that each measure 3/5 foot long. How many pieces of yarn did Michelle cut?
Answer: 7
Step-by-step explanation:
yarn = 4 1/5 = 21/5
measure of one piece = 3/5
no. of pieces of yarn = 21/5÷3/5
= 21/5×5/3
= 105/15 = 7
So the number of pieces of yarn cut will be 7
Answer:
7
Step-by-step explanation:
4.2' yarn
cut into 0.6' pieces
4.2/0.6 =7
consider the triangles shown below. which of the following would also need to be true in order to prove that ABD = ABC?
A.BC BD must be true in order to demonstrate that triangles ABD and ABC are congruent by SSS.
How does the SSS Congruence Theorem work?The SSS Congruence Theorem requires three pairs of corresponding sides to be congruent for two triangles to be considered congruent to one another.
We may infer the two triangles' characteristics from the provided image by looking at them:
AB ≅ AB (reflexive property) (reflexive property)
AC ≅ AD (provided) (given)
The two pairs of corresponding congruent sides are so present. As a result, for SSS to demonstrate that ABD ABC, the following must be true: A. BC BD.
A.BC BD must be true in order to demonstrate that triangles ABD and ABC are congruent by SSS.
The complete question is,
Have a look at the triangles below. In order to demonstrate that ABDABC, which of the following would also need to be true?
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T is the incenter of AQRS. Find QT (to the nearest tenth). R U 17 36% 55 W O
The length of Mid segment QT is 57.56 units.
How Do You Find a Triangle's Incenter?The incenter of a triangle can be discovered by drawing the triangle's angle bisectors and then locating the location of their intersection. This is possible with the aid of a compass.
The three line segments and the three lines that include those segments are equally spaced from the incenter and constitute each of the three sides of the triangle.
the single point where the three internal angle bisectors of a triangle meet and which also serves as the circumference of the circle around which it is inscribed.
The three line segments and the three lines that include those segments are equally spaced from the incenter and constitute each of the three sides of the triangle.
ΔQUT is right triangle
QU = 55
UT= 17
Using Pythagoras Theorem
QT² = QU² + UT²
QT² = 55² + 17²
QT = √3314
QT = 57.56
Thus, The length of Mid segment QT is 57.56 units.
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Exercise 2: ABC is a triangle such that B=80°. BC=5cm and Ĉ=40°. 1) Construct the triangle ABC. 2) The bisector of the angle ABC cuts [AC] at M. a. Calculate MBC. b. What is the nature of triangle MBC? Justify. c. Deduce that MB=MC.
Answer:
Step-by-step explanation:
Exercise 2:
1.To construct the triangle ABC, start by drawing a line segment BC of length 5cm. Using a protractor, measure and mark an angle of 80° at B and an angle of 40° at C. Connect the two marked angles with a line to form triangle ABC.
2.The bisector of angle ABC cuts the line segment AC at M.
a. To calculate MBC, we can use the Angle Bisector Theorem, which states that the ratio of the lengths of the bisector of a given angle of a triangle to the sides of the triangle is equal to the ratio of the other two sides of the triangle. So, MBC/AC = BC/AB. Since angle B=80° and angle C=40°, angle A is (180-(80+40))=60°. Therefore, AB/BC = MC/MB.
b. Using the Angle Bisector Theorem again, we can see that MBC/AC = BC/AB, which means that MBC/5 = 5/AB. And since AB/BC = MC/MB, we can deduce that MB = MC. Therefore, triangle MBC is an isosceles triangle.
c. As we know that MB=MC, we can say that triangle MBC is an isosceles triangle.
Note: To construct the triangle in a more accurate way, you may need a ruler and a compass, and the angles and sides should be measured and drawn with more precision.