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.
Rachel's health-related budget is as follows: The percentage budgeted for health Insurance is four times the percentage for health club dues. The percentage budgeted for prescriptions is equal to one-fourth the percentage budgeted for health insurance. The percentage budgeted for doctor visits is twice the percentage budgeted for prescriptions. a. What is the percentage for health insurance? 12.5% b.What are the percentages budgeted for all categories?
The percentages budgeted for all categories is 14.06%
What is the percentage for health insurance?A total of $900 seems to be spent on various health-related expenses:
medication costs, health club dues, and health insurance
seeing a doctor
If we go back in time, we can observe that the rate of doctor visits is double that of prescriptions, which is half that of health insurance,
which is 1/4 times that of health club dues.
As a result, if we consider x to be health club dues, health insurance is included.
4x medical visits, medicines, and health club dues 2x \s
sums to $900 = 8
The amount set up for health insurance is thus $112.5.
112 .5 * 12.5% = 14.06%
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PLEASE HELP
Determine whether the statement makes sense or does not make sense, and explain your reasoning.
By writing the imaginary number 14, I can immediately see that 14 is the constant and i is the variable.
VIEW IMAGE
The statement does not makes a sense because i is an imaginary unit and has fixed value √-1.
What is meant by value ?
Market price: The monetary value of anything.A just compensation in the form of products, services, or money for the swapped item.When you appreciate something, you view it as significant and valuable. As an illustration, if you value someone's viewpoint, you might seek their counsel before making a significant choice.Value is concerned with how much something is worth, whether in monetary terms or in terms of significance.The things that someone values are known as their values. In other terms, values are what a person or a group of people see as "important." Examples include valor, integrity, freedom, and creativity, among others.To learn more about value refer to
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Julia had a bag filled with gumballs. There were 1 watermelon, 2 lemon-lime, and 3 grape gumballs. What is the correct sample space for the gumballs in her bag?
Sample space = watermelon, lemon-lime, lemon-lime, grape, grape, grape
Sample space = lemon-lime, watermelon, grape
Sample space = 1, 2, 3, 4, 5, 6
Sample space = 1, 2, 3
For the gumballs in Julia's bag
Sample space = lemon-lime, watermelon, grape.
The correct option is B.
What is sample space?A sample space is a collection or a set of possible outcomes of a random experiment. The sample space is represented using the symbol, “S”. The subset of possible outcomes of an experiment is called events. A sample space may contain a number of outcomes that depends on the experiment.
Given,
Number of lemon limes gumballs in the bag = 2 lemon-lime gumballs
Number of watermelon gumball in the bag = 1 watermelon gumball
Number of grape gumballs in the bag = 3 grape gumball
Sample space is the set of all the possible outcomes the experiment
Here, Julia has 1 watermelon, 2 lemon-lime, and 3 grape gumballs
Sample space = lemon-lime, watermelon, grape
Hence { lemon-lime, watermelon, grape} is the sample space for gumballs in Julia's bag.
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What is the area of a square with a side length of x - 8?
The area of the square is given by:
A = x^2 - 16x + 64
What is the area of the square?Remember that the area of a square of side length S is given by the formula:
A = S^2
Here we know that the side length is x - 8, then we can just replace that on the formula above to get:
A = (x - 8)^2
Now we can expand that:
A = (x - 8)^2 = (x - 8)*(x - 8)
A = x^2 - 16x + 64
That is the area.
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The value is a statistic because it is a numerical measurement describing some characteristic of a sample.A health and fitness club surveys 40 randomly selected members and found that the average weight of those questioned is 157 pounds. Determine whether the given value is a statistic or a parameter.
The given value of 157 pounds is a statistic.
This is because it is a numerical measurement describing a characteristic of a sample. A statistic is a value calculated from a sample, whereas a parameter is a value calculated from a population. In this case, the sample is the 40 randomly selected members of the health and fitness club, and the statistic is the average weight of those members. This statistic is used to make inferences about the larger population of all members of the health and fitness club, but it is not the same as the parameter, which would be the true average weight of all members of the club.
Therefore, The given value of 157 pounds is a statistic.
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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.
Use the formula for the cardinal number of the union of two sets to solve the problem.
Set A contains 6 elements, set B contains 13 elements, and 4 elements are common to sets A and B. How many elements are in ALB?
a. 14
B. 15
C. 16
D. 19
D. 19 elements are in ALB.
Where do you look for the AUB complement?| A | =6 and | B | = 13,
4 elements are common to sets A and B.
but | A ∪ B | ≠ 6 + 13.
Image search results for Set A has six components, set B has thirteen, and sets A and B share four elements.
ALB contains how many elements?A. 14 B. 15 C. 16 D. 19.The formula for A union B complement is (A U B)’ = A’ B’ or (A U B)c = Ac Bc, where or c represent the complement of a set. As one of De-Laws Morgan’s of Union of Sets, this formula of A union B complement is named after the mathematician De-Morgan. A U B (which denotes the union of two sets A and B) is a set that contains all of the components of A and B.
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The number of employees for a certain company has been decreasing each year by 8%. If the company currently has 630 employees and this rate continues, find the number of employees in 13 years.
So 213 employees left in the company after 13 years.
Given
Number of employee in the company=630
Decreasing rate in the company per year =8%
Time= 13 years
Let the number left in the company be x
Since the decrease rate is 8% we use 0.08
So after 13 years the employee left are
630(1-0.08)¹³=x
630(0.92)¹³=x
630*.338= 212.94
We can take approx as 213
so x= 213
So 213 employees left in the company after 13 years.
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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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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:
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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she’ll please help the question now pls
The average rate of change of these function f(x), g(x), h(x) on interval [4, 7] from least to greatest is f(x)<g(x)<h(x) with values A1 = -7.5 < A2 = -6 < A3 = -3.
What is a function?
In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.
Average rate of change of any function say S(x) on [a,b] is -
A = [S(b) - S(a)]/b-a....(1)
Now. for function f(x) on interval [4, 7].
Here, use values of f(4) and f(7) from graph and find value of f(x)=y for x=4 and value of f(x)=y for x=7.
f(4) = -10, f(7) = 5
Substitute the values in equation (1) -
A1 = [f(7) - f(4)]/(4 - 7)
A1 = [5 - (-10)]/-2
A1 = 15/-2
A1 = -7.5
Average rate of change for function g(x) on interval [4, 7].
Here, use the values of g(4) and g(7) from table.
g(4) = 7, g(7) = 19
Substitute the values in equation (1) -
A2 = [g(7) - g(4)]/(4 - 7)
A2 = [19 - 7]/-2
A2 = 12/-2
A2 = -6
Average rate of change for function h(x) = x² - 9x + 5 on interval [4, 7].
Here, use the values of h(4) and h(7) by putting x = 4 and x = 7 in function h(x).
h(4) = x² - 9x + 5
h(4) = (4)² - 9(4) + 5
h(4) = 16 - 36 + 5
h(4) = -15
h(7) = x² - 9x + 5
h(7) = (7)² - 9(7) + 5
h(7) = 49 - 63 + 5
h(7) = -9
Substitute the values in equation (1) -
A3 = [h(7) - h(4)]/(4 - 7)
A3 = [-9 - (-15)]/-2
A3 = [-9 + 15]/-2
A3 = 6/-2
A3 = -3
Now, average rate of change of these function f(x), g(x), h(x) from least to greatest is f(x)<g(x)<h(x).
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5. The amount of time, t, to finish a race and
the number of laps, I, around a track
For the given condition number of laps "l" is the independent variable.
What are Variables?A symbol (often a letter) is used in mathematics to represent an unknowable numerical value in an equation or algebraic statement. A variable can be defined as a quantity that is changeable and not fixed. Variables are crucial since they make up a significant portion of algebra.
Given The amount of time, t, to finish a race and the number of laps, I,
there are two types of variables,
dependent and independent variables,
In an algebraic equation, an independent variable is one whose values are not impacted by changes. When there are two variables in an algebraic equation, x and y, and each value of x depends on every other value of y, x is an independent variable, and y is a dependent variable.
for the given condition,
the time taken to finish the race directly varies with the number of laps,
so time is dependent on the number of laps and a number of laps "l" is the independent variable.
Hence the independent variable is the number of laps, "l".
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The complete question is,
The amount of time, t, to finish a race and the number of laps, l, around a track. What is the independent variable?
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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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.
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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4 more the quotient of 24 and number n
Answer:
Step-by-step explanation:
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
A cause-and-effect relationship between two variables can best be determined from which of the following? When the two variables have a correlation. An observational study where the observational units are chosen randomly. A survey conducted using a simple random sample of individuals. A survey conducted using a stratified random sample of individuals. A controlled experiment where the observational units are assigned randomly to treatments.
The answer is A cause- and- effect relationship between two variables can best be determined When the two variables are identified.
Because the cause and effect relationship is chancing when the variables are identified or there exists a direct relationship between the variable. i.e. when the variables are identified or have a retrogression between the variables.The use of a controlled study is the most effective way of establishing reason between variables. In a controlled study, the sample or population is resolve in two, with both groups being similar in nearly every way.
There are three criteria that must be met to establish a cause- effect relationship. The cause must do before the effect. Whenever the cause occurs, the effect must also do. There mustn't be another factor that can explain the relationship between the cause and effect.
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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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I need help please!!
Answer:
Step-by-step explanation:
refreh it
"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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what is the answer?????
Answer unzipped,new bases, sealed
Step-by-step explanation:
cara is ordering mushrooms for her restaurant. the graph shows the cost, y, of ordering x pounds of mushrooms what is the equation of the line what is the cost of ordering 6 pounds of mushrooms? iready quiz derive linear equations
Answer: Based on the information provided, it appears that the graph represents a linear equation, which is a straight line. The equation of a straight line can be represented in the form y = mx + b, where m is the slope of the line and b is the y-intercept.
To find the equation of the line, we need two points on the line. We can use the points (x1, y1) and (x2, y2) to calculate the slope of the line, m, using the formula:
m = (y2 - y1) / (x2 - x1)
Without knowing the coordinates of the points on the graph it is not possible to give the equation of the line.
To find the cost of ordering 6 pounds of mushrooms, we would substitute 6 for x in the equation of the line and solve for y.
y = mx + b
y = m(6) + b
Without the equation of the line, it's not possible to find the cost of ordering 6 pounds of mushrooms.
Step-by-step explanation:
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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Using Tiles to Multiply Two Binomials
Multiply: (x + 3)(x – 4)
The middle term in the simplified product for (x + 3)(x – 4) will be B. -x.
How to calculate the binomial?A polynomial with only terms is a binomial. For instance, the binomial x + 2 is composed of the terms x and 2.
Binomial is the name for an algebraic expression with only two terms. It is a polynomial with two terms. It is also referred to as the sum or difference of two or more monomials. It is a polynomial's most basic form.
The product of (x + 3)(x – 4) will be:
= x² - 4x + 3x - 12
= x² - x - 12
In this case, the middle term in the simplified product is -x.
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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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find (f+g) and (f-g)(x) for f(x)=10x^2+8 and g(x)=2-5x
The requied solution are (f+g)(x) = 10x² + 10 - 5x and (f-g)(x) = 10x² + 6 + 5x.
What is the function?The function is defined as a mathematical expression that defines a relationship between one variable and another variable.
The functions are given in the question, as follows:
f(x) = 10x² + 8 and g(x) = 2 - 5x
To find (f+g)(x) we add f(x) and g(x) term by term.
(f+g)(x) = f(x) + g(x)
Substitute the values of given functions, and we get
(f+g)(x) = 10x² + 8 + (2 - 5x)
(f+g)(x) = 10x² + 10 - 5x
To find (f-g)(x) we subtract g(x) from f(x) term by term.
(f-g)(x) = f(x) + g(x)
(f-g)(x) = 10x² + 8 - (2 - 5x)
(f-g)(x) = 10x² + 6 + 5x
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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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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