Answers
Answer:
Step-by-step explanation:
(2,4)
Answer:
Step-by-step explanation:
Related Questions
Find the equation of line b described below in slope intercept formLine a is parallel to line bLine a passes through the points (1,5) and (2,-4)Line b passes through the point (1,12)
Answers
Given:
Line a is parallel to line b.
1) Line a passes through the points (1,5) and (2,-4).
Its slope is estimated as,
\(\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ (x_1,y_1)=(1,5) \\ (x_2,y_2)=(2,-4) \\ m=\frac{-4-5}{2-1}=\frac{-9}{1}=-9 \end{gathered}\)As the given 2 lines are parallel , it implies that their slope must be equal.
\(\text{therefore, the slope of line b=-9}\)The equation of line b having slope -9 and passing through point (1,12) is given by,
\(\begin{gathered} y-y_1=m(x-x_1)\ldots(\text{ Slope intercept form)} \\ (x_1,y_1)=(1,12) \\ y-12=-9(x-1) \\ y-12=-9x+9 \\ y+9x-21=0 \end{gathered}\)Answer: The equation of line b is y = -9x + 21.
Steven has a stamp collection with 32 stamps. Only 1/4 of the stamps are from the United States. How many stamps are from the U.S?
Answers
Answer:
I believe the answer would be 8 because if you divide 32 by 4 you get eight and that would be 1/4 of 32
Step-by-step explanation:
*not drown to scale
What is the distance between A and D? Enter the answer in the box. Round the answer to the nearest hundredth of an inch.
inches
Answers
Answer:
26.9 inches
Step-by-step explanation:
2x Pythagorean theorem
First we find the length of AC with ABC. AC is the hypotenuse of triangle ABC.
AC = sqrt(7^2+24^2) = sqrt625 = 25.
Now, AD is the hypotenuse of ACD. So AD = sqrt(25^2+10^2) = sqrt(725) = 26.925824 which is about 26.9 inches.
Answer:
26.93 inStep-by-step explanation:
Use Pythagorean:
\(AD^2 = AB^2+BC^2+CD^2\\AD = \sqrt{7^2+24^2+10^2} = \sqrt{725}\) ≈ 26.93 in5.104 greater or less than 5.41
Answers
What is the difference of 620 and 89.7?
Answers
Answer: 530.3
Step-by-step explanation:
Difference means to subtract
620-89.7=530.3
Answer:
530.3
Step-by-step explanation:
You want to subtract 620-89.7. If you want to use the standard algorithm you have 620.0-89.7. You "borrow" from the 2 in the tens place, then "borrow" from the ones place. To subtract 10-3 tenths. Then you subtract the ones place which is 9-9=0 ones. Now you subtract 62-8=53 tens. So you have 530.3 as the difference.
In the table, which TWO relationships describe a function?
Name Tammy Allen Juan Keshia
Hair Color Red Brown Black Brown
Eye Color Hazel Brown Brown Blue
Responses
A Name as a function of hair colorName as a function of hair color
B Hair color as a function of eye colorHair color as a function of eye color
C Eye color as a function of nameEye color as a function of name
D Eye color as a function of hair colorEye color as a function of hair color
E Hair color as a function of nameHair color as a function of name
F Name as a function of eye color
Answers
The two relationships that describe a function in the table are A: Name as a function of hair color, and D: Eye color as a function of hair color.
A function is a relationship between two sets of values in which each element of the first set corresponds to exactly one element of the second set. In this table, for each hair color there is only one associated name, so the relationship between name and hair color is a function. Similarly, for each hair color there is only one associated eye color, so the relationship between eye color and hair color is also a function.
Note that the other relationships listed in the question (B, C, E and F) are not functions because they do not have a one-to-one correspondence between the two sets of values. For example, in the relationship between eye color and name, multiple people (Juan and Keshia) have the same eye color (brown), so this relationship does not describe a function.
Therefore, options A and D are the correct answer.
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11 = 3z + 5
What is this answer?
Answers
Answer:
subtract 5 from each side z=2
Step-by-step explanation:
The ratio of the number of model cars that Jim owns to the number of model cars Terrence owns is 8 : 6. Terrence owns 36 models cars. How many model cars does Jim own?
Answers
The number of Jim's model car is 48
How to determine the number of JIm's carFrom the question, we have the following parameters that can be used in our computation:
Ratio of the number of model cars that Jim owns to the number of model cars Terrence owns is 8 : 6
This means that
Jim : Terrence = 8 : 6
Also from the question, we have
Terrence owns 36 models cars
This means that
Terrence = 36
Substitute the known values in the above equation, so, we have the following representation
Jim : 36 = 8 : 6
Multiply by 6
Jim : 36 = 48 : 36
So, we have
Jim = 48
Hence, the number of car is 48
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help!!!! It’s missing and I forgot to do but I need the answers 1-4 thank you so much your a life saver
Answers
2. y= -3x/4-5/2
3. x=8+y
4 I can’t really see it
what is the equation for the perpendicular bisector of the line segment whose endpoints are (-7, 2) and (-1,-6)
Answers
The equation of the perpendicular bisector of the line segment with endpoints (-7, 2) and (-1, -6) is y = (3/4)x + 1.
To find the equation of the perpendicular bisector of a line segment, we need to determine the midpoint of the line segment and the slope of the line segment. The perpendicular bisector will have a negative reciprocal slope compared to the line segment and will pass through the midpoint.
Given the endpoints (-7, 2) and (-1, -6), we can find the midpoint using the midpoint formula:
Midpoint = ((x1 + x2)/2, (y1 + y2)/2)
Midpoint = ((-7 + (-1))/2, (2 + (-6))/2)
= (-8/2, -4/2)
= (-4, -2)
The midpoint of the line segment is (-4, -2).
Next, we need to find the slope of the line segment using the slope formula:
Slope = (y2 - y1)/(x2 - x1)
Slope = (-6 - 2)/(-1 - (-7))
= (-6 - 2)/(-1 + 7)
= (-8)/(6)
= -4/3
The slope of the line segment is -4/3.
Since the perpendicular bisector has a negative reciprocal slope, the slope of the perpendicular bisector will be 3/4.
Now, we can use the midpoint (-4, -2) and the slope 3/4 in the point-slope form of a line to find the equation of the perpendicular bisector:
y - y1 = m(x - x1)
y - (-2) = (3/4)(x - (-4))
y + 2 = (3/4)(x + 4)
y + 2 = (3/4)x + 3
y = (3/4)x + 1.
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Has the marrying age of a man changed over the years? The United States Bureau of the Census takes a formal count of everyone in the U.S. every 10 years and has provided the following data that gives the median age of an American man at the time of his first marriage.
What does a rate of change of zero mean in this situation?
a.
The median age of a man at the time of his first marriage is, on the average, constant.
b.
The median age of a man at the time of his first marriage is, on the average, decreasing.
c.
The median age of a man at the time of his first marriage is, on the average, increasing.
d.
The rate of change cannot be zero in this situation.
ITs not D so dont say it if you dont know the answer dont reply i put up this post for those who need to get the answer because all other post are wrong.
Answers
For the given data the general trend is neither continuously rising nor falling. thus, the correct answer is option a: The median age of a man at the time of his first marriage is, on the average, constant.
How to calculate rate of change of mean?We can compute the rates of change by deducting the current year's median age from the prior year's median age. A result of zero denotes no change, a result of zero denotes no decline, and a result of one denotes an increase.
\(\text{Rate of Change} = Median\; Age (current \;year) - Median \;Age (previous \;year)\)
\(1910-1920: 24.6 - 25.1 = -0.5\\1920-1930: 24.3 - 24.6 = -0.3\\1930-1940: 24.3 - 24.3 = 0\\1940-1950: 22.8 - 24.3 = -1.5\\1950-1960: 22.8 - 22.8 = 0\\1960-1970: 23.2 - 22.8 = 0.4\\1970-1980: 24.7 - 23.2 = 1.5\\1980-1990: 26.1 - 24.7 = 1.4\\1990-2000: 26.8 - 26.1 = 0.7\\\)
The rates of change, as we can see, alternate between positive and negative values, but the general trend is neither continuously rising nor falling. Several times, the rate of change is zero, showing that, generally speaking, the median age of a man at the time of his first marriage is holding steady through time.
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HELP ASAP! Which of the following tables represents a linear function?
Table A -
x −2 −1 0 1 2
y 5 2 1 2 5
Table B -
x −2 −1 0 1 2
y 5 3 1 −1 −3
Table C -
x 3 3 0 3 3
y −2 −1 0 1 2
Table D -
x 0 1 2 3 4
y 0 −1 2 −3 4
Answers
Answer:
Table B -
x −2 −1 0 1 2y 5 3 1 −1 −3Step-by-step explanation:
You want to know which of the four offered tables represents a linear function.
DifferencesA linear function will have differences in y that have the same ratio to differences in x for all pairs of values in the table.
EvaluationTable A has x-differences that are 1 between adjacent terms. The y-differences are negative for the first pair of table values, but positive for the last pair (2 -5 vs 5 -2).
Table B has x-differences that are 1 between adjacent terms. The y-differences are -2 between any pair of adjacent terms, so their ratio to x-differences is -2/1 = -2, a constant. Table B represents a linear function.
Table C has x-differences that change from 0 to -3 to +3 while y-differences are constant at +1. The ratios of differences are not constant.
Table D has x-differences of +1, and y-differences that alternate in sign and magnitude.
Only Table B represents a linear function.
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solve the system using elimination 2x+3y=12 and 5x-y=13
Answers
The value of x and y for the equations 2x+3y=12 and 5x-y=13 will be 3 and 2 respectively.
What is the equation?An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.
It is given that, the equations are 2x+3y=12 and 5x-y=13.
We have to use the elimination method to solve the equations.
In order to eliminate the variable y multiply the first equation by 1 and the second equation by 3,
⇒(2x+3y=12) × 1
⇒(2x+3y=12) --------(1)
⇒(5x-y=13)×3
⇒15x-3y=39 ------- (2)
Add the equation 1 and 2,
2x+3y+15x-3y=12+39
17x+0=51
17x=51
x=51/17
x=3
Substitute the value of x we get, y=2.
Thus, the value of x and y for the equations 2x+3y=12 and 5x-y=13 will be 3 and 2 respectively.
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A contractor is purchasing some stone tiles for a new patio. Each cost $3 and he wants to spend less than $1200. The size of each tile is 1 square foot. Write an inequality that represents the number of tiles he can purchase with a $1200 limit, and then figure out how large the stone patio can be.
Answers
Answer:
4 0 0 s q. ft.Step-by-step explanation:
3x≤1200; 400 sq. ft.what is the mode following data set: 0.5, 0.3, 0.2, 0.9, 0.3, 0.5, 0.2, 0.3
Answers
Answer:
the mode is 0.3
Step-by-step explanation:
The mode of a data set is the number that occurs most frequently in the set. To easily find the mode, put the numbers in order from least to greatest and count how many times each number occurs. The number that occurs the most is the mode!
hope this helps!!!!!!!!
The mean breaking strength of a ceramic insulator must be at least 10 psi. The process by which this insulator is manufactured must show equivalence to this standard. If the process can manufacture insulators with a mean breaking strength of at least 9.5 psi, it will be considered equivalent to the standard. A random sample of 50 insulators is available, and the sample mean and standard deviation of breaking strength are 9.32 psi and 0.21 psi, respectively. a. State the appropriate hypotheses that must be tested to demonstrate equivalence.
Answers
Answer:
H0: u ≥ 9.5
Ha: u < 9.5
Step-by-step explanation:
The null hypothesis and the alternate hypothesis are reverse of each other.
The claim is either set as the null or alternate hypothesis
The null hypothesis is : H0: u ≥ 9.5 the mean breaking strength of a ceramic insulator is at least 9.5 which is considered equivalent to the standard.
The alternate hypothesis is: Ha: u < 9.5 the mean breaking strength of a ceramic insulator is less than 9.5 which is not considered equivalent to the standard.
PLS QUICK How did the mountainous geography of Athens influence the economy?
The people of Athens mined gold for trade.
The people of Athens were unable to raise any crops.
The people of Athens focused on the military to protect their region.
The people of Athens relied on sea trade.
Answers
Option D. The mountainous geography of Athens influence the economy as The people of Athens relied on sea trade.
How did the terrain of Athens influence the economy ?Greece's rugged terrain caused some areas, particularly Athens, to become dependent on trade. Many Greeks went on to become seafaring tradesmen and merchants. Greeks engaged in trade with other Mediterranean people for pottery, wine, and olive oil. They communicated with the outside world by sailing to neighboring islands.
The geography of the area influenced the ancient Greeks' political system and way of life. Mountains, seas, and islands formed natural barriers between the Greek city-states, forcing the Greeks to relocate to coastal areas.
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Enter "y" or "n" to tell which value of x that make each equation or inequality true.
Answers
Answer:
First row (2x + 5 = 9) is N Y N
Second row (2x + 5 < 9) is Y N Y
Third Row (2x+ 5 _< 9) is N Y Y
Brad buys a jacket that is on sale for 30% off the original price.The expression p - 0.3p can be used to find the sale price of the jacket, where p is the original price of the jacket. If the original price of the jacket is $80, what is the sale price?
Answers
Answer:
$56
Step-by-step explanation:
The jacket is on sales for 30% off the original price = (0.3)
The original price (P) = $80
However, the expression "p - 0.3p" is to be used to find the sales price
The sale price = p - 0.3p
The sale price = $80 - 0.3($80)
The sale price = $80 - $24
The sale price = $56
A point-slope form of a line that has a slope of 4 and goes through (2, 1) is...
Answers
Answer:
\( \huge \orange{y - 1 =4(x - 2) } \\ \)
Step-by-step explanation:
To find an equation of a line in point slope form when given the slope and a point we use the formula
\(y - y_1 = m(x - x_1)\)
From the question we have the final answer as
\(y - 1 = 4(x - 2)\)
Hope this helps you
PLEASE HELP!!!
Triangle ABC has vertices at A(-5,2), B(1,3), and C(-3,0). Determine the coordinates of the vertices for the image of the pre image is translated 4 units right.
A. A’(-9,2),B’(-3,3), C’(-7,0)
B. A’(-4,6),B’(0,7),C’(1,0)
C. A’(-1,2),B’(5,3),C’(1,0)
D. A’ (-5,-2), B’(-1,-1), C’(-3,-4)
Answers
The coordinates of the vertices for the image of the pre image is translated 4 units right are: ’(-1, 2), B’(5, 3), and C’(1, 0).
What is translation on a coordinate plane?Translation on the coordinate plane is sliding a point or figure in any direction without any changes in size or shape.
During translation, the coordinates of the vertices of a figure or point change, and they slide left or right, up, or down without changing size or shape.
Given the question above, we need to find the coordinates of the vertices for the image of the pre image that are translated 4 units right.
So,
\(\rightarrow\sf \boxed{\boxed{-5+4=1=\bold{(-1,2)}}}\)
\(\rightarrow\sf \boxed{\boxed{1+4=5=\bold{(5,3)}}}\)
\(\rightarrow\sf \boxed{\boxed{-3+4=1=\bold{(1,0)}}}\)
Thus, the coordinates of the vertices for the image of the pre image is translated 4 units right are: ’(-1, 2), B’(5, 3), and C’(1, 0).
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A mathematical model is a simplified description of a system or a process. In your opinion, how are mathematical models helpful? What are the advantages and disadvantages of using a model? In what ways are mathematical models linked to the fields of chemistry, biology, and physics? Cite several examples.
Answers
Given statement solution is :- Mathematical models are extremely valuable tools in various fields, including chemistry, biology, and physics. They offer several advantages: Simplification and abstraction, Prediction and simulation, Cost and time efficiency, Insight and understanding.
Mathematical models are extremely valuable tools in various fields, including chemistry, biology, and physics. They offer several advantages:
Simplification and abstraction: Mathematical models allow complex systems or processes to be represented using simplified mathematical equations or algorithms. This simplification helps in understanding the underlying principles and relationships of the system, making it easier to analyze and predict outcomes.
Prediction and simulation: Models enable scientists to make predictions about the behavior of a system under different conditions. They can simulate scenarios that are difficult or impossible to observe in the real world, allowing researchers to explore various hypotheses and make informed decisions.
Cost and time efficiency: Models can be used to explore different scenarios and test hypotheses in a relatively quick and cost-effective manner compared to conducting real-world experiments. They can help guide experimental design by providing insights into the most relevant variables and parameters.
Insight and understanding: Mathematical models often reveal underlying patterns and relationships that may not be immediately apparent from experimental data alone. They provide a framework for organizing and interpreting data, leading to a deeper understanding of the system being studied.
However, mathematical models also have limitations and potential disadvantages:
Simplifying assumptions: Models are based on assumptions and simplifications, which may not fully capture the complexity of the real-world system. If these assumptions are incorrect or oversimplified, the model's predictions may be inaccurate or misleading.
Uncertainty and error: Models are subject to uncertainties and errors stemming from the inherent variability of the system, limitations in data availability or quality, and simplifying assumptions. It is crucial to assess and communicate the uncertainties associated with model predictions.
Validation and verification: Models need to be validated and verified against experimental data to ensure their accuracy and reliability. This process requires rigorous testing and comparison to real-world observations, which can be challenging and time-consuming.
Mathematical models are closely linked to the fields of chemistry, biology, and physics, providing valuable insights and predictions in these disciplines. Here are some examples:
Chemistry: Mathematical models are used to study chemical reactions, reaction kinetics, and molecular dynamics. One example is the use of rate equations to model the kinetics of a chemical reaction, such as the reaction between reactants A and B to form product C.
Biology: Mathematical models play a crucial role in understanding biological systems, such as population dynamics, gene regulation, and the spread of infectious diseases. For instance, epidemiological models like the SIR (Susceptible-Infectious-Recovered) model are used to simulate and predict the spread of diseases within a population.
Physics: Mathematical models are fundamental in physics to describe physical phenomena and predict outcomes. One well-known example is Newton's laws of motion, which can be mathematically modeled to predict the motion of objects under the influence of forces.
Quantum mechanics: Mathematical models, such as Schrödinger's equation, are used to describe the behavior of particles at the quantum level, providing insights into atomic and molecular structures and the behavior of subatomic particles.
Fluid dynamics: Mathematical models, such as the Navier-Stokes equations, are employed to study the behavior of fluids, including airflow, water flow, and weather patterns.
These examples demonstrate the wide range of applications for mathematical models in understanding, predicting, and simulating various phenomena in the fields of chemistry, biology, and physics.
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17 The table below shows the distance a car has traveled.
50
20
f
40
Minutes
Distance
Traveled
(in miles)
What is the meaning of the slope of the linear model for the data?
60
100
a) The car travels 5 miles every minute.
b) The car travels 4 miles every minute.
c) The car travels 4 miles every 5 minutes.
d) The car travels 5 miles every 4 minutes.
125
80
100
Answers
Given statement solution is :- None of the given options (a, b, c, or d) match the meaning of the slope. The correct interpretation is that the car travels approximately 0.8 miles every minute.
To determine the meaning of the slope of the linear model for the given data, let's analyze the information provided. The table represents the distance traveled by a car at different time intervals.
Minutes | Distance Traveled (in miles)
50 | 20
20 | f
40 | 60
100 | a
125 | 80
100 | 100
To find the slope of the linear model, we need to calculate the change in distance divided by the change in time. Let's consider the intervals where the time changes by a fixed amount:
Between 50 minutes and 20 minutes: The distance changes from 20 miles to 'f' miles. We don't have the exact value of 'f', so we can't calculate the slope for this interval.
Between 20 minutes and 40 minutes: The distance changes from 'f' miles to 60 miles. Again, without knowing the value of 'f', we can't calculate the slope for this interval.
Between 40 minutes and 100 minutes: The distance changes from 60 miles to 'a' miles. We don't have the exact value of 'a', so we can't calculate the slope for this interval.
Between 100 minutes and 125 minutes: The distance changes from 'a' miles to 80 miles. Since we still don't have the exact value of 'a', we can't calculate the slope for this interval.
Between 125 minutes and 100 minutes: The distance changes from 80 miles to 100 miles. The time interval is 25 minutes, and the distance change is 100 - 80 = 20 miles.
Therefore, based on the given data, we can conclude that the car travels 20 miles in 25 minutes. To determine the meaning of the slope, we divide the distance change by the time change:
Slope = Distance Change / Time Change
= 20 miles / 25 minutes
= 0.8 miles per minute
So, none of the given options (a, b, c, or d) match the meaning of the slope. The correct interpretation is that the car travels approximately 0.8 miles every minute.
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How many natural numbers are between 34 and 72? and, how many whole numbers between -2 and 25?
Answers
Answer:
There are 37 natural numbers between 34 and 72.
There are 25 whole numbers between -2 and 25.
Step-by-step explanation:
1. Natural numbers between 34 and 72
2. Whole numbers between -2 and 25
1.35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71.
2.0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24.
Which of these ordered pairs is a solution to the inequality?
1/4x ≤ 7/3y +2
Responses
A (80, 6)
B (48, 9)
C (40, 3)
D (2, –6)
Please show step by step as I need to learn how to do these problems. Thank you
Answers
Answer: D
Step-by-step explanation:
To determine which ordered pair is a solution to the inequality, we can substitute the values of x and y into the inequality and check if it is true.
Let's start with ordered pair A (80, 6):
1/4x ≤ 7/3y + 2
1/4(80) ≤ 7/3(6) + 2
20 ≤ 14 + 2
20 ≤ 16
This is not true, so ordered pair A is not a solution to the inequality.
Now let's try ordered pair B (48, 9):
1/4x ≤ 7/3y + 2
1/4(48) ≤ 7/3(9) + 2
12 ≤ 21 + 2
12 ≤ 23
This is also not true, so ordered pair B is not a solution to the inequality.
Next, let's try ordered pair C (40, 3):
1/4x ≤ 7/3y + 2
1/4(40) ≤ 7/3(3) + 2
10 ≤ 7 + 2
10 ≤ 9
This is false, so option C is not a solution to the inequality.
Finally, we have option D: (2, -6)
1/4(2) ≤ 7/3(-6) + 2
1/2 ≤ -14 + 2
1/2 ≤ -12
This is true, so option D is a solution to the inequality.
Therefore, the answer is D: (2, -6).
In the diagram, the parallel lines are cut by transversal BC−→−.If BD−→− bisects ∠ABC and m∠3 = 80, what is m∠ABD?
Answers
The value of m ∠ABD will be;
⇒ ∠ ABD = 50°
What are Parallel lines?Parallel lines are those lines that are equidistance from each other and never intersect each other.
Given that;
In the diagram, the parallel lines are cut by transversal BC.
And, BD bisects ∠ABC and m∠3 = 80.
Now,
Since, The parallel lines are cut by transversal BC.
Hence, We get;
⇒ ∠ 3 + ∠ 2 = 180°
⇒ 80° + ∠ 2 = 180°
⇒ ∠ 2 = 180 - 80
⇒ ∠ 2 = 100
And, We have;
⇒ ∠ 2 = ∠ ABC
⇒ ∠ ABC = 100°
Since, BD bisects ∠ABC.
Hence, We get;
⇒ ∠ ABD = 100 / 2
⇒ ∠ ABD = 50°
Thus, The value of m ∠ABD = 50°
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When blood flows along a blood vessel, the flux F (the volume of blood per unit time that flows past a given point) is proportional to the fourth power of the radius R of the blood vessel. F = kR4 (This is known as Poiseuille's Law; we will show why it is true in Section 8.4.) A partially clogged artery can be expanded by an operation called angioplasty, in which balloon-tipped catheter is inflated inside the artery in order to widen it and restore the normal blood flow Show that the relative change in F is about four times the relative change in R; kR4 dF k(4r3) dR k(kR3 ) kR4 dR dR How will a 5% increase in the radius affect the flow of blood? A 5% increase in the radius corresponds to a/an X increase in blood flow.
Answers
When blood flows along a blood vessel, the amount of blood flowing at a certain point per unit time is called flow F. The 5% increase in the radius affect the flow of blood by 21.55% approximately.
In mathematics, two sets of numbers (usually experimental data) are proportional, or directly proportional, if their corresponding elements have a constant ratio, called the proportionality coefficient or proportionality constant. Two series are inversely proportional if the corresponding elements have a constant product (also called proportionality coefficient).
Directly proportional and inversely proportional relationship:
Let there are two variables p and q.
Then, p and q are said to be directly proportional to each other if
p = k× q
where,
k is some constant number called constant of proportionality.
This directly proportional relationship between p and q is written as
p ∝ q, where that middle sign is the sign of proportionality.
In a directly proportional relationship, increasing one variable will increase another.
Now let m and n are two variables.
Then m and n are said to be inversely proportional to each other if
m = c/ n
⇒ n = c/m (both are equal)
where c is a constant number called constant of proportionality.
This inversely proportional relationship is denoted by
m ∝ 1/n
⇒ n ∝ 1/m
As visible, increasing one variable will decrease the other variable if both are inversely proportional.
For this case, we're given that:
Flux F = k.R⁴ (R being the radius of the blood vessel).
Let the increment in radius be of , and let corresponding increment in flux be of δF
Then we see:
F + δF = k( R+δR)
⇒ δF = k{4R³ ×δR + 6R²× (δR)² + 4R × (δR)³ + (δR)⁴}
This is the relative increment in F from relative increment in value of R
If 5% increment happens, that means we have: δR = R×5/100
= R×20
Thus, we get:
δF = k{4R³ ×δR + 6R²× (δR)² + 4R × (δR)³ + (δR)⁴}
⇒ δF = k{ 4R²×(R/20) + 6R² × (R/20)² +4R × (R/20)³ + (R/20)⁴}
⇒ δF = kR⁴{4/20 + 6/400 + 4/8000+ 1/160000}
⇒ δF = F( 0.21550625)
Its percent with respect to F is x% (say) then:
F× X/100 = F( 0.21550625)
x ≈ 21.55%
Thus, the 5% increase in the radius affect the flow of blood by 21.55% approximately.
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Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
A right rectangular prism has a length of 15 millimeters, width of 3 millimeters, and height of 4 millimeters.
What is the surface area of the prism?
Answers
Answer:
Surface area of the rectangular prism = 234 mm²
Step-by-step explanation:
Length of a right rectangular prism = 15 mm
Width of the rectangular prism = 3 mm
Height of the rectangular prism = 4 mm
Surface area of the rectangular prism = 2(lb + bh + hl)
Here, l = length of the prism
b = Width of the prism
h = Height of the prism
By substituting values in the given formula,
Surface area = 2(15×3 + 3×4 + 15×4)
= 2(45 + 12 + 60)
= 2(117)
= 234 mm²
A pair of Sneakers cost $112 after it was marked up by 75%. How much
did it cost before the mark up?
Answers
Question
A pair of Sneakers cost $112 after it was marked up by 75%. How much
did it cost before the mark-up?
Answer
Divide the gross profit by the cost and multiply by 100 to calculate your percentage markup. In the example, divide $75 by $100 which equals $0.75, and multiply by 100 to give you 75 percent. Your markup on cost price is 75 percent.
Therefore, the answer would be (196)
Answer:
i believe the answer would be $448
Step-by-step explanation:
hopefully this helps :)
have a nice day !!
**please let me know if this was wrong**
A reporter for a local television station visits the city's new upscale shopping mall the day before Christmas to interview shoppers. He questions the first 25 shoppers he meets outside one of department stores at the mall. He asks them whether their overall feelings about Christmas shopping are positive, neutral, or negative. re Select the reason(s) why it may be risky to act as if the first 25 shoppers at this particular location are an SRS of all shoppers in the city. Shoppers at the mall the day before Christmas does not guarantee every shopper in the population has an equal chance to be in the sample Surveying shoppers the day before Christmas is a convenience sample, so it is a simple random sample Surveying shoppers at the mall the day after Christmas may not be a good represenation of all shoppers in the city. Having the reporter ask questions is not a double-blind study.
Answers
The correct option is A shopping center surveys conducted the day before Christmas do not guarantee that every shopper in the population will be included in the sample.
Given that,
The day before Christmas, a reporter from a nearby television station goes to the city's brand-new, upmarket retail center to speak with customers. The first 25 customers he encounter outside one of the mall's department stores are questioned. He inquires as to whether they have a positive, neutral, or negative overall opinion of Christmas shopping.
We have to select the correct option why it might be dangerous to assume that the first 25 customers at this store are representative of all customers in the city.
We know that,
A non-probability sampling technique called convenience sampling includes taking a sample from the nearest area of the population. It is a convenience sample because the reporter in the scenario asked the first 25 people he saw outside one of the department stores at the mall. Each candidate does not have an equal chance of being included in the convenience sample.
The right response is option (A): Shopping center surveys conducted the day before Christmas do not guarantee that every shopper in the population will be included in the sample.
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