1. If g(20)= 35 and g'(20)=-2, estimate the value of g(22). 2. If g(1)=-17 and g'(1)=5, estimate the value of g(1.2). 3. Use the Tangent Line Approximation to estimate the cube root of 9. 4. Use the Tangent Line Approximation to estimate the fifth root of 30.
Answers
1. If g(20) = 35 and g'(20)= -2, in this case we can use the first-order Taylor approximation method to estimate the value of g(22) which is 31.
We can use the information provided in the problem to estimate the value of g(22), which contains the values of g(20) and g'(20). We know that g'(20) equals -2 as the derivative of g(x) for x = 20.
A differentiable function g(x)'s first-order Taylor approximation about x = a is:
g(x) = g(a) + g'(a) (x-a)
When we use this formula with a=20
g(a) = g(20) = 35
g'(a) = g'(20) = -2
x=22
we get:
g(22) ≈ g(20) + g'(20) (22-20)
≈ 35 + (-2) (2) ≈ 31
g(22) ≈ 31
As a result, the value of g(22) is estimated to be 31.
2. If g(1)= -17 and g'(1)= 5, in this case we can use the first-order Taylor approximation method to estimate the value of g(1.2) which is -16.
We can use the information provided in the problem to estimate the value of g(1.2), which contains the values of g(1) and g'(1). We know that g'(1) equals 5 and is the derivative of g(x) at x = 1.
We may use the following formula to get g(1.2):
g(x) = g(a) + g'(a) (x-a)
g(1.2) ≈ g(1) + g'(1) * (1.2 - 1)
We may use the numbers supplied in the problem to replace g(1) = -17 and g'(1) = 5 in the formula above:
g(1.2) ≈ -17 + 5 * (1.2 - 1)
When we simplify the equation, we get;
g(1.2) ≈ -17 + 5 * 0.2
g(1.2) ≈ -17 + 1
g(1.2) ≈ -16
As a result, based on the information provided in the issue, we may estimate that g(1.2) is about equivalent to -16.
3. The Tangent Line Approximation method is used to estimate the cube root of numbers. By using this method it gives us the value of cube root of 9 which is 2.08.
To estimate the cube root of 9 using the tangent line approximation, we must first identify a point around 9 as our starting point. Let's go with 8 because it's a perfect cube and near 9.
We want to approximate the function f(x) = ∛x, which gives us the cube root of x. Taking the derivative, we can derive the equation of the tangent line to this function at x = 8.
f(x)= f'(a) (x-a) + f(a)
f(x) = ∛x
f'(x) = (1/3)x^(-2/3)
At x = 8, the derivative is:
f'(a) = f'(8) = (1/3)(8)^(-2/3) = 1/12
f'(a) = 1/12
So the equation of the tangent line at x = 8 is:
f(x) ≈ 1/12 (x - 8) + 2
Now we can use this tangent line to approximate the value of f(x) at x = 9:
f(9) ≈ 1/12 (9 - 8) + 2
≈ 1/12(1) + 2
≈ 1/12 + 2
f(9) ≈ 25/12 = 2.083333
f(9) ≈ 2.083333
∛9 ≈ 2.08
Therefore, using the tangent line approximation, we estimate the cube root of 9 to be approximately 2.08.
4. The Tangent Line Approximation to estimate the fifth root of of numbers. By using this method it gives us the value of fifth root of 30 which is 1.975.
To estimate the fifth root of 30, we must first identify a function that approximates the fifth root of x near x=30, and then use the tangent line to that function at x=30 to estimate the value. We take 2, because the nearest fifth root is 32.
f(x)= f'(a) (x-a) + f(a)
f(a) = \(\sqrt[5]{a}\)
f'(a) = 1/(5\(\sqrt[5]{a^{4} }\))
a = 32
f(a) = \(\sqrt[5]{32}\) = 2
f'(a) = 1/ (5\(\sqrt[5]{32^{4} }\)) = 1/80
Therefore, substituting the values in the equation.
f(30) = f(32) + f'(32)(30-32)
\(\sqrt[5]{30}\) = 2 + (1/80) (-2)
= 2 - (1/40) = 79/40
f(30) ≈ 1.975
\(\sqrt[5]{30}\) ≈ 1.975
Therefore, using the tangent line approximation, we estimate the fifth root of 30 to be approximately 1.975.
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Related Questions
What is the value of x?
Answers
Answer:
x = 68
Step-by-step explanation:
pls mark me as brainliest !!
Are composite numbers closed under multiplication
Answers
Answer:
Remember that for a subset of a ring to be an ideal it must be closed under addition and under taking multiples by elements of the ring, and in this case the set of all composite integers is not closed under addition.
Step-by-step explanation:
please help it's urgent
0.75x9
Answers
Answer:
6.75
Step-by-step explanation:
0.75 x 9 = 6.75
If it's not right, sorry!
I'm pretty sure it is though!
1. A study is made to see if increasing the substrate concentration has an appreciable effect on the velocity of a chemical reaction. With a substrate concentration # 1, the reaction was run 15 times with an average velocity of 7. 5 micromoles per minutes and a standard deviation of 1. 5 with a substrate concentration #2, 12 runs were made, yielding an average velocity of 8. 8 micromoles per minutes and a sample standard deviation of 1. 2. Is there any reason to believe concentration #2 causes an increase in the mean velocity over concentration #1? use 0-0. 05 level of significance and assume the populations to be approximately normal distribution with equal variance. Instructions 1. Hypothesis.
Answers
There is not enough evidence
What is standard deviation ?An indicator of how much a group of numbers vary or are dispersed is the standard deviation. [1] When the standard deviation is low, the values are more likely to fall within a narrow range, also known as the expected value, whereas when the standard deviation is high, the values tend to be closer to the mean.
For 1.5 moles substrate concentration per liter
Reaction ( n2 ) = 15 runs
average velocity ( x2 ) = 7.5 micromoles per 30 minutes
standard deviation ( s2 ) = 1.5
For 2.0 moles substrate concentration per liter
Reaction( n1 ) = 12 runs
(x1) = 8.8 micromoles on average per 30 minutes
standard deviation ( s1 ) = 1.2
Show Reason to believe that this increase in substrate conc causes an increase in mean velocity
Hypothesis test
H0 : μ1 - μ2 = 0.5
H1 : μ1 - μ2 > 0.5
significance level ( ∝) = 0.01
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the diagram shows triangle ABC. D is on the point AB such that CD is perpendicular to AB. AC=9.4cm, AD=5.2cm and BD=7.8cm. Work out the size of angle ABC.
Answers
Answer:
45°
Step-by-step explanation:
Triangles ADC and BDC are right triangles, since CD⊥AB.
Use Pythagorean to find the length of CD:
CD² + AD² = AC²CD² + 5.2² = 9.4²CD² = 9.4² - 5.2²CD² = 61.32CD = √61.32CD = 7.83Use trigonometry to find the angle ABC:
tan (∠ABC) = CD/BDtan (∠ABC) = 7.83/7.8tan (∠ABC) = 1.0 (rounded)m∠ABC = arctan 1m∠ABC = 45°Find the equation for the plane through perpendicular to the following line. x, y, z, t
Answers
The equation of the plane is ⟨0, 0, -xt, -y⟩. ⟨(x-1), y, z, t⟩ = 0.
Given that the equation for the line is x, y, z, t.
The equation for the plane perpendicular to the given line can be calculated as follows:
Firstly, we know that the vector which is perpendicular to both the line and the plane is the direction of the plane.
Hence the direction of the plane is the cross product of the vector with the given line direction:⟨1, 0, 0, 0⟩ × ⟨x, y, z, t⟩= ⟨0t - 0z, 0z - 0t, 0y - xt, 0x - y⟩= ⟨0, 0, -xt, -y⟩Hence the direction of the plane is ⟨0, 0, -xt, -y⟩.
Now, we need to find any point (x0, y0, z0, t0) on the plane.
Let's assume that the point is (1, 0, 0, 0) since it lies on the line.
Then the equation of the plane can be obtained as:⟨0, 0, -xt, -y⟩ .
⟨(x-x_0), (y-y_0), (z-z_0), (t-t_0)⟩ = 0⟨0, 0, -xt, -y⟩ . ⟨(x-1), y, z, t⟩ = 0
The equation of the plane perpendicular to the line x, y, z, t is given as ⟨0, 0, -xt, -y⟩. ⟨(x-1), y, z, t⟩ = 0.
Therefore, the equation of the plane is ⟨0, 0, -xt, -y⟩. ⟨(x-1), y, z, t⟩ = 0.
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Find the area of the irregular polygon to the right show all work
Answers
Solution:
We are given an irregular pentagon. To calculate the area, we will have to break the pentagon into component shapes
We can break the pentagon into a trapezium and a triangle
The dimensions of the trapezium are :
1st base = 3 units
2nd base = 4 units
Height = 3 units
\(\begin{gathered} Area\text{ of the trapezium = }\frac{1}{2}(a+b)h \\ =\frac{1}{2}(3+4)(3) \\ =10.5\text{ square unit} \end{gathered}\)The dimensions of the triangle are:
Base= 4 units
Height=2 units
\(\begin{gathered} Area\text{ of the triangle = }\frac{1}{2}\text{ x base x height} \\ =\frac{1}{2}\text{ x 4 x 2} \\ =4\text{ square units} \end{gathered}\)Area of the polygon = area of trapezium + area of triangle
= 10.5 square unit + 4 square unit = 14.5 square unit
The answer is 14.5 square units
An union representative studies the weekly income for a senior level worker position in an automobile industry. It is obtained that a 95% confidence interval for the mean weekly income of all employees of the same senior position is ($1371, $1509). Which one of the following interpretations of this interval is correct?
A.
We conclude that 95% of all employees from the this position have income between $1371 and $1509 per week.
B.
We can 95% confident that the sample mean is between $1371 and $1509.
C.
If random samples of nine employees were repeatedly selected from the population of all employees from the this position, then 95% of the time the sample mean income would be between $1371 and $1509.
D.
If random samples of nine employees were repeatedly selected from the population of all employees from the this position, then 95% of the time the population mean income would be between $1371 and $1509.
Answers
C. If random samples of nine employees were repeatedly selected from the population of all employees from this position, then 95% of the time the sample mean income would be between $1371 and $1509.
This interpretation refers to the concept of a confidence interval, which gives a range of values within which the true population mean is likely to fall. In this case, the interval ($1371, $1509) was obtained from a sample of data and suggests that the true mean weekly income for all senior level workers in the automobile industry is likely to be within this range with 95% confidence. Option A is incorrect as it implies that all employees in this position have income within this range, which is not necessarily true. Option B is incorrect as it only refers to the sample mean, not the population mean. Option D is incorrect as it refers to the population mean, which cannot be determined from a sample alone.
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Can someone please help me with this problem. I will give brainliest!
Write the equation of the line that is perpendicular to the y-axis and passes through the point (-4, 5).
Answers
Explanation:
The y axis is vertical. Anything perpendicular to this is horizontal.
All horizontal linear equations are of the form y = k, where k is any number.
In this case, k = 5 so that the line y = 5 goes through all points with y coordinate 5. Two points on this line are (-4,5) and (1,5).
Note how y = 5 is equivalent to y = 0x+5. We see the slope is 0 and the y intercept is 5. Compare this to y = mx+b.
8. The diameter of a circle is 40 m. Find the area of the circle in terms of pi.
Answers
Answer:
Step-by-step explanation:
To find the area of the circle use the formula pi r^2, r is the radius, so half the diamiter. D/2 = 20.
Now we use pi r^2 = pi * 400
So answer is A.
Answer:
Option A 400x m²
Step-by-step explanation:
We know that the diameter of a circle is double of the radius.
So the radius will be 40/2 m = 20 m i.e half of the diameter.
According to the question let the pi be x.
Area of a circle
πr²
= x×20m×20m
= 400x m²
Hence option A is correct.
what is the value of the 5th term
Answers
First term (a1) = -7
Second term (a2) = -2
Common difference: a2 - a1 = -2-(-7) = 5
Hence, Fifth term = a1 + 4d = -7 + 4(5) = 13
Duval had 7/8 quart of milk. He used 1/6 quart for a recipe. How much milk does Duval have left? Show your work.
Answers
Answer:
He has 7/48 left.
Step-by-step explanation:
7/8 X 1/6
In which polygon the number of diagonals is equal with the number of sides
a) pentagon
b) hexagon
c) octagon
d) something else
Answers
Solving linear equations
-12y = 108
Answers
Answer:
Step-by-step explanation:
-12y/-12=108/-12
y=-9
What is the angle between the vectors A---> and - A__>when these vectors are drawn from a common origin?
A) 270°
B) 0°
C) 90°
D) 360°
E) 180°
Answers
Answer:
it is E) 180
Step-by-step explanation:
The angle between the vectors i^ and -i^ is 180 degrees. (E)
The angle between two vectors can be calculated using the dot product formula and the magnitude of the vectors.
The dot product of two vectors a and b is given by a · b = ||a|| ||b|| cos(θ), where θ is the angle between the vectors and ||a|| and ||b|| are the magnitudes of the vectors a and b. In this case, the vectors i^ and -i^ are unit vectors (i.e., their magnitude is 1), and they are pointing in opposite directions.
Hence, the dot product of these vectors is i^ · -i^ = -1, and the cosine of the angle between the vectors is -1 / (1 * 1) = -1. The cosine function maps the range [-1, 1] to the range [0, 180] degrees, and cos(180) = -1. Hence, the angle between the vectors i^ and -i^ is 180 degrees.
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Complete question :
What is the angle between the vectors i^and - i^ when these vectors are drawn from a common origin?
9) 10) 2 20+40. = 60 180-60 = 120 20° 40° 120+40+20 = 180 x = 120I was asked to find the place where there is a question mark which can also be x
Answers
The missing side = 21°
Explanation:The sum angles in a triangle is 180°
angles in the larger triangle:
20° + 40° + the third angle = 180°
60° + third angle = 180°
third angle = 180 - 60
third angle = 120°
When two lines cross, their opposite angles are equal. The colours in green are vertical angles. The opposite angle to the third angle we got will also be 120°
The sum of angles in the smaller triangle
120 + 39 + the missing side = 180
159 + the missing side = 180
The missing side = 180 - 159
The missing side = 21°
Shawna is conducting a study in her cognitive psychology lab about people's ability to
remember rhythms. She played a short rhythm to 125 randomly chosen people. One minute
later, she asked them to repeat it by clapping. She counted the number of people who could
repeat the rhythm correctly.
Repeated rhythm correctly People
40
85
yes
no
Find a 99% confidence interval for p, the proportion of people who cannot repeat the rhythm
after one minute.
Round your answers to the nearest thousandth.
Answers
The 99% confidence interval for the proportion of people who cannot repeat the rhythm after one minute is (0.85, 0.976).
What is rhythm?Rhythm is the pattern of regular or irregular pulses or beats in music or poetry. It is the underlying structure in music, the beat or pulse that provides the framework for a musical composition. It is also the sense of movement created by the alternation of different sounds and silences. Rhythm can be described as a fundamental element of all forms of music and art, as it is the primary way in which music is perceived and experienced.
This can be calculated using the following formula:
p ± (Z *√( p * (1- p ) ) /√n )
Where:
p = sample proportion = 85/125 = 0.68
Z = z-score for 99% confidence interval = 2.575
n = sample size = 125
The 99% confidence interval for the proportion of people who cannot repeat the rhythm after one minute is (0.85, 0.976).
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The 99% confidence interval for the proportion of people who cannot repeat the rhythm after one minute is (0.783, 0.577).
What is confidence interval?A confidence interval is the mean of an estimate minus the variability of that estimate. This is the range of values within which the estimate will fall within a certain level of confidence when the test is repeated. Confidence is an alternative way of expressing probability in statistics.
This can be calculated using the following formula:
p ± (Z ×√( p × (1- p ) ) /√n )
Where:
p = sample proportion
p = 85/125
p = 0.68
Z = z-score for 99% confidence interval
Z = 2.575
n = sample size
n = 125
Now, substitute the values:
0.68 ± (2.575 ×√( 0.68 × (1- 0.68 ) ) /√125 )
For 0.68 + (2.575 ×√( 0.68 × (1- 0.68 ) ) /√125 )
= 0.783
For 0.68 - (2.575 ×√( 0.68 × (1- 0.68 ) ) /√125 )
= 0.577
The 99% confidence interval for the proportion of people who cannot repeat the rhythm after one minute is (0.783, 0.577).
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Given: F = {(0, 1), (2, 4), (4, 6), (6, 8)} and G = {(2, 5), (4, 7), (5, 8), (6, 9), (7, 5)}
Find the common domain of F and G.
{2, 4, 6}
{1, 4, 6, 8}
{0, 2, 4, 6}
Answers
Answer:
A. {2, 4, 6}----------------------
Domain is the set of the first points of ordered pairs.
The domain of F is:
{0, 2, 4, 6}and the domain of G is:
{2, 4, 5, 6, 7}The common domain of the both sets is:
{2, 4, 6}This is matching the option A.
{x: x belongs to N and (x-1)(x-2) = 0}, finite set or infinite set?
Answers
Explanation:
We have a set of x values such that (x-1)(x-2) = 0. Breaking that down leads to either x-1 = 0 or x-2 = 0 through the zero product property. Solving each of those equations gets us x = 1 and x = 2 as the two items in this set.
So the original set your teacher gave you turns into the roster form {1,2}. There are two items in this set and we can see it's a finite set since it does not go on forever. Note that everything in this set is a natural number.
An engineer created a scale drawing of a building using a scale in which 0.25 inch represents 2 feet. The length of the actual building is 120 feet. What is the length in inches of the building in the scale drawing? Record your answer in the box below.
Answers
Answer:
15 in--------------------
The scale is given:
0.25 in ⇒ 2 feetThe length of the actual building is 120 feet, it is 60 times the 2 in, hence the length of the building in the drawing will be 60 times greater than the corresponding part of the scale:
0.25 in x 60 = 15 inFor a reverse mortgage with:
20-year term
loan amount $200,000
Interest rate 8%
There is no origination fee
If the origination fee is $4,000, what is the effective cost if the senior lives out the entire loan?
12.45%
7%
8.88%
16.23%
Answers
The effective cost of the reverse mortgage if the senior lives out the entire loan is 12.45%.
The effective cost, or the total cost of the reverse mortgage if the senior lives out the entire loan, can be calculated as follows:
The answer is 8.88%.
To calculate the effective cost, we need to consider the interest rate and the origination fee. Since the given scenario states that there is no origination fee, we can ignore it for this calculation.
The interest rate is 8%, which means that the loan balance will increase by 8% per year. Over a 20-year term, we need to calculate the total compounded interest on the initial loan amount of $200,000.
Using the compound interest formula, we can calculate the total cost as follows:
Total Cost = Loan Amount * (1 + Interest Rate)^Number of Years
Total Cost = $200,000 * (1 + 0.08)^20
Total Cost ≈ $200,000 * 4.66096
Total Cost ≈ $932,192
Therefore, the effective cost of the reverse mortgage if the senior lives out the entire loan is approximately $932,192.
To determine the effective cost as a percentage, we can calculate the percentage increase in the loan balance over the loan term:
Percentage Increase = (Total Cost - Loan Amount) / Loan Amount * 100
Percentage Increase = ($932,192 - $200,000) / $200,000 * 100
Percentage Increase ≈ $732,192 / $200,000 * 100
Percentage Increase ≈ 366.096%
Thus, the effective cost as a percentage is approximately 366.096%.
However, if the given options for the answer are limited to 12.45%, 7%, 8.88%, and 16.23%, the closest option to the actual effective cost of approximately 366.096% is 8.88%.
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What is the slope of the line X+ Зу = 10
Answers
Answer:
\(-\frac{1}{3}\) is the slope
Step-by-step explanation:
Slope intercept form: \(y=-\frac{1}{3}x+\frac{10}{3}\)
After heating up in a teapot, a cup of hot water is poured at a temperature of
20
3
∘
203
∘
F. The cup sits to cool in a room at a temperature of
6
9
∘
69
∘
F. Newton's Law of Cooling explains that the temperature of the cup of water will decrease proportionally to the difference between the temperature of the water and the temperature of the room, as given by the formula below:
�
=
�
�
+
(
�
0
−
�
�
)
�
−
�
�
T=T
a
+(T
0
−T
a
)e
−kt
�
�
=
T
a
= the temperature surrounding the object
�
0
=
T
0
= the initial temperature of the object
�
=
t= the time in minutes
�
=
T= the temperature of the object after
�
t minutes
�
=
k= decay constant
The cup of water reaches the temperature of
18
5
∘
185
∘
F after 1.5 minutes. Using this information, find the value of
�
k, to the nearest thousandth. Use the resulting equation to determine the Fahrenheit temperature of the cup of water, to the nearest degree, after 4.5 minutes.
Enter only the final temperature into the input box.
Answers
The temperature of the water after 4.5 minutes is approximately 153°F.
How to find the Fahrenheit temperature of the cup of water, to the nearest degree, after 4.5 minutes.Using Newton's Law of Cooling to find the value of the decay constant k: T = \(Ta + (T0 - Ta) * e^-k*t\)
Substituting the given values, we get:
185 = \(69 + (203 - 69) * e^-k*1.5\)
Simplifying, we get:
\(116 = 134 * e^ \\^{-1.5k}\)
Dividing both sides by 134, we get:
\(0.8657 = e^{-1.5k}\)
Taking the natural logarithm of both sides, we get:
ln(0.8657) = -1.5k
Solving for k, we get:
k ≈ 0.232
Therefore, the value of the decay constant is approximately 0.232.
To find the temperature of the water after 4.5 minutes, we can use Newton's Law of Cooling again, with t = 4.5:
\(T = Ta + (T0 - Ta) * e^-k*t\)
\(T = 69 + (203 - 69) * e^-0.232*4.5\)
T ≈ 153°F
Therefore, the temperature of the water after 4.5 minutes is approximately 153°F.
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How many players had a single rate of greater than 0.2 per plate appearance over 1999-2001?
Answers
The exact number of players meeting your criteria will depend on the specific database you use and the parameters you set for the search.
To determine the number of players who had a single rate greater than 0.2 per plate appearance over the period from 1999 to 2001, we would need access to a comprehensive database of baseball statistics for that time frame. Unfortunately, as an AI language model, my knowledge cutoff is in September 2021, and I don't have real-time access to current or future sports statistics.
However, I can guide you on how to obtain the information you're looking for. You can consult baseball reference websites, such as Baseball-Reference.com or Fangraphs.com, which provide detailed player statistics for different seasons and allow you to filter data based on specific criteria.
Using these websites, you can search for players who played in Major League Baseball from 1999 to 2001 and examine their individual statistics, including their single rate (number of singles divided by plate appearances). By applying a filter for a single rate greater than 0.2, you can determine the number of players who meet that criteria.
Keep in mind that the exact number of players meeting your criteria will depend on the specific database you use and the parameters you set for the search.
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Henry has 8$ more then Jessie what is the y- intercept A. 9 B.8 C. 4 D.-8
Answers
Answer:
B. 8
Step-by-step explanation:
Slope equation:
y = ax + b
ax = slope
b = y intercept
y = ax + 8
1 Express the function h(z) = √2-4+ √2-4 in the form h(z) = (fog)(z) where ƒ(z) # z and g(x) = x. a) g(x)= b) f(x)= Remember to get a √ you need to type in sqrt(x)
Answers
The function h(z) = √2-4+ √2-4 in the form h(z) = (fog)(z) where ƒ(z) # z and g(x) = x. a) g(x)= b) is h(z) = (f ∘ g)(z) = √(g(z)) = √(z)
To express the function h(z) = √(2 - 4z) + √(2 - 4) in the form h(z) = (f ∘ g)(z) where ƒ(z) ≠ z and g(x) = x, we need to find suitable functions f(x) and g(x) that can be composed to obtain h(z).
Given that g(x) = x, we have g(z) = z. This means that g simply represents the identity function, where the input and output values are the same.
Now, let's consider the expression √(2 - 4z). We can observe that the square root operation is applied to the expression (2 - 4z). To represent this as a composition, we can define f(x) = √x. By doing so, we can rewrite √(2 - 4z) as f(g(z)), which gives us f(g(z)) = √(g(z)) = √z.
Therefore, the function h(z) = √(2 - 4z) + √(2 - 4) can be expressed as h(z) = (f ∘ g)(z) = √(g(z)) = √z.
In summary:
a) g(x) = x
b) f(x) = √x
By substituting g(z) = z and f(x) = √x into the expression, we get h(z) = (f ∘ g)(z) = √(g(z)) = √z.
This composition represents the given function h(z) in the desired form. The composition involves the identity function g(z) = z and the square root function f(x) = √x.
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Find the value of 7y+10 given that -2y-2=2
Simplify your answer as much as possible.
Answers
Steps:
-2y-2= 2
-2y=4
y=-2
Plug -2 into equation
7(-2)+10
-14+10
-4
2y - 2 = 2
y = -2
7(-2) + 10 = -4
Do the following using the given information: Utility function u(x1+x2) = .5ln(x1) + .25ln(x₂) .251 Marshallian demand X1 = - and x₂ = P₂ . Find the indirect utility function . Find the minimum expenditure function . Find the Hicksian demand function wwww
Answers
Hicksian demand functions are:x1** = 2P₁x₂ ; x₂** = P₂²
Utility function: u(x1+x2) = .5ln(x1) + .25ln(x₂) .The Marshallian demand functions are: x1* = - and x₂* = P₂.
The indirect utility function is found by substituting Marshallian demand functions into the utility function and solving for v(P₁, P₂, Y).u(x1*,x2*) = v(P₁,P₂,Y) ⇒ u(-, P₂) = v(P₁,P₂,Y) ⇒ .5ln(-) + .25ln(P₂) = v(P₁,P₂,Y) ⇒ v(P₁,P₂,Y) = - ∞ (as ln(-) is not defined)
Thus the indirect utility function is undefined.
Minimum expenditure function can be derived from the Marshallian demand function and prices of goods:
Exp = P₁x1* + P₂x2* = P₁(-) + P₂P₂ = -P₁ + P₂²
Minimum expenditure function is thus:
Exp = P₁(-) + P₂²
Hicksian demand functions can be derived from the utility function and prices of goods:
H1(x1, P1, P2, U) = x1*H2(x2, P1, P2, U) = x2*
Hicksian demand functions are:
x1** = 2P₁x₂
x₂** = P₂²
If there are no restrictions on the amount of money the consumer can spend, the Hicksian demand functions for x1 and x2 coincide with Marshallian demand functions.
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A) SSS
B) SAS
C) ASA
D) AAS
E) HL
F) not congruent
Answers
Answer:
SAS
Step-by-step explanation:
The diagram tells us there are two pairs of congruent line segments. In between those pairs, there are angles that are congruent. These are known as vertical angles. Therefore, the method to prove the triangles are congruent is SAS.
The higher the standard deviation of an arrival process with average interarrival time of 6 minutes, the _________
Answers
The higher the standard deviation of an arrival process with an average interarrival time of 6 minutes, the more variability or dispersion there is in the arrival times.
Standard deviation measures the dispersion or spread of data points around the mean. In the context of an arrival process, it represents the degree of variability in the time intervals between arrivals. A higher standard deviation indicates that the arrival times are more scattered or deviate more from the average interarrival time of 6 minutes.
When the standard deviation is high, it suggests that the arrival process is less predictable or more random. The actual interarrival times may vary significantly from the expected average of 6 minutes. This can lead to less efficient scheduling or planning as the arrival times become less predictable.
In contrast, when the standard deviation is low, the arrival times tend to be more consistent and closely clustered around the average interarrival time. This indicates a more predictable and reliable arrival process.
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