let f be the piecewise function defined above. the value of limx→2+f(x) is
Answers
For the piece wise function f(x) = {x² + 3x + 3 x < 2
f(x) = {6 x = 2
f(x) = {6 - 1/2x x > 2, the value of lim_x→2 f(f(x)) is option D: 7/2.
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.
The piecewise function is - f(x) = {x² + 3x + 3 x < 2
f(x) = {6 x = 2
f(x) = {6 - 1/2x x > 2
On applying the limit function -
lim_x→2 f(f(x)) = f(lim_x→2 f(x))
Now deduce the result for -
f(lim_x→2 f(2))
Also check if the limit exists.
Substitute the values in the equation -
For the left side -
lim_x→2^- f(x) = -(2)² + 3(2) + 3
lim_x→2^- f(x) = -4 + 6 + 3
lim_x→2^- f(x) = 5
For the right side -
lim_x→2^+ f(x) = 6 - 1/2(2)
lim_x→2^+ f(x) = 6 - 1
lim_x→2^+ f(x) = 5
Since, the limit on both sides is same, so the limit will be -
f(lim_x→2 f(2)) = f(5)
5 > 2
f(5) = 6 - 1/2(5)
f(5) = 6 - 5/2
f(5) = (12 - 5)/2
f(5) = 7/2
Therefore, the limit f(f(x)) is 7/2.
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Related Questions
find the limit l (if it exists). if it does not exist, explain why. (if an answer does not exist, enter dne.) lim x→49 x − 7x − 49
Answers
The limit does exist for lim x→49 (x^2 - 7x - 49) and it approaches value of 2009.
The limit can be found using algebraic manipulation. First we will try plug in the value and see if we can determine the limit. We have:
lim x→49 (x^2 - 7x - 49) = 49^2 - 7×49 - 49 = 2009
So limit exist at x^2 - 7x - 49 and it can be found out by simple substitution.
So, as x approaches 49, the expression x^2 - 7x - 49 approaches 2009.
Therefore, lim x→49 x^2 - 7x - 49 = 343.
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Jayden is going to invest $97,000 and leave it in an account for 16 years. Assuming the interest is compounded annually, what interest rate, to the nearest hundredth of a percent, would be required in order for Jayden to end up with $143,000?
Answers
An interest rate of 2.5 % is required to obtained a current capital of $ 143,000 after a period of 16 years.
How to find the interest rate of a deposit
In this problem we find that Jayden deposits an amount of money for a period of 16 years and such account is under composite interest, that is, that the account increases its capital continously in time. Compound interest model is shown:
C' = C · (1 + r / 100)ˣ
Where:
C - Initial capital, in monetary units.C' - Current capital, in monetary units. r - Interest rate, in percentage.x - Number of periods, in years.If we know that C = 97,000, C' = 143,000 and x = 16, then the interest rate is:
143,000 = 97,000 · (1 + r / 100)¹⁶
143 / 97 = (1 + r / 100)¹⁶
1.025 = 1 + r / 100
0.025 = r / 100
r = 2.5
The needed interest rate needed for a capital of $ 143,000 after a period of 16 years is equal to 2.5 %.
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How many ways can you split 12 people into 3 teams of 4?
Answers
By using permutations and combinations, We can arrange 12 people into 3 teams of 4 in 5775 different ways.
Here, we will use the concept of permutations and combinations to solve the question.
We have to arrange 12 people into 3 teams of 4.
We know that ⁿCr = n! / [(n - r)! × r!]
No. of ways to select the first 4 people in the first group = ¹²C₄
= 12! / [(12 - 4)! × 4!]
= 12! / [(8! × 4!)]
= 495
No. of ways to select 4 people from the remaining 8 for the second group = ⁸C₄ = 8! / [(8 - 4)! × 4!] = 8! / [(4! × 4!)] = 70
No. of ways to select 4 people from 4 for third group = ⁴C₄ = 4! / [(4 - 4)!] × 4!] = 4! / [(0! ×4!)] = 1
Total no. of ways to select people for group = (495 x 70 x 1) / 3! = 34650 /6 = 5775
Hence, we can split 12 people into 3 teams of 4 in 5775 different ways.
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i asked my class what they had for breakfast. 10 students had cereal, 5 students had eggs, and 3 students had no breakfast. what kind of data do i have?
Answers
The kind of data we have is Categorical data. Data that can be broken down into groups or categories is known as categorical data.
There are three categories in this case: eggs, cereal, and no breakfast These groups include the 10 students who ate cereal, 5 students who ate eggs, and 3 students who did not eat breakfast at all.
A categorical variable is a variable in statistics that can have one of a limited, typically fixed number of possible values and assign each observational unit to a specific group or nominal category based on some qualitative property.
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Mainsail
Headsail
Welcome to the land down under! Spend the day sailing
in Sydney Harbor! Sailboats are made up of two sails,
the mainsail and the headsail. Typically, these sails are
the shape of triangles and these two triangles are
similar. Considering the sailboat pictured below,
determine the value of x and y and the unknown side
lengths.
6+A
X-2
30 ft
5y-3
26 ft
Answers
By using the properties of similar triangles, the values of x and y are respectively, 15 & 7
What is the similarity of triangles?Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent. Triangle resemblance is shown here by the symbol "≈"
Given that,
Side lengths of triangle 1, y + 9, x, x -2
Side lengths of triangle 2, 30, 26, 5y - 3
Both the triangles are similar,
So, we can write
(x - 2)/x = 26/30
After solving it, x = 15
Similarly,
(y + 9)/x = (5y - 3)/30
y = 7
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what is the slope of a line that has the coodinates of (10,23) & (20,36)?
Answers
Step-by-step explanation:
The slope of a line can be calculated as the difference of the y-coordinates divided by the difference of the x-coordinates of two points on that line. In this case, we have two points: (10,23) and (20,36).
So, the slope of the line would be:
(36 - 23) / (20 - 10) = 13 / 10 = 1.3.
Therefore, the slope of the line that has the coordinates of (10,23) and (20,36) is 1.3
7. Josh takes a twenty-question multiple-choice exam where each question has five possible answers. Some of the answers he knows, while others he gets right just by making lucky guesses. Suppose that the conditional probability of his knowing the answer to a randomly selected question given that he got it right is 0. 92. How many of the twenty questions was he prepared for
Answers
The total number of twenty questions prepared by Josh can be find by using the expression k = 20 * P(getting a question right) / (1 + 20 * 0.08 / 0.92), where, k = total question prepared by Josh
Let's call the number of questions Josh was prepared for as "k".
The probability of Josh getting a question right given that he knew the answer is 0.92,
So the probability of him getting a question right by guessing is
1 - 0.92 = 0.08.
The overall probability of Josh getting a question right is the sum of the probability of him getting it right given that he was prepared and the probability of him getting it right by guessing:
P(getting a question right) = P(getting a question right | prepared) * P(prepared) + P(getting a question right | guessed) * P(guessed)
Since each question is either prepared or guessed, the sum of P(prepared) and P(guessed) is 1:
P(getting a question right) = 0.92 * P(prepared) + 0.08 * (1 - P(prepared))
Simplifying the expression:
P(getting a question right) = 0.92 * P(prepared) + 0.08
Since the overall probability of Josh getting a question right is the same for every question,
it must be the same for all twenty questions:
So, we can write it as:
0.92 * P(prepared) + 0.08
= 0.92 * k/20 + 0.08 * (20-k)/20
Dividing both sides by 0.92:
P(prepared) = k/20 = (0.92 * k + 0.08 * 20 - 0.08) / 0.92
Isolating k:
k = 20 * P(prepared) / (1 + 20 * 0.08 / 0.92)
Plugging in the overall probability of Josh getting a question right, we have:
k = 20 * P(getting a question right) / (1 + 20 * 0.08 / 0.92)
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Which statement best explains if the graph correctly represents the proportional relationship y = −2x? (4 points) A coordinate plane is shown. Points are graphed at 2 comma 4 and negative 1 comma 2. The points are joined by a line. a No, the points shown would not be part of y = −2x b No, proportions cannot be represented on a graph c Yes, all proportions can be shown on a graph of this line d Yes, the points shown on the line would be part of y = −2x
Answers
A statement which best explains if the graph correctly represents the proportional relationship y = −2x include the following: D. Yes, the points shown on the line would be part of y = −2x.
What is a proportional relationship?In Mathematics, a proportional relationship can be defined as a type of relationship that generates equivalent ratios, a straight line, and it can be modeled or represented by the following mathematical expression:
y = kx
Where:
k is the constant of proportionality.y and x represent the variables in a proportional relationship.Generally speaking, the graph of any proportional relationship such as the linear equation (y = -2x) is characterized by a straight line as shown in the image attached below, with the following ordered pairs (0, 0), (1, -2),(2, -4), and (-1, 2).
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which of the following is an antiderivative of f(x)=tan(ex π2) on 0≤x≤ln(π2) ?
Answers
The antiderivative of f(x) = tan(eˣ + π/2) on 0≤x≤ln(π/2) is:
⇒ ln |sec([tex]e^{\pi /2}[/tex])| / [tex]e^{\pi /2}[/tex]
Now, For the antiderivative of f(x) = tan(eˣ + π/2) on the interval 0≤x≤ln(π/2), we need to integrate the given function.
Now, using the substitution u = eˣ + π/2.
Then, we have:
du/dx = eˣ
dx = du / eˣ
Using this substitution, we can rewrite the original function as:
f(x) = tan(eˣ + π/2) dx = tan(u) du / eˣ
Now let's integrate this function:
∫tan(u) du / eˣ = - ln |cosec(u)| / eˣ + C
Substituting back u = eˣ+π/2:
ln |cosec(eˣ + π/2)| / eˣ + C
= - ln |cosec(eˣ + π/2)| / eˣ + C
Now we need to evaluate this expression at the limits of integration x = 0 and x = ln(π/2):
F(ln(π/2)) - F(0)
= - ln |cosec([tex]e^{\pi /2 } + \frac{\pi }{2}[/tex])| / [tex]e^{\pi /2}[/tex] + C - (- ln |cos(0)| / [tex]e^{\pi /2}[/tex] + C)
= - ln |sec([tex]e^{\pi /2}[/tex])| / [tex]e^{\pi /2}[/tex] + ln |cos(0)| / [tex]e^{\pi /2}[/tex]
= - ln |sec([tex]e^{\pi /2}[/tex])| / [tex]e^{\pi /2}[/tex] + ln(1) / [tex]e^{\pi /2}[/tex]
= ln |sec([tex]e^{\pi /2}[/tex])| / [tex]e^{\pi /2}[/tex]
So, the antiderivative of f(x) = tan(eˣ + π/2) on 0≤x≤ln(π/2) is:
⇒ ln |sec([tex]e^{\pi /2}[/tex])| / [tex]e^{\pi /2}[/tex]
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Write the decimal expansion for 5 9. ( 7Th GRADE)! HURRY HELPPPP…
Answers
Answer: 0.56
Step-by-step explanation: convert from fraction to decimal
The equation of Line D is y = 3/8x +3. The equation of the line E is y = 3/8x + 8/3, Are line D and Line E perpendicular,parallel or neither.
Answers
The slope of line D and line E will be congruent. Then the lines are parallel to each other.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
If the slopes are different then the lines are intersecting.If the slopes are equal but have different intercepts then the lines are parallel.If the slopes and intercepts are equal then the lines are coincident.If the product of the slope is negative then the lines are perpendicular.The equations are given below.
Line D: y = (3/8)x +3
Line E: y = (3/8)x + 8/3
The slope of line D and line E will be congruent. Then the lines are parallel to each other.
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6.) Vanilla Ice takes out an ordinary loan to pay back a rental company. The bank has a 10.3% ordinary
interest rate for 240 days. What is the principal that Vanilla Ice borrowed if the result is a $330.00 interest
charge?
Answers
Let P be the principal Vanilla Ice borrowed. The interest charge is calculated as P * 10.3% * 240/365.
So, 330 = P * 10.3% * 240/365
Solving for P, we get:
P = 330 / (10.3% * 240/365) = $3,116.71
Therefore, Vanilla Ice borrowed a principal of $3,116.71.
Simple Interest (SI) is calculated based on the principal amount only, and the interest rate stays constant throughout the tenure. The formula for Simple Interest is:
SI = P * R * T
Where:
P = Principal amount
R = Interest rate
T = Time (in years)
Compound Interest (CI) is calculated based on the principal amount and the interest earned on it in previous periods. The interest earned in each period is added to the principal, and the new amount becomes the principal for the next period. This leads to an exponential growth of the invested amount. The formula for Compound Interest is:
CI = P * (1 + R/n)^(nt)
Where:
P = Principal amount
R = Interest rate
n = Number of compounding periods per year
t = Time (in years)
In summary, the main difference between simple and compound interest is that simple interest is calculated only on the principal amount, whereas compound interest is calculated on the principal amount and the accumulated interest.
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Matt is using 2 mixtures of saltwater solution to make a 6% saltwater solution for his aquarium. One mixture is a 2% saltwater solution, and the other is an 8% saltwater solution. Matt made a chart to calculate the correct amount of each solution to use. Using the information in the table, which equation can Matt use to find x, the amount of 2% mixture he needs to use for his aquarium?
Answers
Answer:
matt needs to use more than 2% mixture for his aquarium
Step-by-step explanation:
Can anybody understand this please help
Answers
solve Edson exercises in sets that are each t minutes long. He does 6 sets of push-ups, 3 sets of pull-ups, and 4 sets of sit-ups. Use an expression to represent the time it takes Edson to exercise as the sum of three different terms. Simplify the expression. Enter your answer in the box.
Answers
The time taken by Edson to complete his workout routine is 13 t
What is the unitary method?The unitary method is a method in which you find the value of a unit and then the value of a required number of units.
Given here: Edson exercises in sets that are each t minutes long. He does 6 sets of push-ups, 3 sets of pull-ups, and 4 sets of sit-ups
Now Edson does 6 sets of pushups time taken to finish the sets are
Time ( pushups)=6t
similarly, the time it takes to complete the other exercises are
Time(pull ups)=3t
Time(sit ups)=4t
Thus total time taken is equal to 3t+4t+6t=13t
Hence, The time taken by Edson to complete his workout routine is 13 t
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Which is the independent variable and
which is the dependent variable?
The number of dollar bills, d, is the
?
independent
dependent
variable.
arters, q, is the
every bill she puts in.
variable.
Answers
Answer:The number of dollar bills, d, is the independent variable.
The quarters, q, is the dependent variable.
Step-by-step explanation:
The number of dollar bills, d, is the independent variable.
The quarters, q, is the dependent variable.
Answer:
Step-by-step explanation:
dependent then independent because i passes the lesson.
What is the quotient of 11/14 divided by 11/21
Answers
Answer: 1.5
Step-by-step explanation:
Can anyone help me solve this?
Answers
On the right side, we can just simplify the expression to 1+tanθ+cotθ
The Identity equationYes, this is true.
The left side of the equation can be simplified to 1, which is equal to the right side.
Left side:
(cotθ/1-tanθ)+(tanθ/1-cotθ)
= (cotθ + tanθ)/(1 - tanθ - cotθ)
= (tanθ + cotθ)/(1 - tanθ - cotθ)
= 1/(1 - tanθ - cotθ)
= 1
Right side:
1 + tanθ + cotθ = 1
To prove that this equation is true for any value of θ, we must first expand and simplify each side of the equation. On the left side, we can express the fraction as a product of two terms, giving us (cotθ*(1-tanθ))+(tanθ*(1-cotθ)).We can then factor out cotθ and tanθ, giving us (cotθ*(1-tanθ+1-cotθ))+(tanθ*(1-cotθ+1-tanθ)).We can then combine the terms that are being multiplied by each side to get (cotθ+tanθ)*(1-tanθ-cotθ). Since the brackets are equal to 0, this simplifies to 0*(1-tanθ-cotθ), which is equal to 0.To learn more about Identity equation refer to:
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Answer:
See proof below
Step-by-step explanation:
(Please excuse any typos and point them out to me. It is a pain typing in LateX)
We are asked to prove:
[tex]\dfrac{\cot\theta}{1-\text{\ensuremath{\tan\theta}}}+\dfrac{\tan\theta}{1-\cot\theta}=1+\tan\theta+\cot\theta[/tex]
Since
[tex]\tan\theta =\dfrac {\sin\theta}{\cos\theta}\\\\\cot\theta = \dfrac {\cos\theta}{\sin\theta}\\\\[/tex]
the left side becomes
[tex]\dfrac{\cos\theta/\sin\theta}{1-\sin\theta/\cos\theta}+ \dfrac{{\sin\theta/\cos\theta}}{1-\cos\theta/\sin\theta} \cdots \cdots \cdots(1)[/tex]
For ease of expressing this let
[tex]a = \sin\theta\\b = \cos\theta\\[/tex]
Substituting the above in expression (1) gets us
[tex]\dfrac{b/a}{1- a/b} + \dfrac{a/b}{1-b/a}[/tex]
Let's take the individual terms and simplify each
[tex]\dfrac{b/a}{1- a/b} = \dfrac{b}{a}\cdot \dfrac{1}{1-\dfrac{a}{b}}[/tex]
[tex]\dfrac{1}{1-\dfrac{a}{b}}= \dfrac{1}{\dfrac{b-a}{b}}=\dfrac{b}{b-a}[/tex]
Therefore
[tex]\dfrac{b}{a}\cdot\dfrac{b}{b-a} = \dfrac{b^2}{a(b-a)}[/tex]
For the second term we get
[tex]\dfrac{a/b}{1-b/a} = \dfrac{a^2}{b(a-b)}[/tex]
Noting that (a - b) = - (b - a)
the entire expression becomes
[tex]\dfrac{b^2}{a(b-a)} = - \dfrac{a^2}{b(b-a)}[/tex]
Multiply this expression throughout by the LCM which is
[tex]ab(b-a)[/tex]
[tex]\dfrac{b^2 \cdot b - {a^2}\cdot a}{ab(b-a)}\\\\= \dfrac{b^3 - a^3}{ab(b-a)}\cdots\cdots(2)\\[/tex]
(b -a) cancels in numerator and denominator on both sides giving
For the numerator we have the identity
[tex]b^3 - a^3 = (b-a)(b^2 + ab + b^2)[/tex]
So the expression in (2) becomes
[tex]\dfrac{(b-a)(b^2 + ab + a^2)}{ab(b-a)}\\\\\textrm{(b-a) cancels from the numerator and denominator}\\\\[/tex]
This leaves us with:
[tex]\dfrac{(b^2 + ab + a^2)}{ab}[/tex]
Substituting for a = sinθ and b = cosθ we get
[tex]\dfrac{\cos^2\theta + \sin^2\theta+ \cos\theta\sin\theta}{\sin\theta\cos\theta}[/tex]
Divide each term in the numerator by [tex]\sin\theta \cos\theta[/tex]
==> [tex]\dfrac{cos^2\theta}{\sin\theta\cos\theta} + \dfrac{\sin^2\theta}{\sin\theta\cos\theta}+ \dfrac{\sin\theta\cos\theta}{\sin\theta\cos\theta}}[/tex]
==> [tex]\dfrac{\cos\theta}{\sin\theta} + \dfrac{\sin\theta}{\cos\theta} + 1[/tex]
[tex]\cot\theta + \tan\theta + 1\\== > 1 + \tan\theta + \cot\theta[/tex]
Hence PROVED
Given the four points E(2,5), F(7,1), G(2,-3), and H(-8,5) is EF parallel to GH?
Answers
EF is parallel to GH by using the slope formula. Both the slope is equal to -4/5.
Given that the information below:
E(2,5), F(7,1), G(2.-3) and H(-8,5) is EF parallel to line GH.
By using slope formula method we can compare the slopes of line EF & line GH.
Where m = (y2 - y1 ) / (x2 - x1) slope of segment become (x1,y1) & (x2,y2)
EF Slope = (1-5)/(7-2) = -4/5
GH Slope = (5-(-3)/(-8-2) = 8/-10 = -4/5
By using slope formula method EF slope is -4/5 & GH slope is -4/5. Both the slopes of the equation is equal. In this way we can prove that the EF is parallel to GH.
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How do you convert 50 Kilogram (kg) to Pound (lb)?
Answers
Multiply the mass in kilogrammes by 2.2046226218 to convert 50 kg to pounds.
What makes anything a lb?Libra pondo, which meaning "a pound by weight," was the unit of measurement in ancient Rome when the word "pound" first appeared. According to the BBC, the pondo portion of the sentence is where the English term "pound" originates. However, the word's libra portion is where the abbreviation "lb" comes from.Follow these easy procedures to convert a weight or mass measurement from kilogrammes (kg) to pounds (lbs): Add the conversion factor 2.2046 to the weight. Therefore, 50 kg would be equal to 110.23 kg when multiplied by 2.2046.Multiply the mass in kilogrammes by 2.2046226218 to convert 50 kg to pounds. [lb] = 50 * 2.2046226218 is the formula to convert 50 kilogrammes to lbs.To learn more about Kilogram refer to:
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Lyla invested $140. She earned a simple interest of 3% per year on the initial investment. If no money was added or removed, what is the amount of money Lyla will earn at the end of two years?
Answers
Answer:
8.40
Step-by-step explanation:
Since, the simple interest is,
I= p x r x t
100
Where,
P=Principal
r= rate per periods
t= number of periods
Here, P=140, r=3%, t = 2,
the simple interest will be
I= 140 x 3 x 2
100
= 840
100
=8.40
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Answers
Answer: -21
Step-by-step explanation: first you multiply 4 x -5 or 4(-5) - 1 4 x -5 would give you -20 and -20 - 1, since both are negative we add to get a total of -21 hope this helps.
Small market orders copies of a certain magazine for its magazine rack each week. Let X = demand for the magazine, with the following pmf. X 1 2 3 4 5 6 p(x) 1 14 2 14 3 14 3 14 2 14 3 14 Suppose the store owner actually pays $2. 00 for each copy of the magazine and the price to customers is $4. 0. If magazines left at the end of the week have no salvage value, is it better to order three or four copies of the magazine? [Hint: For both three and four copies ordered, express net revenue as a function of demand X, and then compute the expected revenue. ] What is the expected profit if three magazines are ordered? (Round your answer to two decimal places. ) $ 27/7 Incorrect: Your answer is incorrect. What is the expected profit if four magazines are ordered? (Round your answer to two decimal places. ) $ How many magazines should the store owner order
Answers
Small market orders copies of a certain magazine for its magazine rack each week. The number of copies to order to generate more revenue is 4.
Let the profit y, the demand for the magazine be x , the number owner ordered k , then we get :
y = 4x - 2m ( m > x)
y = 2m ( m ≤ x)
If m = 3 we get
E (y) = 1/14 (4 - 2x3) + 2/14 (4x2 - 2x3) + 3/14 (2x3) + 3/14 (2x3) + 2/14 (2x3) + 3/14 (2x3)
E(y) = 68/14
If m = 4 get,
E (y) = 1/14 (4 - 2x4) + 2/14 (4x2 - 2x4) + 3/14 (4x3 -2x4) + 3/14 (2x4) + 2/14 (2x4) + 3/14 (2x4)
E(y) = 72/14
E (y)m=4 > E(y)m=3
So order number is 4.
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on+may+11,+corlis+took+out+a+loan+for+$2,900,+at+8%+ordinary+interest,+for+82+days.+what+is+the+maturity+date+of+the+loan?
Answers
The maturity date of the loan is July 31st.
To find the maturity date, you first need to find the number of days between May 11th and the maturity date. The loan was taken out for 82 days, so you add 82 days to May 11th to find the maturity date.
For example, if May 11th is day 1, then day 82 would be July 31st. Therefore, the maturity date of the loan is July 31st.
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The formula for the perimeter of a rectangle is. Part a. Rewrite the formula for the perimeter of a rectangle in terms of the width. In your final answer, include all of your work. Part b. In two or more complete sentences, describe the process you followed while isolating the variable in the equation.
Answers
The isolation of variable in the equation will result in the formula - Breadth = (Perimeter - 2length)/2.
As per the known information, the formula of the perimeter of rectangle is -
Perimeter = 2 (length + breadth)
Expanding the formula we get -
Perimeter = 2length + 2breadth
Rewriting in terms of breadth -
2Breadth = Perimeter - 2length
Breadth = (Perimeter - 2length)/2
The process to isolate the variable will require expanding and rewriting the equation with breadth on Left Hand Side of the equation. Now, move the constant on Right Hand Side and you will get the formula.
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price of a stock over a 5-day period.
Closing Price
$104.67
$103.95
$109.35
$108.27
$113.58
Day
Monday
Tuesday
Wednesday
Thursday
Friday
What is the average of the 3-day simple moving averages for these five days to the nearest $0.01?
Answers
The average of the 3-day simple moving averages for these five days to the nearest $0.01 is $105.99, $107.19 and $110.40.
What is a Simple Moving Average?
By dividing the number of periods inside the range by the average of the range of prices, simple moving averages are used.
We are given closing prices of a stock over a 5-day period.
So, 3-day simple moving averages are
For Monday - $104.67
For Tuesday - $103.95
For Wednesday - ($104.67 + $103.95 + $109.35)/3 = $105.99
For Thursday - ($103.95 + $109.35 +$108.27)/3 = $107.19
For Friday - ($113.58 + $109.35 +$108.27)/3 = $110.4
Hence, the average of the 3-day simple moving averages for these five days to the nearest $0.01 is $105.99, $107.19 and $110.40.
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Find the following for each function.
Domain:
Relative Min:
Range:
Increasing:
Relative Max:
Decreasing:
Answers
For the given function; Domain: -4 ≤ x ≤ 4, Range: 0 ≤ y ≤ 3, Relative max: x = 0, y=3, and Relative min: x = -2, y=0 and x = 2, y =0.
What is domain and range?The range of values that we are permitted to enter into our function is known as the domain of a function.
The x values for a function like f make up this set (x).
A function's range is the collection of values it can take as input. The values in this set
Hence, once we input an x value, the function returns. The y values are those.
The domain of the function is the input values, that is the x-coordinates thus,
Domain: -4 ≤ x ≤ 4
Range of the function is the output values, that is the y-coordinate thus,
Range: 0 ≤ y ≤ 3
Relative max is a point where the function changes from increasing to decreasing thus,
Relative max: x = 0, y=3
Relative min is a point where the function changes from decreasing to increasing, thus,
Relative min: x = -2, y=0 and x = 2, y =0
Hence, the Domain: -4 ≤ x ≤ 4, Range: 0 ≤ y ≤ 3, Relative max: x = 0, y=3, and Relative min: x = -2, y=0 and x = 2, y =0.
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Which function has a percent rate of decrease equal to 5%?
A. F(x) = 3(0. 5)*
B. F(x) = 3(1. 5)
C. F(x) = 3(0. 05)
D. F (x) = 3(0. 95)
E. F(x) = 3(1. 05)
Answers
Among the given, the function that has a percent rate of decrease equal to 5% is: F(x) = 3(0.95)
Hence, option (D) is the correct choice.
For (A):
We have,
F(x) = 3(0.5), Here percentage rate decrease = 50%
For (B):
We have,
F(x) = 3(1.5), Here there is percentage rate increase which will be = 50%
For (C):
We have,
F(x) = 3(0.05), Here percentage rate decrease = 95%
For (D)
F(x) = 3(0.95)
Here, percent rate of decrease equal to 5%
This function represents the relationship between input x and the output y where y = 3(0.95^x).
The number 0.95 can be interpreted as 95% of the original value, which means a 5% decrease.
For (A):
We have,
F(x) = 3(1.05), Here there is percentage rate increase which is = 5%
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When u, v are nonzero vectors, then Span{u, v} contains only the line through u and the origin, and the line through v and the origin.
Answers
When u, v are nonzero vectors, then Span{u, v} contains only the line through u and the origin, and the line through v and the origin, this statement is false.
The span of two nonzero vectors u and v, Span{u, v}, is the set of all linear combinations of u and v. This set can include not only the lines through u and the origin, and the line through v and the origin, but also all other points on the plane defined by these two lines.
For example, if u = (1, 0) and v = (0, 1), then Span{u, v} would be the set of all points in the x-y plane, since every point in the plane can be represented as a linear combination of u and v.
Therefore, Span{u, v} contains not only the lines through u and the origin, and the line through v and the origin, but all other points on the plane defined by these two lines.
Correct Question :
When u, v are nonzero vectors, then Span{u, v} contains only the line through u and the origin, and the line through v and the origin. True or fasle.
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How do you convert 200 Kilogram (kg) to Pound (lb)?
Answers
The actual weight of a pound is 0.45359237 kilos.
How much in kilogrammes are converted to pounds?To Change the Price Per Pound (Pp) to the Price Per Kilogram (Kg), In order to convert cost per kilogramme to cost per lb, simply multiply the kg price by 2.2046 to get the lb price.In essence, one kilogramme is equivalent to two pounds (there is a longer decimal position, but I abbreviate it to 2.2046).In the fields of mathematics and engineering, converting from kilogrammes to pounds is a frequent operation; fortunately, it is also a simple one. For most conversions, all you need to do is multiply the number of kilogrammes by 2.2 to get the number of pounds.To learn more about Pound (lb) refer to:
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