Take the function y = f(x), with the independent variable x as well as the dependent variable y, to determine the domain of a. If a value for x successfully enables the creation of a single value y using another value for x, it is said to be in the domain of the function f.
What is a domain?The collection of all potential inputs for a function is its domain.
For instance, the domain of f(x)=x2 and g(x)=1/x are all real integers with the exception of x=0.
The set of numbers x for which a function is defined in a valid manner is known as the domain of the function.
A function's domain is referred to as a closed interval if it is specified across the interval a ≤ x ≤ b.
So, to find the domain of a, consider the function y = f(x), which has the independent variable x and the dependent variable y.
A value for x is said to be in the domain of a function f if it successfully allows the production of a single value y using another value for x.
Therefore, take the function y = f(x), with the independent variable x as well as the dependent variable y, to determine the domain of a. If a value for x successfully enables the creation of a single value y using another value for x, it is said to be in the domain of the function f.
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t=1. I need as soon as possible 1. [30 MARKS] Let t be the 7th digit of your Student ID. Answer each of the following questions:
(a) [5 MARKS] Find the limit of the following sequence:
Xn =
etn3 t2 + 3n+ (t + 1)n3
en [In(1)-In(t+2)] and qn = (Yn)2.
Define the sequences yn = =en
(b) [4 MARKS] If yn converges to I, where does a converge to? Write your answer in terms of I.
(c) [5 MARKS] Define a subsequence a, by choosing every second element of yn (i.e. ak = Y2k). Write down the first 4 elements of an. Where does this subsequence converge to if yn converges to I? Write your answer in terms of 1.
(d) [8 MARKS] Prove the following statement: A sequence can have at-most one limit.
(e) [8 MARKS] Argue whether a and q can converge to two different limits. Using your conclusion, calculate the value of the limit ..
In this question, we are provided with a sequence Xn and a related sequence Yn. We need to find the limit of Xn, determine the limit of a given subsequence yn, prove a statement regarding limits of sequences, and discuss the possibility of different limits for sequences a and q. Finally, we calculate the value of a specific limit.
(a) We are asked to find the limit of the sequence Xn. By simplifying the expression and applying limit properties, we can evaluate the limit of Xn as n approaches infinity.
(b) We need to determine where sequence a converges to if sequence yn converges to I. By understanding the relationship between the sequences and the given convergence, we can express the limit of a in terms of I.
(c) A subsequence an is defined by choosing every second element of yn. We are asked to write down the first four elements of an and identify the convergence point of this subsequence. By considering the pattern of the chosen elements, we can express the limit of an in terms of 1, based on the convergence of yn.
(d) We are required to prove the statement that a sequence can have at most one limit. By utilizing the definition of convergence and assuming two different limits, we can arrive at a contradiction, demonstrating that a sequence cannot have more than one limit.
(e) We are asked to argue whether sequences a and q can converge to different limits. By analyzing the given information and using the conclusion from part (d), we can determine whether it is possible for a and q to have distinct limits. Based on this conclusion, we then calculate the value of the specified limit.
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Can someone help me with this question please.
Answer:
16.8 cubic metres
Step-by-step explanation:
Convert it first to a cubic foot:
1 cubic foot = 6.23 gallons
x cubic foot = 3738 gallons ÷ 6.23 gallons
x = 600 cubic foot
Now convert it to cubic metres:
1 cubic foot = 0.028 cubic metres
600 cubic foot × 0.028 = x cubic metres
16.8 cubic metres = x
What real values of $x$ are not in the domain of\(\($f(x)=\frac{1}{|x^2+3x-4|+|x^2+9x+20|}$?\)
(write in interval notation)
The function $f(x) = \frac{1}{|x^2 + 3x - 4| + |x^2 + 9x + 20|}$ is not defined when the denominator is equal to zero. $(-\infty, -5) \cup (-5, -4) \cup (-4, 1) \cup (1, \infty)$
So we need to find the real values of $x$ where:
$|x^2 + 3x - 4| + |x^2 + 9x + 20| = 0$
We know that the absolute value of a number is always non-negative. So for the equation above to be true, both absolute value expressions must be equal to zero simultaneously:
$x^2 + 3x - 4 = 0$ and $x^2 + 9x + 20 = 0$
Now, we can solve these quadratic equations to find the real values of $x$:
$x^2 + 3x - 4 = (x + 4)(x - 1) = 0$, so $x = -4, 1$
$x^2 + 9x + 20 = (x + 4)(x + 5) = 0$, so $x = -4, -5$
Thus, the real values of $x$ that are not in the domain of the function are $x = -4, 1, -5$. In interval notation, this can be written as: $(-\infty, -5) \cup (-5, -4) \cup (-4, 1) \cup (1, \infty)$
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A-One Talent Agency has 109 clients. 46 of the clients play piano and 58 of the clients play guitar. 17 clients play both the piano and the guitar. How many of the clients do not play either instrument?
Number of clients who do not play either the piano or the guitar is 22
To find the number of clients who do not play either instrument, we need to subtract the number of clients who play either the piano or the guitar or both from the total number of clients.
Let A be the set of clients who play the piano, and B be the set of clients who play the guitar. Then, we can use the formula A union B
|A ∪ B| = |A| + |B| - |A ∩ B|
where |A ∪ B| is the number of clients who play either the piano or the guitar or both, |A| is the number of clients who play the piano, |B| is the number of clients who play the guitar, and |A ∩ B| is the number of clients who play both instruments
Substituting the given values, we get
|A ∪ B| = 46 + 58 - 17
|A ∪ B| = 87
Therefore, the number of clients who do not play either instrument is:
109 - 87 = 22
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In a short sentences please, Prove that the sum of two rational numbers is rational. THANK YOU!!!
The sum of two rational numbers is rational because the sum of any two fractions with rational numerators and denominators can be expressed as a fraction with a rational numerator and denominator.
How does this work?A rational number is any number that can be expressed as a ratio of two integers, where the denominator is not equal to zero. For example, 1/2, -3/4, 6/5, and 0 are all rational numbers.
When we add two rational numbers together, we can use the following formula:
a/b + c/d = (ad + bc) / bd
where a, b, c, and d are integers and b and d are not equal to zero.
This formula tells us that the sum of two rational numbers is also a rational number. The numerator of the sum is found by cross-multiplying the fractions, and the denominator of the sum is found by multiplying the denominators.
For example, if we want to add 1/2 and 2/3 together, we can use the formula above:
1/2 + 2/3 = (1 x 3 + 2 x 2) / (2 x 3) = 7/6
Therefore, the sum of 1/2 and 2/3 is 7/6, which is also a rational number. This formula can be used to prove that the sum of any two rational numbers is also a rational number.
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A rational number is a number that can be written as \(\dfrac{a}{b}\) where \(a,b\in\mathbb{Z}\) and \(b\not=0\).
If one number is \(\dfrac{a}{b}\) and the other is \(\dfrac{c}{d}\), where \(b,d\not=0\), their sum is \(\dfrac{a}{b}+\dfrac{c}{d}=\dfrac{ad+bc}{bd}\). Since the set of integers is closed under addition and multiplication, we can write that \(\dfrac{ad+bc}{bd}=\dfrac{e}{f}\) where \(e,f\in\mathbb{Z}\) and \(f\not=0\), thus proving the sum of two rational numbers is a rational number.
the volume of cube is 64cm3 then the length of its side is
Answer:
4cm
Step-by-step explanation:
l³= 64cm³
l = ³√64 = 4cm
Which graph shows a function whose inverse is also a function?
T
5
4
3
2
+1)
-2.-1
3
4
5
X
Answer:
hello the function graph is turned 90 degree like clock way.
All the plotted graphs represent functions whose inverse is also a function.
What is function?A function is a relation between a dependent and independent variable. We can write the examples of functions as -
y = f(x) = ax + b
y = f(x, y, z) = ax + by + cz
Given is to find the function whose inverse is also a function.
A one to one function is a type of function whose inverse is also a function. The linear equations are one to one functions. They are of the form {y} = ax + b. This means that all of the graphs plotted represent a function whose inverse is also a function. So, we can conclude that all the plotted graphs represent the straight line, and all of them represent functions whose inverse is also a function.
Therefore, all the plotted graphs represent functions whose inverse is also a function.
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HELP PLZ!!!!! A fireman's ladder is placed against a wall. The bottom of the ladder is 15 ft away from the wall and the top of the ladder touches the wall at a point 80 ft above the ground. Assuming that the slope is positive, what is the slope of the ladder? Round your answer to the nearest hundredth.
Answer:
5.3
Step-by-step explanation:
We know that the bottom of the ladder is 15 feet from the wall, and it touches the wall 80 feet above the ground. Imagine it like two points on a graph. One is at the origin (0,0). That represents the bottom of the ladder. The next one is at (80,15), which represents where the top is. To find slope, we divide rise (y-values) over the run (x-values). The y value increases by 80, while the x increases by 15. 80 divided by 15 equals about 5.3
1.2m divided by 40 cm
Answer:3
Step-by-step explanation:
Answer: the answer is 3
Step-by-step explanation:I did the dividing on paper and the answer is 3
1) Convert the expression 3^1/2 to radical form.
Answer:
√3.
Step-by-step explanation:
this is equal to the square root of 3.
Need help on this asap!! Also Thank you in advance!!
Answer:
50/sin90=x/sin45
x=35.36cm
Find the shaded area of the shape
Answer:
340 mm²
Step-by-step explanation:
The shaded area seems to be a parallelogram. To find the area of a parallelogram, all we need to do is multiply the height and base together. In this case, the base is 20 and the height is 17 so the area is 20 * 17 = 340 mm².
Answer:
340 mm^2.
Step-by-step explanation:
The shaded area is a parallelogram whose area = base * altitude
= 20 * 17
= 340 mm^2.
What is another name for the height of a prism or a pyramid?
A. Altitude
B. Length
C. Base
D. Lateral face
Answer:
A . altitude
Step-by-step explanation:
Use this table of average number of three-point shots per game: graph the points, then choose the sentence that best describes this function.
Year Attempts
1991 28.0
1992 29.8
1993 33.0
1994 34.3
1995 34.0
Group of answer choices
A. The average number of three-point shots has remained unchanged since 1991.
B. The average number of three-point shots has decreased since 1991.
C. The average number of three-point shots increased, then decreased greatly since 1991.
D. The average number of three-point shots has increased since 1991.
Answer:
1994 34.3 ese es la respuesta
(-1, 5) (3,y) m=5 whats the value of my and whats the slope <3
Answer:
slope: 5
y = 25
Step-by-step explanation:
slope is m, and m = 5, so slope is 5.
y-5=5(x+1)...........set up point slope form
y-5=5x+5............distribute 5
y=5x+10..............add 5 to both sides
y=5(3)+10............plug in 3
y=25.....................simplify
Step-by-step explanation:
I am not sure you posted the question correctly.
m is the slope already. this comes from the point slope form
y - y1 = m(x - x1)
where x1, y1 are the coordinates of a point on the line.
so, the slope is 5 (and cannot be <3).
so, using the first point we get
y - 5 = 5(x - -1) = 5(x + 1) = 5x + 5
therefore
y = 5x + 10
for (3, y) we put 3 in as x
y = 5×3 + 10 = 15 + 10 = 25
it is (3, 25) for m = 5.
write down the formula to find out profit percent
Answer:
Profit percentage” usually (but not always) refers to “gross profit percentage” which, in turn refers to the “gross profit margin” expressed as a percentage. The formula for gross profit margin is “gross profit” divided by “revenue.”
“Revenue” generally refers to gross income or gross receipts. It is the amount received without accounting for any expenses whatsoever. If you sell two widgets at $50 each, it costs you $10 to produce each widget, you get taxed $5 per widget, your revenue will be $100 ($50×2). The costs associated with generating income is ignored.
“Gross profit” generally refers to revenue minus costs-of-goods-sold (COGS). COGS refers to the direct costs of producing goods. If you sell one gizmo, it costs you $20 in materials and $10 in employee wages to produce the gizmo, and $50 for a salesman to sell the gizmo, your COGS is $30 ($20+$10; the cost of the salesman is not included).
Consider this scenario: You sell two gidgets at $100 each, the materials to manufacture each gidget is $4, the per gidget rental costs of the manufacturing facility is $6, and it takes two hours to produce one gidget and you are paying an employee dedicated to gidget making $15 per hour, it costs $5 per gidget to move gidgets from the production facility to the store, renting the store costs $50, and at the store your salesperson is paid $50.
In the above scenario, your revenue is $200 ($100×2). The direct cost for producing one gidget is $40 ($4 in materials plus $6 in allocated manufacturing plant rent plus $15/hr×2hrs in labor). The costs for transport, renting the store, and labor for salesperson are not direct costs of producing the gidgets, and therefore ignored. Thus, your COGS is $80 ($40×2).
If revenue is $200 and COGS is $80, then gross profit is $120 ($200-$80). Thus, your gross profit margin is 0.6 ($120/$200). Hence, your gross profit percentage is 60% (0.6×100).
Mr. Green used a woodchipper to produce 640 pounds of mulch for his yard. What is the weight, in ounces, for the mulch which he produced?
Answer: 10240 ounces
food safety guidlines recommend that a beef rib roast should cook for 23 minutes per pound based on 325f oven setting. how many hours should it take to cook a 5.17 pound roast?
It should take approximately 1.98 hours, or around 1 hour and 59 minutes, to cook a 5.17 pound beef rib roast based on the recommended guideline of 23 minutes per pound at a 325°F oven setting.
To calculate the cooking time for a 5.17 pound roast, we can use the recommended guideline of 23 minutes per pound. First, we need to convert the weight from pounds to minutes, and then convert minutes to hours.
Cooking time in minutes = 5.17 pounds * 23 minutes/pound
Cooking time in minutes = 118.91 minutes
To convert minutes to hours, we divide the total minutes by 60:
Cooking time in hours = 118.91 minutes / 60
Cooking time in hours ≈ 1.98 hours
Therefore, it should take approximately 1.98 hours to cook a 5.17 pound beef rib roast based on the recommended guideline of 23 minutes per pound at a 325°F oven setting.
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PLEASE HELP!!! VERY EASY MATH EXPLINATION NEEDED!!!
Answer:
18
Step-by-step explanation:
So lets go voer what we know:
There are 6 pieces of ribbon.
Each piece of ribbon is 1 yard long.
We need 1/3 of each ribbon(1/3 yard).
To find this, lets take our 6 pieces of ribbbon, and break them into 3 seperate pieces.
This is because we need ribbons that are 1/3 of a yard. 3 ribbons would make up a single yard.
So:
The 6 yards of ribbon x 3 ribbons that make up 1 yard
6*3
=
18
I hope this makes more sense, and helps you understand better. I can try to explain in a different way if this still doesn't make sense.
I hope this helps! :)
can someone help me with this one?
Answer:
see attached
Step-by-step explanation:
Laptop computers are measured according to the diagonals of their screens.
8 in.
19 in.
A(n) 19-inch laptop has a screen that is 8 inches tall. How wide is the screen?
Round your approximation to 2 decimal places.
Check the picture below.
The area of a square is 81 cm 2 . Find the perimeter of the square.
PLEASE ANSWER!!!
Answer:
36
Step-by-step explanation:
9 times 4 buddy
Eight over 9 and negative fifteen over sixteen
Answer:
Hi! The correct answer is -5/6
Step-by-step explanation:
~Simplify the Expression~
eah’s friends gave her $12 at her birthday party. Then her grandparents gave her some more money. In all she had $112 of birthday money! Let m be the money she got from her grandparents.
Answer:
m reprecents $100
Hope this helps
given a random sample with replacement, what is the expected number of certain sample appearing in the sample
The expected number of "A" appearing in a random sample of size 10 drawn with replacement from a population of 100 is approximately 1,098.77. .
To calculate the expected number of a certain sample appearing in a random sample with replacement, we need to use the probability formula. The probability of a certain sample appearing in any given draw is equal to the size of the sample divided by the total population.
Let's say we have a population of 100 items, and we want to calculate the expected number of a certain sample, say "A", appearing in a random sample of size 10 drawn with replacement. The probability of drawing "A" in any given draw is 1/100.
Now, we need to consider the number of ways in which we can draw a sample of 10 from a population of 100 with replacement. This is given by the formula (n+r-1) choose r, where n is the size of the population, and r is the size of the sample. In our case, this is (100+10-1) choose 10, which equals 109,876,881.
Using these values, we can calculate the expected number of "A" appearing in the sample as follows:
Expected number of A = Probability of A appearing in any given draw x Number of ways of drawing a sample of 10 with replacement
Expected number of A = 1/100 x 109,876,881
Expected number of A = 1,098,768.81
Therefore, the expected number of "A" appearing in a random sample of size 10 drawn with replacement from a population of 100 is approximately 1,098.77.
It's important to note that the actual number of "A" appearing in the sample may vary from this expected value, as the sample is random and subject to chance. However, over multiple samples, the average number of "A" appearing is expected to be close to this value.
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A surveyor holds a laser range finder 3 feet above the ground and determines that the range finder is 92 feet from a building and 106 feet from the top of the building. What is the height h of the building? Round your answer to the nearest tenth.
Answer:
55.64
Step-by-step explanation:
The range finder is 92 feet from the building and 106 feet from the top of the building i.e. hypotheses
We will use the Pythagorean theorem:
x^2 = 106^2 - 92^2
= 11,236 - 8,464
= 2,772
= √2,772
x = 52.64978632
The height of the building:
h = x + 3
= 52.64978632 + 3
= 55.64978632
or
≈ 55.64 feet
Step-by-step explanation:
the answer to the nearest is 55.64
A piece of wood is 2.27 centimeters thick. What is that measurement rounded to the nearest tenth of a centimeter?
Answer:
free pointss from a blocked account lets goooooooooooooooo
Step-by-step explanation:
What is 1.62 divided by 3 in models?
To find the result, we need to find out how many 3s can fit into 1.62; the answer is 0.54 or 54/100.
What is number?Number is a concept used to describe a mathematical representation of an amount or quantity. It is used to count, measure, and label things. Numbers are also used to represent relationships between different things, such as the relationship between two people or between two numbers. Numbers can be used to describe and compare things, such as the size of an object or the duration of a task. They can also be used to solve equations, calculate statistics, and analyze data. Numbers are essential to our everyday lives, as they help us understand the world around us and make sense of it.
1.62 divided by 3 in models can be expressed as 1.62/3. This can be simplified by first carrying out long division, which yields 0.54. To express this in models, we can write it as 54/100. This means that when 1.62 is divided by 3, the result is 0.54 or 54/100.
This is happening because when we divide two numbers, we are essentially splitting the first number into parts that are the same size as the second number. In this case, we are dividing 1.62 into parts that are the same size as 3. To find the result, we need to find out how many 3s can fit into 1.62; the answer is 0.54 or 54/100.
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Reduce each of the following fractions to its simplest form. a. 12⁄18 b. 48⁄54 c. 27⁄90 d. 63⁄77 e. 24⁄32 f. 73⁄365
Answer: A. 2/3 B. 8/9 C. 3/10 D. 9/11 E. 3/4 F. 1/5
Step-by-step explanation:
9 4/5÷3 1/2= i need help with it
Answer:
Step-by-step explanation:
2.8
Answer: 2.8
Step-by-step explanation: It's basic