The limit of h(x) as x approaches infinity is ∞, and as x approaches 0, is undefined due to division by zero.
x h(x)
1 2 + 2
2 1.41 + 1
4 2 + 0.25
8 2.83 + 0.125
16 4 + 0.0625
To find the limit of h(x) as x approaches infinity, we see that h(x) = √(x) + 2/x - 5. As x increases without bounds, the square root of x and 2/x both approach infinity, but the value of -5 is constant. Therefore, the limit of h(x) as x approaches infinity is infinite.
To find the limit of h(x) as x approaches 0, we see that h(x) = √(x) + 2/x - 5. As x approaches 0, the value of the square root of x approaches 0, and the value of 2/x approaches infinity. However, the value of -5 is constant. Therefore, the limit of h(x) as x approaches 0 is -5 + ∞, which is undefined.
The limit of h(x) as x approaches 0 is undefined.
You could also say that the function is not defined at x = 0, meaning that the limit as x approaches 0 does not exist.
It's worth noting that the original function is not defined when x=0 as we are dividing by x, so it's impossible to calculate the limit of this function at that point.
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A mirror with a parabolic cross section is used to collect sunlight on a pipe located at the focus of the mirror. The pipe is located 9 inches from the vertex of the mirror. Write an equation of the parabola that models the cross section of the mirror. Assume that the parabola opens upward.
An equation of the parabola that models the cross section of the mirror is, y = [tex]\frac{x^{2} }{36}[/tex]
Given that,
A mirror with a parabolic cross section is used to collect sunlight on a pipe located at the focus of the mirror.
Define Parabola:A parabola refers to an equation of a curve, such that a point on the curve is equidistant from a fixed point, and a fixed line. The fixed point is called the focus of the parabola, and the fixed line is called the directrix of the parabola.
The pipe is located 9 inches from the vertex of the mirror.
The parabola is open upwards . the vertex of the parabola is (0,0)
and pipe is located 9 inches from the vertex (0,0)
9 inches is the focus of the mirror
The distance between the vertex and the focus = 9
Since parabola is upwards and vertex is (0,0) we use formula,
[tex]4py = x^{2}[/tex]
Where,
p is the distance between the vertex and focus p = 9
Now,
[tex]4*9*y = x^{2}[/tex]
[tex]36y =x^{2}[/tex]
Now isolate y by dividing 36 on both sides, we get
y = [tex]\frac{x^{2} }{36}[/tex]
Therefore,
An equation of the parabola that models the cross section of the mirror is, y = [tex]\frac{x^{2} }{36}[/tex]
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4x - 2 = 9x + 18. Which number do you subtract from both sides, the 4x or the 9x? Explain why.
A business recently upgraded a conference TV they had in their conference room. Originally the TV was 32 inches (across the diagonal) and had a perimeter of 87.16 inches. The new TV is 66 inches across the diagonal. Since the new TV will be recessed in the wall, it will need trim put on the border. What is the perimeter of the new TV? Round your answer to two decimal places.
The perimeter of the new TV will be 179.77 inches.
How to calculate the perimeter?From the information, the TV was 32 inches (across the diagonal) and had a perimeter of 87.16 inches and the new TV is 66 inches across the diagonal.
It should be noted that the perimeter simply means the total length of the boundary of the object. This will be calculated thus:
= (66 × 87.16) / 32
= 5752.56 / 32
= 179.77 inches.
In conclusion, the perimeter is 179.77 inches.
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The table shows how a leading automobile dealer plans to spend its advertising dollars for this year. If this company plans to increase its budget by 5% next year, approximately how much will it spend on social media ads?
Advertising Budget: $81,000
48.5% Television
23% Magazines
20% Newspapers
7% Radio
1% Billboards
0.5% Social Media
A.
Using the concept of percentage, social media budget will cost $425.25
PercentageThis is the expression of a ratio or fraction in percentage form. This is done by multiplying a ratio by 100.
The original advertising budget is $81,000 and they plan to increase it by 5%.
Let's calculate the 5% increase in the budget.
5% of 81000 =
5 / 100 = x / 81000
0.05 = x / 81000
x = 81000 * 0.05
x = 4050
The budget for next year will 81000 + 4050 = 85050
In the breakdown for the advertising budget, social media budget got 0.5%
Let's find 0.5% of 85050
0.5% * 85050
0.5 / 100 = x / 85050
0.005 = x / 85050
x = 0.005 * 85050
x = 425.25
The social media budget is $425.25
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an urn contains four balls numbered 2, 2, 5, and 6. if a person selects a set of two balls at random, what is the expected value of the sum of the numbers on the balls?
7.500 (rounded to 4 decimals) sum of the numbers on the balls.
Suppose we select two distinct balls
Then we have the following possibilities of selecting two balls
(2,2), (2,2) ............, i.e. 2 ways to get a sum of 4...............(2+2 = 4 and 2+2 = 4)
(2,5), (2,5), (5,2), (5,2), i.e. 4 ways to get a sum of 7...............(5+2 = 7 and 2+5 = 7)
(2,6), (2,6), (2,6), (2,6), i.e. 4 ways to get a sum of 8...............(2+6 = 8 and 6+2 = 8)
(6,5), (5,6) , i.e. 2 ways to get a sum of 11...............(5+6 = 11 and 6+5 = 11)
total number of possible outcomes = 2(for a sum of 4) + 4(for a sum of 7) + 4(for a sum of 8) + 2 (for a sum of 11)
= 2 + 4 + 4+2
= 12
So, P(getting a sum of 4) = (number of ways to get a sum of 4)/total number = 2/12
similarly,
P(getting a sum of 7) = (number of ways to get a sum of 7)/total number = 4/12
P(getting a sum of 8) = (number of ways to get a sum of 8)/total number = 4/12
P(getting a sum of 11) = (number of ways to get a sum of 11)/total number = 2/12
We know that expected value E[x] = sum of all individual sum values by their respective probability
= 4*(2/12) +7*(4/12) +8*(4/12) +11*(2/12)
= 0.6667 + 2.3333 + 2.6667 + 1.8333
= 7.500 (rounded to 4 decimals)
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During which phase of the systems life cycle are users trained to use the new system?
Answer:
Step-by-step explanation:
The phase of the systems life cycle during which users are trained to use the new system is called the implementation phase. In this phase, the new system is installed and made operational, and users are trained on how to use it effectively. This phase typically follows the design and development phases and precedes the maintenance phase.
What is the main focus of the implementation phase in the systems life cycle?
The main focus of the implementation phase is training users to use the new system effectively. This includes installing the system and making it operational, as well as providing necessary support and training to ensure users are able to utilize the system efficiently.
The phase of the systems life cycle during which users are trained to use the new system is the implementation phase. This is the phase where the new system is actually implemented and made available for use by the users. It is important to provide training to users during this phase so that they are able to effectively use the new system and understand its functionality.
Therefore, users are trained to use the new system during the implementation phase.
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The implementation phase of the systems life cycle is the time when users are taught how to utilize the new system.
The new system is installed, made operational, and users are instructed on how to utilize it efficiently during the implementation phase. In most cases, this phase comes after the design and development phases and comes before the maintenance period.
Why is user training important during the implementation phase of the systems life cycle?
User training is important during the implementation phase of the systems life cycle because it ensures that users are able to effectively use the new system and understand how it works. This is essential for the successful adoption and utilization of the system by the organization. Without proper training, users may struggle to use the system effectively, leading to reduced productivity and potentially even causing issues with data accuracy and integrity. By providing thorough user training, organizations can ensure that their employees are able to use the new system efficiently and effectively, leading to a successful implementation.
The implementation phase of the systems life cycle is the time when users are taught how to utilise the new system. In this stage, the new system is really put into use and made accessible to users. During this stage, it's crucial to give users training so they can utilize the new system correctly and comprehend its functions.
Therefore, during the implementation phase, users are instructed on how to utilize the new system.
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Which polynomial function could be represented by the graph below?
The polynomial function that could be represented by the graph is; f(x) = x³ + x² - 6x
What is the equation of the Polynomial?Let us find the zeros of the polynomial from the graph. The zeros of the polynomial will be the points where the graph crosses the x-axis.
Thus, we see that the graph crosses the x-axis at x = -3, 0 and 2. Thus, the factors of the polynomial are;
(x - 0), (x + 3) and (x - 2)
Therefore, the equation of the polynomial is;
f(x) = x(x - 2)(x + 3)
Expanding this gives us;
f(x) = x(x² + x - 6)
f(x) = x³ + x² - 6x
We conclude that is the equation of the polynomial represented by the graph.
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How many 5-letter combinations can be created from the letters in the word "friendly"? assume that the order of the letters does not matter.
a. 56
b. 120
c. 6,720
d. 40,320
Number of combinations = 56 combinations can be created from the letters in the word "friendly"
Points to remember
nCₐ = n!/(r!(n - r)!)
The given word is "FRIENDLY"
F R I E N D L Y is a 8 letter word.
To find the number of combinations
5 letters can be selected from 8 letter = 8C₅
8C₅ = 8!/(8 - 5)!5!
= 8!/3!5!
= (8 * 7 * 6* 5!)/(1 * 2 * 3 * 5!)
= 8 * 7
= 56
5 letter combinations can be created from the letters in the world “friendly = 56
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Who find the sum of integers from 1 to 100?
The sum of the integers from 1 to 100 is 5050. You can find this sum by adding all of the integers together or by using the formula for the sum of an arithmetic series.
sum = (number of terms) * (average of the first and last term)In this case, there are 100 terms, and the average of the first and last term is (1 + 100) / 2 = 50.5, so the sum is 100 * 50.5 = 5050.
Another way to find the sum is To find the sum of the integers from 1 to 100, we can add all of the integers together. This can be done by starting with 1 and repeatedly adding 1 to get the next integer, or by using a calculator or computer program to do the calculations for us.
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A movie theater lets you serve yourself candy for $0.79 per ounce. At that price, how much would you pay for 5.27 ounces of candy? Round your answers to the nearest cent.
A principal of $3000 is invested at 7.25% interest, compounded annually. How much will the investment be worth after 10 years?
Use the calculator provided and round your answer to the nearest dollar.
Answer:
$6,232.89 or $6,232.90
Step-by-step explanation:
A=P(1+(r/n))^nt
A= 3000(1+(.075/12))^12*10
A= 3,232.89
3,232.89+3000= 6,232.89
What's the most common number of siblings students in this class have?
Answer:
Three and four and five and zero.
Step-by-step explanation:
Answer:
3 and 4
Step-by-step explanation:
NEED ANSWERS ASAP!!! if an object is moving at a speed of V kilometers per hour, how many meters does it travel in M seconds? (its asking for the equation on how to solve this problem)
How do you solve 3 to the power of 1?
To answer, let's use the exponent rules to solve the power of 1.
What is exponent rule?Exponents, often known as powers, specify how many times the base number must be multiplied.
Exponent rules are principles that are used to simplify expressions using exponents. These principles are also useful in simplifying formulas with exponents that are decimals, fractions, irrational numbers, or negative integers.
Negative exponents Rule: [tex]a^{-m} = 1/a^m[/tex]
Product Rule: [tex]a^m * a^n = a^{(m+n)}[/tex]
Quotient Rule: [tex]a^m/a^n = a^{(m-n)}[/tex]
Power of a Power Rule: [tex](a^m)^n = a^{mn}[/tex]
Here, given that, 3 to the power of 1
The number 3¹ may be expressed as 3 to the power of 1, according to the exponent rule.
The base number in this formula is 3, while the power number is 1, and we know that any integer increased to that same power of that one equals the original number.
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3200 people attended a football game. If 10% of the people who attended were teenagers, how many teenagers attended the game?
Answer:
320 teenagers
Step-by-step explanation:
10% = 0.1
Take 3200 times 0.1 = 320
So, there are 320 teenagers attended the football game.
Kiley, jermaine, and gunther are playing tug-of-war. Kiley and jermaine are on the same side of the rope, and gunther is on the other side. Kiley is exerting a force of 20 n, and jermaine is exerting a force of 25 n.
The positive sign indicates that Gunther pulls to the right.
A force that would result in a balanced force for the game is: 45N
First we define a reference system.
Let's assume the horizontal axis as positive towards the right.
Suppose Kiley and Jermaine pull the rope to the left, while Gunther pulls the rope to the right.
The equilibrium equation is given by:
-20-25+F=0
Where,
F: force with which Gunther pulls the rope.
Clearing F we have:
The positive sign indicates that Gunther pulls to the right.
A force that would result in a balanced force for the game is: 45N
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in a certain large population of adults, the distribution of iq scores is strongly left-skewed with a mean of 122 and a standard deviation of 5. suppose 200 adults are randomly selected from this population for a market research study. the distribution of the sample mean of iq scores is (a) left-skewed with mean 122 and standard deviation 0.35. (b) exactly normal with mean 122 and standard deviation 5. (c) exactly normal with mean 122 and standard deviation 0.35. (d) approximately normal with mean 122 and standard deviation 5. (e) approximately normal with mean 122 and standard deviation 0.35.
The correct answer is e) approximately normal with a mean 122 and standard deviation 0.35.
In this case, the distribution of the sample mean of IQ scores will be approximately normal because the sample size of 200 is sufficiently large. This is known as the Central Limit Theorem, which states that the distribution of the sample mean will be approximately normal as long as the sample size is large enough, regardless of the shape of the distribution of the population.
The mean of the sample mean distribution will be 122, which is the same as the mean of the population. The standard deviation of the sample mean distribution will be smaller than the standard deviation of the population because it is calculated using the sample size rather than the population size.
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can someone help me!
Answer:
( x + 6, y + 4)
Step-by-step explanation:
Let's pick point S at ( -9, -4); it changes to point S' at ( -3, 0)
The x increase by 6, and the y increase by so the answer is
( x + 6, y + 4)
How do you write 6 more than a number?
“6 more than twice m” can be written in the mathematical form as 2m+6.
The question is saying that we have to write “6 more than twice m” as an algebraic expression or into a mathematical expression.
As in the question, it is mentioned that we have to take the number m as a variable.
So, we are going to use this ‘m’ for solving this question.
Let the number be m.
Then, twice of m will be similar to 2 times m or m multiplied by 2.
Therefore, twice m will be 2m.
Now, the question is saying that 6 more than twice m.
“6 more than” means 6 is added to that specific number.
Hence, 6 more than that number which is twice of m will be 2m+6.
Hence, “6 more than twice m” can be written in the mathematical form as 2m+6.
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3kx + 24 = 9kx solve for X
A: -2/k B: 4/k C: -4/k D:2/k
Answer: x= 4/k
Step-by-step explanation:
Answer:
B.) [tex]\frac{4}{k}[/tex]
Step-by-step explanation:
[tex]3kx+24=9kx\\3(kx+8)=9kx\\\frac{3(kx+8)}{3}=\frac{9kx}{3}\\kx+8=3kx\\(kx+8)-kx=(3kx)-kx\\8=2kx\\\frac{8}{2k}=\frac{2kx}{2k}\\\frac{4}{k}=x[/tex]
What are 3 types of sets?
The three types of set based on the number of elements is empty set, finite set and infinite set.
In mathematics, a set is a collection of unique objects. The number of elements in a set can be finite or infinite.
An empty set is a set with no elements. It is also called a null set. For example, a set of natural numbers less than 0.
Finite set is a set containing finite number of elements, that is the number of elements in the set is countable. For example, a set of natural numbers less than 100.
Whereas infinite set is a set with infinite number of elements, that is the number of elements in the set is not countable. For example, a set of natural numbers.
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Nancy is making accessories for the soccer team. She uses 866.18 inches of fabric on headbands for 43 players and 3 coaches. She also uses 378.83 inches of fabric on wristbands for just the players. How much fabric was used on a headband and wristband for each player?
The amount of fabric used on the headband and wristband for each player is 27.64 inches.
Mathematical Operations:
The operations that we use in particular actions like adding and taking away things or adding multiple times, diving things, etc.
The four basic Mathematical operations are addition, subtraction, multiplication, and division.
Here in this problem, we use divisions to solve the problem,
Given that,
Nancy uses 866.18 inches of fabric on headbands for 43 players and 3 coaches. 378.83 inches of fabric used on wristbands for the players only.
Number of headbands made with 866.18 inches
= 43 (player's) + 3 (coach's)
= 46 headbands
The amount of fabric used for 1 head band = (866.18)/46 = 18.83 in
378.83 inches of fabric used on wristbands for the players only.
The amount of fabric used for each wristband = 378.83/43 = 8.81 in
Amount of fabric used on headband and wristband = 18.83 + 8.81
= 27.64 inches
Therefore,
The amount of fabric used on the headband and wristband for each player is 27.64 inches.
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Can this be a biconditional statement and still be true? : “If a polygon is a square, then it has four sides.”
No, the biconditional statement isn't true because It's not necessary that if a polygon has four sides, then It will be a square.
What is Biconditional statement?
A statement that combines a conditional statement with its opposite is known as a biconditional statement. So, if and only if the other conditional is also true, the first conditional is true.
Let's elaborate the statement, “If a polygon is a square, then it has four sides.”
We know that a square has four equal sides and So, if a polygon is a square, it must have four equal sides which states that the given statement is true.
But, if we see its converse, "If a polygon has four sides, then it is a square". It is not necessary that the polygon will be a square.
eg. A parallelogram and rectangle also have four sides, So it could either be a parallelogram, rectangle or a square.
Hence, The given statement is correct but the converse of it, is not correct.
So, It can't be called a biconditional statement.
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What does it mean when a set is closed under addition?
Answer: I don't know
Step-by-step explanation:
Write the inequality that represents the scenerio :
Vanessa has at most $100 in her savings account
Answer: I am bad at math, but I'd say _> is the sign...
Step-by-step explanation:
elloooo
a variable with a value of x1x2 is added to the general linear regression model to account for two predictive variables, x1 and x2 and the effect on the response variable. this type of effect is called
The given type of effect is called predictive.
What is linear regression?
When predicting a variable's value based on the value of another variable, linear regression analysis is used. The dependent variable is the one you're trying to forecast. The independent variable is the one that you are utilizing to forecast the value of the other variable.
Given:
A variable with a value of x1 x2 is added to the general linear regression model to account for two predictive variables, x1 and x2 and the effect on the response variable.
Linear regression is one of the most generally utilized predictive displaying methods.
It is spoken to by a condition = + + , where an is the catch, b is the slant of the line and e is the blunder term.
This condition can be utilized to predict the estimation of an objective variable dependent on a given predictor variable(s).
The predictor variable is the name given to an autonomous variable utilized in regression examinations.
The predictor variable gives data on a related ward variable concerning a specific result.
Hence, the given type of effect is called predictive.
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The question is in the picture below :)
Answer:
Number of international passengers increased then decreased whereas the number of domestic passengers constantly increased
Step-by-step explanation:
Figure P is the result of a transformation on Figure O Which transformation would accomplish this?
Figure P is the result transformation figure O by the rule (x + 1, y-4). In other words, figure O shifted 1 unit left and 4 units downward direction.
What is meaning transformation?
An operation that manipulates a polygon or other two-dimensional object on a plane or coordinate system is known as a transformation. Two-dimensional figures can be transformed mathematically in order to travel about a plane or coordinate system.
The two-dimensional shape without any transformations is known as a preimage or inverse image. The transformed figure is shown in the image.
The coordinate of vertices of figure O are (2,4), (3,5), and (4,2).
The coordinate of vertices of figure P are (3, 0), (4,1), and (5, -2).
The difference between x-coordinates is (3 - 2) = (4 - 3) = (5 - 4) = 1.
The difference between y-coordinates is (0 - 4) = (1 - 5) = ( -2 - 2) = -4.
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Why is 2 a prime number?
2 is a prime number because it has only two factors (1 x 2).
What are prime number?A natural number greater than one that is not the product of two smaller natural numbers is referred to as a prime number. A composite number is a natural number greater than 1 that is not prime.
Numerical tables, which were typically printed before calculators and computers, were used to record all primes or prime factorizations up to a certain limit. The Sieve of Eratosthenes is the most well-known method for making a list of prime numbers.
Given why 2 is prime,
The natural numbers greater than 1 with exactly two factors, i.e. 1, and the number itself, are known as prime numbers.
so 2 has only two multiple
1 and 2,
Hence 2 is a prime number.
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What is the inverse of X²?
Additive inverse of [tex]x^{2}[/tex] is [tex]-x^{2}[/tex].
Multiplicative Inverse of [tex]x^{2}[/tex] is [tex]x^{-2}[/tex].
What is Inverse ?To produce a result equal to 0, add the original number and the additive inverse by simply reversing the sign of the integer. On the basis of negation of the original number, the characteristics of additive inverse are listed below. For instance, if x is the starting number, then -x is x's additive inverse.
A multiplicative inverse or reciprocal for a number x is a number that, when multiplied by x, produces the multiplicative identity, or 1. It is represented by 1/x or x/1. A fraction a/b has a multiplicative inverse of b/a. Divide 1 by the real number to obtain the multiplicative inverse of the number.
A function that "undoes" another function is called an inverse. In other words, if f(x) generates y, then y entered into the inverse of f creates x. An invertible function is one that has an inverse, and the inverse is indicated by the symbol [tex]f^{-1}[/tex] .
Additive inverse of [tex]x^{2}[/tex] is [tex]-x^{2}[/tex].
Multiplicative Inverse of [tex]x^{2}[/tex] is [tex]x^{-2}[/tex].
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