For which of the following intervals does the function (in the image section) have a removable discontinuity?A. [−2.5,−1.5] B. [−1.5,−0.5] C. [−0.5,0.5] D. [0.5,1.5] E. [1.5,2.5]
Answers
Given the function below,
[tex]f(x)=\frac{x+2}{x^4-2x^3-x^2+2x}[/tex]Let us now factorize the denominator
[tex]x^4-2x^3-x^2+2x[/tex]First of all, let us factorize x out from the denominator.
[tex]\begin{gathered} x(\frac{x^4}{x}-\frac{2x^3}{x}-\frac{x^2}{x}+\frac{2x}{x}) \\ x(x^3-2x^2-x+2) \end{gathered}[/tex]Therefore, x is a factor of the denominator.
Let us now factorize the remainder
[tex]x^3-2x^2-x+2[/tex]Let us substitute x = 1 into the function to confirm if it is a factor.
[tex]\begin{gathered} x=1 \\ 1^3-2(1)^2-(1)+2 \\ 1-2-1+2=1+2-1-2=3-3=0 \end{gathered}[/tex]Therefore, (x - 1) is a factor.
Let us now divide the function by (x - 1)
[tex]\frac{x^3-2x^2-x+2}{x-1}=\frac{\left(x-2\right)\left(x+1\right)\left(x-1\right)}{x-1}=(x-2)(x+1)[/tex]Hence, the factors of the denominator are,
[tex]x(x-1)(x+1)(x-2)[/tex]Therefore,
[tex]f(x)=\frac{x+2}{x(x-1)(x+1)(x-2)}[/tex]Now, looking at both the numerator and the denominator, we can observe that there is no common factor between the numerator and the denominator.
Hence, there is no removable discontinuity.
Related Questions
for the line of fit p = -26t + 5,649 , where t is the number of years since 1990 , what is the residual of the data point at t = 5?
Answers
According to the problem, the equation of the line that best fit is
[tex]p=-26t+5649[/tex]To find the population when t = 5, we just have to evaluate the expression.
[tex]\begin{gathered} p=-26\cdot5+5649=-130+5649 \\ p=5519 \end{gathered}[/tex]Note that this value (p=5519) is different from the value assigned in the given table. In this way, the residual refers to the difference between these values.
[tex]r=5530-5519=11[/tex]It's important to know that the residual r=11 is positive because the value shown in the table (empirical data) is greater than the resulting value from the equation.
Therefore, the residual is 11.what percent of 14 is 21?
Answers
Let's calculate the percentage
[tex]\frac{14}{21}=\frac{2}{3}=0.666=66.66\text{ \%}[/tex]The answer would be 66.66%.
Anthony, an aspiring meteorologist, spent the past few weekends studying the clouds. He took detailed notes on the types of clouds observed and the time of day they were observed. Stratocumulus Stratus Morning 4 1 Afternoon 3 7. 8 4 Evening What is the probability that a randomly selected cloud was observed in the afternoon or morning? Simplify any fractions.
Answers
The searched probability is
[tex]P(\text{AFTERNOON }\cup\text{ MORNING)}[/tex]is given by
[tex]P(\text{AFTERNOON }\cup\text{ MORNING)}=\text{ }P(\text{AFTERNOON )}+P(\text{ MORNING)-}P(\text{AFTERNOON }\cap\text{ MORNING)}[/tex]which gives
[tex]P(\text{AFTERNOON }\cup\text{ MORNING)}=P(\text{AFTERNOON )}+P(\text{ MORNING)}[/tex]because the events "afternoon" and "morning" are mutually exclusive. Then, we get
[tex]\begin{gathered} P(\text{AFTERNOON }\cup\text{ MORNING)}=\frac{5}{27}+\frac{10}{27} \\ P(\text{AFTERNOON }\cup\text{ MORNING)}=\frac{15}{27} \end{gathered}[/tex]then, the answer is 15/27
The equation y = 11x represents the liters of water a baseball team drinks each practice. This equation shows that after two practices, the team will have consumed 22 liters of water.
Determine the constant of proportionality.
11
22
0.18
5.5
Answers
The constant of proportionality is equal to 11.
Constant of ProportionalityThe constant of proportionality is the ratio that relates two given values in what is known as a proportional relationship. Other names for the constant of proportionality include the constant ratio, constant rate, unit rate, constant of variation, or even the rate of change.
In this question, the constant of proportionality is that value that doesn't change or represents the number of players while x represented the number of games they played.
The constant of proportionality can be solved mathematically as
[tex]y = 11x\\x = 2\\22 = 11(2)\\22 = 22\\[/tex]
The constant of proportionality is the value that makes y = 11x and it is 11.
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0.0000235 in scientific notation
Answers
Answer:
2.35 × 10⁻⁵
Step-by-step explanation:
Scientific notation (also called "Standard form") is written in the form
a × 10ⁿ where 1 ≤ a < 10 and n is any positive or negative whole number.
To convert a number into scientific notation, move the decimal point to the left or right until there is one digit to the left of the decimal point.
The number of times you have moved the decimal point is the power of 10 (the value of n).
If the decimal point has moved to the left, n is positive.If the decimal point has moved to the right, n is negative.To convert 0.0000235 to scientific notation:
Move the decimal point 5 places to the right so that a = 2.35. As the decimal point has been moved 5 places the right, n = -5.Therefore, 0.0000235 = 2.35 × 10⁻⁵.
Gravel is piled in the shape of a cone. The circumference of the base is 221 ft. The slant height is 43 ft. Find the volume of gravel
Answers
Answer:
Step-by-step explanation:
Give the digits in the hundred thousands place and the ten thousands place.803,519
Answers
Given the number
[tex]803519[/tex]To get the digits in the hundred thousand places and the ten thousand place, we will first list out the values of all the digits
The Hundred thousands place is 8
Estimate the sum or difference
76.81 + 2.17
Answers
The estimated sum of 76.81 and 2.17 is 79.
The first number given to us is 76.81.
The second number given to us is 2.17.
We need to find the estimated sum of the two numbers.
To find the estimated sum, we will round off the numbers to the nearest tenth.
Rounding a number implies simplifying it while retaining its value close to what it was. The end output is less precise but more usable.
After rounding, the first number becomes 76.8.
After rounding, the second number becomes 2.2.
The estimated sum is the addition of these rounded numbers.
The estimated sum is 76.8 + 2.2 = 79.
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Investor A decided to purchase a home with a loan amount of $390,000, 3.30% annually fixed rate for a 30 years term, and one payment per month. What is the monthly payment for this mortgage? Round to the nearest cent
Answers
The monthly payment for this mortgage is $2156
What is simple interest?It is the interest calculated on the principal at a given rate for a time period.
We have,
Principal = $390,000
Rate = 3.30%
Time = 30 years
The simple interest is given by:
SI:
= P x R x T / 100
= (390,000 x 3.30 x 30) / 100
= (390,000 x 330 x 30) / (100 x 100)
= 39 x 330 x 30
= 386100
Total amount to pay in 30 years.
= Principal + SI
= 390,000 + 386,100
= 776100
The monthly payment:
30 years = 12 x 30 months = 360 months
Now,
Monthly payment:
= 776100 / 360
= 2155.83
= $2156
Thus,
The monthly payment for this mortgage is $2156
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twice a number y diminished by 2 is less than or equal to fourteen
Answers
Answer: 2y-2 ≤ 14
Step-by-step explanation:
help me pleaseee!!!
thank you
Answers
The cost C(x) for printing any amount of copies is C(x) = 0.25x + 75.
What is an expression?An expression is in the form of variables and constants separated by the operation of addition and subtraction.
Given the initial cost of producing a newsletter has an initial charge of 75 dollars for formatting and editing and 0.25 dollars for printing each copy.
Here the initial cost is a constant and now of. of copies is a variable in x.
∴ Our equation for expressing the cost C(x) for printing any amount of copies is,
C(x) = 0.25x + 75.
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52. 3×16 I’ve been on this question for a while I don’t know what homework they give kids now days and they do it so different
Answers
Answer: 3x16=48
Step-by-step explanation: Multiplying is just like adding multiple times, so this is 16x3, or adding 16 three times. 16+16+16=48 I hope this helps!
A thermometer shows a temperature of -20 degrees. A chemist recorded this temperature in her notebook using a decimal. Which number did the chemist write in the notebook? 0-21 -21.3 -20.75 -20.34
Answers
hello
to solve this question, we an simply write the answer as -20.13
May u please help me with Geometry. The last one question.
Answers
Beacuse to both sides of the equation you distribute the number that is outside the parentheses when making the product.
Then, you operate on both sides of the equation -7x, that is, you use the additive inverse of 7x
[tex]\begin{gathered} 7x-7-7x=6x-4-7x \\ -7=-1x-4\text{ }\rightarrow\text{ additive inverse property} \\ \end{gathered}[/tex]Then, you operate on both sides of the equation 4, that is, you use the add inverse of -4
[tex]\begin{gathered} -7=-1x-4 \\ -7+4=-1x-4+4 \\ -3=-1x\text{ }\rightarrow\text{ additive inverse property} \end{gathered}[/tex]Finally,
[tex]\begin{gathered} -3=-1x \\ \frac{-3}{-1}=x\text{ }\rightarrow\text{ Division property} \\ 3=x\text{ }\rightarrow\text{ Reflexive property} \end{gathered}[/tex]y4321Find thevertex of thiquadratic.([?], [ ])X-4 -3 -2 -1 0 1 2 3 4-1-2-3-4
Answers
By the graph, we can see that the vertex is placed where x = 1 and y = -3
what is the median? -95, -94, -93, 95, 91, -92, -89, -92, -98
Answers
Given the set of the data:
[tex]-95,-94,-93,95,91,-92,-89,-92,-98[/tex]Arranging the data in order from the least to the greatest:
[tex]-98,-95,-94,-93,-92,-92,-89,91,95[/tex]The number of the data = 9
so, the median is the number which is in the middle
It will be number (9+1)/2 = 10/2 = 5
so, the median = -92
which of the following values make the equations below true 4(x-2)=2x-3(x=2)
Answers
The value of x that makes the equation true where the equation is given as 4(x - 2)=2x - 3 is 5/3
What are linear equations?These are equations with constant average rates of change
How to determine the solution that makes the equation true?The equation is given as
4(x-2)=2x-3
Rewrite the equation properly
So, we have
4(x - 2)=2x - 3
The above equation is a linear function with one variable
So, we have
4(x - 2)=2x - 3
Open the brackets in the above equation
So, we have
4x - 8 =2x - 3
Add 8 to both sides of the equation
So, we have
4x =2x + 5
Subtract 2x from both sides of the equation
So, we have
3x = 5
Divide both sides of the equation by 3
So, we have
x = 5/3
Hence, the value of x in the equation is 5/3
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How is the input force different from the output force? Responses The input force is all of the energy applied to the situation, and the output force is the result. The input force is all of the energy applied to the situation, and the output force is the result. The input force is applied to the problem, and the output force is the movement that results. The input force is applied to the problem, and the output force is the movement that results. The output force is applied to the simple machine, and the input force is the force the simple machine applies to an object. The output force is applied to the simple machine, and the input force is the force the simple machine applies to an object. The input force is applied to the simple machine, and the output force is the force the simple machine applies to an object. also this is 29pts
Answers
By Newton's third law, we can see that the correct option is:
" The input force is applied to the simple machine, and the output force is the force the simple machine applies to an object."
How the input and output forces differ?
By Newton's third law, we know that if a object A exerts a force on object B, then the object B exerts a force of equal magnitude and opposite direction in object A.
The input force in that case would be the one done by object A, and the output force is the one that object B does as a reaction.
With that in mind, we can see that the correct option will be:
" The input force is applied to the simple machine, and the output force is the force the simple machine applies to an object."
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Write an equation using four numbers that multiply to , none of which are opposites.
Answers
An equation using four numbers that add to 0 none of which are opposites is 15 + (-10) + 1 + 4
What is an equation?It should be noted that an equation is simply used to show the relationship between the variables.
Based on the information given, the appropriate equation will be:
= 15 + (-10) + 1 + 4
= 15 - 10 + 1 + 4
= 0
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Write an equation using four numbers that as
add to 0 none of which are opposites.
Find the product. Write the product in rectangular form, using exact values.
Answers
We must find the product of complex numbers and write it in rectangular form i.e. like a+ib where a and b are real numbers. In order to do tthis we first need to write the values of the sine and cosine of 120° and 210°. For this purpose we can use a table displaying the values of the trigonometric functions for several angles. However, these tables usually display the values for angles between 0° and 90° like the following one:
However this table is still useful. 120° is an angle in the second quadrant which means that it has the same sine as an angle of the first quadrant that meets x=180°-120° and its cosine is the same but multiplied by -1. We have x=180°-120°=60° which means that:
[tex]\begin{gathered} \sin120^{\circ}=\sin60^{\circ}=\frac{\sqrt{3}}{2} \\ \cos120^{\circ}=-\cos60^{\circ}=-\frac{1}{2} \end{gathered}[/tex]We can do something similar for 210°. It's in the third quadrant which means that both its sine and cosine are thoes of x=210°-180°=30° but multiplied by -1. Then we get:
[tex]\begin{gathered} \sin210^{\circ}=-\sin30^{\circ}=-\frac{1}{2} \\ \cos210^{\circ}=-\cos30^{\circ}=-\frac{\sqrt{3}}{2} \end{gathered}[/tex]Now that we found the sine and cosine of both angles we can rewrite the product:
[tex]\begin{gathered} \lbrack4(\cos210^{\circ}+i\sin210^{\circ})\rbrack\cdot\lbrack5(\cos(120^{\operatorname{\circ}})+\imaginaryI\sin(120^{\operatorname{\circ}}))\rbrack= \\ =\lbrack4(-\frac{\sqrt{3}}{2}-i\frac{1}{2})\rbrack\cdot\lbrack5(-\frac{1}{2}+\mathrm{i}\frac{\sqrt{3}}{2})\rbrack=\lbrack-2\sqrt{3}-2i\rbrack\cdot\lbrack-\frac{5}{2}+\mathrm{i}\frac{5\sqrt{3}}{2}\rbrack \end{gathered}[/tex]Then we get:
[tex]\begin{gathered} \lbrack-2\sqrt{3}-2i\rbrack\cdot\lbrack-\frac{5}{2}+\mathrm{i}\frac{5\sqrt{3}}{2}\rbrack=2\sqrt{3}\cdot\frac{5}{2}-i2\sqrt{3}\cdot\frac{5\sqrt{3}}{2}+i2\cdot\frac{5}{2}-i\cdot i\cdot2\cdot\frac{5\sqrt{3}}{2} \\ =5\sqrt{3}-i15+i5+5\sqrt{3}=10\sqrt{3}-10i \end{gathered}[/tex]AnswerThen the answer is:
[tex]10\sqrt{3}-i10[/tex]Answer:
20 cis 420o = 20 cis 60o
Step-by-step explanation:
Evelyn's friend, Natalie needs 40 yards of yarn to make 10 quilts. How many yards of yarn does she need to make 12 quilts?
Answers
Answer:
48
Step-by-step explanation:
40 yards / 10 quilts = 4 yards per quilt
12 * 4 = 48
Hope this helps.
Answer:
48 yards
Step-by-step explanation:
Hey there!
To find the answer, we must first find how much yards of yarn she needs for 1 quilt
we do, 40/10 which is 4
Meaning, she needs 4 yards of yarn to make 1 quilt
Now we multiply 4 by 12 since we are making 12 quilts
4 x 12 = 48
So, Natalie needs 48 yards of yarn to make 12 quilts
8. In a recent survey of 1002 people, 701 said that they voted in a recent presidential election.Voting records show that 61% of eligible voters actually did vote.a) Find the 95% confidence interval estimate of the proportion of people who say that they voted.b) Are the survey results consistent with the actual voter turnout of 61%? Why or why not?c) How would the confidence interval change if we increased the confidence level to 99%? Findthe 99% confidence interval estimate to support your answer.
Answers
Here, we want to find the 95% confidence interval estimate of the proporton of people who say that they voted
The proportion of people who say they voted will be;
701/1002 = 0.70
The actual proportion of people that voted = 61% = 0.61
Mathematically, the confidence interval CI will be;
[tex]undefined[/tex]can you help me on the part Drawing the Ace of Spades please
Answers
Solution
There is just one ace of spades
Therefore, the probability of drawing the ace of spade is;
[tex]\frac{1}{52}[/tex]Three students attempt to define the geometric object called an angle.
Can you match the teacher's comments to the definitions?
Answers
The explanation of the geometric shape known as an angle is made by three students. The matching answer is 1-1, 2-2,3-3.
Given that,
The explanation of the geometric shape known as an angle is made by three students.
We have to match the definitions to the teacher's comments.
Step1: definition of angle
Step2: teachers comments
1- Ruby's definition: The amount of turn between two straight lines that have a common vertex.
1-Bingo! you got it.
2-Shriya's definition: Two lines that come together.
2- Were you thinking of intersecting lines?
3- Abhishek's definition: A figure composed of two rays sharing a common endpoint. The common endpoint is known as vertex.
3-You seem to be getting at the idea of the measure of an angle,
not the definition of the angle itself.
Therefore, The matching answer is 1-1, 2-2,3-3.
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A TV has a listed price of $510.99 before tax. If the sales tax rate is 8.25%, find the total cost of the TV with sales tax included.
Round your answer to the nearest cent, as necessary.
Answers
The most appropriate choice for sales tax will be given by-
Total cost of the TV with sales tax included is $553.15
What is sales tax?
Sales tax is a tax imposed by the government on the price of a commodity for the sale of that commodity. Imposing sales tax on a product increases the price of the product. Nowadays, sales tax has been replaced by Goods and Service Tax (GST).
Here,
Listed price of television = $510.99
Rate of sales tax = 8.25%
Sales tax to be added = [tex]\frac{8.25}{100}\times 510.99[/tex]
= $[tex]42.16[/tex]
Total cost of the TV with sales tax included = $(510.99 + 42.16)
= $553.15
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Question
Ben takes out a loan of $2,500 with a 5.5% interest rate that is compounded semi-annually.
If he pays off the loan in 5 years, how much will he end up paying? Round your answer to the nearest dollar.
Answers
Ben end up paying $3279.12 over the course of five years with rate of interest 5.5% for a principal of $2500.
Explanation:Compounding interest semiannually means that at the start of the compounding period, in this case, every six months, the principal of a loan or investment includes the total interest from the previous period.
In the question, we are given the following information:
P = $2500
r = 5.5% = 0.055
t = 5 years
n = 2
The compound interest is calculated as follows:
A = [tex]P(1 + r/n)^{nt}[/tex]
where A denotes the amount, p denotes the principal, r denotes the interest rate, t denotes the time in years, and n denotes the type of compound interest.
A= 2500( 1 + 0.055/2)¹⁰
= 3279.12 ≈ $3279
A = $3279.12
Ben will end up paying $3279.12 at the end of 5 years for n = 2.
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Which of these is a point-slope equation of the line that is perpendicular toy-3= 4(x-10) and passes through (-3, 7)?A.y+7=-1(x-3)B. y+ 7 = 4(x-3)OC. y-7= -4(x+3)OD. y-7=-1/(x+3)
Answers
Given: y-3=4(x-10) passes through (-3,7).
Find: equation of lie that is perpendicular to the given equation
Explanation: y-3=4(x-10)
y-3=4x-40
y=4x-37
for to find the equation of perpendicular line ,
y=mx+c
for to equation of line that is perpendicular to y=4x-37
slope m will be
[tex]-\frac{1}{m}[/tex]so the equation becomes.
[tex]y-7=-\frac{1}{4}(x+3)[/tex]Final answer: option D is correct answer.
Newton sleeps 9hours each night. How many hours does he sleeps in 1 week
Answers
If the measure of arc AB is 64 degrees, what is the measure of angle ADB?
Answers
Answer:— If the measure of arc AB is 64 degrees, what is the measure of angle ADB?0 64 degrees 128 degrees 32 degrees 90 degrees.
Step-by-step explanation:
Your answer is incorrect. A house has increased in value by 24% since it was purchased. If the current value is $527,000, what was the value when it was purchased? $102.000
Answers
We are given the final value of the house after its price was increased by 24%
We must go back to the original price knowing the final price. It's called inverse percentage calculation
To calculate the 24% of the value, we multiply by 24 and divide by 100, that is
value * 24 / 100 = 0.24 * value
The original price of the house is 100%, the increase is 24%, thus the final value of the house is 100% + 24% = 124%
What we were given as data is 124% of the original price of the house
As we did above, to compute 124% of a value, we multiply by 124 and divide by 100. Being P the original price of the house, then the final value is
P * 124% = P * 124 / 100 = 1.24 * P
We know this value:
1.24 * P = $527,000
Divide by 1.24 both sides of the equation
P = $527,000 / 1.24 = $425,000
The original price of the house was $425,000
Let's check it out:
Original price: $425.000
Increase: 0.24 * 425,000 = $102,000
Final Price: $425,000 + $102,000 = $527,000
The condition is met and the question is answered
