Demonstrating that the limit doesn't exist
What is Limits?
The value that a function approaches when the input approaches a certain value is known as a limit. Calculus and mathematical analysis are not possible without limits, which are used to define continuity, derivatives, and integrals.
The limit exists only if the value of the limit along every direction that leads to (1,1) is same.
So by calculating,
lim xy -x-y + 1 / x^2 + y^2 - 2x - 2y + 2
x->1
calculating the limit along the line x = 1
Similarly,
lim xy -x-y + 1 / x^2 + y^2 - 2x - 2y + 2
x->1
calculating the limit along the line y = 1
And the last limit you calculated is along line y=x.
To answer your question, the calculation of the limit along y=1 would not have been necessary. It is sufficient to demonstrate the absence of a limit by giving just two cases in which it appears to vary along several directions.
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HELP PLEASEEEEEEEEEEEEEE
Using equation;
The monthly payment is 67.5 dollars
The hours of labour that is required to replace the water pump is 4 hours
How to use equation to solve a problem?The purchase of the large TV including finance charges is 1615 dollars . A down payment of 400 dollars was paid. The remainder was paid in 18 monthly instalment payment.
Therefore, using equation,
let
x = amount paid each month
The monthly payment can be found as follows:
1615 = 400 + 18x
1615 - 400 = 18x
1215 = 18x
divide both sides by 18
x = 1215 / 18
x = 67.5 dollars
Therefore,
monthly payment = 67.5 dollars
The cost of replacing a water pump was 465 dollars. This include 145 dollars for water pump plus 80 dollars per hour for labour .
The number of hours for labour that was used to replace the water pump can be calculated as follows:
Using equation,
465 = 145 + 80h
where
h = number of hours for labour
465 - 145 = 80h
320 = 80h
h = 320 / 80
h = 4 hours
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What is the value of 7!
Parallelogram
How divide the figure?
Becca works for the Humane Society and had to buy food for the dogs. She bought 5 1/2 pounds of dog food. She feeds each dog about one-third of a pound. How many dogs can she feed?
Becca works for the Humane Society and had to buy food for the dogs. She bought 5 1/2 pounds of dog food. She feeds each dog about one-third of a pound. How many dogs can she feed?
_______________________________________________________
Food ÷ amount of food per dog
5 1/2 pounds of dog food ÷ 1/3
5 1/2 ÷ 1/3 = (10/2 +1/2) ÷ 1/3 = 11/2 ÷ 1/3 = 11/2 x 3/1 = 33/ 2
33/ 2 = 16 1/5 = 16.5
_______________________________________
Can you see the updates?
___________________________________
Answer
She can feed 16.5 (16) dogs with 5 1/2 pounds of dog food
_________________________________________
Do you have any questions regarding the solution?
Please answer please please
As part of your job you spend time each day contacting former customers. During one week, you contacted 15 people on Monday, 12 on Tuesday, 14 on Wednesday, 11 on Thursday, and 13 on Friday. What is the average number of customers contacted each day? Which averaging method did you use?
The average number of customers contacted each day is 13. We used the basic average method which is explained below.
The formula for calculating the average is:
Sum of all the observations ÷ Total number of observations
So, according to the formula
Sum of all the observations = People contacted on (Monday+ tuesday+wednesday+thursday+friday)
= 15+12+14+11+13
= 65
Number of observations = 5
So putting values in the formula, we get
65÷5
= 13
Hence, the average number of customers contacted is 13.
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Find the exact area of thetriangle below.
I am going to draw a picture to ilustrate the solution
Now, we are going to use the trigonometric functions for the right triangle on the left to calculate h
[tex]\sin (30)\text{ = }\frac{h}{10\sqrt[]{3}}\Rightarrow\text{ h= sin(30)}\cdot\text{ 10}\sqrt[]{3\text{ }}=\frac{1}{2}\cdot10\sqrt[]{3}=5\sqrt[]{3}[/tex]Now we use the formula for the area of a triangle
[tex]A=\frac{b\cdot h}{2}=\text{ }\frac{20\cdot5\sqrt[]{3}}{2}=50\sqrt[]{3}[/tex]Select the 3 options below that are equal in value. For example, if one of the terms
equals 0.85, so do the other two.
sample size
area under the curve
proportion
probability
One of the terms equals 0.85, so do the other two:
sample size
proportion
probability
How can sample size be determined?
to calculate the sample size in five easy steps
Define population size or total population.Indicate your error margin.You should assess your level of confidence.Calculate the anticipated variance.finalize the size of your sampleCalculating sample size requires knowledge of or estimation of three or four factors:
the effect size (often the difference between two groups); the population standard deviation (for continuous data); the required power of the experiment to detect the supposed effect; the significance threshold.To learn more about sample size refer to:
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Determine the value of x. Use the Pythagorean Theorem. Show your work.
The value of x (hypotenuse) using the Pythagorean Theorem is 5 units.
What is Pythagorean Theorem?The Pythagorean Theorem states that the squares on the hypotenuse (the side across from the right angle) of a right triangle, or, in familiar algebraic notation, a² + b², are equal to the c² which is the hypotenuse.So, the formula of the Pythagorean Theorem:
c² = a² + b²Where a (AC) = 4 and b (CB) = 3 as the given figure is symmetric and so line CB will be equal to 3.
Now,
c² = a² + b²c² = 4² + 3²c² = 16 + 9c² = 25c = √25c = 5Therefore, the value of x using the Pythagorean Theorem is 5 units.
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Number 12 I don’t get it y’all know ?
Answer:
Approximately $18 each month.
Step-by-step explanation:
This is quite simple. So, we know that there are 12 months in a year. And we know that in a year, the store has given out discounts totaling up to $216. All we have to do is divide the total number by how many months there are in a year.
[tex]216\div12=18[/tex]
This means that the store gives out $18 of discounts per month.
(Also, you don't seem college level)
Can you help break this down. I do not understand at all
Given:
There is an expression given in the question as,
[tex]4x-2(3x-9)[/tex]Required:
We need to find the equal equation in the given option.
Explanation:
First we simplify the given equation
[tex]\begin{gathered} 4x-2(3x-9) \\ =4x-6x+18 \\ =-2x+18 \\ =18-2x \end{gathered}[/tex]Final answer:
[tex]18-2x[/tex]
Please help I need this answer immediately
Answer:
Step-by-step explanation:
−2x−y−2z−4x−2y+3z
Combine −2x and −4x to get −6x.
−6x−y−2z−2y+3z
Combine −y and −2y to get −3y.
−6x−3y−2z+3z
Combine −2z and 3z to get z.
−6x−3y+z
DIFFERENTIATE W.R.T. X
−6
A bank deposit paying simple interest grew from an initial amount of $1100 to $1265 in 6 months. Find the interest rate.
If the bank deposit paying simple interest grew from an initial amount of $1100 to $1265 in 6 months, then the interest rate is 30%
The initial amount = $1100
The final amount = $1265
So simple interest = 1265-1100
= $165
Time period = 6 months = 6/12 years
We know
Simple interest I = P×r×t
Where P is the initial amount
r is the interest rate
t is the time period
Substitute the values in the equation
165 = 1100×r×(6/12)
165 = 550×r
r = 165/550
r = 0.3
r = 30%
Hence, If the bank deposit paying simple interest grew from an initial amount of $1100 to $1265 in 6 months, then the interest rate is 30%
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The pie chart below representsEliana's monthly budget. Whatpercentage of her budget isallocated to savings?
Answer:
percentage = 528/ 3,300*100= 16%
Step-by-step explanation:From the pie chart we can see that saving are 528 dollars, so
now we need to calculate total from the given pie chart, which is
3,300 dollars. So percentage is savings( 528 dollars) divided by total( 3,300 dollars) and then finally multiply by 100
MAKE CONNECTIONS For AC, select an equation you can use to find AB.
O A) 1.5 + 3.7 = AB
O B) AB + 3.7 = 1.5
O c1.5 + AB = 3.7
O D) 1.5 - AB = 3.7
The correct connections for AC will be option b) AB+3.7 = 1.5. Two expressions joined by the equals symbol ("=") form an equation.
What is meant by equation?A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. We determine the value of the variable x as x = 7 by solving this equation.Identity equations and conditional equations are the two types of equations. All possible values of the variables result in an identity. Only certain combinations of the variables' values make a conditional equation true. Two expressions joined by the equals symbol ("=") form an equation.Different types of equationEquation with a line.Extreme EquationEquation with exponents.Equation with logic.Hence, The correct connections for AC will be option b) AB+3.7 = 1.5.
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A large cooler contains 16 lemonade 5 sprite 10 cans of coke and 9 cans of root beers you randomly pick two cans one at a time (without replacement) what is the probability you don’t get two cans of
The most appropriate choice for probability will be given by-
Probability of not getting two cans of coke is [tex]\frac{49}{52}[/tex]
What is probability?
Probability of an event is the chance of occurance of that event.
Probability is calculated by Number of favourable outcomes divided by total number of outcomes
Here,
Number of lemonades in a cooler = 16
Number of sprite in a cooler = 5
Number of cans coke in a cooler = 10
Number of cans of root beers in a cooler = 9
Total number of refreshments = 16 + 5 + 10 + 9
= 40
Probability of getting a can of coke in the first draw = [tex]\frac{10}{40}[/tex]
= [tex]\frac{1}{4}[/tex]
Probability of getting a can of coke in the second draw = [tex]\frac{9}{39}[/tex]
= [tex]\frac{3}{13}[/tex]
Probability of getting two cans of coke in the two draws = [tex]\frac{1}{4} \times \frac{3}{13}[/tex]
= [tex]\frac{3}{52}[/tex]
Probabilty of not getting two cans of coke in the two draws = [tex]1-\frac{3}{52}[/tex]
= [tex]\frac{52-3}{52}[/tex]
= [tex]\frac{49}{52}[/tex]
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x+12% of x= 3.36 help
Answer:
x = 3
Step-by-step explanation:
x + .12x = 3.36 Combine like terms
1.12x = 3.36 Divide both sides of the equation by 1.12
x = 3
=======================================
Work Shown:
12% = 12/100 = 0.12
x + 12% of x = x + 0.12x = 1.12x = 3.36
1.12x = 3.36
x = 3.36/1.12
x = 3
---------------
Check:
12% of 3 = 0.12*3 = 0.36
x + 12% of x = 3 + 12% of 3 = 3 + 0.36 = 3.36
Or you could say 1.12x = 1.12*3 = 3.36
The answer is confirmed.
HELP FOR 100pts
ONLY FOR TWACK
Answer:
3:2
Step-by-step explanation:
solve similar triangles (advanced) khan academy. solve for x
The length of the unknown side of the triangle using similar triangle ratio concept is; x = 24
How to Solve similar triangles?We want to find the length of the unknown side of the similar triangles.
Similar triangles are defined as triangles that have the same shape, but their sizes may vary. All equilateral triangles, squares of any side lengths are examples of similar objects. Thus, we can say that if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.
From the given triangle ADE which is divide into a similar triangle ABC with an unknown side x, we can use the concept of similar triangle ratios to get the unknown value of x as;
6/x = 8/(x + 8)
Cross multiply to get;
6(x + 8) = 8x
6x + 48 = 8x
8x - 6x = 48
2x = 48
x = 48/2
x = 24
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find the length of arc JM. use 3.14 for pi. round to nearest tenth
hello
to solve this problem, we need the formula of length of an arc
[tex]\begin{gathered} L_{\text{arc}}=\frac{\theta}{360}\times2\pi r \\ \end{gathered}[/tex]t find the value of angle JM, we should take into cognizance that the sum of angles in a circle is equal to 360 degree and angle on a straight line is equal to 180 degree
[tex]\begin{gathered} jk+jm+mk=360 \\ 180+jm+90=360 \\ 270+jm=360 \\ jm=360-270 \\ jm=90 \end{gathered}[/tex]now we know the value of angle jm, let's find the length of the radius
[tex]\begin{gathered} \text{radius}=\frac{\text{diameter}}{2} \\ \text{diameter}=16.4 \\ \text{radius(r)}=\frac{16.4}{2}=8.2\text{miles} \end{gathered}[/tex]with all the necessary informations or data required, we can now proceed to solve for the length of arc jm
[tex]\begin{gathered} L_{\text{arc}}=\frac{\theta}{360}\times2\pi r \\ L_{\text{arc}}=\frac{90}{360}\times2\times3.14\times8.2 \\ L=12.87\text{miles} \end{gathered}[/tex]from the calculations above, the length of the arc is equals to 12.87 miles
Answer:
12.9
Step-by-step explanation:
Choose the fraction that is equal to 0.81:
A.9/11
B.81/100
C.8/9
D.80/99
Answer: B
Step-by-step explanation:
Answer:
B. 81 / 100
Step-by-step explanation:
9 / 11 = 0.82
81 / 100 = 0.81
8 / 9 = 0.89
80 / 99 = 0.80
Hope this helps! :)
A staff member lives in Bermondsey and has to be in Birmingham for 10.45 am. It will take her an hour from her home to get to Euston station, for Birmingham train. The journey from Euston to Birmingham takes an hour and ten minutes.Trains to Birmingham run at 5 minutes past the hour, 25 minutes past the hour and 45 minutes past the hour. The venue is a 5-minute walk from the station. What is the latest time that the staff member can leave home to make it in time for the meeting in Birmingham ?
The latest time that the staff member can leave home to make it in time for the meeting in Birmingham is 8.30 am.
Time
Time is used to quantify, measure or compare the duration of events or the intervals between them, and even, sequence events.
Given,
A staff member lives in Bermondsey and has to be in Birmingham for 10.45 am.
Here we need to find the latest time that the staff member can leave home to make it in time for the meeting in Birmingham
From the given details we know identified that,
The staff members has to be present in Birmingham at 10.45am.
But they are all in Bermondsey, it will take 1 hour 10 mins travel to arrive the destination.
So, the time before 1 hour is 9.35 am.
The travel time between train station from home is 1 hour is,
So, the time is 8.35 am.
Venue distance is 5 minutes from station.
So, when we include this then the time to leave the home is,
=> 8.30 am.
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Write the angle relationship for each pair of angles
Types of angles are given below
What are angles?An angle is a figure in Euclidean geometry made up of two rays that share a vertex, or common terminus, and are referred to as the sides of the angle. The plane that contains the rays is where two rays' angles are located. Two planes intersecting at an angle also produces an angle. We call to these as dihedral angles.
Given Data
∠1 and ∠4 are vertical opposite angles.
∠2 and ∠7 are alternate exterior angles.
∠4 and ∠8 are corresponding angles.
∠3 and ∠5 are co interior angle.
∠6 and ∠8 are co linear angles.
∠1 and ∠7 are alternate exterior angle.
∠3 and ∠6 are alternate interior angle.
∠1 and ∠3 are co linear angle.
∠2 and ∠6 are corresponding angles.
∠6 and ∠7 are vertical opposite angle.
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I can’t find the answer for the application
Value of x is 16/91
How to Find value of x ?
In question
(8/7)/(13/9) = x / (2/9)
Divide the numbers 72/91 =x/(2/9)
Multiply all terms by the same value to eliminate fraction denominators182* (72/91) = 182* (x/(2/9))
Cancel multiplied terms that are in the denominator2 *72 = 819 * x
Multiply the numbers144 = 819 * x
Divide both sides by the same factor(144/819) = 819 *x / 819
SimplifyX = 16/91
The value of x is 16/91
Definition of Fraction :
A fraction represents a part of a whole or, more generally, any number of equal parts.In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator.There are in total six types of fractions such as:
Proper fractionImproper fractionMixed fractionLike fractionsUnlike fractionsEquivalent fractionsTo learn more about fractions refer :
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x(x+5)+2x(x-4)
can anyone awnser me this step by step :)
Answer: 3x^2−3x
Step-by-step explanation:
1.) Distribution
2.) Combine like Terms
3.) Combine like Terms.. again
4.) Common Factor
5.) GET UR SOLUTION!!
A vehicle can cover 80 kilometers in 2 ½ hours. How many kilometers can it cover in 6 hours?
1) The probability of getting exactly three girls in a family of five children.
2)The probability of getting at least two boys in a family of seven children.
3) The probability of getting a total of 15 when four dice are thrown.
4) Assume that ten percent of us are left-handed. The probability of getting at least two left-handed people in a group of 7.
5) The probability that when 75 people are surveyed, at least five of them have the same birth date. (Ignore leap years).
Using the binomial distribution, the probabilities are given as follows:
1) Three girls in a family of five children: 0.3125 = 31.25%.
2) At least two boys in a family of seven children: 0.9375 = 93.75%.
3) Total of 15 when four dice are thrown: 0.1080 = 10.80%.
4) At least two left-handed people in a group of 7: 0.1497 = 14.97%.
5) At least five of them have the same birth date: 0%.
What is the binomial distribution formula?The formula for the probability of x successes is:
[tex]P(X = x) = C(n,x).p^{x}.(1-p)^{n-x}[/tex]
[tex]C(n,x) = \frac{n!}{x!(n-x)!}[/tex]
The parameters are given by:
n is the number of trials of the experiment.p is the probability of a success on a single trial of the experiment.Item 1A children is equally as likely to be a boy or a girl, hence the parameters are given as follows:
n = 5, p = 0.5.
The probability is P(X = 3), hence:
P(X = 3) = C(5, 3) x (0.5)³ x (0.5)² = 0.3125 = 31.25%.
Item 2The parameters are:
n = 7, p = 0.5.
The probability of at least two boys is:
P(X >= 2) = 1 - P(X < 2).
In which:
P(X < 2) = P(X = 0) + P(X = 1).
Then:
P(X = 0) = (0.5)^7 = 0.0078.P(X = 1) = C(7,1) x (0.5)^7 = 0.0547.P(X < 2) = P(X = 0) + P(X = 1) = 0.0078 + 0.0547 = 0.0625.P(X >= 2) = 1 - P(X < 2) = 1 - 0.0625 = 0.9375 = 93.75%.Item 3This one is simple probability, number of desired outcomes divided by the number of total outcomes.
When 4 dice are thrown, we have that:
There are 140 outcomes with a sum of 15.There are 6^4 total outcomes.Hence the probability is:
p = 140/(6^4) = 0.1080 = 10.80%.
Item 4The parameters are:
n = 7, p = 0.1.
Hence, similarly to item 2:
P(X = 0) = (0.9)^7 = 0.4783.P(X = 1) = C(7,1) x (0.1) x (0.9)^6 = 0.3720.P(X < 2) = P(X = 0) + P(X = 1) = 0.4783 + 0.3720 = 0.8503.P(X >= 2) = 1 - P(X < 2) = 1 - 0.8503 = 0.1497 = 14.97%.Item 5The parameters are:
n = 75, p = 1/365 = 0.0027.
Then the probability is:
P(X >=5) = 1 - P(X < 5).
In which:
P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4).
Using a calculator, it is found that P(X < 5) = 1, hence the probability is of 0%, as P(X >=5) = 1 - 1 = 0.
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How many people would it be if I did 1.2% of French speakers and 5,053,004, representing the whole population? I needed help on calculating how many people it would be with those two numbers.
60,636.048 people are french speakers when the population is 5,053,004 and only 1.2% are the french speakers.
What is Percent?Percentages are basically fractions with a denominator of 100. We use the percent symbol (%) beside a number to indicate that it is a percentage. A percentage is a relative value that represents the hundredth part of any quantity. One percent (symbolized 1%) is one hundredth part; thus, 100 percent represents the entire amount.
What is method to calculate the percent?To manually calculate percentages, follow these steps:
1. Determine the number's initial format to be converted to a percentage.
The decimal or fraction format of the number to be converted to a percentage can be used. The next mathematical process to be performed on the number will be determined by the initial format.
2. Perform a mathematical calculation on the number to be converted to a percentage.
If the number to be converted to a percentage is a decimal number, such as 0.57, you may not need to proceed to the next step.
3. Multiply the result by 100.
To convert a decimal number, such as 0.57, to a percentage, simply multiply it by 100.
here we need to calculate 1.2% of 5053004
(1.2*5053004)\100
=60636.048
60636.048 people speak french in the country with population of 5053004.
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Fred, Max, and Ken went trick or treating. Fred had 2 bags of candy with 45 pieces each. Max had 3 bags with 20 pieces each and Ken had 4 bags of candy with 15 pieces each. The boys combined the candy and shared it among 12 people. How much candy is leftover?
Answer:
6 pieces of candy will be left.
Step-by-step explanation:
45×2 = 90
20×3 = 60 +
15×4 = 60
Ttl. of candies= 210
Candies ÷ people
210 ÷ 12 = 17.5
17-12= 5.5 (round to the tenth) 5.5-> 6
210-6= 204
you'll get 6 as the difference which is your answer.
Find the distance between the points (−1,0) and (7,6).
The distance between the point (-1,0) and (7,6) is 10.
Distance between the points:
Distance between two points is the length of the line segment that connects the two points in a plane.
The formula to find the distance between the two points is usually given by
d=√((x2 – x1)² + (y2 – y1)²).
Given,
(−1,0) and (7,6).
Here we need to find the distance between these points.
Apply the values on the formula , in order to solve it,
d = √(7 - (-1))² + (6 - 0)²
When we simplify it, then we get,
d = √(7 + 1)² + (6)²
d = √(8)² + 36
d = √64 + 36
d = √100
d = 10
Therefore, the distance is 10.
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