The three types of discontinuity are listed as follows:
Jump Discontinuity.
Infinite Discontinuity.
Removable Discontinuity.
The term discontinuity is referred as if a function is referred to as the point at which a Mathematical object is discontinuous.
The function will be discontinues if they meet the following conditions,
If the function is not defined at the given point.Where as if the function has no limit at the given point.Otherwise if the function is defined and it has a limit at that point.There are 3 type of discontinuity in math and they are listed as jump, infinite and removable.
To know more about Discontinuity here.
https://brainly.com/question/28783981
#SPJ4
Determine the equation of the circle with center (0, -5) containing the point
(-√109,-6).
x^2 + y^2 - 10y + (-85) is equation of the circle with center (0, -5) containing the point (-√109,-6).
How do you find the equation of a circle?To find the equation of a circle with a given center and containing a given point, we can use the distance formula. The distance formula is given by:
d = √((x2 - x1)^2 + (y2 - y1)^2)
where (x1, y1) is the center of the circle and (x2, y2) is the point on the circle. In this case, the center of the circle is (0, -5) and the point on the circle is (-√109, -6). Plugging these values into the distance formula, we get:
d = √((-√109 - 0)^2 + (-6 - (-5))^2)
d = √((-√109)^2 + (-1)^2)
d = √(109 + 1)
d = √110
Since the point (-√109, -6) is on the circle, the distance from the center of the circle to this point is the radius of the circle. Therefore, the radius of the circle is √110.
The equation of a circle with center (h, k) and radius r is given by:
(x - h)^2 + (y - k)^2 = r^2
In this case, the center of the circle is (0, -5) and the radius is √110, so the equation of the circle is:
(x - 0)^2 + (y - (-5))^2 = (√110)^2
x^2 + y^2 - 10y + 25 = 110
x^2 + y^2 - 10y + (-85) = 0
This is the equation of the circle with center (0, -5) and containing the point (-√109, -6).
To learn more about circle equation refer :
https://brainly.com/question/1506955
#SPJ1
What is the mean and standard deviation in which 7% of items are under 35 and 89% are under 63?
The mean and standard deviation are 50.292 and 10.362 respectively.
What is mean and standard deviation?The mean is the average of all available data value. And standard deviation is the measure of how far each data value apart from the mean value.
How to calculate mean and standard deviation of the given data value?We are given, 7% of item are under 35 and 89% of item are under 63.
Let, M refers to mean, and SD refers to standard deviation.
As per given data, P(x<35) = 35%
P(z<Z1) = 0.07
hence, Z-score= Z1 = -1.4758 [obtained from Z table]
we know that the z-score = (observed value - mean)/ standard deviation
Z1 = (x - M)/ SD
- 1.4758 = (35 - M)/ SD
-1.4758SD = 35 -M ......... equation 1
as per the 2nd condition in the given data
89% of items are under 63
so, X= 63, P(X<63)
hence, the z-score = 1.2265 [ obtained from Z table]
Z2= 1.2265= (X- mean)/ SD
1.2265SD = 63 - M.......equation 2
Solving equation 1 and 2, we get standard deviation = 10.362
Mean value = 50.292
To know more about Mean and standard deviation visit:
https://brainly.com/question/23556021
#SPJ4
What is the nature of the roots of x² − 3x 4 0?
The nature of the roots of the given equation x^2 - 3x - 4 = 0 is real and unequal.
The general form of a quadratic equation is ax^2 + bx +c = 0.
Comparing the given equation x^2 - 3x - 4 = 0 with the general form of quadratic equations, we get that:
a = 1, b = -3 and c = -4
If b^2 - 4ac > 0, then we say that the nature of the roots of the equation is real and unequal.
Therefore, b^2 - 4ac = (-3) ^ 2 - 4 x 1 x (-4) = 25 >0
Hence, we conclude that the nature of the roots of the given equation is real and unequal.
The question is incomplete, the complete question is:
What is the nature of the roots of x² − 3x - 4 = 0?
To know more about the nature of roots:
https://brainly.com/question/12383696
#SPJ4
The calls of Hazar was 2370 the last month. He received 1645 calls. The calls of Huzan was less than those of Hazar, but Huzan received more calls than Hazar. Write a system of linear inequalities to represent the situation, then solve it to determine the possible number of calls received by Huzan and the number of calls dialled by him.
The possible values of calls recieved by Huzan is more than 1645 and calls made is less than 2370.
What is Inequalities of equations ?
Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), larger than (or greater than or equal to), or not equal to signs are used in place of the equal sign.Inequality simply means that two things aren't equal. One of the items could be inferior to, superior to, greater than, or equivalent to the other things.
p ≠ q means that p is not equal to qp < q means that p is less than qp > q means that p is greater than qp ≤ q means that p is less than or equal to qp ≥ q means that p is greater than or equal to q
Different kinds of inequality exist. Important inequities include the following: the inequalities of polynomials
Inequalities in absolute values
Logic-based disparities
Calls made by Hazar = 2370
Calls recieved by Hazar = 1645Let the number of Calls by Huzan be x.
And the number of calls recieved by Huzan be y.
Then the inequalities arex< 2370 and y> 1645
The possible values of calls recieved by Huzan is more than 1645 and calls made is less than 2370.
To learn more about inequalities refer to : https://brainly.com/question/28823603
#SPJ1
a normal distribution of scores has a standard deviation of 10. find the z-score corresponding to a score that is 30 points below the mean.
The z-score 30 points below the mean is -3
The normal distribution of scores has a standard deviation(σ) of 10
Below the mean is (X-μ)=-30
The mean (average) of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set.
Z=(X-μ)/σ
Z=-30/10
Z=-3
Therefore, the z-score is -3.
For such more questions about normal distribution
https://brainly.com/question/12421652
#SPJ4
what is the greatest common factor for 32 and 81
(HURRYYY))
Answer:
9 :)))))))))))
In 2005, 13.1 out of every 50 employees at a company were women. If there are 46,043 total company employees, estimate the number of women.
Find the slope from two points
Answer: 7/ -8
Step-by-step explanation:
The slope is rise/run
Our two points are (10,9) ( 2,16)
We see that y increased by 7, and the x decrease by 8
So the slope is 7/ -8
A proportional relationship is shown here:
x = 0, 1.4, 2.8, 4.2, 5.6
y = 0, 1, 2, 3, 4
What is the slope of the line that represents this relationship?
Graph the line that represents this relationship.
Answer:
y=1.4x
Step-by-step explanation:
Find the relationship.
1.4/1=1.4
2.8/2=2.8
and so on so we know it is 1.4
so y=1.4x
Amelia has a summer job mowing the lawn and trimming hedges for a neighbor. The number of minutes that amelia spends mowing the lawn is 10 minutes longer than three times the number of minutes it takes to trim the hedges. It takes Amelia a total of 120 minutes to complete both tasks
Using system of linear equations, Amelia spent 92.5 minutes mowing the lawn and 27.5 minutes trimming the hedges
System of Linear EquationSystem of linear equations is the set of two or more linear equations involving the same variables. A linear equation can be defined as the equations of the first order, whereby the highest power of the variable in the equation is one.
To solve this problem, we have to write a system of linear equation;
Let;
x = number of minute spent mowing lawny = number of minute trimming the hedgesWe can represent the problem with two set of equations as;
x + y = 120 ...eq(i)
x = 3y + 10 ...eq(ii)
From equation 1
x + y = 120
x = 120 - y ..eq(iii)
Put eq(iii) into eq(ii)
120 - y = 3y + 10
collect like terms
120 - 10 = 3y + y
110 = 4y
y = 110 / 4
y = 27.5 minutes
Put y = 27.5 in equ(i)
x + 27.5 = 120
x = 120 - 27.5
x = 92.5 minutes
She spent 92.5 minutes mowing the lawn and 27.5 minutes trimming the hedges.
Learn more on system of linear equation here;
https://brainly.com/question/13729904
#SPJ1
Is an asymptote a continuous function?
An asymptote is a line that a curve approaches but never touches, so it is not part of the curve itself. As a result, an asymptote is not a function. However, the curve that approaches an asymptote may or may not be a continuous function.
A function is continuous if it is defined for all values in its domain and there are no breaks or jumps in the graph of the function.
For example, consider the function f(x) = 1/x. This function has a horizontal asymptote at y = 0, but it is not continuous at x = 0 because the value of the function is undefined at this point (division by zero is not allowed).
On the other hand, consider the function f(x) = ². This function has no asymptotes and is continuous for all values of x.
To know more on asymptote
brainly.com/question/4084552
#SPJ4
Can I claim sickness benefit on Universal Credit?
Yes, you can claim sickness benefits on universal credit.
Here we have to find out if it is possible to claim the sickness benefit on Universal credit.
In order to find that, we must know the definition of universal credit,
The term universal credit refers to a payment to help with your living costs.
Here we have to know that as per the definition of universal credit here you can self-certify for up to the first 7 days of your claim by notifying Universal Credit that you have a health condition that prevents you from working. Then on the 8th day, your condition persists and if you have not already done so, then you will definitely need to submit medical evidence in order to claim for benefit.
To know more about claim here.
https://brainly.com/question/14541748
#SPJ4
Can 55 years old get SSS?
No They can not because you need to be at least 62 years old
What are the 7 whole numbers?
Answer:
There are an infinte amount of whole numbers
Step-by-step explanation:
7 examples are, 0, 3, 7 , 8 ,9 14, 39
What's the numerator for the following rational
expression? 2/f+4/f=?/f
The numerator for the rational expression is 6
How to find the numerator for the rational expression?Let us assume the value of numerator to be x
[tex]\frac{2}{f} +\frac{4}{f} = \frac{x}{f}[/tex]
Since these are fractions with same denominators (like fractions),
[tex]= > \frac{2}{f} +\frac{4}{f} \\\\ = \frac{2 +4}{f}\\\\= \frac{6}{f}[/tex]
x = 6
The numerator for the rational expression is 6
What are fractions?Fractions are used to depict the components of a whole or group of items. Two components make up a fraction. The numerator is the number that appears at the top of the line.It indicates how many equally sized pieces of the entire thing or collection were removed. The denominator is the quantity listed below the line. The total number of identical objects in a collection or the total number of equal sections that the whole is divided into are both displayed.The number of parts we take makes up a fraction when the whole is divided into equal parts.Fractions with same denominators are called like fractions.To learn more about fractions, refer:
https://brainly.com/question/78672
#SPJ1
What is the median of first 5 numbers?
The median of 1,2,3,4,5 is 3.
The median is the middle point in a dataset—half of the data points are smaller than the median and half of the data points are larger.
Here we have to find the median of 1,2,3,4,5.
Here we can see that there are 5 numbers given
so, n= 5 which is an odd number so we will use the formula for finding the median in the case of the odd number of data.
So, M = 5+1/2 = 3
Thus the median is the 3rd term which is 3.
Therefore, the median of 1,2,3,4,5 is 3.
To know more about the median visit: brainly.com/question/28060453
#SPJ4
What are the three 3 semantics models of parameter passing for subprograms?
The three semantics models of parameter passing for subprograms are: in mode, out mode, and inout mode
In this question we need to describe the three semantics models of parameter passing for subprograms.
The three semantics models of parameter passing for subprograms are:
1) in mode: They can receive data from corresponding actual parameters.
2) out mode: They can transmit data to the actual parameter.
3) inout mode: They can do both.
There are two conceptual models of how data transfers take places in parameter transmission: either an actual value is copied (to the caller, to the callee, or both ways), or an access path is transmitted.
Generally, the access path is a simple pointer or reference.
Therefore, in mode, out mode, and inout mode are 3 semantics models of parameter passing for subprograms
Learn more about semantics here:
https://brainly.com/question/30054863
#SPJ4
You plan projects revenue of $5,000, $8,000, and $10,000, in years 1 through 3. Expenses are projected to be $9,000 for each of years 1 through 3. If your only funding need is the gap between revenue and expenses, which is the best estimate of your maximum cumulative funding need?
The best estimate of your maximum cumulative funding needed, based on the projected revenue and the expenses is $ 4, 000.
How to find the maximum cumulative funding needed ?The maximum cumulative funding needed would be the amount that would be total gap between revenue and expenses in the three years that the plan will be in effect.
In year 1, the gap is :
= 5, 000 - 9, 000
= $ - 4, 000
In year 2, the gap is:
= 8, 000 - 9, 000
= $ - 1, 000
In year 3, the gap is:
= 10,000 - 9, 000
= $ 1, 000
The cumulative funding needed is :
= ( -4,000 + - 1, 000 ) + 1, 000
= - $4, 000
You have a maximum cumulative funding needed of $ 4, 000.
Find out more on cumulative funding needed at https://brainly.com/question/14953890
#SPJ1
What SAS stand for in math?
Each interior angle of a regular polygon is 120°.
Find the value of each exterior angle of the polygon.
Answer:
exterior angle = 180° - 120°
= 60°
Answer:
60 degrees
Step-by-step explanation:
180-120=60
Which of the following is a solution of the equation 2x y 10 *?
The solution of the given equation 2x + y = 10 is equal to option b. x = 2 and y = 6.
As given in the question,
Given equation is equal to :
2x + y = 10
Simplify and Check which given option represent the solution of the equation :
a. x = 9
2(9) + y = 10
⇒y = -8
Incorrect option.
b. x = 2
2(2) + y = 10
⇒y = 6
Correct option.
c. x = 1
2(1) + y =10
⇒y = 8
Incorrect option
d. x =4
2(4) + y = 10
⇒y = 2
Incorrect option
Therefore, for the given equation 2x + y = 10 , option b . x = 2 and y = 6 is the correct answer.
The given question is incomplete , the complete question is :
Which of the following is a solution of the equation 2x + y = 10?
a. x = 9 and y = 3
b. x = 2 and y = 6
c. x = 1 and y = 7
d. x = 4 and y = 3
Learn more about the equation here
brainly.com/question/29538993
#SPJ4
What is parallel to Y =- 5x 4?
The system of equations of line parallel to y = -5x + 4 is y = -5x + c where c is any arbitrary value of y-intercept.
The linear equation y = -5x + 4 is a straight line with slope -5 and y-intercept 4.
The slope of parallel lines are equal. So any line with slope -5 is parallel to the line y = -5x + 4. So the equation of a line with slope -5 is
y = -5x + c
where c is a constant
c represent arbitrary value of y-intercept.
For example y = -5x + 2 is a straight line parallel to y = -5x + 4 but having value of y-intercept equal to 2.
--The question is incomplete, answering to the question below--
"What is parallel to y = -5x + 4?"
To know more on linear equations
https://brainly.com/question/30004506
#SPJ4
Problem Solving in Santa's Workshop
Clifford works in the gift-wrapping department of Santa's
workshop. His job is to finish all the packages with a bow.
He is running low on bows and only has 100 bows left. He
begins working at 5:00 a.m. During the first half-hour, he
uses 12 bows. In the second half-hour, he uses 9 bows.
During the third half-hour, he uses 14 bows and in the
fourth half-hour, he uses 11 bows. Clifford uses 16 bows
during the fifth half-hour. If the pattern continues, during
which half-hour will Clifford run out of bows?
Answer:
Eighth half-hour
Step-by-step explanation:
Given pattern:
1st half hour = 12 bows used2nd half hour = 9 bows used3rd half hour = 14 bows used4th half hour = 11 bows used5th half hour = 16 bows usedCalculate the differences between the number of bows used:
[tex]12\underbrace{}_{-3}9\underbrace{}_{+5}14\underbrace{}_{-3}11\underbrace{}_{+5}16[/tex]
Therefore, the pattern for the bows used is:
-3, +5, -3, +5, etc...If the pattern continues:
[tex]12\underbrace{}_{-3}9\underbrace{}_{+5}14\underbrace{}_{-3}11\underbrace{}_{+5}16\underbrace{}_{-3}13\underbrace{}_{+5}18\underbrace{}_{-3}15\underbrace{}_{+5}20[/tex]
6th half hour = 16 - 3 = 13 bows used7th half hour = 13 + 5 = 18 bows used8th half hour = 18 - 3 = 15 bows used9th half hour = 15 + 5 = 20 bows usedCreate a table with the given and found data, and add a cumulative total column:
[tex]\begin{array}{c|c|c}\vphantom{\dfrac12} \textsf{Half Hour} & \textsf{Bows used per half hour} & \sf Cumulative\; total\\\cline{1-3} \vphantom{\dfrac12} \sf 1st & 12 & 12\\\vphantom{\dfrac12} \sf 2nd &9 &21 \\\vphantom{\dfrac12} \sf 3rd & 14&35 \\\vphantom{\dfrac12} \sf 4th & 11& 46\\\vphantom{\dfrac12} \sf 5th & 16& 62\\\vphantom{\dfrac12} \sf 6th & 13& 75\\\vphantom{\dfrac12} \sf 7th &18 & 93\\\vphantom{\dfrac12} \sf 8th & 15& 108\\\vphantom{\dfrac12} \sf 9th & 20& 128\\\end{array}[/tex]
If Clifford has a total of 100 bows, he will run out of bows during the eighth half-hour.
Which is a quadratic equation in FACTORED FORM?
A
f(x)=2x2+5x−12f(x)=2x^2+5x-12f(x)=2x
2
+5x−12
B
f(x)=2x+5f(x)=2x+5f(x)=2x+5
C
f(x)=2(x+5)2−12f(x)=2(x+5)^2-12f(x)=2(x+5)
2
−12
D
f(x)=2(x+5)(x−12)f(x)=2(x+5)(x-12)f(x)=2(x+5)(x−12)
Answer:
Step-by-step explanation: it is b
How do you solve an inequality with 2 answers?
Answer:
Step-by-step explanation:
Example:
If you have the inequality 3<(x/9)+7
Begin with subtraction by subtracting 7 from both sides, rather than beginning with the parentheses x/9.
Do all processes to both sides of the inequality until you have solved for x.
Example: As mentioned in the previous step, you would begin by subtracting 7 from both sides.
So 3<(x/9)+7 becomes, -4<x/9
Now you would multiply both sides by 9 because the fraction x/9 is the same as x divided by 9, and the opposite of division is of course multiplication.
This process leaves you with the solution, -36<x, so x is greater than -36.
Remember that if your problem requires you to multiply or divide by a negative number, then you need to flip the inequality sign when you do so.
For example: If instead of multiplying by 9 in the previous problem you had to multiply by -9, you would get 36>x rather than 36<x.
A number, .f, rounded to 1 d.p. is 49.2
Another number, g,
rounded to 1 d.p. is 7.8
What are the lower and upper bounds of
f - g?
Answer:
3
Step-by-step explanation:
The lower bound of f-g is 41.31 .
The upper bound of f-g is 41.49 .
Given,
A number 'f' rounded to 1 decimal point is Number = 49.2
A number 'g' rounded to 1 decimal point is Number = 7.8
Now,
The range of f rounded to 1 decimal point is [49.15 , 49.24].
The range of g rounded to 1 decimal point is [7.75 , 7.84].
So,
Lower bound of f-g = 49.15 - 7.84
Lower bound of f-g = 41.31
Next,
Upper bound of f-g = 49.24 - 7.75
Upper bound of f-g = 41.49
Therefore the lower bound of f - g is 41.31 and upper bound of f - g is 41.49.
Learn more about lower and upper bound, here:
https://brainly.com/question/32676654
#SPJ4
bowl a contains 2 red chips; bowl b contains two white chips and 1 red chip, and bowl c contains 1 red chip and 1 white chip. a bowl is selected at random, and one chip is taken at random from that bowl. if the selected chip is white, what is the probability that the chip belongs to bowl c?
Therefore the probability that the chip belongs to bowl c is 1/3.
What is the process of probability?Probabilities can be expressed as proportions with a 0–1 range or as percentages with a 0%–100% range. If an event has a probability of 1, it is very certain to occur; if it has a probability of 0, it has no chance of occurring. There are 45 chances out of 100 that an event will occur when its probability is 0.45 (45%).
Here,
A : 2 Red chips
B : 2 White chips
C: One Red and one White chip
P(selecting any bowl) = 1/3
1) We have to find P(W).
The selected chip can be white if it is either selected from Bowl B or Bowl C.
Symbolically this can be written as
P(W) = P(Bowl B and White chips) + P(Bowl A and White chips)
P(W) = [(1/3) × 1/1)] + [(1/3) × (1/2)]
P(W) = (1/3) + (1/6)
P(W) = 1/2
P(W) = 0.5
2) There is only one bowl with both of white and red chips and that bowl is bowl C. So it is possible the other chips in the bowl to red only if it has been selected from Bowl C.
So ,We need to find P(Bowl C | W).
P(Bowl C | W) = P(Bowl C and W)/P(W)
P(Bowl C | W) = (1/3) × (1/2)/(1/2)
P(Bowl C | W) = 1/3
Hence, the required probability is 1/3.
To know more about probability , visit
brainly.com/question/11234923
#SPJ4
Describe the graph of the proportional relationship represented by the equation y = 7.5x.
The graph of the equation y = 7.5x shows the proportional relationship.
What is an equation?An equation is a combination of different variables, in which two mathematical expressions are equal to each other.
The given equation is,
y = 7.5x.
The graph of the equation y = 7.5x is shown below.
At x = 1, the value of y = 7.5,
At x = 2, the value of y = 7.5 x 2 = 15
At x = 3, the value of y = 7.5 x 3 = 22.5
And so on.
The value of y multiplied by 7.5 by increasing value of x by 1.
Thus, the graph of the equation y = 7.5x shows the proportional relationship.
To know more about Equation on:
https://brainly.com/question/187506
#SPJ1
Is the sum of 3 consecutive numbers a multiple of 3?
The sum of 3 consecutive numbers is always of the form 3(x+1) which is always a multiple of 3.
What are consecutive numbers ?
Numbers that follow each other continuously in the order from smallest to largest are called consecutive numbers. For example: 1, 2, 3, 4, 5, 6, and so on are consecutive numbers.
Let us assume: 3 consecutive integers are x, x+1 , x+2.
on adding these three numbers we get,
x + x+1 + x+2 = 3x + 3
which can be further reduced to the form 3(x+1).
If you add any 3 consecutive numbers together it will always equal a multiple of 3, e.g.
1+2+3=6
2+3+4=9
3+4+5=12
4+5+6=15
5+6+7=18
Thus , the sum of 3 consecutive numbers is always of the form 3(x+1) which is always a multiple of 3.
Learn more about consecutive numbers at:
brainly.com/question/17296996
#SPJ4
Which expression can be used to find the sum of the polynomials 9 3x² 8x² 4x 5?
The expression which represents the sum of polynomials (9-3x²) and (-8x²+4x+5) is -11x² + 4x + 14
What is polynomial equation?
A polynomial equation is an algebraic equation that consists of variables and coefficients, which are often real numbers, and exponents which are non-negative integers. Polynomial equations can have one or more terms, and can involve addition, subtraction, multiplication, division, and exponentiation.
According to the given question:
The sum of polynomials can be calculated by combining like terms where there are multiple of the same variable.
= (9-3x²) + (-8x²+4x+5)
= 9 - 3x² - 8x² + 4x + 5
= -11x² + 4x + 14
Therefore, the expression which represents the sum of polynomials (9-3x²) and (-8x²+4x+5) is -11x² + 4x + 14
Complete question:
Which expression can be used to find the sum of the polynomials?
(9-3x²) and (-8x²+4x+5)
To know more about polynomials click-
brainly.com/question/2833285
#SPJ4