Answers
Should be B.
There is a nested function structure. Let's first look at the limit of the interior (f(0)). The point we need to pay attention here is to look at the limits from the right and left. If both values are equal, we can say that it has a limit at that point.
If we express it algebraically;
[tex]lim_{x\to{0^-}}f(x)=lim_{x\to{0^+}}f(x)[/tex] then,[tex]lim_{x\to{0}}f(x)=exist[/tex]The left limit and the right limit of [tex]f(0)[/tex] are equal and equal to [tex]2.[/tex]
[tex]lim_{x\to{0^-}}f(x)=2[/tex][tex]lim_{x\to{0^+}}f(x)=2[/tex]The left limit and the right limit of f(2) are equal and equal to 3.
[tex]lim_{x\to{2^-}}f(x)=3[/tex][tex]lim_{x\to{2^+}}f(x)=3[/tex]As I have drawn with colored arrows in the graph below, we approach from the left and from the right, and if they both point to the same point, we can talk about the existence of the limit at that point. Otherwise, this function does not have a limit at that point.
Related Questions
Line a is perpendicular to line bLine a passes through the points (1,-3) and (9,-5)Line b passes through the point (-8,32)The equation of line b is y=___
Answers
y=4x+64
Explanation:
Two lines are perpendicular if the product of their slopes is -1.
Step 1: Find the slope of the line a
Line a passes through the points (1,-3) and (9,-5)
[tex]\begin{gathered} \text{Slope},m=\frac{Change\text{ in y-axis}}{Change\text{ in x-axis}} \\ =\frac{-5-(-3)}{9-1} \\ =\frac{-5+3}{8} \\ =-\frac{2}{8} \\ =-\frac{1}{4} \end{gathered}[/tex]The slope of line a = -1/4
Step 2: Determine the slope of line b.
Let the slope of line b = k
Since the product of the two slopes is -1:
[tex]\begin{gathered} k\times-\frac{1}{4}=-1 \\ k=-1\times-4 \\ k=4 \end{gathered}[/tex]The slope of line b = 4
Step 3: Find the equation of line b.
Line b passes through the point (x1,y1)=(-8,32) and has a slope, m = 4.
Using the slope-point form of the equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]Substitute the given values
[tex]\begin{gathered} y-32=4\mleft(x-\mleft(-8\mright)\mright) \\ y-32=4\mleft(x+8\mright) \\ y-32=4x+32 \\ y=4x+32+32 \\ y=4x+64 \end{gathered}[/tex]The equation of line b is y=4x+64.
what is the equation of a line perpendicular to y=2x-6 that passes through (5,4)?
Answers
Answer:
[tex]y = -\dfrac{1}{2}x + \dfrac{13}{2} \;\; \text{or}\\\\y = -0.5x + 6.5\\\\[/tex]
Step-by-step explanation:
The slope-intercept form of a straight line is
y = mx + b
where m = slope and b = y-intercept
A line perpendicular to the above line will have a slope = -1/m and an intercept b which has to be determined depending on a point the line passes through
Given
Line 1: y = 2x - 6
Slope m = 2
Line 2 perpendicular to Line 1 will have slope = -1/2 = -0.5
So the equation would be y = (-1/2)x + b
We can solve for b given the info that the line passes through (5,4)
Substitute x = 5 and y = 4 in line 2 equation:
4 = (-1/2)5 + b
4 = -5/2 + b
4 + 5/2 = b
8/2 + 5/2 = b
13/2 = b
or b = 13/2
So equation of line perpendicular to 2x -6 is
y = (-1/2)x + 13/2
or
y = -0.5x + 6.5
poker hand is defined as drawing 5 cards at random without replacement from a deck of 52 playing cards. find the probability of each of the following poker hands: (a) four of a kind (four cards of equal face value and one card of a different value). (b) full house (one pair and one triple of cards with equal face value). (c) three of a kind (three equal face values plus two cards of different values). (d) two pairs (two pairs of equal face value plus one card of a different value). (e) one pair (one pair of equal face value plus three cards of different values)
Answers
(a) We have 13 possibilities that a five-card hand will contain four of a kind.
(b) We have 12 possibilities that a five-card hand will contain a full house.
What do you mean by probability?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.
The probability of an occurrence is a number between 0 and 1, with 1 representing certainty and 0 representing impossibility.
Since there are no other conceivable outcomes and the coin is fair, the odds of both the possibilities, "heads" and "tails," are equally likely to occur. As a result, the probability of either occurrence is half (which could also be written as 0.5)
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a sunflower is planted in a garden and the height of the sunflower increases by 11% per day. 2.53 days after being planted the sunflower is 13 inches tall.
Answers
The sunflower had a height of 13 inches on day 0 and 13.91 inches on day 1.
Because sunflowers are big feeders and require a slightly alkaline soil (pH 6.0 to 7.5), make sure we put them in nutrient-rich soil. Before planting, we should also make sure the soil is weed-free. Since a sunflower is cultivated in a garden, its height grows by 7% every day. The sunflower is 15.7 inches tall 2.79 days after being planted. To get the sunflower's 1-day growth factor, apply the following calculation:
X x (1 + 0.07) ^ 2.79 = 15.7
X x 1.07 ^ 2.79 = 15.7
1.2077X = 15.7
X = 15.7 / 1.2077
X = 13
13 x 1.07 = 13.91
The sunflower therefore measured 13 inches on day 0 and 13.91 inches on day 1.
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A water treatment plant needs to maintain the ph of the water in the reservoir at a certain level. To monitor this, they take 2 oz. Of water at 37 locations every hour, measure the ph at each of those locations, and find their average. If the ph level of the reservoir is ok, the results at each location will have varying results, with an average ph of 8. 5 and a standard deviation of 0. 22. If the ph level of the reservoir is ok, what is the probability that the sample average is more than 8. 42?.
Answers
A water treatment plant needs to maintain the ph of the water in the reservoir at a certain level. Then the probability that the sample is more than 8.42 is 0.0029 or 0.29%.
Using the normal distribution and the central limit theorem,
The mean is μ = 8.5
The standard deviation is σ = 0.22 .
A sample of 37 is taken, hence n = 37, s = 0.22/√37 i.e. s = 0.0362
The probability that the sample average is more than 8.40 is the p-value of Z when X = 8.4, hence:
Z = X - μ/σ
Z = 8.4 - 8.5/0.0362
Z = 2.76
Z = -2.76 has a p-value 0.0029
0.0029 = 0.29% probability that the sample average is more than 8.40.
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Mike Lasueze is a salesperson in the appliance department at Wicklow Appliance Inc. He is guaranteed a minimum salary of $220 per week or 5.5% of his total sales, whichever is greater. What is his gross pay for a week in which his total sales were $8,400?
Answers
For a sale of $8400 made his gross pay is $373.21
In this question, we have been given Mike Lasueze is guaranteed a minimum salary of $220 per week or 5.5 percent of his total sales, whichever is greater.
We need to find his gross pay for a week in which his total sales were $8,400
weekly pay = $220
commission = 5.5% of sales
= 0.055 of sales
let m be the total sale and his gross pay be represented by y
So, we get an equation for the total/gross pay:
y = 0.055x + 220
Required is the gross pay y for x = 8400
y = 0.055(8400) + 220
y = 682
Therefore, for a sale of $8400 made his gross pay is $373.21
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Fill in the missing number.
4 groups of _
equal 24.
Answers
Because 4x6=24
A family drives 4 1/2 miles in 1/10 of an hour. How many miles will they drive in 3/4 hours?
Answers
Which two transformations can be used to obtain the graph of G(x) = -4√x , from the graph of F(x)=√x?
Answers
Given: The base function
[tex]F(x)=\sqrt{x}[/tex]To Determine: The transformation that would give the function G(x)
[tex]G(x)=-4\sqrt{x}[/tex]Solution
Let us plot the graph of the base function and the new function as shown below
It can be observed that there exist a reflection across the x-axis, also a vertical stetch by a factor of 4
Hence, the correct answer is a vertical stretch by a factor of 4, followed by a reflection across the x-axis, OPTION A
Which statement is true?
Hope's dad gives her seven-eighths of a chocolate bar one day and then gives her six-twelfths of a chocolate bar the next day. Hope received approximately 1 chocolate bar.
Dee has ten-twelfths of a cake and gives four-eighths to her neighbor. Dee has approximately one and one-half cakes left.
Joe ran eight-fifteenth of a mile on Thursday. He ran four-fifths of a mile on Friday. Joe ran approximately one-half mile in all.
Monica swam nine-sixteenths of a mile on Tuesday. She swam one and five-eighths of a mile on Wednesday. She swam approximately 2 miles in all.
Answers
Answer:
its {A} Hope gets some of a full chocolate bar
Step-by-step explanation:
she gets 7/8 of a chocolate bar the next day she gets 6/12 7+6=13 so she gets a full chocolate bar
Write the conditional and converse of the statements below:
"parallel lines have the same slope."
Answers
Converse of the statements will be as If two lines are parallel, then they have equal slopes. Conditional statement will be; If two lines have same slopes, then the lines are parallel.
How do parallel lines work?Lines in a plane that are regularly spaced apart are known as parallel lines. Parallel lines don't overlap each other. Perpendicular lines are those that cross at a straight angle of 90 degrees.
Only the slopes of two lines are same then it can be said to be parallel. If two lines have different y-intercepts and equal slopes, they are said to be parallel.
Converse of the statements will be as If two lines are parallel, then they have equal slopes.
Conditional statement will be; If two lines have same slopes, then the lines are parallel.
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Amy has 4 pound of ground pork to make meatballs she uses 3/8 pound per meatball to make 9 meatballs.how many 1/8 pound meatballs can Amy make with the remaining turkey ?
Answers
Amy can make 29 meatballs from the remaining beef.
What are mathematics operations?
An operation is a function in mathematics that converts zero or more input values (also known as "operands" or "arguments") to a well-defined output value.The operation's arity is determined by the number of operands.Binary operations (i.e., operations of arity 2), such as addition and multiplication, and unary operations (i.e., operations of arity 1), such as additive inverse and multiplicative inverse, are the most commonly studied operations.A zero-arity operation, also known as a nullary operation, is a constant.The mixed product is an example of an arity 3 operation, also known as a ternary operation.Amy has 4 pounds of ground beef to make meatballs and he uses 3/8 pound per meatball to make 9 meatballs
We have to subtract 3/8 from 4
= 4 - 3/8
= 29/8
There are 29/8 pounds of ground beef left
Therefore the number of 1/8 pound meatball that can be produced from 29/8 pounds of ground beef can be calculated as follows;
= 29/8 ÷ 1/8
= 29
Hence Amy can make 29 meatballs
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the unit circle has center ▼ left parenthesis 1 comma 1 right parenthesis left parenthesis negative 1 comma negative 1 right parenthesis left parenthesis 0 comma 0 right parenthesis and radius ▼ 1. negative 1. startroot 2 endroot . the equation of the unit circle is ▼ y equals mx plus b. x squared plus y squared equals 1. y equals ax squared .
Answers
x^2+ y^2-2x-2y = 0 has center (1,1) and radius sqrt 2 and the circle x^2+y^2 =1 has center (0,0) and radius 1
the unit circle has center
(1,1) , ( 0,0)
and the unit circle has radius
1 , sqrt 2
for this the equation of the circle is
x^2 + y^2 = 1
if we take center as (0,0) then radius become 1
therefore equation of circle becomes x^2 +y^2 =1
similarly if we take center ( 1,1 ) and radius sqrt 2
then (x -1 )^2 + ( y-1 )^2 =2
x^2 +y^2 -2x- 2y +2 =2
this implies x^2 +y^2 -2x -2y =0
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What is an equation of the line that passes through the point (-4,8)(−4,8) and is parallel to the line x+y=6x+y=6?
Answers
The equation of the line that passes through the point; (-4, 8) and is parallel to x + y = 6 is; x + y = 4.
What is the equation of the line that passes through the given point and is parallel to the given line?By expressing the given linear equation in slope-intercept form; it follows that we have;
x + y = 6
y = -x + 6
Hence, the slope of the equation by comparison with; y = mx + c is; -1.
Therefore, the slope of the required equation is same as the two lines are said to be parallel.
Therefore, the required equation from point-slope form of an equation is;
( y - 8) = -1 ( x - (-4))
y - 8 = -x - 4
x + y = -4 +8
x + y = 4.
Ultimately, the required equation is; x + y = 4.
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Geometry In the figure below, and . Find the values of y and z.
Answers
The measure of the angles x and z is 95 degrees and 30 degrees after applying the property of interior angles.
What is an angle?When two lines or rays converge at the same point, the measurement between them is called a "Angle."
The figure is given in the picture:
From the property of interior angles:
x + 85 = 180
x = 95 degrees
6z - 85 + 85 = 180
z = 180/6
z = 30 degrees
Thus, the measure of the angles x and z is 95 degrees and 30 degrees after applying the property of interior angles.
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Number 1 pls help show your work
Answers
Answer:
60
Step-by-step explanation:
0.2x = 12
x=60
:]
Step 1: convert 20% to 0.20 then multiply it by 12
Solve for t:
2b+2.50t=40
Answers
The value of t after solving 2b+2.50t = 40 is t = (40-2b)/2.50.
According to the question,
We have the following expression:
2b+2.50t = 40
Now, in order to find the value of t, we will move other variables and numbers from the left hand side to the right hand side.
First, moving 2b from the left hand side to the right hand side will result in the change of the sign from plus to minus:
2.50t = 40-2b
Now, 2.50 is in multiplication on the left hand side. So, it will be in the division on the right hand side.
t = (40-2b)/2.50
Hence, the value of t after solving the given expression is t = (40-2b)/2.50.
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Which one is it help
Answers
Answer:
c the last 1
Step-by-step explanation:
bc y where the line ends on y is more than 30 and only 1 line is 5 so 35
Answer:
I think its the last one but it could also be the first
simplify the following expression
Answers
The value of solution of expression is,
⇒ (3⁵)
We have to given that;
The expression is,
⇒ (3³ × 3⁴) ÷ 3²
Now, We can simplify by rule of exponent as;
⇒ (3³ × 3⁴) ÷ 3²
⇒ (3³ ⁺ ⁴) ÷ 3²
⇒ (3⁷) ÷ 3²
⇒ (3⁷⁻²)
⇒ (3⁵)
Thus, The value of solution of expression is,
⇒ (3⁵)
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suppose that your younger sister is applying for entrance to college and has taken the sat. she scored at the 77th percentile on the verbal section of the test and at the 94th percentile on the math section of the test. because you have been studying statistics, she asks you for an interpretation of these values. what would you tell her?
Answers
I would tell her that out of all the people who took the verbal section, 23% scored higher than she did and 77% scored at or below her score. For the math section, 94% of those who took the exam scored at or below her score and 6% scored higher than she did.
Here's the complete question:
Suppose that your younger sister is applying for entrance to college and has taken the sat. she scored at the 77th percentile on the verbal section of the test and at the 94th percentile on the math section of the test. because you have been studying statistics, she asks you for an interpretation of these values. what would you tell her?
I would tell her that out of all the people who took the verbal section, ___% scored higher than she did and ___ % scored at or below her score. For the math section, ___ % of those who took the exam scored at or below her score and ____ % scored higher than she did.
For the Verbal section: 100 - 77 = 23
For the Maths section: 100 - 94 = 6
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Select all the values of x that are solutions of |3x - 6| = 12
A. -18
B. -6
C. -2
D. 2
E. 6
F. 18
Answers
Step by step:
3x6=18
18-6= 12
So X is 6
how do i create a graph of this table? and what expression should i put.
Answers
(-5 , 0) is the point we got after slope-intercept form of equation .
What exactly does slope intercept mean?
A method of formulating a line's equation that makes it simple to identify the slope and y-intercept is known as the slope-intercept form. The point where the line crosses the y-axis is called as the y-intercept, and the slope refers to how sharp the line is.A line has the equation 3x + 4y + 5 = 0. Using the slope intercept form, estimate the line's slope and y-intercept.Equation from the value given table -
1) y = 3x + 15
2) y = 5x + 25
3) y = 7x + 35
4) y = 9x + 45
5) y = 10x + 50
graph attached of all equation .
(-5 , 0) is the point .
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Translate each mathematical sentence into words
Ø⊆N
Answers
"An empty set is included in set N" is the translation of the mathematical sentence.
How to translate a mathematical sentence into wordsA set is defined as a collection of well-defined objects, numbers or things. In set theory, we use different symbols to represent statements.
To translate Ø⊆N, we need to know the meaning of the symbols we have:
Ø means empty set (A set that does not contain anything).
⊆ means subset (is included in)
N means set N
So we can translate Ø⊆N as:
An empty set is included in set N or
Therefore, the mathematical sentence Ø⊆N can be translated as "an empty set is included in set N"
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Type the correct answer in the box. Use numerals instead of words.
What is the solution to this equation?
3(29) 2(n + 4) = 6n
n=
-
Answers
The final value of n is -7 for linear equation 3(n - 9) - 2(n + 4) = 6n.
3(n - 9) - 2(n + 4) = 6n
6n = 3n - 27 - 2n - 8
-6n + n - 35 = 0
-5n = 35
5n = -35
n = -7
Given equation is 3(n-9)-2(n+4)=6n.
Open the brackets for multiplication, 3n - 27 - 2n - 8 = 6n.
After shifting the variables to the left-hand side and constant to the right-hand side, 5n = -35.
As the value of the constant in the above step is negative the final constant value will be also negative, n = -7.
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Type the correct answer in the box. Use numbers instead of words. An expression is shown. 36 ÷ (4 + 2) What is the value of the expression?
Answers
The result of the expression 36 ÷ (4+2) is 6
The expression is
36 ÷ (4+2)
To solve this expression, we have to apply the arithmetic operations in the given expression
An arithmetic operation is the operation specified by combining number or variable with one arithmetic operator. The basic arithmetic operations are addition, subtraction, division and multiplication.
First do the arithmetic operations in the bracket
Add 4 and 2 in the expression
36 ÷ (4+2) = 36 ÷ 6
Divide the number 36 by 6 in the expression
36 ÷ 6 = 6
Hence, the result of the expression 36 ÷ (4+2) is 6
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if q= (7 -1) and r= (-4 5) find | q+ r|
Answers
Answer: 6+1=7
Step-by-step explanation:
Using the concept of a net rate introduced in Problem 2, determine a differential equation governing a population P(t) if the birth rate is proportional to the population present at time t but the death rate is proportional to the square of the population present at time t.
Answers
We may be thinking about either of these choices depending on whether we are talking about immigration or emigration.
[tex]\frac{d P}{d t}=r_g \pm r[/tex]
This is further explained below.
What is a differential equation?Generally, The rates of births and deaths will be represented accordingly by the superscripts [tex]r_b[/tex] and [tex]r_d[/tex].
The model transforms into the following when subjected to the circumstances outlined in the problem:
[tex]\frac{d P}{d t}=r_b P-r_d P^2[/tex]
In conclusion, You need to submit model 1 in order to get more information.
In the event that the proportionality assumptions about birth and death be loosened up, the model that is necessary for issue 1 would become the following:
[tex]\frac{d P}{d t}=r_g \pm r[/tex]
Depending on whether we are discussing immigration or emigration, we may be contemplating either of these options.
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You and your family went out to dinner if the dinner was $52 and you left a 25% tip how much did your dinner cost altogether
Answers
Using percentages we can conclude that the total cost of the dinner was $65.
What is the percentage?A percentage is a number or ratio expressed as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" is also used, the percent sign, "%," is frequently used to indicate it. By dividing the value by the total value and multiplying the result by 100, one can determine the percentage. The percentage calculation formula is (value/total value)100%.So, the total cost of dinner:
The dinner cost was $52.The tip was 25% of the dinner, then we need to find the 25% of 52 as follows:
52/100 × 25 = 13So, the tip was $13.The total cost of the diner was $52 + $13 which is $65.
Therefore, using percentages we can conclude that the total cost of the dinner was $65.
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Find the measure of 44.
H
130⁰
50°
44
130⁰
50°
44 = [?]° i’m slow someone help
Answers
Answer:
Find the measure of each angle. 1. 23. =70°. 2. 45. 5. 24. 9.48 ... Exterior. ANGLE. ¥180-50=130. 6. 213 2106°. =106°. 44-10+42=180. 44 = 148
Step-by-step explanation:
The total cost of a jacket and a pair of shoes was $91.43. if the price of the jacket was $7.65 less than the pair of shoes, what was the price of the jacket? express your answer as a simplified fraction or a decimal rounded to two places.
Answers
The price of the jacket in decimals is $ 41.89
The decimal numeral system is widely used to express both integer and non-integer numbers.
The Hindu-Arabic number system has been expanded to include non-integer values. The term "decimal notation" is used to refer to the way that numbers are represented using the decimal system.The decimal system has been developed to represent any real number in an endless number of decimals by using any number of digits after the decimal separator (see decimal representation). Since there are only a few non-zero digits beyond the decimal separator, the decimal numerals in this context are sometimes referred to as terminating decimals. An unending decimal that, at a given point, continues to use the same set of digits repeatedly is said to be recurrent.Let the price of the jacket be x.
Price of the pair of shoes = x + 7.65
Total cost of both the pieces = x + x + 7.65 = 2x+7.65
But the total cost is $91.43
Hence forming a linear equation we get :
$91.43= 2x+7.65
solving the linear equation for x we get :
x=$ 41.89
hence the cost of the jacket is $ 41.89 .
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