The correct option is; 4: this contradicts the Mean Value Theorem since there exists a c on (1, 7) such that f '(c) = f(7) − f(1) (7 − 1) , but f is not continuous at x = 3.
Explain the term Mean Value Theorem?The Mean Value Theorem says that there occurs a point c in the interval (a,b) so that f'(c) equals the function's average rate of change throughout [a,b] if a function f is continuous just on closed interval [a,b] as well as differentiable just on open interval (a,b).The function being used is;
f(x) = (x - 3)⁻²
If we separate this function according to x, we obtain;
f'(x) = -2/(x - 3)³
Finding all c values f(7) − f(1) = f '(c)(7 − 1).is our goal.
This suggests that;
0.06 - 0.25 = -2/(c - 3)³ x 6
-0.19 = -12/(c - 3)³
(c - 3)³ = 63.157
c = 6.98
If the Mean Value Theorem holds for this function, then f must be continuous on [1,7] and differentiable on (1,7).
But when x = 3, f is not continuous, hence the Mean Value Theorem's prediction is false.
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The complete question is-
Let f(x) = (x − 3)−2. Find all values of c in (1, 7) such that f(7) − f(1) = f '(c)(7 − 1). (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) c = Based off of this information, what conclusions can be made about the Mean Value Theorem?
This contradicts the Mean Value Theorem since f satisfies the hypotheses on the given interval but there does not exist any c on (1, 7) such that f '(c) = f(7) − f(1) 7 − 1 . This does not contradict the Mean Value Theorem since f is not continuous at x = 3. This does not contradict the Mean Value Theorem since f is continuous on (1, 7), and there exists a c on (1, 7) such that f '(c) = f(7) − f(1) 7 − 1 . This contradicts the Mean Value Theorem since there exists a c on (1, 7) such that f '(c) = f(7) − f(1) 7 − 1 , but f is not continuous at x = 3. Nothing can be concluded.A Departmental Store ha 10 rack of confectionery item 5 rack of bread item and 15 of grocery item calculate the percentage of all item in the Departmental Store and which item i in maximum
Total no of racks in the store is 30 and grocery item is maximum.
What is percentage?A figure or ratio that may be stated as a fraction of 100 is a percentage. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.
How to find percentage?Divide the amount by the total value to get the percentage, then multiply the resulting number by 100.
Racks of confectionery items = 10
Racks of bread items = 5
Racks of grocery items = 15
The total no of racks in the departmental store is 30
Using the percentage formula we will calculate the percentage of each item
percentage of confectionery items rack =no. of confectionery racks/total no. of racks x100
=10/30x100=33.33%
percentage of bread items rack = no. of bread racks/total no. of racks x 100
= 5/30x 100=16.66%
percentage of grocery items rack = no. of grocery racks/total no. of racks x 100
= 15/30 x 100 = 50%
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What is a reflection rule that maps each triangle and its image?
The equation of the line is y = x. Then the rule of reflection is (x, y) ⇒ (y, x).
What is a reflection of the point?It is the image of the point which is located in the opposite direction of a given point.
The rule of the refection is given will be
Firstly, the rule for reflecting a point about the line y = x is;
While reflecting on the line y = x, we get the reflected points by swapping the coordinates.
The equation of the line that passes through (0, 0) and (1, 1) is given as,
y - 0 = [(1 - 0) / (1 - 0)](x - 0)
y = x
The equation of the line is y = x. Then the rule of reflection is given as,
(x, y) ⇒ (y, x)
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Is this a function or not a function?
(6, 3) (5, 3) (4, 3) (3, 3)
Complete the equation for a line through point A(-3, 3) and perpendicular to the line passing through (0, -2) and (4, 1).
Answer: Zeli shan tel
Step-by-step explanation:
Drag each tile to the correct location on the inequality. Each tile can be used more than once.
Consider the graphed function.
The domain of the function y = 2x + 5 is [-4, 1), and the range of the function is [5, 7). The graph is also attached below.
What is a graph?A collection of objects is arranged in a graph, where some object pairings are conceptually "linked." Each pair of connected vertices is referred to as an edge, and the objects are represented by mathematical abstractions known as vertices.
Given:
As you can see from the graph, the coordinates of the line are (0, 5) and (1,7),
Calculate the equation of the line as shown below,
y - 5 = (7 - 5) / (1 -0) (x-0)
y - 5 = 2 (x +0)
y = 2x + 5
The domain of the above equation can be determined from the graph,
Domain = [-4, 1)
Range = [5, 7)
The graph is also attached below.
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evaluate the integral. (use c for the constant of integration.) x2 15 + 6x − 9x2 3/2 dx
On integrating the function f(x), we get - (x³/45) + (3x²) - (2x³) + C.
What is integration?An integral is a function, of which a given function is the derivative. Integration is basically used to find the areas of the two-dimensional region and computing volumes of three-dimensional objects. Mathematically, we can write -[tex]$\int_a^b \! f(x) \, \mathrm{d}x.[/tex]
Given is the function, as follows -
f(x) = (x²/15 + 6x - 9x²/{3/2})
The given function is -
f(x) = (x²/15 + 6x - 9x²/{3/2})
∫f(x) = ∫(x²/15 + 6x - 9x²/{3/2}) dx
∫f(x) = ∫(x²/15)dx + ∫(6x)dx - ∫(6x²)dx
∫f(x) = (1/15)(x³/3) + C₁ + (6)(x²/2) + C₂ - (6)(x³/3) + C₃
∫f(x) = (x³/45) + (3x²) - (2x³) + {C₁ + C₂ + C₃}
∫f(x) = x³/45) + (3x²) - (2x³) + C (C = C₁ + C₂ + C₃)
Therefore, on integrating the function f(x), we get (x³/45) + (3x²) - (2x³) + C.
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find the centroid of the region in the first quadrant bounded by the given curves. y = x8, x = y8
The centroid of the region in the first quadrant bounded by the given curves is (81/170, 81/170).
In the given question, we have to find the centroid of the region in the first quadrant bounded by the given curves.
The given curves are:
y = x^8, x = y^8
We can write the curves as
y = x^8...........................(1)
y = x^{1/8}.......................(2)
Now putting the value of y from equation 1 in equation 2, we get
x^8 = x^{1/8}
Now simplifying,
x^{64} = x
x^{64}-x = 0
x(x^{63} - 1) = 0
After equating equal to zero,
x = 0, x = 1
My = [tex]\int_{a\rightarrow b}x[f(x)-g(x)]dx[/tex]
My = [tex]\int_{0}^{1}x[x^{1/8} - x^{8}]dx[/tex]
My = [tex]\int_{0}^{1}[x^{9/8} - x^{9}]dx[/tex]
My = [tex][(8/17)x^{17/8} - (1/10)x^{10}]_{0}^{1}[/tex]
My = (8/17)-(1/10)
My = 63/170
Mx = 1/2[tex]\int_{a\rightarrow b}[(f(x))^2-(g(x))^2]dx[/tex]
Mx = 1/2[tex]\int^{1}_{0}[x^{1/4} - x^{16}]dx[/tex]
Mx = 1/2 [tex][(4/5)x^{5/4} - (1/17)x^{17}]^{1}_{0}[/tex]
Mx = (1/2)[(4/5)- (1/17)]
Mx = 63/170
M = [tex]\int_{a\rightarrow b}[f(x)-g(x)]dx[/tex]
M = [tex]\int^{1}_{0}[x^{1/8} - x^{8}] dx[/tex]
M = [tex][(8/9)x^{9/8} - (1/9)x^{9}]^{1}_{0}[/tex]
M = [(8/9) - (1/9)]
M =7/9
Center of mass(x',y') = (My/M, Mx/M)
Center of mass(x',y') = ((63/170)/(7/9), (63/170)/(7/9))
Center of mass(x',y') = (81/170, 81/170)
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While looking at some reports, a
store manager notes that gold
rings that retail for $688 end up
costing customers $731 once the
sales tax is added. What is the
sales tax percentage?
(round your answer to the nearest hundreths)
6.25% is the the sales tax.
What is Percentage?Percentage, a relative value indicating hundredth parts of any quantity.
Given that a store manager notes that gold rings that retail for $688 end up
costing customers $731 once the sales tax is added.
We need to find the sales tax percentage.
The percentage we can calculate by subtracting original amount minus new amount by original amount and multiplied with 100.
731-688/688
0.0625
Multiply 0.0625 with 100 as it is a hundredth part.
0.0625×100
6.25%
Hence, the sales tax percentage is 6.25%.
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Given that the measurement is in inches find the circumference of the circle to the nearest tenth use 3.14 for. Please show ur work Bc I have too !!
Answer:
25.12 in.
Step-by-step explanation:
C = 2πd
C = 2 × 3.14 × 4 in.
C = 25.12 in.
Complete the statements. Explain.
Question 1
Part A
Enter the correct answers in the boxes.
−4(5+(−2))= (
) (5)+ (
)(−2)
−4 (
) =−20+
The numerical expression is -4(5+(-2)) by solving we get -12 is the number with a negative term.
Given that,
The expression is -4(5+(-2))
We have to find what is the solution for the given numerical expression.
We know that,
Mathematical statements called expressions must contain a minimum of two terms with either numbers, variables, or both, joined by an operator. Addition, subtraction, multiplication, and division are all possible mathematical operations.
Take the numerical expression
-4(5+(-2))
Adding 5+(-2)
Multiply + - we get -
So,
5-2=3
-4(5-2)=-4(3)
Multiply 4 to 3
-4(3)=-12
Therefore, The numerical expression is -4(5+(-2)) by solving we get -12 is the number with a negative term.
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Tyler’ firt and correct equation : 0. 65p 0. 10t = 1. 70
Tyler’ econd and incorrect equation: t =(1. 70. 0. 65p). 0. 10
This equation is incorrect because it is missing a division sign between 1.7 and 0.65p. The correct equation should be t = (1.7 / 0.65p) * 0.10
First, we need to isolate the variable 't' in the equation. To do this, we need to divide both sides of the equation by 0.10. This will give us 0.65p/0.10 = 1.70/0.10, which simplifies to t = (1.7 / 0.65p) * 0.10. This is the correct equation that we need to solve for 't'.
t = (1.7 / 0.65p) * 0.10
t = (1.7 / (0.65 * p)) * 0.10
t = (17 / (6.5 * p)) * 0.1
t = (17 * 0.1) / (6.5 * p)
t = (1.7) / (6.5 * p)
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Which expression is equivalent to 3(−4.2y − 13.6)?
A. 1.2y − 13.6
B. 1.2y − 10.6
C. −12.6y − 13.6
D. −12.6y − 40.8
Answer:
the anwser is b
Step-by-step explanation:
helpppppppppppppppppppppppppppppppppppppppppppppppp asap
Answer: It should be 3rd onem 3/4n=5/8
Step-by-step explanation: if not my bad-
Please help me respond this question
Check the picture below.
Answer:
14.1
Step-by-step explanation:
You add all of your numbers up, and then you divide by how many numbers you have.
Find the sum of the first 20 terms of the sequence below.
27, - 9, + 3, - 1, ...
The sum of the first 20 terms of the geometric sequence is 20.25.
What is a geometric sequence?A geometric sequence is a sequence of numbers in which the ratio between consecutive terms is constant.
Example:
2, 4, 8, 16, 32 is a geometric sequence.
We have,
27, -9, 3, -1,.....
a = 27
Common ratio:
= -9/27 = -1/3
= 3/-9 = -1/3
The sum of the geometric sequence.
S(n) = a (1 - [tex]r^n[/tex]) / (1 - r)
Now,
a = 27,
r = -1/3
S(20):
= 27 (1 - [tex](-1/3)^{20}[/tex]) / (1 + 1/3)
= 27 (1 + 1/[tex]3^{20}[/tex]) / (4/3)
[ (1 + 1/[tex]3^{20}[/tex]) = 1 ]
= 27 x 3/4 x 1
= 20.25
Thus,
The sum of the geometric sequence is 20.25.
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The data represent the number of mines traveled by 10 delivery drivers in a community for one day.
218,223,211,299,231,245,261,278,212,233
What is the first quartile of miles driven?
A. 218
B. 261
C. 215
D. 232
The first quartile of miles driven is 218 miles.
What are quartiles in a data set?Quartiles are three values that divide the sorted data into four parts, each of which has the same observation value.
First quartile: Also known as Q1 or lower quartile. Second Quartile: Also called Q2 or median. Third Quartile: Also known as Q3 or upper quartile.The four quarters that divide the dataset into quartiles are:
At least 25% of the number.The next lowest 25% of the numbers (up to the median).25% of the second highest number (above the median).Up to 25% of the number.Let's arrange the data in an order:
211,212,218,223,231,233,245,261,278,299
Since the data has 10 observation, for which the median will be simply the average of two middle terms i.e.5th and 6th term dividing the data in two halves.
Median: 232
First half: 211,212,218,223,231
Second half: 233,245,261,278,299
As, quartiles are the medians of each half,
First quartile: 218
Third quartile: 261
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at confidence, what is the margin of error and the interval estimate of the number of eligible people under years old who had a driver's license in ?
Part a: The margin of error and the interval estimate is E = 0.027 and 0.6120 < p < 0.666 respectively.
Part b: The margin of error and the interval estimate is E = 0.027 and 0.3900 < p < 0.4440 respectively.
Explain the term margin of error?Your results will deviate by various percentage points from the actual population value, according to your margin of error. It is described as a very small percentage that is allowed for error in calculations.Considering the first query;
The 1995 sample proportion is; P₁ = 0.693.The size of the sample is; n = 1200Since the confidence level for the question is 95%, the level of importance is;
α = (100 - 95)%
α = 0.05
Typically, the crucial value of comes out from normal distribution table of α/2 is;
Z(α/2) = 1.96
Typically, this margin of error is denoted mathematically as follows:
E = Z(α/2)*√P₁(1 - P₁)/n
E = 1.96*√0.639(1 - 0.639)/1200
E = 0.027
Mathematically, a 95% Interval estimate is typically written as;
P₁ - E < p < P₁ +E
0.639 - 0.027 < p < 0.639 + 0.027
0.6120 < p < 0.666
Thus, the margin of error and the interval estimate is E = 0.027 and 0.6120 < p < 0.666 respectively.
Part (b)
The 1995 sample proportion is; p₂ = 0.417Sample size: n = 1200Since the confidence level for the question is 95%, the level of importance is;
α = (100 - 95)%
α = 0.05
Typically, the crucial value of comes from the normal distribution table and is;
Z(α/2) = 1.96
Typically, the margin of error is denoted mathematically as follows:
E = Z(α/2)*√p₂(1 - p₂)/n
E = 1.96*√0.417(1 - 0.417)/1200
E = 0.027
Mathematically, a 95% Interval estimate is typically written as;
P₁ - E < p < P₁ +E
0.417 - 0.027 < p < 0.417 + 0.027
0.3900 < p < 0.4440
Thus, the margin of error and the interval estimate is E = 0.027 and 0.3900 < p < 0.4440 respectively.
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The complete question is-
Fewer young people are driving. In 1995, 63.9% of people under years 20 old who were eligible had a driver's license. Bloomberg reported that percentage had dropped to 41.7% in 2016. Suppose these results are based on a random sample 1,200 of people under 20 years old who were eligible to have a driver's license in 1995 and again in 2016.
a. At 95% confidence, what is the margin of error and the interval estimate of the number of eligible people under 20 years old who had a driver's license in 1995?
Margin of error(to four decimal places)
Interval estimate (to four decimal places)
b. At 95% confidence, what is the margin of error and the interval estimate of the number of eligible people under 20 years old who had a driver's license in 2016?
The functions f(x) and g(x) are shown on the graph.
f(x) = x²
What is g(x)?
10
A. g(x) = 2x²
B. g(x) = (x - 2)²
C. g(x) = (¹ x)²
D. g(x) = (x + 2)²
f(x)
(2,8)
The equation of the transformed function is g(x) = -x² - 2
How to describe the transformation from the parent function?From the question, we have the following function that can be used in our computation:
f(x) = x² -- parent root function
When the graph is examined (see attachment), we have the transformation to be
g(x) = reflect f(x) across the x-axis and a downward shift of 2 units.
Mathematically, this can be represented as
g(x) = -f(x) - 2
Substitute the known values in the above equation, so, we have the following representation
g(x) = -x² - 2
Hence, the transformed function is g(x) = -x² - 2
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The point-lope form of the equation of the line that pae through (–4, –3) and (12, 1) i y – 1 = y-1=1/4(x – 12). What i the tandard form of the equation for thi line?
An equation of line having slope 1/4 and passes through the point (-4,-3) is y = 1/4x - 2
We know that the slope-point form of line is:
(y - y1) = m(x - x1)
Here, we need to find an equation of line having slope 1/4 and passes pae through the point (-4,-3)
let (x1, y1) = (-4, -3)
and m = 1/4
substitute values in above formula,
(y - (-3)) = 1/4 (x +4)
y + 3 = 1/4 (x+4)
y = 1/4x -2
which is slope-intercept form of line (y = mx + b)
Therefore, equation of line is y = 1/4x - 2
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A cylinder has a radius of 14 m and a height of 6 m. what is the exact volume of the cylinder? responses 84π m³ 84 pi, m³ 168π m³ 168 pi, m³ 504π m³ 504 pi, m³ 1176π m³
Answer:
answer is on the photo......
Which expression is equivalent to (ab8)4?
a5b12
ab12
a4b32
ab32
Answer:
The answer is ab32
Step-by-step explanation:
ab x 8 x 4 = ab32
Answer: a^4b^32
Step-by-step explanation: (ab^8)^4 = (ab^8)(ab^8)(ab^8)(ab^8) = a^4b^32
Evaluate the expression for t = 9 and u = 2.
t + u =
the tangent line to a certain curve at any point p(x, y) has an x-intercept equal to 3 4 x. this curve also passes through the point (1, 16). find the equation of this curve.
At any point p(x, y), the tangent line to a particular curve has an x-intercept of 3 4 x. The point is also traversed by this curve (1, 16). The equation of the curve is y - 16 = (3/4)(x - 1)^2
To find the equation of the curve, we first need to find the equation of the tangent line at point P(x, y).
Since the x-intercept is 3/4x, the equation of the tangent line is
y - y_p = (3/4)(x - x_p).
We substitute the given point (1, 16) in the equation to find the value of y_p and x_p which are 16 and 1 respectively.
y - 16
= (3/4)(x - 1).
This equation is the equation of the curve.
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A deck of cards contains red, yellow, and blue cards. The probability of selecting a red card out of a deck is 1 9 . The probability of selecting a yellow card is 3 times the probability of selecting a blue card. What is the probability of randomly selecting a blue card on your first try?
We are given that the probability of selecting a yellow card is 3 times the probability of selecting a blue card, so we can write the following equation:
yellow = 3 * blue
We also know that the sum of the probabilities of selecting a red, yellow, or blue card must be equal to 1, so we can write the following equation:
red + yellow + blue = 1
Substituting the expression for yellow from the first equation into the second equation, we get:
red + 3 * blue + blue = 1
Combining like terms, we get:
red + 4 * blue = 1
We are given that the probability of selecting a red card is 1/9, so we can substitute this value into the equation:
1/9 + 4 * blue = 1
Solving for blue, we get:
blue = (1 - 1/9) / 4
blue = (8/9) / 4
blue = 2/9
Therefore, the probability of selecting a blue card on the first try is 2/9.
Machine fills rate 135 containers per minute how long will it take to fill 1000 containers at the same rate
HOW?
HOW?
7.4
Answer:
7.4 mins
Step-by-step explanation:
135 -----> 1 min
1000 ----> x
1000/135 mins = x
= 7.4 mins
Answer:
To determine how long it will take to fill 1000 containers at a rate of 135 containers per minute, you can use the formula: time = number of containers / filling rate. In this case, the filling rate is 135 containers per minute, and the number of containers you want to fill is 1000. Plugging these values into the formula, we get: time = 1000 / 135 = 7.41 minutes.
12)
60°
-5+ 13x
Please help
-5 + 13x = 60
13x = 65
x = 5
CHECKING:
-5 + 13(5) = 60
-5 + 65 = 60
60 = 60
Step-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-Is this a function or not a function?
answer:
if because x does not have two y
Step-by-step explanation:
I hope it works
pls help i’ll give brainlist to right answer
Answer:
i believe its 5+n ≤ -7
Step-by-step explanation:
the sum of 5 and a number(n) would be 5+n, and no more woukd be the ≤ sign, which would lead to -7
(12a - 5b) - (a + 6b)
The answer is 11(a - b), To solve this expression, we need to perform the subtraction operation on the terms inside the parentheses. First, we subtract the term "a + 6b" from "12a - 5b". This gives us 11a - 11b. Then, we can simplify this expression by combining the like terms 11a and -11b to get 11a - 11b = 11(a - b). This is the final answer.
Select the correct systems of equations. Identify the systems of equations that have a as their point of intersection.
We can identify a correct system of equations after draw the graph of the system. The point of intersection indicates the correct solution of the system.
What is the system of equation?Two or more equations which have the same variables, and we can use these all together. The equations are called a set of equations. We get the solution from the system while plotting in the XY coordinate system.
Such as we have two or more linear equations, and we solve each equation and draw a graph for each. We will notice a point of intersection of the straight lines and that refers the solution of the system of equation.
How can we identify a system of equation that have a point of intersection in the graph?There are many sets or system of equation. Some systems have infinity many solutions and graph of the equations never intersect each other. In the next, there are system of equations such as a set of linear function from where we get a point of intersection after plotting the graphs together. The line of intersection is the correct solution of the system.
On the other hand, there are some sets which have no solution, and they are called inconsistent.
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