Let f and g be differentiable functions. If g and f are inverses of each other,
g(-4)= 7, and f'(7) = 2, then g'(-4) =
Select one answer
A -2
B -1/2
C 1/2
D 2
Answer:
C 1/2
Step-by-step explanation:
You have differentiable functions f and g that are inverses of each other with ...
f(7) = -4f'(7) = 2g(-4) = 7and you want to know g'(-4).
SolutionConsider the composition ...
f(g(x)) = x . . . . . . the functions are inverses of each other.
Differentiating with respect to x, we get ...
f'(g(x))·g'(x) = 1
g'(x) = 1/f'(g(x)) . . . . . . divide by the coefficient of g'(x)
For x = -4, this is ...
g'(-4) = 1/f'(g(-4)) = 1/f'(7) . . . . . use the given values
g'(-4) = 1/2
__
Additional comment
In the attachment, you can consider the red line to be the tangent to f(x) at x=7, and the blue line to be tangent to g(x) at x=-4. The slope of the tangent, g'(-4), is 1/2, the reciprocal of the slope at f(7)=-4.
A function and its inverse are reflections of each other in the line y=x. That line is shown as dashed orange, and the points of interest are marked: (7, -4) and its inverse, (-4, 7).
Questions 11 - 13. Given a standard beta distribution with the following parameters: a = 5 and B = 2 Question 13: Compute P(X<0.2) A. 0.039 B. 0.0149 C. 0.0016 D. 0.026
The P(X<0.2) with standard beta distribution parameters α = 5 and β = 2 is 0.0016.
How to calculated the probability density function in standard beta distribution?
Beta distribution is one of the continuous probability distributions set at interval (0, 1) intervals with two positive parameters α and β.
Probability density function can be calculated by this formula
[tex]\frac{x^{\alpha -1}(1-x)^{\beta -1}}{B(\alpha ,\beta) }[/tex]
B(α,β) is beta function = Γ(α)Γ(β)/Γ(α+β)
Γ(α) is gamma function of alpha
Γ(β) is gamma function of beta
P(X<0.2) = [tex]\frac{0.2^{5-1}(1-0.2)^{2-1}}{B(5,2) }[/tex]
= 0.0016
Excel formula for beta distribution is
=BETA.DIST(x;α;β;TRUE)
Thus, the P(X<0.2) with standard beta distribution parameters α = 5 and β = 2 is 0.0016.
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the standard deviation of utterance is the average number of morphemes that communicators use in their sentences. true or false
The statement which said that "the standard deviation of utterance is the average number of morphemes that communicators use in their sentences", is false.
What is the standard deviation?
Standard deviation is a statistical value that shows the distribution of data in the sample so that it can show how close each point is to the sample mean value. The amount of data that differs from the average can be identified by the standard deviation value.
In conclusion, the standard deviation of utterance is the number of morphemes that are different from the average morpheme used by the communicator in his sentence.
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how do find 1/4 in a number line
Answer:move one part on the right-side of zero
Step-by-step explanation:
Factor the expression in the image please
To factorize this,the answer is [tex]\frac{1}{3} x^{4} y^{2} (\frac{1}{4} y^{} -\frac{1}{3} x)[/tex]
What is Factorization?Factorization is when you break a number down into smaller numbers that, when multiplied together, give you that original number.
The expression above can only be determined by looking at the common factors and using it to answer the question. [tex]\frac{1}{12} x^{4}y^{3} -\frac{1}{9}x^{5}y^{2}[/tex]
To factorize the fractions by looking at the common factor between the both[tex]\frac{1}{3} (\frac{1}{4} -\frac{1}{3} )[/tex]To factorize the indices by looking at the common factor[tex]x^{4}y^{2} (y-x)[/tex]
So, to factorize the expression above[tex]\frac{1}{3} x^{4} y^{2}(\frac{1}{4} y-\frac{1}{3} x)[/tex]
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What is the main difference between vulnerability scanning and penetration testing?.
The main difference between vulnerability scanning and penetration testing is a vulnerability scan is an automated, high-level test that looks for and reports potential vulnerabilities. A penetration test is a detailed hands-on examination by a real person that tries to detect and exploit weaknesses in your system.
vulnerability scanning:
These scans are typically automated and give a beginning look at what could possibly be exploited.
High-quality vulnerability scans can search for over 50,000 vulnerabilities and are required as per PCI DSS, FFIEC, and GLBA mandates.
penetration testing:
A penetration test simulates a hacker attempting to get into a business system through hands-on research and the exploitation of vulnerabilities. Actual analysts, often called ethical hackers, search for vulnerabilities and then try to prove that they can be exploited. Using methods like password cracking, buffer overflow, and SQL injection, they attempt to compromise and extract data from a network in a non damaging way.
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The table below shows results of a survey about who uses the World Wide Web.
User Percent
Business 34%
Education and Government 12%
Home 54%
If 600 people were surveyed, how many people used the World Wide Web for Business?
Examine the triangles, which are similar.
12 mm
18 mm
y
?
12 mm
© 2017 StrongMind. Created using GeoGebra.
How many millimeters long is the missing side?
Note: The triangles may not be drawn to scale.
The missing side of the first triangle is 8 millimeters long.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The relations between variables, either direct or inversely proportional, can be built to find the desired measures in the problem.
We have been given that;
The first triangle has a side length of 12 millimeters, which corresponds to the second triangle's side of 18 millimeters.
The missing side of the first triangle corresponds to a side of 12 millimeters on the second triangle.
Therefore, The relationship between them is;
12/ n = 18/12
n = 12 x 12/18
n = 144 /18
n = 8
Therefore, the missing side of the first triangle is 8 millimeters long.
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Read the following statements:
Statement 1: If it is a square, then it has more than four sides.
Statement 2: If it has less than four sides, then it is a square.
Are the two statements logically equivalent?
A.) Yes, both statements are true.
B.) Yes, both statements are false.
C.) No, only one statement is true.
D.) No, both statements are false.
Answer: No, both statements are false.
Step-by-step explanation: it's logical a square has to have 4 sides no more and no less.
The statements are not logically equivalent because D.) No, both statements are false.
What is a square?A square is a regular quadrilateral in Euclidean geometry, which means it has four equal sides and four equal angles. It can also be defined as a rectangle with two adjacent sides of equal length.
A square is a regular polygon with four equal sides and four equal angles of 90° each. A square is a closed two-dimensional shape with four equal sides and four vertices. Its opposing sides are perpendicular to each other. A square can also be thought of as a rectangle with equal length and width.
In this case, a square has four sides. Therefore, the information given about the square is wrong. The correct option is D.
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Bill started west on road u. S. 50, riding a bicycle at an average rate of 9 mph. Four hours later charles started after bill on a motor cycle and overtook him in 2 hours. What was charles' rate? which equation could be used to solve for charles' rate if it is represented by x? 6 x = 54 2 x = 54 2 x = 36.
The equation could be used to solve for charles' rate if it is represented by x is 2x=54.
In the given question wehave to find the equation could be used to solve for charles' rate if it is represented by x.
Bill riding a bicycle at an average rate of 9 mph.
Charles' rate is x.
So the relative rate = x−9 mph
Distance traveled by Bill in 4 hours = 9*4 =36 mph
Charles' overtook Bill in 2 hours. So
Relative Rate = Distance/Time
x−9=36/2
Multiply by 2 on both side. We get
2(x−9)=36
Simplifying
2x−18=36
Add 18 on both side, we get
2x=36+18
2x=54
Hence, the equation could be used to solve for charles' rate if it is represented by x is 2x=54.
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consider the equation y+4=-1/2(x+8)
The equation of the line in standard form is x + 2y = -16
What are linear equations?Linear equations are the set of equations that have constant slopes or gradient
How to put the equation of a line into standard form?From the question, we have the following equation that can be used in our computation:
y+4=-1/2(x+8)
Rewrite the above equation properly
So, we have the following representation
y + 4 = -1/2(x + 8)
Multiply through the equation by -2
So, we have the following equation
-2(y + 4) = -1/2(x + 8) * -2
Evaluate the products
-2y - 8 = x + 8
To rewrite as standard form is to make the variable stand alone
So, we have
-x -2y = 8 + 8
Evaluate the like terms
So, we have the following representation
-x -2y = 16
Multiply through by -1
x + 2y = -16
Hence, the equation is x + 2y = -16
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Possible question
consider the equation y+4=-1/2(x+8)
Put the equation of a line into standard form
help me with the question on the attached photo please
The width of the shade along line AB, using relations in a right triangle, is of:
337.8 mm.
What are the relations in a right triangle?There are three relations in a right triangle, given as follows:
The sine of an angle of the triangle is represented by the length of the opposite side to the angle divided by the length of the hypotenuse.The cosine of an angle of the triangle is represented by the length of the adjacent side to the angle divided by the length of the hypotenuse.The tangent of an angle of the triangle is represented by the length of the opposite side to the angle divided by the length of the adjacent side to the angle.The width of the shade along-side line AB is of:
100 mm + e1 + e2.
Considering a bisection at the top corner of the shade, we have that:
e1 is the length opposite side to an angle of 50º in a right triangle with hypotenuse of 150 mm, hence:
sin(50º) = e1/150
e1 = 150 x sin(50º)
e1 = 114.9 mm.
Considering a bisection at the bottom corner of the shade, we have that:
e2 is the length opposite side to an angle of 55º in a right triangle with hypotenuse of 150 mm, hence:
sin(55º) = e2/150
e2 = 150 x sin(55º)
e2 = 122.9 mm.
Hence the total width of the shade is of:
100 mm + e1 + e2 = 100 + 114.9 + 122.9 = 337.8 mm.
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It costs $0.75 each to make color copies at a copy
center. At this price, how many copies can be purchased with $60.00?
Answer: 80 copies can be purchased with $60.00.
Step-by-step explanation:
If it costs $0.75 for each color copy, then you would have to divide $60.00 by $0.75, which equals 80 copies.
A bag contains 5 blue balls 4 red balls 3 orange balls. if a ball is picked from the bag at random, what is the probability that it is a blue ball. Answers have been rounded to the tenth place
The probability that it is a blue ball is 5/12 ≈ 0.416.
Given:
A bag contains 5 blue balls 4 red balls 3 orange balls.
Total balls = 5 + 4 + 3
= 12
Number of possible outcomes = 12
Number of favorable outcomes = number of blue balls = 5
Probability = Number of favorable outcomes / Number of possible outcomes.
= 5/12.
= 0.416
Therefore the probability that it is a blue ball is 5/12 ≈ 0.416.
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25 POINTS!! ANSWER FOR BRAINLIST AND SHOW WORK!!!
Answer:
See attached "Image 2" for graph
3 points that are in the system
[tex](6,1)\\(8,-2)\\(7,5)[/tex]
3 points that are not in the system:
[tex](0,0)\\(-2,-6)\\(-8,4)[/tex]
Step-by-step explanation:
Start by writing the equation in slope-intercept form so they can be graphed.
[tex]\left \{ {{y+5 < 2x} \atop {3y\geq -2x+6}} \right. \\\\\left \{ {{y < 2x-5} \atop {y\geq -\frac{2}{3} x+2}} \right. \\\\[/tex]
Now, graph just the lines - LIGHTLY- on the coordinate plane. See the first attached image.
Now, you can shade the correct areas. In the first equation y is LESS THAN the function, so you would shade BELOW the line, and draw the line as a dashed line, not a solid line. This is because y is not EQUAL to the function.
In the second equation y is GREATER than or EQUAL to the function, so draw the line as a solid line and you would SHADE above the line.
In a system of inequalities, the correct area to shade is where the two shaded areas overlap. See the attached image 2 to see how that looks.
Some points that are in the system of inequalities are:
[tex](6,1)\\(8,-2)\\(7,5)[/tex]
These points are NOT in the system:
[tex](0,0)\\(-2,-6)\\(-8,4)[/tex]
pls help!
Simplify the expression to a + bi form:
√4 + √−45 + √49 + √−45
Answer: 9+6i√5
Step-by-step explanation:
√4 + √−45 + √49 + √−45
2 + √45i + 7 + √45i
9 + 3i√5 + 3i√5
9+6i√5
What is the equation of the line that is parallel to the line y=2/3x−4/5 and passes through the point (−3,2)?
A. 2x−3y=−12
B. 3x+2y=4
C. 2x−3y=−6
D. 3x+2y=8
keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above
[tex]y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{2}{3}}x-\cfrac{4}{5}\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
so we're really looking for the equation of a line whose slope is 2/3 and that it passes through (-3 , 2) in standard form
standard form for a linear equation means
• all coefficients must be integers, no fractions
• only the constant on the right-hand-side
• all variables on the left-hand-side, sorted
• "x" must not have a negative coefficient
[tex](\stackrel{x_1}{-3}~,~\stackrel{y_1}{2})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{2}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{2}=\stackrel{m}{ \cfrac{2}{3}}(x-\stackrel{x_1}{(-3)}) \implies y -2= \cfrac{2}{3} (x +3)[/tex]
[tex]\stackrel{\textit{multiplying both sides by }\stackrel{LCD}{3}}{3(y-2)=3\left( \cfrac{2}{3} (x +3) \right)}\implies 3y-6=2(x+3)\implies 3y-6=2x+6 \\\\\\ 3y=2x+12\implies -2x+3y=12\implies {\Large \begin{array}{llll} 2x-3y=-12 \end{array}}[/tex]
1.
What are the rational zeros of the function
f(x) = 5x² - 35x - 300?
A -12,5
B-12, -5,5
-5, 12
D-5, 5, 12
For the given function f(x) = 5x² - 35x -300 the rational zeroes of the given function are 12 and -5.
As given in the question,
Given function is equal to:
f(x) = 5x² - 35x -300
Simplify the given function f(x) = 5x² - 35x -300 to get the rational zeros of the function,
f(x) = 0
⇒ 5x² - 35x -300 = 0
⇒ 5( x² - 7x - 60) = 0
As 5≠ 0 ,
⇒ x² - 7x - 60 = 0
⇒ x² - 12x + 5x- 60 = 0
⇒(x-12) (x+ 5) = 0
⇒ x = 12 or -5
Therefore, for the given function f(x) = 5x² - 35x -300 the rational zeroes of the given function are 12 and -5.
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Determine whether each number is an integer, a rational number that is not an integral or an irrational number
The integers are 3√25, -185/5, rational = -1/4, 0.75, 3√25, -185/5, 4√8, irrational = √13,
An integer is the number zero (0), a positive natural number (1, 2, 3, etc.) or a negative integer with a minus sign.
A rational number is any number that can be written as a fraction, where both the numerator na demoninator that is the top and the bottom number are integers, and the denominator is cannot be zero
An irrational number is a type of real number which cannot be represented as a simple fraction.
A integer can always be a rational number but vice versa is not true.
Integer = 3√25 = 3x5 = 15
-185/5 = -37
rational = -1/4, 0.75, 3√25, -185/5, 4√8
irrational = √13,
Therefore, the integers are 3√25, -185/5, rational = -1/4, 0.75, 3√25, -185/5, 4√8, irrational = √13,
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If the average product of labor is seven units of output per worker per day, the total output of 15 workers will be ______________ units per day.
The total output of 15 workers will be 105 units per day.Work and time are correlated so using this we could solve the question.
What is work and time?
Time is the duration of any activity or work that occurs or continues.
Work is a task or set of activities designed to achieve a specific result.
Main Body:
This can be done by simply multiplying both number of days and total work in one day.Hence the equation become:
total output = total workers*total work done by one person.
Total output = 7*15
hence,total output = 105 units
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I really need help on this one like asap so if someone can help me i'll be very happy. the question is Determine which equation is false, based on the solution set S:{2}.
7 = 6p − 5
4t = 8
3(3c + 1) = 21
5m + 8 = 16
3(3c + 1) = 21 is false
Answer:
3(3c + 1) = 21 is false.
Step-by-step explanation:
what is 20.72 divided by 8 with work shown
Answer:
2.59
Step-by-step explanation:
Answer shown in picture.
-14 feet and 23 feet use absolute value
Answer:
-14 + 23 = 9
Step-by-step explanation:
if you borrow 14 dollars and pay23 dollars you have a change of 9 dollars
A coffee table is on sale for 20% off tej original price of $115.If there is a 7.5% sales tax, what is the final price of the coffee table
Answer:
$85.10
Step-by-step explanation:
115 * .20 = 23
115 - 23 = 92
92 * 0.075 = 6.9
92 - 6.9 + 85.10
For his phone service, Alonzo pays a monthly fee of $17, and he pays an additional $0.07 per minute of use. The least he has been charged in a month is $115.56. What are the possible numbers of minutes he has used his phone in a month? Use m for the number of minutes, and solve your inequality for m .
Answer:
at least 1,408 minutes
Step-by-step explanation:
Let m be the number of minutes.
[tex]17 + .07m \geqslant 115.56[/tex]
[tex].07m \geqslant 98.56[/tex]
[tex]m \geqslant 1408[/tex]
new york i even degree warmer than pari. if it i -8°c in pari, what i the temperature in new york ?
Answer:
-1°C
Step-by-step explanation:
-8+7=-1
Is your s key broken?
Simplify to a single power of 4:
(44) 5
Answer:
4²0=4×5=20=4²0 арлатат
determine if the following orders pairs
The given ordered pair (x, y) represents a linear function
Consider first point (-1, -3) and (0, -1)
The slope of the line is the change in y coordinate with respect to the change in x coordinate of the line.
The slope of the line = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute the value in the equation
The slope of the line = (-1-(-3)) / (0 -(-1)
= (-1+3) / 1
= 2
Consider the next set of points (1, 1) and (2, 3)
The slope of the line = (3-1) / (2-1)
= 2
Here slope of the line is same, therefore it is linear function
Hence, the given ordered pair (x, y) represents a linear function
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What is the difference between the graph of y=x+3 and the graph of y=x-3?
Answer:
y
=
x
+
3
y
=
x
−
3
Step-by-step explanation:
can someone help me pretty pls:)
Answer: Choice B
Step-by-step explanation:
A doesn’t contain any variables
B is literal because you can solve for X
C doesn’t contain any numbers
D is an expression
- Your Welcome
Answer:
C.
Step-by-step explanation:
A literal equation consists of mainly variables.
A. has no variables
B. only has one variable
D. Is not an equation