Answers
The functions and their composites are g⁻¹(6) = 2, h⁻¹(x) = 7x + 8 and (h⁻¹ o h)(1) = 1
Evaluating the functions and their compositesThe one-to-one functions g and h are defined as follows.
g = {(-4, -1), (1, -6), (2, 6), (6, 7)
Also, we have
h(x) = (x - 8)/7
Solving the functions expressions, we have
g⁻¹(6)
This means that we find x when g(x) = 6
From the ordered pairs, we have
g⁻¹(6) = 2
Next, we have
h⁻¹(x)
This means that we calculate the inverse function of h(x)
So, we have
h(x) = (x - 8)/7
This gives
x = (y - 8)/7
7x = y - 8
y = 7x + 8
So, we have
h⁻¹(x) = 7x + 8
Lastly, we have
(h⁻¹ o h)(1) = h⁻¹(h(1))
Using the rule
(h⁻¹ o h)(x) = h⁻¹(h(x)) = x
We have
(h⁻¹ o h)(1) = 1
Hence, the value of (h⁻¹ o h)(1) is 1
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Related Questions
Help please!!!!
Whoever answers right will fat brainliest!
Answers
Answer:
0
Step-by-step explanation:
If we have the function f(x)=sqrt((x-8)/3), where 8 is less than or equal to x which is less than or equal to 16, we can evaluate f(8) as follows:
f(8)=sqrt((8-8)/3)
=sqrt(0/3)
=0
Hope this helps!
A function g is defined below. (a) Write g as a set of ordered pairs. (b) Give the domain and range of g. g(-2) = - 5, g(0) = 0, g(2) = 2, g(4) = - 5 write g as a set of ordered pairs
Answers
Answer:
(a) To write g as a set of ordered pairs, we can use the given function values as follows:
g = {(-2, -5), (0, 0), (2, 2), (4, -5)}
(b) The domain of g is the set of all input values for which the function is defined. In this case, the domain is {-2, 0, 2, 4}.
The range of g is the set of all output values that the function can produce. In this case, the range is {-5, 0, 2}.
Complete the similarity statement
Triangle MTA ~ triangle HTM ~ triangle ___
Answers
The similarity statement is completed as below
Triangle MTA ~ triangle HTM ~ triangle HMA
How to complete the similarity statementA similarity statement is a statement in mathematics that expresses the affinity between two or more figures.
These figures are similar, meaning they have corresponding angles that are identical and sides that are equivalent in size ratio. The same shape is shared by them, although their sizes may be different.
The similar triangles are
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Article lll of the constitution gives congress the power to create a system of federal courts , other than the Supreme Court known as
Answers
The framers of the Constitution believed that as the country grew, more courts would be needed to meet its needs.
Explanation :
The statement that best explains that Article III of the constitution gives congress the ability to create lower courts inferior to the supreme court from "time to time" is that the framers of the Constitution believed that as the country grew, more courts would be needed to meet its needs.
As there will be more framers of the constitution which gave them as a congress the power to create lower courts as they wanted that the congress should have authority over the courts and to control them.
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complete question:
Which statement best explains why Article lll of the constitution gives Congress the ability to create lower courts inferior to the Supreme Court “from time to time”?
If the probability that a randomly chosen college student takes statistics is 0.24, then what is the probability that a randomly chosen college student does not take statistics? Give your answer as a decimal.
Answers
Answer:
The probability that a randomly chosen college student does not take statistics is 0.76.
Step-by-step explanation:
The probability of an event happening and the probability of its complement (the event not happening) must add up to 1. Therefore, if the probability that a randomly chosen college student takes statistics is 0.24, then the probability that they do not take statistics is:
1 - 0.24 = 0.76
So the probability that a randomly chosen college student does not take statistics is 0.76 or 76%.
HELP PLEASE!!! Unit 10 circles homework central angles and arc measurements
Answers
All the arcs are derived as given below.
How did to arrive at the figures above?5)
∡LO = 180°
so
∡KL = ∡ON = 180-90-67
∡KL = ∡ON = 23°
∡OM = 90 + 23 = 113°
∡ NL = 67 + 90 = 157°
7)
Where
(9x + 23) + 31 = 180
9x + 54 = 180
9x = 180-54
9x = 126
x = 126/9
x = 14
9.
(21x-9) = 90+27
21x - 9 = 117
21x = 117 + 9
x = 126/21
x = 6
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HELP PLSZZZZSZZZZZZZZZZ need asap
Answers
Answer:
60 (C)
Step-by-step explanation:
65+55=120
180-120=60
A rare form of malignant tumor occurs in 11 children in a million, so its probability is 0.000011. Four cases of this
tumor occurred in a certain town, which had 17,199 children.
a. Assuming that this tumor occurs as usual, find the mean number of cases in groups of
17,199 children.
b. Using the unrounded mean from part (a), find the probability that the number of tumor cases in a group of
17.199 children is 0 or 1.
c. What is the probability of more than one case?
d. Does the cluster of four cases appear to be attributable to random chance? Why or why not?
Answers
a) The mean number of cases in groups of 17,199 children is 0.187.
b) The probability of 0 or 1 case in a group of 17,199 children is 0.832.
c) The probability of more than one case in a group of 17,199 children is 0.168.
d) The expected number of cases is 3.214 and the actual number of cases is 4
What is the probability?Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain.
For example, if you flip a fair coin, the probability of it landing heads up is 0.5, because there are two equally likely outcomes (heads and tails), and one of them is heads. Similarly, if you roll a fair six-sided die, the probability of rolling a 3 is 1/6, because there are six equally likely outcomes (rolling a 1, 2, 3, 4, 5, or 6), and only one of them is a 3.
According to the given informationa. Assuming that the tumor occurs as usual, the mean number of cases in groups of 17,199 children can be calculated as:
mean = (probability of a single case) x (number of children) = 0.000011 x 17,199 = 0.187
So the mean number of cases in groups of 17,199 children is 0.187.
b. The probability of 0 or 1 case can be found using the Poisson distribution, which models the probability of a certain number of events occurring in a fixed interval of time or space, given the mean rate of occurrence. In this case, the Poisson distribution can be used to find the probability of 0 or 1 case in a group of 17,199 children, given the mean of 0.187.
The probability of 0 or 1 case can be calculated as follows:
P(0 or 1 case) = P(0 case) + P(1 case)
= (e⁽⁻⁰°¹⁸⁷⁾ * 0.187⁰) / 0! + (e⁽⁻⁰°¹⁸⁷⁾ * 0.187¹) / 1!
= 0.832
Therefore, the probability of 0 or 1 case in a group of 17,199 children is 0.832.
c. The probability of more than one case can be found as:
P(more than one case) = 1 - P(0 or 1 case)
= 1 - 0.832
= 0.168
Therefore, the probability of more than one case in a group of 17,199 children is 0.168.
d. To determine whether the cluster of four cases is attributable to random chance, we can compare the actual number of cases with the expected number of cases based on the mean rate of occurrence.
The expected number of cases in a group of 17,199 children can be found by multiplying the mean rate of occurrence (0.187) by the number of groups:
expected number of cases = 0.187 x 17199 = 3.214
Since the expected number of cases is 3.214 and the actual number of cases is 4.
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Add using Scratch Addition. Do your work on paper and upload a screen shot.
45 + 58 + 29 + 59 + 67 + 37 + 55 + 79 + 87
Answers
The expressions using scratch addition is 516
Adding the expressions using Scratch AdditionFrom the question, we have the following parameters that can be used in our computation:
45 + 58 + 29 + 59 + 67 + 37 + 55 + 79 + 87
Using the Scratch method of Addition. we add the numbers one after the other
Using the above as a guide, we have the following:
45 + 58 + 29 + 59 + 67 + 37 + 55 + 79 + 87 = 103 + 29 + 59 + 67 + 37 + 55 + 79 + 87
45 + 58 + 29 + 59 + 67 + 37 + 55 + 79 + 87 = 132 + 59 + 67 + 37 + 55 + 79 + 87
45 + 58 + 29 + 59 + 67 + 37 + 55 + 79 + 87 = 191 + 67 + 37 + 55 + 79 + 87
45 + 58 + 29 + 59 + 67 + 37 + 55 + 79 + 87 = 258 + 37 + 55 + 79 + 87
45 + 58 + 29 + 59 + 67 + 37 + 55 + 79 + 87 = 295 + 55 + 79 + 87
45 + 58 + 29 + 59 + 67 + 37 + 55 + 79 + 87 = 350 + 79 + 87
45 + 58 + 29 + 59 + 67 + 37 + 55 + 79 + 87 = 429+ 87
45 + 58 + 29 + 59 + 67 + 37 + 55 + 79 + 87 = 516
HEnce, the solution is 516
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The indirect measurements, round your answer to the nearest meter. (The figure is not drawn to scale)
Answers
The similar triangle is solved and the width of the river is R = 33.88 m
Given data ,
Let the base of the larger triangle be = 59 m
Let the base of the smaller triangle be = 35 m
Now , height of smaller triangle = 20.1 m
And , width of the river = height of the larger triangle
From the similar triangles , we get
59 / 35 = R / 20.1
Multiply by 20.1 on both sides , we get
R = 33.88 m
Hence , the width of river is 33.88 m
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Three different views of identical cubes are shown at right. What is on the face
opposite the black cirde? Explain/Prove your enswer completely.
A cylinder is sliced at an angle, leaving the shape shown at right. The shorter height
is 12 cm while the longer height is 18 cm. The radius of the base is 4 cm.
What is the volume of this sliced cylinder?
Answers
1) The opposite face of the black circle is, Plus +.
2) The volume of the sliced cylinder is 96π cubic cm.
We have to given that;
Three different views of identical cubes are shown at right.
Now, From first and third dice,
Star is just opposite to symbol ~.
Hence, From second and third dice,
The opposite face of the black circle is, +
2) For the volume of the sliced cylinder, we need to first find the volume of the full cylinder and then subtract the volume of the smaller cylinder that's left after the slice is made.
Hence, The volume of the full cylinder is given by:
V = πr²h
Where r is the radius of the base and h is the height of the full cylinder.
Using the given values, we can find:
V = π(4²)(18)
V = 288π cubic cm
Now, let's find the volume of the smaller cylinder. The shorter height of 12 cm tells us that the slice removed 6 cm from the top of the cylinder. So the height of the smaller cylinder is,
18 - 6 = 12 cm.
The radius remains the same at 4 cm.
Thus, the volume of the smaller cylinder is:
V = π(4²)(12)
V = 192π cubic cm
Finally, we can find the volume of the sliced cylinder by subtracting the volume of the smaller cylinder from the volume of the full cylinder;
⇒ V = (288π) - (192π)
⇒ V = 96π cubic cm
Therefore, the volume of the sliced cylinder is 96π cubic cm.
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The roots of the equation $2x^2-mx+n=0$ sum to $6$ and multiply to $10$. What is the value of $m+n$?
Answers
The value of m + n for the given quadratic equation is 8.
What is a quadratic equation?
A quadratic equation is a polynomial equation of the form:
[tex]ax^{2} +bx+c=0[/tex]
where x is the unknown variable, and a,b and c are constants. The highest power of the variable x in a quadratic equation is 2, hence the term "quadratic". The constants a,b and c are known as the coefficients of the quadratic equation.
According to the given information:
Let's denote the roots of the quadratic equation [tex]2x^{2} -mx+n=0[/tex] as r1 and r2, with r1 and r2 being the roots of the equation.
Given that the sum of the roots is 6 and the product of the roots is 10. This gives us the following equations:
r1 + r2 = 6 ------ (1)
r1*r2 = 10 ------- (2)
We can use these equations to solve for the values of m and n.
The sum of the roots r1 + r2 is also equal to [tex]\frac{-m}{2}[/tex] by Vieta's formulas, which state that the sum of the roots of a quadratic equation [tex]ax^{2} +bx+c=0[/tex] is given by [tex]\frac{-b}{a}[/tex]. Therefore, we can write:
[tex]\frac{-m}{2}[/tex] = 6
Solving for m, we get:
m = -2*6 = -12 ----------(3)
The product of the roots r1*r2 is also equal to n/2 by Vieta's formulas, which states that the product of the roots of a quadratic equation [tex]ax^{2} +bx+c=0\\[/tex] is given by [tex]\frac{c}{a}[/tex]. Therefore, we can write:
n/2 = 10
Solving for n, we get:
n = 2 * 10 = 20 ------------(4)
Now, we can find the value of m+n by substituting the values of m and n from equations (3) and (4) respectively:
m + n = -12 + 20 = 8
So, the value of m+n is 8.
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Let A=[1 2 5 4] B=[-1 1 1 10]. Find A^2 B^2. Hint A^2 = A•A
Answers
The combination of [tex]A_2[/tex] and [tex]B_2[/tex] results in [tex]A_2[/tex] [tex]B_2[/tex] , where [tex]A_2[/tex] is the product of [tex]A_2[/tex] and [tex]B_2[/tex] , and [tex]B_2[/tex] is the product of [tex]B_2[/tex] and [tex]A_2[/tex] . The dot product of both vectors A and B yields a result of 4738 for the product of [tex]A_2[/tex] and [tex]B_2[/tex] .
What is vector?A vector is a mathematical construct with a length and a direction. It is frequently used to symbolise tangible properties like force, velocity, and acceleration. There are numerous techniques to multiply, add, and manipulate vectors. The characteristics and interactions of vectors in higher dimensions are described using vector calculus.
[tex]A_2B_2=A_2.B_2\\\\A_2=A.A\\\\A.A=[1.1+2.2+5.5+4.4][/tex]
=1+4+25+16
=46
[tex]B_2=B.B\\\\B_2=B.B\\\\B.B=[-1.-1+1.1+1.1+10.10][/tex]
=1+1+1+100
=103
[tex]A_2B_2=46.103\\\\A_2B_2=4738[/tex]
Therefore, [tex]A_2B_2=4738[/tex]
The combination of [tex]A_2[/tex] and [tex]B_2[/tex] results in [tex]A_2[/tex] [tex]B_2[/tex] , where [tex]A_2[/tex] is the product of [tex]A_2[/tex] and [tex]B_2[/tex] , and [tex]B_2[/tex] is the product of [tex]B_2[/tex] and [tex]A_2[/tex] . The dot product of both vectors A and B yields a result of 4738 for the product of [tex]A_2[/tex] and [tex]B_2[/tex] .
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PLEASE HELP WILL GIVE BRAINLEST FOR CORRECT ANSWER ONLY !!
(Enlarge photo)
Answers
The length of the diagonal of the cube is x = 3√2 inches
Given data ,
Let the length of the diagonal of the cube be x
Now , the side length of the cube is = 3 inches
From the Pythagoras theorem , we get
x = √s² + s²
On simplifying , we get
x = √ ( 3² + 3² )
x = √18
On simplifying , we get
x = 3√2 inches
Hence , the diagonal is 3√2 inches
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The volume of a rectangular prism is calculated using the formula V=Zoey, where V is the volume of the prism, I and W are the length and width base of the prism, respectively and h is the height of the prism
Answers
Answer:
I'm sorry, but there seems to be an error in the formula you provided. The correct formula for finding the volume (V) of a rectangular prism is V = l x w x h, where l, w, and h are the length, width, and height of the prism, respectively.
NEED HELP WILL GIVE BRAINLIEST AND WILL RATE. Show work and I only need #2
Answers
Changing the base from 5/7 to 7, the end behavior of the function would be given as follows:
As x -> -∞, f(x) -> 0.As x -> ∞, f(x) -> ∞.How to obtain the end behavior of a function?The end behavior of a function is given by the limit of the function is the input x goes to either negative infinity or positive infinity.
The function for this problem is given as follows:
f(x) = 4(5/7)^x.
Changing the base to 7, it would have an absolute value greater than 1, hence the function would be increasing with the end behavior given as follows:
Approaches the horizontal asymptote y = 0 at the left of the graph -> As x -> -∞, f(x) -> 0.Increases as the input increases, that is, as x -> ∞, f(x) -> ∞.More can be learned about the end behavior of a function at brainly.com/question/1365136
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Solve the equation 120 + 1814
x = 180 − 134
x for x.
Answers
Answer:
Step-by-step explanation:
The equation given is:
120 + 1814x = 180 - 134x
We can simplify this equation by adding 134x to both sides:
120 + 1948x = 180
Next, we can subtract 120 from both sides:
1948x = 60
Finally, we can solve for x by dividing both sides by 1948:
x = 60/1948
Therefore, the solution is:
x = 0.0308 (rounded to four decimal places)
Answer:
To solve the equation, we need to first convert the mixed numbers to improper fractions:
120 + 18 1/4 x = 180 − 1 3/4 x
120 + 73/4 x = 180 - 7/4 x (converting mixed numbers to improper fractions)
Multiplying both sides by 4 to eliminate the fractions, we get:
480 + 73x = 720 - 7x
Combining like terms, we get:
80x = 240
Dividing both sides by 80, we get:
x = 3
Therefore, the solution for x is 3.
ASAPP Scott and Lana booked a cruise that departs from Seward, Alaska, but their flight flew into Anchorage, Alaska. The couple decided to travel from Anchorage to Seward on the Alaska Railroad's non-stop Coastal Classic route to enjoy the 117 miles of beautiful scenery. If the train had traveled 13 miles in 30 minutes, how long, in hours, was the non-stop train ride from Anchorage to Seward?
A. 4.5 hours
B. 18 hours
C. 3 hours
D. 9 hours
Answers
A group of 8 friends went to lunch and spent a total of $76, which included the food bill and a tip of $16. They decided to split the bill and tip evenly among themselves. Which equations and solutions describe the situation? Select two options. The equation StartFraction 1 over 8 EndFraction (x + 16) = StartFraction 76 over 8 EndFraction represents the situation, where x is the food bill. The equation StartFraction 1 over 8 EndFraction (x + 16) = 76 represents the situation, where x is the food bill. The solution x = 60 represents the total food bill. The solution x = 60 represents each friend’s share of the food bill and tip. The equation 8 (x + 16) = 76 represents the situation, where x is the food bill.
Answers
An equation and solution that describe the situation is: B. The equation 1/8(x + 16) = 76 represents the situation, where x is the food bill.
How to write an equation to model this situation?In order to write a linear equation to describe this situation, we would a assign variable to the food bill, and then translate the word problem into a linear equation as follows:
Let the variable x represent the total amount of the food bill.
Since this group of 8 friends spent a total of $76, which included the food bill and a tip of $16, and decided to split the bill and tip evenly among themselves, a linear equation that can be used to model this situation is given by;
1/8(x + 16) = 76
(x + 16) = 76(8)
x + 16 = 608
x = 608 - 16
x = $592.
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Plot the numbers -1 1/4 and 5/2 on the number line below. This is due tonight, pls help ):
Answers
5/2 is equal to 2.5 so you would plot it halfway between positive 2 and positive 3
help please I need someone to tutor me with this lol
Answers
Answer:
The domain is (-infinity, infinity), or all real numbers.
The range is (-infinity, infinity), or all real numbers.
Convert 58,080 feet to miles.
Answers
Answer: 11 miles
Step-by-step explanation: 1/5280 = x/58,080
Answer the following questions.
Answers
The questions have been answered below based on the concept of apportionment.
Here, we have,
Apportionment is the challenge of distributing a certain number of items among groups of varying sizes. The Mathematics of Apportionment discusses the mathematical concepts and methods used to allocate identical things fairly among parties with differing claims.
In question 1, the quantity that does not vary from state to state when we apportion congress representatives to different states is called the standard quota.
In question 2, the standard quota is found by dividing the state's population by the standard divisor.
In question 3, the modified divisor in Webster's method is found by dividing the state's population by the modified divisor.
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Plot the numbers -1 1/6 and 7/3 on the number line below.
Answers
The number line where we plotted -1 1/6 and 7/3 is added as an attachment
Plotting -1 1/6 and 7/3 on a number lineFrom the question, we have the following parameters that can be used in our computation:
-1 1/6 and 7/3
To start with, we convert both numbers to the same form
i.e. decimal or fraction
When converted to fractions, we have
-7/6 and 7/3
Rewrite the denominators of the fractions
So, we have
-7/6 and 14/6
This means that we can plot -7/6 at -7 and 7/3 at point 14 where the difference in each interval is 1/6
Using the above as a guide, we have the following:
The number line is attached
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Write the equation of the line that passes through the points (0,6) and (-6,6). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.
Answers
An equation of the line that passes through the points (0, 6) and (-6, 6) is y = 6.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):
y - y₁ = m(x - x₁)
Where:
m represent the slope.x and y represent the points.First of all, we would determine the slope of this line;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (6 - 6)/(-6 - 0)
Slope (m) = 0/-6
Slope (m) = 0.
At data point (0, 6) and a slope of 0, a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 6 = 0(x - 0)
y - 6 = 0
y = 6
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Help plsssssssssssssssssssssssssssss
Answers
Answer:
180 square inches
5 x 6 = 32.5
32.5 x 4 = 130
5 x 5 = 25
25 x 2 = 50
130 + 50 = 180
Step-by-step explanation:
first find the area of all the sides (length times width)
width = 5
length = 6.5
5 x 6.5 = 32.5
32.5 is the area for one side. there are 4 others identical to it
32.5 (one side) x 4 (the amount of sides identical) = 130
then you need to find the area for the bottom/top side
5 = length
5= width
5(L) x 5(W) = 25
25 is the area for the bottom. the top is identical to it
25(bottom side) x 2 (the amount of sides identical)
now add all of the sides up
130 + 50 = 180
Si lanzas una moneda 16 veces, ¿cuál es la mejor predicción posible para el número de veces que caerá cruz?
Answers
A sample of 81 items is taken from a population with a standard deviation of 45 kilograms. The sample mean is 112 kilograms. What weights are included in the 99.7% of confidence interval?
Answers
The confidence interval of the given data is (117, 107).
Given that:
Sample mean X = 112
Standard deviation σ = 45
Sample size n = 81
Confidence level = 99.7%
Z Score = (x − μ )/σ
Z score = 0.9944
Confidence interval = X±z (σ/√n)
= 112±0.9944(45/√81)
= 112±0.9944(5)
= 112±4.972
= 112+4.972 or 112-4.972
= 116.972 or 107.028
= (117, 107)
Therefore, the confidence interval of the given data is (117, 107).
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i need help pleaseee!!!
Answers
The equation of the function g(x) is g(x) = f(x+3) + 4 and g(x) = log₂(x+3) + 4
State g(x) in terms of f(x)To shift the function 3 units left, we replace x with x+3. To shift it 4 units up, we add 4 to the function.
Therefore, the expression for g(x) in terms of f(x) is:
g(x) = f(x+3) + 4
Determine equation of the function g(x)Substituting f(x) = log₂(x), we get:
g(x) = log₂(x+3) + 4
The equation of the function g(x) is g(x) = log₂(x+3) + 4.
State the domain, range, asymptotes of g(x)The domain of g(x) is all x such that x+3 > 0, since the argument of the logarithm must be positive. This gives x > -3.
The range of g(x) is all real numbers, since the logarithm takes on all real values.
The vertical asymptote is x = -3, since this is where the function becomes undefined (the argument of the logarithm becomes 0).
The horizontal asymptote is y = 4, since as x approaches infinity or negative infinity, the function approaches 4.
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work out the some of the interior angles of a pentagon
Answers
"Although part of your question is missing, you might be referring to this full question: Work out the sum of the interior angles of a pentagon".
A pentagon is a polygon with five sides. We can use a formula to get the pentagon's interior angle total. According to the formula, (n-2) x 180 degrees can be used to calculate the total of any polygon's internal angles. This formula can be changed to n=5 for a pentagon, giving us (5-2) x 180 degrees = 540 degrees. Consequently, a pentagon's internal angles add up to 540 degrees.
The sum of the interior angles of a pentagon can also be computed by dividing it by the number of sides, and the result can then be subtracted from 180 degrees to determine each inner angle. So, a pentagon's internal angles are each (540/5)-180 degrees, or 108 degrees.
In conclusion, a pentagon's interior angles add up to 540 degrees, and each interior angle is 108 degrees. In order to solve mathematical problems involving polygons, it can be helpful to comprehend the formulas used to calculate these numbers.
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