Answers
f(x) = 9x-6
g(x) =√(x-4)
(f0g)(x) = f(g(x)) exist if g(x) exist and f(g(x)) exist.
g(1) no exist because : √(1-4) =√(-3) ... no real
conclusion : 1 is not in the domain of : f0g
Related Questions
To convert 2.7 hours into seconds, which two ratios could you multiply by?
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amount of minutes x 60 (for seconds) = amount of seconds.
IN this case
2.7 x 60 = 162 minutes
162 x 60 = 9720 seconds.
so the two rations are 1:60 or (hr: min) then 1:60 or (min: seconds)
hope this helps :D
What addition doubles fact can help you find 4+ 3? Explain how you know
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By using the commutative law of addition, the result of the addition would be 7.
What is commutative property of addition?The commutative property of addition says that it doesn't matter how we add two numbers, the result of the addition would be same.
For two numbers x and y, we have:
x + y = y + x
Thus, if we take 3 numbers as a,b and c, then:
a + b + c = b + a + c = b + c + a = a + c + b = c + a + b = c + b + a
And so for any amount of numbers.
We have been Given that the expression 4 + 3, we need to determine what addition shows that the statement is true.
We know that the sum of 4 and 3 is 7, we can explain that by using the commutative law of addition as shown;
According to the law, A + B = B+ A
4 + 3 = 3 + 4 = 7
Therefore, By using the commutative law of addition, the result of the addition would be 7.
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G the base of a solid is the circle x2 + y2 = 9. cross sections of the solid perpendicular to the x-axis are equilateral triangles. what is the volume, in cubic units, of the solid
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Final answer:
To find the volume of the solid, we can use the formula V = A * h, where A is the area of the base and h is the perpendicular height. Given that the base is a circle and the cross sections of the solid are equilateral triangles, we can calculate the volume by integrating the expression for the area of the cross section from -3 to 3.
Explanation:
To find the volume of the solid, we can use the formula V = A * h, where A is the area of the base and h is the perpendicular height.
Given that the base is a circle with equation x^2 + y^2 = 9, we can determine the radius of the circle to be 3 units.
The cross sections of the solid perpendicular to the x-axis form equilateral triangles. The side length of an equilateral triangle is equal to the radius of the circle, which is 3 units. Since the height of each elemental cylinder is 2y, and the height of an equilateral triangle is h = √(3^2 - (3/2)^2) = √(9 - 9/4) = √(36/4 - 9/4) = √(27/4), the volume of each elemental cylinder is 4π(3^2 - x^2)^(1/2) dx = 4π(27 - 4x^2)^(1/2) dx.
To find the total volume of the solid, we integrate the expression 4π(27 - 4x^2)^(1/2)dx from x = -3 to x = 3.
∫(4π(27 - 4x^2)^(1/2)dx from -3 to 3 = 4π∫(27 - 4x^2)^(1/2)dx from -3 to 3 = 4π∫(27 - 4x^2)^(1/2)dx from -3 to 3 = 4π∫(27 - 4x^2)^(1/2)dx from -3 to 3 = 4π(3^3/3 - (-3)^3/3) = 36π units^3.
Find the general solution of the given system. dx dt = −6x + 4y dy dt = − 7 4 x + 2y
Answers
[tex]\begin{bmatrix}-6&4\\\\-\frac74&2\end{bmatrix}[/tex]
has eigenvalues given by
[tex]\begin{vmatrix}-6-\lambda&4\\\\-\frac74&2-\lambda\end{vmatrix}=\lambda^2+4\lambda-5=(\lambda+5)(\lambda-1)=0[/tex]
The eigenvalues are thus [tex]\lambda_1=-5[/tex] and [tex]\lambda_2=1[/tex].
For the eigenvalue [tex]\lambda_1[/tex], the corresponding eigenvector [tex]\eta_1[/tex] satisfies
[tex]\begin{bmatrix}-1&4\\\\-\frac74&7\end{bmatrix}\begin{bmatrix}\eta_{1,1}\\\eta_{1,2}\end{bmatrix}=\begin{bmatrix}0\\0\end{bmatrix}[/tex]
[tex]\implies\eta_{1,1}=4\eta_{1,2}[/tex]
so that we can choose [tex]\eta_1=\begin{bmatrix}4\\1\end{bmatrix}[/tex].
For [tex]\lamda_2=1[/tex], we have
[tex]\begin{bmatrix}-7&4\\\\-\frac74&1\end{bmatrix}\begin{bmatrix}\eta_{2,1}\\\eta_{2,2}\end{bmatrix}=\begin{bmatrix}0\\0\end{bmatrix}[/tex]
[tex]\implies7\eta_{2,1}=4\eta_{2,2}[/tex]
and we can choose [tex]\eta_2=\begin{bmatrix}4\\7\end{bmatrix}[/tex] for the corresponding eigenvector.
Then the general solution to the ODE system is given by
[tex]\begin{bmatrix}x(t)\\y(t)\end{bmatrix}=C_1\begin{bmatrix}4\\1\end{bmatrix}e^{-5t}+\C_2\begin{bmatrix}4\\7\end{bmatrix}e^t[/tex]
Compare the functions f(x) = x5 and g(x) = 5x by graphing both functions in several viewing rectangles. find all points of intersection of the graphs correct to one decimal place. (enter your answers as a comma-separated list. round any decimal answers to one decimal place.)
Answers
f(x) = x⁵ and g(x) = 5x
are shown in the figure below.
The initial plot interval is -2 ≤ x ≤ 2.
In order to determine the points of intersection (to 1 decimal place accuracy) more graphs (shown in accompanying figures) were necessary.
The points of intersection are
x = -1.5, x = 0, and x = 1.5
Answer:
The points of intersection are x = -1.5, 0, and 1.5 (accurate to 1 decimal place)
To compare the functions f(x) = x^5 and g(x) = 5x, graph both functions and find their points of intersection.
Explanation:To compare the functions f(x) = x^5 and g(x) = 5x, we can graph both functions in several viewing rectangles. By finding the points of intersection of the graphs, we can compare their values at those points.
Start by graphing the function f(x) = x^5 using a graphing calculator or software. This will give us a curve with a steep increase as x gets larger.Next, graph the function g(x) = 5x in the same viewing rectangle as f(x). This will give us a straight line that increases more gradually as x gets larger.Identify the points of intersection between the graphs of f(x) and g(x). These are the x-values at which the two functions have the same y-value. Round these x-values to one decimal place and list them as the points of intersection.) there are exactly 20 students currently enrolled in a class. how many different ways are there to pair up the 20 students, so that each student is paired with one other student
Answers
There are at least two ways to see this (possibly more).
One way is to note that, first, we have to select 2 students for the first pair; that's C(20, 2) (where by C(20, 2) I mean "20 choose 2"; that is, 20! / (18! * 2!). )
Then, for each way of selecting 2 students for the first pair, I have to select 2 of the remaining 18 students for the second pair, so I multiply by C(18, 2).
Continuing in this manner, I get C(20, 2) * C(18, 2) * ... * C(2, 2).
But it doesn't matter in this situation the order in which I pick the pairs of students. Since there are 10! different orders in which I could pick the individual pairs, then I want to divide the above by 10!, giving me the answer
[C(20, 2) * C(18, 2) * ... * C(2, 2)] / 10!.
This is the same as your answer, because C(n , 2) = n(n - 1) / 2, so we can simplify the above as
[(20 * 19) / 2 * (18 * 17) / 2 * ... * (2 * 1) / 2] / 10!
= 20! / [2^10 * 10!]
= 20! / [(2!)^10 * (10!)].
Another way is to reason as follows:
1. First, arrange the 20 students in a line; there are 20! ways to do this
2. We can get a pairing by pairing the 1st and 2nd students in line together, the 3rd and 4th students together, etc.
3. But if I switch the order of the 1st and 2nd student, then this doesn't give a different pairing. I don't want to count both orderings separately, so I divide by 2!
4. The same argument from step 3 holds for the 3rd and 4th student, the 5th and 6th student, etc., so I need to divide by 2! nine more times
5. Finally, the particular order in which I selected the ten pairings are unimportant--for example, the following orderings don't produce different pairings:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20
3, 4, 1, 2, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20
So I need to further divide by the number of ways I can arrange the ten pairs, which is 10!.
Find the product and quotient of 24.6 and 1.2
Answers
Quotient: 24.6 / 1.2 = 20.5
The product of 24.6 an 1.2 is 2.88 and quotient of 24.6 and 1.2 is 2.
What is product and quotient?Product is of two or more numbers is the result of multiplying these numbers, and
Quotient of two numbers is the result of division of these numbers.
Now the given numbers are 2.4 and 1.2.
Now for product of these numbers let us multiply these numbers. So we have,
2.4 x 1.2 = 2.88
Hence the product of 2.4 and 1.2 is 2.88
Again for quotient of 2.4 and 1.2, let us divide these numbers. So we have,
2.4 ÷1.2 = 2
Hence the quotient of 2.4 and 1.2 is 2.
Therefore,The product of 24.6 an 1.2 is 2.88 and quotient of 24.6 and 1.2 is 2.
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a model train engine is 6 inches long the real train is 42 feet long what is the scale factor
Answers
A student club with 30 members need to chose an executive committee. there are five members of the committee and all have equal votes. how many possible sets of members are there for the committee
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HELP PLZ? You want to help build an awards podium for a track meet. If the podium has the dimensions shown, what is its volume?
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volume = l x w x h
area 1 = 3 x 1.5 x 2 = 9 cubic feet
area 2 = 2 x 1.5 x 2 = 6 cubic feet
area 3 = 1.5 x 1 x 2 = 3 cubic feet
9+6+3 = 18 cubic feet total
The volume of Podium is: 18 cubic feet.
Step-by-step explanation:The volume of Podium is equal to the volume of 3 cuboids of different heights.
We know that a volume of cuboid with length l, width b and height h is given by:
Volume= l×b×h
Hence,
Volume of cuboid numbered as 3 is:
Volume= 1×2×1.5= 3 cubic feet.
Volume of cuboid numbered as 2 is:
Volume=2×2×1.5=6 cubic feet.
Similarly volume of cuboid numbered as 1 is:
Volume= 3×1.5×2=9 cubic feet.
Hence, the Volume of Podium is:
3+6+9=18 cubic feet.
write in order from least to greatest
Answers
How many lines of symmetry does the figure have?
0
1
2
3
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so answer is
1
hope it helps
Riverside bank offers to lend you $50,000 at a nominal rate of 6.5%, compounded monthly. the loan (principal plus interest) must be repaid at the end of the year. midwest bank also offers to lend you the $50,000, but it will charge an annual rate of 6.2%, with no interest due until the end of the year. how much higher or lower is the effective annual rate charged by midwest versus the rate charged by riverside
Answers
The effective annual rate of Midwest is 0.2% lower than the rate charged by Riverside.
Further Explanation:
Riverside Bank:
Principal = $50,000
Duration = 1 year
APR = 6.5%
The amount paid after 1 year is
A = 50000(1 + 0.065/12)¹² = $53,348.59
Midwest Bank:
Principal = $50,000
APR = 6.2%
Duration = 1 year
The amount paid after 1 year is
A = 50000*(1 + 0.062) = $53,100.00
The amount charged by Midwest is lower:
Let r = the effective annual rate of Riverside Bank.
Then
50000*(1 + r) = 53348.59
1 + r = 53348.59/50000 = 1.067
r = 0.067 = 6.7%
Effective annual rate:
The viable yearly financing cost is the loan fee that is really earned or paid on a venture, advance or other money related item because of the aftereffect of intensifying over a given timeframe. It is additionally called the powerful loan cost, the viable rate or the yearly comparable rate.
Instructions to Calculate the Effective annual Rate:
1. Determine the expressed loan fee. The expressed financing cost (additionally called yearly rate or ostensible rate) is generally found in the features of the credit or store understanding.
2. Determine the quantity of aggravating periods.
3. Apply the EAR Formula: EAR = (1+ I/n)n – 1.
Subject: mathematics
Level: college
Keywords: Riverside Bank, Midwest Bank, The amount charged by Midwest is lower, Effective annual rate, Instructions to Calculate the Effective annual Rate.
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what is the distance between (-5,5) and (2,6) rounding to the nearest hundred
Answers
need help with this inequality
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|x-4| </ 1
x-4 </ 1
and
x-4 >/ -1
+4 both sides
x </ 5
x >/ 3
this is shown in the graph
52.85 rounded to nearest tenth
Answers
Answer:
The required number is 52.9.
Step-by-step explanation:
Given : Number 52.85
To find : The number rounded to nearest tenth?
Solution :
Rounded to the tenth means round the number so that only one number left after the decimal.
Rules of rounding :
1) If the hundredth place value is >5 or =5 then add 1 to first digit and remove second.
2) If the hundredth place value is <5 ,then hundredth place number is removed.
Now, In the number 52.85
The hundredth place value is 5 so, 1 is added to the 8
Then the required number is 52.9.
While passing a slower car on the highway, i accelerate uniformly from 12 m/s to 24 m/s in a time of 10.0s. How far do you travel during this time and what is the magnitude of your acceleration
Answers
vf-vi=at (final velocity minus initial velocity is equal to acceleration times time)
We know vf, vi, and t so we can solve for acceleration:
24-12=a10
12=10a
a=1.2
That is the acceleration, we will need to integrate with respect to time twice...
v=⌠a dt
v=at+vi , we know a=1.2m/s^2 and vi=12m/s
v=1.2t+12,
x=⌠1.2t+12 dt
x=1.2t^2/2+12t+xo, we can just let xo=0 for this problem...
x(t)=0.6t^2+12t
Now we know that this acceleration lasts for 10 seconds so the distance traveled in that time is:
x(10)=0.6(10^2)+12(10)
x(10)=60+120
x(10)=180 meters
A wheel in this scale drawing is 4 cm wide. The ratio of the drawing is 1:14. How wide is the actual wheel in cm?
Answers
1:14 means that for every 1 cm it is drawn at it is actually 14 cm
so multiply 4 x 14 = 56
it is actually 56 cm wide
The equation of motion for a weight suspended from a particular spring is given by p(t)=2sint3+5cost3p(t)=2sint3+5cost3, where p(t)p(t) is the displacement from the equilibrium position in centimeters, and tt is the time elapsed in seconds. at what time does the weight first reach the equilibrium position?
Answers
Final answer:
To find the time at which the weight first reaches the equilibrium position, set the equation of motion equal to zero and solve for t.
Explanation:
The equation of motion for the weight suspended from the spring is given by p(t) = 2sin(t/3) + 5cos(t/3), where p(t) is the displacement from the equilibrium position in centimeters and t is the time elapsed in seconds. The weight first reaches the equilibrium position when the displacement p(t) equals zero. To find the time at which this occurs, we set the equation equal to zero and solve for t.
2sin(t/3) + 5cos(t/3) = 0
Using trigonometric identities, we can rewrite the equation as:
2sin(t/3) = -5cos(t/3)
Dividing both sides by cos(t/3), we get:
2tan(t/3) = -5
Therefore, to find the time at which the weight first reaches the equilibrium position, we need to solve the equation 2tan(t/3) = -5 for t.
Mary is making Magic Marshmellow cake . The recipe calls for 3/4 cup of milk and 2 eggs per serving. The wants to make enough cake for 20 people . How much milk will Mary need?
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and surely you know how much that is.
500 is 10 times as much as
Answers
The hypergeometric distribution is used when samples are taken from an infinite population with replacement.
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The statement is FALSE
The hypergeometric distribution describes the probability of a certain number of successes in samples taken without replacement from a finite population, not an infinite one as stated in the question.
The hypergeometric distribution is a statistical model used to calculate probabilities in experiments where samples are drawn without replacement from a finite population. Unlike the statement presented in the question, the hypergeometric distribution is not used for infinite populations nor for sampling with replacement; that would be the domain of the binomial distribution.
The cost of a parking permit consists of a one-time administration fee plus a monthly fee. A permit purchased for 12 months costs $660. A permit purchased for 15 months costs $810. What is the administration fee?
Answers
Answer:
answer = 60
Step-by-step explanation:
It might be option A or D. Mine was D
Describe the two possible ways to use the angle of depression that is outside a right triangle to find the measure of an angle inside the triangle?
Answers
=> Angle of depression = 90° - up angle
=> up angle = 90° - angle of depression
2) The angle of depression is equal to the bottom angle of the right triangle.
=> bottom angle = angle of depression.
10 times as many as 1 hundred is
Answers
In January 2008, the temperature in parts of Minnesota fell from 46 F degrees to -14 F degrees over a 24 hour period. What was the average temperature change per hour?
Answers
60/24 = 2.5 degree drop per hr...so the average temp change is -2.5 degrees per hr
The average temperature change per hour is -2.5 F per hour.
What is temperature?Temperature is simply an average measure of the kinetic energy for particles of matter.
Here,
at t = 0 hour, Temp. = 46 F
at t = 24 hours, Temp. = -14 F
Now, average temp change per hour = (T₂-T₁)/(t₂-t₁)
= (-14-46)/(24-0)
= -60/24
= -2.5 F per hour
Thus, the average temperature change per hour is -2.5 F per hour.
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A list of elements from which the sample may be drawn is called a
Answers
What is the constant high temperature at which organisms are able to live in thermal vents and volcanoes? A. 250 degrees Celsius B. 250 degrees Fahrenheit C. 250 degrees Kelvin D. 250 degrees Newton
Answers
Answer:
it is actually 250 degrees Fahrenheit
Step-by-step explanation:
Bob's Skate Shop had a profit of $3,563 during the month of August. The company models its profit using P=x^2+10x-12
, where x is the number of skateboards the company sells. How many skateboards did the company sell during the month of August? A. 50 B. 55 C. 60 D. 75
Answers
The company sold 55 skateboards.
A health clinic has 3 1/2 quarts and 1 gallon of antiseptic wash in inventory.How many fluid ounces of antiseptic wash do they have on hand?
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4 quarts make 1 gallon.
Change the mixed unit volume of antiseptic to just one unit. Which you choose is your choice.
((3 1/2) -4)) quarts = ((7/2)+4)) quarts = (7+8/2) quarts = (15/2) quarts
15/2 quarts = 240 fluid ounces
Answer:
240 fluid ounces
Step-by-step explanation:
A health clinic has [tex]3\frac{1}{2}[/tex] quarts and 1 gallon of antiseptic wash in inventory.
We have to convert the unit of fluid in ounces.
1 quart = 32 ounces
1 gallon = 128 ounces
[tex]3\frac{1}{2}[/tex] quarts = [tex]3\frac{1}{2}[/tex] × 32 = 112 ounces
Total fluid of antiseptic wash = 112 + 128 = 240 fluid ounces
They have 240 fluid ounces of antiseptic wash in hand.