The value of g(x) is (x^3+5) and g(64) = 262149.
According to the statement
we have given that the
f(x)=√x^3 and (fog)(x)=√(x^3+5) and we have to find the value of the g(64).
So, For find the value of g(64), Firstly we have to find the g(x).
So,
We given that
f(x)=√x^3 and (fog)(x)=√(x^3+5)
And here the formula used is
(f o g)(x) = f (g(x))
here (fog)(x)=√(x^3+5) and f(x)=√x^3
From this we get g(x) is (x^3+5)
So,
g(x) = (x^3+5) and
g(64) = ((64)^3+5)
g(64) = 262149.
So, The value of g(x) is (x^3+5) and g(64) = 262149.
Disclaimer: This question was incomplete. Please find the full content below.
Question:
If f(x)=√x^3 and (fog)(x)=√(x^3+5). Then find the value of g(64).
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I take this to mean [tex]f(x) = \sqrt{x^3}[/tex] and [tex](f\circ g)(x) = \sqrt x[/tex].
Let's first find the inverse of [tex]f[/tex].
[tex]f\left(f^{-1}(x)\right) = \sqrt{\left(f^{-1}(x)\right)^3} = x \\\\ \implies \left(f^{-1}(x)\right)^3 = x^2 \\\\ \implies f^{-1}(x) = x^{2/3}[/tex]
(Note that [tex]f[/tex] is defined only if [tex]x^3\ge0[/tex], or [tex]x\ge0[/tex].)
Apply the inverse of [tex]f[/tex] to [tex]f\circ g[/tex].
[tex](f\circ g)(x) = f(g(x)) = \sqrt x \\\\ \implies f^{-1}\left(f(g(x))\right) = f^{-1}(\sqrt x) \\\\ \implies g(x) = \left(\sqrt x\right)^{2/3} = \left(x^{1/2}\right)^{2/3} = x^{1/3} = \sqrt[3]{x}[/tex]
Then
[tex]g(64) = \sqrt[3]{64} = \sqrt[3]{4^3} = \boxed{4}[/tex]
Find an equation of a degree 3 polynomial (in factored form) with the given zeros of f(x): − 3 , 4 , − 3 . Assume the leading coefficient is 1.
f(x) = x³ + 2x² - 15x - 36 is the equation of a degree 3 polynomial (in factored form) with the given zeros of f(x) are − 3 , 4 , − 3 assuming that the leading coefficient is 1. This can be obtained by formula of polynomial function.
Find the required equation:The zeroes or roots of a polynomial function are x values for which f(x) = 0If the zeroes or roots are r₁, r₂, r₃,... then possible polynomial function is⇒ f(x) = a(x - r₁)(x - r₂)(x - r₃)
where a is the leading coefficient
Here in the question it is given that,
Polynomial should be with degree 3zeros of f(x) are − 3 , 4 , − 3By using the formula of polynomial function we get,
⇒ f(x) = a(x - r₁)(x - r₂)(x - r₃)
⇒ f(x) = 1(x - (-3))(x - (4))(x - (-3))
⇒ f(x) = 1(x + 3)(x - 4)(x + 3)
⇒ f(x) = (x + 3)(x² - x - 12)
⇒ f(x) = x³ - x² - 12x + 3x² - 3x - 36
⇒ f(x) = x³ + 2x² - 15x - 36
Hence f(x) = x³ + 2x² - 15x - 36 is the equation of a degree 3 polynomial (in factored form) with the given zeros of f(x): − 3 , 4 , − 3 assuming that the leading coefficient is 1.
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Which of the following represents
the graph of this equation?
y = 1/2|x|
The graph is shown in the attached image.
A projector enlarges an image in the ratio 20:1. What will be the size of an enlargement of a picture that is 8cm by 6cm?
Answer:
160 cm × 120 cm
Step-by-step explanation:
this means 1 cm turns into 20 cm.
so, 8 cm × 6 cm becomes
8×20 = 160 cm × 6×20 = 120 cm
Claire buys a condo for $350,000. The value of the condo appreciates on average 5% per year where she
bought the condo
If you know the rest of the problems on the page then that would help;)
1. The best way that we can represent the condo that Claire bought is by option B. [tex]350000(1.05)^{t}[/tex]
How to determine the functionTo determine the function, we would have to do so by making use of the given equation that we have here.
This is given as
Ct = [tex]A(1+r)^t[/tex]
Where a is the principal
r is the rate of interest and
t is the time
2. we have 70 = 30(1.03)^t
70/30 = (1.03)^t
We have to take the log of the function above in order to find the value of t
t = 28.665
This is approximated to 29
Hence the answer here is option A after 29 weeks.
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2x² + 5x +2can you please give me the answer of 2x + 5 x + 2
Answer:
you better give me brainliest
Step-by-step explanation:
2x +5x+2 = 7x+2
Three students, Alicia, Benjamin, and Caleb, are constructing a square inscribed in a circle with center at point C. Alicia draws two diameters and connects the points where the diameters intersect the circle, in order, around the circle. Benjamin tells Alicia that she was not being very accurate. He says that the diameters must be perpendicular to each other. Then she can connect the points, in order, around the circle. Caleb tells Alicia and Benjamin that he doesn't need to draw the second diameter. He says that because a triangle inscribed in a semicircle is a right triangle, he will simply draw two such triangles, one in each semicircle. Together the two triangles will make a square. Who is correct?
Benjamin is correct about the diameter being perpendicular to each other and the points connected around the circle.
Inscribing a square
The steps involved in inscribing a square in a circle include;
A diameter of the circle is drawn.A perpendicular bisector of the diameter is drawn using the method described as the perpendicular of the line sector. Also known as the diameter of the circle.The resulting four points on the circle are the vertices of the inscribed square.Alicia deductions were;
Draws two diameters and connects the points where the diameters intersect the circle, in order, around the circle
Benjamin's deductions;
The diameters must be perpendicular to each other. Then connect the points, in order, around the circle
Caleb's deduction;
No need to draw the second diameter. A triangle when inscribed in a semicircle is a right triangle, forms semicircles, one in each semicircle. Together the two triangles will make a square.
It can be concluded from their different postulations that Benjamin is correct because the diameter must be perpendicular to each other and the points connected around the circle to form a square.
Thus, Benjamin is correct about the diameter being perpendicular to each other and the points connected around the circle.
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he value of x?
ur answer in the box. need answer quickly! 35 points!
Answer:
x = 46 degrees
Step-by-step explanation:
180 - 134 = 46
Answer:
46°
Step-by-step explanation:
134 + x add to a straight line angle = 180
134+x = 180
x = 46
cual es el valor de 15+b=23
divide the difference of 20 and 6 by the product of 7 and 2
Step-by-step explanation:
Vocabulary (what the words mean):Divide, the same as ÷
divide 6 by 3
by is the same as the symbol
6 ÷ 3 = 2
Difference, This is another way of saying take away or minus
the difference of 6 and 3 is
6 - 3 = 3
Product, This is another word for multiply or times
the product of 2 and 3 is
2 × 3 = 6
Write as an equationdivide (÷) the difference of 20 and 6 (20 - 6) by the product of 7 and 2 (7 × 2)
so
(20 - 6) ÷ (7 × 2)
can you do the rest???
f(x)=2x-6 Match each transformation of f(x) with its description
The transformation of the function is illustrated below
How to match the transformation?Parent function is: f(x) = 2x - 6
Transformations are:
shifts f(x) 4 units down
f(x) → f(x) - 4 ⇒ g(x)= 2x - 6 - 4 = 2x - 10
stretches f(x) by a factor of 4 away from the x-axis
f(x) → 4*f(x) ⇒ g(x) = 4(2x - 6) = 8x - 24
shifts f(x) 4 units right
f(x) → f(x - 4) ⇒ g(x) = 2(x - 4) - 6 = 2x - 14
compresses f(x) by a factor of toward the y-axis (must be 4)
f(x) → f(4x) ⇒ g(x) = 2*4x - 6 = 8x - 6
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Please help pls help mEE THIS IS REALLY CONFUSING MARKING BRAINlIST AND GIvinG 50 POINTS IF CORRECT!!
The ratio of the number of cupcakes to the number of pastries in a box is 7:2. Which table shows the possible amounts of cupcakes and pastries in a box, given the ratio?
Last box
If you found this useful, please mark it as the BRAINLIEST.XDHave a nice day ツAs it's 7:2
The variation is directDifference between x and y must increase in big number as x and y increases
Option D is correct in that manner
Let's double check
7:214:428:856:16during one semester, the time elaine spent doing homework or participating in extracurricular activities was 20 percent less than the time she spent attending class. if she spend a total of 981 hours attending class, doing homework, or participating in extracurricular activities, how many hours did she spend attending class?
Answer:
963 hours
Step-by-step explanation:
I subtracted 20 from the 981
The correct answer for the hours elaine spend attending classes is [tex]817.5[/tex] hours.
Given,
The time spent doing homework was 20% less than the time she spent attending class.
Assume the time Elaine spent attending class is "x" hours.
So, the time spent on these activities is 0.2 * x hours.
Now, the total time spent attending class, doing homework, or in extracurricular activities is 981 hours.
The equation representing the total time is:
[tex]x + 0.2x = 981[/tex]
solve for "x":
[tex]1.2x = 981[/tex]
[tex]x= \dfrac{981}{1.2}[/tex]
[tex]x= 817.5[/tex]
Elaine spent approximately [tex]817.5[/tex] hours attending class.
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Captain's Autos sells 22 used cars on
Monday, and 18 cars on Tuesday. This was
25% of the number of sales for the week.
How many cars did they sell altogether that
week?
Answer:
160
Step-by-step explanation:
22+18=40, and this was 25% of the cars.
So, 40(4)=160 cars were sold that week.
The number of cars Captain's Autos sold in total that week is 160.
What is the unitary method?
The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. Unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit. It is a method that we use for most of the calculations in math.
We are given that;
Number of used car on monday= 22
Number of cars on tuesday= 18
Now,
Let's call the total number of cars sold during the week "x".
We know that the number of cars sold on Monday and Tuesday is 25% of the total number of cars sold during the week. So we can write:
22 + 18 = 0.25x
Simplifying, we get:
40 = 0.25x
Dividing both sides by 0.25, we get:
x = 160
Therefore, by the unitary method the answer will be 160.
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Research suggests that students could benefit from later school starting times. A school administrative team is considering a proposal to move the starting time of the local schools one hour later than the current start time. To measure interest in the proposal, members of the team randomly select subjects attending a large high school soccer tournament played on the high school grounds on a Saturday morning. The team finds that 58% of those surveyed support a later high school start time. Which type of bias is most likely to be present in the survey results?
This is undercoverage bias because adults with older children are more likely to be included in the sample.
This is question wording bias because the phrasing of the later start times question may be confusing to some subjects.
This is nonresponse bias because some of those selected may choose to not provide their opinion on later start times.
This is voluntary response bias because vocal supporters of later start times will be more likely to offer their opinion.
The type of bias which is most likely to be present in the survey results is undercoverage bias because adults with older children are more likely to be included in the sample.
ResearchThis is a diligent inquiry or examination to seek or revise facts, principles, theories,or applications. It is used to make an extensive investigation or search for truth in an experiment.
Bias
In statistics, bias is the difference between the expectation of the sample estimator and the true population value, which reduces the representativeness of the estimator by systematically distorting it
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What operation is being done to the variable in the equation -5m = -40?
Answer:
m=8
Step-by-step explanation:
-5m=-40
divide both side by -5
-5m=-40
-5=-5 answer is m=8
QUESTION 29
Two variables x and y, assume the values x₁= 2, X2 = -8, X3= 4 X4=1 and y₁
=-3 y2 =-8 y3 = 10 y4=6 Calculate x
OA. -1
OB. -4
OC.-7
OD. -9
The sum of the set of x - values given to us is calculated as; ∑X = -1
How to find the the sum of a set of data?We are given;
X1 = 2, X2 = -8, X3 = 4, X4 = -8 and Y1 = -3, Y2 = -8, Y3 = 10, Y4 = 6
1) ∑X = X1 + X2 + X3 + X4
∑X = 2 + (-8) + 4 + 1 = -1
2) ∑Y = Y1 + Y2 + Y3 + Y4
∑Y = 3 + (-8) + 10 + 6
∑Y = -11
3) ∑ X² = X₁² + X₂² + X₃² + X₄²
∑X² = (2)² + (-8)² + (4)² + (1)²
∑X² = 85
4) ∑Y² = Y₁² + Y₂² + Y₃² + Y₄²
∑X² = (-3)² + (-8)² + (10)² + (6)²
∑X² = 209
Complete question is;
Two variables, X and Y assume the values X1 = 2, X2 = -5, X3 = 4, X4 = 1 and Y1 = -3, Y2 = -8, Y3 = 10, Y4 = 6, respectively. Calculate (a) ∑X, (b) ∑ Y, (c) ∑ X² (d) ∑ Y²
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If R={(1,2),(2,3),(3,9),(4,5)} find R-1
Answer:
R-1={(2,1),(3,2),(9,3),(5,4)
Step-by-step explanation:
R-1={(2,1),(3,2),(9,3),(5,4) because (- 1) means reverse in relation
How do you get the statistical notation?
The new curriculum significantly affects the earning potential.
According to the question, Eight kids were chosen at random to take part in a brand-new educational program that emphasizes both academics and mental health education between middle school and high school. The average annual income is $29432. The standard deviation is unknown.
The probability level is given to be 5%.
When the p-value is less than or equal to your significance level, reject the null hypothesis. The alternative theory, which contends that the effect is widespread, is supported by your sample data.
A probability level of 0.05 means that the new curriculum significantly affects the earning potential.
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Which expression is equivalent to (27.3 5.9)47
O 211.3-1.95
O228-(-3) 20.94
O 27.3-5.04
O228-3-20.94
The correct answer is Option 4.
Calculate the volume of a sphere that has a diameter of 7 meters.
Answer:
1436.76
Step-by-step explanation:
use the formula 4piR^3 to solveAnswer:
538.57 m³
Step-by-step explanation:
The formula to find the volume of a sphere is:
V = 4 π r³
Given that,
diameter ⇒ 7 m
∴ radius = d / 2
radius ( r ) = 7 / 2 = 3.5 m
Let us find the volume now.
V = 4 π r³
V = 4 π × ( 3.5 )³
V = 4 π × ( 3.5 )³
V = 4 π × 42.875
V = 4 π × 42.88
V = 12.56 × 42.88
V = 538.57 m³
A chemical company makes two brands of antifreeze. The first brand is 20% pure antifreeze, and the second brand is 45% pure antifreeze. In order to obtain 150 gallons of a mixture that contains 35% pure antifreeze, how many gallons of each brand of antifreeze must be used?
The gallons of the first brand of antifreeze should be 60 gallons.
The gallons of the second brand of antifreeze should be 90 gallons.
What are the linear equations that represent the question?0.2f + 0.45s = 52.50 (0.35 x 150) equation 1
f + s = 150 equation 2
Where:
f = gallons of the first antifreezes = gallons of the second antifreezehow many gallons of each brand of antifreeze must be used?
Multiply equation 2 by 0.2
0.2f + 0.2s = 30 equation 3
Subtract equation 3 from equation 2
0.25s = 22.50
s = 22.50 / 0.25
s = 90
f = 150 - 90 = 60 gallons
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Ms. Oshiro teaches her 27 students to make folded-paper birds. Each student can make about 2 birds in 1 minute. About how many birds can all the students make in 55 minutes? A 3,000 B 1,500 C 100 D 60
Answer:
The answer is 2970
Step-by-step explanation:
Collectively, all the students can make about 54 books rds per minute (27 * 2)
Therefore in 55 minutes there should be 2970
(54*55) :)
Hi! i really need help on this question tell me if u think u know TYSSSM!!!
pila the woodpecker can drill a small hole in a tree trunk with 25 pecks, which is only 1/4% the average number of pecks that she can make each day. How many times per day can pila peck a tree?
well, we know that 25 pecks is 1/4% or namely 0.25%, less than 1%, and let's say the amount of pecks per day will be "x", which is 100% of that.
[tex]\begin{array}{ccll} pecks&\%\\ \cline{1-2} 25 & \frac{1}{4}\\[1em] x& 100 \end{array} \implies \cfrac{25}{x}~~=~~\cfrac{ ~~ \frac{1}{4} ~~ }{100}\implies 2500=x\cfrac{1}{4} \\\\\\ 2500=\cfrac{x}{4}\implies 10000=x[/tex]
Pila can peck a tree approximately 10,000 times per day.
Given that Pila can drill a small hole in a tree trunk with 25 pecks, which is only 1/4 % the average number of pecks that she can make each day.
We need to determine how many times per day can pila peck a tree.
Let's denote the average number of pecks Pila can make in a day as "x."
According to the information given, Pila can drill a small hole in a tree trunk with 25 pecks, which is only 1/4% (0.25%) of the average number of pecks she can make each day.
We can set up the following equation to represent the relationship:
0.25% of x = 25
To solve for x, we first convert 0.25% to decimal form by dividing by 100:
0.25% = 0.25/100 = 0.0025
Now, we can rewrite the equation:
0.0025x = 25
To isolate x, we divide both sides of the equation by 0.0025:
x = 25 / 0.0025
Simplifying the right side gives us:
x = 10,000
Therefore, Pila can peck a tree approximately 10,000 times per day.
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Which of the following number 1001,1002,1004 will be the sum of 994 and a 2 digit number
The number that will be the sum of 994 and a 2 digit number is 1004 (option 3). Details about digits of numbers can be found below.
What is a 2-digit number?A digit is the whole numbers from 0 to 9 and the arabic numerals representing them, which are combined to represent base-ten numbers.
A 2-digit number is any number between 10 and 99.
According to this question, 994 is said to be added to a 2 digit number to result into either 1001, 1002 or 1004.
1001 - 994 = 7 (1 digit)1002 - 994 = 8 (1 digit)1004 - 994 = 10 (2 digit)Therefore, the number that will be the sum of 994 and a 2 digit number is 1004.
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What are the intercept of 2X+3y= 6z=30
Answers:
A (15,0,0) ,(0,27,0) ,(0,0,-5)
B (15,0,0),(0,10,0) ,(0,0,5)
C (10,0,0),(0,15,0,)(0,0,5)
D (15,0,0),(0,10,0),(0,0,-5)
The intercepts of the given equations is as given in the task content is; Choice B; (15,0,0),(0,10,0) ,(0,0,5).
What are the intercepts of the equation as give in the task content?The x-intercept of the given equation can be determined by setting values of y and z to zero.
The y-intercept can be determined by setting x and z to zero.
While the z-intercept can be determined by setting x and y to zero.
Consequently, the X-intercept of the given equations is; 2x +3(0) = 30; x = 15.
Therefore, we have; (15,0,0)
The y-intercept is therefore; 2(0) +3y = 30; 3y = 30; y = 30/3 = 10 and. we have; (0,15,0)
And hence, the z-intercept is; z = 30/6 = 5.
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In a recent year, 28.7% of all registered doctors were female. If there were 52,900 female registered doctors that year, what was the total number of registered doctors?
Step-by-step explanation:
(52900 ÷ 28.7) × 100 = 184320 ( rounded to nearest whole number, since you cannot have half humans)
what is the value of x when the richter scale rating scale is 8.4?
The value of x when the richter scale rating scale is 8.4 is 251188643.151
What is a richter scale?A richter scale is a numerical scale that is used for expressing the magnitude of an earthquake in a geographical area
How the richter scale works?The richter scale takes the amplitude of the earthquake's largest seismic as an input and calculate (and display) the magnitude of an earthquake in the geographical area using a logarithmic function
How to determine the value of x?The formula of a richter scale is expressed as:
log(x) = n
Where n represents the scale rating of the scale
In this case, n = 8.4.
So, we have:
log(x) = 8.4
Express as an exponent
x = 10^8.4
Evaluate the exponent
x = 251188643.151
Hence, the value of x when the richter scale rating scale is 8.4 is 251188643.151
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Please solve this question step by step explanation
The value of ∠B is 60 degrees
How to solve for B?The given parameters are
2∠A = 3∠B = 6∠C
Let the angles in a triangle ABC be ∠A, ∠B and ∠C.
The sum of these angles in the triangle ABC is
∠A + ∠B + ∠C = 180
Multiply the above equation by 2
2 * (∠A + ∠B + ∠C) = 2 * 180
Evaluate the product
2∠A + 2∠B + 2∠C = 360
Recall that 2∠A = 3∠B.
Substitute the above in the equation 2∠A + 2∠B + 2∠C = 360
3∠B + 2∠B + 2∠C = 360
This gives
5∠B + 2∠C = 360
Multiply the above equation by 3
3 * (5∠B + 2∠C) = 3 * 360
Evaluate the product
15∠B + 6∠C = 1080
Recall that 3∠B = 6∠C.
Substitute the above in the equation
So, we have:
15∠B + 3∠B = 1080
Evaluate the like terms
18∠B = 1080
Divide both sides by 18
∠B = 60
Hence, the value of ∠B is 60 degrees
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En la siguiente sucesión numérica 8,7,11,10,14 los dos números siguientes son
To find the missing numbers in the sequence, we must identify the rule by which they change.
The sequence starts at 8 and then decreases by 1, therefore, the second term is 7. The third term increases by 4 units with respect to the second, going from 7 to 11, and the fourth decreases again by 1, now remaining at 10.
The fifth term increases again by 4 units, from 10 to 14. This already gives us a clear idea of the rule that the sequence follows.
Decrease 1, increase 4, decrease 1, increase 4,…₊₄ ₊₄
8 , 7, 11, 10, 14,...,⁻¹ ⁻¹ ⁻¹
In this way, the sixth element must decrease by 1, that is 13 and the seventh must increase by 4, that is 17.
8, 7, 11, 10, 14, 13, 17,…
The next numbers that the numerical sequence are 13 and 17, to complete. ✅
Write your answer as a fraction in simplest form.
-1 3/4 • 2 1/8