Answers
Answers:
\(f(g(x)) = \sqrt[3]{\frac{x+1}{x^3}}\\\\\\g(f(x)) = \frac{\sqrt[3]{x}+1}{x}\)
===============================================
Work Shown:
\(f(x) = \sqrt[3]{x}\\\\\\f(g(x)) = \sqrt[3]{g(x)}\\\\\\f(g(x)) = \sqrt[3]{\frac{x+1}{x^3}}\\\\\\\)
The idea is to replace every x with g(x). Then you'll plug in the definition of g(x).
---------------------------------
Similarly,
\(g(x) = \frac{x+1}{x^3}\\\\\\g(f(x)) = \frac{f(x)+1}{(f(x))^3}\\\\\\g(f(x)) = \frac{\sqrt[3]{x}+1}{(\sqrt[3]{x})^3}\\\\\\g(f(x)) = \frac{\sqrt[3]{x}+1}{x}\\\\\\\)
Related Questions
The map uses a scale of 1 in = 440 ft. On the map, how many inches represent 2 miles
Answers
It is given that
\(1\text{ in = 440 ft}\)To find the number of inches representing 2 miles:
Remember that
\(\begin{gathered} 1\text{ mile = 5280 fe}et\text{ } \\ \therefore \\ 2\text{ miles = 10560 feet} \end{gathered}\)By interpolating,
\(\begin{gathered} \text{If}, \\ 1\text{ inch = 440 fe}et \\ \text{and,} \\ x\text{ inches = 10560 fe}et \end{gathered}\)Then,
\(\begin{gathered} x=\frac{10560\times1}{440} \\ x=24 \end{gathered}\)Therefore, we can conclude that 24 inches will represent 2 miles.
Divide Using Synthetic Division
Answers
The result of the synthetic division is the final row. In this case, the result is -3, 5, -15, 18.
What is polynomial?A polynomial is an expression consisting of variable and coefficient and are used to model real world situation it is an equation of degree greater than one where the exponents of the variables can be any non-negative integer for example the polynomial equation x 2 + 3x + 2 represent a parable of windcraft polynomial are used in name variety of field such as mathematics and physics.
The process of synthetic division is used to divide polynomials of the form ax^n + bx^n-1 + ... + c, where a is the coefficient of the highest power of the variable x.
To divide -3 into the polynomial 1 8 9 -18 0, the following steps should be taken:
Step 1: Line up the divisor, -3, to the left of the polynomial, as shown below:
-3 | 1 8 9 -18 0
Step 2: Bring down the first coefficient in the polynomial, which is 1, and place it directly below the -3.
-3 | 1 8 9 -18 0
-3
Step 3: Multiply the -3 by the first coefficient and place the result in the next row, directly below the 8.
-3 | 1 8 9 -18 0
-3
-3
Step 4: Add the result to the 8, and place the new result in the next row.
-3 | 1 8 9 -18 0
-3
-3
5
Step 5: Repeat steps 3 and 4 for each coefficient in the polynomial.
-3 | 1 8 9 -18 0
-3
-3
5
-15
-15
18
Step 6: The result of the synthetic division is the final row. In this case, the result is -3, 5, -15, 18.
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Complete questions as follows-
Divide Using Synthetic Division
-3|1 8 9 -18 0
Which expression is the exponential form of
Answers
Answer:
\((7x)^{\frac{3}{2} }\)
Find the value of x in each of the following
(please do it step by step and don't spam)
Answers
Answer:
x=120 and x=110 because adjacent angle
Answer:
D= 60 degrees(corresponding angles) Q = 70 degrees (interior angles)
Step-by-step explanation:
For the first one you can find G right away cause they are corresponding angles you know this cause they form an f shape and then after you find G you can find D cause they are corresponding
For the second one you can find V right away cause V and S are corresponding after you find V which is 110 you do interior angles ( Q and V are in a U shape and angles in that shape add upto 180 and are called interior angles) So Since V is 110 , you have to minus 110 degrees from 180 degrees and so Q is equals to 70 degrees
A training field is formed by joining a rectangle and two semicircles, as shown below.
The rectangle is long and wide.
Find the area of the training field. Use the value for , and do not round your answer. Be sure to include the correct unit in your answer.
Answers
Answer:
A training field is formed by joining a rectangle and two semicircles, as shown below. The rectangle is
95m long and
74m wide.
Find the area of the training field. Use the value 3.14 for Pie
for
, and do not round your answer.
Step-by-step explanation:
hope it helps
The height of a regular quadrilateral prism is h = 13 cm, and its lateral area
is AL = 624 cm². Find the following.
1. The surface area of the prism;
2. The volume of the prism.
Answers
The surface area of the prism is 744 cm², the volume of the prism is 624 cm³.
Given:
- Height of the regular quadrilateral prism (h) = 13 cm
- Lateral area of the prism (AL) = 624 cm²
1. Surface Area:
To find the surface area, we need to calculate the area of the two bases and the lateral area of the prism.
The area of each base can be found by dividing the lateral area by the height: A = AL / h = 624 cm² / 13 cm = 48 cm².
Since there are two identical bases, the total base area is 2 times the area of one base, so the total base area is 2 * 48 cm² = 96 cm².
To calculate the surface area, we add the area of the two bases to the lateral area: Surface Area = 2A + AL = 2 * 48 cm² + 624 cm² = 120 cm² + 624 cm² = 744 cm².
Therefore, the surface area of the prism is 744 cm².
2. Volume:
The volume of the prism can be found by multiplying the base area by the height: Volume = A * h = 48 cm² * 13 cm = 624 cm³.
Therefore, the volume of the prism is 624 cm³.
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In the graphic below, one palr of vertical angles is?
Answers
Answer:
1 and 6
Step-by-step explanation:
vertical angles = angles across diagonally which can either be 1 + 6 or 2 + 5, but only 1 + 6 is available
A survey found that women's heights are normally distributed with mean 63.6 in and standard deviation 2.5 in. A branch of the military requires women's heights to be between 58 in and 80 in.
a. Find the percentage of women meeting the height requirement. Are many women being denied the opportunity to join this branch of the military because they are too short or too tall?
b. If this branch of the military changes the height requirements so that all women are eligible except the shortest 1% and the tallest 2%, what are the new height requirements?
Answers
Answer:
(A)
Step-by-step explanation:
The survey follows of women's height a normal distribution.
The height of 98.51% of women that meet the height requirement are between 58 inches and 80 inches.
The new height requirements would be 57.7 to 68.6 inches
The given parameters are:
\mathbf{\mu = 63.5}μ=63.5 --- mean
\mathbf{\sigma = 2.5}σ=2.5 --- standard deviation
(a) Percentage of women between 58 and 80 inches
This means that: x = 58 and x = 80
When x = 58, the z-score is:
\mathbf{z= \frac{x - \mu}{\sigma}}z=
σ
x−μ
This gives
\mathbf{z_1= \frac{58 - 63.5}{2.5}}z
1
=
2.5
58−63.5
\mathbf{z_1= \frac{-5.5}{2.5}}z
1
=
2.5
−5.5
\mathbf{z_1= -2.2}z
1
=−2.2
When x = 80, the z-score is:
\mathbf{z_2= \frac{80 - 63.5}{2.5}}z
2
=
2.5
80−63.5
\mathbf{z_2= \frac{16.5}{2.5}}z
2
=
2.5
16.5
\mathbf{z_2= 6.6}z
2
=6.6
So, the percentage of women is:
\mathbf{p = P(z < z_2) - P(z < z_1)}p=P(z<z
2
)−P(z<z
1
)
Substitute known values
\mathbf{p = P(z < 6.6) - P(z < -2.2)}p=P(z<6.6)−P(z<−2.2)
Using the p-value table, we have:
\mathbf{p = 0.9999982 - 0.0139034}p=0.9999982−0.0139034
\mathbf{p = 0.9860948}p=0.9860948
Express as percentage
\mathbf{p = 0.9860948 \times 100\%}p=0.9860948×100%
\mathbf{p = 98.60948\%}p=98.60948%
Approximate
\mathbf{p = 98.61\%}p=98.61%
This means that:
The height of 98.51% of women that meet the height requirement are between 58 inches and 80 inches.
So, many women (outside this range) would be denied the opportunity, because they are either too short or too tall.
(b) Change of requirement
Shortest = 1%
Tallest = 2%
If the tallest is 2%, then the upper end of the shortest range is 98% (i.e. 100% - 2%).
So, we have:
Shortest = 1% to 98%
This means that:
The p values are: 1% to 98%
Using the z-score table
When p = 1%, z = -2.32635
When p = 98%, z = 2.05375
Next, we calculate the x values from \mathbf{z= \frac{x - \mu}{\sigma}}z=
σ
x−μ
Substitute \mathbf{z = -2.32635}z=−2.32635
\mathbf{-2.32635 = \frac{x - 63.5}{2.5}}−2.32635=
2.5
x−63.5
Multiply through by 2.5
\mathbf{-2.32635 \times 2.5= x - 63.5}−2.32635×2.5=x−63.5
Make x the subject
\mathbf{x = -2.32635 \times 2.5 + 63.5}x=−2.32635×2.5+63.5
\mathbf{x = 57.684125}x=57.684125
Approximate
\mathbf{x = 57.7}x=57.7
Similarly, substitute \mathbf{z = 2.05375}z=2.05375 in \mathbf{z= \frac{x - \mu}{\sigma}}z=
σ
x−μ
\mathbf{2.05375= \frac{x - 63.5}{2.5}}2.05375=
2.5
x−63.5
Multiply through by 2.5
\mathbf{2.05375\times 2.5= x - 63.5}2.05375×2.5=x−63.5
Make x the subject
\mathbf{x= 2.05375\times 2.5 + 63.5}x=2.05375×2.5+63.5
\mathbf{x= 68.634375}x=68.634375
Approximate
\mathbf{x= 68.6}x=68.6
Hence, the new height requirements would be 57.7 to 68.6 inches
Consider the problem of finding the shortest path to a destination city from a start city using roads (e.g., traveling from Arad to Bucharest) using A* search. Which of these heuristics are admissible? There could be multiple such heuristics, select all for full credit. Selecting an inadmissible heuristic has a -50% penalty. Select one or more: I a. Manhattan distance ("go first east/west and then north/south") between a city and start city b. Euclidean distance ("as the crow flies") between a city and destination city c. Twice the Euclidean distance ("as the crow flies") between a city and destination city d. heuristic is o for every city e. heuristic is 1 for every city f. Euclidean distance ("as the crow flies") between a city and start city g. Manhattan distance ("go first east/west and then north/south") between a city and destination city
Answers
Heuristic is 0 for every city Heuristic is 1 for every city Selecting an inadmissible heuristic has a -50% penalty.
To find the shortest path to a destination city from a start city using roads (e.g., traveling from Arad to Bucharest) using A* search, the following heuristics are admissible:
Manhattan distance ("go first east/west and then north/south") between a city and start city.
Euclidean distance ("as the crow flies") between a city and destination city.
Euclidean distance ("as the crow flies") between a city and start city.
Manhattan distance ("go first east/west and then north/south") between a city and destination city.
The following heuristics are inadmissible:
Twice the Euclidean distance ("as the crow flies") between a city and destination city.
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Solve the following system of equations using the elimination method. 6x – 5y = –1 –6x – 4y = 10
Answers
Answer:
x= -1 y= -1
Step-by-step explanation:
Translate this phrase into an algebraic expression,
The sum of 21 and twice Craig's age
Use the variable c to represent Craig's age.
Answers
Answer:
I'm thinking 21 + 2c = I dont really fancy maths but I'm feeling this answer.
Help me pls it would be nice thank youuuuu
Answers
X: -2, -1, 0, 1, 2
Y: -2, 1, 2, 1, -2
Hopefully this is helpful
5. There are two kinds of products (called DA and GA) produced in your company every day. Alsothere are two kinds of materials (denoted by A and B) in need One DA costs one unit of A, one unit of B: one GA costs one unit of A, two units of B. You get $3000 when you sell one DA and $5000 for one GA. The supply of the two materials every day is 12,22. a)What is the maximal profit $ b) How many DA and GA should be produced every day to obtain this maximal profit? Number of DA = Number of GA
Answers
Answer:
a) $56000b) DA = 2, GA = 10Step-by-step explanation:
Given
DA = A + B ⇒ $3000GA = A + 2B ⇒ $5000Number of A = 12Number of B = 22We can see from the equations that
GA - DA = B ⇒ $2000 andA = $1000 and B = $2000 in terms of profitSo greater use of unit B brings greater profit. We don't want any unit is left over, so get this equation.
A + B = 12A + 2B = 22Is the equation set to indicate use of the units A and B
Solving we get
A = 2 and B = 10It this case all the units are used and profit is maximum
2*$3000 + 10*$5000 = $56000Number of DA = 2Number of GA = 10The temperature during a winter day was less than 8 degrees Fahrenheit. Digby wants to write an inequality for the temperature during the winter day. What constant should Digby use in the inequality?
Answers
Since we want the temperature to be less than 8 degrees Fahrenheit, 8 would be the constant that Digby should use in the inequality.
what is inequality ?
An inequality is a mathematical statement that compares two values or expressions using one of the inequality symbols: "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "≠" (not equal to).
To write an inequality for the temperature during a winter day being less than 8 degrees Fahrenheit, we can use the inequality symbol "<" which means "less than."
So, the inequality would be:
Temperature < 8 degrees Fahrenheit
Therefore, Since we want the temperature to be less than 8 degrees Fahrenheit, 8 would be the constant that Digby should use in the inequality.
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Compare using <, >, or =. 7 2/5___ 7 3/8
Answers
Answer:
<
Explanation:
Step 1 - Convert the mixed numbers into decimals
7 2/5
2/5 • 20/20 = 40/ 100
40/ 100 = 0.4
0.4 + 7.0 = 7.4
Therefore, 7 2/5 = 7.4
Step 2 - Convert the mixed numbers into decimals
7 3/8
3/ 8 = 0.375
0.375 + 7.0 = 7.375
Therefore, 7 3/8 = 7.375
Step 3 - Compare
7.4 < 7.375
So, 7 2/5 is less than 7 3/8
In the formula for the area of a circle, what gets multiplied by r?
Answers
Answer:
A. r²
Step-by-step explanation:
The formula for the area of a circle is π r²,
thus the π is multiplied by the r²
(PLEASE ANSWER) Complete the proof that the diagonals of parallelogram ABCD bisect each other.
Answers
The missing statements and reasons in the proof are 5) Δ AEB ≅ Δ CED and Δ AED ≅ Δ CEB, 5) By ASA rule and 6) AE ≅ CE and DE ≅ EB
What is a parallelogram?A parallelogram is a special type of quadrilateral that has both pairs of opposite sides parallel and equal.
Given that, ABCD is a parallelogram, we need to prove that the diagonals of parallelogram ABCD bisect each other.
The proof is as follows,
Statement Reason
1) AB CD and AD BC Given
2) ∠ 1 = ∠ 3 When a transversal crosses
parallel lines, alternate interior
angles are congruent.
3) ∠ 2 = ∠ 4 When a transversal crosses
parallel lines, alternate interior
angles are congruent.
4) AB = CD Opposite sides of a
parallelogram are congruent.
5) Δ AEB ≅ Δ CED
and Δ AED ≅ Δ CEB By ASA rule
6) AE ≅ CE and DE ≅ EB Corresponding parts of
congruent triangles are congruent,
7) Point E bisects both AC and BD Definition of bisector
Hence, proved.
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Hurry - Fill in the blanks
Answers
Answer:
The first value of a relation is an input value and the second value is the output value. A function is a specific type of relation in which each input value has one and only one output value.
An input is an independent value, and the output value is the dependent value, as it depends on the value of the input.
Which vector below goes from (0,0) to (2,2)?
A. c
B. a
C. b
D. d
Answers
Answer:
i say it's A.c
I hope it helped
Fill in the missing terms to complete the factorization. 15x^2 + x - 2 = (? -1) (? + 2)
a- 3x, 5x
b- x, 15x
c- 5x, 3x
d- 15x, x
Answers
The missing term of the factorization equation is A = ( -15x - 1 ) ( x + 2 )
Given data ,
Let the equation be represented as A
Now , the value of A is
A = -15x² - 31x - 2
On simplifying , we get
The expanded form of the expression ( -15x - 1 ) ( x + 2 ) can be calculated using the distributive property of multiplication over addition
So , on factorizing , we get
A = ( -15x - 1 ) ( x + 2 )
Hence , the factorized equation is A = ( -15x - 1 ) ( x + 2 )
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The complete question is attached below :
Fill in the missing terms to complete the factorization. 15x² + x - 2 = (? -1) (? + 2)
a- 3x, 5x
b- x, 15x
c- 5x, 3x
d- 15x, x
The following dataset represents the math test scores for a class of 20 students. 90, 85, 95, 100, 100, 90, 100, 65, 100, 85, 80, 95, 80, 100, 85, 75, 100, 90, 90, 75 Would the mode be a good measure of central tendency for this dataset?
Answers
Answer:
yes
Step-by-step explanation:
The mode is the measure of the central tendency for the given data set. The mode represents the highest frequency of the number
Since in the given data set as we can see that the 100 would be appeared 6 times
So this represent that the mode is 100
So here the mode would be the good measure
Cellular phone usage grew about 22% each year from 1995 (about 34 million) to 2003. Write a function to model cellular phone usage over that time period. What is the cellular usage in 2003?
Answers
Answer:
Given the information you provided, we can model cellular phone usage over time with an exponential growth model. An exponential growth model follows the equation:
`y = a * b^(x - h) + k`
where:
- `y` is the quantity you're interested in (cell phone usage),
- `a` is the initial quantity (34 million in 1995),
- `b` is the growth factor (1.22, representing 22% growth per year),
- `x` is the time (the year),
- `h` is the time at which the initial quantity `a` is given (1995), and
- `k` is the vertical shift of the graph (0 in this case, as we're assuming growth starts from the initial quantity).
So, our specific model becomes:
`y = 34 * 1.22^(x - 1995)`
To find the cellular usage in 2003, we plug 2003 in for x:
`y = 34 * 1.22^(2003 - 1995)`
Calculating this out will give us the cellular usage in 2003.
Let's calculate this:
`y = 34 * 1.22^(2003 - 1995)`
So,
`y = 34 * 1.22^8`
Calculating the above expression gives us:
`y ≈ 97.97` million.
So, the cellular phone usage in 2003, according to this model, is approximately 98 million.
6.SP.2 Understand that a set of data collected to answer a statistical question has a distribution which can be described by its
center, spread, and overall shape.
6.SP.3 Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a
measure of variation describes how its values vary with a single number.
6.SP.4 Display numerical data in plots on a number line, including dot plots, histograms, and box plots.
TASK: You are an employee at a small company. In this company, there are 10 employees who make
$15,000/yr, one manager who makes $100,000/yr, and one CEO who makes $2,000,000/yr. An
employee complained about the salaries to the Department of Labor and the company was brought
under investigation. The CEO responded to the Department of Labor saying:
"The average salary in my company is $187,500. There is no need for concern."
The Data
Employee 2
Employee 3
Employee 4
Employee 5
Employee 6
Employee 1
$15,000
$15,000
$15,000
$15,000
$15,000
$15,000
Employee 7
Employee 8
Employee 9
Employee 10
Manager
CEO
$15,000
$15,000
$15,000
$15,000
$100,000
$2,000,000
Day 1
I.
Which measure of central tendency did the CEO use to describe his company's salaries? (Mean,
Median, Mode)
Was the CEO telling the truth? Explain.
Was the CEO's response a fair description of what is happening in the company?
II.
II.
Answers
If you didn’t know my brush the pool
Compute the height (in meters) of a cylinder with a radius of 2m and
volume 138 cubic meters. Round to the nearest meter.
Answers
Answer: 10.98 meters
Step-by-step explanation:
pick out the odd one from 1050,510,240,105,37.5
Answers
Answer:
37.5
Step-by-step explanation:
WHY???
All others have numbers that add up to 6 (1+0+5+0)
It is a decimal
All others can be divided by 5
All others are at least 3 digits
All others don't contain a seven or a three
Step-by-step explanation:
37.5
is the odd one. I hope it's correct. seriously, j I hope so
Hi! I just need somebody to explain how this is done.
I don’t understand the process of this well and I cant find many videos that explain it. thanks!
Answers
Answer:
Exact form: x = \(\frac{10.8}{sin(57)}\)
Rounded to the Nearest Tenth: x = 12.9
Step-by-step explanation:
In the right-angled triangle, we can use the trigonometry functions to find the length of a side or a measure of an angle
In the given figure
∵ ∠C is the right angle
∴ ΔACB is a right triangle
∵ m∠B = 57°
∵ AC = 10.8
∵ AC is the opposite side of ∠B
∵ AB is opposite to the right angle
∴ AB is the hypotenuse
∵ AB = x
→ We can use the function sine to find x
∵ sin∠B = \(\frac{opposite}{hypotenuse}\)
∴ sin∠B = \(\frac{AC}{AB}\)
→ Substitute the values of ∠B, AC, and AB in the rule of sine above
∴ sin(57°) = \(\frac{10.8}{x}\)
→ By using cross multiplication
∵ x × sin(57°) = 10.8
→ Divide both sides by sin(57°)
∴ x = \(\frac{10.8}{sin(57)}\)
∴ x = 12.87752356
→ Round your answer to the nearest tenth
∴ x = 12.9
Exact form: x = \(\frac{10.8}{sin(57)}\)
Rounded to the Nearest Tenth: x = 12.9
Please do 3 hurry!!!!
Answers
Here is the answer above. Click to view
4. Find the slope and y-intercept of the line 5x – 8y = -20.
Answers
Answer:
Slope is 5/8.
y-intercept is (0, 5/2)
Step-by-step explanation:
Answer:
this is what u need to do
Step-by-step explanation:
first you need to put it into this
\(y=mx+b\)
so this is what is next
\(y=-8(5x)-20\)
\(y=5x+12\)
you decide to go to a star gazing event there are 12 people in the group
Answers
Answer:
whts the question??
Step-by-step explanation:
HELPPPPPP ME PLEASEEEEE!!
Answers
Answer:
Step-by-step explanation:
The quadratic formula is y=ax^2+bx+c
If we move everything to the left side of the equation,
-6x^2=-9x+7 becomes
-6x^2+9x-7=0
a=-6, b=9, c=-7, so the third answer choice