Answer:
D) \(\frac{1}{6}\)
g¹(1) = \(\frac{1}{6}\)
The inverse of the function \(g(x) = \frac{x^{\frac{1}{3} }-1 }{2}\)
Step-by-step explanation:
Step(i):-
Given that f(x) = (2x+1)³
Let y = (2x+1)³
\(y^{\frac{1}{3} } =2x+1\)
\(2x = y^{\frac{1}{3} } -1\)
\(x = \frac{y^{\frac{1}{3} }-1 }{2}\)
Step(ii):-
y = f(x) ⇒ x = f⁻¹ (y)
⇒ \(f^{-1} (y) = \frac{y^{\frac{1}{3} }-1 }{2}\)
\(f^{-1} (x) = \frac{x^{\frac{1}{3} }-1 }{2}\)
The inverse of the given function
\(g(x) = \frac{x^{\frac{1}{3} }-1 }{2}\)
Differentiating equation (i) with respective to 'x', we get
\(g^{l} (x) = \frac{1}{2} X \frac{1}{3} x^{\frac{1}{3} -1}\)
\(g^{l} (x) = \frac{1}{6} x^{\frac{-2}{3} }\)
Final answer:-
Put x=1
\(g^{l} (1) = \frac{1}{6} 1^{\frac{-2}{3} } = \frac{1}{6}\)
Chris bought c tickets to a movie for $8 each. Michele bought m tickets to a movie for $8 each. Which expression can be used to find the total amount Chris and Michele spent for these tickets?
Answer:
8c+8m
Step-by-step explanation:
c tickets are $8 a piece and m tickets are also $8 a piece. as an expression, the equation is not completed and cannot be completed until we know the value of the missing variables. to find the total, you must add the total amount of tickets Chris bought for 8 dollars and add that to the total of tickets Michele bought for 8 dollars
help because i need to learn this
Perimeter of square = 4× side
=> 36cm = 4 × side
=> side = 9cm
Now area of a suqare:
= side × side
= 9× 9
=81 cm2
ach ant has 6 legs. How many legs do 3 ants have?
Ants 1 2 3
Legs 6 ?
Answer:
Step-by-step explanation:
the answer is 18 I think?
Answer:
18
Step-by-step explanation:
6 (legs) x 3 (ants) = 18 legs
It can also be represented as 6+6+6 (18)
hope this helps :)
Please help geometry question Pythagorean theorem
Therefore , the solution of the given problem of triangle comes out to be L = 3(√(h²) + ((w/2²))) + 3h .
What is a triangle exactly?A triangular is a polygon because it has 2 different or more additional parts. It has a straightforward rectangle form. Only the sides A, B, and C can differentiate a triangle from a parallelogram. When the sides are not exactly collinear, Euclidean geometry results in a singular surface rather than a cube. If a shape has three edges and three angles, it is said to be triangular.
Here,
Given the height and breadth of the top of the frame, we can use the Pythagorean theorem to determine the length of each side of the triangle.
Let's assume the height is h feet and the width of the top of the frame is w feet. The triangle's side lengths can then be calculated as follows:
=> s =√((h²) + ((w/2)²))
We must add up the lengths of all the pipe segments that will be used to build the frame in order to determine the total quantity of steel pipe required.
The following formula can be used to determine how much steel tubing is required:
=> L = 3s + 3h
where h is the height of the frame and s is the length of each edge of the triangle.
Using the method instead of s, we obtain:
=> L = 3(√(h²) + ((w/2²))) + 3h
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Select the correct answer. Which function represents the inverse function of the function f(x)=x^2 +5
Answer:
f^(-1)(x) = ±√(x - 5).
Step-by-step explanation:
Replace f(x) with y: y = x^2 + 5.
Swap the x and y variables: x = y^2 + 5.
Solve the equation for y. To do this, we'll rearrange the equation:
x - 5 = y^2.
Take the square root of both sides (considering both positive and negative square roots):
±√(x - 5) = y.
Swap y and x again to express the inverse function:
f^(-1)(x) = ±√(x - 5).
-3x+2y=4
5x-3y= 1
X=
Y=
Answer: For the problem \(-3x+2y=4\), the answer is (look below)
X= \(-\frac{4}{3} +\frac{2y}{3}\)
Y= \(2+\frac{3x}{2}\)
Add \(3x\) to both sides of the equation. 2y = 4 + 3x
Divide each term in 2y = 4 + 3x by 2 and simplify.
For the problem \(5x-3y=1\), the answer is look below)
X= \(\frac{1}{5} +\frac{3y}{5}\)
Y= \(-\frac{1}{3} +\frac{5x}{3}\)
Step-by-step explanation:
Move all terms that don't contain x to the right side and solve.
Move all terms that don't contain y to the right side and solve.
S7. What is the Least Common Multiple for 12 and 30?
A 6
B. 12
C. 30
D. 60
Answer:
D
Step-by-step explanation:
Answer:
D. 60
Step-by-step explanation:
(12 * 30) / 6
360 / 6 = 60
Is a parallelogram but not a rectangle
Answer:
A square
Step-by-step explanation:
A square meets the requirements of a parallelogram.
6 minus twice a number
Answer:
6-2x
Step-by-step explanation:
Mrs. Moss has five and one fourths pounds of dry dog food she will put an equal amount of food into 3 containers. How much dog food will be in each container?
Answer:
1 3/4 pounds of food per serving
is y=-5/9x proportional
Answer:
No
Step-by-step explanation:
I don't think it is proportional
Here it is not proportional.
What is proportional?
Proportional relationships are relationships between two variables where their ratios are equivalent.
Another way to think about them is that, in a proportional relationship, one variable is always a constant value time the other.
Here given that,
\(y=-\frac{5}{9x}\)
Here it is not proportional.
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Solve the following system of equations with the substitution method:
y=3/5x-15
y=-3/4x+12
Answer:
x = 20, y = -3
Step-by-step explanation:
Set both equations equal to each other
\(\displaystyle y=\frac{3}{5}x-15\\\\y=-\frac{3}{4}x+12\\\\\\\\\frac{3}{5}x-15=-\frac{3}{4}x+12\\\\\frac{12}{20}x-15=-\frac{15}{20}x+12\\\\\frac{27}{20}x-15=12\\\\\frac{27}{20}x=27\\\\x=20\\\\y=\frac{3}{5}x-15\\\\y=\frac{3}{5}(20)-15\\\\y=\frac{60}{5}-15\\\\y=12-15\\\\y=-3\)
Sully is having a party and wants to fill his swimming pool. If he only uses his hose, it takes 3 hours more than if he only uses his neighbor's hose. If he uses both hoses together, the pool fills in 5 hours. How long does it take for each hose to fill the pool (in hr)?
Answer:
It takes the neighor's hose 3 hours to fill the pool and it takes Sully's hose 6 hours to fill the pool if each filled alone.
Step-by-step explanation:
This is a work problem, and the way these are done is to figure the amount that each can do based on how much can get done in a single hour.
First thing, in order to have only one variable, we have to put one hose in terms of the other hose.
We know that it takes the neighbor's hose a certain amount of time (there's our unknown) to fill the pool and that it takes Sully's hose that same time plus 3 hours.
neighbor's hose can get the job done in x time
Sully's hose can get the job done in x + 3 time
Now we will figure out how much each can do in a single hour.
If the neighbor's hose takes x hours to fill the pool, then it can get
of the pool filled in 1 hour.
If Sully's hose takes x + 3 hours to fill the pool, then it can get
of the pool filled in 1 hour.
The sum of these takes 2 hours total and 1/2 of the pool gets filled in 1 hour.
Our equation then is:
This equation states in words:
"the amount of the pool that the neighbor's hose can fill in an hour plus the amount of the pool that Sully's hose can fill in an hour will fill half the pool".
Solving for x will give us that time.
Begin to solve this by finding the LCM of those denominators and getting rid of the fractions by reducing. The LCM will be 2x(x + 3). Multiplying each term by that LCD looks like this:
In the first term the x's cancel out, in the second term the (x + 3) cancels out, and in the last term the 2's cancel out leaving us with:
and simplifying gives us:
This is a quadratic that will have to be factored to solve for those values of x. Combine like terms and get everything on one side to get:
Factor this however you find easiest to get the values:
x = 3 hours and x = -2 hours
We all know that the 2 things in math that will never EVER be negative are times and distances/measures, so we can disregard the -2 and say that
x = 3 hours.
To answer our question, then;
It takes the neighbor's hose 3 hours to fill the pool; it takes Sully's hose 3+3 hours = 6 hours to fill the pool.
during a single day at radio station WMZH,the probability that a particular song is played in 3/8.what is the probability that this thing will be played on exactly 2 days out of 3 days ?round to your nearest thousandth
The probability that the song will be played on exactly 2 days out of 5 days is approximately 0.164.
To find the probability that a particular song is played exactly 2 days out of 5 days at radio station WMZH, we can use the binomial probability formula.
The binomial probability formula is given by P(x) = C(n, x) * p^x * (1-p)^(n-x), where P(x) is the probability of x successful outcomes, n is the number of trials, p is the probability of a successful outcome on a single trial, and C(n, x) represents the binomial coefficient, which is the number of ways to choose x items from a set of n items.
In this case, we want to find the probability of the song being played exactly 2 days out of 5 days, so x = 2, n = 5, and p = 3/8.
Using the formula, we have:
P(2) = \(C(5, 2) * (3/8)^2 * (1 - 3/8)^(^5^-^2^)\)
C(5, 2) = 5! / (2! * (5-2)!) = 10
P(2) = 10 * (3/8)^2 * (5/8)^3
P(2) ≈ 0.164 (rounded to three decimal places)
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What is 1 + 1 and explain why using irrational numbers
Answer: 1+1 = Dr. Phill
Step-by-step explanation:
Dr. Phill is the answer for everything, you see, his phillyness is underrated. he has magical wiggly fingers that shine in the sun. he can summon the enderdragon but as a gay drag queen.
therefore, magical wizard, dr. philly pill.
Dan Invests £2500 into his bank account. He receives 5% per year simple interest. How much will Dan have after 2 years? Give your answer to the nearest penny where appropriate.
Please help me give me the answer:
Explanation:
Answer:
Sure, I'd be happy to help you with that!
To calculate Dan's earnings with simple interest, we can use the following formula:
I = P * r * t
where:
I = interest earned
P = principal amount (initial investment)
r = interest rate (as a decimal)
t = time period (in years)
We know that Dan invests £2500 and receives 5% simple interest per year, so:
P = £2500
r = 0.05
t = 2 years
Plugging these values into the formula, we get:
I = £2500 * 0.05 * 2
I = £250
This means that Dan will earn £250 in interest over the 2-year period.
To calculate Dan's total earnings, we simply add the interest earned to the initial investment:
Total earnings = £2500 + £250
Total earnings = £2750
Therefore, Dan will have £2750 in his bank account after 2 years.
Use the magnitudes, rounded to two decimal places, of the 100100 earthquakes included in the accompanying data set to construct a frequency distribution. Use a class width of 0.500.50 and begin with a lower class limit of 0.000.00. Does the frequency distribution appear to be a normal distribution? LOADING... Click the icon to view the earthquake magnitudes. Construct the frequency distribution. Magnitude Frequency 0.000.00-0.490.49 1010 0.500.50-0.990.99 3333 11-1.491.49 3535 1.501.50-1.991.99 1414 22-2.492.49 66 2.502.50-3.993.99 22 (Type integers or decimals. Do not round.) Does the frequency distribution appear to be a normal distribution? The frequency distribution could reasonably be a normal distribution because the frequencies start low, increase, and then decrease, and are roughly symmetric.
Answer:
Step-by-step explanation:
Hello!
To arrange the data in a frequency table you have to determine the class intervals first. Normally you'd choose the number of intervals you want to work with and then calculate the class width by dividing the number ob observations, n, by the number of intervals, then, starting from the minimum value as the lower limit of the first interval, you add the width to calculate the upper interval. For the next interval, you use the upper limit from the previous one and add the width to determine the upper limit, and so on until you reach the desired number of intervals.
For this exercise the width was determined 0.50 and the lower limit for the first interval 0.00:
1st interval: 0.00+0.50= 0.50: [0.00; 0.50)
Then:
[0.50; 1.00)
[1.00; 1.50)
[1.50; 2.00)
[2.00; 2.50)
[2.50; 3.00)
Next is to arrange the data from least to greatest and count how many fit in each interval:
0 , 0,09, 0,18, 0,24, 0,31, 0,36, 0,39, 0,39, 0,41, 0,45, 0,55, 0,55, 0,63, 0,64, 0,64, 0,64, 0,64, 0,64, 0,69, 0,69, 0,71, 0,71, 0,73, 0,74, 0,78 ,0,79, 0,79, 0,79 ,0,83, 0,83, 0,83 , 0,85, 0,89, 0,91, 0,92, 0,92, 0,93,0,94, 0,98, 0,98 ,0,99, 0,99, 0,99,0,99, 1,01, 1,01, 1,01, 1,01, 1,22, 1,23,1,24, 1,24 , 1,24, 1,25 ,1,,25 , ,1,25,1,26 , 1,26, 1,27, 1,28 ,1,31 , 1,33 , 1,34 , 1,34 ,, 1,35, 1,35 , 1,38 , 1,39 , 1,41 , 1,42 , 1,42 , 1,43 , 1,44 , 1,44 , 1,45 , 1,46 , 1,49 , 1,49 , 1,56 , 1,56 , 1,62 , 1,63 , 1,65 , 1,65 , 1,75 , 1,77 , 1,78 , 1,78 , 1,82 , 1,85 , 1,96 , 1,98 , 2,19 , 2,21 , 2,23 , 2,24 , 2,47 , 2,49 , 2,95 , 2,97
See frequency table in attachment alongside with original data.
To check the distribution of the data I've made a QQ-plot with the Normal Quartiles (2nd attachment)
As you can see the Magnitude data is well-adjusted to the theoretical line for the normal distribution, this means that it is most likely that the data has a normal distribution.
I hope this helps!
The fifth-grade teachers at Washington High School are decorating bulletin boards to get
ready for the new school year. They have 4 large bulletin boards that each need 9 yards of
border. There is also a small bulletin board that only needs 12 feet of border. If border is sold
in 40-foot rolls, how many rolls will the teachers use?
The teacher will use 3 rolls only to have perfect measurements.
1 yard = 3 feet
4 large bulletin boards are there each needing 9 yards of border.
That means 4 large bulletin boards in total need
9×4 yards of border
= 36 yards of border
= 108 feet of border
Also, there is a small bulletin board that only needs 12 feet border
Hence, in total there is a need for
108 + 12 = 120 feet border.
The border is sold in 40-foot rolls.
Hence, there is a need for 120/40 rolls
i.e. 3 rolls
Hence, the teacher will use 3 rolls only.
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Answer:
The answer is 3
Step-by-step explanation:
Help pls thank you! It’s math….
Answer:
○ \(\displaystyle (2x + 1)(2x - 5) = 0\)
Step-by-step explanation:
Find two quantities that when differed to 8, they also multiply to 20. Those will be 2 and 10. The TINIER quantity gets the plus symbol because the B-value is −8, therefore 10 gets the minus symbol, leaving 2 with the plus symbol. In extension, sinse we have a leading coefficient greater than one, we need to take extra procedures. Here is how it is done:
\(\displaystyle y = 4x^2 - 8x - 5 \\ \\ y = [4x^2 - 10x] + [2x - 5] \\ \:\:\:\:\:\:\:\:\:\:\:2x[2x - 5]+ 1[2x - 5] \\ \\ \boxed{[2x - 5][2x + 1] = 0}\)
I am joyous to assist you at any time.
hii Question, Why is 2+(-3) equal to -1? Because it is 3 units to the left of 2 on a horizontal number line O Because it is 3 units to the right of 0 on a horizontal number line Because it is 3 units to the left of 0 on a horizontal number line Because it is 3 units to the right of 2 on a horizontal number line
2
Step-by-step explanation:
it kinda like subtracting to get your answer
\(hope \: this \: helps\)
Judith has x math problems to do for homework. Harry has 2 times as many problems to do as Judith. Janessa has 10 more math problems to do than Judith. Which expression represents the total number of math problems Judith, Harry, and Janessa have to do all together
Answer:
4x+10
Step-by-step explanation:
Judith= x
Harry = 2x
Janessa= x+10
expression in total= x+2x+x+10 = 4x+10
List the sample space for rolling a fair 12-sided die.
S = {1, 2, 3, 4, 5, 6}
S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
S = {1}
S = {12}
The sample space for rolling a fair 12-sided die is S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}.
What is sample space?Sample space is a set of all possible outcomes of an experiment or random event. It is the collection of all possible results or outcomes that can occur when a particular event is performed.
In the given question,
The sample space is the set of all possible outcomes of an experiment. In this case, the experiment is rolling a fair 12-sided die. The sample space would include all possible values that the die can land on when rolled.
Since a 12-sided die has 12 equally likely outcomes, the sample space would consist of the numbers 1 through 12. However, only one of the options presented in the question includes all 12 numbers in the sample space, which is S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}.
Option S = {1, 2, 3, 4, 5, 6} represents the sample space of a regular 6-sided die, while options S = {1} and S = {12} only include one possible outcome, which is not applicable for a 12-sided die.
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awnser step. by step
Answer:
2.25
Step-by-step explanation:
answer will be 2.25....
PLEASE HELP 50 POINTS!!
The sum of two consecutive numbers is 157. This equation, where n is the first number, represents the situation:
2n + 1 = 157.
What is the first number?
A. 77
B. 78
C. 79
D. 80
What the meaning of statement this?
The proof demonstrates that given a well-ordered set W, an isomorphic ordinal can be found using the function F. The uniqueness of this ordinal is established using the Replacement Axioms. The set F(W) is shown to exist for each x in W, and if the least F(W) exists, it serves as an isomorphism of VV onto -y.
Lemma 2.7: This is a previously stated lemma that is referenced in the proof. Unfortunately, without the specific details of Lemma 2.7, it's difficult to provide further explanation for its role in the proof.
Well-ordered set W: A well-ordered set is a set where every non-empty subset has a least element. In this proof, W is assumed to be a well-ordered set.
Isomorphic ordinal: An ordinal is a mathematical concept that extends the notion of natural numbers to represent order and magnitude. An isomorphic ordinal refers to an ordinal that has a one-to-one correspondence or mapping with another ordinal, preserving their order and magnitude properties.
Function F: The function F is defined to assign an ordinal o to each element x in W. This means that for every x in W, there is a corresponding ordinal o.
Existence and uniqueness: The proof asserts that if there exists an ordinal o that is isomorphic to a specific initial segment of the ordinal VV (the set of all ordinals), then this ordinal o is unique. In other words, there is only one ordinal that can be mapped to the initial segment of VV given by x.
Replacement Axioms: The Replacement Axioms are principles in set theory that allow the construction of new sets based on existing ones. In this case, the Replacement Axioms are used to assert that the set F(W) exists, which is the collection of all ordinals that can be assigned to elements of W.
For each x in W: The proof states that for every x in W, there exists an ordinal o that can be assigned to it. If there is no such ordinal, the proof suggests considering the least x for which such an ordinal does not exist.
The least F(W): The proof introduces the concept of the least element in the set F(W), denoted as the least F(W). If this least element exists, it serves as an isomorphism (a one-to-one mapping) of the set of all ordinals VV onto the ordinal -y.
Overall, the proof outlines the existence and uniqueness of an isomorphic ordinal that can be obtained from a well-ordered set W using the function F, and it relies on the Replacement Axioms and the concept of least element to establish this result.
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Which of the following is a rational number?
A) -19
B) √17
C)
D) √33
Answer:
A
Step-by-step explanation:
Rational numbers have an ending decimal expansion. If you put the other numbers into a calculator you will se that there is just more numbers after the decimal point
What is the radius and diameter of the following circle?
Radius = cm
diameter= cm
The value of diameter and radius of circle is 7 cm and 3.5cm.
According to the statement
we have given that the a figure of circle and we have to find the radius and the diameter of the circle.
So, We know that the
The radius of a circle runs from its center to its edge, the diameter runs from edge to edge and cuts through the center.
Here from the figure it is clear that the
Diameter of circle = 7cm
and the radius of circle we have to find
So,
Radius of circle = Diameter /2
Substitute the values in it then
Radius of circle = 7cm /2
Radius of circle = 3.5 cm.
So, The value of diameter and radius of circle is 7 cm and 3.5cm.
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find the first derivative with respect to x of the following function: f(x)=(7x+3)(4-3x)
Answer:
19 - 42x
Step-by-step explanation:
To differentiate this, we must use the product rule
f'(x) = (7x+3)'(4-3x) + (4-3x)'(7x+3)
= (7)(4-3x) + (-3)(7x+3)
= 28 - 21x - 21x - 9
= 19 - 42x
please help me asap
Step-by-step explanation:
4/sin45=
\(4 \sqrt{2} \)
How can you find 75% of any number?
Answer:
Multiply the number by 0.75
Step-by-step explanation:
75% of a number is also a number * 75/100
Now 75/100=3/4 so 75% of a number is the number *3/4.
So to find 75% of any number, you just multiply it by 3 and divide it by 4.