The inverse function of g(x) is:
f(x) = (x - 2)^(2/3) + 3
Which function is the inverse of g(x)?Two functions are inverses if their composition is equal to the identity, then if f(x) is the inverse of our function, we must have that:
g( f(x) ) = x
Here we know that:
g(x) = (x - 3)^(3/2) + 2
Evaluating this in f(x) we should get:
g( f(x) = (f(x) - 3)^(3/2) + 2 = x
Now we can solve that for f(x).
(f(x) - 3)^(3/2) + 2 = x
( (f(x) - 3)^(3/2) = x - 2
f(x) - 3 = (x - 2)^(2/3)
f(x) = (x - 2)^(2/3) + 3
That is the inverse function.
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Here is a rectangle.
5 cm
7 cm
5 cm
7 cm
The 6-sided shape is made from two of these rectangles.
Work out the perimeter of this 6-sided shape.
Optional working
Answer:
cm
The perimeter of the 6-sided shape given the length and width of the rectangle is 48 cm
What is the perimeter of the 6-sided shape?The perimeter of a rectangle= 2(length + width)
Length of the rectangle= 7 cm
Width of the rectangle= 5 cm
The perimeter of a rectangle= 2(length + width)
= 2(7 + 5)
= 2(12)
= 24 cm
The 6-sided shape is the combination of two rectangles
So,
Perimeter of the 6-sided shape = 24 cm + 24 cm
= 48 cm
Therefore, the 6-sided shape has the perimeter 48 cm.
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Henry is starting a t-shirt printing business and plans on selling each shirt for $30, with his cost being $8 per shirt. The equipment will cost $1200.
Henry orders 600 shirts and determines that the profit for his new business is modeled by the function P = 22x - 1200. What is the domain of this function in this context?
{0 ≤ x ≤ 600}
{0 ≥ x ≥ 600}
{-1,200 ≤ x ≤ 2,000}
all real numbers
The domain of the function here is {0 ≤ x ≤ 600}. The first option is the right answer.
What is the domain of a function?The domain of a function is the set of all input values (or independent variables) for which the function is defined and produces a valid output (or dependent variable). It is the set of values that can be plugged into a function and yield a valid result.
The domain of this function in this context is {0 ≤ x ≤ 600}.
This is because x represents the number of t-shirts Henry sells and he has ordered 600 shirts. So, he can only sell a non-negative number of shirts (x ≥ 0) and a maximum of 600 shirts (x ≤ 600). Any values outside this range are not meaningful in this context, hence they are not part of the domain.
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Pls help image attached
Algebra 1 10points and brainliest
Using the graph of the function, the value of f(4) is 6.
How to find the value of f(4) of the graph?A function is an expression that shows the relationship between the independent variable and the dependent variable. A function is usually denoted by letters such as f, g, etc.
The set of inputs is called the domain of the function, and the set of outputs is called the codomain. A function maps each input to exactly one output, so it is also sometimes referred to as a mapping.
Using the graph, the value of f(4) can be found by checking for the value y when x = 4. Check the attached image.
Therefore, the value of f(4) is 6
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henry's score on an accounting exam placed him in the 85th percentile in the class. what percentage of students scored higher than henry?
15% of the students scored higher than Henry on the accounting exam.
What is percentiles?
Percentiles are a measure of the relative standing of a value within a set of values. The nth percentile is a value such that n% of the values are less than or equal to that value.
So, if Henry's score is in the 85th percentile, it means that 85% of the scores in the class are less than or equal to his score.
Therefore, 100% - 85% = 15% of the scores in the class are higher than Henry's score. So, 15% of the students scored higher than Henry on the accounting exam.
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I need some help please
What is the range of a function g?
Answer:
A { y | y ∈ ℝ, y ≠ -4, -3 }
Step-by-step explanation:
You want to know the range of the function shown in the graph.
RangeThe range is the vertical extent of the graph, the set of possible function output values.
Here, the function approaches the horizontal asymptote y = -3, but never has that output value. The "hole" at (5, -4) means the function never has the output value -4, either.
The range is all real numbers (ℝ) except -4 and -3.
c^5 x c
help i dont know what the answer is i dont pay attention
Work Shown:
c^5 x c
c^5 x c^1
c^(5+1)
c^6
The rule is to add the exponents when multiplying exponential expressions. The bases must be the same. The rule in symbolic form is a^b*a^c = a^(b+c)
a pyramid is 860 ft high (due to erosion, its current height is slightly less) and has a square base of side 7740 ft. find the work needed to build the pyramid if the density of the stone is estimated at 168 lb/ft .
The work needed to build the pyramid is calculated by multiplying the area of the base by the height and the density of the stone.
The work needed to build the pyramid can be calculated by using the formula Work = Area x Height x Density. The area of the base of the pyramid can be calculated by using the formula Area = Side^2, where Side is the length of the side of the square base. In this case, the side of the square base is 7740 ft. So, the area of the base is 7740^2 ft^2. The height of the pyramid is 860 ft (due to erosion, its current height is slightly less). The density of the stone is estimated at 168 lb/ft. So, the work needed to build the pyramid is calculated by multiplying the area of the base by the height and the density of the stone, like this: Work = 7740^2 ft^2 x 860 ft x 168 lb/ft = 9.76 x 10^9 lb-ft.
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PLEASE HELP ITS URGENT !!
Answer:
4, -2, and -5.
Step-by-step explanation:
All the real solutions of f(x) = 0 are 4, -2, and -5. We know y = f(x) and f(x) = 0. So, we can conclude that y = 0. When y = 0, it means there isn't a point that moves up or down the y axis (vertically). The point would only move horizontally. When looking at the points on the x-axis, we see 4, -2, and -5. Those are on the x-axis and haven't moved vertically. So, the coordinates for those points would be 4, 0, -2, 0, and -5, 0. Remember, y = 0, and 4, -2, and -5 all have a zero in the y value. Therefore, the answer is 4, -2, and -5.
an arc of a circle measures 2.4 radians. to the nearest degree, what is the measure, in degrees, of this arc? (disregard the degree sign when gridding your answer.)
The measure of the arc in degrees is 137.50°
Radian Measure:An angle is said to have a measure of 1 radian if it is subtended at its center by an arc of lengths 1 unit in a unit circle. "rad" is the sign used to represent the radian unit of measurement.
1 degree = π/180 radian 1 radian = 180°/πHere we have
An arc of a circle that measures 2.4 radians.
We need to find the measure in degrees
As we know 1 radian = 180°/π
2.4 radians = [ 180/π ] × 2.4 degrees
= [57.324] × 2.4
= 137.57° ( approx)
Therefore,
The measure of the arc in degrees is 137.50°
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PLEASE HELP
An election poll reported that a candidate had an approval rating of 48% with a margin of error E of 3%. Construct a confidence interval for the proportion of adults who approve of the candidate.
The confidence interval for the proportion of adults who approve of the candidate is given as follows:
(0.45, 0.51).
How to obtain the confidence interval?A confidence interval is obtained as the proportion estimate plus/minus the margin of error.
The parameters for this problem are given as follows:
Proportion estimate: 0.48.Margin of error: 0.03.Hence the bounds of the confidence interval are given as follows:
Lower bound: 0.48 - 0.03 = 0.45.Upper bound: 0.48 + 0.03 = 0.51.More can be learned about confidence intervals at https://brainly.com/question/25890103
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A local restaurant charges $15 for a jumbo cheese pizza and $1.35 for each additional topping. Write an equation, in slope-intercept form, to represent the total cost, y, for x toppings on a jumbo pizza.
A local restaurant charges $15 for a jumbo cheese pizza and $1.35 for each additional topping.
the total cost, y, for x toppings on a jumbo pizza is represented in slope-intercept form, by the equation y = $1.35x + $15
The slope-intercept equation for the total cost, y, for x toppings on a large cheese pizza is y = mx + b, where m is the slope and b is the y-intercept.
First, we must determine the slope (m). The slope shows the $1.35 cost of each subsequent topping. So, m = $1.35.
The y-intercept must then be determined (b). The y-intercept shows the large cheese pizza's starting cost of $15. So, b = $15.
When we plug these values into the equation, we get:
y = $1.35x + $15
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what are the rest of the digits of pi after these 511 11 digits? 3 . 1 4 1 5 9 2 6 5 3 5 8 9 7 9 3 2 3 8 4 6 2 6 4 3 3 8 3 2 7 9 5 0 2 8 8 4 1 9 7 1 6 9 3 9 9 3 7 5 1 0 5 8 2 0 9 7 4 9 4 4 5 9 2 3 0 7 8 1 6 4 0 6 2 8 6 2 0 8 9 9 8 6 2 8 0 3 4 8 2 5 3 4 2 1 1 7 0 6 7 9 8 2 1 4 8 0 8 6 5 1 3 2 8 2 3 0 6 6 4 7 0 9 3 8 4 4 6 0 9 5 5 0 5 8 2 2 3 1 7 2 5 3 5 9 4 0 8 1 2 8 4 8 1 1 1 7 4 5 0 2 8 4 1 0 2 7 0 1 9 3 8 5 2 1 1 0 5 5 5 9 6 4 4 6 2 2 9 4 8 9 5 4 9 3 0 3 8 1 9 6 4 4 2 8 8 1 0 9 7 5 6 6 5 9 3 3 4 4 6 1 2 8 4 7 5 6 4 8 2 3 3 7 8 6 7 8 3 1 6 5 2 7 1 2 0 1 9 0 9 1 4 5 6 4 8 5 6 6 9 2 3 4 6 0 3 4 8 6 1 0 4 5 4 3 2 6 6 4 8 2 1 3 3 9 3 6 0 7 2 6 0 2 4 9 1 4 1 2 7 3 7 2 4 5 8 7 0 0 6 6 0 6 3 1 5 5 8 8 1 7 4 8 8 1 5 2 0 9 2 0 9 6 2 8 2 9 2 5 4 0 9 1 7 1 5 3 6 4 3 6 7 8 9 2 5 9 0 3 6 0 0 1 1 3 3 0 5 3 0 5 4 8 8 2 0 4 6 6 5 2 1 3 8 4 1 4 6 9 5 1 9 4 1 5 1 1 6 0 9 4 3 3 0 5 7 2 7 0 3 6 5 7 5 9 5 9 1 9 5 3 0 9 2 1 8 6 1 1 7 3 8 1 9 3 2 6 1 1 7 9 3 1 0 5 1 1 8 5 4 8 0 7 4 4 6 2 3 7 9 9 6 2 7 4 9 5 6 7 3 5 1 8 8 5 7 5 2 7 2 4 8 9 1 2 2 7 9 3 8 1 8 3 0 1 1 9 4 9 1 2 9 8 3 3 6 7 3 3 6 2 4
Answer:
Here:
4065664308602139494639522473719070217986094370277053921717629317675238467481846766940513200056812714526356082778577134275778960917363717872146844090122495343014654958537105079227968925892354201995611212902196086403441815981362977477130996051870721134999999837
marni burns a candle half of its length everyday that she uses it.
day 1 =18
day2=
day 3 =
day 4=
day 5=
pleaseee help asap tysm !!
Answer: Let's denote the length of the candle on day 1 as L.
On day 2, the length of the candle is L/2, on day 3 it is L/2^2, on day 4 it is L/2^3 and on day 5 it is L/2^4.
So, on day 5, the length of the candle is L/2^4 = L/(222*2) = L/16.
Given that the length of the candle on day 1 is 18 inches, we have:
L = 18
And the length of the candle on day 5 is:
L/16 = 18/16 = 9/8
So, the length of the candle on day 5 is 9/8 inches.
Step-by-step explanation:
i am equivalent to 5/6 . the sum of my numerator and my denominator is 44. the sum of the digits in my denominator is 6. what fraction am i?
The fraction that satisfies the problem is 20/24.
Equivalent fractions are fractions that have the same value, but different numerators and denominators.
If the fraction is equivalent to 5/6, then the numerator and denominator of the fraction is a multiple of 5 and 6, respectively.
Let x be the factor
fraction = 5x / 6x
If the sum of my numerator and my denominator is 44, then:
5x + 6x = 44
11x = 44
x = 4
fraction = 5x / 6x = 20/24
The final statement says that the sum of the digits in the denominator is 6.
2 + 4 = 6
Hence, the fraction is 20/24.
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Chad's phone plan includes a certain amount of data each month. So far this month, he has used 4.3 gigabytes of data. He has less than 6 gigabytes of data left for the rest of the month. Let x represent how many gigabytes of data are included in Chad's phone plan each month. Which inequality describes the problem?
The correct inequality which describes the problem is,
⇒ x - 4.3 < 6
What is Inequality?A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
Chad's phone plan includes a certain amount of data each month.
And, he has used 4.3 gigabytes of data. He has less than 6 gigabytes of data left for the rest of the month.
Now, Let x represent how many gigabytes of data are included in Chad's phone plan each month.
Hence, The correct inequality which describes the problem is,
⇒ x - 4.3 < 6
⇒ x < 6 + 4.3
⇒ x < 10.3
Thus, The correct inequality which describes the problem is,
⇒ x - 4.3 < 6
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Can anyone pls help me to solve this fastt!!
Answer:
f(x) = x + 5
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 5, 0) and (x₂, y₂ ) = (0, 5) ← 2 points on the line
m = [tex]\frac{5-0}{0-(-5)}[/tex] = [tex]\frac{5}{0+5}[/tex] = [tex]\frac{5}{5}[/tex] = 1
the line crosses the y- axis at (0, 5 ) ⇒ c = 5
y = x + 5 , or
f(x) = x + 5
Answer:
x+5
Step-by-step explanation:
Because I said so
grade 4N usually has physical education on a Wednesday at 1:43pm and ends at 2:13 pm. with the new mandated change, at what time will grade 4N PE ends?
The new mandated change is, grade 4N's physical education class will end at 2:23 PM.
Physical education for grade 4N typically lasts 30 minutes and begins at 1:43 PM and concludes at 2:13 PM (2:13 PM - 1:43 PM).
Let's assume that the newly required adjustment extends the end of the class by 10 minutes, making the time change (c) 10 minutes.
Adding the time modification to the existing end time will yield the new end time:
2:13 PM + 10 minutes = 2:23 PM
So, with the new mandated change, grade 4N's physical education class will end at 2:23 PM.
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please help !!!!!
does anyone know the answer?!?
The volume of the ball is 267.95cm³ and the density of the ball is 0.335gcm⁻³
What is density of an objectDensity is a measure of the mass of an object per unit of volume. It is usually expressed in units of grams per cubic centimeter (g/cm3).
In this problem, the density of the ball is calculated as;
density = mass / volume
volume = volume of sphere
volume = 4/3πr³
volume = 4/3 * 3.14 * 4³
volume = 267.95cm³
The volume is 267.95cm³
The density of the ball = mass / volume
density = 90 / 267.95 = 0.335gcm⁻³
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[tex]\sqrt{100}[/tex]
Which of the following is a perfect square trinomial?
(A) 4x2 - 4x + 1
(B) 4x2 - 2x + 2
(C) 4x2 - 4x + 2
(D) 4x2 - 8x + 16
(E) 4x2 - 12x + 16
The perfect square trinomial is 4x² - 4x + 1. The correct answer would be an option (A).
What is the algebraic expression?Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.
The expression is given in option (A), as follows:
4x² - 4x + 1
(2x)² - 2 × 2x × 1 + 1²
Compare to the formula a² - 2 × a × b + b² = (a - b)², and we get
(2x - 1)²
Thus, this is a perfect square trinomial.
Hence, the correct answer would be an option (A).
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HELP ASAP, WILL GIVE BRAINLEIST
Using a standard deck of 52 cards, Lisa drew a card, recorded the suit of the card picked, then replaced it back in the deck. She continued this for a total of 40 draws. The table shows the frequency of each type of card drawn.
Diamonds Spades Hearts Clubs
7 11 9 13
Determine the experimental probability of not selecting a heart.
P(not heart) = 9%
P(not heart) = 10%
P(not heart) = 67.5%
P(not heart) = 77.5%
Step-by-step explanation:
a probability is always the ratio
desired cases / totally possible cases
in our experiment the totally possible cases for pulling not a heart is 40.
7 + 11 + 9 + 13 = 40
in that experiment we see that out of these 40 pulls we got 9 hearts. and therefore 40 - 9 = 31 non-hearts.
so, the experimental probability for not pulling a heart is
31/40 = 0.775 = 77.5%
Answer:
yes 77.5%
Step-by-step explanation:
Pls help me pls pls pls pls help me pleeeeeaaase
Answer: i think its 9
Step-by-step explanation:
Answer:
the answe is defenitly -3
The table below shows the ratios of black to white keys on pianos of various sizes.
Black A 36 63 90
White 13 B 91 C
Determine which table has the correct values for A, B, and C.
The required correct values for A, B, and C is 9, 52, and 130 respectively.
Proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense are they directly proportional or inversely proportional to each other.
Since a standard piano has a ratio of white to black keys is given as,
= 91/63
= 13/9
Now,
13/A =91/63
A = 9
Similarly,
B = 52
C = 130
Thus, the required correction values for A, B, and C is 9, 52, and 130 respectively.
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My geometry teacher sucks i have no clue how to do all four of these
The value of x is 10.
What is the Pythagoras theorem?The Pythagoras theorem states that the square of the longest side must be equal to the sum of the square of the other two sides in a right-angle triangle.
|AC|^2 = |AB|^2 + |BC|^2
Given;
Base=6
Perpendicular=8
Now
x^2=6^2+8^2
X^2=36+64
X^2=100
x=10
Therefore, by pythagoras theorem the answer will be 10.
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A certain forest covers an area of 2500km Suppose that each year this area decreases by 6.25% What will the area be after 15 years Use the calculator provided and round your answer to the nearest square kilometer.
After 15 years, the area of the forest will be approximately 1523.4 km
A percentage is a unit used to express a portion of a whole number as a fraction of 100.
In this scenario, we are know that the area of a forest decreases by 6.25% each year. This means that each year, the area of the forest will decrease by
=> 6.25/100 times its original size.
To find the area of the forest after 15 years, we need to calculate the total decrease in area over 15 years. We can do this by multiplying the original area of the forest by the percentage decrease each year, and then repeating this calculation 15 times.
Starting with the original area of 2500km, we can calculate the first year's decrease by multiplying
=> 2500 x 100/6.25 = 157.5 km.
To find the area after the first year, we subtract
=> 2500 km - 157.5 = 2342.5 km.
We can repeat this calculation for the next 14 years to find the total decrease in area over 15 years. We can also use the calculator provided to simplify the calculation.
To do this, we enter 2500, then press the multiply button, enter 0.0625, then press the equal button, then press the subtract button, and finally enter the result from the previous calculation until we reach the final answer.
This means that the total decrease in area over 15 years was approximately
=> 1523.4 km,
which is equal to 61% of the original area of the forest
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Match the following situation with one of the linear systems. Lewis wants to acquire at most 12 packages of baseball cards. Some packages have 4 rookie cards and some have only 3. In all, there are at most 38 rookie cards.
10 packages are available, some of which contain only 3 and others 4 rookie cards. There are a maximum of 38 rookie cards in all.
what is linear equations ?In math, a linear equation one of that of the form y=mx+b. The slope is B, and the una is m. As y and x are variable, the previous statement is frequently referred to as a "system of equations with 2 variables." Bivariate linear equations are logistic equations with two or more variables. Formulas can be found in various locations, including 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. When such an equation has had the structure y=mx+b, where m represents the slope and b its y-intercept, it is known to as being linear. A model formula is said to be cubic if its solution seems to have the form y=mx+b, wherein m stands for the gradient and b for the y-intercept.
3x + 4y = 38
x + y = 12 ( Multiply by -3)
Hence
3x + 4y = 38
-3x - 3y = -36
Add
y = 2
In the case where y = 2
x = 12 - y
x = 12 - 2
x = 10,
10 packages are available, some of which contain only 3 and others 4 rookie cards. There are a maximum of 38 rookie cards in all.
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positive integers a and b are each less than 6. what is the least possible value for 2*a-a*b?
[tex]a < 6\to \begin{cases} 0\\ 1\\ 2\\ 3\\ 4\\ 5 \end{cases}\hspace{5em}b < 6\to \begin{cases} 0\\ 1\\ 2\\ 3\\ 4\\ 5 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ 2a-ab\implies a(2-b)[/tex]
now, in the expression above, if we set a = 0, we land on 0, if we set b = 2, we land on 0 again, and 0 is the least of all positive integers.
URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
The transformations of the triangle ABC to A'B'C' are (a) and (e)
How to determine the transformationsFrom the question, we have the following parameters that can be used in our computation:
ABC = (-6, 2), (-4, 6) and (-2, 2)
Rotate the triangle by 180 degrees
So, we have the following representation
Image 1 of ABC = (6, -2), (4, -6) and (2, -2)
Translate the triangle 1 units left
So, we have the following representation
A'B'C' = (5, -2), (3, -6) and (1, -2) ---- option (a)
Another possible sequence is as follows
Reflect the triangle across the x and y axes
So, we have the following representation
Image 1 of ABC = (6, -2), (4, -6) and (2, -2)
Translate the triangle 1 units left
So, we have the following representation
A'B'C' = (5, -2), (3, -6) and (1, -2) ---- option (e)
Hence, the transformations are (a) and (e)
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PLEASEEEE. HELPPPPPPPPPP
Answer:
a) 16, b) 16
Step-by-step explanation:
1. Find f. Plug in 2 for x.
[tex]2^{2} +6(2)=16.[/tex]
2. Find g by performing the same action.
2-1=1.
3. Now that we have f and g, we can multiply them.
[tex](fg)(2)=16(1)=16.[/tex]
a) is 16.
4. b) is (gf)(2)=1(16), which is still 16.
b) is 16.