What is the inverse of function ?
f(x) = 64x³-1
O A.
O B.
O c.
O D.
f¹ (2) = 4√x-1
f¹(x) = +¹
4
f¹(z) = Vz+1
64
f¹(x)=√x-4+1
F

Answer:

(- 3, 1.5)

--------------------------

Given system:

The first expression is ready to be substituted as no further operation is required to simplify it.

Find x:

The minimum wage increased by approximately 13.43% from 1987 to 1988.

The minimum wage increased by approximately 3.88% from 2004 to 2005.

a) Assuming minimum wage increased from $3.35 per hour in 1987 to $3.80 per hour in 1988.

To calculate the percent increase, we can use the formula:

percent increase = (new value - old value) / old value * 100%

percent increase = (3.80 - 3.35) / 3.35 * 100% = 13.43%

b) Assuming minimum wage increased from $5.15 per hour in 2004 to $5.35 per hour in 2005.

percent increase = (5.35 - 5.15) / 5.15 * 100% = 3.88%

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The number of cups of milk that Minka pours as a mixed number is found in the attached image.

The total number of cups of milk that Minka pours into her oatmeal is calculated as follows:

First day = 1/4

Second day = 1/4 + 1/4

Second day = 2/4

Third day = 1/4 + 2/4

Third day = 3/4

Fourth day = 1/4 + 3/4

Fourth day = 4/4 or 1

Fifth day =  5/4 or 1/4 + 1

Fifth day = 1 1/4

Sixth day = 1/4 + 5/4

Sixth day = 1 1/2

Seventh day = 1/4 + 6/4

Seventh day = 7/4 or 1 3/4

Eight day = 1/4 + 7/4

Eight day = 8/4 or 2

The completed number line is found in the attached image

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Answer:

L = 4.5

Step-by-step explanation:

You can rewrite the equation as 2L^2 + L - 45 = 0 and then solve using the quadratic formula

L = (-1 plus or minus the sq root of 361) / 4

L = (-1 plus or minus 19) / 4

L = -5 or 4.5 but lengths can't be negative so the length is 4.5

When the level of confidence decreases, the margin of error c. Becomes larger

The margin of error is a gauge of how uncertain a sample-based estimate is. It is impacted by the sample size and level of confidence and shows the potential difference between the estimate and the true population value. The user selects a level of confidence, which is commonly given as a percentage, when we want to generate a confidence interval for a population parameter, such as a mean or proportion. By selecting a degree of confidence of 95%, for instance, we are expressing our confidence that the true population parameter falls inside the interval.

Based on the level of confidence, and sample size the margin of error is determined. In order to account for greater uncertainty, a higher level of confidence necessitates a bigger margin of error, whereas a lower level of confidence necessitates a smaller margin of error. As a result, the margin of error rises as the level of confidence declines, indicating a wider range of values within which the true population parameter is expected to fall.

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The minimum product between the two numbers is 0 and the two numbers are 4 and 0.

here 1st number is x

and 2nd number is y

and the difference between twice a number and another number is 8 so 2x-y = 8

minimum value of

xy

= x(2x-8)

here the eqn is x(2x-8)

and we have to find its minima

If we have a formula expressed as y= ax2+bx+c , we can find the minimum of the quadratic equation according to the following formula: The minimum value is min= c-b2 /4a.

and the minima is at x=4

here the minimum value will be 0

so either value of x=0  or x= 4;

first number is 4 and second is 0

and product of x*y = 0;

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Answer:

Step-by-step explanation:

We can use the formula for a confidence interval for the population mean:

CI = x¯¯¯ ± z*(σ/sqrt(n))

where:

x¯¯¯ is the sample mean, which is 81.

σ is the population standard deviation, which is 11.8 (assuming the sample is drawn from a normally distributed population).

n is the sample size, which is 175.

z is the z-score corresponding to the desired level of confidence, which is 2.33 for a 98% confidence level.

Substituting the known values, we get:

CI = 81 ± 2.33*(11.8/sqrt(175))

Calculating this expression, we get:

CI ≈ (79, 83)

Therefore, a 98% confidence interval for the population mean is approximately (79, 83).

Therefore, the answer is (B) (79, 83).

Applying the knowledge of sets, the number of people that have been to Australia but not Europe is calculated as: 2.

Let's call the number of people who have been to Europe "E" and the number of people who have been to Australia "A". We know that:

E = 11

A = 7

We also know that 5 people have been to both Europe and Australia, so they are counted in both E and A:

E = 11

A = 7

E ∩ A = 5

To find the number of people who have been to Australia but not Europe, we can use the formula:

A - (E ∩ A) = A - 5 = 7 - 5 = 2

Therefore, the 2 people have been to Australia but not Europe.

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The x-axis V is if cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about the specified axis is 488.061745.

V = π/2 [18π² ln[3π] - 9π² + 1]

v = 488.061744630

Volume of the region is V = 488.061745.

The area of a thin cylindrical shell with height dr and radius f(x), where f(x) is the equation of the boundary curve, needs to be integrated over the range of x in order to get the volume produced by rotating a region about the y-axis using the cylindrical shell method.

Here, the interval's lower and higher boundaries are denoted by the letters a and b, while the boundary curve's equation is written as f(x). To acquire the volume, the integration must be run across the specified time frame.

The basic idea behind the cylindrical shell method is to build a series of cylindrical shells by wrapping the area around the y-axis, measure the volume of each shell, and then add all the volumes to get the total volume.

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The instantaneous velocity of the particle at 8 seconds is approximately the change in position over the change in time, or[tex]s(8+Δt) - s(8) / Δt[/tex]. If we use Δt = 0.1, then the instantaneous velocity is approximately s(8.1) - s(8) / 0.1. The approximate position of the particle after 10 seconds is then s(8) + (10-8) * (s(8.1) - s(8) / 0.1).

The instantaneous velocity of a particle is defined as the change in position over the change in time. This can be represented by the equation [tex]s(t+Δt) - s(t) / Δt[/tex]. Here, s(t) is the position of the particle at time t, and t is a small change in time. To approximate the instantaneous velocity at 8 seconds, we can use Δt = 0.1. This gives us an equation of s(8+0.1) - s(8) / 0.1. This equation gives us the velocity at 8 seconds. To approximate the position of the particle after 10 seconds, we can use the equation s(8) + (10-8) * (s(8.1) - s(8) / 0.1). This equation gives us an approximate position of the particle after 10 seconds, using the change in position over the change in time. This equation gives us a good approximation of the position of the particle after 10 seconds, given the information about the particle's position at 8 seconds.

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Convert the percent to a decimal: according to the local weather report, the probability of rain in Boston on February 9 is 78% is 0.78%.

Probability is the measure of how likely an event is to occur. It is expressed as a number between 0 and 1, where 0 indicates impossibility and 1 indicates certainty. Probability theory is used to study random phenomena, such as the outcome of a coin toss or the results of an election. It is also used to make predictions about the future, such as whether it will rain tomorrow.

The probability of choosing a student selected for the AP math class is 13/40 (6 girls and 7 boys selected for the AP math class). Therefore, the probability of choosing a boy or a student selected for the AP math class is 32/40 (19 boys plus 13 students selected for the AP math class out of 40 students).

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The complete question is: According to the local weather report, the probability of rain in Boston on February 9 is 78%. What is 78% converted to a decimal?

The ideal pie charts should always show both the sum of all the pie elements along with the data that constitute the pie slices. Thus the statement in the question is true.

The circle diagram, often known as a pie chart, pie chart, or pie chart, is used to depict qualitative or discrete information. It is used to display the percentage of each variable's values' constituent parts.

To do this, divide the circle into sections proportionate to the relative frequency. Recognize the area of the circle that corresponds to each possible value of the variable as a component. It is characterized as an "exploded cake graph" because it divides the graph into its many components in order to shift one of the portions.

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Answer:

77

Step-by-step explanation:

(V ∪ C) = V + C - (V ∩ C)
This is the same as: (V or C) = V + C - (V and C)

(V ∪ C) represents the number of people that chose chocolate or vanilla (or possibly both)

(V ∩ C) represents the number of people that chose chocolate and vanilla twist.

(V ∪ C) = V + C - (V ∩ C) ⇔ 200 = 162 + 115 - (V ∩ C)
(V ∩ C) = 162 + 115 - 200 = 77

Answer:-

36*5= 180

44*4= 176

28*3= 84

4*2=8

180-176-84= (-80)

-80/8=(-10)

Step-by-step explanation: Hope this helps. Mark me brainliest :)))

The difference between the highest and the lowest guess, on the whole number, is 120.

Subtraction is a mathematical operation. Which is used to remove terms or objects in the expression.

Given:

A table that shows the amount of butter.

Amount of butter

120

130

150

240

From the table;

the highest guess is 240.

And the lowest guess is 120.

So, the difference between the highest and the lowest  guess is,

= 240 - 120

= 120.

And here, 120 is a whole number.

Therefore, the required value is 120.

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If A is a matrix of order m × n, then

Rank of A + Nullity of A = Number of columns in A = n

Now, According to the question:

The rank-nullity theorem states that the dimension of the domain of a linear function is equal to the sum of the dimensions of its range (i.e., the set of values in the codomain that the function actually takes) and kernel (i.e., the set of values in the domain that are mapped to the zero vector in the codomain).

The range null-space decomposition is the representation of a vector space as the direct sum of the range and the null space of a certain power of a given matrix.

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The given question is incomplete,

So, The question is:

What is rank nullity theorem and range and null space ?

2. Scale factor of a dilation that maps Circle A onto a circle congruent to Circle B is: 4/3 . 3. Scale factor of a dilation that maps Circle C onto a circle congruent to Circle A is 1/2.

By rotating, reflecting, or translating a shape on a coordinate plane, a transformation is made. Transformational geometry, a fresh viewpoint on geometry, was first forth by Felix Klein in the 19th century.

The majority of geometric proofs rely on how objects change. Using transformations, we can change any image in a coordinate plane. By using transformational logic, it is possible to comprehend video game graphics more fully.

From the given figure we see that:

Diameter of A = 8

Diameter of B = 6

Diameter of C= 4

2. Scale factor of a dilation that maps Circle A onto a circle congruent to Circle B is:

8/6 = 4/3

3. Scale factor of a dilation that maps Circle C onto a circle congruent to Circle A is:

4/8 = 1/2

4. When a figure is dilated the new figure is similar to the pre-image. The segments, sides, edges, of the new image is dilated by scale factor.

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If the remaining milk is sold for $3.94 per half gallon, then the store initially bought 26 half gallons of milk for the profit of $46.76

What is meant by profit?

Profit is the term used to describe the financial gain experienced when the revenue from a company activity outpaces the costs, costs, and taxes incurred to support the activity in question.

Profit is the amount of money you have after paying for business expenses. Gross profit, operating profit, and net profit are the three basic categories of profit.

If the store bought x half gallons of milk at $2.90 per half gallon, the total cost of the milk would be:

                           total cost = 2.90x

Since the store stored the milk in two refrigerators, there were initially x/2 half gallons in each refrigerator.

Unfortunately, 14 half gallons were ruined, so the number of half gallons of milk remaining for sale is:

                            x - 14

The store then sells the remaining milk for $3.94 per half gallon, so the total revenue from the sale is:

                                total revenue = 3.94(x - 14)

The profit the store made is the difference between the total revenue and the total cost:

                         profit = total revenue - total cost

We know that the store made a profit of $46.76, so we can set up an equation:

46.76 = 3.94(x - 14) - 2.90x

Simplifying and solving for x:

46.76 = 3.94x - 55.16

102.92 = 3.94x

x = 26

So the store initially bought 26 half gallons of milk.

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The given statement follows the commutative property.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The given equation is x+y=y+x

The commutative property states that the change in the order of two numbers in an addition or multiplication operation does not change the sum or the product.

Therefore, the given statement follows the commutative property.

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The correlation coefficient for this set of five students is approximately 0.95.

First we can use the formula:

r = [nΣ(xy) - ΣxΣy] / [√{nΣx^2 - (Σx)^2} √{nΣy^2 - (Σy)^2}]

Where

Using the values given in the table, we can calculate the necessary sums and products:

n = 5

Σx = 173 + 172 + 175 + 176 + 177 = 873

Σy = 62 + 65 + 64 + 66 + 65 = 322

Σx^2 = 173^2 + 172^2 + 175^2 + 176^2 + 177^2 = 150367

Σy^2 = 62^2 + 65^2 + 64^2 + 66^2 + 65^2 = 20410

Σ(xy) = (172)(62) + (173)(65) + (175)(64) + (176)(66) + (177)(65) = 56209

Plugging these values into the formula for r, we get:

r = [5(56209) - (873)(322)] / [√{5(150367) - (873)^2} √{5(20410) - (322)^2}]

Simplifying the numerator and denominator:

r = [281045 - 280506] / [√{5(150367) - (873)^2} √{5(20410) - (322)^2}]

r = 0.95 (rounded to the hundredths place)

Therefore, the correlation coefficient for this set of five students is approximately 0.95.

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The inside length of the longer NBA caskets in inches is, 85.6745

A statistical measure of the degree of variation or dispersion in a set of values is the standard deviation. It offers a way to measure how far apart the individual values in a data set are from the set's mean (average). The square root of the variance is used to calculate the standard deviation, which is denoted by the symbol (sigma).

We are given the distribution here as:

From standard normal tables, we have here:

P(Z < 2.0537) = 0.98

Therefore, P(Z > 2.0537) = 1 - 0.98 = 0.02

Therefore 2.0537 is the z score that would be used here. ( As we are given here that for tallest 2% of the male basketball players, the special caskets for the NBA would be too tall )

Therefore the longest length here is computed as:

= Mean + 2.0537xSD

= 79 + 2.0537x3.25

= 85.6745 inches is the required length here.

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The domain of the function is -6 ≤ x ≤ 6.

The domain of a function is the set of its possible inputs, i.e., the set of input values where for which the function is defined.

A function is defined as the relationship between input and output, Where each input has exactly one output. The inputs are the elements in the domain. The co-domain of the function is the set of output values.

From the graph given the possible input values of x lies from -6 to 6.

Hence, the domain of the function is -6 ≤ x ≤ 6.

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The required point of the beginning is given as Point A. Option B is correct.

Coordinate, is represented as the values on the x-axis and y-axis of the graph. while the coordinate x is called abscissa and the coordinate of the y is called ordinate.

When you move 5 units north, you increase the y-coordinate by 5. When you move 3 units west, you decrease the x-coordinate by 3. So, if you start at an unknown point and move 5 units north and 3 units west, your final position would be at a point with the coordinates (x - 3, y + 5).

Since you ended at point D, and the final coordinates are not given, we cannot determine the starting point without more information.

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Assuming that each face is equally likely to come up.

(a) The sample space for this experiment  = {1, 2, 3}

(b) P(odd number) = 2/3

(c) If the die were loaded so that the face with the 3 on it was twice as likely to come up as each of the other five faces:

(i) The probability of the single events, P(3) = 2/7

(ii) P(even number) = 1/3

(a) The sample space for this experiment is the set of all possible outcomes, which are the numbers 1, 2, and 3 that can appear on the face of the die.

Sample space = {1, 2, 3}

(b) To find the probability of getting an odd number, we need to find the probability of getting a 1 or a 3. There are 3 faces with the number 1 and 1 face with the number 3, so there are 3 + 1 = 4 faces that result in an odd number. There are 6 faces total, so the probability of getting an odd number is 4/6 = 2/3.

P(odd number) = 2/3

(c)

(i) If the die were loaded so that the face with the 3 on it was twice as likely to come up as each of the other five faces, then each of the other five faces would have a probability of 1/7 of coming up, and the face with the 3 on it would have a probability of 2/7 of coming up.

P(1) = P(2) = 1/7

P(3) = 2/7

(ii) To find the probability of getting an even number, we need to find the probability of getting a 2. There are 2 faces with the number 2, so there are 2 faces that result in an even number. There are 6 faces total, so the probability of getting an even number is 2/6 = 1/3.

P(even number) = 1/3

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Answer:

Step-by-step explanation:

The inequality |3x| >= 0 simply states that the absolute value of 3x must be greater than or equal to zero.

Since the absolute value of any number must always be non-negative, this inequality is always true. That means any real number x satisfies the inequality |3x| >= 0.

Therefore, the solution to the inequality |3x| >= 0 is x ∈ R, where R represents the set of all real numbers.

The equations must intersect at a single point then it have the unique solution and the value of h and k are h = -1 and k = 6

A system has no solution if the equations are inconsistent, meaning there is no way to satisfy both equations simultaneously. It has a unique solution if the equations intersect at a single point, meaning there is only one set of values that satisfies both equations.

Let's take a look at the first system of equations, 19.

Equation 1: x + hx = 2

Equation 2: 4x + 8x = k

For the system to have no solution, the equations must be inconsistent. This means they must be parallel and never intersect. To achieve this, we can set the slopes of the lines to be equal but the y-intercepts different. In other words, we need to choose h and k such that:

h = -2 and k = 5

Substituting these values into the equations, we get:

Equation 1: x - 2x = 2

Equation 2: 4x + 8x = 5

You can see that these two equations do not have a common solution. They are inconsistent, meaning there is no point that satisfies both equations.

For the system to have a unique solution, the equations must intersect at a single point. This means the slopes and y-intercepts must be different. To achieve this, we can choose h and k such that:

h = -1 and k = 6

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We can write the equivalent value of the root expression √8√3 as 2√6.

The square root of a number is given by -

y = √x

y² = x

More specifically, we can write -

y = ± √x

Given is the root expression as -

√8√3

We can solve the expression as by finding the square roots of the numbers as -

√8√3 = √8 x √3

√8√3 = √(2 x 2 x 2) x √3

√8√3 = 2√2 x √3

√8√3 = 2√6

So, we can write that -

√8√3 = 2√6

Therefore, we can write the equivalent value of the root expression √8√3 as 2√6.

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Madeline's school building model is 5.33 meter.

Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio. Either of these conditions will prove two triangles are similar.

Given that, Madeline walks a distance of 9.45 meters from the building, then places a mirror flat on the ground, marked with an X at the center.

Use corresponding parts of similar triangles.

Madeline's eyes height/Madeline's distance from x = Buildings height/Buildings distance from X

1.55/2.75 = x/9.45

2.75x=1.55×9.45

2.75x=14.6475

x=14.6475/2.75

x=5.33

Therefore, Madeline's school building model is 5.33 meter.

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The correct answer is option b. When the homoskedasticity assumption is violated, The beta parameter estimates are biased while the rest of the OLS assumptions are correct.

When the homoskedasticity assumption is violated, the ordinary least squares (OLS) estimator is still consistent but no longer efficient. This means that the estimates of the regression coefficients (beta parameters) are still unbiased, but they have higher variances and covariances.

In other words, the OLS estimator is no longer the best linear unbiased estimator (BLUE) and it may be biased when the errors are heteroscedastic. Therefore, option b is correct.

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8. M(x,y) and N(x,y) are functions of x and y, not just y, so the given differential equation is not linear in y.

9. Both M(u,v) and N(u,v) are functions of u, so the given differential equation is linear in u.

8. To match the given differential equation with the first differential equation given in (7), we need to write the given equation in the form of M(x,y)dx + N(x,y)dy = 0. If the resulting M(x,y) and N(x,y) are both functions of y, then the differential equation is linear in y.

Rewriting (y² - 1)dx + xdy = 0 as xdy = (1 - y²)dx and dividing by x(1 - y²), we get (1/x)dy - [(y² - 1)/(x(1 - y²))]dx = 0.

Therefore, we have M(x,y) = (y² - 1)/(x(1 - y²)) and N(x,y) = 1/x. Both M(x,y) and N(x,y) are functions of x and y, not just y, so the given differential equation is not linear in y.

9. To match the given differential equation with the first differential equation given in (7), we need to write the given equation in the form of M(u,v)du + N(u,v)dv = 0. If the resulting M(u,v) and N(u,v) are both functions of u, then the differential equation is linear in u.

We can rewrite the given equation as u dv + (v + uv) du - [tex]ue^u[/tex] du = 0.

Therefore, we have M(u,v) = v + uv - [tex]ue^u[/tex] and N(u,v) = u. Both M(u,v) and N(u,v) are functions of u, so the given differential equation is linear in u.

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