If f(6)=7, find f⁻¹(7)
Assume that the function f is a one-to-one function.

The correct answer is A) 180° rotation about the origin, followed by a translation (x, y) → (x - 2, y + 1).B) 180° rotation about the origin, followed by a translation (x, y) → (x + 2, y - 1).C) Reflection along the line y = x, followed by a 180° rotation about the origin.D) Reflection along the y-axis, followed by a 180° rotation about the origin.

To identify the compositions of transformations that map XYZ onto X"Y"Z", we need to analyze each option and determine the combination of transformations.

A) Translation: (x,y) - (x - 2, y + 1); 180° rotation about the origin

This option consists of a translation and a 180° rotation about the origin. To identify the composition, we perform the operations in reverse order. First, we apply the 180° rotation, and then the translation. Therefore, the composition of transformations for option A is a 180° rotation about the origin followed by a translation of (x, y) → (x - 2, y + 1).

B) Translation: (x,y) - (x + 2, y - 1); 180° rotation about the origin

Similar to option A, this option involves a translation and a 180° rotation. Again, we reverse the order of operations to determine the composition. So, the composition of transformations for option B is a 180° rotation about the origin followed by a translation of (x, y) → (x + 2, y - 1).

C) Reflection along the line y = x; 180° rotation about the origin

This option includes a reflection along the line y = x and a 180° rotation. The order of operations is important, so we perform the reflection first and then the rotation. Hence, the composition of transformations for option C is a reflection along the line y = x followed by a 180° rotation about the origin.

D) Reflection along the y-axis; 180° rotation about the origin

Option D involves a reflection along the y-axis and a 180° rotation. As with the previous options, we need to reverse the order. Thus, the composition of transformations for option D is a reflection along the y-axis followed by a 180° rotation about the origin.

In summary:

A) Composition: 180° rotation about the origin, then a translation (x, y) → (x - 2, y + 1).

B) Composition: 180° rotation about the origin, then a translation (x, y) → (x + 2, y - 1).

C) Composition: Reflection along the line y = x, then a 180° rotation about the origin.

D) Composition: Reflection along the y-axis, then a 180° rotation about the origin.

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Answer:

? = -4

Step-by-step explanation:

Answer: 0.95k + 3.15

Step-by-step explanation:

0.95k is because each of k kilometers costs $0.95.  + 3.15 is because it costs 3.15 as a flat rate regardless of distance

Hope it helps <3

Answer:

.95k+3.15

Step-by-step explanation:

To write an expression you need a variable (k). I look at the directions and I see that the length of the trip is 'k' kilometers. So I pay the flat fee of 3.15 ONE TIME. Then I pay $0.95 for every kilometer I go, so the expression is

->   .95k+3.15

Answer:x=7

Step-by-step explanation: 2(4x-2)=52

8x-4=52

8x=56

x=7

Well they have to  be perpendicual because they cross and parallel means that they are like lines on lines paper, they do not cross, they just keep going. Hope this helps :)

Each component will have a triangle pyramid on top of a rectangle prism. equation The base of the rectangle prism will match the L shape's base, and its height will match the L shape's height.

A math equation is a procedure that connects two claims and uses the equals symbol (=) to denote equivalence. An equation in algebra is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, in the calculation 3x + 5 = 14, the equal sign places a space between the values 3x + 5 and 14. The relationship between the two sentences that are written on each side of a letter may be understood using a mathematical formula. The logo and the specifically software are frequently the same. as in, 2x - 4 Equals 2, for instance.

We must locate a line of symmetry that will separate the irregular form into two congruent sections in order to split it into two rectangular prisms. According to the description, when the two rectangular prisms are pressed together, the three-dimensional form resembles the letter L. We can therefore infer that the plane of symmetry follows the L shape's longitudinal line.

This plane of symmetry can be used to separate the L form into two congruent sections. Each component will have a triangle pyramid on top of a rectangle prism. The base of the rectangle prism will match the L shape's base, and its height will match the L shape's height.

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Answer:

acres he can plant with remaining seeds

Step-by-step explanation:

i got it correct on ttm

Answer:

acres he can plant with remaining seed

Answer:

Irrational

Step-by-step explanation:

The square root of 3 is not a perfect square, therefore it is irrational. Another way you could see if it is rational is if it can be put in a fraction, if it can't, then it is irrational.

Your answer for A is correct.

For B, I would keep the base of the logarithm as simple as possible.

\(y = 100 \cdot 3.24^x \implies \dfrac y{100} = 3.24^x \implies \log_{3.24}\left(\dfrac y{100}\right) = \log_{3.24}(3.24)^x \\\\ \implies x = \log_{3.24} \left(\dfrac y{100}\right)\)

In part A, the function told us the number of students with cell phones (dependent variable) after some number of years post-2000 (independent variable). Our new function turns this around and tells us the time in years after 2000 (dependent) based on how many student have cell phones (independent).

For C, if we set \(y=7200\) students, then we can estimate the time it takes for the all students to acquire cell phones by solving for \(x\).

\(x = \log_{3.24}\left(\dfrac{7200}{100}\right) = \log_{3.24}(72) \approx 3.63794\)

If you're using a typical calculator, it probably won't have buttons for logarithms of any base other than 10 or the natural base \(e\). To work around that, use the change-of-base identity

\(\log_{3.24}(72) = \dfrac{\log_{10}(72)}{\log_{10}(3.24)} = \dfrac{\ln(72)}{\ln(3.24)}\)

At any rate, it would take about 3.64 years for all students to get a cell phone, according to this model.

Answer:

G = LA/Y + D/Y

Isolate the variable by dividing each side by factors that don't contain the variable.

Hoped this helped!

Answer:

Step-by-step explanation:

30-12/3=d

d=drinks he bought

$30-$12=$18

$18/$3=6

he got 6 drinks

Answer:

A

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

1.2^2 = 1.44

1.2 · 1.2 = 1.44

Hope I helped :)

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The largest factor of the sum of y and z is 24.

The replacement approach has the advantage of providing the precise values for the variables (x and y), which correspond to the site of intersection.

When using the "by substitution" method, you must first solve one of the equations provided (you must choose which one) for one of the variables (you must choose which one), after which you must plug this value back into the other equation provided (you must "substitute" for the chosen variable and solve for the other value). The first equation is then used to back-solve for the first variable. The many procedures required in using the replacement approach to solve problems have been described in full above. Use those to discover the solution to a given system of linear equations.

We are given with three equations having three unknowns:

x = z/4

x + y + z = 26

y = 2z

Using the method of substitution, we can now solve for each of the three unknowns.

Since the first equation, x = z/4, is an equation for x in terms of z, and the third equation, y = 2z, is an equation for y in terms of z, we can replace x and y in the second equation by their equivalent expressions as follows:

x + y + z = (z/4) + (2z) + z = 26

We are left with an equation with just one unknown z. We can now solve for z:

(z/4) + (2z) + z = 26

z/4 + 8z/4 + 4z/4 = 13z/4 = 26

z/4 = 2

z = 8

Now that we know z, we can easily solve for y, then compute y + z (note: we can also solve for x, but since we are not interested in the value of x there is no need to do so):

y = 2z = 2(8) = 16

y + z = 16 + 8 = 24

Since the largest factor of any number is the number itself, the largest factor of the sum of y and z is 24.

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To find the number of each type of commercial playing, the simultaneous equations that will be entered into a graphing calculator are:

The total number of commercials played in an hour = 16

The complete minutes for the commercials = 13 minutes

If x = 30-second commercial and y = 60-second commercial, the simultaneous equations can be represented as follows:

30 seconds = 0.5 minutes

60 seconds = 1 minute

Equation 1: x + y = 16

Equation 2: 0.5x + y = 13

Solving the equations by substitution:

Equation 1 becomes x = 16 - y

Equation 2: 0.5(16 - y) + y = 13

8 - 0.5y + y = 13

0.5y = 5

y = 10

x = 16 - y

= 16 - 10

= 6

Check:

0.5(6) + 10 = 13

3 + 10 = 13

13 = 13

Thus, the simultaneous equations for the graphing calculator will be Options B and C.

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a) x + y = 13

b) x + y = 16

c) 0.5x + y = 13

d) 0.5x + y = 16

e) 0.5x + y = 29

Answers:

1. 2

2. 17

3. 16

4. 4

5. 2

6. 8

7. 18

8. 10

Answer:

1. 2

2. 17

3. 16

4. 4

5. 2

6. 8

7. 18

8. 10

Step-by-step explanation:

In a normal population with a mean (μ) of 10 and a standard deviation (σ) of 7, we are asked to calculate probabilities for different scenarios.

(a) To find the proportion of the population less than 18, we need to calculate the cumulative probability up to that value using the standard normal distribution. By standardizing the value of 18 and looking up its corresponding cumulative probability in the standard normal distribution table, we can determine the proportion.

(b) For the probability that a randomly chosen value will be greater than 3, we again need to standardize the value of 3 and find its corresponding cumulative probability in the standard normal distribution table. Since we are looking for values greater than 3, we subtract the cumulative probability from 1 to obtain the probability.

Using the mean and standard deviation provided, along with the standard normal distribution, we can calculate the desired probabilities by finding the corresponding cumulative probabilities and rounding the answers to four decimal places.

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Z-score of Kevin's shoe size compared to the normal population is, 2.5.

How to find comparation of Kevin shoe size to normal population?

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The probability of a hurricane hitting the U.S. coast and being a category 1 hurricane is 0.403, or 40.3%.

The National Oceanic and Atmospheric Administration (NOAA) is a federal agency that is responsible for monitoring and predicting changes in the Earth's environment, including the atmosphere and oceans. One of their main responsibilities is to track and study hurricanes that affect the United States.

According to their data, there have been a total of 290 hurricanes that have hit the U.S. coast between 1851 and 2013. These hurricanes are categorized based on their wind speeds, with categories ranging from 1 to 5.

To create a probability distribution for this data, we need to calculate the probability of each category of hurricane occurring. We can do this by dividing the number of hurricanes in each category by the total number of hurricanes.

Category 1 hurricanes: 117/290 = 0.403
Category 2 hurricanes: 76/290 = 0.262
Category 3 hurricanes: 76/290 = 0.262
Category 4 hurricanes: 18/290 = 0.062
Category 5 hurricanes: 3/290 = 0.010

Therefore, the probability of a hurricane hitting the U.S. coast and being a category 1 hurricane is 0.403, or 40.3%. This means that out of all the hurricanes that have hit the U.S. coast, about 40% of them were category 1 hurricanes. It is important to note that this probability distribution is based on historical data and may not accurately predict the likelihood of future hurricanes.

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Answer:

7.27 is the irrational number

Step-by-step explanation:

7.27 can not turn into a fraction because it keeps on repeating

There are no Irrational numbers in the list.

We have a set of numbers - 7.27, 5, 9215, 2196.

We have to circle out the Irrational ones.

Irrational numbers are the set of real numbers that cannot be expressed in the form of a fraction - p/q where p and q are integers.

According to the question, we have -

7.27, 5, 9215, 2196

Now -

7.27 =  \($\frac{727}{100}\)  → It is Rational.

5 = \($\frac{5}{1}\) → It is Rational.

9215 = \($\frac{9215}{1}\) → It is Rational.

9215 = \($\frac{2196}{1}\) → It is Rational.

All the numbers are Rational as they can be expressed in the form of p/q.

Hence, there are no Irrational numbers in the list.

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Answer:  A

Step-by-step explanation:

When multiplying: Numbers multiply with numbers and for the x's, add the exponents

If there is no exponent, you can assume an imaginary 1 is the exponent

2x⁴ (3x³ − x² + 4x)

= 6x⁷ -2x⁶ + 8x⁵

Answer:

A. \(6x^{7} - 2x^{6} + 8x^{5}\)

Label the parts of the expression:

Outside the parentheses = \(2x^{4}\)

Inside parentheses = \(3x^{3} -x^{2} + 4x\)

You must distribute what is outside the parentheses with all the values inside the parentheses. Distribution means that you multiply what is outside the parentheses with each value inside the parentheses

\(2x^{4}\) × \(3x^{3}\)

\(2x^{4}\) × \(-x^{2}\)

\(2x^{4}\) × \(4x\)

First, multiply the whole numbers of each value before the variables

2 x 3 = 6

2 x -1 = -2

2 x 4 = 8

Now you have:

6\(x^{4}x^{3}\)

-2\(x^{4}x^{2}\)

8\(x^{4} x\)

When you multiply exponents together, you multiply the bases as normal and add the exponents together

\(6x^{4+3}\) = \(6x^{7}\)

\(-2x^{4+2}\) = \(-2x^{6}\)

\(8x^{4+1}\) = \(8x^{5}\)

Put the numbers given above into an expression:

\(6x^{7} -2x^{6} +8x^{5}\)

distribution

variable

like exponents

Answer: 12:2, 18:3, 24:4

Step-by-step explanation: You can multiply 6 by 2, 3, and 4 because the graph has 4 columns. Then multiply the top by 2, 3, and 4,

The length of the segment PS is 100 units.

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse.

From the given image we can see that the segments PT, PQ, and TQ form a right- angled triangle PQT.

Applying Pythagorean theorem to this triangle we have:

PQ^2 + TQ^2 = PT^2

(45)^2 + (TQ)^2 = (53)^2

2025 +  (TQ)^2 = 2809

(TQ)^2 = 2809 - 2025

(TQ)^2 = 784

TQ = 28

Similarly, segments PR, PS, and SR form a right-angled triangle PRS, where TQ = SR = 28 and PR = 96.

Applying Pythagorean theorem to this triangle we have:

PR^2 + SR^2 = PS^2

(96)^2 + (28)^2 = (PS)^2

(PS)^2 = 9216 + 784

(PS)^2 = 10000

PS = 100

Hence, the length of the segment PS is 100 units.

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An equation is formed when two equal expressions. The time the same pump will take to empty a tank containing 108,000 gallons of water is 4.5 hours.

When two equal expressions are added together with the aid of the equal sign "=," an equation is created.

Given that the time it takes a water pump to empty a tank directly correlates with the tank's capacity. Consequently, the relationship can be expressed as,

V ∝ T

V = kT

Substituting the volume and time in the equation,

60,000 gallons = 2.5 hours × k

Solving the equation for k,

k = 60,000 gallons / 2.5 hours

k = 24,000 gallons per hour

Now, the equation for the relationship can be written as,

V = 24,000 gallons per hour × T

Now, the time the same pump will take to empty a tank containing 108,000 gallons of water is,

V = 24,000 gallons per hour × T

108,000 gallons = 24,000 gallons per hour × T

108,000 gallons / 24,000 gallons per hour = T

T = 4.5 hours

Hence, the time the same pump will take to empty a tank containing 108,000 gallons of water is 4.5 hours.

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Answer:

b/c

Step-by-step explanation:

a/b is the equivalent of b/c, sorry if this is incorrect.

Answer:

Your already right on both of them lol

Step-by-step explanation:

Pls brainliest thx! :D

Answer:

you're right

Step-by-step explanation:

it's b, and a!

To find the critical points at which profit is maximized given the total revenue TR = 4700 - 302 and total cost TC = 320/10,500, we need to compute the marginal revenue and marginal cost, equate MR = MC to find the optimal quantity Q∗, verify if Q∗ is a relative maximum point, and compute the maximum profit level (π) by evaluating π∗ = 9(π(Q∗)).

Marginal Revenue (MR) is the derivative of the total revenue function with respect to quantity (Q). In this case, MR = dTR/dQ. By taking the derivative of TR = 4700 - 302 with respect to Q, we can find the expression for MR.

Marginal Cost (MC) is the derivative of the total cost function with respect to quantity (Q). In this case, MC = dTC/dQ. By taking the derivative of TC = 320/10,500 with respect to Q, we can find the expression for MC.

To find the optimal quantity Q∗, we equate MR and MC by setting MR = MC and solve for Q. This is because profit is maximized when MR equals MC.

Once we have found Q∗, we need to verify if it is a relative maximum point. This can be done by checking the second derivative of the profit function and determining if it is negative at Q∗. If the second derivative is negative, it confirms that Q∗ is a relative maximum point.

Finally, to compute the maximum profit level (π∗), we evaluate π(Q∗) by substituting Q∗ into the profit function. In this case, we can multiply the value of π(Q∗) by 9 to obtain the maximum profit level (π∗).

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As the interval becomes infinitesimally small, the average rate of change approaches the instantaneous rate of change. Therefore, the approximation is reasonable.

(a) To determine the average rate of change of f(x) from x = -1 to x = 2, we need to calculate the difference in the function values at these points and divide it by the difference in x-values.

f(x) = 3 - x

f(-1) = 3 - (-1) = 4

f(2) = 3 - 2 = 1

The difference in function values is 4 - 1 = 3, and the difference in x-values is 2 - (-1) = 3.

Average rate of change = (Change in y) / (Change in x) = 3/3 = 1

(b) To determine the average rate of change of f(x) from x = a - 0.001 to x = a, we need to evaluate the function at these points and calculate the difference in function values divided by the difference in x-values.

f(x) = 3 - x

f(a - 0.001) = 3 - (a - 0.001) = 3 - a + 0.001

f(a) = 3 - a

The difference in function values is (3 - a + 0.001) - (3 - a) = 0.001, and the difference in x-values is 0.001.

Average rate of change = (Change in y) / (Change in x) = 0.001 / 0.001 = 1

(c) Using the result from (b), the average rate of change of f(x) from x = 1.999 to x = 2 is also 1.

(d) The average rate of change of f(x) from x = 1.999 to x = 2 approximates the instantaneous rate of change at x = 2 because the interval is very small (0.001) and approaches zero.

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Questions that require responses at fixed intervals along a scale of answers are called scale questions.

Closed-ended questions, such as the Likert Scale, are one of the most popular methods for gauging public opinion. To gauge people's opinions, attitudes, and beliefs, they employ psychometric testing. Statements are used in the questions, and respondents are asked how much they agree or disagree with each assertion. Likert Scale questions typically have a scale from 0 to 10, while shorter scales are also conceivable.

Every sort of research has benefits and drawbacks, and this particular question type has both in spades. The fundamental benefit of Likert Scale questions is that they follow a standard way of data collection, making them simple to comprehend.

Hence, according to the definition questions that require responses at fixed intervals along a scale of answers are called scale questions.

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