Write the absolute value equation that is represented by the graph ​

One possible set of positive integers that satisfies the given condition is the set of powers of 2, i.e., {2, 4, 8, 16, 32, ...}.

To see why this set works, note that any two distinct powers of 2 have a different binary representation, differing in at least one bit. This means that their sum will have one more "1" bit in its binary representation than either of the two numbers being added.

Since any prime number greater than 2 is odd, it follows that the sum of any two distinct powers of 2 will have an even number of distinct prime factors, namely the powers of 2 that appear in its binary representation.

First, let's note that every positive integer can be uniquely expressed as a product of prime powers, e.g., 36 = 2^2 * 3^2. The prime factors of an integer are the primes that appear in its prime factorization, e.g., the prime factors of 36 are 2 and 3.

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The median, mean, range and mode will be 6, 5.4, 9 and 7.

What is median?

The median is the middle number in the data set when the data set is written from least to greatest.

The median is the number in the middle when arranged in an ascending order. The numbers will be:

0, 3, 4, 6, 6, 7, 7, 7, 9.

The median is 6.

The range is the difference between the highest and lowest number which is: = 9 - 0 = 9

The mode is the number that appears most which is 7.

The mean will be the average which will be:

= (0 + 3 + 4 + 6 + 6 + 7 + 7 + 7 + 9) / 9.

= 49/9

= 5.4

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The value of the variable x will be {0, pi/2, pi}. Then the correct option is B.

The trigonometric equation is given below.

\(tan (3\pi/4 - 2x) = - 1\)

We know that the value of tan 3π / 3 is negative one. Then the equation will be

\(tan (3\pi/4 - 2x) = tan 3\pi/4\)

Apply the inverse of the tangent on both sides, then the equation will be

\((3\pi/4 - 2x) = 3\pi/4, -\pi / 4\)

        - 2x = 0, -π

          2x = 0, π

            x = 0, π/2

Then the value of the variable x will be {0, pi/2, pi}.

Then the correct option is B.

Trigonometry is a mathematical field concerned with the inter-dependency of the angles and sides of triangles. This incorporates ideas like sine, cosine, tangent, and the inverse variants of these functions.

Trigonometry finds extensive applications in domains such as physics, engineering, and navigation.

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The Complete Question

Which values represent solutions to the equation? tan(3pi/4 - 2x) = -1, where x ∈ [0,pi]

A) {0, pi}

B) {0, pi/2, pi}

C) {0, pi, 2pi}

D) {0, pi/2, pi ⋅ 3pi/2}

Answer:its 1.2

Step-by-step explanation:

Answer:

1.2

Step-by-step explanation:

took the quiz in edg

This resulted in a probability of 1.0, or 100%, meaning that the puzzle was solved every time it was attempted. This indicates that the probability of successfully solving the puzzle is quite high.

Random Digits Used: 0.9, 0.3, 0.3

Repetition 1:

Successful Attempt (1)

Repetition 2:

Successful Attempt (1)

Repetition 3:

Successful Attempt (1)

Estimated Probability: 3/3 = 1.0

In this experiment, the probability of successfully solving a puzzle was estimated. Three repetitions of the simulation were completed, each using different random digits. The first repetition used the random digit 0.9, the second used 0.3, and the third used 0.3 again. For each repetition, the outcome was successful, meaning the puzzle was solved. This resulted in a probability of 1.0, or 100%, meaning that the puzzle was solved every time it was attempted. This indicates that the probability of successfully solving the puzzle is quite high.

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As per the given question the median size of a new house and the values of different parts of the question will be as follows:

(a) We must locate the period when the rate of change is the smallest in order to establish the period during which the median house size increased the least quickly. Finding the derivative of the following equation will provide us with the rate of change of the house size with respect to time, which we can utilize to do this.

derivative of the function H(x) = 0.359x3 - 15.198x2 + 221.738x + 862.514 given by the equation for the rate of change of the house size with respect to time as

H'(x) = 3 (0.359) x2 - 2 (15.198) x + 221.738

(b) By setting the derivative to 0 and figuring out x, we may determine the moment at which the rate of change is the least. We have x = 3.904 as a result. The time where the rate of change is the smallest is 3.904 years after 1980, or 1984.904, because x denotes the number of years after 1980. This roughly corresponds to 1984, making 1984 the year in which the median house size increased at the slowest rate.

We may enter the value of x into the previous equation to obtain H(1984) = 0.359 x \((1984)^{3}\) - 15.198 x \((1984)^{2}\) + 221.738 ( 984) + 862.514

= 2,532,358 sq ft. as the comparable house size at this time. In 1984, this was the size of the typical home.

We may enter the value of x into the derivative equation to obtain H'(1984) = 3 (0.359) x \((1984)^{2}\) - 2 (15.198 x 1984 + 221.738) = 606.696 sq ft per year, which corresponds to the rate of growth in house size. This represents the median house size's rate of change during the slowest period of growth.

(c) The biggest rate of change must be found in order to pinpoint the period in which the median house size increased most quickly. Finding the derivative equation's greatest value will help us do this. To accomplish this, one can solve for x while setting the derivative equal to 0, then determine the values of x that are either more or less than the answers we obtained. The derivative equation can then be used to solve for the maximum value using these x values.

Using the quadratic formula to solve for x. The quadratic formula is given by x =  \(\frac{(-b ± √(b^2 - 4ac))}{2a}\), where a, b, and c are the coefficients of the quadratic equation. Here, a = 3 (0.359) = 1.077, b = -2 (15.198) = -30.396, and c = 221.738. Putting these values into the quadratic formula gives us x = \(\frac{(30.396 ± √(30.396^2 - 4 (1.077 X 221.738))}{2 (1.077)}\)

=  \(\frac{(30.396 ± √(928.822 - 948.512))}{2.154}\)

=  \(\frac{(30.396 ± √(-19.690))}{2.154}\)

=  \(\frac{15.198}{2.154}\)

= 7.096.

The derivative equation will have a maximum or lowest value at the value of x that we just discovered because it is a quadratic. We can enter this value of x into the derivative equation to obtain H'(7.096) = 3 x 0 and use this result to determine the derivative equation's maximum value.

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Answer:

No

Step-by-step explanation:

2-3= -1

3-2 = 1

a

n

​

=−0,06n+24

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The coordinates in the solution to the systems of inequalities graphically is (6, 2)

From the question, we have the following parameters that can be used in our computation:

x + y > 3

x - 3y < 2

Next, we plot the graph of the system of the inequalities

See attachment for the graph

From the graph, we have solution to the system to be the shaded region

The coordinates in the solution to the systems of inequalities graphically is (6, 2)

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The car gets 46 miles per gallon in the city.

Divide total miles driven in th city by miles per gallon to find total number of gallons of gas used:

10,000 miles / 46 miles per gallon = 217.3913 gallons of gas used.

Now multiply gallons used by price per gallon:

217.3913 x $1.75 = $380.43 per year

Answer:

(0,-1); maximum

Step-by-step explanation:

Answer:

Step-by-step explanation:

3/5 - 2/5 = (3-2)/5 = 1/5

7/10 - 3/10 = (7-3)/10 = 4/10 = 2/5

Velocity is not constant over time and can be influenced by a variety of factors. Changes in velocity can have implications for the relationship between changes in the money supply and the price level, highlighting the complexity of monetary dynamics in an economy.

According to the quantity equation (MV = PQ), changes in the money supply (M) will lead directly to changes in the price level (P) if velocity (V) and real GDP (Q) remain constant. However, velocity is not necessarily constant over time and can be influenced by various factors.

Velocity represents the rate at which money circulates in the economy, indicating how quickly money is used to facilitate transactions. It is influenced by factors such as changes in consumer and business behavior, technological advancements, financial innovation, and shifts in confidence and trust in the economy.

Changes in velocity can occur due to several reasons. For example:

Changes in Transaction Patterns: Shifts in consumer preferences or business practices can alter the frequency and speed of transactions, affecting how money circulates and influencing velocity.

Financial Innovation: Advancements in payment systems, such as the rise of electronic transactions, online banking, or mobile payments, can potentially impact the velocity of money by facilitating faster and more efficient transactions.

Confidence and Economic Stability: Changes in economic conditions, inflation expectations, or financial stability can influence people's willingness to hold money, affecting velocity.

Monetary and Fiscal Policies: Changes in monetary policy, such as interest rate adjustments or changes in the money supply, can indirectly affect velocity by influencing borrowing and spending behavior.

While changes in velocity can occur independently of changes in the money supply, they can also be related. For instance, if the money supply increases without a corresponding increase in the demand for money (velocity decreases), it can put upward pressure on prices. On the other hand, if velocity increases due to changes in transaction patterns or increased economic activity, it can offset the impact of changes in the money supply on prices.

Overall, velocity is not constant over time and can be influenced by a variety of factors. Changes in velocity can have implications for the relationship between changes in the money supply and the price level, highlighting the complexity of monetary dynamics in an economy.

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Answer:

See attached

Step-by-step explanation:

Given the numbers 1,2,3,4 and 5

Let O be the event that the number is Odd

Let E be the event that the number is Prime

Then the intersection of Odd and Prime Numbers: \(O \cap P =\{3,5\}\)

Since 4 is neither odd nor prime, we place it outside of the two circles.

See the attached diagram for the required Venn diagram.

..

SOLUTION

Given:

Let test one point from each of the graphs in the given equation;

For the first graph:

For the second graph:

THE SECOND GRAPH IS CORRECT.

Answer:

The equation of the tangent line to the curve sin(x+y) = 4x - 4y at the point (π,π) is y = (-4/5)x + (8/5) + π.

Step-by-step explanation:

o find the equation of the tangent line to the curve sin(x+y) = 4x - 4y at the point (π,π) using implicit differentiation, we can follow these steps:

Differentiate both sides of the equation with respect to x:

cos(x+y) * (1 + dy/dx) = 4 - 4dy/dx

Simplify by grouping the terms with dy/dx on one side and the rest on the other side:

cos(x+y) * (1 + dy/dx) + 4dy/dx = 4

Substitute x = π and y = π, since we want to find the equation of the tangent line at the point (π,π):

cos(2π) * (1 + dy/dx) + 4dy/dx = 4

Simplify:

-5dy/dx = 4 - cos(2π)

dy/dx = -4/5

Use the point-slope form of the equation of a line to write the equation of the tangent line:

y - π = (-4/5)(x - π)

Simplify:

y = (-4/5)x + (8/5) + π

The equation of the tangent line to the curve sin(x+y) = 4x - 4y at the point (π,π) is y = (-4/5)x + (8/5) + π.

Answer:

8\(\sqrt[3]{2}\)

Step-by-step explanation:

The cube root of -2 to the power of 10 is;

(-2)^10=2^10

2^10=(2^3)*(2^3)*(2^3)*2

You can factor out 2^3=8 of the cube root

So you get 8 times the cube root of 2

Answer:

4b=y-10

Step-by-step explanation:

Answer:

20 +(x+15.5)

Step-by-step explanation:

For the function y=5 cos {x-(π/6)}-1

a) To find the average rate of change, evaluate the function at x = (2π)/3 and x = π/3, and then take the difference between the two values and divide by the difference between the two x-values:

Average rate of change = (y(2π/3) - y(π/3)) / ((2π/3) - (π/3))

First, find y(2π/3) and y(π/3).

y(2π/3) = 5 cos((2π/3) - (π/6)) - 1 = 5 cos(5π/6) - 1 = -5/2 - 1 = -7/2

y(π/3) = 5 cos((π/3) - (π/6)) - 1 = 5 cos(π/6) - 1 = 5/2 - 1 = 3/2

Plugging these values into the formula:

Average rate of change = ((-7/2) - (3/2)) / ((2π/3) - (π/3))

= -5 / (π/3)

= -15/π

Therefore, the average rate of change from x = π/3 to x = (2π)/3 is -15/π.

b) To find the instantaneous rate of change at x = π/2, take the derivative of the function and evaluate it at x = π/2.

y = 5 cos(x - (π/6)) - 1

y' = -5 sin(x - (π/6))

Plugging in x = π/2:

y'(π/2) = -5 sin(π/2 - (π/6)) = -5 sin(π/3) = -5 (√3)/2

Rounding this to the nearest tenth:

y'(π/2) ≈ -4.3

Therefore, the instantaneous rate of change at x = π/2 is approximately -4.3.

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Image transcribed:

4) Consider the function y=5 cos {x-(π/6)}-1

a) Find, in exact form, the average rate of change from x= π/3 to x=(2π)/3  (A-3 marks)

b) Find, to the nearest tenth, the instantaneous rate of change at x=π/2 (A-4 marks) 2

The appropriate hypotheses for this test are: H0: There is no difference in the distribution of responses. Ha: There is a difference in the distribution of responses.

The chosen hypotheses are based on the objective of the investigation, which is to determine if there is convincing evidence that the distribution of responses about eating the potato salad differs between employees who are sick and those who are not sick.

The null hypothesis (H0) assumes that there is no difference in the distribution of responses about eating the potato salad between the sick and non-sick employees. This means that the proportion of employees who ate the potato salad would be the same in both groups, and any observed difference in the distribution of responses is due to random chance or factors unrelated to being sick or not sick.

On the other hand, the alternative hypothesis (Ha) proposes that there is a difference in the distribution of responses about eating the potato salad between the sick and non-sick employees. This suggests that the proportion of employees who ate the potato salad would be significantly different in the two groups, indicating a possible association between consuming the potato salad and getting sick.

By formulating these hypotheses, the investigation aims to evaluate whether the data provides convincing evidence to reject the null hypothesis in favor of the alternative hypothesis, indicating a meaningful relationship between eating the potato salad and falling sick.

Therefore, the correct answer is:

H0: There is no difference in the distribution of responses about eating the potato salad among those who are and are not sick.

Ha: There is a difference in the distribution of responses about eating the potato salad among those who are and are not sick.

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Galaxy distance is 118 mpc.

Given:

Suppose a distant galaxy has a recessional velocity of 8254 km/s. What is its distance given that the hubble constant is 70 km/s/mpc.

According to hubble's law:

v = \(H_0\\\) * D

where

v = velocity = 8254

\(H_0\\\) = hubble constant = 70

D = v/\(H_0\\\)

= 8254/70

= 4127/35

= 117.91

≈ 118 mpc.

Therefore Galaxy distance is 118 mpc.

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Answer:

6

Step-by-step explanation:

Since the x coordinates are the same, you only need to find the difference between the y coordinates. -2-(-8)=-2+8=6. Hope this helps!

Answer:

The model shows that there are 9 pieces that are each ft long.​. The model shows that there are 9 pieces that are - 1.

Answer:

5005

Step-by-step explanation:

6 C 15

(6, 15)

15! / (6! x 9!)

The answer is 5005

C is just a way to say the order the books are picked in is random and ! means factorial. Factorial is when you multiply all the previous numbers up to the number it is. For example, 5! = 1 x 2 x 3 x 4 x 5 and 2! = 1 x 2

Answer:You'll get a detailed solution from a subject matter expert that helps you learn core concepts. Question: Alvin paddled for 3 hours with a 7 -km/h current to reach a campsite. The return trip against the same current took 10 hours. Find the speed of the boat in still water. Alvin paddled for 3 hours with a 7 -km/h current to reach a campsite.

Step-by-step explanation:

Answer:

19

Step-by-step explanation:

Answer:

19

Step-by-step explanation:

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Answer:

40000ftMSL

Step-by-step explanation:

We know that airspeed is measured using a pilot tube

And the air pressure is a function of density given as

Pressure= 1/2 xdensityx V²

So at 40,000ftMSL

Is this is replaced for V in the equation then the density of air will be 1/4 that of sea level

So since we are deriving velocity from pressure and pressure is 1/4 so the velocity Will be half of its pressure since velocity is squared from The equation above