Write the sentence as an absolute value inequality, then solve the inequality.
Half of a number n is at most 5 units from 14.

Answer:

Standard form: 62,080,126

Word form: Sixty-two million, eighty thousand, one hundred twenty-six

Expanded form: 60,000,000 + 2,000,000 + 80,000 + 100 + 20 + 6

Answer:

fortnite

Step-by-step explanation:

fo+rtni+te=fortnite

Answer:

3.75

Step-by-step explanation:

1.5 equals 30 ft so x2 equals 60 then 15 is half of 20 so half of 1.5 in is .75 so 3 plus .75

Answer:

srry i need points

Step-by-step explanation:

Answer:k

Step-by-step explanation:

k

The exponential model that calculates the concentration of bacteria after x weeks can be represented by the equation B(x) = 2.1 million * (3^x), the concentration after 1.6 weeks would be approximately 14.87 million bacteria per milliliter.

This equation assumes that the concentration triples each week, starting from the initial concentration of 2.1 million bacteria per milliliter.

To estimate the concentration after 1.6 weeks, we can substitute x = 1.6 into the exponential model. B(1.6) = 2.1 million * (3^1.6) ≈ 14.87 million bacteria per milliliter. Therefore, after 1.6 weeks, the estimated concentration of bacteria in the river would be approximately 14.87 million bacteria per milliliter.

The exponential model B(x) = 2.1 million * (3^x) represents the concentration of bacteria after x weeks, where the concentration triples each week. By substituting x = 1.6 into the equation, we estimate that the concentration after 1.6 weeks would be approximately 14.87 million bacteria per milliliter.

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To determine the marginal and conditional probability distributions across states, we examine the given joint probability distribution. Let's denote the endowment in period t as yt and in period t+1 as yt+1.

(a) The marginal probability distribution of yt represents the probabilities of different endowment values in period t. From the joint probability distribution, we can see that:

\(Pr(yt=L) = Pr(yt+1=L, yt=L) + Pr(yt+1=L, yt=H) = 0.2 + 0.1 = 0.3Pr(yt=H) = Pr(yt+1=H, yt=L) + Pr(yt+1=H, yt=H) = 0.1 + 0.5 = 0.6\)

The conditional probability distribution represents the probabilities of different endowment values in period t+1 given the endowment value in period t. From the joint probability distribution, we have:

Pr(yt+1=L | yt=L) = 0.2/0.3 ≈ 0.667

Pr(yt+1=H | yt=L) = 0.1/0.3 ≈ 0.333

Pr(yt+1=L | yt=H) = 0.1/0.6 ≈ 0.167

Pr(yt+1=H | yt=H) = 0.5/0.6 ≈ 0.833

(b) The price of a one-period bond represents the expected present value of receiving one unit of the endowment in the next period, given the current state. In period one, the price of a one-period bond for each possible state is given by:

\(Price(y1=L) = Pr(y2=L | y1=L) * 1 + Pr(y2=H | y1=L) * 1 = 0.667 + 0.333 = 1Price(y1=H) = Pr(y2=L | y1=H) * 1 + Pr(y2=H | y1=H) * 1 = 0.167 + 0.833 = 1\)

(c) The price of a ten-period bond represents the expected present value of receiving ten units of the endowment in the next ten periods, given the current state. In period one, the price of a ten-period bond for each possible state is given by:

\(Price(y1=L) = Pr(y2=L | y1=L) * 1 + Pr(y2=H | y1=L) * 2 + ... + Pr(y11=L | y1=L) * 10 = 0.667 + 0.667 + ... + 0.667 = 6.67Price(y1=H) = Pr(y2=L | y1=H) * 1 + Pr(y2=H | y1=H) * 2 + ... + Pr(y11=L | y1=H) * 10 = 0.167 + 0.167 + ... + 0.167 = 1.67\)

(d) The unconditional mean price for the one-year bond is the average of the prices for each possible state in period one:

Unconditional mean price for one-year bond =

(Price(y1=L) + Price(y1=H)) / 2 = (1 + 1) / 2 = 1 The unconditional mean price for the ten-year bond is the average of the prices for each possible state in period one:

Unconditional mean price for ten-year bond = (Price(y1=L) + Price(y1=H)) / 2 = (6.67 +

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The reasonable class interval for a data set with a maximum value of 70 and a minimum value of 1, using 7 classes, would be option b) 10.

The class interval represents the range of values that will be included in each group or class when organizing the data.

To determine a reasonable class interval, we need to consider the range of the data, the number of classes desired, and the level of detail needed. In this case, the range of the data is 70-1=69, and we want to use 7 classes.

Dividing the range by the number of classes (69/7) gives us approximately 10. Therefore, a class interval of 10 is a reasonable choice for summarizing this data set.

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A data set has a mean of 177 and a standard deviation of 20. 11.3% is the coefficient of variance for this collection of data.

The ratio of a data set's standard deviation to its mean, stated as a percentage, is represented by a coefficient of variation (CV), a dimensional measure of variability. It is a practical tool for contrasting the relative variance of two or more data groups with various means or measurement units.

We divide the usual level deviation by the mean, multiply the result by 100, and that number is the coefficient of variation. The coefficient in variation can be computed as follows in this situation: Using the formula CV = (standard deviation / mean) x 100, (20 / 177) x 100, and 11.3%

A low coefficient for variation means that the mean is a good indicator of the data and that the set of data has low relative variability. On the other hand, a high coefficient for variation shows substantial relative variability, which could point to the need for additional research or alternate metrics of central tendency.

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Answer

In the figure, angles C and D are a  

✔ linear pair

Therefore, angle C must measure  

✔ 56°

Step-by-step explanation:

In the given figure, the C and D are considered to be linear pair and the measure of the c should be 56 degrees.

It should be created at the time when the two lines should be intersected with each other at the single point. Also if they are adjacent to each other

Moreover, the sum of the angles for the linear pair should be 180 degrees

Since angle D = 124 degrees

So here angle C should be

= 180 - 124

= 56 degrees

Hence, In the given figure, the C and D are considered to be linear pair and the measure of the c should be 56 degrees.

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Solution:

Simplify the equation and solve.

The solution to the problem is 2281/2630.

Answer:

40%

Step-by-step explanation:

Answer:

27.5

Step-by-step explanation:

The given expression represents a Riemann sum, which approximates the integral of a function over a specific interval. By taking the limit as \(n\) approaches infinity, we can find the exact value of the integral.

The given expression can be rewritten as \(\lim _{n \rightarrow \infty} \sum_{i=1}^{n}\left(1+\frac{4 i}{n}\right)^{3}\left(\frac{5}{n}\right)\). This represents a Riemann sum with \(n\) terms, where each term corresponds to a rectangle of width \(\frac{1}{n}\) and height \(\left(1+\frac{4 i}{n}\right)^{3}\). Taking the limit as \(n\) approaches infinity converts the Riemann sum into an integral. The formula for the sum of \(n\) terms in this case would be \(\int_{0}^{1} \left(1+4x\right)^{3} \, dx\). Evaluating this integral will give us the exact value of the limit.

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Answer:

y = -3.325x + 88.5

Step-by-step explanation:

The equation for slope-intercept form is y = mx + b

m = slope

b = y intercept value

Answer: I am pretty sure the answer is A, 120.

Step-by-step explanation:

Once we have categorized an object, our memory of the object increasingly resembles the category is B) prototype. This means that when we categorize an object, our memory of it begins to resemble the prototype or typical example of that category. For example, if we categorize a bird as a robin, our memory of the bird will increasingly resemble the characteristics of a typical robin.

This happens because our brain uses prototypes as a shortcut to process information and make sense of the world around us. We use prototypes to quickly identify objects and make assumptions about their characteristics based on their category.

our memory of an object after categorization is influenced by the prototype of the category. This helps us to quickly process and make sense of information, but it can also lead to errors and biases in our thinking.


A prototype is a mental image or best example of a category. When we categorize an object, our memory of the object increasingly resembles the prototype because we tend to recall the most representative or typical example of the category.

Once we categorize an object, our memory of the object becomes more like the prototype, which is the best example of the category. This is because we tend to remember the most representative or typical examples of a category.

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Answer:

-5

Step-by-step explanation:

hope it works out for you

The inverse function of f is f⁻¹(x) = 1/3x² + 3 and g(x) is not an inverse of f(x)

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

f(x) = √(3x − 9)

g(x) = 3x² − 9.

To determine the inverse function of f, we start by making the function f(x) as an equation

So, we have

y = √(3x − 9)

Swap variables x and y

x = √(3y − 9)

Square both sides

This gives

3y - 9 = x²

So, we have

3y = x² + 9

Divide both sides by 3

y = 1/3x² + 3

So, we have

f⁻¹(x) = 1/3x² + 3

In (a), we have

Inverse of f(x), f⁻¹(x) = 1/3x² + 3

Also, we have

g(x) = 3x² − 9

Both equations when compared, are not equal

Hence, the functions are not inverse functions

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Complete question

f(x) = √(3x − 9) g(x) = 3x² − 9.

(a) What is the inverse of function f ?

(b) Is f an inverse of g? Show your work algebraically and explain your answer

A household with a credit score of 525 will pay $9,256.00 more than a household with a credit score of 675.

According to my findings, a household with a credit score of 525 will pay $9,256.00 more compared to a household with a credit score of 675.

Mortgage lenders typically charge higher interest rates to individuals with lower credit scores than to those with higher credit scores.

So, if you have a poor credit score, you'll have to pay more for your mortgage than if you had a strong credit score.

You can use the following data to calculate how much more a household with a credit score of 525 will pay compared to a household with a credit score of 675.

The total cost of a $200,000, 30-year fixed-rate mortgage with a 525 credit score and a 4.5% interest rate is $446,668.

The total cost of a $200,000, 30-year fixed-rate mortgage with a 675 credit score and a 3.1% interest rate is $437,412.A household with a credit score of 525 will pay $9,256.00 more than a household with a credit score of 675.

The answer is $9,256.00.

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Answer:

A

Step-by-step explanation:

the other options have a common difference

Answer:

A is not arithmetic series

Step-by-step explanation:

In B,C and D there is arithmetic series as a2-a1=a3-a2

In A. there is no such series.....

Answer:

Look below.

Step-by-step explanation:

Bill: 5, 10, 15, 20, 25, 30...

Daughter: 3, 6, 9, 12, 15...

And so on.

Every 5 Bill does, add 3 to the number before in the daughter boxes..

Answer:

43.98 approximately

Step-by-step explanation:

radius = \(\sqrt{ (5 - 12)^{2} + (-4+4)^{2} }\)

          = \(\sqrt{(-7)^{2} + 0^{2} }\)

          = \(\sqrt{49} = 7\)

diameter = 14

Circumference = diameter x pi

                         = 14π = 43.98 approximately

Answer:

33.33

Step-by-step explanation:

Load vs deformation behavior of wet-mix and dry-mix shotcrete with different reinforcement can be summarized as follows:

Load vs Deformation Behavior of Wet-mix Shotcrete:

- Wet-mix shotcrete exhibits a gradual increase in load with deformation.

- The initial stiffness is relatively low, allowing for greater deformation before reaching its peak load.

- Wet-mix shotcrete tends to exhibit more ductile behavior, with a gradual post-peak load decline.

- The reinforcement in wet-mix shotcrete helps in controlling crack propagation and enhancing overall structural integrity.

Load vs Deformation Behavior of Dry-mix Shotcrete:

- Dry-mix shotcrete exhibits a relatively higher initial stiffness, resulting in less deformation before reaching the peak load.

- It typically shows a brittle behavior with a rapid drop in load after reaching the peak.

- The reinforcement in dry-mix shotcrete primarily helps in preventing the formation and propagation of cracks.

When to Use Wet-mix Shotcrete:

- Wet-mix shotcrete is commonly used in underground construction, such as tunnel linings and underground mines.

- It is suitable for applications where greater flexibility and ductility are required, such as seismic zones or areas with ground movement.

When to Use Dry-mix Shotcrete:

- Dry-mix shotcrete is often used in above-ground applications, such as architectural finishes, structural repairs, and protective coatings.

- It is preferred in situations where rapid strength development is required, as it typically achieves higher early strength than wet-mix shotcrete.

- Dry-mix shotcrete can be used in areas where a more rigid and less deformable material is desired, such as in structural elements subjected to high loads.

Therefore, wet-mix and dry-mix shotcrete exhibit different load vs deformation behavior due to their distinct mixing and application methods. Wet-mix shotcrete offers greater ductility and deformation capacity, making it suitable for applications with dynamic loading or ground movement.

On the other hand, dry-mix shotcrete provides higher early strength and is preferred for applications requiring rapid strength development or where rigidity is essential. The choice between wet-mix and dry-mix shotcrete depends on the specific project requirements, structural considerations, and the anticipated loading conditions.

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27 cd

Step-by-step explanation:

(75 cd)(3m)^2 = (x)(5m)^2

x = (75 cd)(9 m^2)/(25 m^2)

= 27 cd

Answer:

26x-1

Step-by-step explanation:

\((10x^{2} -1)+(8x^{2} +8x-8)\)

Solve for exponents

\(10^{2} =100\\8^{2} = 64\)

(100x -1)+(64x+8x-8)

100x-1+74x-8

100x-74x= 26x

-8+7=-1

26x-1

Hope this helps

We need to know about domain and range of a graph to solve this problem. The domain is (-∞,5) and the range is (-∞,2).

The domain of a function is the input values that the function can take. The range is the set of values that can be the possible output of the function. The domain of a graph are the values that are on the x-axis and the range is on the y-axis. The arrow means that the graph goes on till infinity, a solid sphere means that the graph ends at that point and the ending point is included in the function, a hollow sphere means the graph ends at that point and the ending point is not included in the function. In the graph in the question, along x-axis the values on left goes on till negative infinity and on right the domain is open at 5. For range along y-axis, the range on the left side goes on till negative infinity and on the right it is open at 2.

Therefore we see that the domain of the graph is (-∞,5) and the range is (-∞,2).

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a) after 30 minutes, they will 12.5 m apart

b)  25  is the distance between the boats changing 30 minutes after they leave port

The direction of movement of both boats forms a right angle triangle. The distance travelled due south and due east by both boats represents the legs of the triangle. Their distance apart after t hours represents the hypotenuse of the right angle triangle.

Let x represent the length the shorter leg(west) of the right angle triangle.

Let y represent the length the longer leg(south) of the right angle triangle.

Let z represent the hypotenuse.

Applying Pythagoras theorem

Hypotenuse² = opposite side² + adjacent side²

Therefore

z² = x² + y²

 = 20^2+15^2

 z = 25

but after 30 minutes one travels 10mph

and another 7.5mph

then

z= 12.5

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