John found a pair of sneakers for $68. If sales tax is 6%, what is the total amount he will have to pay for the shoes.

Answer:

3rd one

Step-by-step explanation:

it is the only one with a function and a straight line

Answer:

A,D

Step-by-step explanation:

The given sentence "1024 is the smallest four-digit number that is a perfect square" is true because it is the square of 32.

A perfect square is a number that is the product of two equal integers. It's the product of an integer multiplied by itself. A perfect square is a number that can be expressed as the product of a number and itself. For example, 9, 16, 25, and 36 are perfect squares.

It follows that the square root of a perfect square is a whole number because the product of two equal integers is an integer.

Identify the range of four-digit numbers. Four-digit numbers are those that range from 1000 to 9999.

To check if 1024 is the smallest four-digit perfect square, we should examine whether the smallest perfect square between 1000 and 9999 is 1024. If we square 32, we get 1024, which means that 1024 is a perfect square.

As a result, the statement "1024 is the smallest four-digit number that is a perfect square" is true.

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Answer:

8 and 6

Step-by-step explanation:

If you use x for the first number, and y for the second, you get equations of 3x+5y=54 and x-2=y.

You can substitute the second equation into the first one to solve it. This gives 3x+5(x-2)=54.

The brackets can be expanded to 3x+5x-10=54. Collecting like terms makes it 8x-10=54.

Next, we add 10 to both sides. This gives 8x=64.

From there, we isolate the x by dividing both sides by 8, giving x=8.

To work out the second number, we can sub 8 for x in either equation (I'm using the second one as it's simpler).

This comes to y=8-2, therefore y=6.

**This content is simultaneous equations, which you may wish to revise. I'm always happy to help!

Step-by-step explanation:

we assume day and night are equally long.

and the mouse will start at night of day 1.

then, on day 2, it will first retreat 2 meters (during daylight) and then advance 14 meters (at night).

so, on every full day, the mouse will effectively advance 12 meters (-2 + 14 = 12).

with a starting value of 14 (the first night).

so, we are getting an arithmetic sequence

an = an-1 + c

c = 12 in our case.

a1 = 14

a2 = a1 + 12 = 14+12 = 26

a3 = a2 + 12 = a1 + 12 + 12 = 14 + 2×12 = 38

an = a1 + (n-1)×12 = 14 + 12(n-1)

at what n will it reach 86 ?

86 = 14 + 12(n-1) = 14 + 12n - 12 = 2 + 12n

84 = 12n

n = 7

so, on the 7th day the mouse will reach the surface (if we truly count the first starting night day 1 - this is up to your teacher, but I would).

To prove \(a^{0} = 1\)

Let the first series be  \(a^{1} = a\)

Let the second series be \(a^{2} = a^{2}\)

Let the third series be  \(a^{3} = a^{3}\)    

To find the value of  \(a^{0} = 1\)

Series is a description of the operation of adding infinitely many quantities, one at a time, to a given starting quantity.

By examining the above three series it is found that the product of all the three series differ by 'a' or they have a common difference in value and it can be elaborating the above series:

a , a^2 , a^3 (These are all the values ​​of the above series and  they differ by 'a' which means that series is in A.P)

Therefore the value just before 'a' will be 1 because,

\(a^{0} = 1\)

\(a^{1} = a\)

\(a^{2} = a * a\)

\(a^{3} = a * a^{2}\)

Let;

First expression is X = \(a, a^{2}, a^{3}\)

as we know

Number of terms = X + (Number of terms-1) d

where, X= first term and d= common difference

Therefore X= 1 Or  \(a^{0} = 1\)

Hence proved.

Alternatively,

\(a^{0}\) = \(a^{1-1}\)

\(a^{0}\)  = \(a^{1} * a^{-1}\)

\(a^{0}\)  = \(a * \frac{1}{a}\) (Since \(a^{-1} = \frac{1}{a}\))

\(a^{0}\)  = \(\frac{a}{a}\)

\(a^{0}\)  = 1

Hence Proved

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9514 1404 393

Answer:

Step-by-step explanation:

1. The distributive property tells you the factor outside parentheses multiplies each of the term inside parentheses.

  7(3x -4y) = 7·3x -7·4y = 21x -28y

__

2. Time, speed, and distance are related by ...

  time = distance/speed

  time = (20 mi)/(40 mi/h) = 1/2 h = 30 minutes

The drive takes 30 minutes.

the answer is the 0,1 because the lines all have different slopes but always start at 1.

Answer:

Step-by-step explanation:

the sequence is arithmetic it goes up consistently

You put 15 where n is so the problem would look like an=32(0.98)^n-1

The pants converge

His pants will be very long it is not reasonable

Answer:

73/4

Step-by-step explanation:

20 + 7×(5-3) / (8-6)-4

= 20 + 7×(2) / (2)-4

= 20 + 14 / -8

= 73/4

Answer:

-17

Step-by-step explanation:

Use PEMDAS to simplify. PEMDAS stands for

Simplify:

\(\sf{\dfrac{20+7\times(5-3)}{(8-6)-4}}\)

\(\sf{\dfrac{20+7\times2}{2-4}}\)

\(\sf{\dfrac{20+14}{-2}}\)

\(\sf{\dfrac{34}{-2}}\)

\(\sf{-17}\)

Hence, the answer is -17

The velocity of a particle = i + 2t j

The acceleration of a particle = 2 j

The speed of a particle = \(\sqrt{1 + 4t^{2} }\)

Here,

The position function is, \(r (t ) = ti + t^{2} j +2k\)

We have to find, the velocity, acceleration, and speed of a particle with the given position function.

What is Velocity of a particle with the given position function?

The instantaneous velocity v(t) of a particle is the derivative of the position with respect to time. That is, v(t)=dx/dt.

Now,

The position function is, \(r (t ) = ti + t^{2} j +2k\)

The velocity of a particle = \(\frac{d r(t)}{dt}\)

\(r (t ) = ti + t^{2} j +2k\)

\(\frac{d r(t)}{dt} = i + 2t j\)

The acceleration of a particle = \(\frac{d^{2} r(t)}{dt^{2} }\)

\(r (t ) = ti + t^{2} j +2k\)

\(\frac{d r(t)}{dt} = i + 2t j\)

\(\frac{d^{2} r(t)}{dt^{2} }= 2j\)

The speed of a particle = \(| \frac{d r(t)}{dt}| = |v(t)|\)

\(\frac{d r(t)}{dt} = i + 2t j\)

\(|v(t)|=\sqrt{1 + 4t^{2} }\)

Hence, The velocity of a particle = \(i + 2t j\)

The acceleration of a particle = \(2 j\)

The speed of a particle = \(\sqrt{1 + 4t^{2} }\)

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Answer:

hi

Step-by-step explanation:

hi

Solution:

The rate of change of a graph is the same as the slope of the graph.

The graph that has a rate of change of 1/2 is the graph with a slope of 1/2.

To calculate the slope of a graph,

Considering two clear points from graph C, picking the points (2,-1) and (4,0)

Therefore, the graph that represents a rate of change of 1/2 is the graph of option C.

The slope of the line passing through the points (-5, -4) and (-13, 2) is -3/4.

Slope is simply expressed as a change in y over the change in x.

It is expressed as

\(m = \frac{y_2 - y_1}{x_2 - x_1}\)

Given the points:
(-5, -4) and (-13,2)​

Point (-5, -4):

x₁ = -5

y₁ = -4

Point (-13,2)​:

x₂ = -13

y₂ = 2

Plug the given x and y values into the slope formula and simplify.

\(m = \frac{y_2 - y_1}{x_2 - x_1}\\\\m = \frac{2 - (-4)}{-13 - (-5)}\\\\m = \frac{2 + 4}{-13 + 5}\\\\m = \frac{6}{-8}\\\\m = -\frac{3}{4}\)

Therefore, the slope of the line is -3/4.

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Answer:

-5

Step-by-step explanation:

The correct answer for the first question is D. The data are discrete because the data can take on any value in an interval.

Quiz scores from a college level statistics course are analyzed to determine student progress. This is not a voluntary response sample because the students taking the quiz are required to participate, and their scores are collected for the purpose of analyzing their progress.

For the second question, the data described, which is the number of donations a charity receives each month, is discrete. Discrete data can only take on specific values and cannot be divided into smaller, meaningful intervals. In this case, the number of donations can only be whole numbers, such as 0, 1, 2, and so on. It cannot take on any value in an interval or be represented by fractions or decimals. Therefore, the data is discrete.

It is important to distinguish between discrete and continuous data when analyzing and interpreting data, as different statistical methods and techniques are used for each type. Discrete data is usually counted or measured in whole numbers, while continuous data can take on any value within a given range or interval.

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Answer: can i help wat is a tip

Answer:

60

Step-by-step explanation:

Step 1:

3 x 5 = 15

Step 2:

15 x 4 = 60

Answer:

well 3. x 5 is 15, then multiply by 4 to get 60.

Step-by-step explanation:

Therefore, the own price elasticity of good X is approximately -0.67.(rounded to 2 decimal places)

To calculate the own price elasticity of good X, we need to use the formula:

Own Price Elasticity = (% change in quantity demanded) / (% change in price)

Given that the price of good X is $2 per unit, we can substitute the price (Px) into the demand equation:

Qxd = 12 - 3Px + 3Py

Substituting Px = $2 and Py = $1 into the equation, we get:

Qxd = 12 - 3(2) + 3(1)

= 12 - 6 + 3

= 9

Now, let's calculate the quantity demanded when the price changes by a small amount, let's say $0.10. We can substitute Px = $2.10 into the demand equation:

Qxd' = 12 - 3(2.10) + 3(1)

= 12 - 6.30 + 3

= 8.70

Using these values, we can calculate the percentage change in quantity demanded and the percentage change in price:

% change in quantity demanded = (Qxd' - Qxd) / Qxd * 100

= (8.70 - 9) / 9 * 100

= -0.30 / 9 * 100

= -3.33% (rounded to 2 decimal places)

% change in price = (Px' - Px) / Px * 100

= (2.10 - 2) / 2 * 100

= 0.10 / 2 * 100

= 5%

Now, let's calculate the own price elasticity using the formula:

Own Price Elasticity = (% change in quantity demanded) / (% change inprice)

= -3.33% / 5%

= -0.67 (rounded to 2 decimal places)

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To develop a 95% confidence interval estimate of the population mean rating for Miami International Airport, the student would need to use the sample data obtained from the 50 business travelers. The steps to develop the confidence interval would include the following:

Calculate the sample mean: The mean of the sample data would be calculated by summing all of the ratings and dividing by the sample size (n = 50).

Calculate the standard deviation: The standard deviation of the sample data would be calculated to estimate the variability of the data.

Calculate the standard error: The standard error of the mean would be calculated by dividing the standard deviation by the square root of the sample size (n = 50).

Calculate the critical value: The critical value would be calculated based on the desired confidence level (95%) and the degrees of freedom (n - 1 = 49). The critical value would be used to determine the width of the confidence interval.

Develop the confidence interval: The lower and upper bounds of the confidence interval would be calculated by subtracting and adding the critical value to the sample mean, respectively.

The resulting confidence interval would give an estimate of the population mean rating for Miami International Airport with a 95% level of confidence. The interpretation of the confidence interval would be that if the sampling process were repeated many times, 95% of the resulting confidence intervals would contain the true population mean.

It is important to note that this process assumes that the sample was taken using simple random sampling techniques and that the data follows a normal distribution.

Therefore, The interpretation of the confidence interval would be that if the sampling process were repeated many times, 95% of the resulting confidence intervals would contain the true population mean.

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To develop a 95% confidence interval estimate of the population mean rating for Miami International Airport, the student would need to use the sample data obtained from the 50 business travelers. The steps to develop the confidence interval would include the following:

Calculate the sample mean: The mean of the sample data would be calculated by summing all of the ratings and dividing by the sample size (n = 50).

Calculate the standard deviation: The standard deviation of the sample data would be calculated to estimate the variability of the data.

Calculate the standard error: The standard error of the mean would be calculated by dividing the standard deviation by the square root of the sample size (n = 50).

Calculate the critical value: The critical value would be calculated based on the desired confidence level (95%) and the degrees of freedom (n - 1 = 49). The critical value would be used to determine the width of the confidence interval.

Develop the confidence interval: The lower and upper bounds of the confidence interval would be calculated by subtracting and adding the critical value to the sample mean, respectively.

The resulting confidence interval would give an estimate of the population mean rating for Miami International Airport with a 95% level of confidence. The interpretation of the confidence interval would be that if the sampling process were repeated many times, 95% of the resulting confidence intervals would contain the true population mean.

It is important to note that this process assumes that the sample was taken using simple random sampling techniques and that the data follows a normal distribution.

Therefore, The interpretation of the confidence interval would be that if the sampling process were repeated many times, 95% of the resulting confidence intervals would contain the true population mean.

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The age of Jennifer is 16.

Let Jennifer's age be represented with x

Jonathan's age would be 2x

The sum of their ages would be 48

2x + x = 48

3x = 48

x = 48 /3 = 16

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Answer:  Jennifer is 16

Step-by-step explanation: 2x+y=48, divide by 3 then multiply by 2

Answer:

See below.

Step-by-step explanation:

Jane and John are each hiking a trail in the city.  Jane is on her bike, and John is jogging.

At noon, Jane is at the 5 mile mark and rides at 11 miles per hour.

Also at noon, John is at the 23 mile mark and jogs at 8 miles per hour.

x is the number of hours after noon.

Will Jane catch John?  After how many hours?

When circles overlap in piecewise functions, it introduces complexity to the function's behavior, requiring careful definition and consideration of conditions to ensure a coherent and well-defined mathematical representation.

When circles are overlapping in piecewise functions, it means that there is a common range of values where multiple circles are defined. This can lead to different behaviors and outcomes depending on how the piecewise function is defined and the specific conditions of the overlapping circles.

In the case of piecewise functions involving overlapping circles, the behavior of the function can vary. The function may have multiple solutions or different rules for different regions of the overlapping circles. It can also result in points where the function is discontinuous or undefined.

To handle overlapping circles in piecewise functions, it is important to define the function carefully and consider the conditions for each region of the overlapping circles. This may involve introducing additional conditions or defining separate rules for the overlapping regions to ensure a well-defined and continuous function.

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Answer: A teapot.

Step-by-step explanation:

Answer: ≈30.28 m²

All the work is shown in the picture.

Irreversibilities present in an internal combustion engine include friction, heat transfer, and chemical reaction. Therefore, the correct answer is that all of the answers are correct.

Friction is an important source of irreversibility in internal combustion engines. It occurs due to the rubbing and resistance between moving parts, such as the piston rings, bearings, and valves. Friction leads to energy losses and reduces the engine's efficiency. Heat transfer is another irreversibility in internal combustion engines. During the combustion process, heat is transferred between the high-temperature combustion chamber and the surrounding components, such as the cylinder walls and cooling system. This heat transfer results in energy dissipation and affects the engine's overall performance. Chemical reactions taking place within the engine are also sources of irreversibility. Combustion itself is a chemical reaction that converts fuel and oxidizer into products, releasing heat energy. However, not all fuel molecules undergo complete combustion, leading to the formation of byproducts and pollutants. These incomplete reactions contribute to irreversibilities and affect the engine's efficiency and emissions. Therefore, all of the answers are correct as friction, heat transfer, and chemical reactions are significant irreversibilities present in internal combustion engines that impact their performance and efficiency.

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Answer:

it is because 8 is twice 4 and any number minus twice itself is the numbers opposite and the opposite of 4 which is -4 when multiplied by itself is -4 times -4 which equals 16 or the same as 4 squared

Answer:

Step-by-step explanation:

10

Answer: Using width as diameter=32π Using length as diameter=72π

*I included both possibilities since I didn't see a picture of the way in which the semicircle and rectangle were joined.*

Step-by-step explanation:

In order to solve, you have to know the formula for area of a circle which is A=πr^2 (pi*radius to the 2nd power)

The problem does not give us the radius, but we know that radius is half of the diameter.

To find the diameter, we have to use the side measurement of the rectangle and divide it by 2 to find the radius.

Next, we increase the radius to the 2nd power, giving us the radius of a whole circle.

Finally, we have to divide that by 2 since it's a semi circle otherwise known as half of a circle.

I put the answer in terms of pi since that's the most accurate, but if the question specifically instructs it, you can calculate part of the irrational decimal and round to a certain place value.