Find the average rate of change of the function f(x) = √x from x1 = 4 to x2 = 100. In 2000, 54% of the residents in a large city regularly used newspapers for getting news and this has decreased at an average rate of approximately 1.4% per year since then. Find a linear function in slope-intercept form that models this description. The function should model the percentage of residents, P(x), who regularly used the news outlet x years after 2000.

Positive

Negative

Sorts Explanation

Lines which go / are positive.

Lines which go \ are negative.

That's the best explanation I could do. (Sorry)

Answer:

Pick below

Step-by-step explanation:

Using point(0,-3) slope (9) form the line equation will be :

(y- -3) = 9(x-0)

y +3 = 9x        to convert to y = mx+b form, subtract 3 from both sides)

y = 9x-3          to convert to 'standard(?) 'form  subtract 9x from both sides

y - 9x = -3        or , by multiplying by -1   : 9x -y = 3

What this has to signify would be the fact that there is a the spread of a stimulus through the ventricles.

This is used to refer to the term that has to do with the combination of the different types of waves. These are the Q wave, the R wave as well as the S wave. This is used in ECG measurement. It has to do with the measurement of the chambers of a person heart to check its normal function.

When the ECG are in this category, it can be regarded as a high. This may put a person to have the more likelihood of having a death that is caused by coronary diseases.

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To show that the given functions f1(x) = x and f2(x) = cos(9x) are orthogonal on the interval [-1/9, 6/9], we need to compute the inner product of the two functions and check if the result is zero.

The inner product is defined as the integral of the product of the two functions on the given interval: ∫[-1/9, 6/9] f1(x) * f2(x) dx = ∫[-1/9, 6/9] x * cos(9x) dx Now, we need to evaluate this integral. If the result is zero, then the functions are orthogonal on the given interval.


To show that f1(x) = x and f2(x) = cos(9x) are orthogonal on the interval [-1/9, 6/9], we need to show that their inner product is zero over this interval.

The inner product of two functions f(x) and g(x) over an interval [a, b] is defined as: ∫[a,b] f(x)g(x) dx So, we need to evaluate the following integral: ∫[-1/9, 6/9] xcos(9x) dx To evaluate this integral, we can use integration by parts. Let u = x and dv = cos(9x) dx.

Then, du = dx and v = (1/9)sin(9x). Using the formula for integration by parts, we get: ∫[-1/9, 6/9] xcos(9x) dx = (x/9)sin(9x) ∣[-1/9, 6/9] - ∫[-1/9, 6/9] (1/9)sin(9x) dx Evaluating the first term at the upper and lower limits of integration, we get: (6/9)(sin(6) - sin(-1/9)) - (-1/9)(sin(-1) - sin(-1/9)) Simplifying this expression, we get: (2/3)sin(6) + (1/9)sin(1) + (1/9)sin(1/9) - (2/3)sin(1/9) Now we need to evaluate the second integral: ∫[-1/9, 6/9] (1/9)sin(9x) dx Using the substitution u = 9x, du = 9dx, and simplifying, we get: (1/81)cos(9x) ∣[-1/9, 6/9] .

Evaluating this at the upper and lower limits of integration, we get: (1/81)(cos(6) - cos(-1/9)) - (1/81)(cos(-1) - cos(-1/9)) Simplifying this expression, we get: (1/81)(cos(1) - cos(1/9) - cos(6) + cos(-1/9)) Combining this with the first term we obtained, we get the following expression for the integral: (2/3)sin(6) + (1/9)sin(1) + (1/9)sin(1/9) - (2/3)sin(1/9) - (1/81)(cos(1) - cos(1/9) - cos(6) + cos(-1/9)) This is the final answer in terms of x as the integrand.

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Answer:

The first one.

Step-by-step explanation:

w + w is having 2 w's, which is obviously 2w.

2w + w would be equal to 3w.

2w - w would be equal to w.

w + 2 is just w + 2.

following:

The book "How to Solve It" by George Polya is a classic work in the field of mathematics education. It lays out a four-step method for solving mathematical problems, which includes understanding the problem, devising a plan, carrying out the plan, and reflecting on the solution obtained.

The purpose of the book is to help students and problem solvers develop a systematic and effective approach to solving problems in mathematics and other areas of life. The book is widely used and respected in mathematics education, and its ideas have been applied to many other fields, such as engineering, computer science, and business.

The four steps outlined in the book provide a structure for approaching any problem in a systematic and organized manner, which can be applied to a wide variety of problems in different fields. This structure helps to ensure that all relevant information is considered and that the problem is solved in the most efficient and effective way possible.

Additionally, the step of reflecting on the solution obtained helps to promote a deeper understanding of the problem and the solution, which is important for developing problem-solving skills over time. As a result of its simplicity, clarity, and effectiveness, "How to Solve It" continues to be a popular and highly-regarded book in the field of mathematics education and beyond.

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July is the seventh month of the year in the Gregorian calendar, which is the most widely used calendar system in the world.

It is considered the seventh month because it falls between June, the sixth month, and August, the eighth month. July is also the last month of the second quarter of the year, having 31 days.

July is known for many events and holidays, such as Independence Day in the United States, Canada Day, and Bastille Day in France. It's also the middle of the summer season, and people often take vacations and enjoy outdoor activities during this month.

It's important to note that in different cultures and regions the months of the year may be ordered differently.

For example, some cultures may have a lunar calendar which is based on the cycles of the moon rather than the sun, and the months may be ordered differently.

However, the Gregorian calendar is widely used around the world and it considers July as the seventh month of the year.

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Answer:

the proportion would be 5/8 = r/32

r = 20

Step-by-step explanation:

the number of red stripes would be 20

Answer:

19.2

Step-by-step explanation:

You use the pyth.

15^2+12^2=369

Then find the square root of 392 which is 19.2

I hope this helps! have a good day :)

The length of the diagonal of the screen is 19.2 inches

What is the diagonal of a rectangle?

The diagonal of a rectangle is calculated by the formula

From the Pythagoras Theorem , The hypotenuse² = base² + height² , and

Diagonal of a Rectangle = √ ( Length )² + ( Width )²

Given data ,

The length of the screen of the monitor is L = 15 inches

The width of the screen of the monitor is W = 12 inches

Now ,

The diagonal of the screen of the monitor is calculated by ,

Diagonal of a Rectangle = √ ( Length )² + ( Width )²

So ,

Substituting the value of length L and width W , we get

Diagonal of the screen = √ ( 15 )² + ( 12 )²

                                      = √ ( 225 ) + ( 144 )

                                      = √ 369

                                      ≈ 19.209 inches

Therefore , the diagonal of the screen is 19.209 inches

Hence , The length of the diagonal of the screen is 19.2 inches

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Answer:

m = 2

Step-by-step explanation:

to find the slope you must find (rise)/(run)

the rise is how much it goes up

the run is how much it goes to the right

in this case

it goes up 2 for every 1 to the right

so

(2/1) or just 2 is the slope

Answer:

A data type is an attribute associated with a piece of data that tells a computer system how to interpret its value

Step-by-step explanation:

Data types categorize data and specify its nature, amount characteristics, and behavior. It decides how data is handled within a computer system in terms of storage and manipulation.

Data types categorize data and specify its nature, characteristics, and behavior. It is a crucial part of every data structure and computer language. Primitive data types and complex data types are the two basic divisions of data types. Basic types like numbers, characters, booleans, and strings are examples of primitive data types. Arrays, objects, and records are examples of sophisticated data types that are more complex. Data types specify how information is handled and stored by computer systems. Size, precision, and range are a few examples of the unique qualities that each data type possesses. The arithmetic, comparison, and logic operations that can be carried out on the data are also determined by the data types.

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Answer:

Mark needs 2 kg butter, 2 kg caster sugar, 14 eggs, and 1.5 kg flour.

Step-by-step explanation:

Alright, first you double the number of kids, as Mark wants each kid to have two cupcakes, not one. (Then add 80+80 to get 160)

Now add the adults to children: 160+152=312

now divide by 12 to see how many batches of cupcakes he needs to make.

312÷12=26 So he needs to make 26 batches

Now here are the ingredients needed to make 12 batches of cupcakes (I multiplied the amount of each ingredient by 26)

5200 g (5.2 kg) butter, 5200 g (5.2 kg) caster sugar, 104 eggs, and 6500 g (6.5 kg) flour.

now make the measurements the same as Mark's ingredients (or the other way around)

(to save time I am not showing each one, just the normal ingredients turned into kg and compared)

5 kg butter < 5.2 kg butter

5 kg caster sugar < 5.2 kg butter

90 eggs < 104 eggs

5 kg flour < 6.5 kg flour

Now do a little subtraction.....

5.2 kg-5 kg = 2 kg butter is needed....

5.2 kg - 5 kg = 2 kg caster sugar is needed....

104 - 90 = 14 eggs needed....

6.5 kg - 5 kg = 1.5 kg flour needed....

And there you go!!! Hope this helped!!! :D

The amount of ingredients that Mark still requires after getting it from the kitchen is needed.

The amount of ingredients Mark still needs is

200 g of butter

200 g of caster sugar

14 eggs

1500 g of flour

The number of cupcakes that are needed for 152 adults and 80 children is

\(152+2\times 80=312\)

For the 12 cupcakes the ingredients are

200 g butter

200 g caster sugar

4 eggs

250 g flour

For 1 cupcake the ingredients are

\(\dfrac{200}{12}=\dfrac{50}{3}\ \text{g}\) of butter

\(\dfrac{200}{12}=\dfrac{50}{3}\ \text{g}\) of caster sugar

\(\dfrac{4}{12}=\dfrac{1}{3}\) eggs

\(\dfrac{250}{12}=\dfrac{125}{6}\ \text{g}\) of flour

For 312 cupcakes

\(312\times \dfrac{50}{3}=5200\ \text{g}\) of butter

\(312\times \dfrac{50}{3}=5200\ \text{g}\) of caster sugar

\(312\times \dfrac{1}{3}=104\) eggs

\(312\times \dfrac{125}{6}=6500\ \text{g}\) of flour

The required ingredients are

\(5200-5000=200\ \text{g}\) of butter

\(5200-5000=200\ \text{g}\) of caster sugar

\(104-90=14\) eggs

\(6500-5000=1500\ \text{g}\) of flour

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The fifth term of the arithmetic sequence is -1190.

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms remains constant. To find the fifth term, we can use the formula for the nth term of an arithmetic sequence:

aₙ = a₁ + (n - 1) * d

where aₙ represents the nth term, a₁ is the first term, n is the position of the term, and d is the common difference.

Given that the 100th term is -1240 and the common difference is -25, we can substitute these values into the formula.

Since the fifth term corresponds to n = 5, we can calculate:

a₅ = -1240 + (5 - 1) * (-25)

= -1240 + 4 * (-25)

= -1240 - 100

= -1340

Therefore, the fifth term of the arithmetic sequence is -1190.

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The hypotenuse of the triangle if the legs are 7 and 5 is 8.6.

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. Due to its position opposite the 90° angle, the hypotenuse in this case is the longest side. When the positive integer sides of a right triangle (let's say sides a, b, and c) are squared, the result is an equation known as a Pythagorean triple.

Given that the sides of the triangle are 7 and 5.

The Pythagorean Theorem is given as follows:

a^2 + b^2 = c^2

Substituting the values of a = 7 and b = 5 we have:

(7)^2 + (5)^2 = c^2

49 + 25 = c^2

c^2 = 72

c = 8.6

Hence, the hypotenuse of the triangle if the legs are 7 and 5 is 8.6.

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Answer:

The expanded form of this expression should be 7.5-10n-20.

Step-by-step explanation:

Note: I am not 100% on this answer, so if this is not the response you were looking for, do not hesitate to tell me. Hopefully this answer helps though :)

Answer:

-2.5(-3+4n+8)

7.5-10n-20

-22.5-10n

Answer:

.......................................................

Answer:

Hey there!

\(8x^3+2x^2-20x-5\)

\((8x^3+2x^2)+(-20x-5)\)

\(2x^2(4x+1)+(-5)(4x+1)\)

\((2x^2-5)(4x+1)\)

Let me know if this helps :)

The solution of the expression are,

⇒ (4x + 1) (2x² - 5)

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ 8x³ + 2x² - 20x - 5

Now, We can simplify as;

⇒ 8x³ + 2x² - 20x - 5

⇒ (8x³ + 2x² )  + (- 20x - 5)

⇒ 2x² (4x + 1) - 5 (4x + 1)

⇒ (4x + 1) (2x² - 5)

Thus, The solution of the expression are,

⇒ (4x + 1) (2x² - 5)

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Answer:

The model will be 15 in. long

Step-by-step explanation:

x is the length of the model

so x/100 = 9/60

x = 100(9/60) = 15

Answer:

As cosine returns a value between -1 and 1, the amplitude will simply be the coefficient of the cosine function.  In this case it's 2.3, which tells us that the amplitude is also 2.3

Answer:

1) They were multiplied by one power of ten because 2.5x 1^10 is 25, and so that it is easier to divide.

19.625/ 2.5 * 10/10 = 196.25/25

Hope this helps plz hit the crown ;D

Answer:

359.2 cubic inches

Step-by-step explanation:

The interquartile range is 3 rebounds.

What is the interquartile range?

An interquartile range is a measure of the difference between the upper and lower quartiles of a dataset.

W can find the values of the upper and lower quartile and median from a box plot.

The middle line is the median and the first line is the lower quartile and the last line is the upper quartile.

The formula used is Upper quartile - Lower quartile.

We have,

From the box plot,

Median = 10

The upper quartile = 11

The lower quartile = 8

Now,

Interquartile range.

= Upper quartile - Lower quartile

= 11 - 8

= 3

Thus,

The interquartile range is 3.

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There is a ''negative correlation'' in the data set.

Hence, Option B is correct.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Now, By the graph;

The graph shows points that are grouped together and are decreasing.

And, The gathered data shows that there is a possibility to get correlation between them.

Thus, The group of data is decreasing.

So, the correlation of the data will be negative in nature.

Therefore, It can be said that the "There is a negative correlation in the data set".

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Answer:

Original: $733 million

Sequel: $860 million

Step-by-step explanation:

Let's say the original movie grossed x dollars. Since the sequel grossed 127 million more than that, we can write the expression x + 127 to represent the sequel.

Their total is 1593 million, so let's add them up:

x + (x + 127) = 1593

2x + 127 = 1593

2x = 1466

x = 1466/2 = 733

To find the sequel gross amount, add 127 to 733:

127 + 733 = 860

So, the original movie grossed $733 million, while the sequel grossed $860 million.

Answer:

-250

Step-by-step explanation:

assuming he starts at 0 pts -50 * 5 = -250

x is 5. y is 65. there you go!.

The decay of 90Sr follows an exponential decay model, with a half-life of 29 years.  The answer is approximately 116 years.

The decay of a radioactive substance is commonly modeled using the exponential decay equation:

N = N0 * (1/2)^(t/t1/2)

where N is the current amount of the substance, N0 is the initial amount, t is the time elapsed, and t1/2 is the half-life of the substance.

To determine the time required for 100.0 g of 90Sr to decay to 6.25 g, we can set N = 6.25 g, N0 = 100.0 g, and t1/2 = 29 years, and solve for t.

6.25 g = 100.0 g * (1/2)^(t/29)

Dividing both sides by 100.0 g, we get:

0.0625 = (1/2)^(t/29)

Taking the logarithm of both sides with base 2, we get:

log2(0.0625) = t/29

Solving for t, we get:

t = 29 * log2(0.0625) ≈ 116 years

Therefore, it would take approximately 116 years for 100.0 g of 90Sr to decay to 6.25 g, assuming the decay follows the exponential decay model.

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The statements that are true if the variables given, represent the periods of salaries, include:

]

If y represents the yearly salary then that means that in relation to the biweekly salary, this can be found as :

Biweekly salary = Annual salary / 26 biannual periods

b = y / 26

If y is the yearly salary, it can be found by:

= Number of weeks in year x Weekly salary

= 52 w

y, being the yearly salary, would also be found as:

= Monthly salary x number of months in year

= 12m

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Options for this question include :

b = y/26

y = m/12

y = 52w

12m =y

26y = b