modify the proof of theorem 2.1.4 to show that there does not exist a rational number t such that t 2

An inequality that can be used to determine p, the number of people who can go to the amusement park, is,

28.75p + 17.25 ≤ 345.

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.

Given:

A group of friends wants to go to the amusement park.

They have no more than $345 to spend on parking and admission.

Parking is $17.25, and tickets cost $28.75 per person, including tax.

An inequality that can be used to determine p, the number of people who can go to the amusement park, is,

28.75p + 17.25 ≤ 345.

Therefore, an inequality is 28.75p + 17.25 ≤ 345.

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The correct illustration of plotting the points is attached in the image.

few of the points are (2, - 1), (3, 1), (4, 3), and (5, 5).

The set of ordered pairings (x, y) where f(x) = y makes up the graph of a function.

These pairs are Cartesian coordinates of points in two-dimensional space and so constitute a subset of this plane in the general case when f(x) are real values.

From the given information first, we plot a point (1, - 3) on the x-y coordinate.

Plotting more points by moving up 2 and right 1 would be, (x + 1, y + 2).

So, Some of such points are,

(2, - 1), (3, 1), (4, 3), and (5, 5).

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The dilations relation is C'D = (3/4)CD.

Dilation of a figure will leave its sides get scaled (multiplied) by same number. That number is called the scale factor of that dilation.

Its also called scaling of a figure, but due the involvement of coordinates, it involves a center of a dilation, which is like a pinned point which stays at same place after dilation.

Its like we enlarge or shorten the size of the figure (or keep it same, when scale factor = 1).

Given;

First, we want to dilate point C using D as the center of dilation with a scale factor = 3/4.

This only means that we will have the new point C', such that:

C'D = (3/4)*CD

Where CD is the distance between points C and D

Therefore, the dilation will be C'D = (3/4)*CD.

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The domain of the function is [-2, 2) while the range is [4, 2) (along the y -axis).

The domain of a function is the input value for which the function exists while the range is the output value for which the function exists.

here, we have,

For the graph, the domain lie across the x-axis. The domain of the function is [-2, 2) while the range is [4, 2) (along the y -axis).

Note that point where the circles are shaded shows a closed interval

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This is  referred to Fermat's Little Theorem, which states that if p is a prime number and a is an integer such that 0 < a < p, then a^(p-1) ≡ 1 (mod p).

In other words, if we raise a to the power of p-1 and divide by p, the remainder will always be 1. This theorem can be used to efficiently test the primality of a number or to find modular inverses in modular arithmetic.

Fermat's Little Theorem is a fundamental result in number theory and has important applications in cryptography and computer science. The theorem states that if p is a prime number and a is an integer such that 0 < a < p, then a^(p-1) ≡ 1 (mod p). This can be expressed as:

a^(p-1) = 1 + kp where k is an integer.

This theorem is a direct consequence of the fact that the set of integers from 1 to p-1 (mod p) form a group under multiplication (mod p). This group is known as the group of units modulo p, and the order of this group is p-1. Hence, a^(p-1) must be congruent to 1 (mod p) since it is the product of all elements in the group.

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The solution is, the water level if today is the 5th day is 235 lit.

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here, we have,

The expression 7w + 200 liters are the water level which drops in a particular reservoir in w days.

then, for 5 days it will be,

7*5 + 200

=35+200

= 235

Hence, The solution is, the water level if today is the 5th day is 235 lit.

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The simple three-period moving average forecast for period 6 is 68.33.

The simple three-period moving average is a method for smoothing out fluctuations in a time series data by taking the average of the three most recent data points. To find the forecast for period 6, we calculate the average of the demand in periods 4, 5, and 6. In this case, the forecast for period 6 is 68.33. To find this, we sum the demand in periods 4, 5, and 6 and divide by 3. (70 + 69 + ?)/3 = 68.33, where the '?' represents the demand in period 6.

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The 95% confidence interval for the population mean is approximately (1,218, 1,271)

A 95% confidence interval for the population mean can be calculated as follows:

Calculate the standard error (SE) of the mean: SE = standard deviation/sqrt (sample size) = 38 / sqrt(16) = 12.56

Use the t-distribution to find the critical value, t*, for a 95% confidence level and degrees of freedom (df) = sample size - 1 = 15.

Calculate the margin of error (ME) as ME = t* * SE = t* * 12.56.

Calculate the lower bound and upper bound of the confidence interval: lower bound = sample mean - ME = 1,245 - ME; upper bound = sample mean + ME = 1,245 + ME.

Since the degrees of freedom for this sample size is quite small, the critical value for t-distribution can be approximated using a t-table for a 95% confidence level and df = 15. The critical value is approximately 2.131.

So, the margin of error is ME = 2.131 * 12.56 = 26.86, and the 95% confidence interval for the population mean is:

Lower bound: 1,245 - 26.86 = 1,218 (rounded to the nearest whole number)

Upper bound: 1,245 + 26.86 = 1,271 (rounded to the nearest whole number)

Therefore, the 95% confidence interval for the population mean is approximately (1,218, 1,271).

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The total area from given figure is 53.13 square units.

Area is the amount of space occupied by a two-dimensional figure. In other words, it is the quantity that measures the number of unit squares that cover the surface of a closed figure. The standard unit of area is square units which is generally represented as square inches, square feet, etc.

From the graph, we can see three shapes rectangle with length= 6 units and width= 5 units, triangle with height = 6 units and base = 3 units and semicircle with diameter = 6 units

Here, area of a rectangle is Length×Width

= 6×5

= 30 square units

Area of a triangle = 1/2 ×Base×Height

= 1/2 ×3×6

= 9 square units

Area of a semicircle = πr²/2

= 3.14×3²/2

= 3.14×4.5

= 14.13 square units

Total area = 30+9+14.13

= 53.13 square units

Therefore, the total area from given figure is 53.13 square units.

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The value of n from the given equation is 30.5.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The given equation is 57,491 = 1,885n

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

Now, n=57,491/1885

n=30.5

Therefore, the value of n is 30.5.

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"Your question is incomplete, probably the complete question/missing part is:"

Solve to find the value of n

57,491 = 1,885n

The correct statement predicting the closest product is : 20

A fraction represented with its quotient and remainder is a mixed fraction. For example, 2 1/3 is a mixed fraction, where 2 is the quotient, and 1 is the remainder. So, a mixed fraction is a combination of a whole number and a proper fraction.

Given here : Two mixed fractions as 5⁵/₂₉ and 3¹²/₁₃

But 5⁵/₂₉=150/29 and 3¹²/₁₃=51/13

Thus the product of the two mixed fractions are as follows

150/29×51/13 =20.292

Clearly the most reasonable product is 20

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The perimeter of the figure on the right is 40.26 yrd.  .

A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length. The perimeter of a circle or an ellipse is called its circumference. Calculating the perimeter has several practical applications.

Perimeter refers to the total outside length of an object.

here, we have,

from the given figure we get,

the radius of the circle = 6 yrd.

then, the perimeter = 2*pi* 6

                                = 37.68 yrd.

now, the figure is 3/4 th of the circle,

so, perimeter = 37.68 * 3/4 + 12

                      = 40.26 yrd.

Hence, The perimeter of the figure on the right is 40.26 yrd.  .

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The given system of simultaneous equations has no solutions.

In mathematics, a set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.

Given is the system of simultaneous equations as -

y = 3x + 9

6x − 2y = 6

Refer to the graph of the equations attached. The value of {x} and {y} for which both the equations are true is given by the point of intersection of both lines. Since both lines are parallel, there is no point of intersection and hence no solution.

Therefore, the given system of simultaneous equations has no solutions.

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Answer:

I believe this is a zero polynomial since it has only one number

Answer:

3x is a monomial

Step-by-step explanation:

Monomial (One term) – 3x

Binomial (Two Term) – 7a-5

Trinomial (Three Term) – x^2-x-2

Answer:

  (a)  three angles: 62°, 34°, and 84°

Step-by-step explanation:

You want to know which specification can result in an infinite number of triangles.

If only the angles are specified, the sides can have an infinite number of (related) lengths.

  three angles: 62°, 34°, and 84° will create an infinite number of triangles

Assuming the side lengths can form a triangle, they will specify exactly one triangle.

Lengths 3 cm, 5 cm, and 10 cm cannot form a triangle.

When two sides are specified along with the angle between them, exactly one triangle can be formed.

The missing code that can be used to replace / missing code / so that the code segment works as intended is x >= 10.

The code segment is intended to store the sum of all multiples of 10 between 10 and 100, inclusive. The value of x starts at 100 and is decremented by 10 on each iteration of the loop, until it reaches 10. The sum of all the multiples of 10 between 10 and 100 is stored in the variable total.

The missing code in the while statement determines when the loop will stop. If we use x >= 10 as a replacement for / missing code /, the loop will run as long as x is greater than or equal to 10. When x reaches 10, the loop will stop.

Here's the complete code:

int x = 100;

int total = 0;

while(x >= 10)

{

   total = total + x;

   x = x - 10;

}

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Your question is incomplete but probably the complete question is:

Consider the following code segment, which is intended to store the sum of all multiples of 10 between 10 and 100, inclusive (10 + 20 + ... + 100), in the variable total.

int x = 100;

int total = 0;

while( / missing code / )

{

total = total + x;

x = x - 10;

}

Which of the following can be used as a replacement for / missing code / so that the code segment works as intended?

A x < 100

B x <= 100

C x > 10

D x >= 10

E x != 10

The journal entries to record the receipt of the application money and its allotment to share capital and Allotment Account are as follows:

Debit Cash Rs. 300,000

Credit Share Application Account Rs. 300,000

(To record the receipt of the money on application)

Debit Share Application Account Rs. 300,000

Credit Share Capital Rs. 150,000

Credit Share Allotment Account Rs. 150,000

(To record the transfer of the application money to the Share Capital and the Allotment accounts, respectively.)

Journal entries are the initial records kept of business transactions.

Journal entries are made as transactions occur on a daily basis.

Authorized capital = Rs. 1,000,000

The number of shares issued = 5,000

The par value = Rs. 100

The premium = Rs. 10 (Rs. 100 x 10%)

The issuance price per share = Rs. 110 (Rs. 100 + Rs. 10)

The expected amount to be received on application = Rs. 30 per share

The number of applications received = 10,000

Application money = Rs. 300,000

Excess Application = Rs. 150,000

Cash Rs. 300,000

Share Application Account Rs. 300,000

Share Application Account Rs. 300,000

Share Capital Rs. 150,000

Share Allotment Account Rs. 150,000

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There are 8 nickels does Richard have.

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

We have to given that;

Richard has 17 coins with a value of 76 cents.

And, The coins are nickels, dimes, and pennies. He has twice as many pennies as dimes.

Now, Let p = number of pennies

n = number of nickels

d = number of dimes

Hence, We can formulate;

⇒ p(1) + n(5) + d(10) = 76

⇒ p + 5n + 10d = 76  .. (i)

Here, He has twice as many pennies as dimes.

⇒ p = 2d

And, Richard has 17 coins.

⇒ p + d + n = 17 .. (ii)

Substitute p = 2d in equation (i) and (ii),

⇒ p + 5n + 10d = 76  

⇒ 2d + 5n + 10d = 76  

⇒ 5n + 12d = 76  .. (iii)

⇒ p + d + n = 17

⇒ 2d + d + n = 17

⇒ n + 3d = 17  .. (iv)

Solve equation (iii) and (iv), we get;

⇒ d = 3

⇒ n = 8

Hence, There are 8 nickels.

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The amount (present value) that Speedy Movers borrowed for a debt that accumulated to $52,467.60 in four years was $43,604.16.

The present value is the amount that Speedy Movers borrowed four years ago at 4.68% interest compounded semi-annually to accumulate to a future value of $52,467.60.

The present value is determined using discounting while the future value is computed by compounding.

We can determine both the present value and the future value using an online finance calculator.

N (# of periods) = 8 semiannual periods (4 years x 2)

I/Y (Interest per year) = 4.68%

PMT (Periodic Payment) = $0

FV (Future Value) = $52467.60

Results:

Present Value (PV) = $43,604.16

Total Interest = $8,863.44

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Answer: 39.805

Step-by-step explanation: 39.81 - 39.8 = 0.01

0.01 x 0.5 = 0.005

39.8 + 0.005 = 39.805

The cost of each bag of walnut can be determined following the below steps and each bag of walnut is $1.89

Total receipt= $17.92

4 batches of chocolate chip walnut cookies requires 4 bags each of chocolate chips and walnuts if each batch requires 1 bag each of chocolate chips and walnuts

Cost of chocolate chips = $2.59

Cost of 4 bags of chocolate chips = 4($2.59)

= $10.36

Total cost of 4 bags of walnuts = Total receipt - Cost of 4 bags of chocolate chips

= $17.92 - $10.36

= $7.56

Cost of each bag of walnut= Total cost of 4 bags of walnuts / 4

= $7.56 / 4

= $1.89

Therefore, each bag of walnut cost $1.89

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Answer: Step 1: Divide 17.92 by 4

              Step 2: Subtract 2.59 from 4.48

Step-by-step explanation:

Angle BAC is equal to 72 degrees, which is calculated by subtracting 2 times the angle of intersection between lines p and q (34 degrees) from 180 degrees.

Given that two lines p and q intersect at X at an angle of 34 degrees

Let A be a point inside the 34 degree angle formed by p and q

Then, let B be the reflection of A through line p, and let C be the reflection of A through line q

To find angle BAC,

we must first understand that a reflection of a point across a line results in an angle equal in measure to its original angle, but on opposite sides of the line of reflection.

In this case, because A is inside the 34 degree angle formed by lines p and q,

angle AXB must be equal to 34 degrees

angle AXC must also be equal to 34 degrees

Therefore, angle BAC must be equal to 180 degrees minus 2 times 34 degrees, or 72 degrees.

In conclusion, the angle BAC is equal to 72 degrees.

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According to the table, the information does indeed justify using a normal model to approximation population characteristics.

The answer to the query is:

The following numbers are one standard deviation away:

= 0.33 + 0.36

= 0.69

According to the empirical rule, this value is:

= 0.68

As a result, and in accordance with the empirical rule, the quantities were always 0.95 with two standard deviations. Consequently, the data's empirical rule was followed.

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The correct question is-

The mean and standard deviation of the sample data collected on continuous variable x are −0.25 and 0.03, respectively. The following table shows the relative frequencies of the data in the given intervals.

Based on the table, do the data support the use of a normal model to approximate population characteristics?

The total number of plants is given as follows:

168 plants.

The total number of plants is obtained applying the proportions in the context of this problem.

The variable that represents the total number of plants is given as follows:

n.

The fraction of the number of plants that needed water is given as follows:

3/8.

The fraction 3/8 of n is equivalent to an amount of 63, hence the total amount of plants is obtained as follows:

3n/8 = 63

3n = 63 x 8

n = 21 x 8(simplifying by 3).

n = 168 plants.

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Answer:

62.5 square feet

Step-by-step explanation:

Let's call the width of the rectangle w. Since the ratio of the length to the width is 5 to 2, the length can be expressed as 5/2 times the width:

l = 5/2 * w

We know the length is 12.5 feet, so we can use that information to solve for the width:

12.5 = 5/2 * w

w = 12.5 * 2/5

w = 5

The width of the rectangle is 5 feet.

The perimeter of the rectangle is calculated by adding up the lengths of all four sides:

p = 2 * (l + w)

p = 2 * (12.5 + 5)

p = 2 * 17.5

p = 35

The perimeter of the rectangle is 35 feet.

The area of the rectangle is calculated by multiplying the length and width:

a = l * w

a = 12.5 * 5

a = 62.5

The area of the rectangle is 62.5 square feet.

Answer:

She earned $9.50 an hour

Step-by-step explanation:

Answer:

she earned $9.50

Step-by-step explanation:

76.00 ÷ 8 = $9.50

The  probability density function (pdf) of X can be written as fx(x) = 3x, where 0 < x < 1.

The given probability density function (pdf) is fx(x) = cx, where 0 < x < 1 and c is a constant. To find the value of c, we can use the property that the integral of the pdf over the entire sample space must equal 1, as the sum of all probabilities in the sample space must equal 1. Thus, the equation to find c is:

[tex]\int\limits^1_0{cx} \,dx = 1[/tex]

Solving for c, we have:

c = 3.

Therefore, the pdf of X can be written as fx(x) = 3x, where 0 < x < 1. This function can be used to find probabilities and other statistical measures related to the random variable X.

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Answer:

No, the rectangles are not proportional.

Step-by-step explanation:

I say this because the area of the first one is 10ft x 12ft = 120 ft

But, the answer to the second rectangle is 9ft x 8ft = 72ft

Proportional means corresponding in size

So, the rectangles above are not proportional.

Hope this helps!