after driving to a riverfront parking lot, bob plans to run south along the river, turn around, and return to the parking lot, running north along the same path. after running 3.25 miles south, he decides to run for only 50 minutes more. if bob runs at a constant rate of 8 minutes per mile, how many miles farther south can he run and still be able to return to the parking lot in 50 minutes?

Discrete mathematics is a branch of mathematics that deals with objects that can assume only distinct, separated values and can be counted. It has played a significant role in reducing cultural distinctions by providing a unifying language for the field of mathematics and a common understanding for solving problems across cultures.

Through discrete mathematics, people from different backgrounds and cultures can communicate and collaborate more effectively, breaking down cultural barriers and promoting unity.

For example, discrete mathematics has been used to create algorithms that solve complex problems in computer science, cryptography, and optimization, making it possible for people from different cultures to work together to solve these problems.

Additionally, the standardization of mathematical language and symbols through discrete mathematics has made it easier for people to understand and share mathematical ideas across cultures, further promoting unity and reducing cultural distinctions.

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Step-by-step explanation:

the simplest way for me is

1. to convert both terms into full fractions (not mixed numbers).

2. then to bring both fractions to the same denominator.

3. and then do the actual calculation.

and if needed, we can

4. then convert the result back into mixed numbers.

1.

15 1/2 = (15×2 + 1)/2 = 31/2

1 11/20 = (1×20 + 11)/20 = 31/20

2.

we need to convert 31/2 into a fraction .../20, so that we can actually combine it with the 31/20.

how do we get from 2 to 20 ? by multiplying by 10.

in order to keep the value of the fraction unchanged, we need to do the same multiplication also to the numerator :

31/2 × 10/10 = 310/20

3.

310/20 + 31/20 = 341/20

4.

341/20 = (17×20 + 1)/20 = 17 1/20

to get this you do an integer division and note the remainder.

341/20 = 17 remainder 1

Sandy's experimental probability was exactly the same as the theoretical probability for all three experiments.

For the given geometry the perimeter is 37 units, area is 118.55 square units and the type is pentagon.

The space enclosed by a pentagon's sides is referred to as the pentagon's area. Various techniques can be used to compute it depending on the dimensions that are known. The kind of pentagon also makes a difference. For instance, if it is a normal pentagon, the area can be determined using a single formula; but, if it is an irregular pentagon, we must divide it into various polygons and add their areas to determine the pentagon's area.

The perimeter is the sum of length of all the sides of a pentagon.

P = 5s

P = 5(7.4) = 37 units.

The area of the pentagon is given as:

A = 1/2 (P)(a)

Substitute the value of P = 37 and a = 6.4086:

A = 1/2 (37)(6.4086) = 118.55 square units.

Type: Pentagon.

Hence, for the given geometry the perimeter is 37 units, area is 118.55 square units and the type is pentagon.

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The solution is, the sequence is, {3, 31, 49, ..............}

An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.

For instance, the sequence 5, 7, 9, 11, 13, 15.. . is an arithmetic progression with a common difference of 2.

here, we have,

t(0) = 3

and that the sum of the first three terms ( t(0), t(1) , and t(2) ) is 63

let, the 1st term = a

common difference = d

so, we have,

a = 3

and, a+ a+d + a+ 2d = 63

or, 9+ 3d = 63

or, 3d = 54

or, d = 18

Hence, The solution is, the sequence is, {3, 31, 49, ..............}

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Answer:

[-23.27 < x]

Step-by-step explanation:

Distribute -15/4 to the numbers in the parenthesis:

[tex]\frac{-15}{4}*2x[/tex] = [tex]-\frac{30}{4}[/tex]

[tex]\frac{-15}{4}*-\frac{2}{3}[/tex] = [tex]\frac{5}{2}[/tex]

[tex]-\frac{30}{4} + \frac{5}{2} < 64 + \frac{11}{4}x[/tex]

Combine like terms:

[tex]-5 < 64 + \frac{11}{4}x[/tex]

Subtract 64 from both sides:

[tex]-64 < \frac{11}{4}x[/tex]

Multiply both sides by 4:

[tex]-256 < 11x[/tex]

Divide both sides by 11:

[tex][-23.27 < x][/tex]

Answer:

Step-by-step explanation:

620 cm^2

Step-by-step explanation:

Area of isosceles triangles:

A = (b×h) ÷ 2

Substitute

(24 × 5) ÷ 2

120 ÷ 2 = 60 cm^2

There are 2 triangles so:

60 × 2 = 120 cm^2

Area of 2 identical rectangles:

- They are identical and this is shown by the two short lines which indicate that this is an isosceles triangle. They have 2 identical sides.

A = L × W

Substitute

10 × 13 = 130

Because there are two:

130 × 2 = 260 cm^2

Area of the rectangle at the bottom:

- Let's not forget the rectangle at the bottom of this shape.

A = L × W

Substitute

24 × 10 = 240 cm^2

Add these all together to get the total surface area:

120 + 260 + 240 = 620 cm^2

Answer: 620 cm^2

Answer:

620cm squared

Step-by-step explanation:

a=bxh/2

so this means

24x5/2=area of one triangle(60cm squared)

since there are two .that means the area for both triangles is 120cm squared

for the recatngles:

a=lxw

Substitute

10 × 13 = 130

since there are 2 of them,

130 × 2 = 260 cm^2

the rectangle on the bottom:

a=lxw

24x10=240cm squared

240+260+120=620

To determine the width:

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As a point estimator for, we utilise x-bar (sample mean) (mu, population mean)

The average value in mathematics is the middle number, which is calculated by dividing the total number of numbers by the sum of all the numbers. A set of data's average is calculated by adding up all the values and dividing the result by the total number of values.

We use the x-bar (sample mean) as a point estimator for (mu, population mean). As long as the sample is random, this estimator's impartial long-run distribution is centred at (mu).

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Complete question -

The probability of the coach’s basketball team winning the tournament most accurately impossible.

3.03 percent Chance of A

As a result, you could say there is a 3.03% Probability instead of saying there are 1 to 32 Odds.

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of occurrences that follow a probability distribution.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.

A basketball coach determines the team has a 1 32 probability of winning a tournament.

The probability of the coach’s basketball team winning the tournament most accurately impossible.

The complete question is

A basketball coach determines the team has a 1/32 probability of winning a tournament. Which choice describes the probability of the coach's basketball team winning the tournament most accurately?

answer choices

certain

impossible

likely

unlikely

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The function to derive an nth Taylor polynomial is y = nthTaylorPolyExp( n, x )

%y = nthTaylorPolyExp( n, x )is a function that returns 3rd Taylor polynomial of exponential function at x=0.

%       n is an input argument, which indicates the degree of Taylor

%           polynomial.

%       x is an input argument

%       y is the output.

y=zeros('like',x);

% ============= YOUR CODE HERE ==============

% Instructions: Return nth Taylor polynomial of exponential function at x=0.

%               You can use built-in function factorial(n) to return n!,

%               and use for loop to get the sum.

for i = 0:n

     % y = y + (-1)^i * (x.^(2 * i)) / factorial(2 * i); is my version, but its incorrect.

end

Thus, the function to derive an nth Taylor polynomial is y = nthTaylorPolyExp( n, x )

Complete question: How do I write the function to derive an nth taylor polynomial?

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The best way to report for (515 x 0.0025) is 25.86 and it is done using the concept of significant figures.

Given (515 x 0.0025) + 24.57

We are asked to report the answer in the best way. This can be done using the concept of significant figures.

We can see that 515 has 3 significant figures

0.0025 has 4 significant figures ( we have to consider the zeros after the decimal)

24.57 has 4 significant figures

Thus the best answer will have 4 significant figures.

(515 * 0.0025 ) + 24.57 = 25.8575 = 25.86

We have to round off the answer to 4 significant figures, thus it'll be 25.86 ( 5 becomes 6 because the figure next to 5 is 7, thus 5 will be rounded off to 6 )

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Answer: The values that make the denominator equal to zero for a rational expression are known as restricted values. How do you identify restrictions in rational expressions? The restriction is that the denominator can not be equal to zero. So in this problem, since 4x is in the denominator it can not equal zero.

The student must earn a 74 on the final exam to pass the course with an average of 70.

The student's current average score is (64 + 69 + 73) / 3 = 66.

To find the score the student needs to earn on the final exam to maintain an average of 70, we can set up an equation:

(64 + 69 + 73 + x) / 4 = 70

Where x is the score the student needs to earn on the final exam.

Solving for x:

(64 + 69 + 73 + x) = 280

x = 280 - 64 - 69 - 73 = 74

So, the student must earn a 74 on the final exam to pass the course with an average of 70.

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The capacity of the elevator is 15 children or 11 adults. If 9 children are currently on the elevator, then there are 15 - 9 = 6 spots available for either children or adults.

However, since the maximum number of adults the elevator can hold is 11, the answer to the question is 11 - 9 = 2 adults can still get in.

You can act for the unknown amounts by the use of variables. Follow ignoring the description is and convert it one by one mathematically. For example, if it is asked to increase some item by 5, then you can add 5 in that item to increase it by 5.

If a thing is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.

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Any equation with one or more terms and one or more derivatives of the dependent variable with respect to the independent variable is referred to as a differential equation.

Here i attached answer.

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Answer: y = -4x + 29

Step-by-step explanation:

To find the equation of the line passing through the points (-3, 17) and (2, -3), we can use the slope-point form of a line, which is given by:

y - y1 = m(x - x1)

Where (x1, y1) is a point on the line, m is the slope of the line, and (x, y) are the coordinates of any other point on the line. To find the slope of the line, we can use the formula:

m = (y2 - y1) / (x2 - x1)

Plugging in the coordinates of the two points, we have:

m = (-3 - 17) / (2 - (-3)) = -20 / 5 = -4

Next, we plug in the coordinates of one of the points and the slope into the slope-point form of a line:

y - 17 = -4(x - (-3))

Expanding the right side:

y - 17 = -4x + 12

Adding 17 to both sides:

y = -4x + 29

So the equation of the line passing through the points (-3, 17) and (2, -3) is: y = -4x + 29

Answer:

1/8

Step-by-step explanation:

The coin is flipped three times; the total number of outcomes = 2 × 2 × 2 = 8. P(X) = |X| / |Ω| = 1/8.

The equivalent fractions are
1.) 5/6 > 4/6

5.) 7/8 > 4/8
9.) 8/10 < 15/10
13.) 6/8 < 7/8

what is a fraction?

A fraction is a mathematical expression that represents a part of a whole or a division of one quantity into equal parts. It consists of two parts, a numerator and a denominator. The numerator represents the number of equal parts of the whole and the denominator represents the total number of parts the whole is divided into.

1.) 5/6 ___ 2/3

To compare these fractions, it's best to find equivalent fractions with a common denominator. A common denominator for 6 and 3 is 6. So, to make the denominator of 2/3 equal to 6, multiply both the numerator and denominator by 2:

2/3 * 2/2 = 4/6

Now, both 5/6 and 4/6 have a common denominator of 6. So, we can easily compare:

5/6 __ 4/6

5/6 is greater than 4/6, so the answer is 5/6 > 4/6

5.) 7/8 ___ 1/2

To compare these fractions, it's best to find equivalent fractions with a common denominator. A common denominator for 8 and 2 is 8. So, to make the denominator of 1/2 equal to 8, multiply both the numerator and denominator by 4:

1/2 * 4/4 = 4/8

Now, both 7/8 and 4/8 have a common denominator of 8. So, we can easily compare:

7/8 __ 4/8

7/8 is greater than 4/8, so the answer is 7/8 > 4/8

9.) 8/10 ___ 3/4

To compare these fractions, it's best to find equivalent fractions with a common denominator. A common denominator for 10 and 4 is 10. So, to make the denominator of 3/4 equal to 10, multiply both the numerator and denominator by 5/5:

3/4 * 5/5 = 15/10

Now, both 8/10 and 15/10 have a common denominator of 10. So, we can easily compare:

8/10 __ 15/10

8/10 is less than 15/10, so the answer is 8/10 < 15/10

13.) 3/4 ___ 7/8

To compare these fractions, it's best to find equivalent fractions with a common denominator. A common denominator for 4 and 8 is 8. So, to make the denominator of 3/4 equal to 8, multiply both the numerator and denominator by 2:

3/4 * 2/2 = 6/8

Now, both 6/8 and 7/8 have a common denominator of 8. So, we can easily compare:

6/8 __ 7/8

6/8 is less than 7/8, so the answer is 6/8 < 7/8

Hence, the equivalent fractions are
1.) 5/6 > 4/6

5.) 7/8 > 4/8
9.) 8/10 < 15/10
13.) 6/8 < 7/8

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The portion of the parabola from t=-1 to t=1 can be parametrized as x=2t²-4 and y=t.

A parabola is a symmetrical and U-shaped curve that is defined by a mathematical equation.

In this case, we will use the variable t to represent the y-coordinate and find the corresponding x-coordinate. The equation becomes y=t, and substituting this into the original equation, we get

=> x=2t²-4.

To find the portion of the parabola where -1≤t≤1, we can plot the points (x, y) for various values of t in this range.

when t=-1,

=> x=2(-1)²-4 = 0.

And when

t=1, x=2(1)²-4 = -2.

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The order of the group generated by matrices a and b under matrix multiplication is a process of multiplying the matrices and counting the number of distinct matrices that can be produced.

A matrix is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns.

The order of a group generated by matrices a and b refers to the number of distinct matrices that can be produced by multiplying a and b a certain number of times.

To find the order of the group, we need to start by multiplying a and b and see if we get any new matrices. If we do, we keep multiplying those matrices until we get back to the original matrices a and b.

The order of the group is the number of distinct matrices we get in this process.

It is important to note that matrix multiplication is associative, which means that the order in which we multiply the matrices does not affect the result. Also, the identity matrix is a special matrix that, when multiplied by any matrix, produces the same matrix.

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By applying linear equation concept, it can be concluded that the line representing the artist whose downloads have remained constant over the month is the horizontal one, line m.

Linear equation is an equation that contains one or more variables, where each variable has the power of one.

Linear equation graph with a particular slope will be formed if this equation is depicted in a Cartesian diagram. The slope is usually called the gradient of the line (m), so the equation can be written as y = mx + c.

If the line graph is sloping to the right indicates that the gradient is positive. Conversely, if the line graph is sloping to the left indicates that the gradient is negative.

Therefore, the line representing the artist whose downloads have remained constant over the month is the horizontal one, line m.

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When ΔKLM is dilated with a scale factor of 2 the new ΔK'L'M' has vertices K'(4,10), L'(8,4) and M'(4,4).

What is dilation?

Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. The initial shape should be stretched or contracted during a dilatation.

The ΔKLM has the coordinates of vertices - K(2,5), L(4,2) and M(2,2)

If the scale factor is 2, then every coordinate point of the original triangle is multiplied by the scale factor 2.

When the triangle is dilated with the scale factor of 2, the coordinate points formula becomes -

(x,y) → (2x,2y)

So, obtain the new triangle ΔK'L'M' -

K(2,5) → [2(2),2(5)] → K'(4,10)

L(4,2) → [2(4),2(2)] → L'(8,4)

M(2,2) → [2(2),2(2)] → M'(4,4)

The graph for the new coordinates have been ploted.

Therefore, the new coordinates are K'(4,10), L'(8,4) and M'(4,4).

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The equations are solved to give

1. y = 13

2. x = 3

3. b = 3

It is important to note that algebraic expressions are expressions composed of variables, terms, factors, constants and coefficients.

From the information given, we have that the expressions are;

3y+5=2y-8

Now, collect like terms

3y - 2y = -8 - 5

subtract the like terms

y = 13

-2(x-1)=3x-13

expand the bracket

-2x + 2= 3x - 13

collect like terms

-2x -3x = -13 - 2

subtract the like terms

-5x = -15

x = 3

3b+4+b=16

collect like terms

4b = 12

b = 3

Hence, the values are 13. 3 and 3

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The number of hot dogs will Team A need to sell to reach its goal is 690.

What is the linear equation in one variable?

A linear equation in one variable is an equation that can be written in the form: y = mx + b,where "x" is the independent variable, "y" is the dependent variable, "m" is the slope of the line, and "b" is the y-intercept.

Let the number of dogs be x.

1.48x - 20 = 1000
1.48x = 1020
x = 1020/1.48
x = 690

Hence, the number of hot dogs will Team A need to sell to reach its goal is 690.

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The area of the paperboard that remains is 268.83 square inches.

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.

Given that, a rectangular paperboard measuring 22 in long and 18 in wide has a semicircle cut out.

Area of rectangular paperboard length×width

= 22×18

= 396 square inches

Area of a semicircle = 1/2 ×πr²

Here, r=18/2 = 9 inches

= 1/2 ×3.14×9²

= 127.17 square inches

So, remaining area = 396-127.17

= 268.83 square inches

Therefore, the area of the paperboard that remains is 268.83 square inches.

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The function of parking in the garage is C(t) = 6 + 2.4t

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

Rate each hour = 2.40

Initial rate = 6.00

The function is then represented as

C(t) = Initial rate + Rate each hour * number of hours

So, we have:

C(t) = 6 + 2.4t

Hence, the function is C(t) = 6 + 2.4t

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Answer:

Let x be the amount Pam has, then Dan has x - $3.00 and Sam has x + x - $3.00 + $1.00 = 2x + $1.00

The total amount of money they have is x + x - $3.00 + 2x + $1.00 = 31.00

So, 4x + $1.00 = 31.00

Subtracting $1.00 from both sides gives 4x = 30.00

Finally, dividing both sides by 4 gives x = $7.50

So Pam has $7.50, Dan has $7.50 - $3.00 = $4.50, and Sam has $7.50 + $4.50 + $1.00 = $13.00.

A trigonometric ratios calculator is a tool that helps you find the sine, cosine, and tangent ratios in a right triangle. To use a trigonometric ratios calculator, you need to enter the lengths of the sides of the right triangle and the calculator will calculate the values of the sine, cosine, and tangent ratios for the angles in the triangle.

Here's how you can use a trigonometric ratios calculator to find the sine, cosine, and tangent ratios in a right triangle:

1. Enter the lengths of the sides of the right triangle into the calculator.

2. Select the angle for which you want to find the trigonometric ratios.

3. The calculator will display the values of the sine, cosine, and tangent ratios for the selected angle.

Note that the trigonometric ratios are defined only for right triangles, so it's important to make sure that the triangle you are working with is a right triangle before using a trigonometric ratios calculator.

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A trigonometric ratios calculator is a tool that helps you find the sine, cosine, and tangent ratios in a right triangle. To use a trigonometric ratios calculator, you need to enter the lengths of the sides of the right triangle and the calculator will calculate the values of the sine, cosine, and tangent ratios for the angles in the triangle.

Here's how you can use a trigonometric ratios calculator to find the sine, cosine, and tangent ratios in a right triangle:

1. Enter the lengths of the sides of the right triangle into the calculator.

2. Select the angle for which you want to find the trigonometric ratios.

3. The calculator will display the values of the sine, cosine, and tangent ratios for the selected angle.

Note that the trigonometric ratios are defined only for right triangles, so it's important to make sure that the triangle you are working with is a right triangle before using a trigonometric ratios calculator.

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Answer:

A = 112

Step-by-step explanation:

Area of rectangle = LW

x = 2

L = x + 6 = 2 + 6 = 8

W = 9x − 4 = 9(2) − 4 = 18 - 4 = 14

A = LW = 8(14) = 112

Answer: A = 112          

Your welcome for the help