a. Are the integers closed under addition and subtraction? In other words, when you add or subtract two integers, is the result always an integer? Justify your response.

b. Give a counterexample to show that the whole numbers are not closed under subtraction.

Answer:

There is no real solution set for this equation

Step-by-step explanation:

We have

[tex]\sqrt{2x-1}+7=4[/tex]

Move 7 to the right side:

[tex]\sqrt{2x-1}+7-7=4-7\\\\\sqrt{2x-1}=-3\\\\[/tex]

If we treat 2x - 1 as a function f(x) then we are getting

[tex]\sqrt{f(x)} = -3\\\\[/tex]

But the square root of a function cannot be negative for real values of x

Hence there is no real solution set

If the post office is 13 blocks away from the library and each block is 275 meters, approximately, the distance from the post office to the library, in miles, is 2.2 miles.

To determine the distance or the number of miles from the post office to the library, we use unit conversions and mathematical operations (multiplication and division).

Using multiplication, the number of blocks is converted to meters.

The distance is converted from meters to miles by division.

The distance of a block in the city = 275 meters

The number of blocks from the library to the post office = 13 blocks

The distance from the post office to the library = 3,575 meters (13 x 275)

1,609.34 Meters = 1 Miles

The distance in miles from the post office to the library = 2.2 miles (3,575/1,609.34)

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The width of the leftover brass is 18 1/2 inches.

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

Initial length = 36 inches

Length of each piece = 8 3/4 inches

The width of the leftover brass is then calculated as

Width = Initial length - 2 * Length of each piece

substitute the known values in the above equation, so, we have the following representation

Width = 36 - 2 * (8 3/4)

Evaluate

Width = 18 1/2

hence, the width is 18 1/2 inches

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Answer:

2048

Step-by-step explanation:

Find out what [tex]16^{3}[/tex] is:

16x16x16 =

4096.

Now lets divide it by 2:

4096/2 =

2048.

2048 would be your answer to your problem.

The two previous terms of 248 are 64 and 18.

A term-to-term rule is a rule that will describe calculating the following terms of a sequence given by the previous term.

In the given problem, the rule is to subtract 2 and multiply by 4.

Considering that the third term is 248. we can utilize the rule to figure out the subsequent term.

248 = (4 * (x - 2))

248 = 4x - 8

256 = 4x

x = 64

So the subsequent term is 64.

To find the initial term, we can utilize a similar rule once more

64 = (4 * (x - 2))

64 = 4x - 8

72 = 4x

x = 18

So the initial term is 18.

Therefore, the two previous terms of 248 are 64 and 18.

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There was a 125% change in the price of the house.

The answer can be deduced to be above 100% because the revised price represented an increase from the initial 100,000.

Tom's house cost $100000 in the year 2000.

In 2008 he sold his house for $125000.

Whatever the case, in order to solve this problem,

you must divide 100,000 by 125,000 to discover the answer. 125,000/100,000=1.25.

Then 1.25 can be converted to 125%.

So, There was a 125% change in the price of the house.

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Answer:

Mixed Number: [tex]\frac{7}{2}[/tex]

Regular [tex]3\frac{1}{2}[/tex]

Explantion \/ \/

The cost of the wings per dollar is 1.2 wings per dollar ($15 / 18 wings = $0.83 per wing). The cost of 18 wings is $15. To calculate the cost of the wings per dollar, divide the total cost of the wings ($15) by the number of wings (18).

1. Divide the total cost of the wings ($15) by the number of wings (18).

2. The result of this calculation is the cost of each wing ($15 / 18 = $0.83).

3. Divide 1 by the cost of each wing ($1 / $0.83 = 1.2 wings per dollar).

The cost of 18 wings is $15. To calculate the cost of the wings per dollar, divide the total cost of the wings ($15) by the number of wings (18). This calculation will give the cost of each wing ($15 / 18 = $0.83). To find the number of wings per dollar, divide 1 by the cost of each wing ($1 / $0.83 = 1.2 wings per dollar). This means that for every dollar spent, 1.2 wings can be purchased.

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Answer:

Step-by-step explanation:

honolululuulu

The linear function relating S to N is given as follows:

S(n) = 1800 + 60n.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

For which the parameters are given as follows:

The parameter values for this problem are given as follows:

m = 60, b = 1800.

Hence the function is defined as follows:

S(n) = 1800 + 60n.

The function is graphed on the image given at the end of the answer.

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The probability that the first item is not the first to be delivered is 0.6667

Represent the events that the first, second, and third items arrive on the first day of February A, B, and C, respectively.

So, the probability that one of the other two items arrives first is

1/3 + 1/3 = 2/3.

The probability that the first item is not the first to be delivered is

1 - 2/3 = 1/3

Evaluate

1 - 2/3 = 0.6667

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When a  transformation is applied to a figure to create a new figure then Dilation do not preserve congruence but do preserve orientations.

Rotations, reflections, translations, and dilation are only a few of the many transformations. Dilation do not preserve congruence but do preserve orientations. Rotations, reflections, and translations all preserve congruence and are referred to as isometries.

Maintaining congruence refers to a transformation where the side lengths and angle measurements of the Image and Pre-Image are the same.

An object's orientation refers to how its related parts are ordered. As long as the components of an item remain in the same sequence, rotation and translation retain orientation. Orientation is not maintained by reflection.

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The length of the base is 2√15 units. The median of an isosceles triangle divides the triangle into two equal parts.

What is an isosceles triangle?

An isosceles triangle in geometry is a triangle with two equal-length sides. It can be specified as having exactly two equal-length sides or at least two equal-length sides, with the latter definition including the equilateral triangle as an exception.

A median in a triangle is a line that runs from one corner (or vertice) to the centre of the other side. Triangle congruence makes it easy to demonstrate an isosceles triangle's property that the median to the base is perpendicular to the base.

According to the Pythagorean theorem,

AD² + BD² = AB²

7² +  BD² = 8²

BD² = 64 - 49

BD² = 15

BD = √15

The median divides the base into two equal parts.

The length of the base is 2√15.

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Answer:

126 cans in total / 6 cans per row

126/6 = 21 rows of cans

Using arithmetic operations it is found that -

It took Castenea 10 hours and 36 minutes to finish the first book Eragon.

The number of pages in Castenea's second book Eldest is 707.

What is arithmetic operation?

A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.

The number of pages in Eragon is = 530 pages

The rate for Castanea's reading is = 1 page/72 seconds

The time taken by Castanea to finish the first book is -

Time Taken = Number of Pages × Time taken to read 1 page

Use the arithmetic operation of multiplication.

Substitute the values in the equation -

Time Taken = 530 × 72

Time Taken = 38160 seconds

To convert seconds into minutes use the arithmetic operation of division.

38160 / 60 = 636 minutes

To convert minutes into hour use the arithmetic operation of division.

636 / 60 = 10.6 hour

Therefore, it took Castanea 10 hours 36 minutes to finish the first book.

The time took by Castanea to finish the second book = 14 hours 8 minutes and 24 seconds

To convert hours into minutes use the arithmetic operation of multiplication.

14 × 60 = 840 minutes

To convert minutes into seconds use the arithmetic operation of multiplication.

848 × 60 = 50880 seconds

Use the arithmetic operation of addition to get the total seconds -

50880 + 24 = 50904 seconds

The rate for Castanea's reading is = 1 page/72 seconds

The number of pages in Castanea's second book is -

Number of Pages = Time Taken in total/Time taken to read 1 page

Use the arithmetic operation of division.

Substitute the values in the equation -

Number of Pages = 50904/72

Number of Pages = 707

Therefore, there were seven pages in the second book.

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Answer:7 games

2 cases= x games

you give 4 or 2 from each case

divide 10 by 2 and get 5 them add 2 to your answer and get 7 GAMES

BOOM!!

The bearing of point A from point O is 256°.

In mathematics, a bearing is the angle in degrees measured clockwise from north. Bearings are usually given as a three-figure bearing. For example, 30° clockwise from north is usually written as 030°.

Given that, angle x= 076° and angle y = 111°.

Now, the bearing of point A from point O is

180°+ 076°

= 256°

Therefore, the bearing of point A from point O is 256°.

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The size of angle x = 46 degree.

Now, According to the question:

A triangle in which at least two sides are equal is called an isosceles triangle. Following this fact, if two sides of a triangle are equal, then the angles opposite to those sides are also equal.

"Information available from the question"

Since Δ ABC is equilateral then interior angles = 60°

Since CE = DE then Δ CDE is isosceles and the base angles are congruent,

So,

∠ ECD = [tex]\frac{180-32}{2}[/tex] = [tex]\frac{148}{2}[/tex] = 74 degree

BCD is a straight line, then the 3 angles on it sum to 180°, that is

60° + 74° + x = 180°

134° + x = 180° ( subtract 134° from both sides )

Hence, The size of angle x = 46°

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Answer:

well the best I can say is maybe multiply all of the numbers

[tex]5 \times 7 \times 9 = x \div 3[/tex]

35*9=x÷3

315÷3

just do the 315÷3 and you should get an answer

4x−2y=14

Step-by-step explanation:

Answer:

The solution to the system of linear equations is x = 4, y = 1.

Step-by-step explanation:

Given system of linear equations:

[tex]\begin{cases}4x-2y=14\\y=\dfrac{1}{2}x-1\end{cases}[/tex]

To solve the system of linear equations by the method of substitution, substitute the second equation into the first equation:

[tex]\implies 4x-2\left(\dfrac{1}{2}x-1\right)=14[/tex]

Solve the equation for x:

[tex]\implies 4x-x+2=14[/tex]

[tex]\implies 3x+2=14[/tex]

[tex]\implies 3x=12[/tex]

[tex]\implies x=4[/tex]

Substitute the found value of x into the second equation and solve for y:

[tex]\implies y=\dfrac{1}{2}(4)-1[/tex]

[tex]\implies y=2-1[/tex]

[tex]\implies y=1[/tex]

Therefore, the solution to the system of linear equations is:

Answer: Let x be the number of points scored by each girl and y be the number of points scored by each boy.

We know that:

3x + 2y = 27 (the total number of points scored by the 3 girls and 2 boys)

3x - 2y = 15 (the difference between the number of points scored by the girls and the number of points scored by the boys)

We can use the second equation to find the value of one of the variables and substitute it into the first equation.

3x - 2y = 15

3x = 15 + 2y

Substitute this into the first equation:

(15 + 2y) + 2y = 27

2y = 12

y = 6

Now that we know that each boy scored 6 points, we can substitute that back into the second equation to find the number of points each girl scored:

3x - 2y = 15

3x - 2(6) = 15

3x = 27

x = 9

So each girl scored 9 points and each boy scored 6 points.

Step-by-step explanation:

On a team have 3 girls and 2 boys

Let say  each girl points scored=x

Let say  each boy points scored=y

Total scored by 3 girls and 2 boys =27

                                              3x +2y=27----------1

The difference between points of  3 girls and 2 boys =15

                                               3x-2y=15---------2

Solve equation 1 and 2

From 2nd equation

we can rewrite as :

                          3x=15+2y---------3

Submit 3rd equation in 1st equation.

             15+2y+2y=27

                          4y=27-15

                          4y=12

                            y=3

Therfore, each boy points scored=3

For find each girl scored points

Submit y=3 in 1st equation.

                     3x+2(3)=27

                              3x=27-6

                              3x=21

                                x=7

Therfore, each girl points scored=7

Therfore,number of points each boy scored by =3points

Therfore,number of points each girl scored by =7points

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The GDP using value added approach is $3.50

GDP using value added approach is calculated by obtaining the sum total of value added by each production unit.

Value added by Farmer Fred = Price of output - Cost of inputs = $0.50 - $0 = $0.50

Value added by Baker Bob = Price of output - Cost of inputs = $1.50 - $0.50 = $1.00

Value added by Trucker Tom = Price of output - Cost of inputs = $2.25 - $1.50 = $0.75

Value added by Retail Rob = Price of output - Cost of inputs = $3.50 - $2.25 = $1.25

GDP = Value added by Farmer Fred + Value added by Baker Bob + Value added by Trucker Tom + Value Added by Retail Rob

GDP = $0.50 + $1.00 + $0.75 + $1.25

GDP = $3.50

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Answer: 43

Step-by-step explanation:

Multiply 8.6 and 10 then subtract 7 then you do 4.3 times 10 then you subtract then subtract the values you get

The conclusions that can be made from this table include:

A percentage simply has to do with the a value or ratio which can be stated as a fraction of 100. It should be noted that when we want to we calculate a percentage of a number, we simply divide it and then multiply the value that is gotten by 100.

From the information, factory A for those who need repairs is 0.05 in the first year. In this case, among cars from factory A, a larger percentage of cars do not need repairs than do need repairs in the first year.

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The area of the circle, as a function of x, will be:

A(x) = 3.14*(3ft + 2x)²

We know that for a circle of radius R, the area is:

A = pi*R²

Where pi = 3.14

In this case we have a circular plot of land with a diameter of 6ft, then the radius (half of that) is:

R = 6ft/2 = 3ft

And then we have a walkway with a width of 2x, then the radius of the circle that includes the walkway is:

R' = 3ft + 2x

Replacing that in the area equation we will get:

A(x) = 3.14*(3ft + 2x)²

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So, the probability that you see at least one shooting star in the period of an hour is 59.04%.

The probability of seeing at least one shooting star in a 15-minute interval is 20%, so the probability of not seeing a shooting star in that interval is 80%. The probability of not seeing a shooting star in an hour-long period is the product of the probability of not seeing a shooting star in each of the four 15-minute intervals, which is 0.8 * 0.8 * 0.8 * 0.8 = 0.4096 or 40.96%. Therefore, the probability of seeing at least one shooting star in an hour-long period is 1 - 0.4096 = 59.04%.

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The area of the border is 72 square inches - 80 square inches = -8 square inches.

What is rectangle ?

A rectangle is a four-sided geometric shape with four right angles. The opposite sides of a rectangle are of equal length and parallel to each other, and the opposite angles are equal. The length and width of a rectangle are its two dimensions, with the length being the longer side and the width being the shorter side.

To find the area of the border, subtract the area of the photograph from the total area of the photograph and the frame. The total area of the photograph and the frame is the area of the frame (which is just the border) plus the area of the photograph.

The area of the photograph is 8 inches * 10 inches = 80 square inches

The area of the frame is the perimeter of the photograph (28 + 210) multiplied by the width of the border, which is 2 inches. So the area of the frame is 2*(28 + 210) = 2*36 = 72 square inches.

Therefore, the area of the border is 72 square inches - 80 square inches = -8 square inches.

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(a)The class width = 3

(b) The class midpoint of the first class = 51

(c) The class boundaries of the first class =  (49.5, 52.5)

Consider the frequency distribution in the following image.

We know that in  frequency distribution the class width is nothing but the distance between the lower limits of consecutive classes.

Whereas the range is the difference between the maximum and minimum data entries.

The smallest number is 50, and the largest is 62.

So the range is 62 - 50 = 12

We know that the formula for the class width:

Class width= upper limit – lower limit +1

So, the class width = 52 - 50 + 1

                               = 3

The formula for the midpoint of each class:

midpoint = (lower limit of class + upper limit of class)/2

Let us assume that m be the midpoint of the first class.

Using above formula of midpoint:

m = (50 + 52)/2

m = 51

We know that the class boundaries are nothing but the end points of an open interval which contains the class interval.

So, the class boundaries of the first class = (49.5, 52.5)

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Any p-value less than 0.05 is a cause to reject the null hypothesis.

What is Null Hypothesis?

The statement "The null hypothesis is a claim about population parameter that is assumed to be false until it is declared false" is false. The null hypothesis is denoted by H0 assumes that the claim you are trying to prove did not happen. It is a claim about a population parameter that is assumed to be true until it is declared false.

In this case, 0.015 is the only option for p-value that would lead to a rejection of the null hypothesis (if the level of significance for the test is 0.05).

Any p-value less than 0.05 is a cause to reject the null hypothesis.

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Since J and M are base angles of trapezoid JKLM, the measure of k is 168°.

The base angles of an isosceles trapezoid are congruent and equal. This ultimately implies that, an isosceles trapezoid has base angles that are always equal in magnitude.

By equating the given base measures of isosceles trapezoid JKLM, we can determine the specific value of x and angle k as follows;

m∠J = m∠M

4x + 1 = 12x - 95

By re-arranging and collecting like terms, we have the following:

12x - 4x = 95 + 1

8x = 96

By dividing both sides of the equation by 8, we have the following:

x = 96/8

x = 12.

Therefore, the measure of k is given by:

m∠k = 180 - 12

m∠k = 168°.

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