a triangular field has boundaries of lengths 170m,195m and 210m,find the size of the largest interior angle of the field

The linear programming model that can be used to determine the number of units of each model in order to maximize the profit is x2 <= 280 (Lady-Sport Frames), 2 x1 + 2.5 x2 <= 1000 (Assembly & Test).

When a linear function is exposed to various constraints, it is maximised or reduced using the mathematical modelling technique known as linear programming. In commercial planning, industrial engineering, and—to a lesser extent—the social and physical sciences, this method has proven helpful for directing quantitative decisions.

A linear programming problem can be solved by determining the best value.

a)Let x1 be number of EZ-Riders produced.

Let x2 be number of Lady-Sports produced.

The Objective is to maximize the profit contribution:

Max 2,400 x1 + 1,800 x 2

The Constraints are: Engine Manufacturing Time <= 2100 hours

Lady-Sport Frames <= 280 frames

Assembly & Test <= 1000 hours

6 x1 + 3 x2 <= 2100 (Engine Manufacturing)

x2 <= 280 (Lady-Sport Frames)

2 x1 + 2.5 x2 <= 1000 (Assembly & Test)

We also need bounds x1 and x2 => 0.

So the full model is:

Max 2,400 x1 + 1,800 x2

Subject to 6 x1 + 3 x2 <= 2100 (Engine Manufacturing)

x2 <= 280 (Lady-Sport Frames)

2 x1 + 2.5 x2 <= 1000 (Assembly & Test)

x1 => 0, x2 => 0

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Answer: To find the unit price for each fork, we need to divide the total cost of the box by the number of forks in the box.

The cost of the box is $4.98, and the box contains 96 forks. So the unit price for each fork is:

$4.98 ÷ 96 = $0.051875

Rounding to the nearest cent, the unit price for each fork is $0.05.

Step-by-step explanation:

Using the unitary method, we found that the cost of one fork of brand B is $0.051.

What is meant by the unitary method?

The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, and then multiplying that value to determine the required value. We typically utilise this technique for maths computations. This method allows us to calculate both the value of many units from the value of one unit and the value of many units from the value of one unit.

The worth of many things is supplied in the unitary technique, and we must either determine the value of more or fewer items. To do that, we must first determine the value of a single item by division and then determine the value of further or more items by multiplication.

Given,

The number of forks in a box of brand B = 96

  Price of 96 forks = $4.98

The unit price of brand B = Cost of one fork

Using the unitary method,

96 forks = $4.98

1 fork = $4.98 / 96 = $0.051

Therefore using the unitary method, we found that the cost of one fork of brand B is $0.051.

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Square root of 8 plus square root of 1 equal 3.82842712

Algebraic integers

The square roots of an integer are algebraic integers —more specifically quadratic integers. The square root of a positive integer is the product of the roots of its prime factors, because the square root of a product is the product of the square roots of the factors.

⇒ 3.8 rounded.

⇒ = 3.82842712

Hence, Square root of 8 plus square root of 1 equal 3.82842712

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Answer:

Answer:

See attached image and explanation below

Step-by-step explanation:

For the first table:
The cumulative frequency for each class interval is obtained by adding that class frequency to the sum of all frequencies less than that class interval

So the table will look as in the first image attached

The second table talks about cumulative relative frequency and it uses the same technique as above but we are dealing with relative rather than absolute frequencies

The second image shows the correct values

Your relative frequency table (the third image you posted) is correct

Answer:

y = (12 / (25/12)^7) * (25/12)^x

Step-by-step explanation:

To write an exponential model given two points, we can use the general form of an exponential function:

y = ab^x

where y is the dependent variable, x is the independent variable, b is the base or growth factor, and a is the initial value when x = 0.

Using the two given points, we can form a system of equations:

12 = ab^7 (1)

25 = ab^8 (2)

Dividing equation (2) by equation (1), we get:

25/12 = b^(8-7) = b

So the base of the exponential function is b = 25/12.

To find the initial value a, we can substitute b into either of the original equations. Let's use equation (1):

12 = a(25/12)^7

Simplifying, we get:

a = 12 / (25/12)^7

Therefore, the exponential model that fits the given points is:

y = (12 / (25/12)^7) * (25/12)^x

The measurement of x, in the given circle, is 5 cm.

A circle is a round-shaped figure that has no corners or edges. In geometry, a circle can be defined as a closed, two-dimensional curved shape.

Given is a circle with a tangent of 6 cm and a secant of length 4+x, we need to find the measurement of x,

Using properties of circle,

6² = 4·(4+x)

36/4 = 4+x

9 = 4+x

x = 5

Hence, the measurement of x, in the given circle, is 5 cm.

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The solution to the given inequality w > 2w - 9 is w < 9.

Inequality is defined as mathematical pieces of information that have a minimum of two terms including variables or numbers that are not equal.

The "inequality" is given in the question, as follows:

w > 2w - 9

We have to solve the above inequality for w.

⇒ w > 2w - 9

Rearrange the term of variable w in the above inequality,

⇒ w - 2w > - 9

Apply the subtraction operation and solve for w:

⇒ - w > - 9

Multiply the negative sign and flip the sign of inequality:

⇒ w < 9

Thus, the solution to the given inequality is w < 9.

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Answer:

true

Step-by-step explanation:

cause I’ve done this before

Answer:

Step-by-step explanation:

(a) To find the number of students who did not like either sport, we can use the formula:

Total students = Students who like basketball + Students who like hockey - Students who like both sports + Students who like neither sport

We know that the total number of students surveyed is 30, and we also know the number of students who like basketball, hockey, and both sports. We can use this information to solve for the number of students who like neither sport:

30 = 13 + 18 - 4 + Students who like neither sport

Simplifying this equation, we get:

3 = Students who like neither sport

Therefore, there were 3 students who did not like either sport.

(b) To find the number of students who liked exactly one of the sports, we can subtract the number of students who liked both sports from the total number of students who liked at least one of the sports. We know that 13 students liked basketball, 18 students liked hockey, and 4 students liked both sports. To find the number of students who liked at least one sport, we can add the number of students who liked basketball and the number of students who liked hockey, but we need to make sure we don't count the 4 students who liked both sports twice:

Number of students who liked at least one sport = Students who like basketball + Students who like hockey - Students who like both sports

Number of students who liked at least one sport = 13 + 18 - 4 = 27

Therefore, the number of students who liked exactly one sport is:

Number of students who liked exactly one sport = Number of students who liked at least one sport - Number of students who liked both sports

Number of students who liked exactly one sport = 27 - 4 = 23

So there were 23 students who liked exactly one of the sports.

Answer:0.047

Step-by-step explanation: This is actually easy  you need to divide using long division and put the numbers of the division that you use to subtract and then you get the answer.

The number of each denomination is: 13 of the $10-dollars bills.

Let x be number of the $20 dollars bills. Then, the number of the $10 dollars bills is (x+2), according to the condition.

The money equation will then be:

20x + 10*(x+2) = 350

Now, solve for x.  

20x + 10x + 20 = 350

30x = 350 -20

30x = 330

x = 330/30

x = 11

So, 11 of the $20 dollars bills and 11 +2 = 13 of the $10-dollars bills.

Full question "Part of the proceeds from a garage sale was ​$350 worth of ​$10 and ​$20 bills. If there were 2 more $10 bills than $20 bills, find the number of each denomination.

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Answer:

[tex]x < -3\text{ or }x > 3[/tex]

Step-by-step explanation:

[tex]|1-2x|-4 > 1\\|1-2x| > 5\\\\1-2x > 5\\-2x > 6\\x < -3\\\\1-2x < -5\\-2x < -6\\x > 3[/tex]

Answer:

Step-by-step explanation:

The two numbers that multiply to -140 also have to add to -13, so that means that the larger of the two numbers needs to be negative, and the other number positive.

7 x -20 = -140

7 - 20 = -13

Answer:its 1.4>1.3

Step-by-step explanation:I THINK ITS 1.4>1.3

Answer:

===================================================

Work Shown:

x = amount invested at 9%

y = amount invested at 3%

x+y = 2300 invested total, which solves to y = 2300-x

0.09x+0.03y = 189 dollars of total profit

Applying substitution to solve.

0.09x+0.03y = 189

0.09x+0.03(y) = 189

0.09x+0.03(2300-x) = 189

0.09x+69-0.03x = 189

0.06x+69 = 189

0.06x = 189-69

0.06x = 120

x = 120/0.06

x = 2000

y = 2300-x = 2300-2000 = 300

The solution as an ordered pair is (x, y) = (2000, 300)

Therefore, $2000 was invested at 9%, and $300 was invested at 3%.

Answer:

middle set of data

Step-by-step explanation:

The point slope form of a linear equation is an equation that describes the relationship between two variables, x and y, in terms of their linear relationship.

It takes the form:.y - y₁ = m(x - x₁)

where (x₁, y₁) is a point on the line and m is the slope of the line.

In this form, you can find the equation of a line if you know a point on the line and the slope of the line. You can also use this form to find the equation of a line if you are given two points on the line, by first finding the slope using the two points, and then plugging in one of the points and the slope into the equation.

The point slope form can be useful in a variety of contexts, such as in graphing and in solving problems involving rates of change.

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Answer:

24 inch cubes are needed to fill the bottom layer of the prism.

On solving the provided question we can say that at a simple 12% annual percentage rate, it would take approximately 6 years for capital to double.

In mathematics, a ratio or number expressed as a percentage of 100 is called a percentage. Also occasionally used are the acronyms "pct.," "pct," and "pc." Nonetheless, the percentage symbol "%" is widely used to represent it. The % quantity is dimensionally empty. Basically, percentages are fractions when the denominator is 100.

The annual rate of return is 12%, so we can calculate:

Time to double = 72 / 12 = 6 years

Therefore, at a simple 12% annual rate, it would take approximately 6 years for capital to double.

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The correct question is -

How long does it take for capital to double at a simple 12% annual rate?

Please find attached the graph of the parabola, y = x² - 4·x + 4, created with MS Excel, showing the points;

A parabola is the locus of a point that moves such that its distance from a point (known as the focus) and a line (known as the directrix), are the same.

1. The quadratic function is; y = x² - 4·x + 4

The x-coordinates of the vertex of the quadratic function, f(x) = a·x² + b·x + c, can be found using the formula;

x = -b/(2·a)

The x-coordinates of the graph of the equation, y = x² - 4·x + 4, is the point;

x = -(-4)/(2 × 1) = 2

The y-value of the vertex is therefore;

y = 2² - 4 × 2 + 4 = 0

The coordinates of the vertex is therefore; (2, 0)

2. The y-intercept is the point the graph intersects the y-axis, which is the point the x-value is zero, therefore;

The coordinate of the y-value of the y-intercept is therefore;

y = 0² - 4 × 0 + 4 = 4

The y-intercept is therefore; (0, 4)

3. A point on a function can be plugging a value of the input as follows;

The point at x = 1 is; y = 1² - 4×1 + 4 = 1

Therefore, another point on the graph is; (1, 1)

4. The axis of symmetry is the vertical line passing through the vertex, with an equation which is the x-value of the vertex

The x-value of the vertex is; x = 2, therefore, the axis of symmetry is the line; x = 2

The reflection of a point (x, y) about the vertical y-axis is the point (-x, y)

Therefore, the image of the reflection of the y-intercept, (0, 4) about the line x = 2 will be the point (4, 4)

The reflection of the point (1, 1), about the line x = 2 is the point (3, 1)

The above points can be used to graph the parabola, y = x² - 4·x + 4.

Please find attached the graph of the parabola created with MS Excel.

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The statement if Cathy does not love horses, she is not a gambler is valid.

Relative frequency is the ratio of the considered sub group's count to the total count. (so its frequency of the considered sub group relative to the total frequency).

We are given;

The two arguements

Now,

A). The argument is valid. This is an example of the disjunctive syllogism, which is a valid form of argument. If we have a disjunction "A or B", and we know that A is false, then we can conclude that B must be true. In this case, "she will go to school or she will get a job" is the disjunction, and "she will not get a job" tells us that "she will not get a job" is true. Therefore, we can conclude that "she will go to school" must be true.

B). The argument is invalid. This is an example of the fallacy of affirming the consequent. The conditional statement "if Cathy is a gambler, then she lives in Marine" tells us that if Cathy is a gambler, then she lives in Marine. However, it does not tell us anything about whether Cathy is a gambler or not. The fact that "Cathy lives in Marine and she loves horses" does not give us any information about whether Cathy is a gambler or not.

Therefore, by the given conditions answer "if Cathy does not love horses, she is not a gambler" will be valid

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Statements B , D and E are True.

Statements A and C are False.

The space that any three-dimensional solid occupies is known as its volume. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere.

A. Prism A and C have the same volume. - False

The volume of Prism A is 5 x 6 x 4 = 120 cubic cm, while the volume of Prism C is 7 x 3 x 5 = 105 cubic cm.

B. Prism B has a greater volume than Prism C. - True

The volume of Prism B is 8 x 4 x 3 = 96 cubic cm, while the volume of Prism C is 7 x 3 x 5 = 105 cubic cm.

C. Prism B has the least volume. - False

The volume of Prism A is 5 x 6 x 4 = 120 cubic cm, which is greater than the volume of Prism B.

D. The volume of Prism A is 120 cubic centimeters. - True

As calculated above, the volume of Prism A is 120 cubic cm.

E. The volume of Prism C is less than the volume of Prism A. - True

As calculated above, the volume of Prism C is 105 cubic cm, which is less than the volume of Prism A.

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The circumference of a circle is given by the formula C = 2πr, where r is the radius of the circle.

Since the diameter of the garden is 42m, the radius is half of that, which is:

r = 42m / 2 = 21m

The circumference of the circular garden is therefore:

C = 2πr = 2π(21m) = 42πm

If the gardener makes 4 rounds of the fence, he will need to purchase 4 times the circumference of the garden in barbed wire. Therefore, the length of barbed wire he needs to purchase is:

4 x 42πm = 168πm

This is approximately equal to 527.79m, if we use the value of π to two decimal places.

Answer:

528 M

Step-by-step explanation:

CIRCUMFERENCE OF GARDEN= 2 pi r

r=42/2 =21

circumference = 2x (22/7) x21

=132 m

To make 4 rounds= 4 x 132 = 528m

Value of integral ∫cos(x) + sin(x) 9 dx sin(2x) is  

-9cos(x)sin(2x) + sin(2x)sin(x) + c.sin(2x)

In mathematics, integrals are the continuous analogues of sums and are used to calculate areas, volumes, and their generalizations. Integration (the process of computing an integral) is one of the two basic operations in calculus, the other being differentiation.

Given,

∫(cos(x) + sin(x).9)dx . sin2x

simplifying

sin(2x) ∫(9sinx + cosx)dx

sin(2x) (9∫sin(x)dx+∫cos(x)dx)

sin(2x) (-9cos(x) + sin(x) + c)

Using distributive law

= sin(2x)(-9cos(x)) + sin(2x)sin(x) + sin(2x).c

= -9cos(x)sin(2x) + sin(2x)sin(x) + c.sin(2x)

Hence,  -9cos(x)sin(2x) + sin(2x)sin(x) + c.sin(2x) is the value of integral

∫(cos(x) + sin(x) . 9)dx sin(2x)

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The speed of the satellite around the earth in miles per hour is 8659.09 miles per hour.

Measurement is the method of comparing the properties of a quantity or object using a standard quantity.

Measurement is important to determine the quantity of any object.

A same quantity can have more than one type of measurement which can be converted to each other.

Given,

Speed of the satellite in feet per second = 12700 feet per second (ft/s)

We have,

5280 feet = 1 mile

1 feet = 1/5280 mile

12700 feet = 12700/ 5280 miles

Also,

60 minute = 1 hour

1 minute = 1/60 hour

60 seconds = 1 minute = 1/60 hour

1 second = 1/3600 hour

12700 feet per second =  12700/ 5280 miles ÷ 1/3600 hour

                                      = 8659.09 miles per hour.

Hence the speed converted is 8659.09 miles per hour.

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Answer:

Step-by-step explanation:

n+7=8

n=1

There are 840 ways for Yunseol to draw four cards from Ms. Q's deck, such that no two cards have the same color.

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

Colors = (1, 2, 3, 4, 5, 6, and 7).

To solve this problem, we can use the multiplication principle of counting.

We need to choose one card from each of the four colors, we use the following:

To count the total number of ways to draw four cards, we multiply the number of choices at each stage:

Total number of ways = 7 × 6 × 5 × 4 = 840

Hence, there are 840 ways for Yunseol to draw four cards

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Based on the graph, we can see that the relationship between the number of stuffed animals and the number of action figures is proportional since the line passes through the origin (0, 0), which is a characteristic of proportional relationships.

Mathematical relationships between two variables that have a constant multiple of one another are known as proportional relationships. This implies that when one variable rises or falls by a particular factor, the other variable rises or falls by the same amount as well.

In other words, a straight line on a graph that runs through the origin (0, 0) can be used to illustrate a proportionate connection. This is due to the fact that they are proportional, therefore when one variable is equal to zero, the other variable must likewise be zero.

To graph the linear relationship between the number of stuffed animals, x, and the number of action figures, y, we can use the two given data points: (20, 15) and (60, 45).

First, we can find the slope of the line that passes through these two points using the slope formula:

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

where (x1, y1) = (20, 15) and (x2, y2) = (60, 45)

slope = (45 - 15) / (60 - 20) = 30 / 40 = 0.75

Next, we can use the point-slope form of the equation of a line to write the equation of the line that passes through the two points:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) = (20, 15)

y - 15 = 0.75(x - 20)

y - 15 = 0.75x - 15

y = 0.75x

Now we can graph the line by plotting the two given points and drawing a straight line passing through them:

Linear relationship graph

Based on the graph, we can see that the relationship between the number of stuffed animals and the number of action figures is proportional, since the line passes through the origin (0, 0), which is a characteristic of proportional relationships.

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Answer: the distance between the points (-2, 5) and (-4, -5) is approximately 10.198 units.

Step-by-step explanation:

(-2, 5) and (-4,-5) are two points in the coordinate plane.

The first point (-2, 5) has an x-coordinate of -2 and a y-coordinate of 5. This point is 2 units to the left of the y-axis and 5 units above the x-axis.

The second point (-4, -5) has an x-coordinate of -4 and a y-coordinate of -5. This point is 4 units to the left of the y-axis and 5 units below the x-axis.

To find the distance between these two points, we can use the distance formula:

distance = sqrt[(x2 - x1)^2 + (y2 - y1)^2]

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

distance = sqrt[(-4 - (-2))^2 + (-5 - 5)^2] = sqrt[(-2)^2 + (-10)^2] = sqrt[104]

So the distance between the points (-2, 5) and (-4, -5) is approximately 10.198 units.