As part of an experiment to test different liquid fertilizers, a sprinkler has to be set to cover an area of 140 square yards in the shape of a sector of a circle of radius 50 yards. Through what angle should the sprinkler be set to rotate? If necessary, round the answer to two decimal places

The measures of three angles are 40.5°, 43.5° and 95.8°.

Law of Sines In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of any triangle to the sines of its angles.

The formula for sine rule is sinA/a=sinB/b=sinC/c

Given that, an interior designer plans to use triangular tiles that are 8 cm×9 cm×13 cm for a backsplash.

Using cosine rule, we get

9²= 8²+ 13²- 2(8)(13) cos θ (angle opposite 9 cm side.)

81=64+169-208 cos θ

81-233=-208 cos θ

-208 cos θ=-152

cos θ=-152/(-208)

cos θ=0.7307

θ=43.7°

Using sine rule,

The formula for sine rule is sinA/a=sinB/b=sinC/c

sinA/8 =sin43°/9=sinC/13

sinA/8 =0.7307/9

sinA/8=0.0811

sinA=0.6495

A=40.5°

So, ∠A+∠B+∠C=180°

40.5°+43.7°+∠C=180°

∠C=95.8°

Therefore, the measures of three angles are 40.5°, 43.5° and 95.8°.

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To find the remainder 10 when dividing 2x³ 3x² 8x by 2x 1, the polynomial must be augmented with -12.

A polynomial is an expression that consists of variables, exponents, and coefficients. It is a mathematical function composed of two or more terms, each of which is a number or a variable multiplied by an exponent. It can be used to represent a variety of relationships in mathematics, including equations, linear functions, quadratic functions, and more.

Therefore, the polynomial that will leave a remainder 10 when divided by 2x 1 is 2x³ 3x² 8x -12.

This is because if we divide the polynomial by 2x 1, the remainder will be the last term of the resulting polynomial, which is -12.

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The closest estimate of x when the functions satisfy the condition f(x) = g(x) is 1.65

What is a function?

Function is a mathematical law that establishes the relationship between an independent variable and a dependent variable.

Given,

[tex]f(x) =[/tex] [tex]\log\x_{3} (2x)[/tex]

[tex]g(x) = -4x^{2} + 3x +7[/tex]

Now plotting both the graphs in Desmos, we got the result as in the below figures.

Given f(x) = g(x)

So from the graphs, we can find an intersecting point. This intersecting point is common to both f(x) and g(x)

Therefore from the graph, the closest estimate of x is 1.65.

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Answer:

If x-3 is directly proportional to the square of y, then we can say that:

(x-3) = ky^2

Where k is a constant of proportionality.

If x=5 when y=2, we can substitute these values into the equation to find the value of k:

(5-3) = k(2)^2

2 = 4k

k = 0.5

Now that we have the value of k, we can use it to find the value of x when y=6:

(x-3) = (0.5)(6)^2

x-3 = 18

x = 21

So, if x is directly proportional to the square of y and x=5 when y=2, then x=21 when y=6.

The equation that shows the relationship between the weight and number of months. y =  79.5 + 5.5x

In science and technology, the weight of an object is the force acting on an object due to gravity. Some standard textbooks define weight as a vector quantity, the gravitational force acting on an object. Others define weight as a scalar quantity, the magnitude of  gravitational force. Still others define it as the size of the reaction force applied to the body by mechanisms resisting the influence of gravity: weight is a quantity measured, for example, by a spring balance.

Given that ; Total Month = 11 months

Gained weight at the rate =  5.5 kilograms per month.

Assume initial weight W,

The initial weight + total month  x rate = 140

w + 11 x 5.5 = 140

w = 79.5

if y is total weight after x months

y = 79.5 + 5.5x

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The best approach to solve the problem is writing an equation. Given Avelina earns half of what Gus earns, the equation becomes Avelina's earnings = Gus's earnings / 2. On substituting Gus's earnings with $125, we get Avelina's earnings to be $62.50.

The best problem-solving strategy that would be apt to solve this problem, 'Avelina earned half as much money as Gus. If Gus earned $125.00, how much money did Avelina earn?' is to write an equation. We know that Avelina earned half of what Gus earned. This can be represented by the equation: Avelina's earnings = Gus's earnings / 2.

Since we know that Gus earned $125, we can substitute this value into our equation: Avelina's earnings = $125 / 2. Solving this equation gives us the answer: Avelina earned $62.50.

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The lowest ratio for 54 m in 2.5 hours will be:

= 54 / 2.5 is 21.6 : 1.

Ratio in Mathematics simply demonstrates how many times one number can be able to fit into another number. It should be noted that ratios contrast two numbers by dividing them. In this case, A/B will be the formula if one is comparing one variable (A) to another variable (B).

This simply indicates that you're dividing the variable A by B. Let USA say for instance, the ratio will be 3/10 if A is 5

3 and B is 10.

In this case, the lowest ratio for 54 m in 2.5 hours will be:

= 54 / 2.5.

= 21.6 / 1

= 21.6:1

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Substitution method is a method used to solve equations. It involves replacing a variable with its given value, which helps to isolate it and solve for the unknown. For example, if we have the equation 2x+5=17, we can solve for x by substituting 17 for 2x+5 and then subtracting 5 from both sides to obtain x=12.

The substitution method is a technique used to solve systems of equations. An example of the substitution method would be solving the system of equations:

x + 2y = 5

3x + 6y = 15

First, solve the first equation for x:

x = 5 - 2y

Substitute the expression for x into the second equation:

3(5 - 2y) + 6y = 15

Simplify:

15 - 6y + 6y = 15

Solve for y:

15 = 15

Now substitute the value of y back into the expression for x:

x = 5 - 2(3)

Solve for x:

x = -1

Therefore, the solution to the system of equations is:

x = -1, y = 3

Substitute x in equation 1 into equation 2, solve, then substitute y back into equation 1.

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Answer:

  -2

Step-by-step explanation:

You want to know the dilation scale factor that gives triangle A'B'C from triangle ABC.

We notice that point A' is 4 units down and 2 units right of C, whereas A is 2 units up and 1 unit left of C. The ratio of these distances is the scale factor.

If up and right are positive, then ...

  k = (A' -C)/(A -C) = (2, -4)/(-1, 2) = -2

The dilation scale factor is -2.

198.5 is the answer

50X4-(3÷2)=198.5

Answer: 198.5

Step-by-step explanation:

= 50x4-(3 divided by 2)

= 50x4-(3/2)

= (50 x 4) - ( 3/2 )

= (200) - (3/2)

= 200 - 1.5

= 198.5

We will plot the graph for a LN function by keeping in mind that the domain must be greater than 0.

LN means natural logarithm. LN function denotes natural logarithm function. It has also another name, logarithm of base e.

It is expressed as

y = ㏑x that is the inverse of                            

the natural base exponential function

y = ex

If we have a logarithm function, f(x) = y = ln x

while plotting with the above function, ln x can be found for only the positive value of x and there is no value of ln x for negative values.

The properties of the graph of the LN function are following.

The domain of the LN function is only the real numbers that means x > 0.

The ranges of the LN function are all real number.

The coordinate of x intercept of the LN function is (1, 0).

The graph of LN function will be such that it will never touch the Y axis although it always approaches to it.

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Answer:

The answer is 5⁻¹ or 1/5

Step-by-step explanation:

5²/5³

Here, we know that the base is the same i.e., 5 so, will use the property;

5² ÷ 5³

5² ⁻ ³ = 5⁻¹ = 1/5

Thus, The answer is 5⁻¹ or 1/5

We refer to the enlargement or reduction of one of two figures as a similarity transformation. For example: When one of two figures can be produced from the other and the ratio of their corresponding sides is equal, we say that the two figures are comparable. Similar figures come in a variety of sizes and shapes.

Either a geometric similarity or a matrix transformation that produces a likeness are referred to as "similarity transformations" in this context. Space items are changed into comparable things by similarity transformations. Fractals and iterated function systems are based on essential principles such as similarity transformations and the idea of self-similarity.

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The area of a triangle when three side lengths are calculated by Heron's Formula. Heron's Formula states that the area of a triangle is equal to the square root of s(s-a)(s-b)(s-c)

To calculate the area of a triangle when three side lengths are given, we can use Heron's Formula. Heron's Formula states that the area of a triangle is equal to the square root of s(s-a)(s-b)(s-c) where s is half the perimeter of the triangle and a, b, and c are the lengths of the sides of the triangle.

To calculate the area of the triangle given three side lengths, we first need to calculate the perimeter (p) of the triangle. The formula for the perimeter is p=a+b+c.

Then, use this formula to calculate s, which is half the perimeter.

s = p/2

Once s is calculated, plug it into Heron's Formula to calculate the area of the triangle.

Area = √s(s-a)(s-b)(s-c)

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Answer:

Pitcher 2

Step-by-step explanation:

Pitcher 1  = 4 x 1.25 = 5ml concentration

Pitcher 2 = 5 x 2 = 10ml concentration

therefore, pitcher 2 has more concentration :)

hope this helped

For the given equations , the solutions are as follows :

(a) the equation [tex]6x + 8 = 7x + 13[/tex] has exactly one solution , and the solution is  .

(b) the equation [tex]6x + 8 = 2(3x + 4)[/tex] has Infinitely Many Solutions .

(c) the equation [tex]6x + 8 = 6x + 13[/tex] has No Solution .

Equation (a) ;

the equation is given as [tex]6x + 8 = 7x + 13[/tex] , we solve the equation further ,

we get ;

[tex]7x - 6x = 13 - 8[/tex] ;

[tex]x = 5[/tex] ;

So , the equation has exactly one solution and the solution is [tex]x = 5[/tex] .

Equation (b) ;

the equation is given as [tex]6x + 8 = 2(3x + 4)[/tex] , we solve equation further ,

we get ;

[tex]6x + 8 = 6x + 8[/tex] ;

On solving further ,

we have ;

[tex]8 = 8[/tex] ;

So , the equation has infinitely many solutions .

Equation (c) ;

the equation is given as [tex]6x + 8 = 6x + 13[/tex] , we solve equation further ,

we get ;

[tex]8 = 13[/tex] ;

and we know that [tex]8\neq 3[/tex] ,

So , the equation have No Solution .

The given question is incomplete , the complete question is

For each equation determine whether it has no solutions, exactly one solution, or is true . for all values of x (and has infinitely many solutions). If an equation has one solution, solve to find the value of x that makes the statement true.

(a) 6x + 8 = 7x + 13

(b) 6x + 8 = 2(3x + 4)

(c) 6x + 8 = 6x + 13

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The explanation of four quadrant are explained below.

In the coordinate plane the first coordinate or the x-coordinate will refer to the number which corresponds with the point's horizontal location as determined by the number on the x-axis.

And the second coordinate known as the y-coordinate, will refer to the number which corresponds with the point's vertical location as determined by the number on the y-axis.

By using these x and y values, we have divide the graph, into four part such as Quadrant I, Quadrant II, Quadrant III and Quadrant IV.

Here we want to know that each quadrant contains certain directions.

=> Quadrant 1 placed on 0 to 90 degrees.

=> Quadrant 2 placed on 90 to 180 degrees.

=> Quadrant 3 placed on 180 to 270 degrees.

=> Quadrant 4 placed on 270 to 360 degrees.

And the value in the quadrant are like as follows:

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The equation of line is given by y = 13.45x - 7.95 where the slope of the line is m = 13.45 and y is the weight in kilograms , x is the number of months

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

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

Given data ,

Let the equation of line be represented as A

Now , the value of A is

The weight in kilograms = y

The number of months = x

Let the first point be represented as P = P ( 11 , 140 )

Let the second point be represented as Q = Q ( 1 , 5.5 )

Now , the slope of the line is given by

Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 140 - 5.5 ) / ( 11 - 1 )

Slope m = 134.5 / 10

Slope m = 13.45

Now , the equation of line is y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 140 = 13.45 ( x - 11 )

On simplifying the equation , we get

y - 140 = 13.45x - 147.95

Adding 140 on both sides of the equation , we get

y = 13.45x - 7.95

when x = 11 months

y = 13.45 ( 11 ) - 7.95

y = 147.95 - 7.95

y = 140 kilograms

Therefore , the value of A is y = 13.45x - 7.95

Hence , the equation is y = 13.45x - 7.95

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Starting out with the fraction of 5/9, Jess would be thinking of the fraction 144/125 at the end of the game if the ten coin flips turn out to be {THTTHTHTTT}.

Since both outcomes are equally likely, the probability of getting heads is 0.5 and the probability of getting tails is also 0.5. Alternatively, the probability of getting H or T in a coin flip is 1.

Probability is an important method for comprehending and making judgments regarding uncertain occurrences in many disciplines, including statistics, finance, and science. It aids in quantifying and forecasting the probability of specific events, enabling us to make better educated choices and comprehend the degree of risk involved with various activities. In summary, probability is a key idea in decision-making and risk management because it is a potent instrument for comprehending and managing uncertainty.

Taking the sequence of coin flips in ten tires, i.e THTTHTHTTT , and starting from the fraction 5/9, the fraction that jess would be thinking at the end of the game can be calculated as,

5/9 * (6/5)^7 *(5/6)^3 , since there are 7 Tails and 3 Heads during the whole game. Which is equal to the fraction 144/125.

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The value of the expression using the distributive property is 5x + 50.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

5 (x - 10)

The distributive property of multiplication over addition states that,

a x (b +  c) = a x b + a x c

Now,

5 (x - 10)

= 5x + 5 x 10

= 5x + 50

Thus,

The expresssion is 5x + 10

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A normal distribution of a random variable cannot be described (D) by a graph that is centered on the mean.

A continuous probability distribution for a real-valued random variable in statistics is known as a normal distribution or Gaussian distribution.

Since all three of these variables are equal in a normal distribution, they serve as the center of the graph and can either be zero or not.

An example of a continuous probability distribution is the normal distribution, in which the majority of data points cluster in the middle of the range while the remaining ones taper off symmetrically toward either extreme.

The distribution's mean is another name for the center of the range.

Therefore, a normal distribution of a random variable cannot be described (D) by a graph that is centered on the mean.

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a. A function that models the population of the city's years after 2010 is:

f(x) = 50,000 * (1 + 0.05)^(x-2010)

where x is the number of years after 2010.

b. The population of the city in 2017 (7 years after 2010) is:

f(2017) = 50,000 * (1 + 0.05)^7

           = 65,128

c. The population of the city in 2020 (10 years after 2010) is:

f(2020) = 50,000 * (1 + 0.05)^10

            = 76,923.1

The population of the city in 2030 (20 years after 2010) is:

f(2030) = 50,000 * (1 + 0.05)^20

            = 129,382

d. The population in 2020 is 76,923.1, and the population in 2010 is 50,000, so the population grows by:

= 76,923.1 / 50,000

= 1.53846

The population in 2030 is 129,382, and the population in 2020 is 76,923.1, so the population grows by:

= 129,382 / 76,923.1

= 1.6859  

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The value of x with points A ( 4, 3 ) and B ( x ,5 ) on the circle and O(2,3) as centre is equal to 2.

As given in the question,

Points A(4,3 ) and B ( x, 5 ) are on the circle.

Centre of the circle is represented by O( 2,3)

OA and OB represents the radius of the circle.

This implies

OA = OB

Using distance formula we get,

√ ( 2 - 4 )² + ( 3 - 3 )² = √ ( 2 - x )² + ( 3 - 5 )²

⇒ √ 4 + 0 = √ 4 - 4x + x² + 4

⇒4 =  4 - 4x + x² + 4

⇒4 - 4x + x² = 0

⇒ ( x - 2 )² = 0

⇒ x - 2 = 0

⇒ x = 2

Therefore, the value of x for the given point of the circle is equal to 2.

The above question is incomplete , the complete question is :

What is the value of x , if the points A(4, 3) & B(x, 5) are on the circles with Centre O(2, 3), find the value of x.

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The distance from concord to Matthews is solved to be 14.8 miles

Information from the question include

charlotte is 7 miles south of concord

Matthews is 13 miles west of charlotte

the distance from concord to matthews = ?

The required distance is solved using using Pythagoras theorem given by the  the formula

hypotenuse² = opposite² + adjacent²

plugging the values as in the problem

let x be the required distance

x² = 13² + 7²

x² = 169 + 49

x² =  218

x = √218

x = 14.7648

x = 14.8 (to 3 SF)

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Yes, the order of the quantities in an inequality matters, and examples are given to show why.

The four inequality symbols, along with their meaning, are presented as follows:

It is known that the number 5 is greater than the number 3, hence the inequality that describes these numbers is given as follows:

5 > 3.

However, if we tried to apply the commutative property, that is, changing the order of the numbers, we would have that:

3 > 5.

Which is a false statement, as the number 3 is less than the number 5, and not more.

This shows that the order of the symbols in an inequality in fact does matter.

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Answer:

You have to draw a graph.

Step-by-step explanation:

Multiply all of your sides together to figure out the area then plot the points.

To Solve the inequalities , we take the variables on a side and the numbers on the other side and then apply mathematical operations to solve it .

What is Inequality ?

The Inequality is defined as a relationship between two values that are not equal to each other .

The method of solving the inequalities is a little different than solving equations.

To solve the inequalities, some simple rules should be followed .

(i) The inequality does not change if any number or variable is added or subtracted from both sides.

Similarly, the value of inequality is not affected if the same number is multiplied on both the sides.

(ii) If the inequality is divided by a negative variable or number on both  sides, then the inequality sign gets reversed.

(iii) On dividing inequality by a positive number, there is no change.

For Example : Solve the inequality [tex]4x+6 > 3x+7[/tex] ;

subtracting [tex]3x[/tex] from both the sides ,

we get ;

[tex]x+6 > 7[/tex],

Now subtracting [tex]6[/tex] from both sides of the inequality;

we get ;

[tex]x > 1[/tex] .

Therefore , the solution of the inequality [tex]4x+6 > 3x+7[/tex] is [tex]x > 1[/tex] .

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Answer: 7 hours

Step-by-step explanation: blake is gains 10 more miles then Jake each hour so if you divide 70 by 10 you get 7.

Therefore, N2 and 2N are not equal, they are different mathematical expressions.

A finite collection of symbols that are well-formed in accordance with context-dependent principles is referred to as an expression or mathematical expression.

A mark, sign, or term that denotes, denotes, or is taken to denote a concept, an item, or a connection is known as a symbol. By connecting seemingly unrelated ideas and events, symbols let individuals look beyond the known and the visible.

No, N2 and 2N are not the same.

N2 is the square of N, which means it is N multiplied by itself. For example, if N = 5, then N2 = 5*5 = 25.

2N, on the other hand, is N multiplied by 2. For example, if N = 5, then 2N = 5*2 = 10.

So, N2 and 2N are not equal, they are different mathematical expressions.

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