The balance in an account after several transaction is shown in the table. Is the relationship between the balance and the number of withdrawals of linear? Blank If so, find the constant rate of change. Write the slope as a unit rate and explain your reasoning. ​

The value of the angle 'x' in the right-angle triangle will be 42.99°.

It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.

Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.

The value of the variable 'x' is given by the sine of the angle 'x'. Then we have

sin x = 15 / 22

sin x = 0.6818

sin x = sin 42.99°

x = 42.99°

The value of the angle 'x' in the right-angle triangle will be 42.99°.

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The equation which is used to find the number of chocolates candy in the jar is given by 18 + 24 + 19 + n = 82 , the number of chocolate candy in the jar is equal to 21.

Number of strawberry candy in the jar = 18

Number of cherry candy in the jar = 24

Number of lime flavored candies = 19

Let 'n' be the number of chocolate candy in the jar

Total number of candy in the jar = 82

Equation used to represent the given condition is :

18 + 24 + 19 + n = 82

⇒ 61 + n = 82

⇒ n = 82 - 61

⇒ n = 21

Therefore, the equation required to represent the number of chocolate candy is 18 + 24 + 19 + n = 82 and the value of n is equal to 21.

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Answer:

ferris wheel: 2

roller coaster: 4

Step-by-step explanation:

Variables

y = ferris wheel tickets

x = roller coaster tickets

Two equations

5y + 4x = 26

5y + 3x = 22

Using Elimination (minus the top and bottom)

We get:

x = 4 (because 5y - 5y is zero, 4x - 3x is x, and 26 - 22 is 4)

Since the roller coaster price is know, you can sub it into any of the two equations and fine ferris wheel price.

5y + 3(4) = 22

5y + 12 = 22

5y = 10

y = 2

Therefore:

ferris wheel charges 2 tickets

roller coaster charges 4 tickets

Answer:

Step-by-step explanation:

Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.

Vince works in an amusement park and is helping decorate it with strands of lights. This morning, he used a total of 16 strands of lights to decorate 2 bushes and 1 tree. This afternoon, he strung lights on 3 bushes and 4 trees, using a total of 44 strands. Assuming that all bushes are decorated one way and all trees are decorated another, how many strands did Vince use on each?

Vince decorated every bush with

strands of lights and every tree with

strands.

The volume of the pool is 768 cubic feet.

What is the Volume?

In mathematics, volume refers to the amount of space occupied by a three-dimensional object. It is a measure of the total amount of space enclosed within the boundaries of an object. The volume of an object is usually measured in cubic units, such as cubic meters (m³), cubic feet (ft³), or cubic centimeters (cm³).

To find the volume of the pool, we need to multiply its length, width, and depth. Looking at the figure, we see that the length of the pool is 16 ft, the width is 6 ft, and the depth is 8 ft.

So, the volume of the pool is:

V = length x width x depth = 16 ft x 6 ft x 8 ft = 768 cubic feet

Hence, the volume of the pool is 768 cubic feet.

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Answer:

If A=30 and B= 70 the first unknown angle Y would be 100. When using the E.A.T  (exterior angle theorem) you add the 2 remote interior angles to get the exterior angle. (Y)

Unknown angle 2 is a interior angle, so we know all 3 of the interior angles must equal 180.

30+70=100

180-100=80

C=80

Step-by-step explanation:

When we solve the provided question, the equations will be - > x = 1/2 y + 5

A mathematical equation is a formula that joins two statements and indicates equality with the equal symbol (=). In algebra, an equation is a mathematical statement that establishes the equality of two mathematical expressions. In the equation 3x + 5 = 14, for example, the equal sign separates the variables 3x + 5 and 14. A mathematical formula describes the relationship between the two sentences on either side of a letter. There is commonly only one parameter, which also provides as the symbol. For instance, 2x - 4 = 2.

Here, the equations will be -

x = 1/2 y + 5

2x + 3y = 14

2(1/2y + 5) +3y = -14

y = -6    

and x 2

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The surface area of the net is 108 squate feet

The complete question is added as an attachment

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

A net that has the following shapes

The area of the net is the sum of the individual areas

So, we have

Area = 8 * 12 + 2 * 0.5 * 3 * 4

Evaluate

Area = 108

Hence, teh area is 108 squate feet

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The value of x and y in the system of equations, are 10 and 44, therefore, the number of booster pack and premade deck are 10 and 44 respectively.

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 that, a deck contains 266 cards which have 9 booster packs and 4 premade decks, and 10 booster packs and 5 premade decks, which included a total of 320 cards.

Let the number of booster pack and premade deck be x and y,

Establishing the system of equations,

9x + 4y = 266....(i)

10x + 5y = 320

2x + y = 64...(ii)

Multiplying eq(ii) by 4 and subtract eq(ii) from eq(i)

(9x + 4y = 266) - (8x + 4y = 256)

x = 10

Put x = 10 in eq(ii)

20 + y = 64

y = 44

Hence, the value of x and y in the system of equations, are 10 and 44, therefore, the number of booster pack and premade deck are 10 and 44 respectively.

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The order of processes that support the central dogma are:1.DNA replication: the process by which DNA makes a copy of itself.

2.Transcription: the process by which RNA is synthesized from a DNA template.

3.Translation: the process by which proteins are synthesized from RNA templates.

The central dogma of molecular biology describes the flow of genetic information within a biological system. The method by which DNA instructions are translated into useful products is known as the "Central Dogma." Francis Crick, who discovered the structure of DNA, first put up the idea in 1958.

The order of processes that support the central dogma are:

1.DNA replication: the process by which DNA makes a copy of itself.

2.Transcription: the process by which RNA is synthesized from a DNA template.

3.Translation: the process by which proteins are synthesized from RNA templates.

In summary, the central dogma can be described as follows: DNA is replicated to make more DNA, DNA is transcribed into RNA, and RNA is translated into proteins.

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For a diamond having volume 161 mm³, the value for side length is 7 mm.

What is volume?

Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.

The formula for volume of diamond is given as -

V = 0.47 s³

Here, s represents the side length of each edge.

The value for volume of diamond is given as -

Volume = 161 mm³

Plug in the values in the equation -

Volume = 0.47 s³

161 = 0.47 s³

s³ = 161 / 0.47

s³ = 342.553

s = ∛342.553

s = ∛342.553

s = 6.996 mm

Therefore, the side length measures 6.996 ≈ 7 mm.

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The function f(x) = x⁵ - x³ + x is odd. It satisfies the condition f(-x) = -f(x), making it an odd function.

To determine whether the function f(x) = x⁵ - x³ + x is even, odd, or neither, we need to test if the function satisfies the following conditions for all x:

f(-x) = f(x) for even functions

f(-x) = -f(x) for odd functions

If the function satisfies neither of these conditions, then it is neither even nor odd.

Testing f(-x) = f(x):

f(-x) = (-x)⁵ - (-x)³ + (-x) = -x⁵ + x³ - x

f(x) = x⁵ - x³ + x

Since f(-x) is not equal to f(x), the function is not even.

Testing f(-x) = -f(x):

f(-x) = (-x)⁵ - (-x)³ + (-x) = -x⁵ + x³ - x

-f(x) = -(x⁵ - x³ + x) = -x⁵ + x³ - x

Since f(-x) = -f(x), the function is odd.

Therefore, the given function f(x) = x⁵ - x³ + x is odd.

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Answer:

142 degrees

Step-by-step explanation:

since line GJ is a straight line, its angle measure is 180 degrees. The measure of angle HZJ is 38. Angle HZJ and angle HZG are supplementary, which means their angle measures add up to 180 degrees. So,

180-38=142.

Hope this answer helps!! :D

If LA Galaxy has won 36% of their soccer matches, this means that they have won 36/100 * 50 = 18 matches.

So, they have won 18 matches out of 50.

Step-by-step explanation:

percentage of soccer matches won = 36%

total matches = 50

matches won = 36/100 * 50

=18

When a rectangular pyramid is sliced by a plane that is perpendicular to its base but does not pass through its vertex, the resulting cross section is a trapezoid.

To understand why this is the case, it is helpful to visualize a rectangular pyramid. A rectangular pyramid is a three-dimensional figure with a rectangular base and four triangular faces that meet at a single point at the top, known as the vertex.

If a plane is passed through the pyramid perpendicular to the base but not through the vertex, it will intersect each of the four triangular faces of the pyramid at a different angle, resulting in a cross section that has four sides.

Since the base of the rectangular pyramid is a rectangle, the two opposite sides of the trapezoid cross section will be parallel, and the other two sides will be non-parallel. The shape and size of the trapezoid cross section will depend on the orientation of the plane with respect to the rectangular pyramid.

In summary, when a rectangular pyramid is sliced by a plane that is perpendicular to its base but does not pass through its vertex, the resulting cross section is a trapezoid with two parallel sides and two non-parallel sides.

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Answer:

28 cups of Flower

Ratio Table:

2,4,6,8

7,14,21,28

Step-by-step explanation:

2x4/7x4=8/28

The correct option is C which is out of 30000 there will be 27000 deaths.

According to its definition, a percentage is any number relative to 100. It is shown with the sign %. "Out of 100" is what the percentage means. Consider dividing any quantity or item into 100 identical bits.

Given, according to the website, 90% of the 30,000 deaths caused by unsafe water and filthy living conditions that occur every week around the world involve children under the age of five. All of the following interpretations of this statistic are accurate.

The percentage of deaths will be calculated as:-

Percentage = 30000 x 90%

Percentage = 30000 x 0.9

Percentage = 27000

Therefore, the number of deaths will be 27000.

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In the given case the set of 56 students who returned surveys is an example of a sample

A sample would be the 56 students who responded to the surveys. A sample is a portion of the population that is chosen for a study in research. American college students would be the population in this scenario. The 56 students who returned the surveys were chosen at random for the sample by the researcher.

The researcher is attempting to guarantee that the sample is representative of the greater population of American college students by utilising a random selection process. The researcher discovered that these students spend an average of 4.1 hours per week working on course material outside of class based on the data collected from the sample. This is an example of a descriptive statistic that provides a summary of the information gleaned from the sample.

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Answer:

[tex]\mbox{\large $0.5 + 0.16 \bar {3}$ = \boxed{\dfrac{199}{300}}}[/tex]

Step-by-step explanation:

[tex]0.16\bar{3} = 0.16333333333\\[/tex]

the 3 repeats until infinity

Let's multiply this by 100 to move the non-repeating part to the left of the decimal point

0.1633333333...... x 100 = 16.333333333333333...

.333333 = 1/3

Therefore the recurring number multiplied by 100 is
[tex]16 + \dfrac{1}{3} = \dfrac{16 \times 3 + 1}{3}=\dfrac{49}{3}[/tex]

Since this fraction was arrived at by multiplying by 100, divide this fraction by 100 to get back the fraction in its original decimal value of 0.163333

[tex]\dfrac{49}{3} \div 100[/tex]

To divide by a number, multiply by the reciprocal of that number

Reciprocal of 100 is 1/100:

[tex]\dfrac{49}{3} \div 100 = \dfrac{49}{3} \times \dfrac{1}{100} = \dfrac{49}{300}[/tex]

(You can verify this by dividing 49 by 300 in a calculator and seeing that the result is 0.163333333333333333333 i.e. 0.16333 recurring

We want to add 0.5 to this.

0.5 = [tex]\dfrac{1}{2}[/tex]

so
0.5 + 0.16333333 = 0.6633333

[tex]= \dfrac{1}{2} + \dfrac{49}{300}[/tex]

We can write [tex]\dfrac{1}{2}[/tex] as [tex]\dfrac{150}{300}[/tex]  by multiplying numerator and denominator by 150

So we get

[tex]0.5 + 0.1633333 = \dfrac{150}{300} + \dfrac{49}{300} = \dfrac{150+49}{300} = \dfrac{199}{300}[/tex]

If you perform this division on a calculator you will get the answer as 0.663333 = [tex]0.66\bar{3}[/tex] which is what you get when you add 0.5 and [tex]0.16\bar{3}[/tex]

The answer choices  50(1.15)  and 57.5 below are equivalent to 50(1+0.15)

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a complete sentence. Any one of the following mathematical operations can be used. A sentence has the following structure: Number/variable, Math Operator, Number/Variable is an expression.

The order of operations is a rule that specifies the right procedure to follow when evaluating a mathematical equation. Using the acronym PEMDAS, we can memorize this order: parentheses, exponents, multiplication, and division (left to right), addition and subtraction (from left to right).

50(1+0.15)

Add the numbers

= 50(1.15)

Multiply the  numbers

= 57.5

The answer choices  50(1.15)  and 57.5 below are equivalent to 50(1+0.15)

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The rate constant at 42.4 based on trial E is Value[k = 2.68 X 10^-3] and Units[M-1 s-1]

The rate constant at 42.4 0C is [acetone] initial = 0.2 M, [H+] initial = 0.01 M, so rate= k [acetone] [H+] 5.37 X 10^-6 = k X 0.2 X 0.01, k = 2.68 X 10^-3 , and the order of the reaction is two therefore the unit of the speed constant is M-1 s-1. reaction rate constants and rate laws is a fundamental concept in chemical kinetics, which is the study of the rates and mechanisms of chemical reactions. Reaction rate constants are specific to a particular reaction and are influenced by several factors, including temperature, concentration of reactants and products, the presence of a catalyst, and the activation energy of the reaction. The rate constant is related to the activation energy through the Arrhenius equation, which is given by k = A * exp(-Ea/RT), where k is the rate constant, A is the pre-exponential factor, Ea is the activation energy, R is the gas constant, and T is the absolute temperature. The rate law of a chemical reaction describes the mathematical relationship between the rate of the reaction and the concentrations of the reactants. It is determined experimentally by measuring the initial rate of the reaction under different concentrations of the reactants. The rate law is typically expressed as Rate = k[A]^m[B]^n, where k is the rate constant, A and B are the concentrations of reactants, and m and n are the orders of the reaction with respect to A and B, respectively.

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The measure of center should the charity use to accurately represent the data is The mean of 49 is the most accurate to use to show that they have plenty of money, the correct option is C,

The mean is the average value which can be calculated by dividing the sum of observations by the number of observations

Mean = Sum of observations/the number of observations

Median represents the middle value of the given data when arranged in a particular order.

We are given that;

The list of donation is as follows

11, 18, 35, 39, 45, 45, 46, 47, 49, 49, 50, 50, 50, 50, 56, 57, 58, 59

Now,

Mean is the middle term of the data

Here,

Middle term of data=49

Therefore, the mean of the given list will be 49.

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By applying repeated and independent measures concepts, it can be concluded that there are 11 individuals participated in the repeated-measures research study and 12 individuals participated in the independent-measures research study (option D).

In a repeated-measures research study, the degree of freedom (df) is calculated by subtracting 1 from the number of individuals in the study (n). Therefore, if df = 10, then the number of individuals in the study is 10 + 1 = 11.

Whilst, in an independent-measures research study, the degree of freedom (df) is calculated by subtracting 2 from the number of individuals in the study (n). Therefore, if df = 10, then the number of individuals in the study is 10 + 2 = 12.

Therefore, it can be concluded that there are 11 individuals participated in the repeated-measures research study and 12 individuals participated in the independent-measures research study (option D).

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r as a percent is a) a = 79, b = 1.002, and r = 0.2%.

The formula given, q = abt = a(1+r)t, represents exponential growth, where a is the starting value, b is the growth factor, r is the growth rate, t is the time period, and q is the final value after t periods.

Given q = 79(1.002)^t, we can see that:

a = 79 (the starting value)

b = 1.002 (the growth factor)

r = 0.2% or 0.002 (the growth rate, expressed as a decimal)

So, the correct answer is a) a = 79, b = 1.002, and r = 0.2%.

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By solving a system of equations we can see that there are 400 main-floor seats and 200 balcony seats.

Let x = number of seats on the main-floor

y = number of balcony seats

We know that if all the seats are sold, then the total income is $4,200, we can write the equation:

x*8 + y*5 = $4,200

And if 25% of the main-floor and 40% of the balcony seats are sold, then we get an income of $1200, then we can write:

0.25*x*8 + 0.4*y*5 = $1,200

x*2 + y*2 = $1,200

2(x + y) = $1200

x + y = $600

x = 600 - y

putting the value of x in equation1)

8(600-y) + 5y = 4200

4800 - 8y + 5y = 4200

3y = 600

y = 200

and x = 600 - 200 = 400

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If there are 15 boys and 17 girls in a math class then, the ratio of boys to girls is Option A. 15:17

The ratio of boys to girls in the math class is 15:17. This can be found by dividing the number of boys by the number of girls, which gives:

15/17

This ratio cannot be simplified because 15 and 17 do not have any common factors other than 1. Therefore, the ratio of boys to girls is 15:17.

The ratio of boys to girls in a math class is the relationship between the number of boys and the number of girls. The ratio is a way of expressing the comparison between two quantities. In this case, there are 15 boys and 17 girls in the class. To find the ratio of boys to girls, we divide the number of boys by the number of girls, which gives 15/17. This ratio cannot be simplified further because 15 and 17 do not have any common factors other than 1. Therefore, the ratio of boys to girls in the math class is 15:17. This means that for every 15 boys in the class, there are 17 girls.

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The equivalent expression to 14^6 is given as follows:

[(14^5)^3]/14^9.

When two terms with the same base and different exponents are divided, we keep the base and subtract the exponents.

The power of power exponential rule states that when a single base is elevated to multiple powers, the powers are multiplied.

Then the expression with the desired value of 14^6 is obtained as follows:

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To add a single edge to a graph to create an Euler path, we must connect two existing vertices with an odd degree.

In graph theory, an Euler path is a path that visits every edge of a graph exactly once. However, not all graphs have an Euler path. If a graph has an Euler path, it must have either zero or two vertices with an odd degree. In this scenario, we are given a graph and are asked to add a single edge to create an Euler path.

To add a single edge to the graph, we must connect two existing vertices that have an odd degree. This is because adding a new vertex would change the degree of the graph and potentially affect the existence of an Euler path. Therefore, we must carefully consider the degree of each vertex before adding the edge.

Let's consider a graph:

     A

    / \

   B---C

  / \ / \

 D---E---F

In this graph, vertices B, E, and F have an odd degree. To create an Euler path, we must connect two of these vertices with a new edge. Let's choose B and E, and add the edge (B, E) to the graph.

    A

    / \

   B---C

  / \ / \

 D---E---F

Now, the graph has only one vertex with an odd degree, which is C. This means that the graph has an Euler path that starts at C, visits every edge exactly once, and ends at A.

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