What is the length of the unknown side on the following right triangle?

The next value in the sequence is 80.

In arithmetic, what are sequences?

Sequences are ordered sequences of numbers, also referred to as "terms," such as 2,5,8. Some sequences adhere to a particular pattern that can be exploited to make them infinitely long. For instance, 2,5,8 conforms to the pattern "add 3," thus we can now proceed with the sequence. Formulas for sequences can be used to locate any term inside the sequence.

What does a mathematical series mean?

A series is the cumulative total of a given set of terms in mathematics. However, considerably more generality is possible. Typically, these phrases refer to real or complex numbers.

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If Rachel found this rate of change for the scenario represented in the table.  you can conclude from her work that:

1. The function is continuous.

3. The scenario is represented by a linear function, since the rate of change is constant.

5. For every additional hour, 53 cups of juice are poured.

Rate of change can be defined as the rate in which a variable is changing as a result of another variables.

You can conclude from her work that the function is continuous, the scenario is represented by a linear function due to the fact that the rate of change is constant and lastly based on the table for every additional hour, 53 cups of juice are poured.

Therefore the correct option is 1,3,5.

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The complete question is:

Rachel found the following rate of change for the scenario represented in this table.

A 2-column table with 5 rows. Column 1 is labeled Time (hours) with entries 4, 5, 6, 7, 8. Column 2 is labeled Berries picked with entries 128, 181, 234, 287, 340.

What can you conclude from her work?

Check all that apply.

The scenario is represented by a linear function,

since the rate of change is constant.

The scenario is represented by a nonlinear function,

since the rate of change is constant.

The berries are picked at a constant rate of 53 per

hour.

The berries are not picked at a constant rate.

The seller ought to bring more medium-sized shirts because these are the best-selling size.

From the graph we can see that total small shirt sold = 160

Total number of sale of small shirt = 225

Now remaining shirts = Total small shirt sold/Total number of sale

Now remaining shirts = 160/225 × 100

Now remaining shirts = 71

Total medium shirt sold = 335

Total number of sale of medium shirt = 375

Now remaining shirts = Total shirt sold/Total number of sale

Now remaining shirts = 335/375 × 100

Now remaining shirts = 89

Total large shirt sold = 275

Total number of sale of large shirt = 325

Now remaining shirts = Total shirt sold/Total number of sale

Now remaining shirts = 275/325 × 100

Now remaining shirts = 85

Total X-large shirt sold = 125

Total number of sale of X-large shirt = 175

Now remaining shirts = Total shirt sold/Total number of sale

Now remaining shirts = 125/175 × 100

Now remaining shirts = 71

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The complete question is given below:

Answer:

it is There are 4 cups of water for each cup of sugar

Step-by-step explanation:

The description of the piecewise function y is -2x + 3.

It is necessary to optically estimate the coordinates of the points because not everything is visible (particularly for the leftmost point).

We have the following considerations, I believe:

(-6, 1.5) (-3, 3) (-3, 3)

(-3, 2) (1, 2) (1, 2)

(1, 1) (6, -9) (6, -9)

the basic function definition appears on all three segments.

y = ax + b

X is always a factor of a, which is the line function's slope.

When a point on a line moves from one end to the other, the ratio y/x shows how many units change when x moves by a specific number of units.

b represents the y-intercept, or the value of y when x = 0.

(-6, 1.5) is followed by the first part and then (-3, 3).

x is modified by +3 units (from -6 to -3).

y shifts by 1.5 or 3/2 units (from 1.5 to 3).

the line has a slope of 3/2/3, which is 3/(23) = 1/2.

supplying the initial portion

y = (1/2)x + b

When we solve for b using a single point's coordinates (for example, -3, 3), we obtain b:

3 = (1/2)×-3 + b

3 = -3/2 + b

6/2 + 3/2 = b

9/2 = b

total equation is

y = (1/2)x + 9/2 = (x + 9)/2

The second portion is a straight line with no slope at all.

y = 2

Third segment, from (1, 1) to (6, -9)

5 units are added to x. (from 1 to 6).

By, y shifts

y = -2x + 3.

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By organizing countless data points into comprehensible ranges or bins, the histogram, which resembles a bar graph in appearance, condenses a data series into an understandable visual. So Histograms based on data on housing, prices and salaries typically are skewed to the right.

A histogram in statistics is a graphic depiction of the data distribution. The histogram is shown as a collection of rectangles that are next to one another, where each bar represents a different type of data.

A branch of mathematics called statistics is used in many different fields. Frequency is the term for how often numbers appear in statistical data; it can be shown as a table and is known as a frequency distribution.

A histogram is a bar graph-like data visualization that groups various class levels into columns along the horizontal x-axis. The numerical count or percentage of occurrences for each column in the data are shown on the vertical y-axis.

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Answer:

x = 6.6

Step-by-step explanation:

Proportions:

6.8 ⇒ 8.2

5.5 ⇒ P

P = 8.2 * 5.5 / 6.8

P = 6.6    (Rounded to the nearest tenth)

A chocolate frog costs $0.35. The result is obtained by using elimination and substitution method.

To eliminate equations, we can either add or subtract the equations. Substitution is substituting the value of one variable in the other equation.

We have

Find the cost of a chocolate frog!

Let's say

We rewrite the problem mathematically.

A = 15 cents + B ... (equation 1)

3B + 2A = $1.30 ... (equation 2)

We know that $1 = 100 cents. Multiplied by 2, the equation 1 will be

2A = 30 cents + 2B

2A = $0.3 + 2B ... (equation 3)

We eliminate the equation 1 and 3.

3B + 2A = $1.30

2A - 2B = $0.3 _

5B = $1.0

B = $0.2

We substitute the value of B in equation 3.

2A - 2B = $0.3

2A - 2($0.2) = $0.3

2A - $0.4 = $0.3

2A = $0.7

A = $0.35

Hence, the cost of a chocolate frog is $0.35.

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Answer:

Data handling refers to the process of collecting, storing, manipulating, and analyzing data. This can include tasks such as inputting data into a computer system, organizing and storing data in a database, cleaning and preprocessing data to make it usable, and performing statistical or other types of analysis on the data. It also includes visualization of data to make it more understandable. Data handling is an important aspect of many fields, such as business, science, and technology, as it allows for the efficient management and analysis of large amounts of information.

Answer:

Data handling is the process of ensuring that research data is stored, archived or disposed off in a safe and secure manner during and after the conclusion of a research project. This includes the development of policies and procedures to manage data handled electronically as well as through non-electronic means .

If f(3) = 3 - |2x - 5| is given then the value of f(0) + f(-4) would be -8.

What is the function?

A function is a mathematical relationship between a set of inputs (also known as domain) and a set of possible outputs (also known as range). The inputs are usually represented by variables, such as 'x' in the examples you provided.

To find f(3), we need to plug in x = 3 into the equation:

f(3) = 3 - |2(3) - 5| = 3 - |6 - 5| = 3 - |1| = 3 - 1 = 2

To find f(0), we need to plug in x = 0 into the equation:

f(0) = 3 - |2(0) - 5| = 3 - |-5| = 3 - 5 = -2

To find f(-4), we need to plug in x = -4 into the equation:

f(-4) = 3 - |2(-4) - 5| = 3 - |-9| = 3 - 9 = -6

Now we can add f(0) + f(-4) = -2 + (-6) = -8

Hence, if f(3) = 3 - |2x - 5| is given then the value of f(0) + f(-4) would be -8.

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To represent the number of boxes sold when the total sales are equal to $1600 on a number line, we can simply mark the x-coordinate of the point (420,1600) on the number line.

The point of intersection between the horizontal line y = 1600 and the graphed function b) = 3.756 + 25x is (420,1600), which means Alan would have to sell 420 boxes to make $1600 in total sales.

To represent the number of boxes sold when the total sales are equal to $1600 on a number line, we can simply mark the x-coordinate of the point (420,1600) on the number line. To the left of this point, the number of boxes sold would be less than 420, and to the right of this point, the number of boxes sold would be more than 420. At the point (420,1600), Alan would have sold exactly 420 boxes and made a total of $1600 in sales.

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Answer:

The price of the oven, including tax, before the discount is applied is $336.46. This is calculated by taking the sale price of $251.85 and multiplying that by 1.25 (which is 100% + 25% discount).

The point where he  buried his treasure is (6.28,9.84)

First of all, we are going to find the equation of the line which describes the first path crossed by the horseman.  In order to find it we have to take into account that the vector V  provides us with the direction of this path. We can associate the direction with the slope of the line. The slope is defined by the ratio of vertical changes to horizontal changes between two points.  

According to the V=6i+5j, we can determine that:

Vertical change (y)= 5

Horizontal change (x)=6

Slope=\frac{5}{6}

Now, using the point-slope form:

y-y₁=m(x-x₁)

The chosen point is the point where the horseman began riding (-2,5). Therefore:

m=5/6

y1=5

x1=-2

y-5=5/6(x+2)

y=5x/6-10/3

Since the horseman at some point turned at a right angle towards village B  and he unchanged his direction until arrived in village B, the second path must be described by a line perpendicular to the first path.  

We should know that two lines are perpendicular if and only if their slopes are negative reciprocals This means m1*m2=-1

m₁=5/6

m₂=-1/m₁=-6/5

In order to find the equation of the second path, we will use again the point-slope form.

The chosen point is the point where is located Village B (2,11)

y-11=-6/5(x-2)

y=-6x/5+13.4

The coordinates of the point where the horseman buried a jar full of silver coins correspond to the intersection of path 1 and path 2. Therefore we are going to equal the two equations of each path.

5x/6-10/3=-6x/5+13.4

Solving this equality for x

X=6.28

Replacing this value in any of the equations of the paths

Y=9.84.

Finally, the point where he buried his treasure is (6.28,9.84).

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Answer:

Step-by-step explanation:sega

A factory produces 72 bottles of juices in one minute.

Meaning of rate:

A rate is a special ratio in which two words are expressed using different units. The price is $69 for 12 ounces of corn if a 12-ounce can costs that much. This is not a ratio of two comparable units, like shirts, for example. This is a ratio between the units of cents and ounces.

We must divide the quantity of bottles produced by the time it takes to make them in order to determine the factory's production rate in bottles per minute. The factory in this instance produced 360 bottles in 5 minutes, resulting in the following production rate:

= 360 bottles / 5 minutes

= 72 bottles/minute

This means that the factory produces 72 bottles of juice per minute.

Hence, the factory produces 72 bottles of juice per minute.

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The following question may be like:

A factory bottles 360 bottles of juice in 5 minutes. Find the factory's unit rate of bottles per minute.

The solution of the equation 3(2x - 7) = 3 is x = 4 and the equation has a single solution.

Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign.

Therefore, let's solve the equation as follows:

3(2x - 7) = 3

open the bracket

3(2x - 7) = 3

6x  - 21 = 3

add 21 to both sides of the equation

6x  - 21 = 3

6x  - 21 + 21 = 3 + 21

6x = 24

divide both sides by 6

6x / 6 = 24 / 6

x = 4

Therefore, the equation has only one solution.  The solution of the equation is x = 4.

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Answer:

Step-by-step explanation:

To find out how much the man spent per shirt, you need to divide the total cost of the shirts by the number of shirts.We know that the man spent $250 on the suit and $398 on the four shirts. To find the total cost of the shirts, you can add these two amounts:$250 + $398 = $648To find the cost per shirt, you need to divide the total cost of the shirts by the number of shirts:$648 / 4 = $162So the man spent $162 per shirt.

The output of a classification system is usually a discrete value, usually a label or class, which represents the predicted result of the model.

A classification system can be expressed mathematically using a decision boundary. This boundary is defined by a decision function that maps the input data to a discrete output. The decision boundary is determined by setting a threshold for the output of the decision function, such that if the output exceeds the threshold, the predicted class is labeled as a "positive" output and if the output is below the threshold, the predicted class is labeled as a "negative" output.

The output of a regression system is usually a continuous value, which represents the predicted result of the model. A regression system can be expressed mathematically using a linear equation which maps the input data to a continuous output. The equation is determined by fitting a line to the data, such that the line best fits the data points. The value of the output is then calculated by evaluating the equation at a given point in the input data.

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The system of equations for the stuffed animals should the company manufacture to maximize profit P in dollars is P = 20x + 30y

The term equation in math is called as an expression or a statement that comprises two algebraic expressions with the same value and are separated by an equal symbol in between them.

Here we know that we have to determine the number of each of three types of souvenirs to be made.

Here let us consider that x, y, and z denote the respective numbers of type-A, type-B, and type-C souvenirs to be made.

Here we know that the total amount of time that machine I is used is given by 2x + y + z minutes and must equal 180 minutes.

Here the known details will leads to the equation

=> 2x + y + z = 180

While we take the similar considerations on the use of machines II and III lead to the following equations which is written as

=> x + 3y+2z = 300

=> 2x + y + 2z = 240

Here we have also identified the the stuffed animals should the company manufacture to maximize profit P in dollars as,

=>  P = 20x+30y

Here we know that the subject to the constraints plush stuffing trim x ≥ 0 y ≥ 0.

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The cash received by Shamar from bank deposit ticket is (c) $908.11

When making a deposit into a bank account, a bank customer typically includes a little paper document called a deposit slip.

A deposit slip includes the date, the depositor's name, their account number, the sums being deposited, and a breakdown of the type of deposit (cash, checks, or a particular amount of cash the depositor wants back from a check deposit).

The deposit slip is evidence that the bank confirmed receiving the customer's funds.

In this problem, the total amount deposit through check or other mode is $1108.11 and $ 200 deducted by bank as processing fee.

So the final amount or cash Shamar received is

= $1108.11 - $ 200.00

= $ 908.11

The cash received by Shamar from bank deposit ticket is (c) $908.11

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The solution of the system is x = 5 and y = 40.

A simultaneous equation is anyone or more equations that can have the same number of unknowns and be solved concurrently. The system of equations is a simultaneous equation.

Given:

system of equations,

8x=x+35    {equation 1}

y=8x          {equation 2}

From equation 1,

8x = x+35

7x = 35

x = 5

Substituting the value of x to the equation 2,

And y  = 8(5)

y = 40

Therefore, the solution is x = 5 and y = 40.

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Answer: 6.1 or 6 1/10

Step-by-step explanation:

4+1 = 5

1/2 + 3/5 = 5/10 + 6/10

5/10 + 6/10 = 11/10

11/10 = 1 1/10

1 1/10 + 5 = 6.1 or 6 1/10

On expanding the expression "(1/2)(-2x + 4y)" , the equivalent expression is -x + 2y  .

An expression is defined as the sentence that have a minimum of two numbers or variables and at least one math operation in it.

For Example : 2x + 3y is an expression .

The expression is : "(1/2)(-2x + 4y)"   ;

By using distributive property which means that a(b+c) = ab + ac ,

we multiply by (1/2) with both the terms ;

⇒ (1/2)(-2x) + (1/2)(4y)  ;

Simplifying further ,

we have ;

⇒ -2x/2 + 4y/2  ;

Further simplifying we get ⇒ -x + 2y  ;

Therefore , the equivalent expression is -x + 2y  .

The given question is incomplete , the complete question is

Expand to write an equivalent expression:  (1/2)(-2x + 4y) .

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C = 310g is the equation that correctly shows the relationship between cost, C, and loads of gravel, g

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Given, Freddy is building a house and has 5 loads of gravel delivered for the work. His total cost for the gravel is $1750.

Since,

Cost of 5 loads of gravel is = 1750

Cost of 1 load of gravel = 1750/5

Cost of 1 load of gravel = 310$

the relationship between cost, C, and loads of gravel, g:

C = 310 * g

Therefore,  equation that correctly shows the relationship between cost, C, and loads of gravel, g is C = 310g.

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Answer:

D and C

Step-by-step explanation:

C:  Has a negative slope which will go down

D:  Has a negative slope which will also go down

Student A is incorrect. The student started at 0 on the y-axis, did not need to move horizontally on the graph, and so moved horizontally to 2 on the x-axis. The student should have started at 0 on the x-axis, moved horizontally to the graph, and then moved vertically to -6, which student B did.

The value of x at which we want to find the numeric value of the function is given as follows:

x = 2.

Tracing a vertical line through x = 2, it will cross the graph of the function at y = -6, hence the numeric value is given as follows:

f(2) = -6.

Meaning that student B is correct.

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The fraction of the total distance to her aunt’s house was traveled on Sunday is  1 3/35

The term called fraction in math is defined as the number is expressed as a quotient, in which the numerator is divided by the denominator.

Here we have know that Leslie's family traveled 2/7 of the distance to her aunt’s house on Saturday and they traveled 4/5 of the remaining distance on Sunday.

Then the total distance is calculated by adding the given fraction, then we get,

=> 2/7 + 4/5

Here we have the unlike denominators find the Least Common Denominator (LCD),

LCD of 7 and 5 = 35

Now, we have to multiply numerators and denominators to get the LCD in all fraction denominators, then we get,

=> 10/35 + 28/35

=> 38/35

When we Simplifying the answer, then we get,

=> 1 3/35

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