What is the justification for step 1 in the solution process?
8x + 15 = 11x + 2
Step 1: 8x = 11x
13

Answer:

Second one

20/50=v/100

Step by step explanation:

Cross multiplying;

(20×100)÷50 = v

v = 40

The system of linear inequalities that represents the graph is:

y ≥ x - 2

y ≥ -3x + 2

The system of linear inequalities for the given graph can be written as explained below.

Inequality 1:

Slope (m) = rise/run = 3/3 = 1

The y-intercept (b) = -2

Since the line is a solid line and the shaded region is above the line, the inequality sign to use is, ≥. Therefore, substitute m = 1 and b = -2 into y ≥ mx + b:

y ≥ x - 2

Inequality 2:

Slope (m) = rise/run = -3/1 = -3

The y-intercept (b) = 2

Since the line is a solid line and the shaded region is above the line, the inequality sign to use is, ≥. Therefore, substitute m = -3 and b = 2 into y ≥ mx + b:

y ≥ -3x + 2

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Answer: The expression (6-√)(15-√) can be simplified by using the distributive property of multiplication over addition:

(6-√)(15-√) = 6 * 15 + 6 * (-√) + (-√) * 15 + (-√) * (-√)

Expanding the first two terms:

6 * 15 = 90

6 * (-√) = -6√

Next, we'll use the identity for the product of two square roots:

(-√) * 15 + (-√) * (-√) = 15√ - √^2

Since the square root of a positive number is positive, √^2 = √. So:

15√ - √^2 = 15√ - √

Putting everything together:

(6-√)(15-√) = 90 - 6√ + 15√ - √

Combining like terms:

(6-√)(15-√) = 90 + 9√

So, the expression (6-√)(15-√) without a perfect square factor in the radicand is:

(6-√)(15-√) = 90 + 9√

Therefore, the answer is:

(6-√)(15-√) = A. 35 + 9√.

Step-by-step explanation:

While rolling, a wheel with a diameter of 19/2 ft makes 133 revolutions. the distance that is traveled by the wheel Use 22/7  is 3,971 ft.

The concept that wiullbe used here is circumference

The circumference of a circle can be calculated using the formula

C = (d π )

where d= diameter =19/2 ft

C=( 19/2)* (22 / 7)

= 209 / 7 ft

It should be noted that a wheel= 133 revolutions:

Then the Distance  can be calculated as :

=( 209 / 7)  * (133)

= (209 * 19 )

= 3,971 ft

Therefore, option D is correct.

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Answer: smaller

Step-by-step explanation:

hope this helpsss

Answer:

The answer to this question depends on the values of the numbers involved. In general, when you multiply a number by a fraction, the product will be smaller than the largest factor if the fraction is less than 1. For example, if you multiply 5 by 1/2, the product is 2.5, which is smaller than 5. On the other hand, if you multiply a number by a fraction that is greater than 1, the product will be larger than the largest factor. For example, if you multiply 5 by 2/1, the product is 10, which is larger than 5.

In conclusion, the size of the product obtained from multiplying a number by a fraction depends on the values of the numbers involved and can be either smaller or larger than the largest factor.

Answer: Since a cylinder has a circular base which is counted when measuring the surface area and is unchanged with a doubled height the surface area will increase but won't be doubled. It will only be doubled if the circle's radius is doubled aswell.

Step-by-step explanation:  ^^ please mark 5 star and give thanks.

Answer:

The answer is 15. First, you find the number that’s four more than six- 4+6=10. Next find the number that’s two thirds of ten. If one half of ten is five, multiply that by three, and you get 15.

The correct option is A, equilibrium price increases from $6 to $8.

In economics, equilibrium is a state in which the supply and demand for a product or service are balanced, resulting in a stable price. This can occur in a free market, where the price of a good or service is determined by the interaction of buyers and sellers.

Overall, equilibrium is a fundamental concept in many different fields, representing a state of balance or stability in a system or situation.

If the demand schedule changes from D2 to D1, then the demand curve shifts to the left. As a result, the new equilibrium point will be where the new demand curve (D1) intersects with the supply curve (S1).

From the table, we can see that the new equilibrium point is at a price of $8 and a quantity of 15. Therefore, the equilibrium price increases from $6 to $8, but the equilibrium quantity decreases from 15 to 13.

So the correct answer is: equilibrium price increases from $6 to $8.

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The inequality is solved using graphical method to give a solution of

The system of equation are y ≥ 1/3 x + 4 and y ≤ -5/3 x - 2

Using x values of -5, 0, 5

y ≥ 1/3 x + 4

x = -5, y ≥ 1/3 (-5) + 4, y ≥ 7/3

x = 0, y ≥ 1/3 (0) + 4, y ≥ 4

x = 5, y ≥ 1/3 (5) + 4, y ≥ 17/3

table of values

x    y

-5  7/3

0   4

5   17/3

y ≤ -5/3 x - 2

x = -5, y ≥ -5/3 (-5) - 2,  y ≤  19/3

x = 0, y ≥ -5/3 (0) - 2,  y ≤  -2

x = 5, y ≥ -5/3 (5) - 2,  y ≤  -31/3

table of values

x    y

-5  19/3

0   -2

5   -31/3

The graph is attached and the solution is (-3, 3)

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Answer:

17^1 . ......................

The distribution of the data is typically considered to be skewed to the right if the median is higher than the mean.

So the distribution of the data is typically considered to be skewed to the right if the median is higher than the mean (positively skewed). In other words, the distribution's tail is longer to the right than to the left. Take the following values, for instance, 1, 2, 3, 5, 100, as part of a dataset. This dataset has a mean of 22.2 and a median of 3, with the mean being (1 + 2 + 3 + 5 + 100) / 5 = 22.2. The distribution is positively skewed with a lengthy tail of high values in this instance because the median is significantly lower than the mean. If a few extreme values in the dataset are significantly higher than the remainder of the range, the distribution may be positively skewed.

Therefore, In other words, the distribution's tail is longer to the right than to the left. Take the following values, for instance, 1, 2, 3, 5, 100, as part of a dataset. This dataset has a mean of 22.2 and a median of 3, with the mean being (1 + 2 + 3 + 5 + 100) / 5 = 22.2.

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Melanie's account balance after t years is, A = 500 x [tex](1 + 0.00425)^{4t[/tex].

Compound interest is when you receive interest on both your interest income and your savings.

Given:

Initial deposit = $ 500

Interest rate = 1.7 % = 0.017/4 = annual compounded quarterly

Now, Account balance = Initial deposit x [tex](1 + r)^{4t[/tex]

                                   A = 500 x [tex](1 + 0.00425)^{4t[/tex]

Where:

A = Account balance

4t = Number of quarters (4 x Number of t years)

Suppose we want to calculate the account balance after 4.5 years, then we substitute this way:

A = 500 x [tex](1 + 0.00425)^{4(4.5)[/tex]

A = 500 x (1 + 0.00425)¹⁸

A = 539.66

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The volume of  cylinder is 25.85 cubic feet

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

The formula for volume of cylinder V=πr²h

Where V is volume, r is radius of cylinder and h is height of cylinder.

The cylinder has a height of 4.2 feet and

a segment from one point on the circular base to another point on the base through the center labeled 2.8 feet, which is equal to the diameter of the circular base.

Diameter =2.8 feet

Radius =1.4 feet.

V=3.14×1.4²×4.2

V = 25.85 cubic feet

Hence, the volume of  cylinder is 25.85 cubic feet

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Answer:

b or 25.85

Step-by-step explanation: V=pir^2h

the radius is half of the diameter so it would be 1.4. then do 1.4 and square it, getting 1/96. then, multiply 1.96, 4.2, and pi, or 3.14 in this case. After multiplying those, you get 25.8484848, or 25.85.

Hope this helps!

Algorithm is a set of instructions for solving a problem or performing a task, typically designed for a computer to follow.

An algorithm is essentially a step-by-step procedure for solving a problem or accomplishing a specific task. It is used in various fields, including mathematics, computer science, engineering, and many others. In computer science, algorithms are essential for software development and programming, as they provide a systematic approach to designing and implementing complex programs. The process of developing an algorithm typically involves breaking down a problem into smaller sub-problems, identifying the key steps required to solve each sub-problem, and then putting the steps together in the correct order to form a complete solution.

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If there were two people dividing the cost of the gift, each person would spend $180. If there were three people dividing the cost, each person would spend $120. If there were five people dividing the cost, each person would spend $72. If there were ten people dividing the cost, each person would spend $36. If there were one hundred people dividing the cost, each person would spend $3.60. The rest of the answers are given below.

2. Let n be the number of people contributing to the gift and c be the total cost of the gift. Then the function that could be used to model the amount each person would spend is:

f(n) = c/n

3. (Table and graph attached)

As the number of people contributing to the gift increases, the amount per person decreases. This can be seen in both the table and the graph.

4. Domain: The function is defined for all positive integers, as it doesn't make sense to have a fractional or negative number of people contributing to the gift.

Range: The range of the function is also all positive real numbers, as the amount per person can be any positive value depending on the number of people contributing.

Increasing/decreasing: The function is decreasing, as the amount per person decreases as the number of people contributing increases.

Maxima/minima: There are no maxima or minima, as the function is continuously decreasing.

Discrete/continuous: The function is continuous.

End behavior: As the number of people contributing approaches infinity, the amount per person approaches zero.

Intercepts: The function has a y-intercept of $360, which represents the cost of the gift if only one person is contributing.

Asymptotes: There is a horizontal asymptote at y=0, which represents the limit of how low the amount per person can go as the number of people contributing increases.

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The value of x, in the solution of the system of equations, is 6.

To find the value of x in the solution for the system of equations, we need to use the substitution method. First, we need to rearrange one of the equations to solve for one variable in terms of the other. Let's rearrange the second equation to solve for y:

18 - 2y = 2x

2y = 18 - 2x

y = 9 - x

Now, we can substitute the value of y from the second equation into the first equation:

6x - 3(9 - x) = 27

6x - 27 + 3x = 279

9x = 54

x = 6

Therefore, the value of x in the solution for the system of equations is 6.

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Answer: 0

Step-by-step explanation:

12x^3

divide both sides by 12

x^3=0

The two rectangles are joined to get the shape. And the area of the shape is 258 square feet.

The amount region shows how much an area is on a planar or hemispherical cup. Surface region alludes to the region of an open surface or the boundary of a multi-object, while the region of a plane locale or plane field alludes to the region of a structure or planar material.

The shape is a mix of the two rectangular shapes. Then the region is likewise the amount of these two square shapes. Then we have

A = (18 - 8) x (21 - 12) + 21 x 8

A = 10 x 9 + 21 x 8

A = 90 + 168

A = 258 square feet

The two rectangles are joined to get the shape. And the area of the shape is 258 square feet.

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Parameters are a set of values or characteristics that help to define or limit a system or process.

In computer programming, parameters are values or arguments that are passed to a function or method to specify how it should operate. Parameters can also be used in mathematical equations, scientific experiments, and other fields to specify conditions or constraints.

For example, in the equation y = mx + b, m and b are parameters that determine the slope and intercept of the line.

In a scientific experiment, parameters might include the temperature, pressure, or other conditions under which the experiment is conducted. In computer programming, parameters can be used to specify the input data, options, or other information that a function or method needs to operate correctly.

Overall, parameters are an important tool for defining and controlling systems, processes, and functions in a wide range of fields. By specifying parameters, we can ensure that a system operates in a predictable and consistent manner, and that we can accurately measure and compare results.

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Answer:

Jose swims the faster per lap

Step-by-step explanation:

The value of the variable x as required to be determined from the given image is; 11.

As evident in the task content; it can be inferred that there are similar triangles from the image.

Since the ratio of corresponding sides of similar triangles are equal; we have that;

x / 22 = (9+3) / (9+3+12)

x / 22 = 12 / 24

x = (22 × 12) / 24

x = 11.

Ultimately, the value of x from the given image is; 11.

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The right answer is a. The mean is bigger than the median and the mode when the data is positively skewed.

A characteristic of information that is gathered for analysis and reference is referred to as data. Numerous analytical tools can be used to measure data and facilitate conclusion-making. The data gathered is used for corporate management and scientific research, allowing management to make more informed decisions.

The right answer is a. The mean is bigger than the median and the mode when the data is positively skewed. The tail of the data set is said to point to the right when the data is positively skewed. The mean and median, on the other hand, are always lower than the mode in a distribution that is negatively skewed. Skewness, in general, is a distortion that differs from typical data collection.

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Answer: Length = 90 meters

Width = 20 meters

Step-by-step explanation: Step 1: The formula for the area of a rectangle is A = length x width, so we can solve for the length of the field:

A = 2000

length x width = 2000

length = 2000 / width

Step 2: The formula for the perimeter of a rectangle is P = 2(length + width), so we can solve for the width of the field:

P = 180

2(length + width) = 180

2length + 2width = 180

2width = 180 - 2length

width = (180 - 2length) / 2

Step 3: Substitute the equation for width into the equation for length to solve for length:

A = 2000

length x (180 - 2length) / 2 = 2000

2length2 - 180length + 2000 = 0

length2 - 90length + 1000 = 0

(length - 90)(length - 10) = 0

length = 90

Step 4: Substitute the value of length into the equation for width to solve for width:

width = (180 - 2length) / 2

width = (180 - 2(90))

The number of times Esi will pick a green block is found to be 128.

The stated question is-

probability = favourable outcome / total outcome

P = 32 / 50 = 16/25

Total picks = 200

Thus,

= 200 * 16/25

= 8*16

= 128

Thus, the number of times Esi will pick a green block is found to be 128.

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Answer:

$29.12

Step-by-step explanation:

x - .25x = 25.95

.75x = 25.95   Divide both sides by .75

x = 34.60

the original cost of the sweater was $34.60

34.60 x .8  If you take off 20%, you are leaving on 80%

$29.12  This is the purchase price of 20% off of the original cost.

To maximize the number of interviews, 12 undergraduate students, 4 graduate students, and 4 faculty members should be hired. The maximum number of interviews that can be conducted is 684.

Let x, y, and z be the number of undergraduate students, graduate students, and faculty members hired, respectively. The objective is to maximize the number of interviews, which is given by the function

N = 18x + 25y + 30z.

The total cost of hiring interviewers is given by the function

C = 100x + 150y + 200z.

The constraints are x + y + z ≤ 20 (due to transportation limitations), and C ≤ 3200 (the budget constraint). Using linear programming techniques, we can solve for the optimal values of x, y, and z, which are 12, 4, and 4, respectively.

The maximum number of interviews is 18(12) + 25(4) + 30(4) = 684.

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The minimum number of tables that the store must sell in order to meet the requirements is 9 tables.

A system of inequality is a set of inequalities in which we perform the operations to find the range of the solution.

Given that, an online furniture store sells chairs for $100 each and tables for $550 each. Every day, the store can ship at most 21 pieces of furniture and must sell no less than $5700 worth of chairs and tables. If 10 chairs were sold, we are asked to determine the minimum number of tables that the store must sell in order to meet the requirements.

Let x be the number of chairs sold and y be the number of tables sold.

Chairs are sold for $100 each, then x chairs cost $100x.

Tables are sold for $550 each, then y tables cost $550y.

Every day, the store can ship at most 21 pieces of furniture, then,

x+y ≤ 21

Store must sell no less than $5,700 worth of chairs and tables, then

100x+550y ≥ 5700

If 10 chairs were sold, then x=10 substitute this value into both inequalities:

100·10+550y ≥ 5700

[tex]8\frac{6}{11}[/tex] ≤ y ≤ 11

Hence, the minimum number of tables that the store must sell in order to meet the requirements is 9 tables.

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Answer:

$65.394

Step-by-step explanation:

The bill is $60.55, and you have to pay 8% tax.

8% = 0.08

60.55 times 0.08 = $4.844

So, the

8% tax = $4.844

What is the new total?

We take

60.55 + 4.844 = $65.394

So, the new total is $65.394

Answer:

$65.39

Step-by-step explanation:

multiply 60.55 by .08. then add 4.84 to 60.55