1) Which of the following relations are functions?

The y-intercept of line is at (0, -6) and the domain is (-∞, ∞).

What is the linear system?

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables..

Given,

The mathematical function has an absolute minimum at x = 15.

The average rate of change of the function between x = 20 and x = 25 is 0.

The mathematical function is increasing for all x such that 15 < x < 22.

The line intersects the y-axis at (0, -6). Then the y-intercept of the line is (0, -6).

The domain of the linear function will be a real number.

And the range of the linear function is also real number.

Hence , The y-intercept of line is at (0, -6) and the domain is (-∞, ∞).

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The value of the solution of (f.g)(t) is 2t^2-3t+7

A function is a type of rule that produces one output for a single input. Source of the image: Alex Federspiel. This is illustrated by the equation y=x2. Any input for x results in a single output for y. Considering that x is the input value, we would state that y is a function of x.

Types of Functions

Many – one function. Onto – function (Surjective Function) Into – function. Polynomial function

In the given equation,

f.g (t) is 2t^2-3t+7

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The unit price of the gloves is $ 1.173.

To find the Unit price of the gloves find 1 dozen gloves by dividing the total price by the number of dozens. From that find the unit price by dividing a dozen gloves price by 12 as 1 dozen = 12.

Here we have

A contractor purchases 5 dozen pairs of padded work gloves for ​$70.40.

She incorrectly calculates the unit price as ​$13.44 per pair for the expense report.

Cost of 1 dozen pairs of padded work gloves = $70.40/5

Cost of 1 dozen pairs of padded work gloves = $ 14.08

Here 1 dozen = 12 gloves

Let 'x' be the Unit price

=> 60x = 70.40

=> x = 70.40/60

=> x = 1.173    

Therefore,

The unit price of the pair of gloves is $ 1.173.  

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Answer:

[tex]\textrm{P(no yellow on two picks )} = \dfrac{16}{121}[/tex]

Step-by-step explanation:

The total number of pens is 1 + 3 + 7 = 11 out of which 7 are yellow.

(We don't really care what color the other pens are since we are interested only in the yellow pens)

[tex]\textrm{P(yellow on first pick )} = \dfrac{\textrm{Number of yellow pens}}{\textrm{Total number of pens}} = \dfrac{7}{11}[/tex]

The probability of not getting a yellow on first pick is the complement of this probability and is 1 less than the probability of picking an yellow

[tex]\textrm{P(not yellow on first pick )} = 1- \dfrac{7}{11} = \dfrac{4}{11}[/tex]

Since we are putting back the pen after the first pick, the total number of pens as well as pens of each color remain the same.

Therefore the probability of not getting a yellow on second pick is the same as the first pick and is [tex]\dfrac{4}{11}[/tex]

The combined probability of not getting an yellow on both picks is the product of these probabilities

[tex]\textrm{P(no yellow on two picks )} = \dfrac{4}{11}\cdot \dfrac{4}{11} = \dfrac{16}{121}[/tex]

The length of hypotenuse = 5.2 centimeters.

The triangle that has at least one angle 90 degrees is called right angle triangle. The largest side length of a right triangle is termed as hypotenuse.

The Pythagorean theorem is applicable for right-angled triangle. The theorem stated that the square of hypotenuse is equal to the sum of the square of the remaining two side lengths. If a right-angled triangle has hypotenuse H and other two side length b and o respectively, then H² = b² + o².

Assume this right-angled triangle is named as ABC, AC is the hypotenuse and AB and BC is the other sides.

As AB = 2 cm and BC = 4.8 cm

then according to the Pythagorean theorem AC² = AB²+ BC²

                                                                     AC²= 2² + 4.8²

Hypotenuse AC = 5.2 centimeter.

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The statement can be represented symbolically as: (P) ∨ (Q) → (S)

How to represent a statement in symbolic form?

Representing a statement in symbolic form involves using logical symbols and logical operators to create a logical expression that captures the meaning of the statement. Here are some common symbols and operators used in symbolic logic:

To put the statement "Michael does not have the time or money to complete the project" into symbolic form, we first need to identify the key phrases and declare them as symbols. Here are a few possible ways to do this:

(P) Michael does not have the time

(Q) Michael does not have the money

(R) Michael does not have the time or money

(S) Michael can not complete the project

We can put them in different ways, depending on the statement you want to make.

Then the statement can be represented symbolically as:

(P) ∨ (Q) → (S)

This means Michael does not have the time or the money or both, which leads him to not be able to complete the project.

Alternatively, we can use the following representation

(R) → (S)

This means Michael does not have the time or the money or both, which leads him to not be able to complete the project.

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After 4 year he will have maxed out his vacation days.

A geometric sequence is a set of integers that follows a pattern in which the following term is determined by multiplying the previous one by a factor known as the common ratio, or r.

Given:

After first year one day of paid vacation.

After second year 3 day of paid vacation.

So, the sequence is 1, 3, 9,.....

Common ratio, r = 3/1 = 3

maximum paid vacation days , [tex]a_n[/tex]= 27

Using [tex]a_n = a r^{n-1[/tex]

Then, 27 = 1 x [tex]r ^{ (n-1)[/tex]

27 = [tex]3^{n-1[/tex]

3³ =  [tex]3^{n-1[/tex]

now, comparing the base

n-1 = 3

n=4

Hence, after 4 year his vacation mxed out.

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The basis for Col A is linearly independent.

Two matrices are equal if and only if their shapes are same, and they've got the same elements for each corresponding row and column positions.

We are given that;

A = [3 7 3 3 6 4 0 -4 4 3 10 0] ~ [1 0 0 2 1 0 4 4 0 -2 -3 0]

Now,

To find a basis for Col A, we need to find the columns of A that correspond to the pivot columns of the echelon form. The pivot columns are the columns that have a leading 1 in a row. In this case, the pivot columns are the first, second, and fourth columns. Therefore, a basis for Col A is given by the vectors in those columns of A. We can write them as:

​3303​​,​76−410​​,​3440​​

These three vectors are linearly independent and span Col A, so they form a basis for Col A.

Therefore, by matrices the answer will be linearly independent.

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Answer:

[tex]16203[/tex] days

Step-by-step explanation:

There are 60 seconds per minute, so 3600 sec/hour, and 86400 seconds per day, so the answer is about [tex]16203[/tex] days.

The number 1 is called a unit. It has no prime factors and is neither prime nor composite. The number is  6 and 42.

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One is referred to as a unit. It is neither prime nor composite and lacks any prime factors. The digits are 6 and 42.

A number's factors, and more specifically its prime factorization, can be expressed as factor trees. There are factors for each branch of the tree. The branch comes to an end and the number is circled once the factor at the branch's end is a prime number, leaving only itself and one as potential factors.

A factor tree is a technique that enables us to determine the prime factors of a given integer. With this approach, we factorize the inputted number until no further factors can be discovered. Prime factorization is the list of prime factors or numbers that we would multiply together to arrive at the given number.

Therefore, the correct answer is option a) 6 and 42.

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The value of y will be 90 more than its value on the graph, when x = 11. The solution has been obtained using the linear equations.

What is a linear equation?

The equation is a linear equation that has the greatest degree of one. In a linear equation with an exponent greater than one, this indicates that there are no variables. A straight line is produced on the graph by this equation.

From the given information, we need to initially form the equation

We are given different points

Let us take two points as (3,270) and (4,360)

Using slope-intercept form, we get the equation as

⇒y=90x+0

⇒y=90x

Now, putting x=11, we get

y = 990

Hence, the value of y will be 90 more than its value on the graph, when x = 11.

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Answer:

x=2

Step-by-step explanation:

4x + 2(x - 4) is equivalent to x +2

first, distribute. 4x+2x-8

next, combine like terms. 6x-8

6x-8 = x+2

we need to group all the variable terms on one side, and all the constant terms on the other side of the equation. (6x-8)+(8-x)=(x+2)+(8-x)

get rid of the parenthesis. 6x-8+8-x=x+2+8-x

combine like terms. 6x-x-8+8=x-x+2+8

solve. 5x=10

divide both by 5. 5x/5=10/5

x=2

Answer:

Follow me if this helped you

Step-by-step explanation:

a)The claims of the Sun-American are not consistent with each other. The probability that four or more out of every 15 unemployment beneficiaries have jobs is 0.9095, but the expected number of employed beneficiaries exceeds 7, which is more than 4.

236.5 ft depth will the pressure acting on the object.

The m is the slope, and b is the y-intercept, therefore f(x) = mx + b.

You are given the value of m = 4.44 (lb/in2) for every 10 feet of descent; however, you need f(x) to be a function of the depth in inches, thus you must determine what m is for every inch of fall.

120 inches are equal to 10 feet multiplied by (12 inches per foot).

Every 120 inches of fall, then, gives rise to m = 4.44.

m = 4.44 / 120 = 0.037 for each inch of fall

Consequently, f(x) = 0.037x + b

The fact that f(0) = 15 and b = 15 can be used to find b.

f(x) = 0.037x + 15 is the equation as a result.

Set f(x) = 120 and work out x to obtain the pressure at that point.

120 = 0.037x + 15 0.037x = 105 x, or 105 / 0.037 = 2837.8 inches, or roughly 236.5 ft.

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All the correct values are,

a)⇒ f (0) = - 1

b)⇒ f (1) = 1

c)⇒ f (-1) = - 3

d)⇒ f (a) = 2a - 1

e)⇒ g (0) = - 4

f)⇒ g (-2) = 0

g)⇒ g (3) = 5

h)⇒ g (t) = t² - 4

i)⇒ f (a+5) = 2a + 9

What is Function?

A relation between a set of inputs having one output each is called a function.

Given that;

The function are,

⇒ f (x) = 2x - 1

⇒ g (x) = x² - 4

Now, We can find all the values by substituting as;

a) f (0)

⇒ f (x) = 2x - 1

Put x = 0;

⇒ f (0) = 2×0 - 1

⇒ f (0) = - 1

b) f (1)

⇒ f (x) = 2x - 1

Put x = 1;

⇒ f (1) = 2×1 - 1

⇒ f (1) = 1

c) f (-1)

⇒ f (x) = 2x - 1

Put x = -1;

⇒ f (-1) = 2×-1 - 1

⇒ f (-1) = - 2 - 1

⇒ f (-1) = - 3

d) f (a)

⇒ f (x) = 2x - 1

Put x = a;

⇒ f (a) = 2×a - 1

⇒ f (a) = 2a - 1

e) g (0)

⇒ g (x) = x² - 4

Put x = 0;

⇒ g (0) = 0² - 4

⇒ g (0) = - 4

f) g (-2)

⇒ g (x) = x² - 4

Put x = -2;

⇒ g (-2) = -2² - 4

⇒ g (-2) = 4 - 4

⇒ g (-2) = 0

g) g (3)

⇒ g (x) = x² - 4

Put x = 3;

⇒ g (3) = 3² - 4

⇒ g (3) = 5

h) g (t)

⇒ g (x) = x² - 4

Put x = t;

⇒ g (t) = t² - 4

i) f (a+5)

⇒ f (x) = 2x - 1

Put x = a + 5;

⇒ f (a+5) = 2×(a + 5) - 1

⇒ f (a+5) = 2a + 10 - 1

⇒ f (a+5) = 2a + 9

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Answer:

Step-by-step explanation:

-2y + 9 = -1

Adding 2y to both sides:

9 = 2y - 1

Adding 1 to both sides:

10 = 2y

Dividing both sides by 2:

y = 5

Therefore, the value of y that makes the equation true is y = 5

It will stand for the 15.1, not The 151.

So therefore here you got almost correct the answer,

but you misunderstood about the leaves because the leaves will stand for the decimal.

The 10th means that after the decimal,

So the foundation must be the 15.1.

15.4, 15.7, 16.5 16.6 17.8 18.3 18.6 and 18.6.

A stem and leaf diagram is a way of displaying a collection of numbers. The ‘stem’ consists of the first part of every number, usually the first digit(s) and the ‘leaf’ consists of the latter part of every number, usually the last digit. We need to know how to draw them and how to use them.

Draw a stem-and-leaf diagram to represent Scott’s data.

Step 1: Figure out what our key will be. The stem will be the first two digits, whilst the leaf will be the last digit. Our key is any number that is in the list, represented in terms of a stem and leaf.

Step 2: Use our key to draw our stem part of the diagram, which will have to include: 15,16,17,18,

Step 3: Rewrite the data in numerical order.

151, 154, 154, 157, 165, 166, 178, 183, 186, 186

Step 4: Fill in the ‘leaf’ values (the last digit of every value) alongside the correct ‘stem’ value, to complete the stem and leaf diagram.

14 15 1447 16 56 17 8 18 366

14  

15       1447

16       56

17        8

18       366

151 , 154 , 154 , 157

165 , 166

178

183 , 186 ,186

it will stand for the 15.1, not The 151. So therefore here you got almost correct the answer, but you misunderstood about the leaves because the leaves will stand for the decimal. The 10th means that after the decimal, So the foundation must be the 15.1, 15.4, 15.7, 16.5 16.6 17.8 18.3 18.6 and 18.6.

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The correct option is option D) A statistic is a random variable.

We derive the above answer due to the following reason,

Any statistic is a random variable with its own distribution referred to as the sampling distribution as it is a function of sample values and there may be several samples taken from a given population.

The probability distribution of a statistic that is acquired by the continuous sampling of a particular population is called the sampling distribution. It outlines a variety of potential possibilities for a statistic, such as the mean or mode of a population's mean or the mode of a variable.

There are three standard types of sampling distributions in statistics:

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A data set's attributes are enumerated through descriptive statistics. You can use inferential statistics to test a hypothesis or determine whether your data can be applied to a larger population.

Two sets of pupils with scores from various classes are highlighted, Using descriptive statistics, determine the mode of the following data: Using descriptive and inferential statistics, determine the z score for the given data.

Measurements of variability and measures of central tendency make up descriptive statistics (spread). Mean, median, and mode are examples of central tendency metrics. Variability measures include standard deviation, variance, minimum and maximum variables, kurtosis, and skewness.

correlation analysis, A set of independent variables and a dependent variable, such as Hypothesis Tests, are related in regression models. To compare entire populations or evaluate the correlations between variables, hypothesis testing is utilised along with samples and confidence intervals.

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The complete question is " Identify the type of data​ (qualitative/quantitative) and the level of measurement for the

expenses of respondents in a survey?"

Consequently, the probability of producing precisely one girl or exactly one male 0.25 + 0.25 = 0.5P(x = 1) = 4C1 * 0.5^1 * 0.5^3; 0.9375 ; 0.5

Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty.

Due to this:

p = 0.5

Modeling the probability of how many females the couple has:

[tex]P(x =x) is equal to nCx * px * (1 - p) (n - x)\\P(x = 0) = 4C0 * 0.5^0 * 0.5^4 = 0.0625\\\=P(x = 1) = 4C1 * 0.5^1 * 0.5^3 = 0.25\\P(x = 2) = 4C2 * 0.5^2 * 0.5^2 = 0.375\\P(x = 3) = 4C3 * 0.5^3 * 0.5^1 = 0.25\\P(x = 4) = 4C4 * 0.5^4 * 0.5^0 = 0.0625[/tex]

likelihood of having at least one female

N = 4 trials in total.

P(x 1) is equal to p(x = 1) plus p(x = 2) plus p(x = 3) plus p(x = 4)

Employing the relation

P(x =x) is equal to nCx * px * (1 - p) (n - x)

use a calculator

P(x ≥ 1) = 0.9375

Chances of getting just one female or exactly one boy

3 females OR 3 boys OR 1 boy

P(x = 1)

P(x =x) is equal to nCx * px * (1 - p) (n - x)

P(x = 1) = 4 * 0.5 * 0.125

P(x = 1) = 0.25

The likelihood of getting one girl and three males or vice versa is 0.25

Consequently, the likelihood of producing precisely one girl or exactly one male

0.25 + 0.25 = 0.5P(x = 1) = 4C1 * 0.5^1 * 0.5^3 is 0.9375 ; 0.5

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Here we are given that Gracie sold 15x + 4xy in her inventory and Mariella sold -15x +3x -2xy on weekends. We need to find combined inventory.

For that simplify add both the expressions as ,

15x + 4xy + (-15x) + 3x - 2xy

15x + 4xy - 15x + 3x - 2xy

Group like terms ,

(15x + 3x - 15x ) + (4xy - 2xy)

simplify,

3x + 2xy [ required answer]

And we are done!

We want to reduce x by 30%. Thus, the reduced price is:

x - 0.20x = 0.70x

More informally, if you take away 30%, you're left with 70%.

This question is similar to previous one so I used that answer launguage here also

The percentage of salt (by mass) in this mixture is calculated to be

information from the problem

A mixture is made by combining 1.97 lb of salt

and 5.37 lb of water

The question is a percentage problem, percentage deals with a fraction hundred.

The percentage of the salt in the mixture is calculated by first finding the mass of the mixture

mass of the mixture = mass of salt used + mass of water that made the solution

mass of the mixture = 1.97 lb + 5.37 lb

mass of the mixture = 7.34 lb

The percentage of salt in the mixture

= 1.97 / 7.34 * 100

= 0.2684 * 100

= 26.8%

The percentage of salt in the mixture is 26.8%

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The number of mosaics tiles in each side of the square  floor is 7 tiles.

Since a square has four equal sides and four equal angles, it is a regular quadrilateral. It may alternatively be explained as a rectangle with two neighboring sides that are of equal length.

A square can have many different characteristics. The following list includes some of a square's key characteristics.

The total number of mosaic tiles = 49

Let the lenght of each side of the floor be x

Therefore,

x² = 49

⇒ x = 7

The number of mosaics tiles in each side of the floor is 7 tiles.

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The slope of the given data is 25.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

Jon paid $200 for 8 classes at gold dawn yoga studio.

the cost, y, is proportional to the number of classes purchased, x

The slope will be cost of each class

200/8=25

So the equation will be y=25x

25 is the slope.

Hence, the slope of the given data is 25.

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Answer: The first orange is the best deal at $0.8 per orange. The second cand is the best deal at $0.45 per candy.

Step-by-step explanation:

First orange: 5 for $4 equals $4/5 per orange, which equals $0.8 per orange.

Second orange: 10 for $9 roughly equals $1.111 per orange

Third orange: $0.82 each

The first orange is the best deal at $0.8 per orange

First candy: 3 for $1.5 equals $1.5/3 per candy, which equals $0.5 per candy.

Second candy: 4 for $1.8 equals $0.45 per candy

Third candy, 10 for $4.6 equals $0.46 per candy

The shape that represents the sample mean of the 81 students who are selected is; Approximately normal

When a distribution of data is defined as skewed, it means that it does not take the normal distribution's bell shape. Rather, it tends to distort with values either to the left or right of the center of the data.

Now, the Central Limit Theorem states specifically that the distribution of sample mean is normally distributed. It goes further to state that if the population values from which the sample originates is not normally distributed, the sample distribution will be normal. This effect will lead to  increases as sample size increases.

Thus, we can conclude that the shape is normally distributed

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Complete question is;

Suppose the mean GPA of School A students is 3.5 and the standard deviation is 0.7 it is well known that this distribution is left-skewed. A random sample of n = 81 students will be drawn. What is the shape of the sampling distribution of the random variable ¯X.  which represents the sample mean of the 81 students who are selected.?

- Left- skewed

- right-skewed

- approximately normal

- we cannot determine this from the information given.

Monthly payment for United bank = $1207.70, monthly payment for capitol bank =$1834.62. Total interest from United bank = $75600 and from capitol bank = $135000.

Total interest is determined by the addition of all the interest payments.

United bank offers mortgage at an APR of 4.2%

APR means annual percentage rate.

mortgage is offered for the period of 15 years.

initial principal amount of Marcy = $120000

we need to determine the monthly payment from United bank.

at first, we will determine the rate of interest per month.

monthly interest rate = (4.2) / (100 × 12) = 0.0035

1 year = 12 months

15 years = 15×12 = 180 months

monthly payment is calculated by the formula = [rate + (rate) / {(1+rate)∧month}⁻¹] ×principal

monthly payment = [ 0.0035 + (0.0035) / {(1+0.0035)∧180}⁻¹] ×120000

                          = $1207.70

from united bank monthly payment = $1207.70

Now we calculate the monthly payment from Capitol bank.

APR for capitol bank = 4.5%

number of years for which mortgage is issued = 25 years

number of months = 12×25 = 300.

monthly interest rate = (4.5) / (100×12) = 0.00375

monthly payment for capitol bank = [0.00375 + (0.00375) / {(1+0.00375)∧300}⁻¹] × 120000

                 = 1834.62

monthly payment from Capitol bank = $1834.62

total interest from Capitol bank = principal money × yearly interest rate × time period.

Total interest = 120000 × 4.5/100× 25

                        = $135000 for the Capitol bank

Total interest from United bank = principal amount × yearly interest × time period

            = 120000× 4.2/100 × 15

total interest from united bank   = $75600

United bank has lower total interest.

difference in monthly payment = 1834.62 - 1207.70

                                                   = 626.92 dollars

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The sum of all a triangle's sides' lengths is the formula for calculating a triangle's perimeter.

The whole length of a shape's boundary is referred to in geometry as the perimeter of the shape. By multiplying the lengths of all the sides and edges that surround an object, the perimeter may be calculated. It is measured in measures of length that are linear, such as centimeters, meters, inches, or feet.

The sum of all a triangle's sides' lengths is the formula for calculating a triangle's perimeter.

Add the sides' lengths to find a triangle's perimeter. As an illustration, the perimeter of a triangle with sides a, b, and c is given by P = a + b + c.

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541 + 279 = 820 is the number bond for the expression 540 + 280.

A number bond is a simple addition sum that has become so familiar to a child that they can recognise it and complete it almost immediately, with recall as automatic as that of an entry from a multiplication table in multiplication. Number bonds are used in the teaching of mathematics at the primary school level.

When given the other two numbers, a child who "knows" this number bond should be able to instantly fill in any one of these three numbers if it were missing, without having to "work it out." Number bonds are frequently taught in sets whose sums are common round numbers like 10 or 20.

We can find the number bond by simply adding 1 to first term and subtracting 1 from 2nd term.

540 + 280 = 820

(540 + 1) + (280 -1) = 820

541 + 279 = 820

Thus, 541 + 279 = 820 is the number bond for 540 + 280.

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