A gallon of paint can cover 250 square feet. Find how many gallon containers of paint
should be bought to paint 3 coats on each wall of a rectangular room with dimensions
16 feet by 8 feet and walls that are 10-feet tall.

The total time taken by Carmen in climbing the rocks will be 2¹/₄ hours.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Carmen went rock climbing at the climbing gym for 1¹/₂ hours on Thursday. On Saturday, she went to Castle Rock State Park and climbed for  1¹/₂ times as long.

The total time of climbing will be calculated as:-

Time = 1¹/₂ x 1¹/₂

Time = ( 3 / 2 ) x ( 3 / 2 )

Time = 9 / 4

Time = 2¹/₄ hours.

Hence, the climbing time would be 2¹/₄ hours.

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The solution is Option C.

The equation of line is y = 2x - 2 , where the slope m = 2

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

2x - y = 2   be equation (1)

On simplifying the equation , we get

Adding y on both sides of the equation , we get

y + 2 = 2x

Subtracting 2 on both sides of the equation , we get

y = 2x - 2

Therefore , the value of A is y = 2x - 2

Hence , the equation of line is y = 2x - 2 and the graph is plotted

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Both lines A and line B have the same slope, hence they are parallel

An equation is an expression that uses mathematical operations to show the relationship between numbers and variables. Types of equations are linear, quadratic, cubic and so on.

The standard form of a linear equation is:

Ax + By = C

Where A, B and C are constants

The slope intercept form of a linear equation is:

y = mx + b

Where m is the slope and b is the y intercept

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

m = (y₂ - y₁) / (x₂ - x₁)

Two lines are parallel to each other if they have the same slope.

Line A passes through the points (0,4) and (4, 0)

Slope = (0 - 4) / (4 - 0) = -1

Line B passes through the points (0,7) and (7, 0)

Slope = (0 - 7) / (7 - 0) = -1

Since both lines have the same slope, they are parallel

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The solution for the given inequalities is x≥15 or x≤1. Therefore, option A is the correct answer.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

The given inequalities are 3x + 7 ≤ 4x-8 or-2x + 3≥1.

Here, 3x + 7 ≤ 4x-8

Subtract 3x on both the sides of an inequality, we get

7 ≤ x-8

Add 8 on both the sides of an inequality, we get

15≤ x

x≥15

Here, -2x + 3≥1

Subtract 3 on both the sides of an inequality, we get

-2x≥-2

Divide -2 on both the sides of an inequality, we get

x≤1

So, x≥15 or x≤1

Therefore, option A is the correct answer.

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Answer:

Either SF: 1.2 or SF: 0.8. The scale factor that Stacey could use to dilate the current dimensions and meet the customer's requirements are:

When Stacey dilates the rug using a scale factor, the new dimensions of the rug will be found by multiplying the current dimensions by the scale factor.

For a scale factor of 1.2, the new width and length will be:

Width: * 1.2 =

Length: * 1.2 =

Since the new width is less than 8, the scale factor of 1.2 meets the customer's requirements.

For a scale factor of 0.8, the new width and length will be:

Width: * 0.8 =

Length: * 0.8 =

Since the new width is also less than 8, the scale factor of 0.8 meets the customer's requirements.

So, either SF: 1.2 or SF: 0.8 can be used by Stacey to dilate the current dimensions and meet the customer's requirements.

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The answer is neither A nor B for the following definite integral.The definite integral is the difference between the values of the antiderivative evaluated at the limits of integration.

The antiderivative of tet(i-j-5k) with respect to t is not a standard mathematical function, and its exact form cannot be determined without more information about the function tet(i-j-5k). The indefinite integral is represented by an arbitrary constant "c". The definite integral is the difference between the values of the antiderivative evaluated at the limits of integration, and the value of the definite integral can only be found if the limits of integration are known. Therefore, the answer is neither A nor B.

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The limit value for each function is:

a) To calculate limt→[infinity]p(t), we can start by dividing the numerator and denominator of the equation by t, to get:

p(t) = t/t-1

Next, we can take the limit of this expression as t approaches infinity:

limt→[infinity]p(t) = limt→[infinity]t/t-1

Since t is the only variable in the expression, as t approaches infinity, the expression will approach infinity as well. Therefore, limt→[infinity]p(t) = ∞

b) To calculate limt→1+p(t), we can start by rewriting the equation as p(t) = 1/(t-1). Next, we can take the limit of this expression as t approaches 1:

limt→1+p(t) = limt→1 1/(t-1)

Now, we can use the limit laws to simplify the expression:

limt→1+p(t) = 1/limt→1(t-1)

Since the denominator is approaching 0 as t approaches 1, the expression approaches infinity. Therefore, limt→1+p(t) = 1.

c) To calculate limt→2p(t), we can start by dividing the numerator and denominator of the equation by t2, to get:

p(t) = 1/t-1

Next, we can take the limit of this expression as t approaches 2:

limt→2p(t) = limt→2 1/t-1

Now, we can use the limit laws to simplify the expression:

limt→2p(t) = 1/limt→2(t-1)

Since the denominator is approaching 0 as t approaches 2, the expression approaches infinity. Therefore, limt→2p(t) = 0.

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The man should seek a payment of $725.08

The amount of money he wants to receive can be calculated using the formula for compound interest:

A = P * (1 + r/n)^(nt)

where A = $2400 ---- final amount

P = principal

r = 6%, -- interest rate

n = 12 --- number of times the interest is compounded

t = 20, number of years (20).

So, we have

2400 = P * (1 + 6%/12)^(12 * 20)

This gives

P = 2400/3.310

Evaluate

P = 725.08

So, the man should seek a payment of $725.08

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Answer:

min -1 max 3

Step-by-step explanation:

min: when x= -10 so f(x) = ∛-1 = -1

max: when x= 18 so f(x) = ∛27= 3

The required simplified form of the given monomial is 11x²y + 6xy².

Expressions are defined as mathematical statements that have a minimum of two terms containing variables or numbers.

The monomial is given in the question, as follows

16x²y - 4xy²- 5x²y + 10xy²

Rearrange the like terms in the above expression,

16x²y - 5x²y - 4xy² + 10xy²

Add similar elements,

11x²y - 4xy² + 10xy²

Subtract similar elements, and we get

11x²y + 6xy²

Thus, the required simplified form is 11x²y + 6xy².

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The percent of the time you would expect the mean of the sample size of 25 to fall between 66 and 74 is 68.27%, to be less than 70 is 50%, and to be greater than 68 is 84.13%.

a. If a population has a mean of 100 and a standard deviation of 20, then the mean of the sampling distribution of a sample size of n=252 will be 100. This is because the sample means of a sampling distribution will always be equal to the population mean.

b. The standard deviation of the sampling distribution of a sample size of n=25 is 4. This is calculated using the formula: σx = σ/√n, where σ is the population standard deviation (20) and n is the sample size (25).

c. The percentage of the time you would expect the mean of the sample size to fall between 66 and 74 is 68.27%. This is calculated using the Z-score formula, which is (x-μ)/σ, where x is the upper limit (74), μ is the population mean (70), and σ is the population standard deviation (10). The Z-score for the upper limit is (74-70)/10=0.4. We then use the standard normal table to find the area between -∞ and 0.4, which is 0.6827.

d. The percentage of the time you would expect the mean of the sample size to be less than 70 is 50%. This is because the Z-score for a mean of 70 is 0, and the area below 0 is 0.5 or 50%.

e. The percentage of the time you would expect the mean of the sample size to be greater than 68 is 84.13%. This is calculated using the Z-score formula, which is (x-μ)/σ, where x is the lower limit (68), μ is the population mean (70), and σ is the population standard deviation (10). The Z-score for the lower limit is (68-70)/10=-0.2. We then use the standard normal table to find the area between -∞ and -0.2, which is 0.8413.

The percent of the time you would expect the mean of the sample size of 25 to fall between 66 and 74 is 68.27%, to be less than 70 is 50%, and to be greater than 68 is 84.13%.

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We went to Vietnam on a holiday and spent a week in the north of the country. 2. I've got a rabbit and a dog. The rabbit's called Snowy and the dog's called Eric.

A brief, monosyllabic word called an article is used to indicate whether a noun is specific or not. Normally, articles come before nouns, and because they are employed to describe the noun, they can be thought of as adjectives.

1. We went to Vietnam on a holiday and spent a week in the north of the country.

2. I've got a rabbit and a dog. The rabbit's called Snowy and the dog's called Eric.

school photo, Kim is standing on the right and Harry is standing in the

middle next to the Headmaster.

4. I live in a flat in the centre of London, very close to the Big Ben and

Houses of Parliament.

5. Loch Ness is a Monster.

most famous lake in the Scotland because of the Loch Ness

6. David has a job working for the United Nations in a far away from his office. It takes him an hour to get to work.

7. They found the Titanic at the bottom of the Atlantic Ocean.

8. In the USA, most people go to work by clinic because he had

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Answer:

A = 3 * B + 4

Step-by-step explanation:

A - 4=3 * B (given)

A = 3 * B + 4

The position of each point on the membrane for t>0 is given by u(x,y,t) = x(x-1)y(y-1) + (14+u) c2t.

The position of each point on the membrane can be determined by solving the equation u xx + u yy = c2u, where u is the displacement of the membrane from its equilibrium position and c is the speed of the wave propagation. Since we are given f(x,y) = x(x-1)y(y-1), we can solve this equation to find u. Differentiating f(x,y) twice with respect to x and y gives us the corresponding derivatives of u. Plugging these derivatives into the equation gives us u xx + u yy = (14+u) c2. Solving this equation yields the displacement of each point on the membrane for t>0. Thus, the position of each point on the membrane for t>0 is given by u(x,y,t) = x(x-1)y(y-1) + (14+u) c2t.

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Answer:

negative one and one-fourth, negative one-half

Step-by-step explanation:

it seems to be the only possible answer because the y value is negative one half

Answer: negative one and one-fourth, negative one-half

When making or analysing a histogram, you should keep in mind the following words and concepts.

Skewness of a normal distribution

kurtosis

Your histogram will be symmetrical if the data on which it is based are regularly distributed.

Your histogram will be positively biassed if it has more little than large numbers. Your histogram will be negatively skewed if there are more large than little numbers.

positive skew... mean... median... mode... mode Mean Median Mode = median = mean with a negative skew

A histogram's overall look is related to kurtosis in addition to skewness:

tall and lean... leptokurtic typical... mesokurtic broad and short platykurtic

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The value of x based on the information about the triangle is 3.

It should be noted that the total sum of angles in a triangle is 180°. Based on the information given, this will be illustrated as:

180 - (180 - 140) - (180 - 99)

= 180 - 40 - 81

= 59

Therefore, 41x - 2 + 59 = 180

41x = 180 + 2 - 59

41x = 123

Divide

x = 123 / 41.

x = 3.

The value of x is 3.

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Shaded region is between the lines corresponding to both inequalities.

Point that satisfy both inequalities is (-6/7 , 19/7)

Inequalities are the mathematical expressions in which both sides are not-equal. In inequality, unlike in equations, we compare two values.

Given inequalities

y<(-5/6)x+2

equation of the line becomes

y = (-5/6)x + 2           ------(1)

y>(1/3)x+3

equation of the line becomes

y = (1/3)x + 3               --------(2)

By the inequalities

(1/3)x + 3 < y < (-5/6)x + 2

shaded region should be between the lines.

Solving equation 1 and 2

(-5/6)x + 2 = (1/3)x + 3

(-5/6)x - (1/3)x = 3 - 2

(-5 - 2)x/6 = 1

-7x = 6

x = -6/7

Putting value of x in equation 2

y = (1/3)(-6/7) + 3

y = -2/7 + 3

y = (-2 + 21)/7

y = 19/7

Point is (-6/7 , 19/7)

Hence, point that satisfy both inequalities is (-6/7 , 19/7),

shaded region is between both lines corresponding to the inequalities.

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The domain of a function is the set of its possible inputs. it means that  the set of input values  for which the function is defined.

The domain of Function A is the set of real numbers.

The domain of Function B is the set of real numbers greater than or equal to zero.

Here, function A is given that,  

Since, above function can take any value as its input.

That is function is defined for every value of x.

Therefore, The domain of Function A is the set of real numbers.

Here, graph of function B is attached.

From graph of function B, it is observed that graph of function is right side of Y - axis and starting from x = 0.  It means that function B can take any value greater than equal to zero.

Therefore, The domain of Function B is the set of real numbers greater than or equal to zero.

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To determine whether the vector field f(x,y) = (6x + 5y)i + (x - 2y)j is conservative, we must first calculate its curl. The curl of the vector field is the vector field given by the equation:

curl(f(x,y)) = (5 - 2)i + (1 + 6)j = 3i + 7j

Since the curl of the vector field is equal to zero, this means that the vector field is conservative.

To find the potential function for this vector field, we need to calculate the line integral of the vector field along any closed path. In other words, we need to calculate the following integral:

V(x,y) = ∫C f(x,y) ⋅ ds

Where C is any closed path. We can solve this integral using the fundamental theorem of calculus, which states that the line integral of a conservative vector field is equal to the difference between the potential function evaluated at the two end points of the path.

Thus, we can solve for the potential function by finding the value of the potential function at two points and taking the difference of these values. For example, we can choose the points (0,0) and (1,1). At (0,0), the potential function is 0, and at (1,1), the potential function is 3 + 5 + (-2) + 1 = 7. Thus, the potential function is V(x,y) = 3x^2 + xy + 2y^2.

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[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{f(x) = 2x^2 - x - 12}[/tex]

[tex]\mathsf{f(x) = 2(8)^2 - 8 - 12}[/tex]

[tex]\mathsf{f(x) = 2(8^2) - 8 - 12}[/tex]

[tex]\mathsf{f(x) = 2(8 \times 8) - 8 - 12}[/tex]

[tex]\mathsf{f(x) = 2(64) - 8 - 12}[/tex]

[tex]\mathsf{f(x) = 128 - 8 - 12}[/tex]

[tex]\mathsf{f(x) = 120 - 12}[/tex]

[tex]\mathsf{f(x) = 108}[/tex]

[tex]\huge\text{Therefore your answer should be: }[/tex]

[tex]\huge\boxed{\mathsf{f(x) = 108}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

In a case whereby Grandma Gertrude gave 13 pieces of jewelry and Grandma Fien gave y pieces of jewelry to the Carlson sisters to divide evenly among themselves the number of pieces of jewelry that each sister receive can be expreesed as (13 + y)/5.

The concept that will be used here is simplification. The pieces of jewelry by Grandma Gertrude is 13 pieces

Then the pieces of jewelry by Grandma Fien can be seen as " y ".

Since 5 Carlson sisters available . The number of pieces of jewelry each sister receive. can be calculated as:

Total jewlry= (13 + y) which is needed by  5 sisters, the each of the sisters will have = [(13 + y)/5]

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complete quesion:

Grandma Gertrude gave 13 pieces of jewelry and Grandma Fien gave y pieces of jewelry to the Carlson sisters to divide evenly among themselves. There are 5 Carlson sisters.

How many pieces of jewelry did each sister receive?

Answer:

Step-by-step explanation:

C= 2pi

15= diameter. Radius= 13/2. R= 7.5

C= 2 times pi times 7.2

C=13 pi

C= 47.1

The solution to the system of equations shown in the graph is (6, -2)

An equation is an expression that uses mathematical operations to show the relationship between numbers and variables. Types of equations are linear, quadratic, cubic and so on.

The standard form of a linear equation is:

Ax + By = C

Where A, B and C are constants

The slope intercept form of a linear equation is:

y = mx + b

Where m is the slope and b is the y intercept

The solution to a system of linear equations is the point where the two lines meet.

The lines meet at where the x value is 6 and the y value is -2, hence the solution is (6, -2)

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Relative value is the opposite of absolute value. while absolute cost examines the cost of an asset or organisation with out evaluating it to any others, relative fee is primarily based on the value of similar assets or businesses.

Relative value is a technique of determining an asset's worth that takes into account the value of similar belongings. that is in contrast with absolute price, which seems most effective at an asset's intrinsic value and does not evaluate it to other assets. Absolute change refers to the easy difference inside the indicator over two intervals in time, i.e. Relative change expresses the absolute exchange as a percentage of the price of the indicator in the earlier length.  A relative maximum or minimum happens at turning factors at the curve wherein because the absolute minimal and most are the proper values over the entire area of the function. In different words the absolute minimum and most are bounded by means of the area of the function.

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The flag have four lines of symmetry.

A coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space.

A line of symmetry is the line that divides a shape or an object into two equal and symmetrical parts.

The given flag has four lines of symmetry.

We can cut the flag in to half by horizonal way.

In the vertical way.

and we can make the flag to half by diagonal way in two ways.

Hence, the flag have four lines of symmetry.

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The stem-leaf representation of the data is,

0|7 9 9

1|0 1 3 4 4 4 4 5 5 7 7

2|0 5 7

3|5.

The values of the data are divided into a stem and a leaf in a stem-leaf plot.

The initial digit or digits will be put in the stem position, and the final digit will be written in the leaf position.

Let us first rearrange the data in ascending order,

78, 95, 96, 103, 112, 134, 141, 145, 147, 148, 153, 158, 172, 172, 200, 255, 271, 359.

The data is down with the truncated leaf unit of 10, 1|4 represents a number in the 140s.

0|7 9 9

1|0 1 3 4 4 4 4 5 5 7 7

2|0 5 7

3|5.

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Answer:

  see attached

Step-by-step explanation:

You want instructions for drawing a triangle with side lengths 6 cm, 7 cm, and 9 cm.

It works reasonably well to ...

The point where the arcs cross is the third vertex of the triangle.

The equation that represents "triple the input, then subtract 5" will be written as y = 3x - 5.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The output is less than 5 to 3 times the input.

Let 'x' be the input and 'y' be the output. Then the equation is given as,

y = 3x - 5

The equation that represents "triple the input, then subtract 5" will be written as y = 3x - 5.

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