-Question 4
Jen weighs 100 pounds, Jack weighs 120 pounds, and Billy weighs 80 pounds. What is their average weight?

Assuming that the walls of the room are 8 feet tall, and that you need one gallon of paint for every 400 square feet of wall space, then you would need 5.125 gallons of paint to paint the walls of the room.

1. Calculate the square footage of the walls:

10.5ft x 7ft x 2 (sides of walls) = 147 sq. ft

2. Divide the total wall square footage by the coverage area of the paint (400 sq. ft.):

147 sq. ft. ÷ 400 sq. ft. = 0.36 gallons

3. Add 10% extra paint for wastage:

0.36 gallons x 1.1 = 0.396 gallons

4. Round up to the nearest gallon:

0.396 gallons = 0.4 gallons

5. Multiply the gallon of paint by 4 (4 walls):

0.4 gallons x 4 = 1.6 gallons

6. Round up to the nearest gallon:

1.6 gallons = 2 gallons

Hence, you would need 5.125 gallons of paint to paint the walls of the room.

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The fraction number 35 / 80 equivalent to the fraction numbers will be 7 / 16 and 21 / 48. Then the correct options are C and E.

The equivalent is the expression that is in different forms but is equal to the same value.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The fraction number is given below.

⇒ 35 / 80

⇒ 7 / 16

⇒ 21 / 48

The fraction number 35 / 80 equivalent to the fraction numbers will be 7 / 16 and 21 / 48. Then the correct options are C and E.

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Answer: $1.31

Step-by-step explanation:

if you use todays cast

Therefore , the solution of the given problem of function comes out to be the cost of every month is $5 ( 5%) dollar increases every month.

The exponential distribution frequently addresses the elapsed time before a particular event. Consider the exponential distribution of the time (starting right now) before an earthquake happens. Other examples include how long long-distance business calls last (in minutes) and how long an automobile battery lasts (in months).

Here,

Given data :

f(x) = ax,

5% is greater than I growth

$100 = 100 %

After one month =

$105 = 105 %

so $5 ( 5%) dollar increases every month

Therefore , the solution of the given problem of function comes out to be the cost of every month is $5 ( 5%) dollar increases every month.

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The complete question is "An exponential function can be used to simulate the price each night at a hotel. The price per night was $100 when the hotel first opened, and it has been rising by 5% annually since then. find the value of interest."

The number of sodas sold was three times the number of hot dogs sold, so if we set up an equation, it would be 3x + x = 220, where x is the number of hot dogs sold. To solve this equation, we can subtract x from both sides, leaving us with 2x = 220. Then, we can divide both sides by 2, leaving us with x = 110. This means that 110 hot dogs were sold and 3x = 330 sodas were sold.

Answer:

4

Step-by-step explanation:

Step 1:

Substitute:

0.5(17)-1.5(3)

Step 2:

Multiply:

8.5-4.5

Step 3:

Subtract:

4

Answer: - 15x

Step-by-step explanation:

The polynomial with the given zeros can be written as:

p(x) = x^3 + 4x^2 + x - 6

If a polynomial has a leading coefficient a and the N zeros {x₁, x₂, ...} then we can write the polynomial as:

p(x) = a*(x - x₁)*(x - x₂)*...

Here we know that the leading coefficient is 1, and the zeros are:

{-3, -2, 1}

Then the polynomial is:

p(x) = (x + 3)*(x + 2)*(x - 1)

p(x) = (x^2 + 5x + 6)*(x - 1)

p(x) = x^3 - x^2 + 5x^2 - 5x + 6x - 6

p(x) = x^3 + 4x^2 + x - 6

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The graph of the image of the rectangle DEFG after 270° rotation counterclockwise is created using Microsoft Word and included here in the exercise

A pair of numbers called coordinates can be used to determine the position of a point or shape in a two-dimensional plane. A point's position on a 2D plane is described using the phrases "x-coordinate" and "y-coordinate."

A specific point on a grid, also known as a coordinate plane, is identified by coordinates, a pair of numbers (also known as Cartesian coordinates), or sporadically a letter and a number. The two axes of a coordinate plane, which has four quadrants, are the x (horizontal) and y (vertical) axes (vertical).

To find a point's coordinates in a coordinate system, perform the opposite.

Starting at the point, slide up or down a vertical line until you reach the x-axis. It's where your x-coordinate is.

Repeat the preceding procedures while adhering to a horizontal line to obtain the y-coordinate. The x and y coordinates can be used to find a location on the coordinate axes. The x and y coordinates of two points can be used to determine their separation. Using the x and y coordinates for two points simplifies the process of determining a line's slope.

The coordinates of the vertices of the rectangle DEFG are;

D(7, 8), E(10, 8), F(10, 9), G(7, 9)

A rotation of 270° counterclockwise about the origin gives;

Point of preimage = (x, y), point of image after the rotation = (y, -x)

The preimage point D(7, 8) has the image point as D'(8, -7) after the 270° CCW rotation

Similarly, after the 270°CCW rotation, we have;

The preimage point E(10, 8) has an image at E'(8, -10)

The preimage point F(10, 9) has an image at F'(9, -10)

The preimage point G(7, 9) has an image at G'(9, -7)

The graph of the image of the rectangle DEFG after 270° rotation counterclockwise is created using Microsoft Word and included here in the exercise

The complete question is,

Graph the image of rectangle DEFG after a rotation 270° counterclockwise around the origin

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Answer: -3x^3-28x^2-x+14

Step-by-step explanation:

(3x-2)(-x^2-10x-7)

1: We would usually use the FOIL method, but since we don't have binomials we are going to start with the first number in our problem.

3x x -x^2=-3x^3

3x x -10x= -30x^2

3x x -7= -21x

-2 x -x^2=2x^2

-2 x -10x= 20x

-2 x -7=14

2. Add like terms

-3x^3-28x^2-x+14

1 . Price of car 8 years later is $4305.

The price of a car that was bought for $10,000 and has depreciated 10% yearly can be calculated by multiplying the original price of the car ($10,000) by (1 - 0.10) raised to the power of the number of years (8). It means the car will lose 10% of its value each year for 8 years. Therefore, the price of the car 8 years later would be $4304.67. This is the final amount after 8 years of deprecation on the original price of the car.

2. The yearly value of the card 25 years later is $16.93 and equation of price is given by 5 * (1 + 0.05)^t where t is time.

The formula used to calculate the future value of an item that appreciates at a certain annual rate is called compounding. In this case, the baseball card was bought for $5 and has appreciated at a rate of 5% per year. The formula used to find the value of the card 25 years later is "Price = initial value * (1 + interest rate)^number of years". Plugging in the given values, we get: "Price = 5 * (1 + 0.05)^25"

Price=5(1+0.05)^25

Price=5(1.05)^25

Price=16.93

so the final price of baseball is $16.93

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The solution of the quadratic inequality x² - 3x + 2 < 0 is 1 < x < 2

Standard form of a quadratic equation is:

ax² + bx + c = 0

If we change the equal sign '=' to inequality signs <, >, ≤ , ≥ , then it becomes a quadratic inequality.

To solve a quadratic inequality,  first find its roots or the solution of its corresponding quadratic equation. Then, evaluate the signs around the roots.

The given quadratic inequality is:

x² - 3x + 2 < 0

First we find the roots by solving the corresponding quadratic equation:

x² - 3x + 2 = 0

(x - 1) (x - 2) = 0

x = 1 or x = 2

Now, since the coefficient of x² is positive, it means the graph of f(x) = x² - 3x + 2 opens upward. The function intercepts x-axis at x = 1 and x = 2, it means that f(x) < 0 at the interval 1 < x < 2.

Hence, the solution is 1 < x < 2

Your question is incomplete, but most likely your question was:

What are the solutions of quadratic inequality x² - 3x + 2 < 0 ?

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Therefore, the appropriate response for function problem  is Option B) This cat weighs 4 kilos at 7 months of age.

A science called mathematics studies numbers, its variations, arithmetic and the local tissue, shapes, and both their existing and projected places. The relationship between a group of inputs, which each have a corresponding output, is described by a function. A function is a collection of inputs that together produce a single variable, recognizable output with each input. A city, municipality, or scope—often referred to as a realm—is assigned to each function. Usually, the letter f is used to represent functions (x).

Here,

When the cat is m months old, w provides the cat's weight in kg.

the meaning of w(7) = 4 must be determined.

We already know that w represents weight in kilos.

When we enter the age in years, it returns the weight, which is what we consider to be the input.

W(7) stands for the weight of the cat at 7 months old.

where w(7) = 4 denotes the cat's weight at 7 months old, which is 4 kilograms.

Therefore, the appropriate response is Option B) This cat weighs 4 kilos at 7 months of age.

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The fraction of the marble in the bag are blue is 4/15

The term fraction can be found by dividing part of a whole by the whole. Here the example if 2 students out of a total of 4 are picked, then the part is 2 and the whole is 4 while the fraction is 2 by 4.

Here we have given that a bag has 16 blue, 20 red, and 24 green marbles.

And we need to find the fraction of the marbles in the bag are blue

While looking into the given question, we have identified that the number of blue marbles is 16.

And the total number of marbles is calculated by adding the number of each marbles, then we get,

=> 16 + 20 + 24 = 60.

Here we know the the resulting fraction is obtained by the number of blue marbles out of the total marbles is,

Then it can be written as

=> 16/60

When we simplify this one then we get,

=> 4/15

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If seven pound of fertilizer can cover 1400 square feet, 2 pounds of fertilizer can cover 400 square feet.

Therefore the answer is 400 square feet.

If seven pounds of fertilizer can cover 1400 square feet, we can set up the following proportion:

7 pounds / 1400 square feet = x pounds / y square feet

So y square feet = ( x pounds × 1400 square feet) / 7 pounds

To find out how many square feet can be covered by 2 pounds of fertilizer, we can solve for y by substituting in 2 for x:

y square feet = ( 2 pounds × 1400 square feet) / 7 pounds

y square feet = 2 × 1400 / 7

y square feet = 2800 / 7

y square feet = 400

So 2 pounds of fertilizer can cover 400 square feet.

--The question is incomplete, complete question is given below--

"Seven pound of fertilizer can cover 1400 square feet. How many square feet can be covered by 2 pound of fertilizer?"

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Answer:

(-4,-2)

Step-by-step explanation:

To solve this system of equations, we can substitute the expression for y in the second equation:

5x + 2(x+2) = -24

We can then simplify and solve for x:

5x + 2x + 4 = -24

7x = -28

x = -4

We can then substitute this value of x back into the first equation to find the value of y:

y = -4 + 2

y = -2

So the solution of the system of equations is (x, y) = (-4, -2)

The greatest number of rolls that Melissa received if she spent less than $63 is 206.

Linear inequalities are defined as those expressions which are connected by inequality signs like >, <, ≤, ≥ and ≠ and the value of the exponent of the variable is 1.

Cost for a large sandwich roll = $0.25

Cost for a small sandwich roll = $0.15

Let x be the number of small rolls that Melissa ordered.

Then number of large rolls she ordered = x + 130

Total cost for the rolls = 0.25(x + 130) + 0.15x

Melissa spent less than $63.

0.25(x + 130) + 0.15x < 63

(0.25x) + (0.25 × 130) + 0.15x < 63

0.4x + 32.5 < 63

0.4x < 30.5

x < 76.25 ≈ 76

Number of small rolls she ordered maximum is 76.

Number of large rolls she ordered is 76 + 130 = 206

Hence Melissa ordered 206 large rolls at maximum.

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The percent error for the given actual and estimated age of the fossils discovered by the researcher is equal to 11.11%.

As given in the question,

Actual estimated age of the fossil =3200 year old

Expected age discovered by the researcher of the fossil = 3600 year old

Formula for percent error is given by :

Percent error = | ( Actual age - Expected age ) / (Expected age) | × 100

Substitute the values we get,

Percent error = | ( 3200 - 3600 )/ 3600 | × 100

⇒ Percent error = 0.111111 × 100

⇒ Percent error = 11.11 %

Therefore, the percent error of the fossil discovered by the researcher is given by 11.11%.

The above question is incomplete , the complete question is :

A researcher estimates that a fossil is 3200 years old. Using carbon-14 dating, a procedure used to determine the age of an object, the researcher discovers that the fossil is 3600 years old.

Find the percent error?

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Answer:

$6.36

Step-by-step explanation:

6 x 1.06 = 6.36

The hourly rate of Sheila Blige if she worked for 40 regular hours and 8 overtime hours and paid a gross of $884.00 is $17

Total regular hours worked = 40

Total overtime hours worked = 8

Total gross pay = $884.00

Let

Hourly rate = x

Overtime rate = 1.5x

So,

40x + 8(1.5x) = 884

40x + 12x = 884

52x = 884

divide both sides by 52

x = 884 / 52

x = $17

Therefore,

Hourly rate = x

= $17

Overtime rate = 1.5x

= 1.5(17)

= $25.5

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As a result, the answer to the provided equation problem is 1.39500 profit and 2.400 loss.

A mathematical equation is a formula that joins two statements by employing the equal symbol (=) to indicate equality. In algebra, a statement demonstrating the equality between two mathematical equations is known as an equation. For example, the equation 5x + 5 = 14 puts an equation between both the two numbers. Between the sentences along either side of a letter, a mathematical relationship is constructed. Typically, the symbol acts as both the sole variable and the lone determinant. As an illustration, 8x - 4 = 2.

Here,

A C number of vehicles

Monthly expenses are subtracted from total monthly income to determine profit.

=> (25-6)C - (23500-6000) (23500-6000) (23500-6000)

=> P = 19C-17500

3000 autos need to be maintained,

Earnings are 19(3000)-17500.

Gain: $39500

If 900 automobiles are received in a given month, a profit or loss will result.

Earnings are 19(900)-17500.

Gain: -400.

Yes, a loss.

The solution to the given equation's issue is thus 1.39500 profit and 2.400 loss.

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Answer:

78 that he added

Step-by-step explanation: not needed

The school's population in the year 2017 is given by the equation A = 1620

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the school's population in 2017 be represented as A

Now , the equation will be

The school's population in 2016 = 1500 students

The percentage of increase in population = 8 %

So , school's population in 2017 A = school's population in 2016 + ( 8/100 ) x school's population in 2016

Substituting the values in the equation , we get

The school's population in 2017 A = 1500 + ( 0.08 x 1500 )

On simplifying the equation , we get

The school's population in 2017 A = 1500 + 120

The school's population in 2017 A = 1620 students

Hence , the population is 1620 students

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The daily increase in Mrs. Miller's daily class is $2 more than it is in Mr. Taylor's class.

Option D is the correct answer.

The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

We have,

Mr. Taylor:

The coordinates from the graph.

(1, 10), ), (2, 20), (3, 30)

The rate of change.

= (20 - 10) / (2 - 1)

= 10

This means,

Each day the amount is increased by $10.

Mrs. Miller:

From the table,

(3, 24), (5, 60)

Rate of change.

= (60 - 24) / (5 - 3)

= 36 / 2

= 12

This means,

Each day the amount is increased by $12.

Thus,

Mrs. Miller's daily increase is $12.

Mr. Taylor's daily increase is $10.

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The horizontal line test is used to determine if a given function is one-to-one, which means that for every unique x-value, there is a unique y-value.

A function that is one-to-one can be inverted, meaning that it has an inverse function. Inverse functions are important in many areas of mathematics, such as solving equations, finding derivatives, and studying geometric transformations.

The horizontal line test is used because it provides a simple and easy way to determine if a function is one-to-one without having to solve for the inverse function. By drawing a horizontal line through the graph of a function and seeing if the line intersects the graph at most once, it is possible to determine if the function is one-to-one without the need for complex calculations or algebraic manipulations.

Another reason is that the horizontal line test can be applied to functions that are defined on a closed interval or on all real numbers and it is a visual way to understand if a function is one-to-one.

In conclusion, the horizontal line test is used to determine if a given function is one-to-one, which is important because one-to-one functions can be inverted.

The test is simple and easy to apply, and it provides a visual way to understand if a function is one-to-one without the need for complex calculations or algebraic manipulations. It can be applied to functions that are defined on a closed interval or on all real numbers.

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Answer: 3 : 8

Step-by-step explanation:

red to blue is 3 : 5

blue to yellow is 3 : 8

red to yellow is 3 : 8

Each angle is 53 degrees, 32 degrees, and 95 degrees.

A triangle is a three-sided polygon that is sometimes (but not always) referred to as the trigon. Every triangle has three sides and three angles, which may or may not be the same. Triangles are three-sided polygons with three vertices. The angles of the triangle are formed by connecting the three sides end to end at a point. The total of the triangle's three angles equals 180 degrees. A triangle is a three-sided polygon with three vertices. The angle produced within the triangle is 180 degrees. It signifies that the total of a triangle's internal angles equals 180°.

Here,

The sum of angles of triangle is 180 degrees.

4x+5+7x+11+2x+8=180

13x+24=180

13x=156

x=12

T=4x+5

=4*12+5

=53 degree

U=2x+8

=2*12+8

=32 degree

V=7x+11

=7*12+11

=95 degree

The measure of each angle is 53 degree, 32 degree and 95 degree.

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The fourth graph (the right graph in the bottom row) is discovered to represent the function f using translation notions (x).

A sort of transformation called a translation involves moving each point in a figure the same distance in the same direction.

In terms of operations like multiplication or sum/subtraction in its definition, a translation is represented as a change in the function graph.

has a vertex at the origin and [tex]$f(x)=\sqrt{x}$[/tex] is the parent function.

In this issue, the translated function is [tex]$f(x)=2 \sqrt{x+1}$[/tex] It was left 1 unit relocated and vertically stretched by a factor of 2 units, resulting in a new vertex position of (0,-1).

As a result, the fourth graph, on the right side of the bottom row, represents the function f. (x).

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The two main types of coordinate systems used in mathematics and physics are Cartesian and Polar Coordinates.

A coordinate system is a system used to identify and locate a point in space. It is the basis for maps, navigation and surveying. Coordinate systems can be two-dimensional or three-dimensional, and can use a variety of units such as latitude, longitude, and feet. Coordinate systems are used in a variety of fields such as engineering, architecture, geology, and navigation. Coordinate systems help to identify and locate points in space and are essential for charting and mapping the physical world.

Cartesian Coordinates, named after the French mathematician and philosopher René Descartes, use a two-dimensional plane to represent points with an x-axis and a y-axis. These coordinates are expressed as ordered pairs (x,y) and represent points in relation to the origin (0,0). This can be used to plot graphs and equations, and is the most commonly used coordinate system.

Polar Coordinates are based on a two-dimensional plane centered on a pole. Points are expressed as ordered pairs (r,θ) where r is the distance from the pole and θ is the angle from the polar axis. This coordinate system is useful for finding distances and angles in a circle. It is used frequently in physics and astronomy.

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