The length of a rectangular poster is 9 more inches than three times its width. The area of the poster is 30 square inches. Solve for the dimensions (length and width) of the poster.

As the value of x (time in seconds) increases, the height of the soccer ball decreases until it hits the ground at x=3.

what is domain of the function?

The domain of a function is the set of all possible values of the input variable (independent variable) for which the function is defined. It is the set of all x-values for which the function produces a valid output. In order to determine the domain of a function, one needs to consider any restrictions or limitations that the function may have.

The given problem is related to the motion of a soccer ball kicked by Lin. The height of the soccer ball (in feet) is a function of time (in seconds), and it is represented by a graph.

Domain: The domain of the function is the set of all possible values of the input variable (time in seconds). In this case, the soccer ball was in the air for 3 seconds, so the domain is [0, 3], which means that the height function is defined for all values of time between 0 and 3 seconds, including 0 and 3.

Range: The range of the function is the set of all possible values of the output variable (height of the soccer ball in feet). In this case, the soccer ball reached a height of approximately 30 ft while it was in the air. Therefore, the range of the function is [0, 30], which means that the height of the soccer ball is defined for all values between 0 and 30 feet, including 0 and 30.

Line of symmetry: The line of symmetry is a vertical line that passes through the vertex of the parabola (in this case, the highest point that the soccer ball reaches). The parabolic graph of the soccer ball's height function is symmetric with respect to the vertical line passing through the midpoint of the domain. Since the domain is [0, 3], the midpoint is (3/2, 0), so the line of symmetry is x = 3/2.

As the value of x (time in seconds) increases, the height of the soccer ball decreases until it hits the ground at x=3. As the value of x decreases from 3 to 0, the height of the soccer ball increases from 0 to 30 and then decreases again as it hits the ground. The rate of change of the height of the soccer ball is not constant but rather depends on the shape of the parabolic graph of the height function.

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The height of the flagpole is approximately 23,047.11 feet.

To resolve this issue, we can make use of the similar triangles property. The teacher, the flagpole, and each of their corresponding triangles are similar because they have the same angles.

Let h be the height of the flagpole. Then, we can set up the following proportion:

h / 3112 = 612 / 9

When we simplify this ratio, we obtain:

h = (3112 x 612) / 9

h = 207424 / 9

h ≈ 23,047.11 feet

Hence, the flagpole is roughly 23,047.11 feet tall.

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The graph representing the inequality 2.5 is less than the product of −0.5 and a number is number line with open circle on point negative 5 and arrow shaded to the left.

Inequalities are defined as those expressions which are connected by inequality signs like >, <, ≤, ≥ and ≠.

Given inequality is,

2.5 is less than the product of −0.5 and a number.

2.5 < -0.5x

We have to isolate x on one side.

Dividing both sides by -0.5,

-5 > x

The inequality sign changes when a negative number is divided.

Or x < -5

So the solutions of the inequality are all the numbers less than -5.

So the graph of the inequality will be a number line where an open circle is at -5, since the point -5 is not included.

Since the solutions are less than -5, arrow is shaded to the left.

Hence the second option is the correct one.

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Considering  A, B, C, and D are colinear the length of line BC is 7cm.

In mathematics, a circle is a geometric shape that consists of all points that are the same distance from a fixed point called the center. This distance is called the radius of the circle. A circle is a two-dimensional object and is usually represented by a curved line, often drawn as a closed shape.

Since line DE is tangent to circle A at point E, we know that line AE is perpendicular to line DE. Therefore, we can use the Pythagorean theorem to find the length of AE:

AE² = AD²- DE²

Since A, B, C, and D are collinear, we can find AD by subtracting CD from BC:

AD = BC - CD

Substituting this into the equation above, we get:

AE² = (BC - CD)² - DE²

We are given that CD = 8cm and DE = 12cm, so we can substitute these values into the equation:

AE² = (BC - 8)² - 12²

We also know that AE = BE, since E is the point of tangency. Therefore, we can use the Pythagorean theorem again to find the length of BE:

BE² = AE² + AB²

Substituting AE^2 with the expression we found above, we get:

BE² = (BC - 8)² - 12² + AB²

Since A, B, C, and D are collinear, we know that AB + BC = CD = 8cm. Solving for AB, we get:

AB = 8 - B

Substituting this into the expression for BE², we get:

BE² = (BC - 8)² - 12² + (8 - BC)²

Simplifying this expression, we get:

BE^² = -16BC + 256

We want to find the value of BC, so we set BE equal to 12cm (since DE = 12cm):

12² = -16BC + 256

144 = -16BC + 256

-112 = -16BC

BC = 7 cm

Therefore,considering  A, B, C, and D are colinear the length of line BC is 7cm.

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a. The omnibus null hypothesis and alternative hypothesis are H0: μA = μB = μC and H1: μA ≠ μB ≠ μC respectively. b. The statistical values are F(2,12) = 4.03, p < 0.05. As the F-ratio = 4.03 is greater than the critical value = 3.89, the null hypothesis is rejected. c. It is concluded that there exist a significant difference in the severity of anxiety symptoms after undergoing the art therapy program between the three cities. d. The eta-squared and omega-squared values are 0.40 and 0.34 respectively.

a. The omnibus null hypothesis is that there is no difference in the severity of anxiety symptoms after undergoing the art therapy program between the three cities. The alternative hypothesis is that there is a difference in the severity of anxiety symptoms after undergoing the art therapy program between the three cities.

H0: μA = μB = μC
H1: μA ≠ μB ≠ μC

b. To conduct an appropriate statistical test, we will use ANOVA (Analysis of Variance). The steps for the calculation are as follows:

Step 1: Calculate the grand mean (GM) of all the scores.

GM = (22+22+40+25+22+34+30+27+30+42+28+27+33+21+39)/15 = 29.6

Step 2: Calculate the sum of squares between groups (SSB).

SSB = 5((22+22+40+25+22)/5 - 29.6)^2 + 5((34+30+27+30+42)/5 - 29.6)^2 + 5((28+27+33+21+39)/5 - 29.6)^2 = 340.4

Step 3: Calculate the sum of squares within groups (SSW).

SSW = (22-24.2)^2 + (22-24.2)^2 + (40-24.2)^2 + (25-24.2)^2 + (22-24.2)^2 + (34-32.6)^2 + (30-32.6)^2 + (27-32.6)^2 + (30-32.6)^2 + (42-32.6)^2 + (28-29.6)^2 + (27-29.6)^2 + (33-29.6)^2 + (21-29.6)^2 + (39-29.6)^2 = 506.8

Step 4: Calculate the mean square between groups (MSB) and the mean square within groups (MSW).

MSB = SSB/dfB = 340.4/2 = 170.2
MSW = SSW/dfW = 506.8/12 = 42.23

Step 5: Calculate the F-ratio.

F = MSB/MSW = 170.2/42.23 = 4.03

Step 6: Compare the F-ratio with the critical value from the F-distribution table with dfB = 2 and dfW = 12 at a significance criterion of 5%.

The critical value is 3.89.

Step 7: Make a decision and state the relevant statistical values.

Since the F-ratio (4.03) is greater than the critical value (3.89), we reject the null hypothesis and conclude that there is a significant difference in the severity of anxiety symptoms after undergoing the art therapy program between the three cities. The relevant statistical values are F(2,12) = 4.03, p < 0.05.

c. The statistical conclusion for the outcome in (b) is that there is a significant difference in the severity of anxiety symptoms after undergoing the art therapy program between the three cities.

d. The eta-squared and omega-squared values for the overall effects of the independent variable on severity of anxiety symptoms are calculated as follows:

Eta-squared (η^2) = SSB/SST = 340.4/(340.4+506.8) = 0.40

Omega-squared (ω^2) = (SSB - dfB*MSW)/(SST + MSW) = (340.4 - 2*42.23)/(340.4+506.8+42.23) = 0.34

The numerical formulas used are:

η^2 = SSB/SST
ω^2 = (SSB - dfB*MSW)/(SST + MSW)

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Answer:

Step-by-step explanation:

1500 + 5000x 0.055 - $1775

1500 + 10000 x 0.055 = $2050

with option 1 he would make 1775 to 2050

                   2400 + 5000 x0.04 =2600

                   2400 + 10000 x 0.04 = 2800

With option 2 hw would make $2600 to $2800

                                     simple calculation  :)

The expression will be 5 + 11x.

What is an expression?

An expression in mathematics is a combination of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.)

It is possible to compare expressions to phrases. In English, a phrase by itself may contain an action, but it does not constitute a whole sentence.

Explanation: 3 + 7

Let the number to be "x"

Step 1 : the number is multiplied by - 8

           So, -8 x

Step 2 : subtracted from the sum of 5 and 3 times the number

       So,  (5 +3x) - (-8x)

           = 5+3x + 8x

           = 5 + 11x

Hence, The final expression will be 5 + 11x.

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15 quarters of a cupcake, which is equivalent to 3.75 cupcakes in total.

Two or more expressions with an Equal sign is called as Equation.

5 halves of a cupcake for your family, which is equivalent to 2.5 cupcakes.

To divide this evenly among your two friends who each want a quarter of a cupcake, we can start by converting the amount of cupcakes you have to quarters:

2.5 cupcakes × 4 quarters/cupcake = 10 quarters of a cupcake

Now we can divide the 10 quarters of a cupcake equally between your two friends:

10 quarters of a cupcake / 2 friends = 5 quarters of a cupcake per friend

Hence, a total of 5 + 5 + 5 = 15 quarters of a cupcake, which is equivalent to 3.75 cupcakes in total.

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Answer:

IQR - 31

You first need to find the median. After find the middle number in the numbers before and after your median. This will give you your first and third quartile. Add these together then divide by two. This will give your IQR.

The probability that a hotel room costs $227 or more per night in New York City is 0.3406.

It is a branch of mathematics that deals with the occurrence of a random event.

Lets standardize the value of $227 per night using the formula:

z = (x - μ) / σ

where x is the value we are interested in, μ is the mean of the distribution, and σ is the standard deviation of the distribution. Substituting the given values, we get:

z = (227 - 205) / 54

z = 0.4074

We need to find the probability that a hotel room costs $227 or more per night, which is equivalent to finding the probability that a standardized value is greater than or equal to 0.4074.

Using a standard normal table, we find:

P(Z ≥ 0.4074) = 1 - P(Z < 0.4074)

P(Z ≥ 0.4074) = 1 - 0.6594

P(Z ≥ 0.4074) = 0.3406

Therefore, the probability that a hotel room costs $227 or more per night in New York City is approximately 0.3406.

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The probability that a hotel room costs $227 or more per night is 0.3446

Probability distribution yields the possible outcomes for any random event. It is also defined based on the underlying sample space as a set of possible outcomes of any random experiment. These settings could be a set of real numbers or a set of vectors or a set of any entities. It is a part of probability and statistics.

Random experiments are defined as the result of an experiment, whose outcome cannot be predicted. Suppose, if we toss a coin, we cannot predict, what outcome it will appear either it will come as Head or as Tail. The possible result of a random experiment is called an outcome. And the set of outcomes is called a sample point. With the help of these experiments or events, we can always create a probability pattern table in terms of variables and probabilities.

GIven,

The mean hotel room rate ( [tex]\mu[/tex])  is $205 per night and standard deviation    ([tex]\sigma[/tex]) of $54. A.

p( x > 225 )

we can't this to standard normal using   [tex]z =\frac{X- \mu}{\sigma}[/tex]

                                                         [tex]z=\frac{227-205}{54} \approx0.4074[/tex]

p (z > 0.4074 ) = area to the right  at 0.4074

p( x > 225 )  = p (z > 0.4074 )  = 1 - p (z < 0.4074)

                                                = 1 - 0.6554 (from z table)

                                                =  0.3446

Hence, probability that a hotel room costs $227 or more per night (to 4 decimals) 0.3446

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The expression (z²+10z+25)/(z²-3z-40) in simplest form is (z+5)/(z-8), with the restriction that z cannot be equal to 8.

The expression (z²)+10z+25)/(z²-3z-40) can be simplified by factoring both the numerator and denominator.

First, factor the numerator:
(z²+10z+25) = (z+5)(z+5)

Next, factor the denominator:
(z²-3z-40) = (z-8)(z+5)

Now, the expression can be simplified by canceling out the common factor of (z+5):
(z+5)(z+5)/(z-8)(z+5) = (z+5)/(z-8)

Therefore, the expression in simplest form is (z+5)/(z-8).

There are restrictions on the variable in this expression. The denominator cannot be equal to zero, so we must exclude any values of z that would make the denominator zero.

The denominator is (z-8), so the restriction is:
z-8 ≠ 0

Solving for z, we find that the restriction is:
z ≠ 8

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Option C. (x+2)/(x-3)*(4)/(x+2) is the equivalent rational expression to (4)/(x-3).

The rational expression that is equivalent to this expression (4)/(x-3) is option C. (x+2)/(x-3)*(4)/(x+2).
We can simplify the rational expression (x+2)/(x-3)*(4)/(x+2) by canceling out the common factor (x+2) from the numerator and denominator. This will give us the equivalent rational expression:

(x+2)/(x-3)*(4)/(x+2) = (4)/(x-3)

Therefore, option C. (x+2)/(x-3)*(4)/(x+2) is the equivalent rational expression to (4)/(x-3).

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Answer: To rewrite the function to show how quickly the weeds grow each day, we need to use the fact that there are 7 days in a week. Let's divide both sides of the original function by 7 to get:

f(x/7) = 3(1.05)^(x/7)

This function gives the amount of weed growth after x/7 weeks, which is equivalent to x days. To find the daily weed growth rate, we need to take the derivative of this function with respect to x and evaluate it at x=0:

f'(0) = (d/dx) 3(1.05)^(x/7)

Using the chain rule, we get:

f'(0) = 3ln(1.05)/7 ≈ 0.00797

This means that the weeds grow at a daily rate of approximately 0.797%, or 0.00797 as a decimal.

Step-by-step explanation:

The dependent variable and independent variable in the 15th question is

t = dependent and m = independent variable.

A variable is a quantity that may change within the context of a mathematical problem or experiment.

Given is a statement, The temperature, t, of water and the number of minutes, m, the water is in the freezer, we need to identity the dependent variable and independent variable for this statement,

Independent variable :-

It is a variable that doesn't change by the other variables.

Dependent variable :-

The dependent variable is the variable that is used for tested in an experiment.

Here, the temperature of the water is dependent on the number of minutes it has been kept in the freezer,

So, the temperature of the water is the dependent variable and the number of minutes it has been kept in the freezer is the independent variable.

Hence, the dependent variable and independent variable in the 15th question is t = dependent and m = independent variable.

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The question 17 is not completely mentioned

The amount in the second case is more. Then the better job is the second one.

In other words, the collection of all feasible values for the parameters that satisfy the specified mathematical equation is the convenient storage of the bunch of equations.

If he can make $2,000 worth of sales per week. Then the total amount in the first case is given as,

⇒ $31,200 + $2,000 x 0.09 x 52

⇒ $40,560

And the total amount in the second case is given as,

⇒ $26,000 + $2,000 x 0.15 x 52

⇒ $41,600

The amount in the second case is more. Then the better job is the second one.

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The final answer sum of f(x) and g(x) is [tex]x^2 + 6x - 40[/tex], which is a polynomial in simplest form.

To find the sum of two functions, we simply need to add their respective terms together.

In this case, we have:

f(x) = [tex]x^2 + 5x - 36[/tex]

g(x) = x - 4

So, f(x) + g(x) = [tex](x^2 + 5x - 36)[/tex] +[tex](x - 4) = x^2 + 6x - 40[/tex]

Therefore, the sum of f(x) and g(x) is [tex]x^2 + 6x - 40[/tex], which is a polynomial in simplest form.

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Answer:

962.084375 meters² or 306.25π

Step-by-step explanation:

A diameter is a line that goes straight through the center of the circle. Since it goes through the center, it creates 2 radii. This splits the diameter into 2 separate parts, and since the diameter is 25 meters, that means that the radius will be 25/2 = 17.5 meters.

The formula for the area of a circle is pi • r²

Since we know the radius (17.5), we can solve this expression:

pi • 17.5²

pi • 306.25

If we use 3.1415 for pi, we get962.084375 meters²

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The coordinates of the image of EB are (0, -1) and (-6, 18).

Dilation is a process for creating similar figures by changing the dimensions.

The center of dilation is given as (3, -1) and the scale factor is 3.

The distance between the center of dilation and point E is:

d = √((3-2)² + (-1-(-1))²) = 1

The distance between the center of dilation and point B is:

d = √((3-0)² + (-1-5)²) = sqrt(65)

To find the new distance, we multiply the distance by the scale factor:

For point E: 3 × 1 = 3

For point B: 3 × √(65)

Now, we can find the coordinates of the image:

For point E:

x = 3 × (2 - 3) + 3 = -3 + 3 = 0

y = 3 × (-1 -(-1)) -1 = 0 - 1 = -1

So the image of E is (0, -1).

For point B:

x = 3 × (0 - 3) + 3 = -9 + 3 = -6

y = 3 × (5 -(-1)) -1 = 18

So the image of B is (-6, 18).

Therefore, the coordinates of the image of EB are (0, -1) and (-6, 18).

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The equation of the parabola in intercept form is y = -6(x+ 16 )(x + 2).    

A parabola is a type of curve that is formed when a point called the focus moves along a straight line called the directrix.

In other words a parabola is defined as the set of all points in a plane that are equidistant to the focus and the directrix.

The shape of a parabola is similar to a U or a V shape, and it can either be open upwards or downwards, depending on the orientation of the curve.

The Intercept form of a parabola is given by

                             y = a(x - p)(x - q)  

Where p and q are the x - coordinates at which the parabola crosses the x-axis (i.e, the x-intercepts).

Here we have

The parabola in intercept form that passes through (-18,72) with x-intercepts of -16 and -2

Let y = a(x-p)(x-q) is the equation of parabola    

From the data, x-intercepts p = - 16 and p = -2

=> y = a(x+ 16 )(x + 2)  ---- (1)

Given that the parabola passes through (-18, 72)

=> 72 = a(- 18 + 16 )(-8 + 2)  

=> 72 = a(-2)(-6)  

=> 72 = - 12a

=>  a = - 6

Substitute a = -6 in equation (1)

=> y = -6(x+ 16 )(x + 2)        

Therefore,

The equation of the parabola in intercept form is y = -6(x+ 16 )(x + 2).    

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The probability of generating a value between -0.9900 and 2.9000 from a standard normal distribution is 0.4781. The probability of generating a value between -2.4200 and 2.4200 from a standard normal distribution is 0.9804. The probability of generating a value between -0.9900 and 20.1 from a standard normal distribution is 1.0000.

The standard normal distribution, also called the z-distribution, is a special normal distribution where the mean is 0 and the standard deviation is 1. Any normal distribution can be standardized by converting its values into z scores.The standard normal distribution is one of the forms of the normal distribution. It occurs when a normal random variable has a mean equal to zero and a standard deviation equal to one. In other words, a normal distribution with a mean 0 and standard deviation of 1 is called the standard normal distribution.

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The correct option that describes the number and type of solutions of the quadratic equation is: There are two unequal real solutions. The correct answer alternative is option a.

The discriminant of a quadratic equation is the part of the equation under the square root in the quadratic formula, which is b² - 4ac. In the given equation, 2x² - 7x + 4 = 0, the values of a, b, and c are 2, -7, and 4, respectively.

To compute the discriminant, we plug in these values into the formula:

Discriminant = b² - 4ac
= (-7)² - 4(2)(4)
= 49 - 32
= 17

The discriminant is 17.

To determine the number and type of solutions of the quadratic equation, we look at the value of the discriminant. If the discriminant is greater than 0, there are two unequal real solutions. If the discriminant is equal to 0, there is one real solution. If the discriminant is less than 0, there are two imaginary solutions.

Since the discriminant in this case is 17, which is greater than 0, there are two unequal real solutions. Therefore, the correct answer is (a) There are two unequal real solutions.

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the answer is 6 uniforms. 57/9.5=6

Answer: y = 5/6x

Step-by-step explanation:

It is a direct variation.

[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \stackrel{ doubled }{\$ 1600}\\ P=\textit{original amount deposited}\dotfill & \$800\\ r=rate\to 8\%\to \frac{8}{100}\dotfill &0.08\\ t=years \end{cases}[/tex]

[tex]1600 = 800e^{0.08\cdot t} \implies \cfrac{1600}{800}=e^{0.08t}\implies 2=e^{0.08t} \\\\\\ \log_e(2)=\log_e(e^{0.08t})\implies \log_e(2)=0.08t\implies \ln(2)=0.08t \\\\\\ \cfrac{\ln(2)}{0.08}=t\implies 8.66\approx t\qquad \textit{about 8 years and 241 days}[/tex]

Answer:

Step-by-step explanation:

you can set two ratios equal to each other to solve for the unknown (the amount of bananas).

11:3 as x:1

then cross multiply to get an equation. divide both sides by 3 to isolate X. plug that into a calculator and your answer is 3.6 repeating which rounds to 4 oz of bananas

The length of one side of the square is 1.5 units

The complete question is added as an attachment

From the question, we have

The triangle and the squate have the same perimeter

The perimeter is the sum of the side lengths

So, we have

Triangle = 3x + 4x + 5x

Square = 4 * (x + 1)

Evaluate

Triangle = 12x

Square = 4x + 4

So, we have

4x + 4 = 12x

Evaluate

8x = 4

So, we havr

x = 0.5

From the figure, we have

Length = x + 1

Evaluate

Length = 0.5 + 1

So, we have

Length = 1.5

Hence, the length is 1.5

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Answer:

8183.27

Step-by-step explanation:

Answer:

8183.3

Step-by-step explanation:

500(1+0.15)20=8183.27 round it to become 8183.3

Therefore, approximately 408 packages of paper can be put on the shelf.

Area is a measure of the amount of space inside a two-dimensional shape or surface. It is usually expressed in square units such as square meters, square inches, or square feet. The area of a shape can be found by multiplying the length of the shape by its width. The concept of area is used in many areas of mathematics and in a wide range of real-world applications, including architecture, engineering, physics, and geography. The ability to calculate the area of a shape is an important skill in many fields and is a fundamental concept in geometry.

Here,

To solve this problem, we need to find the number of packages of paper that can fit on the warehouse shelf by dividing the total shelf area by the area of each package.

First, we need to convert the height of the shelf from feet and inches to inches:

1 foot = 12 inches

1' 5" = 1 * 12 + 5 = 17 inches

Next, we need to convert the length of the shelf from yards to inches:

1 yard = 36 inches

2 yards = 2 * 36 = 72 inches

Now we can find the area of the warehouse shelf:

Area = length * height

Area = 72 inches * 17 inches

Area = 1224 square inches

The area of each package of paper is:

Area = height * width

Area = 2 inches * 1.5 inches

Area = 3 square inches

Now we can find the number of packages of paper that can fit on the warehouse shelf:

Number of packages = Shelf area / Package area

Number of packages = 1224 square inches / 3 square inches

Number of packages ≈ 408

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Answer:

The original cost for 1 pound of coffee is $4.50, and Gabriel wants to buy 4 pounds, so the total cost without the coupon would be:

4 pounds x $4.50/pound = $18

With the coupon, Gabriel can subtract $2 from the final amount, so the total cost with the coupon would be:

$18 - $2 = $16

Therefore, Gabriel would have to pay $16 to buy 4 pounds of coffee with the coupon.

To write an expression for the cost to buy p pounds of coffee, we can use the formula:

cost = price per pound x number of pounds - coupon

If Gabriel buys at least one pound of coffee, then the expression would be:

cost = $4.50p - $2

So the cost to buy p pounds of coffee can be calculated by plugging in the desired value for p into this expression.

The number of $0.49$ stamps Paula bought is s = (1274 - 49s / 21) + 6.

To solve the equation 0.49s + 0.21(s - 6) = 12.74 for s, we can multiply both sides by 100 to get:

49s + 21(s - 6) = 1274

Now, we can move the 21(s - 6) term to the left side of the equation and the 49s term to the right side of the equation. To do this, we will subtract the 49s from both sides of the equation, which yields:

21(s - 6) = 1274 - 49s

Next, we can divide both sides of the equation by 21 to isolate the (s - 6) term, resulting in:

(s - 6) = 1274 - 49s / 21

Finally, we can add 6 to both sides of the equation to solve for the number of $0.49$ stamps that Paula bought:

s = (1274 - 49s / 21) + 6

Therefore, the number of $0.49$ stamps Paula bought is s = (1274 - 49s / 21) + 6.

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