A company that sells paper has a tiered pricing model based on how much paper you buy. If you buy less than 10 reams, they charge you $7 per ream and a shipping cost of $8. If you buy 10 or more reams but less than 20 reams, they charge you $6 per ream and a shipping cost of $16. If you buy 20 or more reams, they charge you $6 per ream and shipping is free.
a. Write a function that models the price in terms of the number of reams bought.
b. What is the domain of the function?
c. What is the range of the function?
d. How much will it cost to buy 25 reams of paper?
f. How much paper can you buy for $60?

The value of proᵥᵥv is (-30/37)i + (42/37)j and the decomposed vector v into v₁ and v₂ are  6 + 6j and -5i + j - 6 respectively.

a. To find the projection of w onto v (proᵥᵥw), we can use the formula,

proᵥᵥw = (w · ȳ)ȳ where ȳ is the unit vector in the direction of v.

First, let's find the unit vector in the direction of v,

|v| = √((-5)² + 7²) = √(74)

ȳ = v/|v| = (-5/√(74))i + (7/√(74))j

Next, let's find the dot product of w and ȳ,

w · ȳ = (-1)(-5/√(74)) + (-1)(7/√(74))

w · ȳ  = 12/√(74)

Finally, we can find the projection of w onto v,

proᵥᵥw = (w · ȳ)ȳ = (12/√(74))((-5/√(74))i + (7/√(74))j)

(w · ȳ)ȳ = (-60/74)i + (84/74)j

(w · ȳ)ȳ = (-30/37)i + (42/37)j

Therefore, the projection of w onto v is (-30/37)i + (42/37)j.

b. v₁ = ((v · w)/|w|²)w

v₂ = v - v₁ where |w| is the magnitude of w. First, let's find |w|,

|w| = √((-1)² + (-1)²)

|w| = √(2)

Next, let's find v · w,

v · w = (-5)(-1) + (7)(-1)

v · w = -12

Using the formula, we can find v₁,

v₁ = ((v · w)/|w|²)w = (-12/2)(-1 - j)

v₁ = 6 + 6j

Now, finding v₂,

v₂ = v - v₁

v₂ = (-5i + 7j) - (6 + 6j)

v₂ = -5i + (7 - 6)j - 6

v₂ = -5i + j - 6

As a result, the vector v can be divided into two parts: v₁ = 6 + 6j and v₂ = -5i + j - 6, where v₁ is parallel to w and v₂ is orthogonal to w.

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Complete question - Given v = - 5i + 7j and w = - 1 - j.

a. Find proᵥᵥv

b. Decompose v into two vectors v₁ and v₂ where v₁ is parallel to w and v₂ is orthogonal to w.

Answer:

yes

Step-by-step explanation:

the factor theorem says if (x + a) is a factor of a polynomial f(x) then f(- a) = 0

given (x+ 5) then if f(- 5) = 0 , (x + 5) is a factor

4[tex](-5)^{4}[/tex] + 16(- 5)³ - 6(- 5)² + 73(- 5) + 15

= 4(625)+ 16(- 125) - 6(25) - 365 + 15

= 2500 - 2000  - 150 - 350

= 500 - 500

= 0

then (x + 5) is a factor of the given polynomial

Answer: 6/1

Step-by-step explanation: 2/1 x 3/1 = 6/1

Answer:

[tex] {m}^{2} + 7m - 30 = [/tex]

[tex](m - 3)(m + 10)[/tex]

The total is $24,947.06 plus $9,647.06 in compound interest.

One way to earn or pay interest on interest is through compound interest. It denotes that interest will be charged on both the main amount and the accrued interest in the subsequent period. Savings or investments can expand over time with the aid of compound interest.

We can use the following formula to determine compound future value:

FV = P * (r/n + 1)(n*t)

where P is the principal, r is the yearly interest rate, n is the number of times interest is compounded annually, and t is the amount of time in years.

Your values have led us to:

FV = 15300 * (1 + 0.08/4)²⁴

FV = $24,947.06

The total is $24,947.06 plus $9,647.06 in interest.

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Using a normal distribution calculator and entering the mean as 300, the standard deviation as 30 and the range (300 to 390), the probability that a given tree has between 300 and 390 apples is 0.4987 or 49.87%.

Probability refers to the chance or likelihood that an expected event occurs out of many possible events.

Probability lies between 0 and 1, depending on the degree of certainty.

Mean = 300

Standard deviation = 30

Range = 300 to 390

Thus, the probability that a given tree has between 300 and 390 apples is 0.4987 or 49.87%.

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In the given diagram, the areas of the figures are as follows:

Area of the rectangle is 1/6 cm²

Area of the parallelogram is 12 m²

From the question, we are to calculate the areas of the given plane shapes

From the diagram, we have a rectangle and a parallelogram

The area of a rectangle is given by the formula

Area = l × w

Where l is the length

and w is the width

From the given information,

l = 1/2 cm

w = 1/3 cm

Thus,

Area = 1/2 cm × 1/3 cm

Area = 1/6 cm²

Hence, the area of the rectangle is 1/6 cm²

For the parallelogram

The area of a parallelogram is given by the formula

Area = b × h

Where b is the base length

and h is the perpendicular height

From the given information,

b = 6 m

h = 2 m

Thus,

Area = 6 m × 2 m

Area = 12 m²

Hence, the area of the parallelogram is 12 m²

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The events committee is surveying only 1.5% of the student population by asking the girls' basketball team about the school dance.

To calculate the percentage of the student population being surveyed, you can use the formula:

Percentage = (Number of students surveyed / Total number of students) * 100

In this case, the number of students surveyed is 15 (girls' basketball team), and the total number of students is 1,000.

Percentage = (15 / 1,000) * 100 = 1.5%

So, the events committee is surveying only 1.5% of the student population by asking the girls' basketball team about the school dance.

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The events committee wants to survey students about a school dance. The committee is

meeting in the gym, where the girls' basketball team is practicing. They survey the

players on the girls' basketball team.

If there are 1,000 students in the school, and the girls' basketball team has 15 players, what percentage of the student population is being surveyed by the events committee about the school dance?

Ilana ran a total distance of 23.725 miles during her first week of training for a half marathon.

Distance refers to the amount of space or physical separation between two points or objects. It is a measure of how far apart two objects or points are from each other.

Ilana will run 4.125 miles each day for the first three days, which gives a total distance of:

4.125 miles/day × 3 days = 12.375 miles

For the next two days, she will run 5.675 miles per day, which gives a total distance of:

5.675 miles/day × 2 days = 11.35 miles

To find the total distance that Ilana ran during her first training week, we simply add the distances from the first three days and the next two days:

12.375 miles + 11.35 miles = 23.725 miles

Therefore, Ilana ran a total of 23.725 miles during her first week of training.

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Answer: your answer would be A.

Answer:

Step-by-step explanation:

(a)  Given:   r=4  h=3

Formula for cylinder:  V=Bh = [tex]\pi r^{2} h[/tex]  

Solution:

V= [tex]\pi r^{2} h[/tex]

V= [tex]\pi[/tex]4²(3)            >square

V= [tex]\pi[/tex] (16)(3)         >multiply numbers

V=48[tex]\pi[/tex]                >leave as pi

(b)  Given: 4  h=6

This volume will be greater because you are multiplying by 6 instead of 4

V=96[tex]\pi[/tex]

Answer:

the formula: Speed = Distance / Time.

Let's break down the problem into two parts:

a) Find the average speed of the motorist.

Let's assume the average speed of the motorist is "v" km/h.

The distance the motorist traveled in 1 1/2 hours is given by: Distance = Speed × Time = v × (3/2) km.

The distance the cyclist traveled in 1 1/2 hours (opposite direction) is given by: Distance = Speed × Time = 45 × (3/2) km.

Since they passed each other, the sum of their distances should be equal to the distance between Town A and Town B.

So, we can set up the equation: v × (3/2) + 45 × (3/2) = Distance between Town A and Town B.

b) Find the distance between Town A and Town B.

When the motorist reached Town B 2 hours later, the cyclist was 30 km away from Town A.

We can set up the equation: Distance between Town A and Town B = v × 2 + 30.

Now, let's solve the equations:

v × (3/2) + 45 × (3/2) = v × 2 + 30.

Simplifying the equation, we have: (3v + 135)/2 = 2v + 30.

Multiplying both sides of the equation by 2 to eliminate the fraction, we get: 3v + 135 = 4v + 60.

Subtracting 3v from both sides of the equation, we have: v = 75.

Therefore, the average speed of the motorist is 75 km/h.

To find the distance between Town A and Town B, we substitute the value of v into the equation:

Distance between Town A and Town B = v × 2 + 30 = 75 × 2 + 30 = 150 + 30 = 180 km.

Therefore, the distance between Town A and Town B is 180 km.

The table for the function y = f(x) - 5 is

x    f(x) - 5

5   -33

-3    -5

-2     2

0    21

From the question, we have the following parameters that can be used in our computation:

x    f(x)

5   -28

-3    0

-2     7

0    26

To create a table for the function y = f(x) - 5, we subtract 5 from the values of f(x)

using the above as a guide, we have the following:

x    f(x) - 5

5   -28 - 5

-3    0 - 5

-2     7 - 5

0    26 - 5

Evaluate

x    f(x) - 5

5   -33

-3    -5

-2     2

0    21

This represents the table for the function y = f(x) - 5

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The area of the shaded shape is 62.5cm^2.

To find the area of the shaded shape, we need to break it down into simpler shapes that we can calculate the area of. From the image, we can see that the shape is composed of a rectangle and two right-angled triangles.

First, we need to find the dimensions of the rectangle. Since the shape has vertical and horizontal lines of symmetry passing through its center, we know that the rectangle is divided into four equal parts.

Therefore, the length of the rectangle is twice the length of one of the triangles, which is 5cm. So, the length of the rectangle is 2 x 5cm = 10cm. The width of the rectangle is also 5cm.

Next, we need to find the area of each of the triangles. We know that the base of each triangle is 5cm, and the height is half of the width of the rectangle, which is 2.5cm. Therefore, the area of each triangle is:

0.5 x base x height = 0.5 x 5cm x 2.5cm = 6.25cm^2

So, the total area of the two triangles is 2 x 6.25cm^2 = 12.5cm^2.

Finally, we can find the area of the shaded shape by adding the area of the rectangle and the area of the triangles:

Area = rectangle area + triangle area = 10cm x 5cm + 12.5cm^2 = 62.5cm^2.

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Answer:

First problem: x = 5.7√2 = (57√2)/10

Second problem: x = 10√3

Answer:A=OE+L

Step-by-step explanation:

880000=51000+L

Liabilities=370000

680000=2x

The amount of its equity of 340000 for the second problem

Answer:3,000

Step-by-step explanation:

Answer:

it is a zero dimensional point

Step-by-step explanation:

points are an exact location represented by a dot.

points do not have dimension (length, width, or height)

Answer:

(r, y)=(10,-2)

Step-by-step explanation: Hope this helps :)

The clear difference between an angle bisector and a segment bisector is that angle bisector passes through the apex of an angle while segment bisector passes through the midpoint of the line segment.

An angle bisector is defined as the line the divides an angle into two equal parts by passing through its apex.

A segment bisector is defined as the line that divides a segment at the midpoint into two parts.

The difference between angel bisector and segment bisector is that angle bisector passes through the apex of an angle while segment bisector passes through the midpoint of the line segment.

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Answer:

B

Step-by-step explanation:

let the mid-point of DE be ( x , y )

x = (8+4)/2 = 6

y = (6+10)/2 = 8

the mid- point of DE is ( 6 , 8 )

If house is purchased for $313,000 with a 15% down payment, the monthly payment for the mortgage is $1,906.33.

To find the monthly payment for a mortgage secured at 7% for 25 years on a house purchased for $313,000 with a 15% down payment, we can use the formula for calculating mortgage payments:

P = L[c(1 + c)ⁿ]/[(1 + c)ⁿ - 1]

Where P is the monthly payment,

L is the loan amount (which is the purchase price minus the down payment),

c is the monthly interest rate (which is the annual interest rate divided by 12),  

n is the total number of monthly payments (which is the number of years multiplied by 12).

Substituting the given values, we get:

L = $313,000 - 0.15($313,000) = $266,050

c = 0.07/12 = 0.00583

n = 25 x 12 = 300

Plugging these values into the formula, we get:

P = $266,050[0.00583(1 + 0.00583)³⁰⁰]/[(1 + 0.00583)³⁰⁰ - 1]

Simplifying the expression, we get:

P = $1,906.33

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Open and clear communication is crucial when discussing estate planning and wills with family members to prevent misunderstandings and hurt feelings.

1. It is understandable that Brennan and Maureen feel shocked and disappointed with the reduced inheritance.

While it is not required for parents to disclose every detail of their estate planning to their children, it would have been helpful if they had discussed the impact of the gifts on their estate and their final inheritance.

Clear communication can prevent misunderstandings and hurt feelings in the future.

2. Brennan and Maureen have a responsibility to discuss the will with their parents. It is essential to have an open and honest conversation about their parents' wishes and intentions to avoid any confusion or disputes in the future.

While it can be uncomfortable to talk about death and inheritance, it is a crucial conversation to have.

3. It can be a difficult and emotional topic to discuss, but it is important to have open communication to ensure that everyone's wishes are respected and honored. It may be helpful to consult with a lawyer or financial advisor to ensure that the will is properly drafted and that everyone's needs are addressed.

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The equation that represent the number of bracelets b and the number of rings r is 6b + 8r > 600 and 2b + 4r < 275, hence, option A is correct.

Let b represent the number of bracelets and r represent the number of rings that Marisol makes. Marisol plans to sell each bracelet for $6 and each ring for $8. So the amount she earns from selling bracelets is 6b and the amount she earns from selling rings is 8r.

The craft fair committee charges a $25 fee to sell at the fair. So Marisol's total earnings after paying the fee is 6b + 8r - 25. It costs Marisol $2 to make a bracelet and $4 to make a ring. So the total cost of making b bracelets and r rings is 2b + 4r. To make a profit, Marisol's earnings must be greater than her costs,

6b + 8r - 25 > 2b + 4r

Simplifying this inequality, we get,

4b + 4r > 25

We also know that Marisol wants to sell at least $600 in jewelry. This can be expressed as,

6b + 8r > 600

Finally, Marisol wants to spend less than $300 for supplies and the fee. This can be expressed as,

2b + 4r + 25 < 300

Simplifying this inequality, we get,

2b + 4r < 275

Therefore, the system of inequalities that represents the situation is,

6b + 8r > 600

4b + 4r > 25

2b + 4r < 275

where b represents the number of bracelets and r represents the number of rings that Marisol makes.

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Therefore, the coordinates of  [tex]S'[/tex] are  [tex](-2, -1)[/tex] .

A series of numbers called coordinates is used to describe a point's location in a two- or three-dimensional space.

Typically, coordinates in a two-dimensional space are expressed as a pair of integers (x, y), where x denotes the point's horizontal location (also known as the abscissa) and y denotes its vertical position (also known as the ordinate).

Coordinates are commonly expressed as a triplet of numbers (x, y, z) in a three-dimensional space, where x, y, and z stand for the locations along the x, y, and z axes, respectively.

In order to describe the location of objects or points in space, coordinates are often employed in a variety of disciplines, including mathematics, physics, engineering, and computer graphics.

To rotate a point 180° about the origin, we need to negate the x-coordinate and the y-coordinate of the point.

So to find the coordinates of S', we can apply this rule to the coordinates of S:

x-coordinate of   [tex]S' = -x-[/tex] coordinate of [tex]S = -(2) = -2[/tex]

y-coordinate of  [tex]S' = -y-[/tex]  coordinate of  [tex]S = -(1) = -1[/tex]

Therefore, the coordinates of S' are [tex](-2, -1).[/tex]

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Answer:

I'm sorry, but there is no feature for this in this game.  But, there is a grid and a sizing tool.  You'll just have to make an educated guess based on the size of your character and your character's stage of life (baby, toddler, kid, teen, adult).  Hope I helped!  I once had the same question, but just did this.  I think each big grid square maybe is 3-5 ft?

If the total distance available is 92.75 yards, and there is a sign 5 yards before the starting line, the actual distance available for the race is:

92.75 - 5 = 87.75 yards

Since there are 5 sections of the race, each section covers:

87.75 / 5 = 17.55 yards

Therefore, each section of the race is 17.55 yards long.

the rate of interest is 11.25%.we can use simple interest formula get answer as above

what is simple interest ?

Simple interest is a type of interest that is calculated as a percentage of the principal amount of a loan or investment, and is based only on the original amount of money that was borrowed or invested.

In the given question,

We can use the formula for simple interest to solve for the rate:

Simple Interest = (Principal x Rate x Time) / 100

Substituting the given values, we get:

$900 = (400 x Rate x 20) / 100

Multiplying both sides by 100 and dividing by 400 x 20, we get:

Rate = $900 / (400 x 20) = 0.1125 or 11.25%

Therefore, the rate of interest is 11.25%.

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The result of the row 1 multiplication by 1/4 is determined as  [¹/₂  0 ].

The resultant of the row multiplication in the Matrice is calculated by applying the following method;

row 1 in the given matrices = [2 0]

To multiply row by 1/4, we will multiply each entity by 1/4 as shown below;

[2 0] x 1/4 = 1/4(2 0)

= [¹/₂  0 ]

Thus, the result of the row multiplication is determined by multiplying each entry in row 1, that is 2, and 0 by 1/4.

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