5) Naomi is sewing some clothing. She has 53 yards of fabric to use. She
uses 9 yards of fabric to make a short-sleeved shirt and 16 yards of fabric to
make a long-sleeved shirt. Write an inequality to represent how many of each type
of shirt she could make with the fabric she has.

Answer:product * . . . x is 3/4 as many as y x = (3/4)y. So, "3/4 as many oranges as apples" means. "number of oranges is 3/4 number of apples"

Step-by-step explanation:

This product can be replicated by combining a long put option with a strike price of $50 and the stock itself. The long put option provides downside protection if the ending value of the stock is below or at the starting value. The stock investment captures the upside potential if the ending value is greater than the starting value. By combining these two, the desired payoff structure of the product can be achieved.

To replicate the payoff structure of the given product using put options and the stock, we need to determine the number of put options and shares of stock required in the portfolio.

Let's break down the replication into two cases based on the ending value of the stock:

1. Ending value below or at the starting value ($50):

In this case, the product pays 1000 - 15 × ending value. To replicate this payoff, we need to ensure that the portfolio's value also equals 1000 - 15 × ending value. Since the product does not provide any additional cash flows in this scenario, we can replicate it by holding a long position in put options.

2. Ending value greater than the starting value:

In this case, the product pays 250 + 5 × max [ending value - 50, 0]. To replicate this payoff, we need to ensure that the portfolio's value matches the product's payoff. We can achieve this by holding a combination of put options and shares of stock.

Now let's calculate the number of put options and shares of stock required to replicate the product in each case:

1. Ending value below or at the starting value ($50):

Since the product only pays based on the ending value, and the ending value is below or equal to the starting value, the portfolio should only consist of put options. The number of put options required will be determined by the product's payoff formula: 1000 - 15 × ending value.

2. Ending value greater than the starting value:

In this case, the portfolio needs to replicate the product's payoff using put options and shares of stock. The number of put options and shares required will be determined by the product's payoff formula: 250 + 5 × max [ending value - 50, 0].

1. Ending value below or at the starting value ($50):

Portfolio: Long put options

Number of put options: Determined by 1000 - 15 × ending value

2. Ending value greater than the starting value:

Portfolio: Long put options + Long shares of stock

Number of put options: Determined by 250 + 5 × max [ending value - 50, 0]

Number of shares of stock: Determined by 250 + 5 × max [ending value - 50, 0]

To replicate the given product's payoff using put options and the stock, we divide it into two cases based on the ending value of the stock.

1. Ending value below or at the starting value ($50):

In this case, the product pays 1000 - 15 × ending value. To replicate this payoff, we need to hold a long position in put options. The number of put options required will be determined by the product's payoff formula: 1000 - 15 × ending value.

For example, if the ending value is $40:

Number of put options = 1000 - 15 × 40 = 400

Therefore, to replicate the product's payoff in this case, we would hold a long position in 400 put options.

2. Ending value greater than the starting value:

In this case, the product pays 250 + 5 × max [ending value - 50, 0]. To replicate this payoff, we need to hold a combination of put options and shares of stock. The number of put options and shares required will be determined by the product's payoff formula: 250 + 5 × max [ending value - 50, 0].

For example, if the ending value is $60:

Number of put options = 250 + 5 × max [60 - 50, 0] = 250 + 5 × 10 = 300

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Answer:

1.C 2.D

Step-by-step explanation:

Answer:

1 is C and 2 is D

Step-by-step explanation:

Answer: The cats cost more

also there is a typo

Step-by-step explanation:

I bought 1 dog and 3 cats a total cost of $7.75. the three cats cost more so in all the cats must cost 3.56$

Step-by-step explanation:

\(3x (x - x - 30) =( 3x \times x) - (3x \times x) -( 3x \times 30) = {3x}^{2} - {3x}^{2} - 90x = - 90x \\ \)

Answer: as a square and four semicircles

Step-by-step explanation:

The composite shape area can be found by first decomposing the figure as: a square and four semicircles.

Area is the measure of a region's size on a surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of a three-dimensional object.

here, we have,

to Find the Area of a Composite Figure:

To find the area of a composite figure, the first thing to do is to identify the individual shapes that make up the figure, then find the area of each shape before adding all the areas together.

For a composite figure that is comprised of a square and 4 semicircles, the composite figure would be decomposed into: a square and four semicircles.

Hence, The composite shape area can be found by first decomposing the figure as: a square and four semicircles.

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The function f(x) = x^2-1 when evaluated with 2, gives the value 3.

A function can then be defined as a set of ordered pairs. Function is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

For the given situation,

Stan evaluated a function with a value and got 3 as the result.

For this statement, we can frame many functions with different inputs.

Let us consider the function,

(1)  \(f(x)=2x-3\)

Now substitute x = 3,

⇒ \(f(3)=2(3)-3\)

⇒ \(f(3)=6-3\\\)

⇒ \(f(3)=3\)

(2) \(f(x)=x^{2} -1\\\)

Now put x = 2,

⇒ \(f(2)=2^{2}-1\)

⇒ \(f(2)=4-1\)

⇒ \(f(2)=3\)

Similarly we can make many functions that has the value 3 as the result.

Hence we can conclude that the function f(x) = x^2-1 when evaluated with 2, gives the value 3.

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The peak is at y = 24 feet, the vertex point (h, k) is (16, 24). Plugging these values into the equation, we get:

y = |x - 16| + 24

This equation models the roof line of Terry's house.

To model the roof line of Terry's house, we can use the concept of absolute value. The equation for an absolute value function can be written as:

y = |x - h| + k

where (h, k) represents the vertex of the absolute value graph.

In this case, the peak of the roof line is at 24 feet. Since the width of the house is 32 feet, the vertex of the absolute value graph will be at the midpoint of the width, which is 16 feet. Therefore, h = 16.

Since the peak is at y = 24 feet, the vertex point (h, k) is (16, 24). Plugging these values into the equation, we get:

y = |x - 16| + 24

This equation models the roof line of Terry's house.

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The equation x⁴ - 4x³ + x² + 12x - 12 = 0 can be factored as (x - 2)(x - 3)(x² + 2) = 0. The roots of the equation are x = 2, x = 3, and x = ±√2i.

To find the roots of the equation x⁴ - 4x³ + x² + 12x - 12 = 0, we can factor the equation by grouping.

Grouping the terms, we have:

x³(x - 4) + x(x - 4) + 12(x - 1) = 0

Factoring out common factors, we get:

x³(x - 4) + x(x - 4) + 12(x - 1) = 0

(x - 4)(x³ + x + 12) = 0

The first factor, (x - 4), gives us one root, x = 4.

To find the remaining roots, we focus on the quadratic factor, x³ + x + 12. This quadratic cannot be further factored using real numbers, but we can find its roots using complex numbers.

By applying the quadratic formula, we find the roots of x³ + x + 12 = 0 as x = -√2i, x = √2i, and x = 3.

Therefore, the roots of the equation x⁴ - 4x³ + x² + 12x - 12 = 0 are x = 4, x = 3, x = -√2i, and x = √2i.

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-14 is the value of the expression b - 3a at a =6 and b = 4.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Given an expression b - 3a

For this expression given,

a = 6 and b = 4

Thus the value of expression at given values

=> b - 3a

=> 4 - 3 * 6

=>4 - 18

=> -14

Therefore, the value of the expression b - 3a at a =6 and b = 4 is -14.

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The gradient of the line is 2

\(Distance AB = \sqrt{[(5-(-3))^2 + (2-4)^2]}= \sqrt{68} \\Distance AC = \sqrt{[(-3-0)^2 + (4-(-3))^2]} = \sqrt{58} \\Distance BC = \sqrt{[(5-0)^2 + (2-(-3))^2]}= \sqrt{50}\)

mAB = (2 - 4) / (5 - (-3)) = -1/2

This is the slope of AB

-1 / (-1/2) = 2

we have to find the point that is perpendicular to AB

(-3 + 5) / 2 = 1

(4 + 2) / 2 = 3

1 , 3 are  perpendicular to AB

y - 3 = 2(x - 1)

y - 3 = 2x - 2

y = 2x + 1

There fore the gradient of the line is 2

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Answer:

The answer is 13! which equals 6227020800.

Using a system of equations, it is found that there are 10 baskets that hold 4 meals in the shop.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are given by:

There are 25 baskets in the shop, hence:

x + y = 25 -> x = 25 - y

They can hold a total of 70 meals, hence:

2x + 4y = 70

2(25 - y) + 4y = 70

2y = 20

y = 10

There are 10 baskets that hold 4 meals in the shop.

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Answer:

number of $8 sold= 200

Number of $10 tickets sold= $150

Number of $12 tickets sold = $50

Step-by-step explanation:

Let the quantity of $8 ticket be represented as  x

Let the quantity of $10 ticket be represented as  y

Let the quantity of $12 ticket be represented as  z

Such that total tikets sold = 400 can be represented as x+y+z= 400

Prices of$8, $10 and $12 gave a total income of $3,700  such that it can be represented as

8x +10y + 12z =$3,700

Also given that combined number of $8 and $10 priced tickets sold was 7 times the number of $12 tickets sold, we have that

x+y = 7z

Giving us the equations to solve to  be

x+y+z= 400------ equation 1

8x +10y + 12z =$3,700---- equation 2

x+y = 7z------equation 3

Step 2- solving

Putting equation 3 i n equation 1, we have that

7z+z = 400

8z= 400

z= 400/8= 50

also puting the value of z= 50 in equation 1

x+y+z= 400

x+y+50= 400

x+y = 350---- equation 4

putting z= 50 into equaton 2 and solving out

8x +10y + 12z =$3,700

8x +10y + 12x 50 =$3,700

8x +10y + 600 =$3,700

8x +10y =3,700 - 600

8x +10y=3,100---------equation 5

Multiplying equation 4 by 8  and subtracting from equation 5

8x +10y=3,100

-8x+8y= 2,800

2y=300

y= 300/2

y=150

to find x, when y= 150 using equation 4

x+y = 350

x= 350-150

x= 200

Therefore number of $8 sold= 200

Number of $10 tickets sold= $150

Number of $12 tickets sold = $50

Answer: y = -x+5

Step-by-step explanation:

Answer:

19.5625

Step-by-step explanation:

To find the mean, you add all of your values together and divide by the number of values you have.

Here are the values in the dot plot listed:

12, 12, 15, 15, 15, 15, 16, 18, 20, 20, 22, 25, 25, 25, 29, 29

To find the mean:

(12 + 12 + 15 + 15 + 15 + 15 + 16 + 18 + 20 + 20 + 22 + 25 + 25 + 25 + 29 + 29)/16 = 19.5625

If A has rank 6, then it has 6 linearly independent rows and its row space has dimension 6. If the rank of A is less than 6, then the dimension of the row space will be less than 6.

The row space of a matrix is the span of its row vectors. Therefore, the dimension of the row space is equal to the number of linearly independent rows of the matrix.

For a 9x6 matrix A, the largest possible dimension of the row space is 6. This is because there can be at most 6 linearly independent rows in a 9x6 matrix. If there were more than 6 linearly independent rows, then the matrix would have rank greater than 6, which is impossible since the maximum rank of a 9x6 matrix is 6.

For a 6x9 matrix A, the largest possible dimension of the row space is also 6. This is because the number of linearly independent rows cannot exceed the number of columns in the matrix.

Therefore, if A has rank 6, then it has 6 linearly independent rows and its row space has dimension 6.

However, if the rank of A is less than 6, then the dimension of the row space will be less than 6.

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The ending balance based on the information given will be $2000.

From the information, it was stated that there are 2 checks for $500 and 2 bills for $2000 with $5000.

It should be noted that bill is a expense and will be deducted.

This will be illustrated as:

= $5000 + (2 × $500) - (2 × $2000)

= $5000 + $1000 - $4000

= $2000

Therefore, the ending balance based on the information given will be $2000.

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Answer:

tha points ssry

Step-by-step explanation:

ssry

As you can see above the given polynomial simplified is equal to:

The leading coefficient is the coefficient of the term of highest degree.

The term with highest degree in the given polynomial is:

Answer:

$20

Step-by-step explanation:

Kenny's gameplay: 1 month

Angie's gameplay: 3 months

1+3= 4

Kenny bought 1 software pack

Angie bought 2 software packs

1+2= 3

Each software package= $30

So 30×3= 90

Total cost= $170

170-90= 80

80÷4= $20

There you go :)

Answer:

\(IJ=KJ=15\)

Step-by-step explanation:

\(HIJ=HJK\\4p+3=3p+6\\p=3\\IJ=KJ=3*3+6=15\)

Solving a system of equations we can see that each pair of pants costs €82.94 and each coat costs €26.37

Let's define the variables:

x = cost of a pant

y = cost of a coat.

First, we know that:

3x + 2y = 245

And then there are discounts of 20% and 5%, and the cost of one of each is 100.75, then:

0.8x + 0.95y = 100.75

Then we have a system of equations:

3x + 2y = 245

0.8x + 0.95y = 100.75

We can isolate x on the second equation to get:

x = (100.75 - 0.96y)/0.8

x = 125.9 - 1.2y

Replace that in the other equation:

3*(125.9 - 1.2y) + 2y = 245

Solving for y:

3*125.9 - 3*1.2y + 2y = 245

y*(2 - 3*1.2) = 245 - 3*125.9

y = (245 - 3*125.9)/(2 - 3*1.2)

y = 82.94

Then the value of x is:

x = 125.9 - 1.2*82.94

x = 26.37

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(a) The greatest common divisor of \(x^3\) - 6x - 7 and \(x^4\) is 1.

(b) The greatest common divisor of \(x^2\)- 1 and 2\(x^7\) - 4x\(^5\) + 2 is 1.

(a) To find the greatest common divisor (GCD) of the polynomials, we can use polynomial long division.

Dividing \(x^3\) - 6x - 7 by \(x^4\), we get a remainder of \(x^3\) - 6x - 7.

Since the remainder is non-zero, the GCD of \(x^3\) - 6x - 7 and \(x^4\) is 1.

(b) To find the GCD of \(x^2\) - 1 and 2\(x^7\) - 4\(x^5\) + 2, we can again use polynomial long division.

Dividing 2\(x^7\) - 4\(x^5\) + 2 by \(x^2\) - 1, we get a remainder of 2\(x^5\) + 2.

Since the remainder is non-zero, the GCD of \(x^2\) - 1 and 2\(x^7\) - 4\(x^5\) + 2 is 1.

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Answer:

12 teaspoons

Step-by-step explanation:

Answer:

31p+13

Step-by-step explanation:

After expanding: 21p+28+10p-15

After simplifying: 31p+13

Answer:

7

Step-by-step explanation:

7x(92+7) = 693

(7x92) = 644

(7x92) +

(7x7) = 49

644 + 49 = 693

Answer:

A = 4π units²

Step-by-step explanation:

The area (A) of a circle is calculated as

A = πr² ( r is the radius ) , then

A = π × 2² = 4π units²

Answer:

Step-by-step explanation:

Since the area pollute sis assumed to be a circle, we will be using the formula for calculating the area of a circle to solve the problem.

Area of a circle A = πr²

r is the radius of the circle

The rate at which the area is increasing is expressed as dA/dt. According to chain rule, dA/dt = dA/dr*dr/dt where;

dr/dt is the rate at which the area is increasing.

If dA/dr = 2πr (by mere differentiation)

dA/dt = 2πr * dr/dt

Given dr/dt = 3ft/sec and r = 30feet

dA/dt = 2π(30) * 3

dA/dt = 180π ft/sec

Hence, the area is increasing at the rate of 180π ft/sec

See below for the solution to the systems of equations

System of equations 1

Here, we have

y = -5x/3 + 3

y = x/3 -3

We start by plotting the graph of both equations

Next, we write out the point of intersection of the equations

See attachment for the equation of the system

From the attached graph, the point of intersection of the equations is (3, -2)

Hence, the solution to the system is (3, -2)

System of equations 2

Here, we have

y = 4x + 3

y = -x -2

We start by plotting the graph of both equations

Next, we write out the point of intersection of the equations

See attachment for the equation of the system

From the attached graph, the point of intersection of the equations is (-1, -1)

Hence, the solution to the system is (-1, -1)

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