Tara has two store coupons. Coupon 1 gives her $10 off on one item. Coupon 2 gives her 10% off on one item. Tara can use both coupons together on one item in the store and choose which coupon to apply first. For an item that has an original price of x dollars, let f be the function that models the discount price of the item using only coupon 1 and let g be the function that models the discount price of the item using only coupon 2. The price of each item in this store is more than $20 . Which of the following statements best explains which coupon should be applied first when using both coupons to give Tara a lower price?

In total, the number of greetings will be 1159.

Mathematical symbols used to represent quantities or values include numbers. They are employed in the measurement, comparison, addition, subtraction, multiplication, and division processes in mathematics. According to their qualities and properties, numbers can be categorized into a variety of groups, including natural numbers, whole numbers, integers, rational numbers, irrational numbers, real numbers, and complex numbers. There are specific properties and guidelines for mathematical operations for each group of numbers. Mathematics depends on numbers, which are also utilized in many other disciplines, including science, engineering, economics, and statistics.

The number of greetings exchanged between the host and the other mothers and daughters must be counted first. Since there is only one host, the number of mother-daughter pairs is 20 - 1 = 19. There are thus a total of 38 greetings, 19 between the host and the other moms, and 19 between the host and the other daughters.

The number of pleasantries exchanged between the guest mums and everyone else must next be tallied. The host, the other mothers, and the daughters must all be greeted, making a total of 20 - 1 = 19 guest mothers. Thus, each host mother must extend 1 + 19 + 20 = 40 greetings. There will be 760 greetings exchanged between the guest mothers and everyone, or 19 x 40.

The number of pleasantries exchanged between the mothers and the invited girls must also be tallied. Moreover, there are 20 guest girls, so 19 of them must welcome the mothers. As a result, there will be 361 pleasantries exchanged between the mothers and the guest daughters.

In total, the number of greetings will be 38 + 760 + 361 = 1159.

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Answer:

See below

Step-by-step explanation:

My man, how did you even get these numbers??? no whole number multiplied by 6.65 even equals 22??? Regardless, here's what I did.

a) r = 40/2 = 20

A = πr^2 = (3.14)(20)^2 = 1256

b) 1256/50 = 25.12 basically, 26

c) 26 x 6.65 = 172.9

Thoughts and prayers my guy. Keep trying

Answer:

A. 1256[tex]ft^{2}[/tex] B. 26 pounds C. $172.90

Step-by-step explanation:

PART A

1st find the radius of the area

radius = diameter / 2

r = 40/2

radius = 20ft

Area of circle = radius^2* pi

Area = 400 * 3.14

Area = 1256 [tex]ft.^{2}[/tex]

PART B

1256 / 50 = 25.12

Because we can only buy full pounds and we need the whole area to be reseeded, we round 25.12 to 26.

26 pounds of seeds will be needed to reseed the whole area.

PART C

Multiply the number of pounds of seeds needed to be bought by 6.65

26 x 6.65

$172.90 for the total cost of grass seeds

Four rational numbers between 1/5 and 1/6 are; 41/240, 42/240, 43/240, 44/240

A rational number is defined as a number that can be expressed as the quotient of fraction p/q of two integers, a numerator p, and a non-zero denominator q.

First, we have to make the denominators the same.

We multiply 1/5 by 48 and 1/6 by 40 to get:

48/240 and 40/240

Thus, the other rational numbers between them are;

41/240, 42/240, 43/240, 44/240

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Complete question is;

Find four rational numbers between 1/5 and 1/6 ​

The equation is slope-intercept form is equal to y = 5x - 3.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

Based on the information provided, we can logically deduce the following data points on the line:

At point (0, -3), a linear equation of this line can be calculated in slope-intercept form as follows:

y - (-3) = (2 + 3)/(1 - 0)(x - 0)

y + 3 = 5x

y = 5x - 3.

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Answer:

2570 is ten times smaller than 25700

Step-by-step explanation:

The production possibility frontier based on the information is attached.

PPF0 is the curve before technological progress. PPF1 is the the curve after the advance in technology.

Before the advance in technology, the opportunity cost of treating HIV/AIDS increases as the world moves down along its PPF.

After the advance in technology, the opportunity cost of treating more HIV/ AIDS cases decreases as the world has to give up less other goods and services to treat additional HIV/AIDS patients. Or, by giving up the same amount of other goods and services, world can treat more HIV/AIDS patients now.

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The statement that must be true for the parallelogram is

Alternate internal angles are pairs of angles that lie on opposite sides of a transversal line intersecting two parallel lines. The angles are on the interior (between the two parallel lines) and are not adjacent to each other.

These angles are equal in measure (i.e., they are congruent), which means that if one angle has a certain degree of measure, the other angle will have the same degree of measure.

In the problem, the diagonal of the parallelogram is the transversal line and it is used to make the alternate internal angle theorem possible

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Answer:

y = |x - 3| - 1

Step-by-step explanation:

The vertex of the absolute value function graphed is (3, -1). The formula for absolute value is y = a |x - h| + k, where (h, k) is the vertex. The a stretches the graph, although this graph isn't stretched. So a is 1, which is the same as multiplying by 1. Plugging 3 as h and -1 as k into the formula results in y = |x - 3| - 1.

1. The difference between the temperature is 14°C.

2. The value of the expression will be -3x - 6y + 27.

The difference between the temperature will be:

= -10 + 24

= 14°C.

For the second part of your question, to clear the parenthesis in the expression "12 - 3(x + 2y - 5)", you can first simplify the expression inside the parenthesis:

x + 2y - 5

Next, multiply this expression by 3:

3(x + 2y - 5) = 3x + 6y - 15

Finally, substitute this back into the original expression:

12 - 3(x + 2y - 5) = 12 - (3x + 6y - 15) = 12 - 3x - 6y + 15 = -3x - 6y + 27

So, the final expression after clearing the parenthesis and combining like terms is -3x - 6y + 27.

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Answer: 6 pounds and 12 pounds.

Step-by-step explanation:

1.5(x)+2.4(18-x)=2.1(18)

1.5x+43.2-2.4x=37.8

1.5x+43.2=37.8+2.4x

0.9x=5.4

x=6 pounds of $1.50 candy

18-6=12 pounds of $2.40 candy

(check my work to see if it's correct :))

The length of the both pieces are 1ft and 9ft respectively. Option C

We have from the information given that;

Now, substitute the values, we get

x + 6 + 3x =10

Collect the like terms

x + 3x = 10 -6

Add the like terms

4x = 10 - 6

Substract the like terms

4x = 4

Make 'x' the subject of formula by dividing both sides by 4, we get;

x = 4/4

divide the values

x = 1

Thus, the values are 1ft and 9ft

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Answer:

Below

Step-by-step explanation:

2^3  /  2^7 =   2^(3-7)   =   2^(-4)   =   1/ (2^4)   =   1/16   =   .0625  

   ~~~~pick your poison

The required expression [tex]2^3/2^7[/tex], after simplification is equivalent to 1/16.

To simplify the expression [tex]2^3/2^7[/tex], we can apply the rule of exponentiation that states when dividing two numbers with the same base, we subtract the exponents.

In this case, the base is 2.

Using the rule, we subtract the exponent of the denominator from the exponent of the numerator:

[tex]2^3/2^7 = 2^{7} = 2^{-4}[/tex]

The expression [tex]2^{-4}[/tex] can be further simplified by using the rule that states any number raised to a negative exponent is equal to the reciprocal of the number raised to the positive exponent:

[tex]2^{-4} = 1/2^4[/tex]
      = 1/16

Therefore, the expression [tex]2^3/2^7[/tex] is equivalent to 1/16.

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Answer:

Step-by-step explanation:

a) The second stop is the third floor:

The first stop is the first floor, so the probability of going up from the first floor is 3/4.

The next stop is the third floor, so the probability of going up from the second floor (which is the first floor in this scenario) to the third floor is 3/4.

The probability of both events happening is the product of the individual probabilities: (3/4) * (3/4) = 9/16.

b) The third stop is the fourth floor:

The first stop is the first floor, so the probability of going up from the first floor is 3/4.

The next stop is the third floor, so the probability of going up from the first floor to the third floor is 3/4.

The next stop is the fourth floor, so the probability of going down from the third floor to the fourth floor is 1/4.

The probability of all three events happening is the product of the individual probabilities: (3/4) * (3/4) * (1/4) = 3/16.

c) The fourth stop is the first floor:

The first stop is the first floor, so the probability of going up from the first floor is 3/4.

The next stop is the third floor, so the probability of going up from the first floor to the third floor is 3/4.

The next stop is the fourth floor, so the probability of going down from the third floor to the fourth floor is 1/4.

The next stop is the first floor, so the probability of going down from the fourth floor to the first floor is 3/4.

The probability of all four events happening is the product of the individual probabilities: (3/4) * (3/4) * (1/4) * (3/4) = 9/64.

There are 36 possible outcomes from rolling a die twice (or two dice once) and these result in sums from 2 to 12.

Possible ways to make a sum of 2: 1

Possible ways to make a sum of 3: 2

Possible ways to make a sum of 4: 3

Possible ways to make a sum of 5: 4

Possible ways to make a sum of 6: 5

Possible ways to make a sum of 7: 6

Possible ways to make a sum of 8: 5

Possible ways to make a sum of 9: 4

Possible ways to make a sum of 10: 3

Possible ways to make a sum of 11: 2

Possible ways to make a sum of 12: 1

This means there are 21 ways to make a sum greater than 6.

21/36 ≈ 58.33%

There are 24 ways to make sums that are not divisible by 3 and not divisible by 6.   (Note that if a number isn't divisible by 3, it's also not divisible by 6, so that's a weird thing to include.)

24/36 ≈ 66.67%

The equation that can be used to find the length of the remaining side is z² = 14² - 9²

Using the Pythagorean theorem that states that the square of the hypotenuse side is equal or equivalent to the sum of square of the other two sides.

This is represented as;

x² = y² + z²

Given that the parameters are enumerated as;

Now, substitute the values

14² = 9² + z²

collect like terms

z² = 14² - 9²

Hence, the equation is z² = 14² - 9²

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The length of the remaining side can be calculated using 14² = x² + 9² is 10.7 units

An equation is an expression that shows how numbers and variables are linked together using mathematical operations such as addition, subtraction, multiplication and division.

Pythagoras theorem is used to show the relationship between the sides of a right angled triangle. It is given as:

hypotenuse² = adjacent² + opposite²

Let x represent the missing side.

The hypotenuse of a right triangle has a length of 14 units and a side that is 9 units long. Hence:

14² = x² + 9²

x² = 14² - 9²

x² = 115

x = 10.7 units

The length of the remaining side is 10.7 units

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The lengths for which the area will be less than 175 cm² are less than 25 cm

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

Width = 7 cm

Area = Less than  175 cm²

The formula of area is represented as

Area = Length * Width

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

Length * Width < 175

substitute the known values in the above equation, so, we have the following representation

Length * 7 < 175

Divide by 7

Length < 25

Hence, the length is less than 25

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Answer: A) No values of k are the expressions 12d + 8 and 4(3d + 5) - 8 equivalent.

They are the same if one amount or value has the same value as another.

We need to set the formulae 12d + 8 and 4(3d + 5) - 8 equal to one another and solve for k to get the values of k for which they are equivalent:

12d + 8 = 4(3d + 5) - 8

When we simplify this equation, we obtain:

12d + 8 = 12d + 12

When we take away 12d from both sides, we obtain:

8 = 12

There are no variables of k for which the expressions are similar because this equation is false for all values of d.

As a result, the response is A) No values.

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The algebraic equation for the statement is 21 = 2 x - 5

Algebraic equations can be written using mathematical symbols and operations to represent relationships between variables or quantities. Variables are the quantities that the equation is trying to represent or solve for.

There is only one variable here and we can call it x.

The number is doubled so the representation would be :

= 2 x

This is then decreased by 5 and becomes :

= 2 x - 5

This is equated to 21 to become:

21 = 2 x - 5

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The value of the camper after 5 years is given as follows:

$15,155.2.

An exponential function is defined as follows:

y = a(b)^x.

In which:

From the table, the rate of change is given as follows:

b = 29600/37000

b = 0.8.

Then the value of the camper after five years can be obtained applying the recursion, multiplying the value after 4 years by the rate of change of 0.8, as follows:

18944 x 0.8 = $15,155.2.

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The given expressions {4x^3+2x^2+6x+7}/{2x+1} and 2x^2+3+(4/{2x+1}) are equal at x = 10, they are not equal at x = -1/2, and they are equal for all x other than -1/2.

Substitute x = 10 in the given expressions, we get

{4x^3+2x^2+6x+7}/{2x+1}

= (4000+200+60+7)/21

=203.19

2x^2+3+(4/{2x+1}.)

200+3+4/21

=203.19

Hence, the given expressions are equal when x = 10

Now substitute x = -1/2 in the given expressions

={4x^3+2x^2+6x+7}/{2x+1}

=(4*-1/8+2*1/4+6*-1/2+7)/0

2x^2+3+(4/{2x+1}.)

=2*1/4+3+4/0

When we substitute the value x= -1/2 then it divide by 0 and value will be infinite and hence we can say that the values are not equal at x = -1/2

2x^2+3+(4/{2x+1}.) take LCM

{4x^3+2x^2+6x+7}/{2x+1} here both expression are equal and  we can't able find the value at x = -1/2 but for other value of x they are equal.

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The required value of x is equivalent to 30 units.

The state of likeness can be referred to as a similarity. When two elements, things, ideas, or people resemble one another, they are said to be similar. Example: In terms of the number of sides, a square and a rectangle are comparable ( four sides for each). The state of being different can be used to define a difference.

To find the value of x we will use the similarity which corresponding sides of similar triangle are Proportional.

So;

50/x = 75/45

2/x = 3/45

x = 30 units

Thus, required value of x is  30 units.

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Answer:  

Translates to x-(x+6) which simplifies to -6

=====================================================

Explanation:

x = some number

x+6 = the sum of x and 6

x-(x+6) = subtract the previous amount from x

x-x-6 .... distribute the negative through to each term

-6

No matter what number you started with, you'll always end up with -6 as the fully simplified answer. The x variables cancel.

Example:

Pick 10 as the starting number. Subtract off 10+6 = 16 to get 10-16 = -6.

A physical quantity with both magnitude and direction is called a vector quantity.

A vector quantity is a physical quantity that has both magnitude and direction. One example of a vector quantity is velocity, which is defined as the rate of change of an object's position with respect to time. Velocity is a vector quantity because it has both a magnitude (speed) and a direction (the object's motion). For instance, if an object is moving with a speed of 20 meters per second to the north, its velocity would be 20 meters per second north. If the object's direction changes to east, its velocity would become 20 meters per second east. Therefore, velocity is a vector quantity because its value depends not only on the speed of the object but also on the direction in which it is moving.

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Complete Question

Write down a vector quantity and explain your response.

Answer:

122.3°

Step-by-step explanation:

Vertical angles are congruent.  That means that they have the same measurement.

The Ratios, Rate and unit rate are used to solve many real-world problems.

Let us defined ratios, rates and unit rates and see the real world examples below.

As a ratio is a comparison of two numbers or measurements.

For example, if a store sells 5 black color pens and 7 blue color pens, then the ratio of black to blue pens is 5 to 7.

A rate is also a ratio in which the two terms are in different units.

For example, if 2 galloons of milk costs 8 dollar, then the rate is 2galloons for

8 dollar. And the unit is galloons per dollar.

As Rates are used in our daily life, such as when we work 40 hours per week or take 2 liters of water per day. When rates are expressed as a quantity of 1, such as 2 liters of water per day  that is, per 1 day or 6 miles per hour that is, per 1 hour. So they can be defined as unit rates.

Hope this helps

Answer:

to describe the same relationship between quantities or to compare two quantities. A rate is a special type of ratio that compares quantities with unlike units. A unit rate compares a quantity of something with a single unit of a different quantity.

Answer:

A=25t.

Step-by-step explanation:

..........................

Answer:

860,000.

Step-by-step explanation:

If the sales in 2022 were up 75% from 800,000, the sales in 2022 would be 800,000 + (800,000 * 75%) = 800,000 + 600,000 = 1,400,000.

To find the sales for 2021, we'll have to use the average annual growth rate to find the sales in between 2012 and 2022.

Let's assume that the sales grew linearly, so the average annual growth rate would be (1,400,000 - 800,000) / (2022 - 2012) = 600,000 / 10 = 60,000.

The sales in 2021 would then be 800,000 + 60,000 = 860,000.

The function g(x) = (x - 3)³ is shown in the graph. The solution has been obtained by using the concept of transformation.

What is transformation?

Any action that moves a polygon or other two-dimensional object on a plane or coordinate system is referred to as a transformation.

Translation, rotation, reflection, and dilation are all methods of transformation.

We are given a graph, from which we can say that when x = 3, then y = 0

The function must satisfy these values.

The functions g(x) = (x + 3)³ , g(x) = x³ + 3 and g(x) = x³ − 3 does not satisfy the point (3,0).

Also, the translation is 3 units to the right.

So the function shown in the graph is g(x) = (x - 3)³.

Hence, the transformed function is g(x) = (x - 3)³.

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Question: If the parent function is f(x) = x³, which transformed function is show in the graph?

g(x) = (x − 3)³ , g(x) = (x + 3)³ , g(x) = x³ + 3 , g(x) = x³ − 3

Answer:(4x^2 + y^2)(2x + y)(2x - y)

Step-by-step explanation:

16x^4 - y^4

= (4x2)^2 - (y^2)^2

= (4x^2 +y^2)(4x^2 - y^2)

=(4x^2 + y^2)( (2x)^2 -y^2)

= (4x^2 + y^2)(2x + y)(2x - y).