Joe is creating shirts for his ultimate frisbee team. The total cost to produce x shirts can be represented by f ( x ) = 3 x 2 + 2 . Find the average rate of change of the total cost as his shirt production increases from 10 to 20.

When 65 inches are converted to feet, the result is 5.41667 feet.

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Yes, the relation x y 2 cos(x − y) = c defines an implicit solution of the differential equation.

To verify this we can use Implicit Function Theorem. According to the theorem, if a relation f(x,y) = c is given, then if the partial derivative of f(x,y) concerning y is nonzero at the point (x0,y0), there is a unique function y = g(x) such that f(x,g(x)) = c.

In this case, the partial derivative of f(x,y) concerning y is -2 sin(x-y). At the point (x0,y0), this derivative is nonzero, so there exists a unique function y = g(x) such that f(x,g(x)) = c. This implies that the given relation does indeed define an implicit solution of the differential equation.

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The effects of poor scale interpretation in maths​ are discussed below.

Poor scale interpretation in mathematics can have significant effects on various areas of life and work that require the use of mathematical concepts and skills. Some of the consequences of poor scale interpretation are:

1. Inaccurate Results: Poor interpretation of scales on graphs, charts, and other mathematical representations can lead to incorrect conclusions and decisions based on the resulting data.

2. Miscommunication: Poor scale interpretation can result in misinterpretation of information and lead to miscommunication between individuals and groups.

3. Ineffective Problem Solving: Poor scale interpretation can hinder the ability to solve mathematical problems effectively, resulting in incorrect solutions and wasted time and resources.

4. Limited Career Opportunities: Poor scale interpretation skills can limit career opportunities in fields that require mathematical proficiency, such as engineering, finance, and technology.

5. Low Confidence and Motivation: Poor scale interpretation skills can lead to frustration and low confidence in mathematics, causing students and individuals to lose interest in the subject.

To avoid the negative effects of poor scale interpretation, it is important to receive proper mathematical education and training, and to continually practice and improve one's mathematical skills. Additionally, seeking help and guidance from teachers and mentors can be beneficial in improving one's scale interpretation skills.

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To find the second derivative of y(t) at t = 0, we can use the chain rule. We can write the given equation as dy/dt = f(y), where f(y) = (4-3y)/(5+2y).

Then the second derivative of y at t = 0 can be calculated as: d2y/dt2 (0) = f'(y) * dy/dt (0) = f'(0)f(0) = [-3/(5+20)](4-30)/(5+2*0) = -3/5.

A differential equation is an equation that relates one or more unknown functions and their derivatives. It is mainly used in the fields of biology, physics, engineering, economics, and other sciences.

A differential equation states how a rate of change (a "differential") in one variable is related to other variables. For example, the Single Spring simulation involves a differential equation that describes the displacement of a spring in response to a force.

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The system of equations has a unique solution. The solution is (0,-5.5).

What is the system of equations?

A system of equations in algebra consists of two or more equations and looks for common answers to the equations. "A set of equations satisfied by the same set of variables is called a system of linear equations."

According to the discussion above, a system of equations is a collection of equations that aim to find a common solution for all of the variables.

The system of equations is

4x - 4y = 22 ....(i)

y = -5.5  ...(ii)

Putting x = 0 in 4x - 4y = 22:

4 × 0 - 4y = 22

- 4y = 22

y = -5.5

Putting x = 1 in 4x - 4y = 22:

4 × 1 - 4y = 22

- 4y = 18

y = -4.5

The points on equation (i) are (0,-5.5) and (1, -4.5).

The points on the line y = -5.5 are (-3,-5.5), (2,-5.5).

Plot the points and join them.

The intersection point is the solution of the system of equations.

The solution is x = 0 and y = -5.5

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To reach the goal of $1,200, the organization needs to sell at least 28 standard tickets (1,200 / 42 = 28.57) or 28 VIP tickets (1,200 / 43 = 27.91). They can also combine the sales of standard and VIP tickets to reach the goal.

The charitable organization is hosting a black-tie benefit event and aims to raise at least $1,200 through ticket sales.

The standard tickets are priced at $21 each, while the VIP tickets are priced at $43 each.

To reach the goal of $1,200, the organization needs to sell a minimum of 28 standard tickets ($1,200 / $21 = 57.14).

However, if they only sell VIP tickets, they will need to sell at least 28 VIP tickets ($1,200 / $43 = 27.91).

Finally, they can also achieve their goal by selling a combination of standard and VIP tickets.

For example, they can sell 20 standard tickets and 8 VIP tickets, which would result in a total of 20 * $21 + 8 * $43 = $840 + $344 = $1,184, reaching their goal of $1,200.

In conclusion, the charitable organization has multiple options to reach their goal of $1,200 through ticket sales for their black-tie benefit event.

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Answer:

11.55m², 181.12mm²,11ft,

Step-by-step explanation:

Simplify the expression.

and multiply A=1/2bh

Over the course of a career, a college graduate can anticipate making, on average, $60,000 more money than a high school graduate.

Links are regarded to as appropriate when they typically have the same ratio. For instance, the trees in an estate and or the number of peaches in a harvest in apples depend on the average number of apples provided by each tree. A linear correlation between two numbers as well as variables is referred to as being proportional in mathematics. When the primary quantity doubles, the other amount also does so. Once one of the variables is reduced to 1/100th of its previous value, the other decreases as well. If two components are proportional, it suggests that if one rises, the other climbs as well, and their correlation is continuous at all values. The diameter and circumference of such a circle are used as an example.

given

The true statement is

starting salary = $60,000

average = $60,000 / 3

= $ 20,000

Over the course of a career, a college graduate can anticipate making, on average, $60,000 more money than a high school graduate.

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Using the inscribed angle theorem:

7. m<A = 79°

8. m<B = 90°

9. m(BC) = 152°

The Inscribed Angle Theorem states that if two chords of a circle intersect, the measure of the inscribed angle formed by the two chords is equal to half the measure of the central angle that subtends the same arc as the inscribed angle.

Applying the inscribed angle theorem, we have:

7. m<A = 1/2(158)

m<A = 79°

8. m<B = 1/2(180)

m<B = 90°

9. m(BC) = 2(76)

m(BC) = 152°

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After 6 hours, Anderson and Addison will be 126 miles apart.

Let's call the time they have been traveling "t" (in hours).

Anderson will have traveled 15t miles and Addison will have traveled 6t miles. The total distance between them is 15t + 6t = 21t miles.

We know that they need to be 126 miles apart, so we can set up the equation:

21t = 126

Now we can solve for t:

t = 126 / 21

t = 6

So after 6 hours, they both will be 126 miles apart.

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Answer:

10

Step-by-step explanation:

The GCF of 80 and 90 is 10.

The value of x in the equation (x + 7)² - 11 = 0 are x = -7 + √11 and x = -7 - √11

Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign.

The variable to be solved is x . Variables are numbers represented by letters in an equation.]

Therefore,

(x + 7)² - 11 = 0

(x + 7)(x + 7) - 11 = 0

x² + 7x + 7x + 49 - 11 = 0

x² + 14x + 38 = 0

Therefore, let's factorise the quadratic equation as follows:

x² + 14x + 38 = 0

Using the quadratic formula,

[tex]\frac{-b+\sqrt{b^{2}-4ac } }{2a}[/tex] or [tex]\frac{-b-\sqrt{b^{2}-4ac } }{2a}[/tex]

Hence,

a = 1

b = 14

c = 38

Therefore,

x = -7 + √11 and x = -7 - √11

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Answer: -10x - 15

Step-by-step explanation:

The distributive property is used when you multiply a number over an addition or subtraction problem.

5  x  (-2x - 3)

Step 1

Take 5 and multiply it by -2x

5  x  -2x = -10x

Step 2

Take 5 and multiply it by - 3

5  x  - 3 = -15

Step 3

Put the entire problem together.

5  x  (-2x - 3) = -10x - 15

The measurements associated with student life are categorized as follows: length of time to complete an exam is a ratio, time of first class is an interval, major field of study is nominal, course evaluation scale is ordinal, score on last exam is a ratio, and age of student is a ratio.

(a) Length of time to complete an exam - Ratio: This is measured on a scale of time, and can be expressed as a ratio (i.e. the amount of time spent on the exam divided by the total time allotted for the exam).

(b) Time of first class - Interval: The time of the first class is measured on a scale of minutes, hours, and days, and can be expressed as an interval (i.e. the amount of time between two classes).

(c) Major field of study - Nominal: This is a categorical measurement and can be expressed as a nominal variable (i.e. the student's major field of study is either engineering, business, etc).

(d) Course evaluation scale: poor, acceptable, good - Ordinal: This is a scale of quality and can be expressed as an ordinal variable (i.e. the quality of the course can be rated as poor, acceptable, or good).

(e) Score on last exam (based on 100 possible points) - Ratio: This is measured on a scale of points, and can be expressed as a ratio (i.e. the student's score on the exam divided by the total number of points possible).

(f) Age of student - Ratio: This is measured on a scale of years, and can be expressed as a ratio (i.e. the student's age divided by the total number of years they have been alive).

The measurements associated with student life are categorized as follows: length of time to complete an exam is a ratio, time of first class is an interval, major field of study is nominal, course evaluation scale is ordinal, score on last exam is a ratio, and age of student is a ratio.

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The day that Cardi B paid back the loan is given as follows:

June 3rd.

The balance of an account after t years, using simple interest, that is, a single compounding per year, is given by the equation presented as follows:

A(t) = P(1 + rt).

In which the parameters of the equation are explained as follows:

The parameter values for this problem are given as follows:

A = 17873.97, P = 17500, r = 0.065.

Hence the time in years is obtained as follows:

17873.97 = 17500(1 + 0.065t)

1 + 0.065t = 17873.97/17500

1 + 0.065t = 1.02136971429

t = (1.02136971429 - 1)/0.065

t = 0.32876483523

A year is composed by 365 days, hence the time in days is given as follows:

0.32876483523 x 365 = 120 days.

120 days after February 3rd is June 3rd.

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Value 02 = 16 represents the population variance.

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lim x→4 2x x − 4 − 8 x − 4 = lim x→4 2x x − 4 − lim x→4 8 x − 4, If lim x→5 f(x) = 0 and lim x→5 g(x) = 0, then lim x→5 f(x) g(x) does not exist,  If f(3) = 2 and lim x→3+ f(x) = 2, then lim x→3− f(x) = 2, If lim t→0 h(t) does not exist, then h(0) cannot exist all these Limits statement are False

A limit in mathematics is a value that a function approaches when the input gets closer to a certain value. Limits are used to find a function's derivative and integral as well as to characterize how a function behaves around particular places.

lim x -> c f(x) = L

(a) False.

According to the rules of limits, if both limits are present, the limit of a sum of two functions is equal to the total of their limits. The assertion, however, cannot be valid if one or both of the boundaries do not exist.

(b) False.

According to the limit laws, if the sum of two functions approaches 0, then the sum of their limits also does. The opposite of this statement is untrue, though.

In this instance, even if x approaches 5 and both f(x) and g(x) approach 0, the product of their limits, f(x)g(x), may not exist at all or may approach a non-zero value.

(c) False.

A function's limit as x gets closer to a number from the right is not always the same as the limit as x gets closer to the same number from the left.

Although f(3) = 2 in this instance and lim x3+ f(x) = 2, the limit of f(x) as x approaches 3 from the left may not be 2.

(d) False.

The absence of a limit does not imply the existence of the function's value at that time.

In this instance, the value of h(0) may still exist even though the limit of h(t) as t approaches 0 does not exist.

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All these given Limit statement are False.

(a) lim x→4 2x x − 4 − 8 x − 4 = lim x→4 2x x − 4 − lim x→4 8 x − 4

(b) If lim x→5 f(x) = 0 and lim x→5 g(x) = 0, then lim x→5 f(x) g(x) does not exist

(c) If f(3) = 2 and lim x→3+ f(x) = 2, then lim x→3− f(x) = 2

(d) If lim t→0 h(t) does not exist, then h(0) cannot exist.

A limit in mathematics is a value that a function approaches when the input gets closer to a certain value. Limits are used to find a function's derivative and integral as well as to characterize how a function behaves around particular places.

lim x -> c f(x) = L

(a) False.

According to the rules of limits, if both limits are present, the limit of a sum of two functions is equal to the total of their limits. The assertion, however, cannot be valid if one or both of the boundaries do not exist.

(b) False.

According to the limit laws, if the sum of two functions approaches 0, then the sum of their limits also does. The opposite of this statement is untrue, though.

In this instance, even if x approaches 5 and both f(x) and g(x) approach 0, the product of their limits, f(x)g(x), may not exist at all or may approach a non-zero value.

(c) False.

A function's limit as x gets closer to a number from the right is not always the same as the limit as x gets closer to the same number from the left.

Although f(3) = 2 in this instance and lim x3+ f(x) = 2, the limit of f(x) as x approaches 3 from the left may not be 2.

(d) False.

The absence of a limit does not imply the existence of the function's value at that time.

In this instance, the value of h(0) may still exist even though the limit of h(t) as t approaches 0 does not exist.

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Answer:

Step-by-step explanation:

3/6

The probability of two calls to be made in first quarter = 15/60 * (15/60) = 1/16

Probability of a call to happen within 6 minutes within each other is 6/60 = 1/10 = 0.1

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

A statistical function known as a probability distribution explains all the potential values and probabilities for a random variable within a certain range.

The uniform probability distribution is a distribution composed by two bounds, given by a and b, in which each possible outcome within these two bounds is equally as likely.

The probability that a call is made in the first quarter is 15/60

Now the probability of two calls to be made in first quarter = 15/60 * (15/60) = 1/16

Probability of a call to happen within 6 minutes within each other is 6/60 = 1/10 = 0.1

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In algebra, a number exists even equal to itself according to the reflexive property of equality. The equality's reflexive quality. If a is a number, then. a = a.

In algebra, a number is always equal to itself according to the reflexive property of equality. The equality's reflexive quality. If a is a number, then. a = a.

2. AD = BC due to the congruence of a rectangle's opposite sides.

3. Due to the reflexive property of congruence, DC=DC, each segment is identical to itself.

4. ADC and BCD are right angles since any rectangle's internal angles are right angles (Definition of rectangle).

5. Since they form right angles and all right angles are congruent, ADC=BCD.

6. ADC and BCD are congruent because they have two congruent sides (AD with BC and DC with DC) and a congruent angle between them: Side Angle Postulate Side Congruence Postulate (SAS Congruence Postulate).

7. AC must match BD because Congruent Parts in Congruent Triangles must match (CPCTC).

Statement                                    Reason

1. Rectangle ABCD                         Given

2. AD=BC                                        Opposite sides of a rectangle are congruent

3. DC=DC                                        Reflexive Property of Congruence

4. <ADC and <BCD are                  Definition of rectangle

  right angles

5.  <ADC=<BCD                              All right angles are congruent

6. ∆ADC=∆BCD                              SAS Congruence Postulate

7. AC=BD                                        CPCTC  

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Answer is 2.7 million liters/hour

What is speed?

Speed tells us how fast something or someone is travelling.

The flow rate of water can be calculated as the cross-sectional area of the channel multiplied by the speed of the water.

The cross-sectional area of the channel can be calculated as width x depth = 15 cm x 2.5 cm = 37.5 cm^2

The flow rate of water can be calculated as 37.5 cm^2 x 20 cm/s = 750 cm^3/s

To convert this to liters, we need to multiply by 1000 to convert cubic centimeters to cubic centimeters:

750 cm^3/s x (1000 cm^3/L) = 750 L/s

Finally, to find the amount of water that flows into the lake in 1 hour, we need to multiply the flow rate by the number of seconds in an hour:

750 L/s x (3600 s/hr) = 2700000 L/hr = 2.7 million liters/hour.

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Answer:

4x/5

Step-by-step explanation:

the price of the jacket before goes down = x

20/100*x = x/5

the original price of the jacket= x-(x/5) = 4x/5

Answer:

Step-by-step explanation:

The answer will be the third one because 2/3 * (3/10 X 1) is the same as 2/3 already being multiplied to 3/10.

If you use a calculator and put 2/3 * (3/10 X 1), you will get 0.2 and if you put (2/3 * 3/10) x 1 you will also 0.2.

So (2/3 * 3/10) x 1 is equal to 2/3 * (3/10 X 1)

The function g(x) is defined as follows:

g(x) = 2x - 12.

The inverse function is obtained exchanging the variables x and y, and then isolating y, thus:

The fact that the variables are exchanged means that the functions are symmetric over the line y = x.

As the lines are symmetric over the line y = x, these following statements regarding the composition of a function with it's inverse is given as follows:

We have that f(2x - 12) = x, hence the function g(x) is defined as follows:

g(x) = 2x - 12.

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Answer:

25,000g

Step-by-step explanation:

multiply the mass value by 1000

25 x 1000 = 25,000g

The value for the following order of the given iterative formula of xₙ + 1 = 3/4 xₙ₋₁ are:

Iterative formula is used to process a repeating procedure to produce a series of results

We have an iterative formula of:

xₙ + 1 = 3/4 xₙ₋₁

We know that:

x₁ = 2

Hence:

x₂ + 1 = 3/4 x₁

x₂ + 1 = 3/4 (2)

x₂ + 1 = 3/2

x₂ = 1/2 = 0.5

x₃ + 1 = 3/4 x₂

x₃ + 1 = 3/4 (1/2)

x₃ + 1 = 3/8

x₃ = -5/8 = - 0.63

x₄ + 1 = 3/4 x₃

x₄ + 1 = 3/4 (-5/8)

x₄ + 1 = -15/32

x₄  = - 47/32 = -1.47

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The length of the new line is twice the length of the old line and total length is given by the equation L = (3/8 ) of an inch

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 length of the old line be A

Now , the value of A = 1/8 of an inch

Let the length of the new line be B

Now , the value of B = 1/4 of an inch

So , the equation will be

The number of times the new line is greater than old line is given by

B / A = x

Substituting the values in the equation , we get

x = ( 1/4 ) / ( 1/8 )

x = 8/4

x = 2 times

So , the total length of the line = A + B

Substituting the values in the equation , we get

The total length of the line L = ( 1/4 ) + ( 1/8 )

The total length of the line L = 3/8 of an inch

Hence , the equation is L = (3/8 ) of an inch

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The cube root of a cube of the number is the same number for any number. Thus, option A is the answer.

In the given question,

[tex]\sqrt[3]{7} = 7^{1/3} \\[/tex]

We have to prove L.H.S = R.H.S

Let's take R.H.S

= [tex]7^{1/3}\\[/tex]

Taking a cube for this,

[tex]= (7^{1/3} )^{3}[/tex]

We can separate this into three terms.

[tex]= 7^{1/3} . 7^{1/3} . 7^{1/3}[/tex]

We know that [tex]x^{n}. x^{m} = x^{n+m}[/tex]

Then,

[tex]= 7^{1/3 + 1/3 +1/3} \\= 7^{3/3}\\ = 7[/tex]

From L.H.S

We have to take cube root,

[tex](\sqrt[3]{7})^{3} \\= 7[/tex]

Hence, L.H.S = R.H.S, and it is verified.

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The required probabilities = 0.16

The required probabilities = 0.68

The Z-score quantifies the discrepancy between a given value and the standard deviation. The Z-score, also known as the standard score, indicates how many standard deviations a specific data point deviates from the mean. In essence, standard deviation represents the degree of variability present in a particular data collection.

As given that,

μ = 36.2

σ = 10

As per empirical Rule:

μ± σ = 36.2 ±10 = 26.2, 46.2 = 68%

μ± 2σ = 36.2 ±20 = 16.2, 56.2 = 95%

μ ± 3σ = 36.2 ±30 = 6.2, 66.2 = 99.7%

less than 26.2:

13.5% + 2.35% + 0.15% = 0.16

between 26.2 and 36.2:

68% = 0.68

The required probabilities = 0.16

The required probabilities = 0.68

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