Quick help would be appreciated : )

Quick Help Would Be Appreciated : )

Answers

Answer 1

The number of liters of fuel required for the vehicle to travel 1, 428 kilometers is 5. 67

What is inverse variation?

Inverse variation can be defined as the relationship between two variables, so that if the value of one of the variable increases the value of the other variable decreases.

Example: If a varies inversely as b

This can be represented as;

a ∝ 1/b

Then,

ab = k

Where k is the proportionality constant

From the information given, we have that;

The number of kilometers = xThe liters of fuel = y

x ∝ 1/ y

Then,

xy = k

Substitute the values

476 (17) = k

k = 8092

If x = 1428 and k = 8092

Let's determine the value of y

y = k/x

y = 8092/1428

y = 5. 67 liters

Hence, the value is 5. 67 liters

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Related Questions

Annalise withdraws $22.50 each day from
her account for a week. How can you represent the change in the
account for the week?
(PLEASE HELP QUICK)

Answers

The rate of change in the account for a week is $157.5.

Annalise has some money in her bank account. She withdraws $22.50 per day from her account for a week. We need to represent the change in the account for the week. The number of days in a week is seven. So, it means that she withdraws money from her bank account daily for seven days. The total amount of money withdrawn from the bank account is the product of the withdrawal amount per day and the total number of days in a week.

A = $22.5*7 = $157.5

Let the initial amount of money in the bank be "$x". The change in the bank balance is $157.5. The current balance is $(x - 157.5).

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Alan travels eight and two thirds kilometers to get to school. He ran one and ten elevenths kilometers and walked the rest. How many kilometers were left to walk? (4 points)

a
six and two thirty thirds kilometers

b
five and twenty five thirty thirds kilometers

c
six and twenty five thirty thirds kilometers

d
six and twenty thirty thirds kilometers

Answers

The Kilometer that Alan was left to walk is given as c six and twenty five thirty thirds kilometers

How to solve for the kilometer

In order to solve for the solution, we would have to write out the expressions in mathematical forms first

eight and two thirds kilometers = [tex]8\frac{2}{3}[/tex]

This is is the time that Alan is said to travel for him to get to school

The expression one and ten elevenths is written mathematically as [tex]1\frac{10}{11}[/tex]

This is the kilometer that he spent running.

We are to find the time that was used to walk to school.

To get this we have to subtract the kilometer that he ran from the total kilometer that he traveled.

[tex]8\frac{2}{3} - 1\frac{10}{11}[/tex]

we have to express as a mixed fraction then we would subtract

26/3 - 21/11

= 286 - 63 / 33

= 223/33

= 6.75

= 6 25/33

Hence the solution is C.

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A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6. Which statements are always true regarding the diagram? Select three options. m∠5 + m∠3 = m∠4 m∠3 + m∠4 + m∠5 = 180° m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°

Answers

Considering the triangle with exterior angles and interior angles as described. The statements that are true include

m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°

How to determine the statements that are correct

The problem is solved considering this 3 theorems about triangles

exterior angle of a triangle theoremlinear pair theoremsum of angles in a triangle

exterior angles theorem: m∠2 + m∠3 = m∠6

If a triangle side is created, the outside angle that results is equal to the sum of the two opposite internal angles.

Linear pair theorem: m∠5 + m∠6 =180°

Linear pairs are particular instances of supplementary angles that only involve two neighboring angles.

Sum of angles in a triangle is equal to 180 degrees:

m∠2 + m∠3 + m∠5 = 180°

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Michael is having party. He'll have 12 tables for every 32 guests. Complete the table below to find the number of guests he can seat with 3
tables.
Number of guests 32
Number of tables 3

Answers

A proportion can be used to solve for the missing value.
x/3=32/12
Use cross multiplication to get the equation 12x=96
Divide both sides by 12 to get x=8
Micheal can seat 8 guests with 3 tables

please help me with this​

Answers

Answer: final answer = 3/8

Step-by-step explanation:
it says 1/8 + 1/4. before you can add them you have to make sure that both fractions have the same denominator first you have to make both of the bottom denominators the same so its 1/8+2/8.
1/8+2/8=3/8

which of the following is a quantitative research method that aims to observe the relationship between an independent variable and a dependent variable? a.) a questionnaire b.) secondary data analysis c.) a focus group d.) an experiment

Answers

The correct option is  a.) a questionnaire, used as observing the relationship between independent variable as well as a dependent variable is the goal of a quantitative research technique known as employed as.

Define the term quantitative research method?

Quantitative methods place an emphasis on accurate measurements or the statistical, quantitative, or numerical evaluation of information gathered through surveys, polls, and other types of research, as well as the manipulation of statistical data that has already been obtained using computing methods.

Quantitative research involves gathering numerical information and using it to understand a specific event or generalise it across groups of individuals.

Its primary attributes are:

Typically, organised research tools are used to acquire the data.Given its high reliability, the research study can typically be replicated or redone.The researcher has a specific study question to which unbiased solutions are sought.Before data is collected, the study's various components are all carefully designed.Numbers and statistics make up data, which are frequently displayed in tables, charts, and other non-textual formats.

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A statement that two numbers or expressions are equal is a(n)

Answers

A statement that two numbers or expressions are equal is an equation.

What is an equation?

An equation is a mathematical expression that states that two expressions are equal. An equation's solution is the value that, when substituted for the variable, makes the equation true. To accomplish our goal, we employ two equality principles: the addition principle and the multiplication principle.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.

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Evaluate to find the value of x.
-2x - 6 = -18

Answers

Answer:

x=6

Step-by-step explanation:

-2x-6=-18

     +6. +6

-2x=-12

/-2. /-2

x=6

Hopes this helps please mark brainliest

if he uses upper and lower control limits of 520 and 480 hours, what is the probability that a sample mean is out of control?( assuming the process standard deviation is known to be 20 hours)

Answers

0.0456  is the probability that a sample mean is out of control.

What is probability in math?

Probability refers to potential. The subject of this area of mathematics is the occurrence of random events.The range of the value is 0 to 1. To forecast how likely events are to occur, probability has been introduced in mathematics.

UCL = 520

LCL = 480

Mean (X ) = 500

Standard Deviation of sample (Sn) = 11.55

Z (for UCL) = (UCL - Mean)/Sn

Z (for UCL) = (520-500)/10

Z (for UCL) = 2

Z (for LCL) = (LCL - Mean)/Sn

Z (for LCL) = (480 - 500)/10

Z (for LCL) = -2

*Use Z table to find confidence level between Z value of -2 and 2.

Confidence level = 0.4772 + 0.4772

Confidence level = 0.9544

Risk (α ) = 1 - confidence level

Risk (α) = 1 - 0.9544

Risk (α) = 0.0456

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30% of the tickets sold at a school carnival were early-admission tickets. If the school sold 100 tickets in all, how many early-admission tickets did it sell?

Answers

The number of early-admission tickets that it sells is 30.

How to calculate the number of early admission?

From the information, 30% of the tickets sold at a school carnival were early-admission tickets and the school sold 100 tickets in all.

Therefore, the number of early admission will be:

= Percentage for early admission × Total number of tickets

= 30% × 100

= 0.3 × 100

= 30

Therefore, there are 30 early admission.

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an educational psychologist wanted to know the effects of four different methods of teaching arithmetic. using 12 classrooms, each method was used in the classes. at the end of the school year, all the pupils took the same achievement test, and the means for groups receiving different methods were compared. answer the following questions about the study. a. what was the dependent variable? b. what was the independent variable? c. what was a controlled variable? d. give an example of a parameter.

Answers

The dependent variable depends on a particular situation. The independent variable does depends on the result of an experiment. The controlled variable is a variable whose value is constant.

What is dependent variable?

The variable being measured or tested in an experiment is known as the dependent variable. The results of the participants' tests, for instance, since that is what is being measured, would be the dependent variable in a study looking at how tutoring affects test scores.

What is independent variable?

This isn't the same as an experiment's independent variable, which is a variable that can stand on its own. Tutoring would be the independent variable in the aforementioned case. The dependent variable (test results), however, may alter depending on the independent variable (tutoring).

What is controlled variable?

Anything kept constant or constrained in a research study is referred to as a control variable. Despite not being relevant to the study's objectives, this variable is controlled because it might have an impact on the results.

Numbers called parameters are used to define the characteristics of entire populations. Statistics are numerical representations of sample characteristics. One population parameter is the average income in the United States.

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what is the value of m and n?​

Answers

The value of m is 36 degrees and the value of n is 27 degrees

Consider the triangle on right side

Two sides of the triangle is equal, therefore it is an isosceles triangle.

One angle of the triangle = 126 degrees

Other two angles of the triangle is equal

The sum of interior angles of the triangle is 180 degrees

Then, the equation will be

126 + n + n = 180

2n + 126 = 180

2n = 180 - 126

2n = 54

n = 54/2

n = 27 degrees

Consider the full triangle

The equation will be

(m +27) + 90 +27 = 180

m + 27 + 90 + 27 = 180

m + 144 = 180

m = 180 - 144

m = 36  degrees

Hence, the value of m is 36 degrees and the value of n is 27 degrees

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help meeeeeeeeeeee pleaseeeeeeeeeee rn rnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeeeeee pleaseeeeeeeeeee rn rnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

The equation of the parabola from the vertex is f(x) = 7(x - 3)² + 5

How to determine the equation of the parabola?

The equation of the function is given as

f(x) = 7x²

Also, we have

Vertex = (3, 5)

The form of the equation is given as

f(x) = a(x - h)² + k

Where

Vertex = (h, k)

This means that

Vertex = (h, k) = (3, 5)

Substitute (h, k) = (3, 5) in the equation f(x) = a(x - h)² + k

So, we have

f(x) = a(x - 3)² + 5

This also means that

f(x) = 7(x - 3)² + 5

The 7 is gotten from f(x) = 7x²

Hence, the equation of the parabola is f(x) = 7(x - 3)² + 5

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Janet attends state university and lives in an on campus dorm suite with 5 friends. They share cost of the monthly upgraded cable bill for their suite. Below is a listing of the bills for their freshman year. 9. Round the following value
Σ
619
X₁
to the nearest dollar.
Interpret the answer in the context of the problem.

Answers

Answer:

Step-by-step explanation:       Step 1

1 of 2

step 1.2659 ;[26 Discovery Group

October 20

Last

Trade Time

Chg

Open

52-week High

52-week Low

Sales in 100s

High

Low

 

$38.50

4:00 P.M. ET

$1.56

$37.22

$76.19

$22.78

19,700

$40.10

$36.77

\begin{matrix} \text{Discovery Group} & \text{}\\ \text{October 20} & \text{}\\ \text{Last} & \text{\$42.00}\\ \text{Trade Time} & \text{4:00 P.M. ET}\\ \text{Chg} & \text{\$1.50}\\ \text{Open} & \text{\$42.50}\\ \text{52-week High} & \text{\$76.19}\\ \text{52-week Low} & \text{\$22.78}\\ \text{Sales in 100s} & \text{23,600}\\ \text{High} & \text{\$42.50}\\ \text{Low} & \text{\$42.00}\\ \end{matrix}

Discovery Group

October 20

Last

Trade Time

Chg

Open

52-week High

52-week Low

Sales in 100s

High

Low

 

$42.00

4:00 P.M. ET

$1.50

$42.50

$76.19

$22.78

23,600

$42.50

$42.00

Write 10x - 5y = -30 in slopeintercept form.
y =
X +

Answers

Answer:

[tex]y=2x+6[/tex]

Step-by-step explanation:

Slope-intercept form is [tex]y=mx+b[/tex].

Therefore, rearranging the given formula:

[tex]10x-5y=-30[/tex]

[tex]-5y=-10x-30[/tex]

[tex]\frac{-5y}{-5}=\frac{-10x}{-5}-\frac{30}{-5}[/tex]

[tex]y=2x-(-6)[/tex]

[tex]y=2x+6[/tex]

Answer: y=2x+6

Step-by-step explanation:

A slope-intercept form is y=mx+b

Hence,

[tex]10x-5y=-30\\\\10x-5y+5y=-30+5y\\\\10x=-30+5y\\\\10x+30=-30+5y+30\\\\10x+30=5y[/tex]

Divide both parts of the equation by 5:

2x+6=y

Thus, y=2x+6

What are the advantages of bankruptcy? a. Exempted items are allowed. b. Certain incomes are unaffected. c. Debts are erased. d. "Exempted items are allowed" and "An automatic stay is enacted". e. All of these choices are correct. f. An automatic stay is enacted.

Answers

The advantages of bankruptcy include the following: e. All of these choices are correct.

What is bankruptcy?

In Financial accounting, bankruptcy can be defined as a legal process that is initiated when an individual or business organization (debtors) is relieved of the responsibility to pay their debts, honor its financial obligations to creditors, or protect them while they are trying to repay their debt.

The advantages of bankruptcy.

Generally speaking, there are several advantages of bankruptcy and these include the following:

Some certain incomes are unaffected by bankruptcy.All of the debts are erased.An automatic stay would be enacted.Exempted assets such as unemployment benefits and retirement accounts are retained or allowed.

In conclusion, we can reasonably infer and logically deduce that bankruptcy is generally considered as both a friend and foe (enemy).

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20-foot extension ladder set base six feet from house How far up will ladder reach?

Answers

The top of the 20-foot ladder used for painting will be  19 feet up from the base of the house

How to determine how high up the house the ladder will go

information given in the question

Brian borrowed a 20-foot extension ladder: hypotenuse = 20-foot ladder

he sets the base of the ladder six feet from the house

adjacent = 6 feet from the house

opposite =  how far up will the top of the ladder reach = ?

The problem is solved using the Pythagoras theorem is applicable to right angle triangle.  the formula of the theorem is

hypotenuse² = adjacent² + opposite²

substituting the values into the equation

let x be thow far up will the top of the ladder reach

20² = 6² + x²

400 = 36 + x²

400 - 36 = x²

x² = 364

x = √364

x = 19.08

The ladder Brain borrowed will go 19 feet high

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complete question

Brian borrowed a 20-foot extension ladder to use to paint his house. If he sets the base of the ladder six feet from the house how far up will the top of the ladder reach?

What are the workings of this question? How to arrive at the answer?

Answers

The variation equation that connects x and y is y³ = 4.5x(x - 1) and the value of y is 4.48 when x equals  5

The equation that connects x and y?

From the question, the variation statement is given as

The cube of y is directly proportional to x(x - 1)

Also, we have the initial values of x and y to be

x = 3 and y= 3

When the variation statement is represented as an equation, we have:

y³ = kx(x - 1)

Where k is the variation constant

Substitute the known values in the above equation So, we have the following equation

3³ = k x 3 x (3 - 1)

Evaluate

27 = 6k

Divide both sides by 6

k = 4.5

Substitute k = 4.5 in y³ = kx(x - 1)

y³ = 4.5x(x - 1)

Hence, the equation is y³ = 4.5x(x - 1)

The value of y

Here, we are given that

x = 5

Substitute 5 for x in the equation y³ = 4.5x(x - 1)

So, we have

y³ = 4.5 x 5 x (5 - 1)

Evaluate

y³ = 90

Take the cube root of both sides

y = 4.48

Hence, the value of y is 4.48

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Which statement is true? All decimals are rational. All rational numbers can be written as the quotient of Integers

Answers

The statement that is true is All rational numbers can be written as the quotient of Integers

What are rational numbers ?

Any number that can be written as a fraction and has an integer as both the numerator and the denominator is referred to as rational number.

In a rational number, the denominator cannot be zero.

Integer refers to whole numbers. They are generally of two types the positive integers and the negative integers

Quotients refers to the end product of division example 2 ÷ 1 = 2/1

2/1 is the quotient, both 2 and 1 are integers

All decimals are rational - A counter example to this is √2

It has decimal and not a rational number because it cannot be represented as a fraction

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The statement that is true is All rational numbers can be written as the quotient of Integers

What are rational numbers ?

Any number that can be written as a fraction and has an integer as both the numerator and the denominator is referred to as rational number.

In a rational number, the denominator cannot be zero.

Integer refers to whole numbers. They are generally of two types the positive integers and the negative integers

Quotients refers to the end product of division example 2 ÷ 1 = 2/1

2/1 is the quotient, both 2 and 1 are integers

All decimals are rational - A counter example to this is √2

It has decimal and not a rational number because it cannot be represented as a fraction

if sec2a is 3 find the value of sina.​

Answers

By using trigonometry, it can be calculated that

The value of sina is [tex]\pm \frac{1}{\sqrt{3}}[/tex]

What is Trigonometry?

Trigonometry shows the relationship between sides and angles of a right angled triangle.

There are six trigonometrical functions. They are

[tex]sin \theta, \ cos\theta, \ tan \theta, \ cot\theta, \ sec\theta, \ cosec\theta[/tex]

[tex]sin\theta = \frac{perpendicular}{hypotenuse}\\\\cos\theta = \frac{base}{hypotenuse}\\\\tan\theta = \frac{perpendicular}{base}\\\\cot\theta = \frac{base}{perpendicular}\\\\sec\theta = \frac{hypotenuse}{base}\\\\cosec\theta = \frac{hypotenuse}{perpendicular}[/tex]

Trigonometry is a very important tool in mathematics.

Here, the trigonometric equation is

sec 2a = 3

cos 2a = [tex]\frac{1}{3}[/tex]

we know,

[tex]1 - cos 2a = 2 sin^2a\\\\1 - \frac{1}{3} = 2sin^2a\\\\2 sin^2a = \frac{2}{3}\\\\sin^2a = \frac{2}{3} \times \frac{1}{2}\\\\sin^2a = \frac{1}{3}\\\\ sina = \pm \frac{1}{\sqrt{3}}[/tex]

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Dev’ car currently ha 18 gallon of ga in the tank. He ue about 0. 04 gallon for every mile he drive. Dev want to go on a car trip over the weekend and have at leat 2 gallon of ga left in hi tank to get to work on Monday. What i the olution of the inequality that determine how far Dev can travel over the weekend? (Example 2) Let x repreent the number of mile Dev travel

Answers

The solution of the inequality that determines how far Dev can travel over the weekend is -

x ≤ 400 miles.

What is a expression? What is a mathematical equation? What is Equation Modelling?

A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

We have Dave who is planning a car trip for weekend.

Assume that [x] represents the number of miles Dev can travel.

We can write the inequality as -

18 - 0.04x ≤ 2

0.04x ≤ 16

x ≤ 400 miles

Therefore, the solution of the inequality that determines how far Dev can travel over the weekend is -

x ≤ 400 miles.

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air is pumped into a spherical balloon at the constant rate of 200 cubic centimeters per second. how fast is the surface area of the balloon changing when the radius is 5 centimeters?

Answers

The rate of change of the surface area of the balloon is 32cm²/sec

We know that volume of the sphere is,

V = 4/3πr³

Given,

dV / dt = +200

r = 5cm

d(SA) / dt = ?

dV / dt = 4πr² dr/dt

80 = 4π (25) dr/dt

dr / dt = 0.8 / π

SA = 4πr²

d(SA) / dt = 8πr dr / dt

d(SA) / dt = 8π × 5 × 0.8 / π

d(SA) / dt = 32cm²/sec

Hence the rate of change of the surface area is 32cm²/sec

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Select the correct symbol to make 11⎯⎯⎯⎯√ , 1 of 1.
Select Choice
323 a true statement.

Answers

The correct inequality symbol that makes the statement true is:

1000 < (6²)³.

How to choose the inequality symbol?

The inequality symbols, and their meaning, are presented as follows:

> x: greater than x.< x: less than x.≥ x: at least x.≤ at most x.

In the context of this problem, the numbers being compared are presented as follows:

1000 and (6²)³.

The power of power property of a number with multiple exponents means that the base is kept while the exponents are multiplied.

The number in which this property is applied in this problem is (6²)³, in which:

The base is of 6.The exponents are of 2 and 3.

Hence the equivalent number is given as follows:

(6²)³ = 6^6 = 6 x 6 x 6 x 6 x 6 x 6 = 46,656

Which is a greater number than 1,000, meaning that 1,000 is less than the number, and the inequality is:

1000 < (6²)³.

Missing Information

The problem is given by the image at the end of the answer.

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Activity 8. Counting the roots of polynomial equation

by inspection determine the number of real roots of each polynomial equation. Roots multiply n are counted n times

1. (x-4)(x+3)^2(x-1)^3=0
2. X^2(x^3-1)=0
3. X(x+3)(x-6)^2=0
4. 3x(x^3-1)^2=0
5. (x^3-8)(x^4+1)=0​

patulong po plss.

Answers

The number of real roots found are-

1. (x-4)(x+3)^2(x-1)^3=0 ; 6 real roots.

2. X^2(x^3-1)=0 ; 3 real roots.

3. X(x+3)(x-6)^2=0 ; 4 real roots.

4. 3x(x^3-1)^2=0 ; 3 real roots.

5. (x^3-8)(x^4+1)=0​ ; 1 real roots.

Define the term roots of polynomial?If a root is not imaginary (defined as a number as in form a + bi, whereby I is a number which is not on any real number line, which is why the name imaginary), it is said to be real.

Consider the given cases-

1. (x-4)(x+3)^2(x-1)^3=0,

Put each equals zero.

x – 4 = 0 or (x + 3)^2 = 0 or (x – 1)^3 = 0,

Thus,

x = 4

x = –3 twice

x = 1 thrice

All are real numbers, thus given polynomial has 6 real roots.

2. x^2(x^3-1)=0

Put each equals zero.

x² = 0

x³ – 1 = x³ – 1³ = (x – 1)(x² + x + 1) = 0

The quadratic expressions has 2 imaginary roots.

Use the discriminant formula to find-

D = b² – 4ac = 1² – 4(1)(1) = 1 – 4 = –3 < 0.

Thus, roots that are not real.

So, the real roots of this polynomial : 0(twice) and 1.

Hence, thus given polynomial has 3 real roots.

3. x(x+3)(x-6)^2=0

Put each equals zero.

x = 0

x = 3

x = 6 twice

Hence, thus given polynomial has 4 real roots.

4. 3x(x^3-1)^2=0

Put each equals zero.

3x = 0 and  x = 0

(x^3 – 1)² = [(x – 1)(x² + x + 1)]² = (x – 1)²(x² + x + 1)² = 0,

Here, only two roots are real

The quadratic expression do have unreal roots, thus 1 twice are the real roots.

Hence, thus given polynomial has 3 real roots..

5. (x^3-8)(x^4+1)=0

Put each equals zero.

x³ – 8 = x³ – 2³ = (x – 2)(x² + 2x + 4) = 0

There is only one real root i.e, 2, the quadratic expression do have imaginary roots

Check using the discriminant formula

D = b² – 4ac = 2² – 4(1)(4) = 4 – 16 = – 12 < 0.

x⁴ + 1 = 0 has imaginary roots.

Hence, thus given polynomial has 1 real roots..

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Please help me, I need the answer asap

Find m<2

28
62
56
142

Answers

The given equation  m<2 = 28⁰ so here in this case option A is correct .

What three characteristics do angles have?A transversal's corresponding angles are equal when it crosses two parallel lines.Angles that are vertically opposite are equal.All of the interior angles alternately are equal.Every other external angle is equivalent.On the same side of the transversal, the pair of internal angles is additional.

Simplification:

       <1 = <3

<1 = 5x + 8              ………………equation 1.

<3 = 12x – 20         ………………equation 2.

         

By angle property <1 = <3  [ given ]

and

<1 = <2   [ vertically opposite angles ]

We have some options so we can use it to get answer more quickly:

Put <1=28 and <3=28

And solve it for X.

28 = 5x + 8                     Eq1

20=5x => x=4

28 = 12x - 20                 Eq2

28 + 20 = 12x

48 = 12x

4 = x

X = 4

As <1 = <2 ( vertically opposite angles )

From the first equation  <1 = <2  = 5x + 8 ......( equation 3)

Putting the value of x = 4 in (equation 3)

<2 = 5* 4+ 8

<2=28

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A city doubles its size every 5 years. If the population is currently 469,900, what will the
population be in 20 years?

Answers

the population would be 7,518,400


469,900 • 2^20/5


* 20/5 is part of the exponent

Answer:

7518400

Step-by-step explanation:

Doubling time model:

         [tex]P= P_o 2^{\frac{t}{D}}[/tex]

Here, P is the initial value, D is the time taken to double the quantity, t is the given period of time.

 [tex]P_o = 469,900\\\\\\D = 5 \ years\\t = 20 \ years[/tex]

                    [tex]P = 469,900 * 2^\frac{20}{5}\\\\P = 469,900 * 2^4[/tex]

                         = 469,900 * 2 * 2 * 2 * 2

                         = 7518400

a tank contains 1360l of pure water. a solution that contains 0.02kg of sugar per liter enters a tank at the rate 2 l/min. the solution is mixed and drains from the tank at the same rate. how much sugar is in the tank initially? find the amount of sugar in the tank after t minutes. find the concentration of sugar in the solution in the tank after 60 minutes

Answers

a) Amount of sugar in the tank initially is 0.

b) The amount of sugar in the tank after t minutes is 13.6(1 - [tex]e^{\frac{4t}{1360} }[/tex]).

c) The concentration of sugar in the solution in the tank after 60 minutes is 3.672.

a) Assign the sugar content of the tank for time t to the symbol A(t). Starting with only clean water, the tank

A(0) = 0

b) Sugar flows in at a rate of

(0.02 kg/L) × (2 L/min) = 0.04 kg/min

and flows out at a rate of

(A(t) ÷ 1360 kg/L) × (2 L/min) = (2A(t) ÷ 1360) kg/min

so that the net rate of change of A(t) is governed by the ODE,

dA(t) ÷ dt = (4 ÷ 100) - (2A(t) ÷ 1360)

A'(t) + (2A(t) ÷ 1360) = 2 ÷ 100

Multiply both sides by the integrating factor [tex]e^{\frac{4t}{1360} }[/tex] to condense the left side into the derivative of a product:

[tex]e^{\frac{4t}{1360} }[/tex] A'(t) + (2 [tex]e^{\frac{4t}{1360} }[/tex] A(t) ÷ 1360) = 4 [tex]e^{\frac{4t}{1360} }[/tex] ÷ 100

( [tex]e^{\frac{4t}{1360} }[/tex] A(t))' = 4 [tex]e^{\frac{4t}{1360} }[/tex] ÷ 100

Integrate both sides:

[tex]e^{\frac{4t}{1360} }[/tex] A(t) = ∫ 4 [tex]e^{\frac{4t}{1360} }[/tex] ÷ 100

[tex]e^{\frac{4t}{1360} }[/tex] A(t) = 13.6 [tex]e^{\frac{4t}{1360} }[/tex] + C

Solve A(t);

A(t) = 13.6 + C [tex]e^{\frac{4t}{1360} }[/tex]

A(0) = 0, substitute the value

0 = 13.6 + C [tex]e^{\frac{4t}{1360} }[/tex]

C = -13.6

so that the amount of sugar at any time t is,

A(t) =  13.6 - 13.6[tex]e^{\frac{4t}{1360} }[/tex]

A(t) = 13.6(1 - [tex]e^{\frac{4t}{1360} }[/tex])

c) As t → 60, the exponential term converges to 0 and is left with

[tex]\lim_{t \to \(60}[/tex] A(t) = 13.6 × (1 - 0.73)

[tex]\lim_{t \to \(60}[/tex] A(t) = 3.672 kgs of sugar.

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I need help with number 7.

Answers

With the help of the given trendline equation, the length of the flight will be 3,613.34 miles.

What are equations?A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A mathematical statement that has an "equal to" symbol between two expressions with equal values is called an equation. As in 3x + 5 Equals 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others.

So, the length of the flight will be:

The trendline equation is: T = 458 + 0.15DT is the cost which is given as $1000 and D is the distance.

Now, calculate for D as follows:

T = 458 + 0.15D1000 = 458 + 0.15D1000 - 458 = 0.15D0.15D = 542D = 542/0.15D = 3,613.33

We can write as D = 3,613.34

Therefore, with the help of the given trendline equation, the length of the flight will be 3,613.34 miles.

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The area of the rectangle ABCD is 28[tex]cm^{2}[/tex]

a) What is the length of side AB in terms of x?

length of AB = (Answer here) (1)

b) If the area of rectangle ABCD is 28[tex]cm^{2}[/tex], we can show that [tex]x^{2}[/tex] + ax = b where a and b are integer values.

Work out the values of a and b.

a = (Answer here) (1) b = (Answer here) (1)

Answers

Answer:

see explanation

Step-by-step explanation:

(a)

AB = 4 + x

(b)

the area (A) of rectangle ABCD is calculated as

A = length × breadth

   = AB × AD

   = (4 + x)(6 + x) ← expand using FOIL

   = 24 + 10x + x²

given A = 28 , then

x² + 10x + 24 = 28 ( subtract 24 from both sides )

x² + 10x = 4 ← in the form x² + ax = b

with a = 10 and b = 4

Partition a line segment in the given ratio.
Point V lies on TU such that TV:UV is 5:2. Graph V.

Answers

Check the picture below.

[tex]\textit{internal division of a line segment using ratios} \\\\\\ T(-5,9)\qquad U(9,2)\qquad \qquad \stackrel{\textit{ratio from T to U}}{5:2} \\\\\\ \cfrac{T\underline{V}}{\underline{V} U} = \cfrac{5}{2}\implies \cfrac{T}{U} = \cfrac{5}{2}\implies 2T=5U\implies 2(-5,9)=5(9,2)[/tex]

[tex](\stackrel{x}{-10}~~,~~ \stackrel{y}{18})=(\stackrel{x}{45}~~,~~ \stackrel{y}{10}) \implies V=\underset{\textit{sum of the ratios}}{\left( \cfrac{\stackrel{\textit{sum of x's}}{-10 +45}}{5+2}~~,~~\cfrac{\stackrel{\textit{sum of y's}}{18 +10}}{5+2} \right)} \\\\\\ V=\left( \cfrac{ 35 }{ 7 }~~,~~\cfrac{ 28}{ 7 } \right)\implies {\Large \begin{array}{llll} V=(5~~,~~4) \end{array}}[/tex]

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