IF T² = 4π² (h² + k²)
hg
Express k² in terms of T, g and h

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

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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The variance of the number of packages that will be filled before the process is stopped will be 600 when the probability of falling outside the specification is 0.04.

Variability is measured by the variance. The average of the squared deviations from the mean is used to calculate it. The degree of spread in your data set is indicated by variance. The variance is greater in relation to the mean the more dispersed the data. In statistics, the variance is used to assess how accurately the mean summarizes all of the data. For instance, more range exists within the set the higher the variance. 

P(fail)=0.04

P(pass)=0.96

variance=(1-P)/P²

=(1-0.04)/0.0016

=0.96/0.0016

variance=600

When the likelihood of falling outside the specification is 0.04, the range of packages that will be filled before the process is stopped is 600.

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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]

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

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

So, the length of the flight will be:

Now, calculate for D as follows:

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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She needs to complete 20 laps for a total distance of 0.5 kilometer.

1 kilometers = 1000 meters

0.5 kilometers = 500 meters

Length of swimming pool = 25 meters

That means, she covers 25 meters in 1 lap.

Laps to cover 500 meters = 500/25

                                            = 20

Hence, she needs to do 20 laps.

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

What is probability in math?

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

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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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

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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The correct result would be (x, y) = (5, 17); because both lines pass through this point.

Given,

In the question:

Two lines. C and D are represented by the equations.

We have :

Line C. y = x + 12

Line D. y = 3X + 2

Now, According to the question:

y = x + 12

y = 3X + 2

Substitute into one of the equations

x + 12 = 3x + 2

Solve the equation:

Combine like terms:

x - 3x = 2 - 12

-2x = -10

x = -10/-2

x = 5

Put the value of x in equation of Line C

y = x + 12

y = 5 + 12

y = 17

Hence, The correct result would be (x, y) = (5, 17); because both lines pass through this point.

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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

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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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

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)

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

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

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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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

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

​

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

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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The correct inequality symbol that makes the statement true is:

1000 < (6²)³.

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

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:

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.

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

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Answer: Positive

Step-by-step explanation: It would be positive because the question is asking how much money they lost. The lost a positive amount of money.

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

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?

The surface area of the triangular prsim is 290.4 in² and the right option is B. 290.4 in².

Surface area is the space occupied by a two-dimensional flat surface is called the area. It is measured in square units.

To calculate the surface area of the triangular prism, we use the formula below.

Fromula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, the right option is B. 290.4 in².

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

x ≤ 400 miles.

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

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.

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

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

The problem is solved considering this 3 theorems about triangles

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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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.

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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