solve the following inequality for h then simplify
8h-2>3h+2

Sarah can blow 7 minutes to blow 21 balloons

The unitary method is a method in which you find the value of a unit and then the value of a required number of units.

Given here: Sarah can blow 3 balloons in 1 minute

Then unit rate of sarah is 3 balloons per minute

Thus the time she would take to blow 21 balloons is 21/3=7 minutes

Hence, Sarah can blow 7 minutes to blow 21 balloons

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Answer:

i belive the first up 3 un its and the second is 5

Step-by-step explanation:i think i had this  on a test question if wrong pls tell me will help through it

The equation would be 20x + 0.50y

What is an equation?

A mathematical statement that establishes the equality of two mathematical expressions is the definition of an equation.

How to write an equation?

For writing an equation we need variables (alphabet that represents unknown quantity) and quantity that needs to be represented.

let the total members be x and total rentals be y.

Therefore the equation formed will be = 20x +0.50y

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Answer:

D. tan 0 = 8/15 and A. sec 0 = 17/15

Step-by-step explanation:

Cos 0 = adjacent/ hypotenus

Adj = 15 and Hyp =17

Using pythagoras theory

Opp^2 = 17^2 - 15^2

Opp^2 = 289 - 225

Opp^2 = 64

Therefore Opp = 8 which is the square root of 64

tan 0 = opp/adj

tan 0 = 8/15

Sec 0 is the multiplicative inverse of cos 0

Answer:

6 inches per year/ 6;1

Step-by-step explanation:

30;5 can be simplified into a unit rate by dividing by 5. 30/5=6 and 5/5=1. So its 6 inches per one year

Change from rectangular to cylindrical coordinates. (Let r ≥ 0 and 0 ≤ Θ≤ 2π.)

(a) (9√3, 9,-4) as (18, π/6, -4).

(b) (8,-6,8) as (10, -0.6435, 8).

Cylindrical coordinates can be defined as a set of three coordinates that are used to locate a point in the cylindrical coordinate system. When the polar coordinates are extended to a three-dimensional plane, an additional z coordinate is added. These three measures together form cylindrical coordinates. The coordinates describe two distances and one angle.

(a) To change from rectangular to cylindrical coordinates, we use the following conversions:

x = r cos(Θ)

y = r sin(Θ)

z = z

Given the point (9√3, 9, -4), we can find the cylindrical coordinates (r, Θ, z) as follows:

r = √(x² + y² ) = √((9√3)²  + 9² ) = √(243 + 81) = √324 = 18

Θ = tan⁻¹(y/x) = tan⁻¹(9/9√3) = tan⁻¹(1/√3) = π/6

z = z = -4

Therefore, in cylindrical coordinates, the point (9√3, 9, -4) is represented as (18, π/6, -4).

(b) Given the point (8, -6, 8), we can find the cylindrical coordinates (r, theta, z) as follows:

r = √(x² + y² ) = √(8²  + (-6)² ) = √(64 + 36) = √100 = 10

Θ = tan⁻¹(y/x) = tan⁻¹((-6)/8) = tan⁻¹(-3/4) = -0.6435 (approx.)

z = z = 8

Therefore, in cylindrical coordinates, the point (8, -6, 8) is represented as (10, -0.6435, 8)

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The above question is incomplete the complete question is:

Change from rectangular to cylindrical coordinates. (Let r ≥ 0 and 0 ≤ Θ≤ 2π.)

(a) (9√3, 9,-4)

(b) (8,-6,8)

the answer is n = -3

*********************************************************

a). To maximize production within the budget, 600 units of labor and 100 units of capital should be purchased. b). The maximum production under the budgetary constraint is approximately 8,366 units.

a). To maximize production, we need to allocate the budget efficiently between labor and capital. We can calculate the number of units of labor and capital by dividing the budgeted amount by the cost per unit. The budget of $576,000 divided by the cost of labor per unit ($400) gives us 1,440 units of labor. Similarly, dividing the budget by the cost of capital per unit ($2,400) gives us 240 units of capital. However, this allocation does not maximize production within the budgetary constraint.

b). To find the optimal allocation, we can use the partial derivatives of the production function with respect to L and K. Taking the partial derivative of the production function with respect to L, we get 37.5L^(-0.25)K^0.25. Equating this to the budgeted amount of labor (600 units), we can solve for K, which comes out to be 100 units. Similarly, by taking the partial derivative of the production function with respect to K, we get 12.5L^0.75K^(-0.75). Equating this to the budgeted amount of capital (100 units), we can solve for L, which comes out to be 600 units.

By substituting these values into the production function, we can calculate the maximum number of units of production, which is approximately 8,366 units.

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Answer:

X=-2

Step-by-step explanation:

!:'=/,)_"86"&8_)&485)&($8

Answer:

$19.00

Step-by-step explanation:

She made 52.50.

she had -14.

52.50-14= 38.50

tickets are 9.50

9.50×2= 19.00

hope this helps let me kno if i did somthing wrong!

answer: 16 minutes

Step-by-step explanation:

0.8 would mean 80% of 20minutes.

80/100 × 20 =

=1600/100

=16 minutes

Answer:

D

Step-by-step explanation:

The arithmetic sequence with a common difference of 2 is 13,15,17,19. The correct option is D.

The sequence in which every next number is the addition of the constant quantity in the series is termed as the arithmetic progression.

A number series is a number-based sequence. In the number series questions, we must identify the rules that lead to the formation of a number series.

The common difference is equal to 2. The arithmetic sequence will be written as,

13,15,17,19

Therefore, the arithmetic sequence with a common difference of 2 is 13,15,17,19. The correct option is D.

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The solutions to the systems of linear equations by elimination method are listed below:

In this problem we find four cases of two linear equations with two variables. There are different methods to solve the system, herein we must use elimination method to find the solution to each system of linear equations, which takes advantage of adding / subtracting linear equations and multiplying linear equations by scalars in order to get every solution set.

Case 1

x - y = 1

x + y = 3

First, add the two equations:

(x - y) + (x + y) = 1 + 3

2 · x = 4

x = 2

Second, determine the variable y:

y = 3 - x

y = 3 - 2

y = 1

Point (x, y) = (2, 1) is a solution of the system of equations.

Case 2

x + y = 1

x + y = 11

Subtract the second equation from the first one:

(x + y) - (x + y) = 1 - 11

0 = - 10 (CRASH!)

The system of linear equations has no solution.

Case 3

x + 4 · y = 11

x - 6 · y = 11

First, subtract the second equation from the first equation:

(x + 4 · y) - (x - 6 · y) = 11 - 11

10 · y = 0

y = 0

Second, determine the variable y:

x = 11 + 6 · y

x = 11 + 6 · 0

x = 11 + 0

x = 11

Point (x, y) = (0, 11) is a solution of the system of equations.

Case 4

- 3 · x + 3 · y = 6

x + 3 · y = 18

First, subtract the second equation from the first equation:

(- 3 · x + 3 · y) - (x + 3 · y) = 6 - 18

- 4 · x = - 12

x = 3

Second, determine the variable y:

3 · y = 18 - x

3 · y = 18 - 3

3 · y = 15

y = 5

Point (x, y) = (3, 5) is a solution of the system of equations.

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The work done on the chair that weighs 50 N  and lifted to a height of 0.5 m and carried 10 m across the room is 500 joules.

To calculate the work done on the chair, you can use the formula:

Work = Force × Distance × cos(θ)

where:

- Force is the amount of force applied to the chair (in newtons, N)

- Distance is the displacement or distance covered while carrying the chair (in meters, m)

- θ is the angle between the direction of the force and the direction of displacement (if the force is applied vertically upward, then θ = 0°, and the cosine of 0° is 1)

In this case, the force applied to the chair is its weight, which is given as 50 N. The distance covered is 10 m, and the angle between the applied force and the displacement is 0° (since the force is applied vertically upward, perpendicular to the horizontal displacement).

Therefore, the work done on the chair is:

Work = 50 N × 10 m × cos(0°)

     = 50 N × 10 m × 1

     = 500 N·m

The unit for work is the newton-meter (N·m), which is also known as the joule (J). Therefore, the work done on the chair is 500 joules.

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Answer:

The answer is Option A

Step-by-step explanation:

Start by dividing 54 by 6 which will give you 9

then divide b² by b^5 which will give you b³ at the denominator

then a^8÷a^-4

using indices...

=a^8-(-4)

=a^12

at the numerator

put everything together and you'll have...

9a^12/b³

A. \( \frac{9 \: {a}^{12} }{ {b}^{3} }\) ✅

\(\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}\)

\(54 {a}^{8} {b}^{2} \div 6 {a}^{ - 4} {b}^{5} \)

To solve the expression in a simpler way, single out the like terms.

Now, we have

\( \frac{54}{6} . \frac{ {a}^{8} }{ {a}^{ - 4} } . \frac{ {b}^{2} }{ {b}^{5} } \\ \\ = 9 \: {a}^{8 - ( - 4)} {b}^{2 - 5} \\ \\ (∵ \frac{ {a}^{m} }{ {a}^{n} } = {a}^{m - n} ) \\ \\ = 9 \: {a}^{8 + 4} {b}^{ - 3} \\ \\ = 9 \: {a}^{12} {b}^{ - 3} \\ \\ ( \: or \: ) \\ \\ = \frac{9 \: {a}^{12} }{ {b}^{3} } \\ \\ (∵ {a}^{ - m} = \frac{1}{ {a}^{m} } )\)

\(\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{!}}}}}\)

The length of the segment BP of the chord BD is 5.25 inches.

Given a circle Z.

AC and BD are the chords.

Two chords intersect at the point P.

By Intersecting Chords theorem, if two chords are intersected at a point, then the products of the lengths of segments are equal.

Using this theorem,

AP . PC = BP . PD

3.5 × 6 = 4 × BP

Solving,

BP = 5.25 inches

Hence the length is 5.25 inches.

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Answer:

17,19,21

Step-by-step explanation:

let the first odd number be "x"

formular : (x)+(x+2)+(x+4).

3x+6=57

3x=57-6

3x=51

x=51/3

x=17

apply the formular.

17,(17+2),(17+4)

17,19,21.

Answer:

t + 3

Step-by-step explanation:

Calculate the number of latex

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The expected instantaneous rate of change, denoted as r, for a geometric Brownian motion stock price (St) represents the average rate at which the stock price is expected to change at any given point in time. It is typically expressed as a constant or a deterministic function.

On the other hand, the expected return, denoted as r - 0.5σ^2, on the stock ln(St) over an interval of time [0,t] represents the average rate of growth or change in the logarithm of the stock price over that time period. It takes into account the volatility of the stock, represented by σ, and adjusts the expected rate of return accordingly.

The key difference between the two is that the expected instantaneous rate of change (r) for the stock price represents the average rate of change at any given moment, while the expected return (r - 0.5σ^2)t on the stock ln(St) over an interval of time considers the cumulative effect of volatility on the rate of return over that specific time period.

In other words, the expected instantaneous rate of change focuses on the average rate of change at a specific point in time, disregarding the impact of volatility. On the other hand, the expected return over a given interval of time accounts for the volatility in the stock price and adjusts the expected rate of return to reflect the effect of that volatility.

The expected instantaneous rate of change (r) for a geometric Brownian motion stock price represents the average rate of change at any given moment, while the expected return (r - 0.5σ^2)t on the stock ln(St) over an interval of time considers the cumulative effect of volatility on the rate of return over that specific time period.

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The radius of the smaller windmill with a circumference of about 376 feet is D. 60 feet.

The radius of a circle represents the distance from the center of the circle to any point on its circumference.

The radius can be determined by dividing the circumference by 2π.

r = C/2π

r = radius

C = circumference

π = pi (22/7 or 3.143)

The circumference of the large windmill = 660 feet

The diameter = 210 feet

The circumference of the small windmill = 376

The radius of the circumference = 376 ÷ 2(22/7)

= 60 feet

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The determinant of matrix A is 7.

The inverse of matrix A is:

`A^-1 = [-13/28 3/28 1/28; 13/20 -7/20 0; 7/20 -3/20 1/20]`

The obtained A^-1 is indeed the inverse of A.

The determinant of matrix A is 7.

Given matrix A = `[1 2 3; 2 -1 -1; 3 2 2]`.

(i) Determinant of A

To find the determinant of A, use the formula:

`det(A) = a11(A22A33 - A23A32) - a12(A21A33 - A23A31) + a13(A21A32 - A22A31)`

where a11, a12, a13, a21, a22, a23, a31, a32 and a33 are the elements of matrix A.

Substituting values,

`det(A) = 1(-1×2 - 2×2) - 2(2×2 - 3×2) + 3(2×(-1) - 3×(-1))`

= -10 + 2 + 15`

= 7

Therefore, the determinant of matrix A is 7.

(ii) Inverse of A

The inverse of matrix A can be found as follows:

`[A|I] = [1 2 3|1 0 0; 2 -1 -1|0 1 0; 3 2 2|0 0 1]`

`R2 = R2 - 2R1,

R3 = R3 - 3R1

=> [A|I] = [1 2 3|1 0 0; 0 -5 -7|-2 1 0; 0 -4 -7|-3 0 1]``

R2 = -R2/5,

R3 = -R3/4

=> [A|I] = [1 2 3|1 0 0; 0 1 7/5|2/5 -1/5 0; 0 1 7/4|3/4 0 -1/4]``

R1 = R1 - 3R2 - 2R3

=> [A|I] = [1 0 0|-13/28 3/28 1/28; 0 1 0|13/20 -7/20 0; 0 0 1|7/20 -3/20 1/20]`

Therefore, the inverse of matrix A is:

`A^-1 = [-13/28 3/28 1/28; 13/20 -7/20 0; 7/20 -3/20 1/20]`.

(iii) Verification of the obtained inverse

The product of A and A^-1 should give the identity matrix I.

Let's check:

`A × A^-1 = [1 2 3; 2 -1 -1; 3 2 2] × [-13/28 3/28 1/28; 13/20 -7/20 0; 7/20 -3/20 1/20]``

= [-13/28 + 39/28 + 21/28 3/28 - 6/28 + 6/28 1/28 - 1/28 + 2/28;``13/10 - 26/20 7/5 - 14/5 0 0; 21/10 - 39/20 7/10 - 14/10 1/5 - 2/5]``

= [1 0 0; 0 1 0; 0 0 1]`

The product of A and A^-1 gives the identity matrix I.

Hence, the obtained A^-1 is indeed the inverse of A.

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Answer:

  0.253 m/s

Step-by-step explanation:

You want to know the horizontal component of motion of a passenger riding a Ferris wheel when they are 1/27 of the way around the circle and their rate of rise is 0.06 m/s.

The wheel makes one revolution in 27 minutes, so the angular displacement is changing at the rate of (360°)/(27 min) = 13 1/3°/min.

After 1 minute, the passenger is following a path that has an angle of elevation of 13 1/3°.

The ratio of vertical speed to horizontal speed will be the tangent of the angle of elevation:

  Vv/Vh = tan(13 1/3°)

Then the horizontal speed will be ...

  Vh = Vv/tan(13 1/3°) = (0.06 m/s)/0.237004

  Vh ≈ 0.253 m/s

The passenger's horizontal motion is about 0.253 m/s.

Answer:

30 quarts

Step-by-step explanation:

4 quarts = 1 gallon

7.5 gallons * 4 quarts/ 1 gallon = 30 quarts

The system of equations has one solution. The two equations are intersecting lines.

The substitution method is one of the algebraic methods to solve simultaneous linear equations. It involves substituting the value of any one of the variables from one equation into the other equation.

We have the equations are:

y = 12 x + 2 ___eq.(1)

2y = x + 4 ____eq.(2)

You have to plug in y for 12x+2 in the second equation.

2(12x+2)=x+4

Simplify the equation:

24x + 4 = x + 4

Subtract 24x from each side

4 = -23x+4

Subtract 4 from each side

0 = 23x

Divide each side by 23

x=0

Now, plug in 0 to one equation.

y=12(0)+2

y=2

The lines intersect at one point, (0,2)

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Answer:

(5x+4)(x+3)

Step-by-step explanation:

hope this helps :)

Answer:

5x2+19x+12

=(5x+4)(x+3)

Answer:

no solutions

Step-by-step explanation:

We can solve this system using elimination. In this case, we can eliminate x and y by subtracting the two equations:

0=15-12

0=3

This is not true, meaning the system does NOT have any solutions.

OR

The equation for a line is:

y=mx+b

m: slope

b: y-intercept

Here we can see the two lines have the same slope, meaning they are parallel. If they are parallel, they do not intersect which means there is no solution.

The volume of a cinder cone volcano will be 110872040 cubic feet.​

The volume of a cone is defined as the amount of space occupied by a cone in a three-dimensional plane.

The volume of the cone (V) = 1/3 πhr²

Given,

Radius of cone (r) = 1100/2 = 550 feet

Height of cone (h) = 350 feet

The volume of a cinder cone volcano = 1/3 πhr²

Substitute the values of h and r,

The volume of a cinder cone volcano = 1/3 × 3.14× (550)² × (350)

The volume of a cinder cone volcano = 110872040 cubic feet.​

Thus, the volume of a cinder cone volcano will be 110872040 cubic feet.​

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Answer:

option 6b):) is correct

Answer:

180/360 = 1/2 = 50/100 = 50%

Step-by-step explanation:

Answer:

50%

Step-by-step explanation:

A full circle is 360°.

\(\frac{180}{360} =\frac{1}{2} =\frac{50}{100} =\) 50%

Additionally, it notes that the first digit of a six-digit number must be nonzero. The options provided are a, b, c, d, and e.

To determine the number of six-digit numbers, we need to consider the range of possible values for each digit. Since the first digit cannot be zero, there are 9 choices (1-9) for the first digit. For the remaining five digits, each can be any digit from 0 to 9, resulting in 10 choices for each digit.

Therefore, the total number of six-digit numbers is calculated as 9 * 10 * 10 * 10 * 10 * 10 = 900,000.

To determine how many of these six-digit numbers contain the digit 5, we need to fix one of the digits as 5 and consider the remaining five digits. Each of the remaining digits has 10 choices (0-9), so there are 10 * 10 * 10 * 10 * 10 = 100,000 numbers that contain the digit 5.

In summary, there are 900,000 six-digit numbers in total, and out of these, 100,000 contain the digit 5. The options a, b, c, d, and e were not mentioned in the question, so they are not applicable to this context.

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