what is 0.6 as a fraction

The rocket will take approximately 7.5 seconds to reach the ground after reaching its maximum height.

The equation h = -16t^2 + 120t + 200 represents the height of the rocket at time t seconds. To find the time it takes for the rocket to reach the ground, we need to determine when the height is equal to zero. This occurs when the rocket touches the ground. Setting the equation equal to zero, we get -16t^2 + 120t + 200 = 0. By solving this quadratic equation, we find two solutions: t ≈ 0.74 seconds and t ≈ 7.5 seconds. Since time cannot be negative, we discard the 0.74 seconds solution. Therefore, it will take approximately 7.5 seconds for the rocket to reach the ground after reaching its maximum height.

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The two numbers are 28 and 36

The problem can be solved using algebraic equations and methods, specifically using the principles of solving systems of equations and factoring quadratic equations.

To solve for the two numbers use their product and difference and form two equations as follows and solve the two numbers

Here we have

The product of two numbers is 1008

The difference between the two numbers is 18  

Let 'x' and 'y' be the two numbers

From the data,

=> xy = 1008 --- (1)

=> x - y = 18

=> x = 18 + y ---- (2)

From (1) and (2)

=>  (18 + y)(y) = 1008

=>  y² + 18y = 1008

=>  y² + 18y - 1008 = 0  

Now factorize the above equation for the value of y

=>  y² - 28y + 36y  - 1008 = 0    [ Splitting middles term ]

=>  y [y - 28] + 36 [y - 28] = 0

=>  [ y - 28] [ y + 36] = 0  

=>  y - 28 = 0

=>  y = 28

=> y + 36 = 0

=> y = - 36

Here y cannot be negative hence take y = 28

From (1) x(28) = 1008

=> x = 1008/28 = 36

Therefore,

The two numbers are 28 and 36

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From the data points given the linear equation in slope-intercept form is y = -1/2x + 4.

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

The first two data points are - (-3,5.5) and (-1,4.5)

The slope-intercept form of the equation is -

y = mx + b

m represents the slope of the linear equation.

To find the value of m use the formula -

(y2 - y1)/(x2 - x1)

Substitute the values into the equation -

(4.5 - 5.5)/[(-1) - (-3)]

Use the arithmetic operation of subtraction -

(-1)/(-1 + 3)

-1 / 2

So, the slope m is m = -1/2

Now, the equation becomes y = -1/2x + b

To find the value of b substitute the  values of x and y in the equation -

5.5 = -1/2(-3) + b

5.5 = 3/2 + b

5.5 = 1.5 + b

b = 5.5 - 1.5

b = 4

So, now the equation becomes - y = -1/2x + 4

The graph for the equation is plotted.

Therefore, the equation is y = -1/2x + 4.

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We have to find the area of the region between y=x^(1/2) and y=x^(1/3) for 0≤x≤1.

To find the area of the region between y=x^(1/2) and y=x^(1/3) for 0≤x≤1, we have to integrate x^(1/2) and x^(1/3) with respect to x. That is, Area = ∫0¹ [x^(1/2) - x^(1/3)] dx= [2/3 x^(3/2) - 3/4 x^(4/3)] from 0 to 1= [2/3 (1)^(3/2) - 3/4 (1)^(4/3)] - [2/3 (0)^(3/2) - 3/4 (0)^(4/3)]= 0.2857 square units

Therefore, the area of the region between y=x^(1/2) and y=x^(1/3) for 0≤x≤1 is 0.2857 square units. Note: The question  but the answer has been provided in the format requested.

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Answer:

Option 3

Step-by-step explanation:

If you multiply the numbers inside the root of option 3, you get the equation

2 * 2 * 3 * 3 * 5

Which equals 180

Replacing the root sign will show that you have the right answer.

The requreid surface area of the sphere with a radius of 19 cm is 4536.46 cm².

To determine the exact surface area of the sphere with a diameter of 19 cm.

The surface area of the sphere is given as,
Surface area of the sphere = 4πr²

Substitute the value of the radius, r = 19 in the above formula,
Surface area of the sphere = 4*3.14*19²
                                             = 4536.46 cm²

Thus, the requreid surface area of the sphere with a radius of 19 cm is 4536.46 cm².

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The answers, rounded to the appropriate number of significant figures, are as follows:

(a) 1.088 ×\(10^2\)

(b) 2.132

(c) 1.3331 ×\(10^1\) and

(d) 1.05.

Let's calculate the answers to the given operations using the appropriate number of significant figures.

(a) 8.370×1.3×10

To perform this multiplication, we multiply the decimal numbers and add the exponents of 10:

8.370 × 1.3 × 10 = 10.881 × 10 = 1.0881 × \(10^2\)

Since the original numbers have four significant figures, we round the final answer to four significant figures:

1.088 × \(10^2\)

(b) 4.265/2.0

For division, we divide the decimal numbers:

4.265 ÷ 2.0 = 2.1325

Since both numbers have four significant figures, the answer should be rounded to four significant figures:

2.132

(c) (1.2588×\(10^3\))×(1.06×\(10^-^2\))

To multiply these numbers, we multiply the decimal numbers and add the exponents:

(1.2588 × \(10^3\)) × (1.06 × \(10^-^2\)) = 1.333128 × \(10^1\)

Since the original numbers have five significant figures, we round the final answer to five significant figures:

1.3331 × \(10^1\)

(d) \((1.11)^(^1^/^2^)\)

To calculate the square root, we raise the number to the power of 1/2:

\((1.11)^(^1^/^2^)\)= 1.0524

Since the original number has three significant figures, the answer should be rounded to three significant figures:

1.05

It's important to note that the significant figures in a result are determined by the original data and the operations performed. The final answers provided above reflect the appropriate number of significant figures based on the given information and the rules for significant figures.

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Answer:

x = 23

7x - 11 = 4x + 58

(7x - 4x) - 11 = (4x - 4x) + 58

3x - 11 = 58

3x (- 11 + 11) = 58 + 11

3x = 69

3x/3 = 69/3

x = 23

Answer:

x=23°

Step-by-step explanation:

(7x - 11)=(4x + 58)

7x-4x=58+11

3x=69

x=23

Answer:

578 cm^2

Step-by-step explanation:

The surface area is given by one circle of radius 4 (the other is missing!), plus a "rectangle" (the lateral surface) of sides 21 and \(2\pi \times 4\) (the length of the circumference at the base). Adding them up we get:\(\pi \times4^2 + 21\times 2\pi\times4 = 184\pi \approx 578 cm^2\)

Answer:

column 1

5 × 98

33 x 12

3 x 6

100 x .1

8 x (3/4)

3×7

4×2

column 2

5(100-2)

33(10+2)

3(10-4)

100(0.06+0.04)

8(1/2+1/4)

3(3+4)

4(6-4)

column 3

5×100-5×2

33×10+33×2

3×10-3×4

100×0.04×100×0.06

8×1/2+8×1/4

3×3+3×4

4×6-4×4

column 4

500-10

330+66

30-12

4+6

4+2

9+12

24-16

value

490

396

18

10

6

21

8

the last row could also be 8x1

Answer:

You can say x to the power of 2 or you can say x squared.

Hope that answers your question!

The solution of the system of linear equations determines if the system has no solution, one solution, or an infinite number of solutions

2·x - 3·y = 3 and -4·x + 6·y = 6

3·x - 2·y = 3 and x + 2·y = 5

-8·x + 12·y = -12 and 2·x - 3·y = 3

y = -x + 2 and y = 3·x - 2

A system of equations is a set of two or more equations that are formed by the same variable.

Each of the equations are solved as follows to determine whether it has no solution, one solution, or an infinite number of solutions

1. 2·x - 3·y = 3 and -4·x + 6·y = 6

Multiplying the first equation by 2, we get; 4·x - 6·y = 6.

Adding the above equation to the second equation,we get;

4·x - 6·y + (-4·x + 6·y) = 6 + 6 = 12

0 = 12 (False)

Therefore, the system has no solution

2. 3·x - 2·y = 3 and x + 2·y = 5

Adding the two equations, we get;

3·x - 2·y + (x + 2·y) = 3 + 5 = 8

4·x = 8

x = 8/4 = 2

Substituting x = 2 into the second equation, we get;

x + 2·y = 5

2 + 2·y = 5

2·y = 5 - 2 = 3

y = 3/2 = 1.5

y = 1.5

Therefore, the system has one solution

3. -8·x + 12·y = -12 and 2·x - 3·y = 3

Multiplying the second equation by 4, we get; 8·x - 12·y = 12

Adding the product of the second equation and 4 to the first equation we get;

8·x - 12·y + (-8·x + 12·y) = 12 + (-12) = 0

0 = 0

Therefore, the system has infinite number of solutions

4. y = -x + 2 and y = 3·x - 2

Substituting y = -x + 2 into the second equation, we get;

-x + 2 = 3·x - 2

3·x - 2 = -x + 2

3·x + x = 2 + 2 = 4

4·x = 4

x = 4/4 = 1

x = 1

y = -x + 2

y = -1 + 2 = 1

y = 1

Therefore, the system has one solution.

Therefore, the first system has no solution, the second system has one solution, the third system has an infinite number of solutions, and the fourth system has one solution.

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Answer:

$55.13

Step-by-step explanation:

50 * 1.05 = 52.5

We do this step twice because the interest is for 2 years.

52.5 * 1.05 = 55.125

This rounds up to 55.13, your final answer!

Answer:

= 40.5π square inches

Step-by-step explanation:

Oatmeal is packaged in a right circular cylindrical container that has a radius of 1.5 inches and a height of 12 inches. What is the surface area of this container in terms of π?

The formula for the surface Area of a cylinder = 2πr( r + h)

r = 1.5 inches

h = 12 inches

Hence,

2 × π × 1.5( 1.5 + 12)

3π(13.5)

= 40.5π square inches

The surface area of the cylinder is

= 40.5π square inches

To determine the exact concentration of the solution made, one can divide the mass of the solute with the volume of the solution.

A solution is the substance formed by the mixture of solute in solvent. The solute may or may not be dissolved in the solution. One can determine the exact concentration of the solution if the mass of solute added in the specific volume of solution is known. If the solution is made by someone else, then its concentration can be determined by process of titration.

The concentration of a solution is expressed in the form of moles or grams per unit liter. If the solution is unknown and only its dissolved chemical is known, then titration will help in determining the closest value of concentration if performed without human error. In titration, the use of glassware that that is more precise than the flasks, beakers, and graduated cylinders are used.

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Refer to complete question below:

How do we determine concentration a solution? If it is a solution that we have made up, we can readily do the calculations required. But what if it is a solution that someone else has made? What technique can be used to gather information about a solution that we are given with no other information than the name of the chemical dissolved.

The salary of Kayden after 4 years will be $ 221,952.00

The annual salary is $48000

Salary rise is $4500

The rate of the this salary can be found out by \(\frac{48,000- 4500}{48000}\)

= \(\frac{43,500}{48,000}\) × 100

= 90.6 %

The time interval is 4 years

thus the prinicipal amount is given as $48000.

thus simple interest is P × R × T/ 100

which when calculated will give us

simple interest = $221,952.00

$221,952.00 is the total amount accrued from simple interest on a principal of $48,000.00 at a rate of 90.6% per year for 4 years. This includes both principal and interest.

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The Answer is x2=4, x1=0, and x3=0; S1=1, S2=0. Therefore, S2=0 is basic and S1=1 is nonbasic. x1=0 is basic and X1=6, X2=4, and X3=0 are nonbasic.

The basic feasible solution from the given tableau X1 X2 Хз S1 S2 Z 0 0160 6 -1 1 1 0 148 2 4 0 -6 -10 -5 0 0 1143 is:x2=4, x1=0, and x3=0; S1=1, S2=0. Therefore, S2=0 is basic and S1=1 is nonbasic. x1=0 is basic and X1=6, X2=4, and X3=0 are nonbasic. The basic feasible solution is achieved when all the constraints in a linear programming problem are met. The constraints can be in the form of equations or inequalities. The linear programming problem provides the optimal values for a given objective function. The optimal values are determined by the constraints that are involved in the problem. In the given problem, X2 and S1 are basic, and X1, Xx3, and S2 are nonbasic. Indicate which variables are basic and which are nonbasic.The variables that are basic and nonbasic can be calculated from the tableau. The basic variables are those that have the coefficients of 1 in the final column. The nonbasic variables are those that have the coefficients of 0 in the final column. Therefore, x2=4, x1=0, and x3=0; S1=1, S2=0. Therefore, S2=0 is basic and S1=1 is nonbasic. x1=0 is basic and X1=6, X2=4, and X3=0 are nonbasic.

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Answer:

b is the right answer

Step-by-step explanation:

Answer:

Undefined

Step-by-step explanation:

Since all of the x inputs are 0, the slope will always have a 0 in the denominator, which means it is undefined.

Using a sample mean of a specific size would be beneficial in situations where it is impractical or impossible to gather data from an entire population. By taking a sample and calculating the mean, we can make reliable inferences about the population mean, saving time and resources.

1. Limited Resources: In some cases, it may be infeasible or too costly to collect data from an entire population. For example, if you want to determine the average height of all people in a country, it would be impractical to measure every single person. Instead, you can select a representative sample.

2. Time Constraints: Conducting a study on an entire population might require a significant amount of time. For time-sensitive situations, using a sample mean of a specific size allows for quicker data collection and analysis. This is especially true when immediate decisions or interventions are necessary.

3. Accuracy: Sampling can provide accurate estimates of the population mean when done properly. By ensuring that the sample is representative and randomly selected, statistical techniques can be applied to estimate the population mean with a desired level of confidence.

4. Cost-Effectiveness: Collecting data from an entire population can be expensive and time-consuming. By using a sample, you can significantly reduce the costs associated with data collection, analysis, and other resources required for a full population study.

5. Feasibility: In certain cases, accessing the entire population might be logistically challenging. For instance, if you want to determine the average income of all households in a country, it would be difficult to gather data from every single household. A representative sample can provide reliable estimates without the need for accessing the entire population.

In conclusion, utilizing a sample mean of a specific size is beneficial when resources, time, accuracy, cost, and feasibility considerations make it impractical to collect data from an entire population. By employing statistical techniques on a well-designed sample, we can make valid inferences about the population mean, saving resources while still obtaining reliable results.

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Linear equation is equation in which each term has at max one degree. The correct option is B.

Linear equation is equation in which each term has at max one degree. Linear equation in variable x and y can be written in the form y = mx + c

Linear equation with two variables, when graphed on cartesian plane with axes of those variables, give a straight line.

Given the When the car begins, it is 200 miles from Kingston. After 2 hours, it is 80 miles from Kingston. Therefore, the speed of the car can be written as,

m = (200-80) miles / (0-2)hours = -60miles per hour

Since, the total distance is 200 miles, and the relation between the distance and the time is linear we can write the function that describes the car's distance from kingston is,

y = -60x + 200

Hence, the correct option is B.

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To find dy, we need to differentiate the given function y = x² with respect to x. Taking the derivative will give us the rate of change of y with respect to x.

dy/dx = 2x

Therefore, dy = 2x dx

Now, let's consider the second part of the question.

The price p (in dollars) and the demand x for a particular clock radio are related by the equation x = 5000 - 50p.

To express the price p in terms of the demand x, we can rearrange the equation as follows:

x = 5000 - 50p

Rearranging for p, we get:

50p = 5000 - x

Dividing both sides by 50, we have:

p = (5000 - x) / 50

So, the price p in terms of the demand x is given by p = (5000 - x) / 50.

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Step-by-step explanation:

f(x)=3x+5

3*6+5=23

f(0)=3*0+5=5

f(1)=3*1+5=8

Answer:

1

Step-by-step explanation:

i think

Answer:

1/2, 1/10, and 1/14 s the answer.

Step-by-step explanation:

The first set of numbers are integers, the second set is whole numbers, the fourth set is imaginary numbers, and the fifth set is irrational numbers. The third set is rational because it can be written as a fracton but not integers because they aren't whole numbers or their opposites.

For the parameterizations r(t) = (t, 3 cos t, 3 sin t) and r(r) = (t^2, sin t - t cos t, cos t + t sin t), the unit tangent vectors are T(t) = (1/√10, -3 sin t / √10, 3 cos t / √10) and T(t) = (2t / √(4t^2 + 2), (cos t + t sin t) / √(4t^2 + 2), (-sin t + t cos t) / √(4t^2 + 2)) respectively, and the curvature is κ(t) = 3 / 10 and κ(t) = (2 - 4t^2) / (4t^2 + 2)^(3/2) respectively.

To find the unit tangent vector T(t) and unit normal vector N(t) for the given parameterizations, and subsequently calculate the curvature using Formula 9, we'll evaluate them for both cases:

(b) For r(t) = (t, 3 cos t, 3 sin t):

Calculate the first derivative r'(t) = (1, -3 sin t, 3 cos t).

Compute the magnitude of r'(t): ||r'(t)|| = √(1^2 + (-3 sin t)^2 + (3 cos t)^2) = √(1 + 9 sin^2 t + 9 cos^2 t) = √(10).

Obtain the unit tangent vector: T(t) = r'(t) / ||r'(t)|| = (1/√10, -3 sin t / √10, 3 cos t / √10).

Calculate the derivative of T(t): T'(t) = (0, -3 cos t / √10, -3 sin t / √10).

Calculate the magnitude of T'(t): ||T'(t)|| = √((-3 cos t / √10)^2 + (-3 sin t / √10)^2) = 3 / √10.

Compute the curvature using Formula 9: κ(t) = ||T'(t)|| / ||r'(t)|| = (3 / √10) / √10 = 3 / 10.

Therefore, for r(t) = (t, 3 cos t, 3 sin t), the unit tangent vector T(t) is (1/√10, -3 sin t / √10, 3 cos t / √10), and the curvature κ(t) is 3 / 10.

For r(r) = (t^2, sin t - t cos t, cos t + t sin t), t > 0:

Calculate the first derivative r'(t) = (2t, cos t + t sin t, -sin t + t cos t).

Compute the magnitude of r'(t): ||r'(t)|| = √((2t)^2 + (cos t + t sin t)^2 + (-sin t + t cos t)^2) = √(4t^2 + cos^2 t + 2t cos t sin t + sin^2 t + sin^2 t - 2t cos t sin t + t^2 cos^2 t) = √(4t^2 + 2).

Obtain the unit tangent vector: T(t) = r'(t) / ||r'(t)|| = (2t / √(4t^2 + 2), (cos t + t sin t) / √(4t^2 + 2), (-sin t + t cos t) / √(4t^2 + 2)).

Calculate the derivative of T(t): T'(t) = ((2 - 4t^2) / (4t^2 + 2)^(3/2), (-sin t + t cos t + t cos t + t^2 sin t) / √(4t^2 + 2), (-cos t + t sin t - t sin t + t^2 cos t) / √(4t^2 + 2)).

Calculate the magnitude of T'(t): ||T'(t)|| = √(((2 - 4t^2) / (4t^2 + 2)^3

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Answer:

Here you go!

Step-by-step explanation:

Answer:

If circles A and B are congruent, then AC, CD, DB, and BA are all congruent since they are all radii. We then have:

ACDB is a rhombus.

ADB is an equilateral triangle.

CD is perpendicular to AB.

CD bisects AB.

Answer:

slope: 1/2

Step-by-step explanation:

Finding the slope:

(8,4)      (4,2)

(x1, y1)   (x2, y2)

Subtract the x values and subtract the y values. (x1 - x-2) and (y1 - y2)

8 - 4 = 4

4 - 2 = 2

The slope is written as rise over run or y over x.

So, 2/4

Simplify: 1/2

Answer:

the slope is 1/2!

Step-by-step explanation:

(2-4)/(4-8) = -2/-4 = 1/2

When finding the slope of a line you need to do the rise over run!

Answer:

Answer:

r = 6 in

Step-by-step explanation:

The volume of a cylinder of radius r and height or length h is

V = πr²h.

Here, we need to solve for the radius; we get:

     V

------------- = r²

     πh

                                       904.23 in³

This works out to    r² = ----------------- = 35.97 in²

                                            π(8 in)

Finally, take the square root of this result to find the radius, r:

r = √35.97 in² = 6 inches