The half-life of carbon-14 is 5,730 years. Express the amount of
carbon-14 remaining as a function of time, t. In addition, there is
a bone fragment is found that contains 30% of its original
carbon-1

Answer:

2^2 * 3^3

Step-by-step explanation:

108 = 2*2*3*3*3

= 2^2 * 3^3.

Answer:

(4,2)

Step-by-step explanation:

Answer: x = 0

Step-by-step explanation:

The distance is the same that was covered.

Distance is speed multiplied by time.

Mr O takes 30 minutes and Mr Gordon takes 1 hour.

So the speed of Mr O is given by:

Convert the speed in meter per second.

The speed of mr G is:

So the difference between the speeds is:

So Mr O is 2.9167 m/s faster than Mr Gordon.

The formula we need to use is given above. In this formula, we will substitute the desired values. Let's start.

A) First, we can start by analyzing the first premise. The team has \(8\) wins and \(5\) losses. It earned \(8 \times 3 = 24\) points in total from the matches it won and \(1\times5=5\) points in total from the matches it drew. Therefore, it earned \(24+5=29\) points.

B) After \(39\) matches, the team managed to earn \(54\) points in total. \(12\) of these matches have ended in draws. Therefore, this team has won and lost a total of \(39-12=27\) matches. This number includes all matches won and lost. In total, the team earned \(12\times1=12\) points from the \(12\) matches that ended in a draw.

\(54-12=42\) points is the points earned after \(27\) matches. By dividing \(42\) by \(3\) ( because \(3\) points is the score obtained as a result of the matches won), we find how many matches team won. \(42\div3=14\) matches won.

That leaves \(27-14=13\) matches. These represent the matches team lost.

Finally, the answers are below.

\(A)29\)
\(B)13\)

Answer:

  a) 29 points

  b) 13 losses

Step-by-step explanation:

You want to know points and losses for different teams using the formula P = 3W +D, where W is wins and D is draws.

The number of points the team has is ...

  P = 3W +D

  P = 3(8) +(5) = 29

The team has 29 points.

You want the number of losses the team has if it has 54 points and 12 draws after 39 games.

The number of wins is given by ...

  P = 3W +D

  54 = 3W +12

  42 = 3W

  14 = W

Then the number of losses is ...

  W +D +L = 39

  14 +12 +L = 39 . . . substitute the known values

  L = 13 . . . . . . . . . . subtract 26 from both sides

The team lost 13 games.

__

Additional comment

In part B, we can solve for the number of losses directly, using 39-12-x as the number of wins when there are x losses. Simplifying 3W +D -P = 0 can make it easy to solve for x. (In the attached, we let the calculator do the simplification.)

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The probability that sample mean will lie between 0.2245 and 0.2260 mm is 0.7079.

Normal Distribution:

The mean of the sample means is equal to the population when the distribution is normal and the standard deviation of the sample means is the ratio of the population standard deviation divided by the square root of the sample size.

The mean,

μ=0.2250 mm

The standard deviation,

σ=0.0042 mm

The sample size,

n=40

The probability that sample mean will lie between 0.2245 and 0.2260 mm:

P(0.2245<x<0.2260) = P(Z<1.51)−P(Z<−0.75)

P(0.2245<x<0.2260)  = 0.7079

Hence , the probability that sample mean will lie between 0.2245 and 0.2260 mm is 0.7079.

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Answer:

2(x + 1.7) = 42.7

Step-by-step explanation:

Answer:

82 or more

Step-by-step explanation:

Answer:

Step-by-step explanation:

average for 3 tests >90

total for 3 tests>90×3

or total for 3 tests>270

total of 2 tests=92+96=188

so score in third test >(270-188)

or >82

Answer:

.38

Step-by-step explanation:

1/16 * 6 = 6/16

Divide the top and bottom by 2

3/8

.375

Round to 2 decimal places

.38

Answer:

A

   8

   6                                                                               * negative times a negative

  -5.9                                                                              is a positive *

× -9.7

_______

   4.13

+ 53.10

_______

 57.23

The ratio of basketballs to baseballs is 5 : 4 means out of 9 balls there are 5 basketballs and 4 baseballs.

A ratio is a comparison between two similar quantities in simplest form.

Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.

Written as quantity₁ ∝ quantity₂ or quantity₁ = kquantity₂

In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.

quantity₁ ∝ 1/quantity₂.

quantity₁ = K.1/quantity₂.

Given, The ratio of basketballs to baseballs is 5 : 4.

this means out of 9 balls there is 5 basketballs and 4 baseballs.

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The portfolio weights for stock A and stock B are approximately 55.69% and 44.31%, respectively.

To calculate the portfolio weights for stock A and stock B, we need to determine the total value of the portfolio and the proportion of each stock's value within that total.

The total value of the portfolio can be calculated as follows:

Total value = (Number of shares of stock A × Price per share of stock A) + (Number of shares of stock B × Price per share of stock B)

Total value = (135 × $84) + (110 × $82)

Total value = $11,340 + $9,020

Total value = $20,360

Now, we can calculate the portfolio weights for each stock:

Weight of stock A = (Value of stock A ÷ Total value) × 100%

Weight of stock A = (($84 × 135) ÷ $20,360) × 100%

Weight of stock A = $11,340 ÷ $20,360

Weight of stock A ≈ 0.5569 or 55.69%

Weight of stock B = (Value of stock B ÷ Total value) × 100%

Weight of stock B = (($82 × 110) ÷ $20,360) × 100%

Weight of stock B = $9,020 ÷ $20,360

Weight of stock B ≈ 0.4431 or 44.31%

Therefore, the portfolio weights for stock A and stock B are approximately 55.69% and 44.31%, respectively.

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Answer:

-28

Step-by-step explanation:

We have the equation \(5x-3y\) and are given that \(x=-2, y=6\).  To solve this equation, we simply replace the variables with their real value.  In action, this would be \(5(-2)-3(6)=-10-18=-28\).

The argument is valid. The argument is valid based on the direct truth-table method.

To test the validity of the argument, we can use the direct truth-table method. Let's break down the argument and construct the truth table for the given premises and the conclusion:

Premises:

G ⊃ H

R ≡ G

~H v G

Conclusion:

R • H

Constructing the truth table:

We have three propositions: G, H, and R. Each proposition can have two truth values, true (T) or false (F). Therefore, we need 2^3 (8) rows in the truth table to evaluate all possible combinations.

By evaluating the truth table, we find that in all rows where the premises (1, 2, 3) are true, the conclusion (R • H) is also true. There is no row where the premises are true, but the conclusion is false. Therefore, the argument is valid.

The argument is valid based on the direct truth-table method. This means that if the premises (G ⊃ H, R ≡ G, ~H v G) are true, then the conclusion (R • H) must also be true.

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Based on the analysis, discuss any differences observed between the two training methods. Discuss the analysis and findings. Reflect on the results of the analysis.

However, I can guide you on how to approach the analysis and provide you with a general outline of the steps you can follow:

Read the case problem

Review the case problem from Chapter 11 of the ebook related to the Air Force training program.

Perform the analysis

a) Run the F-test two-sample for variances:

Using Excel's Data Analysis ToolPak, follow the instructions from the provided video to perform an F-test two-sample for variances on the training data file.

b) Summarize the training time data:

Calculate appropriate descriptive statistics (e.g., mean, standard deviation) for each training method. Compare the summary statistics to identify similarities or differences between the two methods.

c) Conduct a hypothesis test on the difference between population means:

Perform a hypothesis test (e.g., independent t-test) to assess whether there is a statistically significant difference between the population means of the two training methods. Interpret and discuss the findings.

d) Calculate standard deviation and variance:

Compute the standard deviation and variance for each training method. Compare the values to gain insights into the variability within each method.

e) Conduct a hypothesis test on the equality of population variances:

Perform a hypothesis test (e.g., F-test) to determine if there is a significant difference in population variances between the two training methods. Analyze the results and discuss the findings.

f) Draw conclusions and provide recommendations:

Based on the analysis, discuss any differences observed between the two training methods. Provide a conclusion and recommendation on which training method appears to be more effective. Justify your recommendation with supporting evidence from the analysis.

Discuss the analysis and findings

Reflect on the results of the analysis. Identify any surprising or noteworthy findings. Formulate recommendations based on the findings and include specific details from the managerial report to support your recommendations.

Please note that without access to the actual data or case problem, the guidance provided is general in nature. It's important to adapt the steps to the specific case problem and data provided in the ebook.

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\(D = \frac{1}{2} dk\)

\(k = \frac{2D}{d} \)

Answer:

well 126/3 is 42. if 1/6 of those 42 kids that coach B had, 7 of those kids had medication. because 42 divided by 6 is 7 and only 1/6 of the kids had medication. (didn't understand exactly what you meant, hope this helps)

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let's call the two natural numbers x and y. We know that:

x + y = 45 (Equation 1)

xy = 4x^2 (Equation 2)

We can solve Equation 1 for y:

y = 45 - x

Then, we can substitute this into Equation 2:

x(45 - x) = 4x^2

Expanding and simplifying:

45x - x^2 = 4x^2

5x^2 - 45x = 0

We can factor out x:

x(5x - 45) = 0

This gives us two possible solutions: x = 0 or x = 9. Since we are dealing with natural numbers, x cannot be 0. Therefore, x = 9.

We can substitute this back into Equation 1 to find y:

9 + y = 45

y = 36

So the two natural numbers are 9 and 36.

Let's assume that the two natural numbers are x and y, where x is the smaller number.

From the problem, we know that:

x + y = 45 ... (1) (The sum of the two numbers is 45)

xy = 4x^2 ... (2) (The product of the two numbers is four times the square of the lesser number)

We can rearrange equation (1) to get:

y = 45 - x

Substituting this into equation (2), we get:

x(45 - x) = 4x^2

Expanding the left side and simplifying, we get:

45x - x^2 = 4x^2

Rearranging and simplifying further, we get a quadratic equation:

5x^2 - 45x = 0

We can factor out x to get:

x(5x - 45) = 0

So, either x = 0 (which is not a natural number) or 5x - 45 = 0.

Solving for x, we get:

5x - 45 = 0

5x = 45

x = 9

So the smaller number is 9, and using equation (1), we can find that the larger number is:

y = 45 - x = 45 - 9 = 36

Therefore, the two natural numbers are 9 and 36.

Hello! :)

Here is a graph for x < -10/3 or x > 2/3.

THEDIPER

The sum of the numbers 3+6+9+12+....+150 is 3825. To find the sum of an arithmetic series, you can use the formula:

Sum = (n * (a1 + an)) / 2

where n is the number of integers, a1 is the first integer, and an is the last integer.

In this case, the series is 3, 6, 9, ..., 150, and it's an arithmetic series with a common difference of 3. To find the number of integers (n) in the series, use the formula:

n = ((an - a1) / common difference) + 1

n = ((150 - 3) / 3) + 1 = (147 / 3) + 1 = 49 + 1 = 50

Now, use the sum formula:

Sum = (n * (a1 + an)) / 2
Sum = (50 * (3 + 150)) / 2
Sum = (50 * 153) / 2
Sum = 7650 / 2
Sum = 3825

So the sum of the given series is 3825.

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The derivative of f(x) is [cot(2x) * cot(x) - csc(2x)] / csc(x).

To find the derivative of f(x) = cot(2x) / csc(x), we can use the quotient rule and the derivatives of cot(x) and csc(x).

The quotient rule states that if we have a function h(x) = g(x) / k(x), then the derivative of h(x) is given by:

h'(x) = (g'(x) * k(x) - g(x) * k'(x)) / (k(x))^2

Let's apply the quotient rule to f(x) = cot(2x) / csc(x).

First, we need to find the derivatives of cot(2x) and csc(x).

The derivative of cot(x) is given by:

(d/dx) cot(x) = -\(csc^{2}\) (x)

The derivative of csc(x) is given by:

(d/dx) csc(x) = -csc(x) * cot(x)

Now, let's substitute these derivatives into the quotient rule formula:

f'(x) = [(d/dx) cot(2x) * csc(x) - cot(2x) * (d/dx) csc(x)] / \((csc(x))^{2}\)

Substituting the derivatives:

f'(x) = [-\(csc^{2}\) (2x) * csc(x) - cot(2x) * (-csc(x) * cot(x))] /  \((csc(x))^{2}\)

Simplifying:

f'(x) = [-\(csc^{2}\) (2x) * csc(x) + csc(x) * cot(2x) * cot(x)] /  \((csc(x))^{2}\)

Combining terms:

f'(x) = [csc(x) * (cot(2x) * cot(x) - csc(2x))] /  \((csc(x))^{2}\)

Simplifying further:

f'(x) = [cot(2x) * cot(x) - csc(2x)] / csc(x)

Therefore, the derivative of f(x) = cot(2x) / csc(x) is:

df/dx = [cot(2x) * cot(x) - csc(2x)] / csc(x)

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Answer:

2334

Step-by-step explanation:

hi

Answer:

4.92 ft

Step-by-step explanation:

The ladder is the hypotenuse of a right triangle

adjacent  leg / hypotenuse =  cos 75

cos 75 = adjacent leg / 19

19 cos 75 ° = adjacent leg = 4.92 ft

Answer:

(A)All real solutions

Step-by-step explanation:

Given the function g(x) shown on the graph

One of the points of the parabola is  (-3.5, 0).

The point x=-3.5 is one of the solution of the parabola since it intersects the x-axis at that point.

The other point of intersection is on the positive side between 0 and 1.

Therefore, g(x) has two solutions: One negative real number and one positive real  number.

Therefore, g(x) has all real solutions.

The correct option is A.

Answer:

All solutions that lie on g(x)

Step-by-step explanation:

I took the test and that's the correct answer...

Answer:

my answer is A

Step-by-step explanation:

if you work out the equation where you know that at the x intercept y=0 you will find A to be true

Data types provide the information to the runtime about how much space is required in the memory. Datatypes helps to allocate memory. In OOPs bases programming languages it also helps to decide where memory should be allocated like heap and stack memory.

Data types allow a compiler to allocate the right memory space for a variable, and also let it perform type checking, marking sure the program uses the variables correctly per their defined type.

A data type is an attribute associated with a piece of data that tells a computer system how to interrupt its value. Understanding the data types ensures that data is collected in the preferred format and the value of each property is as expected.

Choosing the right data types for your tables, stored procedures, and variables not only improves performance by ensuring a correct execution plan, but it also improves data integrity by ensuring that the correct data is stored within a database.

Data type and length are the most fundamental integrity constraints applied to data in a database. Simply by specifying the data type for each column when a table is created, DB2 automatically ensures that only the correct type of data is stored in that column. Processes that attempt to insert or update the data to a non-conforming value will be rejected. Furthermore, a maximum length is assigned to the column to prohibit larger values from being stored in the table.

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Answer:

x = 6

Step-by-step explanation:

Love proportions!

3x+2(x+6) = 35(21)

21(3x+2) = 35(x+6)

63x + 42 = 35x + 210

28x = 168

x = 6

The dimensions of the rectangular base of the building with the given perimeter are 120ft and 285ft.

The perimeter of rectangle is expressed as;

P = 2( l + w )

Given the data in the question;

Let x represent the width of the rectangular base.

Plug these values into the equation above.

P = 2( l + w )

810 = 2( (3x-75) + x )

810 = 6x - 150 + 2x

810 = 8x - 150

8x = 810 + 150

8x = 960

x = 960/8

x = 120

Hence,

Width of the rectangle = x = 120ft

Length of the rectangle = 3x-75 = 3(120) - 75 = 285ft

Therefore, the dimensions of the rectangular base of the building with the given perimeter are 120ft and 285ft.

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Answer:

30°, 60°, 90°

Step-by-step explanation:

sum the parts of the ratio, 1 + 2 + 3 = 6 parts

divide the sum of the angles in a triangle. 180° by 6 to find the value of one part of the ratio.

180° ÷ 6 = 30° ← value of 1 part of the ratio , then

2 parts = 2 × 30° = 60°

3 parts = 3 × 30° = 90°

The 3 angles are 30°, 60° and 90°