The radioactive substance cesium-137 has a half-life of 30 years. The amount A (t) (in grams) of a sample of cesium-137 remaining after t years is given by the
following exponential function.
- 647 (12)
A (t) = 64
30
Find the initial amount in the sample and the amount remaining after 100 years.
Round your answers to the nearest gram
?

Answer:

a. A function f such that the equation f(x + h) = f(x) + f(h) is not true for all values of x and h is a function that is not linear. For example, a function f(x) = x^2 is not linear because it does not satisfy the equation f(x + h) = f(x) + f(h).

b. A function f such that the equation f(x + h) = f(x) + f(h) is true for all values of x and h is a linear function. For example, a function f(x) = mx + b, where m and b are constants, is a linear function because it satisfies the equation f(x + h) = f(x) + f(h).

c. Let f(x) = 2x. If we choose x = 3 and h = 2, then f(x + h) = f(3 + 2) = f(5) = 2(5) = 10, and f(x) + f(h) = f(3) + f(2) = 2(3) + 2(2) = 6 + 4 = 10. Therefore, the equation f(x + h) = f(x) + f(h) is true in this case.

The average rate of change of a t over the interval 0 30 t is 0.03 pounds per day.

To find the average rate of change, we need to calculate the slope of the line representing the function a t( ) over the interval 0 to 30.

The slope is calculated by taking the change in a t over the change in t.

We can calculate the change in a t by subtracting the a t value at the start of the interval (0) from the a t value at the end of the interval (30):

a t (30) - a t (0) = 6.687 - 0 = 6.687

We can calculate the change in t by subtracting the t value at the start of the interval (0) from the t value at the end of the interval (30):

t (30) - t (0) = 30 - 0 = 30

We can now calculate the slope by dividing the change in a t by the change in t:

Slope = 6.687 / 30 = 0.03

The average rate of change of a t over the interval 0 30 t is 0.03 pounds per day.

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An appropriate method of controlling for any confounding variables is;

The group assigned to the old drug should also drink an entire glass of water with the drug

In an experiment, there are three primary types of variables, namely;

Dependent variable

Independent variable or explanatory variable.

Confounding variable.

We know that explanatory variable seems to have some effects on the dependent variable but then confounding variable also affects the dependent variable in some way. Thus, confounding variables are having the hidden effect on the main variable.

A confounding variable is defined as an explanatory variable that was considered in a study whose effect cannot be distinguished from a second explanatory variable in the study.

Now, in this question we can say that the confounding variables could be;

-price of a daily ski pass

-temperature

-whether it has snowed recently

The method for controlling any of these is that The group assigned to the old drug should also drink an entire glass of water with the drug

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Answer: (x,y)=(12,8)

Step-by-step explanation:

The probability of the person over 40 years of age who drinks root beer is equal to 0.1176.

As given in the question,

Total number of people is equal to 255

From the given table :

Number of people who drinks root beer and over 40 years of age is

= 30

Required probability  who drinks root beer and over 40 years of age is given by :

= ( Number of favourable outcomes ) / ( total number of outcomes )

= ( 30 / 255 )

= 0.1176

Therefore, the required probability of the people over the age of 40 years and drinks root beer is given by 0.1176.

The above question is incomplete , the complete question is :

                                          Cola                     Root Beer              Lemon-line

Under 21 years of age  :       40                        25                         20

Between 21 and 40      :        35                        20                        30

Over 40 years of age   :        20                        30                        35                 If one of the 255 subjects is randomly selected, find the probability that the person is over 40 years of age or that they drink root beer.

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The block's density can be calculated using the equation d=25g/8.4 cm.

Two things are equal, according to an equation.

For instance, 10 + 2 equals 6 + 6.

Simply put, this means that 10 plus 2 equals or is the same as 6 plus 6.

In an equation, the unknown could be present, as in 10 + x = 6 + 6.

So, find the block's volume first:

= Length * Width * Height

= 2 x 3 x 1.4

= 8.4 cm

Now that you know the volume and the mass, you can add them to the density formula, which is as follows:

= Mass / Volume

Assuming density is represented by the symbol b, the formula would be:

d = 25 g / 8.4 cm

Therefore, the block's density can be calculated using the equation d=25g/8.4 cm.

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Correct question:

A student is trying to identify the composition of a pure metal block by determining its density. The student records the mass of the sample to be 25.00 g. The rectangular block is 2.0 cm x 3.0 cm x 1.4 cm.

Which equation is necessary to determine the density sample?

Answer:

110 cm^2 & 39 cm^3

Step-by-step explanation:

Volume = Length x Width x Height. With that in mind, volume is 39 cm^3

Surface Area = Area of all the shapes

2(13 x 1) + 2(13 x 3) + 2(3 x 1) =110 cm^

Answer:

allows companies to easily and quickly fulfill customer orders as soon as they come in

Step-by-step explanation:

Holding excess inventory will allow companies to easily and quickly fulfill customer orders as soon as they come in, all without having to worry about waiting on their stock to come in to ship an order out.

To create the tables and calculate the average mean, we need to have a set of data that we want to organize in a tabular form. The table should have columns for the data values, frequency, and frequency subtotal. The frequency column will show how many times a particular data value appears in the set.

The frequency subtotal column will be used to find the sum of the product of each data value and its corresponding frequency.

The average mean can be calculated by dividing the sum of the frequency subtotal by the total frequency.

Mean = ([tex]f_{1}x_{1}[/tex] + [tex]f_{2}x_{2}[/tex]+ [tex]f_{3}x_{3}[/tex]+ ... + [tex]f_{n}x_{n}[/tex]) / ([tex]f_{1}[/tex]+[tex]f_{2}[/tex]+[tex]f_{3}[/tex]+...+[tex]f_{n}[/tex])

By creating this table, we can easily see the distribution of the data and can calculate the average mean. This method of organizing data in tabular form is commonly used in statistics and data analysis, and it is an efficient way of summarizing and understanding large sets of data.

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y = c * 5e^t / ln(t) is the general solution to 1/ln(t)(5e^t c) .We can simplify this expression by applying the chain rule of differentiation. The chain rule states that if y = f(u) and u = g(x), then

dy/dx = dy/du * du/dx.  

The given expression is 1/ln(t)(5e^t c) .

In this case, we can let y = 5e^t c and u = ln(t).

Taking the derivative with respect to t, we get:

dy/dt = 5e^t c * (du/dt) / u

Since u = ln(t), we can use the chain rule again to find du/dt:

du/dt = 1/t

Plugging this back into the original expression, we get:

dy/dt = 5e^t c * (1/t) / ln(t)

Now we can factor out the constant c, which is an arbitrary constant of integration, giving us the final answer:

y = c * 5e^t / ln(t)

So the final answer is: y = c * 5e^t / ln(t)

It's important to note that this is only the general solution of the function, if we have an initial condition then we can find the specific solution for the function

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Answer:

41 mg magnesium

42 mg calcium

Step-by-step explanation:

87% of magnesium; 48 mg of magnesium

44% of calcium; 96 mg of calcium

87% × 48 mg magnesium = 0.87 × 48 mg magnesium = 41 mg magnesium

44% × 96 mg calcium = 0.44 × 96 mg calcium = 42 mg calcium

An expression which is equivalent to 5 - 2(3x + 4) is,

⇒ - 3 - 6x

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The expression is,

⇒ 5 - 2 (3x + 4)

Now, We can solve the expression as;

⇒ 5 - 2 (3x + 4)

⇒ 5 - 2 × 3x - 2 × 4

⇒ 5 - 6x - 8

⇒ - 3 - 6x

Thus, The equivalent expression is,

⇒ - 3 - 6x

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According to the information provided, it should be noted that the 750 seniors in her school make up the population of interest, and the parameter of interest is the percentage of seniors who intend to attend the prom.

Given,

Additionally, a strictly random sample is required in order to create a confidence interval. Additionally, the sample size should be examined to see if it adequately represents the population.

Using the z critical of 1.645, a 90% confidence interval will be built. The sample proportion in this case will be:

= 36/50 = 0.72

Q = 1 - 0.72 = 0.28

n = 50

As a result, the standard error will be equal to 50 squared times the multiplication of 0.72 and 0.28. This amounts to 0.0635.

For a big sample randomly selected among 750 seniors, the interval on the context suggests that we are 90% confident that the fraction of those who desire to attend the prom falls within the interval.

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The procedures below can be used to determine a triangle's length BD.

In th that is presented;

The holding ratio is, therefore, as follows:

12 : x = 27 : x + 5

12 / x = 27 / (x + 5 )

When we cross multiply these, we obtain:

12 ( x + 5 ) = 27x

12x + 60 = 27x

Taking the x values on one side, we obtain:

27x - 12x = 60

15x = 60

x = 60/15

x= 4

The length of line BD is:

= BC + CD

= x + x + 5

After entering the value of x, we get

= 4 + 4 + 5

= 13

As a result, the length of the line BD is 13.

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The total score will be used to determine the student’s final admissions status.

I would like to build a program that calculates a student's score for a college admissions test. The program will be based on the coding requirements outlined by the college board, which include a list, an algorithm that uses sequencing, selection and iteration and a procedure that uses parameters.

The list will contain the student’s scores for each section of the admissions test. The algorithm will use sequencing to add the scores of each section together. Selection will then be used to determine whether the student has met the minimum requirements, and iteration will be used to keep track of any sections that were not completed. The procedure will be used to calculate the student’s total score, using parameters such as the number of sections completed and the scores for each section. The total score will be used to determine the student’s final admissions status.

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The standard deviation is $8,000. So, the standard deviation measured in thousands of dollars, is 8. and The mean is the average. So the average, measured in thousands of dollars, is 56.

Average salary: 56

Standard deviation of the salary: 8

$56,000 dollars is 56 thousand dollars.

$8,000 is 8 thousand dollars.

The mean is the average. So the average, measured in thousands of dollars, is 56.

The standard deviation is $8,000. So, the standard deviation measured in thousands of dollars, is 8.

complete question

Let X denote the average starting salary for 2014 U.S. college graduates, measured in dollars. Suppose that the average annual salary is $56,000 dollars, with a standard deviation of 8,000. Find the mean and standard deviation when salary is measured in thousands of dollars.

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The new function that takes that longer doubling time into account with starting quantity will be Aₙ = A₁ (1)ⁿ.

Consider the function:

y = a (1 ± r)ˣ

Where x is the number of times this growth occurs, a = initial amount, and r = fraction by which this growth occurs.

As per Moore's Regulation, the multiplying time for the number of semiconductors that can be placed on a microprocessor is roughly two years. That's what ongoing information proposes, starting around 2013, the pace of development anticipated by Moore's Regulation does not hold anymore.

The rate is 0%, then the equation is given as,

Aₙ = A₁ (1 + 0)ⁿ

Aₙ = A₁ (1)ⁿ

The new function that takes that longer doubling time into account with starting quantity will be Aₙ = A₁ (1)ⁿ.

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Answer:

HJ = 8.4

Step-by-step explanation:

tangents to a circle from an external point are congruent , then

HJ = HI

the angle between a tangent and a radius of the circle at the point of contact is a right angle.

so Δ OHI is right with ∠ OIH = 90°

using Pythagoras' identity in the right triangle

HI² + OI² = OH² , that is

HI² + 8² = 11.6²

HI² + 64 = 134.56 ( subtract 64 from both sides )

HI² = 70.56 ( take square root of both sides )

HI = [tex]\sqrt{70.56}[/tex] = 8.4

Then

HJ = HI = 8.4

Efficiency.Compared to solar panels' efficiency range of 18% to 22%, wind turbines typically capture 60% of the energy that flows through them.

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No, the standardized test statistic t does not indicate that you should reject the null hypothesis.

The value of the test statistic t only tells you how much of an effect the independent variable has on the dependent variable. To determine whether to reject the null hypothesis, you must compare the value of t to a critical value based on the sample size, the level of significance, and the degrees of freedom.

The standardized test statistic t does not indicate whether you should reject the null hypothesis. To determine this, you must compare the value of t to a critical value based on the sample size, level of significance, and degrees of freedom.

No, the standardized test statistic t does not indicate that you should reject the null hypothesis.

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The statements that are listed above that are not propositions include the following:

A proposition statement is defined as the statement that is either a true statement or false statement but can not be both.

From the given statements,the statement that is a true proposition include the following:

The statement that is a false proposition include the following:

The statement will you be my valentine? is not a proposition but a declarative question that needs to be answered.

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Answer:

Please see answer below

Step-by-step explanation:

An estimate is an answer to a problem that is close to the solution, but not necessarily exact. Estimation usually requires rounding

Usually you perform the estimate prior to computing actual values.

Let's look at the numbers

591 can be rounded to 600, 211 can be rounded to 200

Then, in your equations instead of using actual numbers we use the estimates

600 - 200 = 400

500 - 400 = 100

Note this is off quite a bit because we are rounding to the nearest 100

Instead if we round to the nearest tens we get

591 ==> 590
211 ==> 210

520==> 520

So we get

590 - 210 = 380

520 - 380 = 140

A little more work but a more accurate estimate

The volume of the given cylinder is 11304 cm³.

Volume is the measure of the capacity that an object holds.

Formula to find the volume of the object is Volume = Area of a base × Height.

Given that, radius of a cylinder is 20 cm and depth of a cylinder is 9 cm.

We know that, the volume of a cylinder is πr²h.

Now, volume = 3.14×20²×9

= 3.14×400×9

= 11304 cm³

Therefore, the volume of the given cylinder is 11304 cm³.

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Answer:

5089.4cm

Step-by-step explanation:

9² x pi x 20 =5089.3800

the final equations are.:

A relationship between a group of inputs and one output is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.

We have the following function:

(x)  = 3x - 7

The function f translated 6 units up and 2 units rights:

6 units up:

y  = 3x - 7 + 6

2 units rigth:

y  = 3(x-2) - 7 + 6

y  = 3x - 6 - 7 + 6

Finally:

g(x)  = 3x - 7

The function f reflected about the y-axis and translated 7 units left:

reflected about the y-axis:

y = 3(-x) - 7

y = -3x - 7

translated 7 units left:

y = -3(x+7) - 7

y = -3x - 21 - 7

y = -3x -28

Finally:

g(x) = -3x - 28

The function f stretched vertically by a factor of 2 and translated up by 5 units:

stretched vertically by a factor:

y = 6x - 14

translated up by 5 units:

y = 6x - 14 + 5

y = 6x - 9

Finally:

g(x) = 6x - 9

The function f stretched vertically by a factor of 4 and translated up by 9 units:

stretched vertically by a factor of 4:

y = 12x - 28

translated up by 9 units:

y = 12x - 28 + 9

y = 12x - 19

Finally:

g(x) = 12x - 19

Thus, the final equations are.:

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The volume of the segment formed when a sphere of radius r is cut by a plane is equal to (πh2(3r-h))/3. This can be found by using the formula for the volume of a spherical segment, where h is the height of the segment and r is the radius of the sphere.

Step 1: Calculate the volume of a sphere using the formula V = (4/3)πr3

Step 2: Calculate the volume of a cone using the formula V = (1/3)πr2h

Step 3: Calculate the difference between the two volumes to find the volume of the segment.

Step 4: The volume of the segment is (πh2(3r-h))/3.

To calculate the volume of the segment formed when a sphere of radius r is cut by a plane, we use the formula for the volume of a spherical segment. First, we calculate the volume of the sphere using the formula V = (4/3)πr3, then the volume of the cone using the formula V = (1/3)πr2h. By subtracting the two volumes, we find the volume of the segment, which is (πh2(3r-h))/3. This formula is useful in finding the volume of any segment formed when a sphere is cut by a plane.

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180° anticlockwise rotation will turn the rectangle into one that is NOT consistent with the original rectangle.

The correct option is B.

Two figures are referred to as congruent if their size and shape are the same. For instance, because they are the same size and shape, the rectangles ABCD and PQRS are congruent rectangles.

Identical shapes are referred to as congruent shapes. The angles and sides that correspond to each other are the same. To accomplish this, we must examine each shape's sides and angles. Two congruent shapes will perfectly fit on top of each other.

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I understand that the question you are looking for is:

A rectangle is graphed on a coordinate grid. Which transformation will result in a rectangle that is NOT congruent to the original rectangle?

A.  A dilation by a scale factor of

B.  rotation of 180° counterclockwise

C. translation 90°  units to the right

D. reflection across the x-axis

answer : A rotation of 180 digress counterclockwise

Answer:2x3x4

Step-by-step explanation:

The value of m∠1 is 50°. The solution is obtained using properties of angle and triangle.

What is an angle?

When two rays are brought together at a single point, an angle is created. The two rays in this instance are referred to as the arms of the angle, while the common point is known as the node or vertex. The symbol "∠" stands for an angle. Angle is a derivative of the Latin word "Angulus."

In the figure, we are given a right-angled triangle which means that one angle in the triangle measures 90°.

We are given an exterior angle equal to 140°.

We know that angles on a straight line form a linear pair which means that their sum is 180°.

Let the angle on the straight line be 'x'.

So, we get

⇒x + 140° = 180°

⇒x = 40°

Now, we know that in a triangle, the sum of all the angles is 180°.

Therefore,

⇒m∠1 + 90° + 40° = 180°

⇒m∠1 + 130° = 180°

⇒m∠1 = 50°

Hence, the value of m∠1 is 50°.

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The likelihood that at least 1610 members of the sample agree is 0.3385.

Given,

sample std = sqrt[0.62 × 0.38/2577]

= 0.0096

sample proportion = 1610/2577

= 0.6240

z(0.6240) = (0.6240-0.62)/0.0096

= 0.4167

P(x >= 1610) = P(z >= 0.4167)

Then we get,

= 0.3385

Hence, The likelihood that at least 1610 members of the sample agree is 0.3385.

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The regression equation is y = 15.98x + 43.76. The predicted value for the final grade when a student spends an equation of 8 hours each week on math is 87.8.

The regression equation is found by using a linear regression analysis. First, the data points are plotted on a graph. Then, the best-fit line is determined. The equation of the line is then calculated by finding the slope (m) and y-intercept (b).

The slope (m) is calculated by taking the difference between the two y-values divided by the difference between the two x-values.

m = (y2 - y1) / (x2 - x1)

The y-intercept (b) is calculated by substituting the values of m and one of the data points into the equation of a line, and solving for b.

b = y - mx

Once the values of m and b are determined, the regression equation can be determined:

y = mx + b

For this data set, the regression equation is y = 15.98x + 43.76.

To find the predicted value for the final grade when a student spends an average of 8 hours each week on math, the value of x is substituted into the equation, and the result is rounded to one decimal place.

y = 15.98(8) + 43.76

y = 87.8

Therefore, the predicted value for the final grade when a student spends an average of 8 hours each week on math is 87.8.

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