Carbon-14 has a half-life of 5,700 years. Scientists use this fact to determine the age of things made of organic material. Suppose the
average page of a book containing approximately 0.5 mg of carbon-14 is put into a time capsule. How much carbon-14 will each page
contain after each of the following years?
A) 11,400 years
B) 22,800 years

Answer:

Step-by-step explanation:

so in group 1 out of 12 rolls u landed on 4 four times

in group 2 out of 3 rolls u landed on it 1 time

in group 3 u landed on it 1 time

and in group 4 (i assume) u landed on it 1 time

add the denominators

so  7/35 which simplified is 1/5

Answer:

x= 81°

Step-by-step explanation:

the interior angles of a quadrilaterial add up to 360°

143+80+56+x=360

condense left side: 279+x=360

isolate x: 279-279+x=360-279

x= 81°

Answer:

False

Step-by-step explanation:

It does not have an equal sign, therefore making it a false equation

The correct answer is E. increase, more people will use buses, and buses are greater producers of carbon emissions than cars.

An increase in the gas tax in the United States to the level of European countries would have implications for carbon emissions. If the gas tax is increased.

It would likely result in more people choosing alternative modes of transportation, such as buses, which are known to be greater producers of carbon emissions compared to cars. Therefore, the increase in the gas tax could lead to an unintended consequence of higher carbon emissions.

This highlights the complex relationship between taxes, transportation choices, and environmental impact, emphasizing the need for comprehensive policies that consider the broader implications of such changes.

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Answer:

(2,3),(4,3),(-2,-3),(-4,-3)

Step-by-step explanation:

A function is defined as a relation in which each domain element (x-value) is paired with exactly one range element (y-value).

This means that each value we input for x must have only one possible output. If the same x-value yields more than one y-value, it is not a function.

The correct answer, as shown above, meets the criteria of a function, as each x-value is shown to produce exactly one y-value. In this set of ordered pairs, if x = 2, then y = 3, and if x = -2, then x = -3.

A set of ordered pairs is not a function if there are ordered pairs with the same x-values but different y-values.

In the other sets of ordered pairs, one x-value has more than one possible y-value. Let's use the last set as an example:

(5,1),(5,2),(5,3),(5,4)

Inputting 5 as x produces four different y values; there is no one y value for the x-value. y could equal 1, 2, 3, or 4.

Area of base = 52

height = 5

Volume = 260

To find the volume of a rectangular prism all you need to do is multiply the length * width * height.

the area of base is the length * width = 13 * 4 = 52

then you multiply that by the height = 52 * 5 = 260

a) According to the central limit theorem, the mean is $142 and the standard deviation is $0.7488.

b) Nearly normal according to the central limit theorem.

c) 0.0901 = 9.01% probability that the average cable service paid by a sample of cable service customers exceeds $170 in the central limit theorem.

Normal probability distribution:

The normal probability distribution, discovered by Abraham De Moivre in 1733, approximates the binomial probability distribution when a particular experiment has a very large number of trials. In 1774 Laplace studied the mathematical properties of the normal probability distribution. By historical error, the discovery of the normal distribution was attributed to Gauss, first mentioned in his 1809 paper. In the 19th century, many scientists discovered that measurement errors in a particular experiment followed a pattern (usual error curve). ), which was very well approximated by this probability distribution.

Central Limit Theorem:

The central limit theorem is a statistical theory that for large sample sizes with finite variance, samples are normally distributed and the mean of the sample is approximately equal to the mean of the entire population.

According to the Question:

The average monthly charge is $142 with a standard deviation of $29.

This is μ = 142 and σ = 29

Part a:

The mean and standard deviation of the sampling distribution of x to show your research and support your argument:

1500 samples (over 30).

According to the Central Limit Theorem

The mean is 142 $

The standard deviation is s = \(\frac{29}{\sqrt{1500} }\) = 0.7488

Part b:

Shape of sampling distribution of X.

Due to the large sample size, the shape of the sample distribution is almost normal. According to the central limit theorem, which states that the sampling distribution converges to the normal distribution as the sample size increases. Mean ~ N(142, 0.749²)

Part C:

The probability that the average cable service paid by a sample of cable service customers exceeds $170.

Therefore, by the central limit theorem, the p-value of Z when X= 170

                         Z =  x - μ/ σ

By the Central Limit Theorem:

   Z = 170 - 142 / 0.7488

      = 28/ 0.7488

      = 37.34 exceeds 0.9099

Using the Z probability calculator :

P(Z > 1.335) = 0.09093

Complete Question:

The amount people pay for cable service varies quite a bit but the mean monthly fee is $142 and the standard deviation is $29. the distribution is not normal many people pay about $76 for basic cable and about $160 for premium service but some pay much more. a sample survey is designed to ask a simple random sample of 1,500 cable service customers how much they pay. let x hat be the mean amount paid.

Part a: what are the mean an standard deviation of the sample distribution of x hat show your work and justify your reasoning.

Part b: what is the shape of the sampling distribution of x hat justify your answer.

Part C: what is the probability that the average cable service paid by the sample of cable service customers will exceed $170? show your work.

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Answer:

SAS, because vertical angles are congruent.

This is False in light of the stated statement. Due to the employment of a regression line to calculate the mean of y for x that are outside the x-range of the data.

How is regression calculated?

Y = mX + b, where X is the predictive (independent) factor, m is really the approximately slope, and b is the expected intercept, is the methodology for simple linear regression.

The relationship between scattered data points in any set is shown by a regression line. When there is a linear pattern, it displays the relationship between the dependent y variable and independent x variables.

The correlation between the independent variables (IVs) and the dependent variable is described by a linear regression equation (DV). The DV for the IV values you indicate can also be predicted for new values.

Hence we get the required answer.

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Answer:

135

285

300

Step-by-step explanation:

Answer:

The answer would be -19.8

Step-by-step explanation:

Hope this helps

Answer:

You show them in pictures.

This is 2/3.



This is 3/5.



They’re pretty similar, but you can tell that more is shaded in the first than the second. If they’re 8 though, then they’re probably in 2nd or 3rd grade. They’ll get it.

Another suggested pic:



Answer:

\(\frac{1}{2}*\frac{|x-5|}{2}\)=\(\frac{|x-5|}{2}\)

The same person also took a midterm in their marketing course and the class mean for this exam was 77 with a standard deviation of 4.7. The z-score for the score on this exam is 1.9. Calculate the actual score this person received for the marketing exam (to 2 decimal places).

Here is how we can calculate the actual score this person received for the marketing exam. First, we know that the Z score is given by the formula:

Z = (X - μ)/ σ

where X = actual score, μ = Mean, σ = Standard Deviation

Given that the Z score is 1.9, i.e., Z = 1.9

Hence,X = μ + Zσ

On substituting the given values, we get: X = 77 + 1.9 * 4.7X = 86.13 (approx.)

Therefore, the actual score that this person received for the marketing exam is 86.13 (to 2 decimal places).Note that the score is rounded to 2 decimal places as required by the question.

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2n^3 + 3n + 10 can be written as a polynomial of the form Q(n^3), where Q(n^3) represents the set of polynomials of the form a(n^3).

To prove that the expression 2n^3 + 3n + 10 is in the set Q(n^3), where Q(n^3) represents the set of polynomials of the form a(n^3), we need to show that the expression can be written in the form a(n^3) for some constant "a".

Let's start by factoring out the common factor of n^3 from each term:

2n^3 + 3n + 10 = n^3(2 + 3/n^2 + 10/n^3)

Now, let's rewrite the expression as a single term multiplied by n^3:

2n^3 + 3n + 10 = (2 + 3/n^2 + 10/n^3)n^3

Simplifying the expression inside the parentheses:

= (2n^3 + 3n^2 + 10n^3)/n^3

= (12n^3 + 3n^2)/n^3

= 12 + 3/n

ow, we can see that the expression can be written in the form a(n^3), where a = 12 and n^3 = 3/n.

Therefore, we have shown that 2n^3 + 3n + 10 can be written as a polynomial of the form Q(n^3), where Q(n^3) represents the set of polynomials of the form a(n^3).

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If we substitute y = 1 into the equation, we can calculate x as x = 2/1 = 2. This means that when y = 1, the value of x is 2.

Given an inverse variation between x and y, such that xy = 2, we can express this mathematically as x = 2/y.

Given x varies inversely with y and xy = 2,

We can rewrite this as x = 2/y

Substituting y = 1,

x = 2/1

x = 2

Given an inverse variation between x and y, such that xy = 2, we can express this mathematically as x = 2/y. This means that as y increases, x decreases,  Therefore, if we know the value of y, we can calculate the value of x. If we substitute y = 1 into the equation, we can calculate x as x = 2/1 = 2. This means that when y = 1, the value of x is 2.

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Answer: Yes, only angles can be reflected over diagonal lines.

Step-by-step explanation:

see photo

Answer:

x = 27

Step-by-step explanation:

Answer:

An expression is a number, a variable, or a combination of numbers and variables and operation symbols. An equation is made up of two expressions connected by an equal sign.

Step-by-step explanation:

Hopes this help.

Answer:

342

Step-by-step explanation:

((18*18)/2)+(6*3)

324+18

342

The perimeter of the regular octagon with an apothem of 4 units will be 26.51 units.

All the sides of the regular polygon are congruent to each other. The perimeter of the regular polygon of n sides will be the product of the number of the side and the side length of the regular polygon.

P = (Side length) x n

The Apothem of a regular octagon is 5 units. Then the side length of the regular octagon is given as,

tan (360° / (2 × 8)) = (n/2) ÷ 4

tan 22.5° = n / 8

n = 3.3137

Then the perimeter is given as,

P = 8 x 3.3137

P = 26.51 units

The perimeter of the regular octagon with an apothem of 4 units will be 26.51 units.

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13) No, The triangle is not similar.

14) No, The triangle is not similar.

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

The triangles is shown in figure with sides.

Here,

13) The sides of triangles are,

In triangle KJL;

KJ = 87

LJ = 95

In triangle JHG;

JH = 72

JG = 68

Clearly, The there corresponding sides are not equal and also the ratio of there corresponding sides are also not equal.

Hence, The both triangle are not Similar.

14) The sides of triangles are,

In triangle ABE;

AE = 21

BE = 16 + 26 = 42

In triangle ECD;

EC = 16

ED = 32

Clearly, The there corresponding sides are not equal and also the ratio of there corresponding sides are also not equal.

Hence, The both triangle are not Similar.

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Answer:

6. Line graph

Step-by-step explanation:

It shows how information changes over time

Answer:

\(\sf P(A \cap B)=\dfrac{1}{4}\)

Step-by-step explanation:

\(\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}\)

Event A - spinning violet or yellow

Assuming that the spinner has 4 different colors (red, orange, violet and yellow) - see attachment.

\(\implies \sf P(A) = \dfrac{2}{4}=\dfrac{1}{2}\)

Event B - rolling an even number

Assuming the number cube has 6 sides numbered 1, 2, 3, 4, 5 and 6.  Therefore, the even numbers are 2, 4 and 6.

\(\implies \sf P(B)=\dfrac{3}{6}=\dfrac{1}{2}\)

Events A and B are independent events as the outcome of one event does not affect the outcome of the other event.

For independent events A and B:

\(\implies \sf P(A \cap B)=P(A)P(B)\)

To find P(A and B), substitute the found values of P(A) and P(B):

\(\implies \sf P(A \cap B)=\dfrac{1}{2} \times \dfrac{1}{2}=\dfrac{1}{4}\)

P(A)

P(B)

3 even nos are 2,4,6

P(A\(\cap\))

The function that best approximates f(x) as h approaches 0 is c. tan(x)/x.

For values of h very close to 0, the function that best approximates f(x) = tan(x) is option c. tan(x)/x.

To understand why, let's examine the behavior of each function as h approaches 0:

a. sin(x): As h approaches 0, sin(x+h) - sin(x) / h approaches the derivative of sin(x), which is cos(x). Therefore, sin(x) is not the best approximation for f(x) as h approaches 0.

b. sin(x)/x: As h approaches 0, sin(x+h) - sin(x) / h approaches the derivative of sin(x), which is cos(x). Dividing by x helps to account for the change in slope as x approaches 0. Therefore, sin(x)/x provides a better approximation for f(x) as h approaches 0.

c. tan(x)/x: As h approaches 0, tan(x+h) - tan(x) / h approaches the derivative of tan(x), which is sec^2(x). Dividing by x helps to account for the change in slope as x approaches 0. Therefore, tan(x)/x provides the best approximation for f(x) as h approaches 0.

d. sec(x): The secant function is the reciprocal of the cosine function, and it does not provide a good approximation for f(x) as h approaches 0.

e. sec^2(x): As h approaches 0, sec(x+h) - sec(x) / h approaches the derivative of sec(x), which is sec(x) * tan(x). Therefore, sec^2(x) does not provide the best approximation for f(x) as h approaches 0.

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The confidence interval to find the margin of error and the sample mean:

(0.256,0.380) The sample mean is the average value obtained from the sample data.

To find the margin of error and the sample mean, we need more information.

The confidence interval (0.256, 0.380) provides the range of possible values for the true population mean.

However, without knowing the sample size or the level of confidence associated with the interval, we cannot calculate the margin of error or the sample mean.

The margin of error is typically calculated by multiplying the standard error by the appropriate critical value, based on the desired level of confidence. The sample mean is the average value obtained from the sample data.

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Answer:

C 100 inches/ minute * 1 ft/ 12 inches

Step-by-step explanation:

100 inches/ minute

We need to convert inches to ft

12 inches = 1 ft

100 inches/ minute * 1 ft/ 12 inches

Answer:

y-2x=4

Step-by-step explanation:

the slope is 2

the opposite reciprocal is -1/2

2/1 = 2

a) To calculate the pressure at 12 hours of shut-in:

substitute the given values into the pressure buildup equation and solve for P(t=12).

b) Superposition in time is used in pressure buildup analysis by adding or summing the responses of multiple transient tests to analyze and interpret reservoir behavior and properties.

We have,

a) To calculate the pressure in the production well at 12 hours of a shut-in, we can use the equation for pressure transient analysis during shut-in periods, known as the pressure buildup equation:

P(t) = Pi + (Q / (4πKh)) * log((0.14ϕμCt(t + Δt)) / (Bo(ΔP + Δt)))

Where:

P(t) = Pressure at time t

Pi = Initial reservoir pressure

Q = Flow rate

K = Permeability

h = Reservoir thickness

ϕ = Porosity

μ = Viscosity

Ct = Total compressibility

t = Shut-in time (12 hours)

Δt = Time since the start of the flow period

Bo = Oil formation volume factor

ΔP = Pressure drop during the flow period

Given:

Pi = 3100 psi

Q = 200 STB/day

K = 45 md

h = 60 ft

ϕ = 15%

μ = 1.2 cp

Ct = 15x10^-6 psi^-1

Bo = 1.3 bbl/STB

t = 12 hours

Δt = 48 hours

ΔP = Pi - P(t=Δt) = Pi - (Q / (4πKh)) * log((0.14ϕμCt(Δt + Δt)) / (Bo(ΔP + Δt)))

Substituting the given values into the equation:

ΔP = 3100 - (200 / (4π * 45 * 60)) * log((0.14 * 0.15 * 1.2 * 15x\(10^{-6}\) * (48 + 48)) / (1.3 * (3100 - (200 / (4π * 45 * 60)) * log((0.14 * 0.15 * 1.2 * 15 x \(10^{-6}\) * (48 + 48)) / (1.3 * (0 + 48))))))

After evaluating the equation, we can find the pressure in the production well at 12 hours of shut-in.

b) Superposition in time is a principle used in pressure transient analysis to analyze and interpret pressure build-up tests.

It involves adding or superimposing the responses of multiple transient tests to simulate the pressure behavior of a reservoir.

The principle of superposition states that the response of a reservoir to a series of pressure changes is the sum of the individual responses to each change.

Superposition allows us to combine the information obtained from multiple tests and obtain a more comprehensive understanding of the reservoir's behavior and properties.

It is a powerful technique used in reservoir engineering to optimize production strategies and make informed decisions regarding reservoir management.

Thus,

a) To calculate the pressure at 12 hours of shut-in:

substitute the given values into the pressure buildup equation and solve for P(t=12).

b) Superposition in time is used in pressure buildup analysis by adding or summing the responses of multiple transient tests to analyze and interpret reservoir behavior and properties.

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