Radium - 226 has a half-life of 1600 years. Suppose we have a 300 g sample. A) How much of the sample remains after 200 years? B) How long will it take for the sample to reach 50g? O A) 105.61 g B) Approximately 619 years OA) 288.1 g B) Approximately 3,500 years A) 275.1 g B) Approximately 4, 136 years.
Previous question

Answer:

scientific notation

= 2.34e8

scientific e notation

= 234 × 106

engineering notation

million; prefix mega- (M)

= 2.34 × 108

standard form

8

Order of Magnitude

for scientific and standard forms

= 234000000

(real number)

= two hundred thirty-four million

word form

Step-by-step explanation:

Isabella would have $2970.63 in the account 14 years after her initial investment.

Isabella invested $1300 in an account that pays 4.5% interest compounded annually.

Assuming no deposits or withdrawals are made, find how much money Isabella would have in the account 14 years after her initial investment. Round to the nearest tenth (if necessary).

The formula for calculating the compound interest is given by

A=P(1+r/n)^(nt)

where A is the final amount,P is the initial principal balance,r is the interest rate,n is the number of times the interest is compounded per year,t is the time in years.

Since the interest is compounded annually, n = 1

Let's substitute the given values in the formula.

A = 1300(1 + 0.045/1)^(1 × 14)A = 1300(1.045)^14A = 1300 × 2.2851A = 2970.63

Hence, Isabella would have $2970.63 in the account 14 years after her initial investment.

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video of length minute and a half is most effective.

video is no doubt the most effective and top-performing content on social media. But uploading a social media is not as simple as uploading a simple video. there are lots of decisions (i,e the story, content, style, filter, back view, etc) to make in order to achieve overall goals for the good video uploading. the most important is the length of the video.  if your content is excellent but your video is too short in length of too long in length then it will not achieve the goal according to expectations.

if your video is appropriate, your content is good and your video is 1 and half a minutes or 2 minutes long then it is the most effective one.

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The transformation from the graph of graph of f(x)=3(x-4)²+6 to the graph of g(x)=f(x+2)-1 is :

The function g is of the form y = f(x-h) + k where h = horizontal shift and k = the vertical shift.

So the graph of g is a horizontal translation of h units  and a vertical translation k unit(s)  of the graph of f.

To arrive at g(x) from f(x), three alterations are executed. Initially, a horizontal shift occurs resulting in two units moving towards leftward direction: this change can be denoted through converting instances of "f(x)" into "f(x+2)".

Following that, we observe a vertical drop occurring one unit down. This change is instantaneously made through appending "-1" at end.

Subsequently, there's an upwards vertical stretching effect achieved with use of multiplication by factor three while manipulating existing coefficient value for squared term inside original function.

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Answer:

Remember that the slope of perpendicular lines are negative reciprocals of each other.

Step-by-step explanation:

y = 1 - 2x     the slope is -2     the value of the x term.

So the slope of the new line using point (- 1, 2)  is  1/2.

Now use y = mx + b where y = -1, x = 2, and m = 1/2 .

y = mx + b

-1 = 1/2(2) + b                solve for "b", the y-intersect

-1 =  1 + b

-2 = b

The line that is perpendicular to y = 1 - 2x  is  y = 1/2x - 2

Answer: -61

Step-by-step explanation:A = -2{(-5× -1) - (3 × -2)} + -2{(-5×4) - (-2×1)} + -5{(4×3) - (-1×2)}

= -2{(5-(-6)} + -2{(-20 -(-2)} + -5{(12-(-2)}

= -2(5 + 6) + -2(-20+2) + -5(12+2)

= -2(11) + -2(-18) + -5(14)

= -22 + 36 -75

= -61

Answer:

b) -51

Step-by-step explanation:

just took test

To determine the necessary sample size to obtain an interval width of 50 ppm for a confidence level of 95%, we need to use the formula for sample size calculation for estimating a population mean.

The formula for sample size calculation is:

n = (Z * σ / E)^2

In this case, the desired margin of error is 50 ppm, which means the interval width is 2 * E = 50 ppm. Therefore, E = 25 ppm.

The Z-score corresponding to a 95% confidence level is approximately 1.96.

Given that the investigators made a rough guess of 175 for the value of σ (standard deviation) before collecting data.

We can substitute these values into the sample size formula:

n = (1.96 * 175 / 25)^2

Simplifying the calculation:

n = (7 * 175)^2

n = 1225^2

n ≈ 1,500,625

Therefore, a sample size of approximately 1,500,625 would be necessary to obtain an interval width of 50 ppm for a confidence level of 95%.

To obtain an interval width of 50 ppm with a confidence level of 95%, a sample size of approximately 1,500,625 is required. This is calculated using the formula for sample size estimation, considering a desired margin of error of 25 ppm and a standard deviation estimate of 175. The Z-score corresponding to a 95% confidence level is used to determine the sample size.

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Answer:

Hello,

y=4x-2

Step-by-step explanation:

1: slope.

\(\displaystyle \lim_{n \to \infty} \dfrac{f(x)}{x}\\\\= \lim_{n \to \infty} \dfrac{4x^2+6x-1)}{x(x+2)}\\\\= \lim_{n \to \infty} \dfrac{4x^2}{x^2}\\\\=\boxed{4}\\\)

2:

\(\displaystyle \lim_{n \to \infty} (f(x)-4x)\\\\= \lim_{n \to \infty} (\dfrac{4x^2+6x-1}{x+2}-4x)\\\\= \lim_{n \to \infty} (\dfrac{4x^2+6x-1-4x^2-8x}{x+2})\\\\= \lim_{n \to \infty} (\dfrac{-2x-2}{x+2})\\\\= \lim_{n \to \infty} (\dfrac{-2x}{x})\\\\=\boxed{-2}\\\)

Slant asymptote is     y=4x-2

Rayne sell each desk at the price of $125.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Given the following information;

The Number of desks sold = 3

The Amount of rent paid = $4

The Amount paid to carpenter = 1/2 of revenue

The Amount left = $185.50

If Rayee gave half of his revenue to the carpenter and then had $185.50 left.

The his revenue before paying the carpenter will be twice what he has left will be;

($185.50 * 2) = $371

Hence, the total revenue from the sale of 3 desk = ($371 + rent)

= (371 + 4)

= $375

Then each desk cost :

$375 / 3 = 125

Hence, Rayne sell each desk at the price of $125.

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The addition is one of the four fundamental mathematical operations. The selling price of each desk is $122.33.

The addition is one of the four fundamental mathematical operations, the others being subtraction, multiplication, and division. When two whole numbers are added together, the total quantity or sum of those values is obtained.

Revenue generated = Revenue left with Rayne + Revenue with carpenter

Since Rayne gave half of his revenue to the carpenter, therefore, both of them will have the same revenue will them

Revenue generated = Revenue left with Rayne + Revenue left with Rayne

Revenue generated = 2(Revenue left with Rayne)

Revenue generated = 2($185.50)

Revenue generated = $371

Also, Rayne paid a booth rent of $4. Therefore, the total revenue generated will be,

Total revenue generated = Revenue generated + $4

                                          = $371 + $4

                                          = $367

Since Rayne sell 3 desks, therefore, the selling price of each desk will be,

Selling price = $367 / 3

                     = $122.33

Hence, the selling price of each desk is $122.33.

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Answer:

\(3240^{0}\)

Step-by-step explanation

n = Number of sides

Sum of interior angles of a regular polygon = (n - 2) x \(180^{o}\)

                                                                        = (20 - 2) x  \(180^{o}\)

                                                                        = 18 x \(180^{o}\)

                                                                        = \(3240^{o}\)

The correct inequality is -5 - 3x > 10.

Let's substitute x = -6 into each inequality to determine which one is true.

1) -5 - 3x > 10

Substituting x = -6:

-5 - 3(-6) > 10

-5 + 18 > 10

13 > 10

2) -3 - 5x < -14

Substituting x = -6:

-3 - 5(-6) < -14

-3 + 30 < -14

27 < -14

3) 1 - 2x > 13

Substituting x = -6:

1 - 2(-6) > 13

1 + 12 > 13

13 > 13

4) 2 - x < -3

Substituting x = -6:

2 - (-6) < -3

2 + 6 < -3

8 < -3

Based on the substitutions, we find that the only inequality that is true when x = -6 is:

-5 - 3x > 10

Therefore, the correct inequality is -5 - 3x > 10.

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The correct answer is "Number of Skipped Classes".

The question seems to be related to a quiz where the first blank has options from which one has to be selected, while the second blank is left empty to be filled by the correct option.

Out of the three options given for the first blank, "Incorrect Number of Sex Partners" and "Incorrect

Number of Drinks" do not seem to fit in the context of a quiz where grades are given on the basis of academic performance.Therefore, the correct option for the first blank would be "Number of Skipped Classes".

This option is relevant in the context of a quiz since students' attendance is an essential part of their academic performance and, in many cases, the grades are allocated based on attendance marks.

If a student has skipped classes, it would definitely impact their academic performance, which makes this option the most appropriate one. In conclusion, the correct answer for the second blank is "Number of Skipped Classes".

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The expected number of students participating in each activity would be:

Playing: 45 students

Reading story books: 30 students

Watching TV: 20 students

Listening to music: 10 students

Painting: 15 students

To determine the number of students expected to participate in each activity, you can calculate the percentage of students engaging in each activity and then apply that percentage to the total student population of 2,000.

Playing: 45 students

Percentage: (45 / 2,000) x 100% = 2.25%

Expected number of students: 2.25% of 2,000 = 45

Reading story books: 30 students

Percentage: (30 / 2,000) x 100% = 1.5%

Expected number of students: 1.5% of 2,000 = 30

Watching TV: 20 students

Percentage: (20 / 2,000) x 100% = 1%

Expected number of students: 1% of 2,000 = 20

Listening to music: 10 students

Percentage: (10 / 2,000) * 100% = 0.5%

Expected number of students: 0.5% of 2,000 = 10

Painting: 15 students

Percentage: (15 / 2,000) x 100% = 0.75%

Expected number of students: 0.75% of 2,000 = 15

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the C-CAPM with power utility and lognormal consumption growth predicts that the representative agent in country A will consume more in the current period and that the price of an identical financial asset will be lower compared to country B.

The C-CAPM is a financial model that relates the consumption patterns and asset prices in an economy. In this scenario, the difference in subjective discount factors implies that the representative agent in country A values future consumption relatively less compared to country B. As a result, the representative agent in country A tends to consume more in the current period, prioritizing immediate consumption over saving for the future.

Furthermore, the C-CAPM suggests that the price of an identical financial asset, such as a stock or bond, will be lower in country A. This is because the higher subjective discount factor in country A implies a higher expected return requirement for investors. As a result, investors in country A will demand a higher risk premium, leading to a lower price for the financial asset.

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Answer:

H 1.613 cm

Step-by-step explanation:

porque tienes que estar más mi metido fracis

Answer:

9

Step-by-step explanation:

Because each new term is obtained by adding 2 to the previous term, we identify this as an arithmetic sequence.  The first term. a(1). is 3 and the common difference (d) is 2.  

The general formula for an arithmetic sequence is a(n) = a(1) + d(n -1)

Here the specific formula is a(n) = 3 + 2(n - 1)

and the fourth term, a(4), is 3 + 2(4 - 1), or 3 + 6, or 9

To find the minimum score required for an A grade, we need to determine the cutoff point that corresponds to the top 13% of scores.

Given that the scores on the test are normally distributed with a mean of 69.5 and a standard deviation of 9.5, we can use the standard normal distribution to calculate the cutoff point. Using a standard normal distribution table or a statistical calculator, we find that the z-score corresponding to the top 13% is approximately 1.04. To find the corresponding raw score, we can use the formula:

x = μ + (z * σ)

where x is the raw score, μ is the mean, z is the z-score, and σ is the standard deviation. Plugging in the values, we have:

x = 69.5 + (1.04 * 9.5) ≈ 79.58

Rounding this to the nearest whole number, the minimum score required for an A grade would be 80. Therefore, a student would need to score at least 80 on the test to achieve an A grade according to the professor's grading scheme.

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The only kind of data generated by observational research is correlations or patterns in the data that have been observed. By using correlations, one variable's value can be used to predict the value of another.

Explanation:

Accurate predictions using data correlation can be ensured by using a variety of methods. Firstly, it is important to ensure that the data is free from errors and is of high quality. This can be done by cleaning and validating the data to remove any inconsistencies and outliers. Secondly, it is important to analyze the data thoroughly and identify any patterns or trends. Furthermore, it is beneficial to use appropriate statistical tests and algorithms such as linear regression, logistic regression, and decision trees to identify the predictive relationships between the variables. Finally, it is important to evaluate the model’s performance to determine the accuracy of the predictions.

The most effective methods for ensuring accurate predictions using data correlation are:

1. Perform Exploratory Data Analysis: Exploratory data analysis is an essential step in any predictive modeling process. It involves exploring the data to identify patterns, trends, and relationships within the data. This helps to identify any potential issues or biases within the data that could affect the accuracy of predictions.

2. Use Statistical Tests: Statistical tests can be used to measure the strength of the relationship between two variables. These tests can help to identify which variables are most strongly correlated with each other and can help to determine which variables should be used in a predictive model.

3. Use Machine Learning Algorithms: Machine learning algorithms can be used to create predictive models that can identify and learn patterns in the data. These algorithms are particularly effective at identifying complex relationships between variables that may not be identified by statistical tests.

4. Validate Predictions: Predictions should always be validated to ensure that they are accurate and reliable. This can be done by comparing the predictions against known outcomes or by testing the model on a separate data set.

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Explanation

1) If a consistent system has exactly one solution, it is independent.

2) A system of equations is called an inconsistent system of equations if there is no solution because the lines are parallel.

Answer: Independent system and inconsistent system

Answer:

4 selections

Step-by-step explanation:

We are told in the question that:

Josie selected 6 books from the library. However, he can only check out 4 books at a time.

The number of possible selections can he make is 4 selections. This is because, He can only take 4 books out of the library at a time. This is the standard.

Answer:

D. 48

Step-by-step explanation:

For (2,12), x is multiplied by 6 to get y.

For (4,28), x is multiplied by 7 to get y.

For (6,y), x should be multiplied by 8 to get y, which would be 48

Answer:

I think its 44

Step-by-step explanation:

because it adds up to 16, you subtract 12 and 28 you get 16 at 16 to 24 equals 44, 16+28=44

Answer:

Infinity

Step-by-step explanation:

Topic: Fraction and relations:

Your domain (Input to a fraction, usually known as your "x") can be any Real number.

But, when you are dealing with a fraction or even square roots you have to be careful because:

You cannot have a ZERO as your denominator and you cannot have NEGATIVE number inside of the square root.

The 2 problems can have infinite solution because it is not a fraction or square root problem and it doesn't break the 2 rules mentioned above.

Answer:

-4(y - 2) = 12

Standard form:

−4y − 4 = 0

Factorization:

−4(y + 1) = 0

Solutions:

y = −4

4

= −1

Step-by-step explanation:

The total amount jamal paid is $305.

Given:

Jamal treated his family with a family brunch at the cost of $250.

The sales tax was 4%.

The tip is 18%.

to find the sales tax.

The amount he paid for sales tax is $ 10.

to find the tip.

Jamal left a tip of $45.

Thus the total amount paid by Jamal is,

A statement which describes a translation that would produce ΔDEF from the pre-image of triangle ΔABC include the following: A. To the right five units, and up two units.

In Mathematics, the translation of a geometric figure to the right simply means adding a digit to the value on the x-coordinate (x-axis) of the pre-image of a function while a geometric figure that is translated up simply means adding a digit to the value on the y-coordinate (y-axis) of the pre-image or parent function.

Next, we would determine the translation rule as follows;

ΔABC → ΔDEF = (2 + 5, 1 + 2) = D (7, 3)

ΔABC → ΔDEF = (4 + 5, 4 + 2) = E (9, 6)

ΔABC → ΔDEF = (4 + 5, 1 + 2) = F (9, 3)

Therefore, the translation rule is given by this mathematical expression ΔABC → ΔDEF = (x + 5, y + 2). This ultimately implies that, triangle ABC (ΔABC) was translated by five units to the right and up two units in order to produce triangle DEF (ΔDEF).

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We have to show that the set of numbers of the form a + b√2, where a and b are rational numbers, forms a field with respect to addition and multiplication.

To start, we need to show that the set of numbers is closed under addition and multiplication. This means that if we add or multiply two numbers in the set, the result must also be in the set.

For addition, let's take two numbers in the set, say (a1 + b1√2) and (a2 + b2√2). When we add them, we get (a1 + a2) + (b1 + b2)√2. Since a1, a2, b1, and b2 are all rational numbers, their sum is also a rational number. So, the result of adding two numbers in the set is always another number in the set, which means that the set is closed under addition.

For multiplication, let's take two numbers in the set, say (a1 + b1√2) and (a2 + b2√2). When we multiply them, we get (a1a2 + 2b1b2) + (a1b2 + a2b1)√2. Again, since all the numbers involved are rational, the result is also a rational number. This means that the set is closed under multiplication as well.

Next, we need to show that the set satisfies the commutative, associative, and distributive laws for both addition and multiplication. This means that the order in which we add or multiply numbers in the set does not matter, and that addition and multiplication can be combined in a predictable way.

The commutative, associative, and distributive laws for addition and multiplication are well-known for rational numbers, and it can be easily verified that they hold for this set as well.

Finally, we need to show that the set has additive and multiplicative inverses. This means that for each number in the set, there exists another number in the set such that when added (or multiplied) to the original number, the result is 0 (or 1).

It can be shown that for any number of the form a + b√2, its additive inverse is -a - b√2, and its multiplicative inverse is (a / (a^2 + 2b^2)) - (b / (a^2 + 2b^2))√2, assuming that a^2 + 2b^2 is not equal to 0. Both of these are also rational numbers, since they are obtained by dividing rational numbers.

So, we have shown that the set of numbers of the form a + b√2, where a and b are rational numbers, is closed under addition and multiplication, satisfies the commutative, associative, and distributive laws, and has additive and multiplicative inverses. This means that the set of numbers forms a field with respect to addition and multiplication.

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A triangle is a three-edged polygon with three vertices. The length of QS is equal to 17 units.

How do triangles work?

A triangle is a polygon having three vertices and three edges. It is a fundamental geometric figure. A triangle's total angles are always equal to 180 degrees.

Given that the line segment RQ is bisected at point T by the perpendicular bisector Line l. As a result, RT = QT is the length of the two lines.

Now, in ΔRST and ΔQST,

RT ≅ QT

ST ≅ ST {Common side}

Now, since the two triangles are the right-angled triangle, therefore, the two triangles are congruent. Thus, we can write,

RS = SQ

Given that the Line segment, RS is 3x+2. Line segment SQ is 5x-8.

RS = SQ

3x + 2 = 5x - 8

2 + 8 = 5x - 3x

10 = 2x

x = 5

QS = 5x - 8

    = 5(5) - 8

    = 25 - 8

    = 17 units

Hence, the length of QS is equal to 17 units.

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