It would take 1 person 70 days of work to
build a house extension.
2 people have been working for 7 days on
this house extension.
a) How many days would it have taken 1
person to do this amount of work?
b) How many days would it take 1 person to
finish building this house extension?

The solution to the given differential equation is:ln|1/√(1 - y^2) + y/√(1 - y^2)| = x + C where C is the constant of integration.

To solve the differential equation dy/dx = x/(1 - y^2) by separation of variables, we can rewrite it as:

(1 - y^2) dy = x dx

Now we can separate the variables by bringing all the y-related terms to one side and x-related terms to the other side:

(1 - y^2) dy = x dx

1/(1 - y^2) dy = x dx

Integrating both sides with respect to their respective variables, we get:

∫1/(1 - y^2) dy = ∫x dx

To integrate the left side, we can use partial fraction decomposition or trigonometric substitution. Let's use the latter approach:

Using the substitution y = sin(theta), we have dy = cos(theta) d(theta) and (1 - y^2) = (1 - sin^2(theta)) = cos^2(theta). The integral becomes:

∫1/cos^2(theta) * cos(theta) d(theta) = ∫sec(theta) d(theta) = ln|sec(theta) + tan(theta)| + C

Now, we need to substitute back y = sin(theta):

ln|sec(theta) + tan(theta)| + C = ln|sec(arcsin(y)) + tan(arcsin(y))| + C = ln|1/√(1 - y^2) + y/√(1 - y^2)| + C

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The most appropriate statistical test to determine if there is a difference in history of fracture in the past 5 years between 60-year-old men with normal bone density, those with osteopenia, and those with osteoporosis is the chi-square test for independence.

       The chi-square test for independence is used to determine whether there is a relationship between two categorical variables. In this case, the two variables are bone density (normal, osteopenia, osteoporosis) and history of fracture in the past 5 years (at least once or none). The test determines if there is a significant association between these two variables, and if so, how strong the association is. The null hypothesis is that there is no association between the two variables, while the alternative hypothesis is that there is a significant association. The test calculates a chi-square statistic and a p-value, which is compared to a significance level to determine if the null hypothesis should be rejected.

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The most appropriate statistical test to determine if there is a difference in history of fracture in the past 5 years between 60-year-old men with normal bone density, those with osteopenia, and those with osteoporosis is the chi-square test for independence.

      The chi-square test for independence is used to determine whether there is a relationship between two categorical variables. In this case, the two variables are bone density (normal, osteopenia, osteoporosis) and history of fracture in the past 5 years (at least once or none). The test determines if there is a significant association between these two variables, and if so, how strong the association is. The null hypothesis is that there is no association between the two variables, while the alternative hypothesis is that there is a significant association. The test calculates a chi-square statistic and a p-value, which is compared to a significance level to determine if the null hypothesis should be rejected.

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Answer: 8

Step-by-step explanation:

9+10+6+7=32

32/4=8

Census data comparing earnings by gender and race can be used to provide evidence of discrimination or lack thereof.

However, it is important to interpret this data cautiously as there may be factors beyond discrimination that contribute to observed differentials. Culture and individual choice are two such factors. For example, certain cultural norms may dictate that women and minorities pursue lower-paying careers, or that they prioritize family responsibilities over career advancement. Similarly, individual choices such as level of education, experience, and negotiation skills can also contribute to differences in earnings.
While caution must be exercised when interpreting census data, there is still evidence to suggest that discrimination does exist. For instance, studies have shown that even when controlling for factors such as education and experience, women and minorities still earn less than their white male counterparts. This suggests that there are systemic barriers preventing these groups from achieving equal pay. Moreover, the fact that certain industries and occupations are dominated by men and have wider pay gaps also suggests discrimination.
However, it is also important to acknowledge that these issues are politically sensitive and can be difficult to address. Some may argue that affirmative action policies aimed at promoting diversity and equal pay are discriminatory against white men. Others may argue that there are no barriers to equal pay, and that individuals should be responsible for their own career choices. Ultimately, the interpretation of census data should be based on a nuanced understanding of all these factors.

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Therefore, the probability that the product will pass both inspections is 0.42.

To find the probability that the product will pass both inspections, we need to multiply the probabilities of passing each inspection:

P(passing both inspections) = P(passing first inspection) * P(passing second inspection | passed first inspection)

The probability of passing the first inspection is 1 - 0.4 = 0.6 (since the probability of rejection is 0.4).

The probability of passing the second inspection, given that the product passed the first inspection, is 1 - 0.3 = 0.7 (since the probability of rejection is 0.3).

So, we have:

P(passing both inspections) = 0.6 * 0.7 = 0.42

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Answer:

scienific

Step-by-step explanation:

Answer:

The probability of having no more than 5 cases this month is 0.421.

We can calculate this probability by using the following formula:

P(X <= 5) = ∑_{x=0}^5 P(X = x)

where P(X = x) is the probability of having x cases.

The probability of having 0 cases is 0.316, the probability of having 1 case is 0.368, the probability of having 2 cases is 0.201, the probability of having 3 cases is 0.075, and the probability of having 4 cases is 0.031.

Plugging these values into the formula, we get the following:

P(X <= 5) = 0.316 + 0.368 + 0.201 + 0.075 + 0.031 = 0.421

Therefore, the probability of having no more than 5 cases this month is 0.421.

Step-by-step explanation:

The solutions to the equation √(2x² - 7) - x = 3 are x = -2 and x = 8 and x = -2 is an extraneous solution

From the question, we have the following parameters that can be used in our computation:

√2x²-7-x=3

Express properly

So, we have

√(2x² - 7) - x = 3

Add x to both sides of the equation

This gives

√(2x² - 7) = x + 3

Take the square roots of both sides

So, we have

2x² - 7 = x² + 6x + 9

So, we have

x²  - 6x - 16 = 0

When solved for x, we have

x = -2 and x = 8

Hence, the solutions to the equation are x = -2 and x = 8 and x = -2 is an extraneous solution

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It rained approximately 4.47 inches on Tuesday.

The meaning of SUBTRACT is to take away by or as if by deducting. How to use subtract in a sentence.

On Monday, it rained 4(1/2) inches.

On Tuesday, it rained 0.03 inches less than on Monday.

To find out how much it rained on Tuesday, we need to subtract 0.03 inches from the rainfall on Monday.

4(1/2) inches - 0.03 inches = 4.5 inches - 0.03 inches = 4.47 inches

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We need to first determine how many total spins there were. Nolan spun the spinner 12 times. We also know that the spinner has 5 equal parts and there are 5 possible toys to win. Therefore, the probability of the spinner landing on bat is 4/12 or 1/3. This means that out of all the spins, one-third of them landed on bat.
Next, we need to determine how many times the spinner landed on bat. Looking at the data, we can see that the spinner landed on bat 4 times.
It's important to note that this probability is based on the 12 trial spins that Nolan conducted before the guests arrived. The actual probability of winning a specific toy during the festival may differ due to the randomness of each spin.
Based on the data you provided, we can determine the probability of the spinner landing on "bat." Out of the 12 spins Nolan tried, the spinner landed on "bat" 4 times. To calculate the probability, we simply divide the number of successful outcomes (landing on "bat") by the total number of trials (12 spins):
Probability of landing on "bat" = (Number of times "bat" occurred) / (Total number of spins)
Probability of landing on "bat" = 4/12
By simplifying the fraction, we get:
Probability of landing on "bat" = 1/3
So, the probability of the spinner landing on "bat" is 1/3 or approximately 33.33%.

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To determine how many sections of pipe the plumber needs to buy, we need to calculate the total length of pipe required and divide it by the length of each section available for purchase. In this case, the plumber needs eight sections, each 3'2" long, and the pipe is sold in 10' sections. The answer will indicate the number of sections the plumber must buy.

  The length of each section of pipe needed is 3'2", which can be converted to 3.17 feet. To find the total length of pipe required, we multiply the length of each section by the number of sections needed:

Total length of pipe = 3.17 feet/section × 8 sections = 25.36 feet

Since the pipe is sold in 10' sections, we need to determine how many 10' sections are needed to cover a length of 25.36 feet. Dividing the total length by the length of each section, we get:

Number of sections needed = 25.36 feet ÷ 10 feet/section = 2.54 sections

Since we can't purchase a fraction of a section, the plumber needs to buy 3 sections of pipe (as 2.54 is closer to 3 than 2).

Therefore, the answer is option C - 3.

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To determine how many sections of pipe the plumber needs to buy, we need to calculate the total length of pipe required and divide it by the length of each section available for purchase. In this case, the plumber needs eight sections, each 3'2" long, and the pipe is sold in 10' sections. The answer will indicate the number of sections the plumber must buy.

    The length of each section of pipe needed is 3'2", which can be converted to 3.17 feet. To find the total length of pipe required, we multiply the length of each section by the number of sections needed:

Total length of pipe = 3.17 feet/section × 8 sections = 25.36 feet

Since the pipe is sold in 10' sections, we need to determine how many 10' sections are needed to cover a length of 25.36 feet. Dividing the total length by the length of each section, we get:

Number of sections needed = 25.36 feet ÷ 10 feet/section = 2.54 sections

Since we can't purchase a fraction of a section, the plumber needs to buy 3 sections of pipe (as 2.54 is closer to 3 than 2).

Therefore, the answer is option C - 3.

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They would spend approximately 13.33 hours driving if they plan to cover a total distance of 800 miles at an average speed of 60mph.

To answer this question, we need to use the formula: time = distance/speed. In this case, the distance is 800 miles and the average speed is 60mph. Therefore, the time spent driving can be calculated as:
Time = 800 miles / 60 mph
Simplifying this equation, we get:
Time = 13.33 hours
So, the total time that they would spend driving is 13.33 hours. It's important to note that this is the average time it would take them if they maintained a constant speed of 60mph throughout their journey. However, if they encountered traffic, roadworks, or took any breaks during their trip, the actual time spent driving would be longer than this.
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Answer:A

Step-by-step explanation:

To determine the possible values of h, we can apply the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

In this case, we have side lengths measuring 3x cm, 7x cm, and h cm. Therefore, the possible values of h must satisfy the following conditions:

h + 3x > 7x

h + 7x > 3x

3x + 7x > h

Simplifying these inequalities, we have:

h > 4x

h > -4x (since we have h + 7x > 3x, we can subtract 7x from both sides)

10x > h

From these conditions, we can conclude that h must be greater than 4x and less than 10x. So, the expression that describes the possible values of h is:

h > 4x and h < 10x

Alternatively, we can write it as:

4x < h < 10x

Therefore, the correct option is A) 4x.

To determine the number of offspring with skin darker than their parents, we need more information about the specific genetic inheritance patterns and traits involved.

The answer depends on factors such as the dominance or recessiveness of genes controlling skin color, the genotype of the parents, and the specific combination of alleles passed on to the offspring.

Without additional information, it is not possible to provide an accurate count of the number of offspring with darker skin. Genetic inheritance is a complex process that involves multiple genes and interactions, making it necessary to consider specific genetic traits and their inheritance patterns to determine the outcome.

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The mood of the argument is categorical and the figure is EIO. To determine the mood and figure of the given argument, we'll first identify the premises and conclusion, and then assign the appropriate categorical proposition to each statement.

The argument can be rewritten as:

Premise 1: Some dictators are not warmongers. (Some D are not W)
Premise 2: No dictators are egomaniacs. (No D are E)
Premise 3: Some egomaniacs are warmongers. (Some E are W)
Conclusion: Some dictators are not warmongers. (Some D are not W)

Now, let's assign the categorical propositions to each statement:
Premise 1: I (Some D are not W)
Premise 2: E (No D are E)
Premise 3: I (Some E are W)
Conclusion: O (Some D are not W)

The mood of the argument is IEO.

Next, we'll determine the figure by looking at the placement of the middle term (E) in the premises:
Premise 2: No D are E (subject-middle term)
Premise 3: Some E are W (middle term-predicate)

The figure is 1 because the middle term is the subject of one premise and the predicate of the other premise.

So, the mood and figure of the argument are IEO-1. Therefore, the correct answer is:

IEO - 1

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Answer:

[tex]\large \sf \longrightarrow \: {3}^{5} [/tex]

[tex]\large \sf \longrightarrow \: 3 \times 3 \times 3 \times 3 \times 3[/tex]

[tex] \large\sf \longrightarrow \: 9 \times 9 \times 3[/tex]

[tex] \large\sf \longrightarrow \: 9 \times 27[/tex]

[tex] \large\sf \longrightarrow \: 243[/tex]

______________________________________________________

Answer:

Step-by-step explanation:

3⁵

Here,

[tex]\large\sf{3 }^{5 }[/tex]

[tex]\large\sf{=3 \times 3 \times 3 \times 3 \times 3 }[/tex]

[tex]\large\bf{= 243}[/tex]

The time taken to triple the principal investemet for an interest compounded semi-annually is approximately 267 months.

The formula accrued amount in a compounded interest is expressed as;

[tex]A = P( 1 + \frac{r}{n})^{(nt)}[/tex]

Where A is accrued amount, P is principal, r is interest rate and t is time.

Given that:

P = principal amount (initial investment) = $2000

A = final amount (triple the initial investment) = 3 × $2000 = $6000

r = interest rate per period = 5%

n = number of compounding periods per year n = 2

t = time in years = ?

First, convert R as a percent to r as a decimal

r = R/100

r = 5/100

r = 0.05

Plug the given values into the above formula and solve for time taken t.

[tex]A = P( 1 + \frac{r}{n})^{(nt)}\\\\t = \frac{In(\frac{A}{P}) }{n(In( 1 + \frac{r}{n}) } \\\\t = \frac{In(\frac{6000}{2000}) }{2(In( 1 + \frac{0.05}{2}) } \\\\t = 22.246\ years \\\\t = 267\ months[/tex]

Therefore, the time taken is approximately 267 months.

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Answer: 4140, 4060, and 4109

Step-by-step explanation:

4140: looking at the tens place (4) it is less than 5 so it rounds to 4100

4060: the tens place (6) is bigger than 5 so you add a 1 to the hundreds place everything behind it becomes a 0. and equal to 4100.

4109: everything behind becomes a 0

a. It will take 392 minutes for just 1 machine to produce same batch.

b. it will take 49 minutes for 8 machines to produce same batch.

a) To get minutes its take for just 1 machine, we will use the following formula:

Time = (Number of machines * Original time) / New number of machines

Time = (7 * 56) / 1

Time = 392 / 1

Time = 392 minutes

b. To get minutes its take for just 8 machine, we will use the following formula:

Time = (Number of machines * Original time) / New number of machines

Time = (7 * 56) / 8

Time = 392 / 8

Time = 49 minutes.

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1/2 is the probability that the number will add up to more than 4. Option C is correct

Probability is defined as the likelihood or chance that an event will occur.

Probability = Expected/Total

From the given spinner, the total outcome is expressed according to the permutation

For orange spin

3P2 = 3!
3P2  = 6

For green spin

4P2 = 4!/2!
4P2 = 12

If they are both spinned, the probability that the sum will be more than 4 are:

Expected (orange) = {(2,3)}

Expected (green) = {((1, 3), (3, 4) (2, 4), (2,3)}

Pr(number added is 4) = 1/6 + 4/12

Pr(number added is 4)  = 2+4/12

Pr(number added is 4)  = 1/2

Hence the probability that the number will add up to more than 4 is 1/2

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Answer:

2(p - 32)(p + 2)

Step-by-step explanation:

2p² - 60p - 128 ← factor out common factor 2 from each term

= 2(p² - 30p - 64) ← factor the quadratic

consider the factors of the constant term ( - 64) which sum to give the coefficient of the p- term (- 30)

the factors are - 32 and + 2 , since

- 32 × + 2 = - 64 and - 32 + 2 = - 30 , then

p² - 30p - 64 = (p - 32)(p + 2) , so

2p² - 60p - 128 = 2(p - 32)(p + 2)

The factors of a quadratic equation 2p² - 60p - 128 are (p - 4) and (p - 32).

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. In other terms, a "polynomial function of degree 2" is a quadratic function.

To factorize a quadratic equation of the form ax² + bx + c, we need to find two numbers that multiply to ac and add up to b. In this case, we have:

a = 2, b = -60, c = -128

The product of a and c is:

ac = 2 × (-128) = -256

We need to find two numbers that multiply to -256 and add up to -60. We can start by listing the factors of -256:

1, -1, 2, -2, 4, -4, 8, -8, 16, -16, 32, -32, 64, -64, 128, -128, 256, -256

We can see that -16 and 16 are a pair of factors that multiply to -256. We can also see that -16 + 16 = 0, which is not what we want. We need factors that add up to -60, not to 0.

We can try the next pair of factors, -32 and 8. These multiply to -256 and add up to -24. This is closer to what we want, but we need factors that add up to -60.

We can try the next pair of factors, -64 and 4. These multiply to -256 and add up to -60. This is what we need, so we can use these factors to factorize the quadratic equation:

2p² - 60p - 128 = 2(p - 4)(p - 32)

Therefore, the factors of the quadratic equation are (p - 4) and (p - 32).

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Hello

4/2 + 7/2 - 3/2

= 11/2 - 3/2

= 8/2

= 4

Answer:

1

You're welcome!

A coefficient is a constant which stands in front of a variable

For example, the coefficient of 3x is 3.  

Or, the coefficient of 9xy is 9

Same with 2x^2*z.  2

In this case, because there is nothing visible, the coefficient is 1.

a) The probability of picking at least one green marble is given as follows: 5/9, option D.

b) The expected number of repetitions with the same color is given as follows: 150 repetitions.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The number of outcomes in this problem is given as follows:

9.

The number of outcomes in which at least one green was picked is:

5.

Hence the probability is of:

p = 5/9.

3 outcomes had the same color, (G,G), (O,O) and (B,B), hence the probability is given as follows:

p = 3/9

p = 1/3

Out of 450 repetitions, the amount is given as follows:

E(X) =  1/3 x 450 = 150 repetitions.

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Mandy's Candies sells an average of 68 pounds of fudge and 81 pounds of toffee each month. Option B

Using  a system of equations to solve this

Let f be the number of pounds of fudge sold each month, and

t be the number of pounds of toffee sold each month.

Then we have:

f + t = 149    (equation 1)

8.12f + 7.62t = 1169.38   (equation 2)

We can solve for f in equation 1:

f = 149 - t

Substituting this into equation 2, we get:

8.12(149 - t) + 7.62t = 1169.38

Simplifying and solving for t, we get:

1209.88 - 0.5t = 1169.38

0.5t = 40.5

t = 81

Substituting this back into equation 1, we get:

f + 81 = 149

f = 68

Therefore, Mandy's Candies sells an average of 68 pounds of fudge and 81 pounds of toffee each month.

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[tex]\textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ V=158055.04\\ h=78 \end{cases}\implies 158055.04=\cfrac{\pi r^2(78)}{3} \\\\\\ (3)158055.04=78\pi r^2\implies \cfrac{(3)158055.04}{78\pi }=r^2 \\\\\\ \sqrt{\cfrac{(3)158055.04}{78\pi }}=r\implies \sqrt{\cfrac{(3)158055.04}{78(3.14) }}=r\implies 44=r[/tex]

The normal distribution is often used to model real-world phenomena, and one of its important properties is that about two-thirds of observations fall within one standard deviation of the mean. This makes it useful for analyzing data sets with a large number of observations, such as in Variation 2 or egg roulette.

Many natural phenomena do not follow a perfectly normal distribution, but certain aspects of these phenomena may be modeled using a normal distribution with some degree of accuracy. For example, the distribution of hemoglobin levels in a population may not be perfectly normal, but it may be close enough to a normal distribution for practical purposes.

The central limit theorem states that as the sample size increases, the distribution of the sample means approaches a normal distribution, regardless of the distribution of the original population. The sample size required to see this effect depends on the shape of the original distribution, but generally, a sample size of 30 or more is often considered sufficient to see a normal distribution emerge.

The results of many studies may involve adding up a large number of random events, but it is important to note that this does not necessarily mean that the results are normally distributed. However, the central limit theorem suggests that the distribution of the means of many independent random variables will approach a normal distribution, which can be useful in statistical analysis.

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As per the properties of parallel lines and interior alternate angles postulate, we can prove that:

⇒ m ∠5+ m ∠2+ m ∠6 = 180°

Given that;

Line y || z

i.e. y is parallel to z.

To Prove:

⇒ m ∠5+ m ∠2+ m ∠6 = 180°

Since, It is given that the lines y and z are parallel to each other.

m∠5, m∠1 are interior alternate angles because lines y and z are parallel and one line AC cuts them.

So, m∠5 = m∠1  ..... (1)

Similarly,

m∠6, m∠3  are interior alternate angles because lines y and z are parallel and one line AB cuts them.

So, m∠6 = m∠3  ...... (2)

Now, we know that the line y is a straight line and A is one point on it.

Sum of all the angles on one side of a line on a point is always equal to 180 degree .

i.e. ⇒ m ∠1+ m ∠2+ m ∠3 = 180°

Using equations (1) and (2):

We can see that:

⇒ m ∠5+ m ∠2+ m ∠6 = 180°

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Answer:

10.6

Step-by-step explanation:

To find out how long the person must leave the money in the bank until it reaches $22,600, we can use the formula for compound interest:

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

Where:

A = the final amount (22600 dollars in this case)

P = the principal amount (9500 dollars)

r = the annual interest rate (5.75% expressed as 0.0575)

n = the number of times the interest is compounded per year (in this case, annually, so n = 1)

t = the time in years

Substituting the given values into the formula, we have:

22600 = 9500(1 + 0.0575/1)^(1*t)

Simplifying:

2.3789 = (1.0575)^t

To solve for t, we take the logarithm of both sides:

log(2.3789) = log((1.0575)^t)

Using logarithm properties, we can bring the exponent down:

log(2.3789) = t * log(1.0575)

Now, we can solve for t by dividing both sides of the equation:

t = log(2.3789) / log(1.0575)

Using a calculator, we find:

t ≈ 10.6

Therefore, the person must leave the money in the bank for approximately 10.6 years to reach $22,600.

Answer:

Use the radioactive decay formula: A = Ao*2^(-t/h), where

A = 722*2^(-17/71)

find 2^(-17/71) with a calc

A = 722*.847076

A = 611.59 kg after 17 hrs

Step-by-step explanation:

Answer:

The formula for the amount of radioactive material remaining after a certain time can be expressed as:

N(t) = N₀ * (1/2)^(t/h)

Where:

N(t) is the amount of radioactive material remaining after time t

N₀ is the initial amount of radioactive material

h is the half-life of the material

Substituting the given values, we have:

N(14) = 439 * (1/2)^(14/76)

N(14) = 386.377 kg

Therefore, the amount of radioactive material remaining after 14 hours is 386.377 kg. The answer is option (d).

Step-by-step explanation: