What multiplies to -25 and adds to 0?

Correct answers -

a.Rate of change of water in the pool at t= 5 hours

b. Total volume of water in the pool at t=10 hours

c. Average rate of change of water in the pool = 389.31 gallons/hour

To answer the given questions, let's go step by step:

a. To find the rate of change of water in the pool at t=5 hours, we need to calculate the difference between the rate of water being pumped into the pool and the rate of water leaking from the pool at that specific time.

Rate of change of water in the pool at t=5 hours = P(5) - L(5)

P(5) = 1170 gal/hour (given)

L(5) = [tex]0.3e^5[/tex] gal/hour (given)

Substituting the values into the equation:

Rate of change of water in the pool at t= 5 hours = 1170 - [tex]0.3e^5[/tex]

b. To write an integral expression to calculate the total volume of water in the pool at t=10 hours, we need to integrate the rate of water being pumped into the pool over the time interval [0, 10] and subtract the integral of the rate of water leaking from the pool over the same interval.

Total volume of water in the pool at t=10 hours = ∫[0,10] P(t) - ∫[0,10] L(t) dt

P(t) = 1170 gal/hour (given)

L(t) = [tex]0.3e^t[/tex] gal/hour (given)

Calculating the integrals:

∫[0,10] P(t) dt = ∫[0,10] 1170 dt = 1170t | [0,10] = 1170 × 10 - 1170 × 0 = 11700 gallons

∫[0,10] L(t) dt = ∫[0,10] 0.3[tex]e^t[/tex] dt = 0.3 ∫[0,10] [tex]e^t[/tex]dt = 0.3 ([tex]e^t[/tex]) | [0,10] = 0.3 × ([tex]e^{10} - e^0[/tex]) ≈ 0.3 × (22025 - 1) ≈ 6606.9 gallons

Total volume of water in the pool at t=10 hours = 11700 - 6606.9 ≈ 5093.1 gallons

c. To find the average rate of change of water in the pool over the 10 hours, we need to divide the change in volume by the time interval.

Average rate of change of water in the pool = (Change in volume) / (Time interval)

Change in volume = Total volume of water in the pool at t=10 hours - Initial volume of water in the pool

Change in volume = 5093.1 - 1200 = 3893.1 gallons

Time interval = 10 hours

Average rate of change of water in the pool = 3893.1 / 10 = 389.31 gallons/hour

d. To find the absolute maximum volume of water in the pool over the interval [0,10], we need to find the maximum value of the volume function within that interval.

To determine this, we can find the critical points by setting the derivative of the volume function equal to zero and check the endpoints of the interval.

Since the volume function is not provided, we cannot directly find the absolute maximum volume without additional information.

Final answers-

a.Rate of change of water in the pool at t= 5 hours

b. Total volume of water in the pool at t=10 hours

c. Average rate of change of water in the pool = 389.31 gallons/hour

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For the given right angle triangle ABC  (A) option is the correct answer.

We have,

A right triangle, also known as a right-angled triangle, or more technically an orthogonal triangle, was originally known as a triangle, is a triangle with one right angle and two perpendicular sides. Trigonometry is based on the relationship between the sides and various angles of a right triangle.

What is the correct statement for right triangle ABC ?

Cos A = Sin ( 90˚- A )

Since at 90˚ Sine function convert into cosine function and (90˚- A) results in first quadrant where sine function is positive.

Therefore Cos A = Cos A

Hence the correct option is (a) option Cos A = Sin ( 90˚- A )

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complete question:

attached below.

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.

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

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.

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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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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The better statistics to compare the distribution are given as follows:

A. Mean and standard deviation.

The mean of a data-set is given by the sum of all observations in the data-set divided by the cardinality of the data-set, which represents the number of observations in the data-set.

The standard deviation of a data-set is calculated as square root of the sum of the differences squared between each observation and the mean of the data-set, divided by the cardinality of the data-set.

These two measures should be used as both distributions in this problem are symmetric, meaning that they do not contain outliers.

If the distribution contained outliers, then the median and the IQR should have been used.

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The correct statement according to the zero product property is the one in option B.

The zero product property says that if the product of two numbers A and B is zero, then either A or (and) B are equal to zero.

Then if:

(x + 10)*x = 0

Then we have that either:

x = 0

or:

x + 10 = 0

x = -10

Then the correct option is B:

"Either x = 0 or x + 10 =0"

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Answer:

scienific

Step-by-step explanation:

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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The value of length JK is 11

A tangent is a straight line that touches any part of the circumference. A circumference is the outer body of a circle.

A theorem of tangency states that if lines comes from thesame point of a circumference and meet at a point , then the lines are equal.

Therefore we can say that;

JA = JB = 5

AL = LC = 9

CK = LK - LC

= 15 -9

= 6

BK = LK = 6

therefore ;

JK = BK + JP

= 6+5

= 11

Therefore the value of JK is 11

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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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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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The steps correcting the error;

Step 1: Convert the mixed fraction to improper fractions

Step 2: Find the lowest common  factor

27/8

A fraction can be defined as the part of a whole number, variable or element.

The different types of fractions are;

From the information given, we have that;

10 1/4 - 6 7/8

First, convert the mixed fractions to improper fractions, we have that;

Multiply the numerator of the fraction by the whole number then add the numerator

41/4 - 55/8

Find the LCM

82 - 55 /8

subtract the value

27/8

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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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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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The area of the trapezium ABCD is 136 square cm

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

The image of the trapezium (see attachment)

The area of the trapezium ABCD is calculated as

Area = 1/2 * Sum of opposite sides * Height

When the given values are substituted in the above equation, we have the following equation

Area = 1/2 * (14 + 20) * 8

Evaluate the sum

Area = 1/2 * 34 * 8

Evaluate the products

Area = 136

Hence, the area of the trapezium ABCD is 136 square cm

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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 value of x such that f(x) = -24 is given as follows:

x = -3.

The exponential function in the context of this problem is defined as follows:

[tex]f(x) = -3(0.5)^x[/tex]

The numeric value of the function is given as follows:

f(x) = -24.

Hence we can equal the definition to -24 to obtain the value of x, as follows:

[tex]-3(0.5)^x = -24[/tex]

[tex]0.5^x = 8[/tex]

We have that:

Hence:

[tex]2^{-x} = 2^3[/tex]

x = -3.

Which is the solution to the exponential function in this problem.

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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:

[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]

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.

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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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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Answer:

The height of the new cylindrical tank is approximately 54.10 cm when rounded to two decimal places.

Step-by-step explanation:

Find the volume of the water in the original tank using the formula for the volume of a cylinder:

V1 = π(10.5cm)^2(20cm) ≈ 6939.25 cm^3

Since the amount of water is conserved, set the volume of the water in the new tank equal to V1:

V2 = π(10cm)^2(h)

π(10.5cm)^2(20cm) = π(10cm)^2(h)

Simplifying, we get:

4410 = 100h

h ≈ 44.10 cm

However, this is the height that the water would reach if it was poured into a cylinder with a radius of 10 cm. To find the actual height of the new tank, add the radius of the new tank (which is also 10 cm) to this height:

h_new = h + r = 44.10 + 10 = 54.10 cm

Therefore, the height of the new tank is approximately 54.10 cm when rounded to two decimal places.

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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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: 8

Step-by-step explanation:

9+10+6+7=32

32/4=8

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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