The can of lead below has a surface area of 18064.in^2.if the diameter of the can is 5 inches, didn’t he height if the can

the system of equations is: [tex]300x + 450y = 6000[/tex]

[tex]y = x + 5[/tex]

Let's define the variables:

Let "x" be the number of cans of soup purchased by Samuel.

Let "y" be the number of frozen dinners purchased by Samuel.

According to the given information, each can of soup has 300 mg of sodium and each frozen dinner has 450 mg of sodium. Samuel purchased 5 more frozen dinners than cans of soup, so we can write the following equations:

The total sodium from cans of soup: 300x mg

The total sodium from frozen dinners: 450y mg

The total sodium from both cans of soup and frozen dinners: [tex]6000 mg[/tex]

So the first equation is:

[tex]300x + 450y = 6000[/tex]  (since the total sodium from cans of soup and frozen dinners is 6000 mg)

Since Samuel purchased 5 more frozen dinners than cans of soup, we can write the second equation:

[tex]y = x + 5[/tex] (since y is 5 more than x)

Therefore,  the system of equations is:

[tex]300x + 450y = 6000[/tex]

[tex]y = x + 5[/tex]

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The value of Cscθ is 1/y.

What is a trigonometric function?

The right-angled triangle's angle and the ratio of its two side lengths are related by the trigonometric functions, which are actual functions. They are extensively employed in all fields of geometry-related study, including geodesy, solid mechanics, celestial mechanics, and many others.

Here, we have

Given: if p(x,y) is the point on the unit circle defined by the real number theta.

We have to find the value of the csc theta.

P(x,y) is the point on the unit circle  (the unit circle has a radius of 1 and center (0,0))

Now in a diagram, we can see that

OA= x

AP= y

radius OP =1

∠POA =θ

Now in ΔAOP

Cscθ = hypotenuse/opposite side

Cscθ = OP/AP

Cscθ = 1/y

Hence, the value of Cscθ is 1/y.

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Answer: The altitude of the triangle is [tex]h = 7 \sqrt{3}.[/tex]

Step-by-step explanation:

Suppose that we separate the equilateral triangle with the altitude of the triangle, as shown in the diagram I attached.

Then the length of the altitude [tex]h[/tex] can be found through the Pythagorean theorem:

[tex]h = \sqrt{14^2-\left( \frac{14}{2} \right)^2} = \sqrt{147} = \boxed{7 \sqrt{3}}.[/tex]

Therefore, the altitude of the equilateral triangle is [tex]h = 7 \sqrt{3}.[/tex]

The statistical question that can result in numerical data is "How many hours this week did you spend on homework?"

The statistical question that can result in numerical data is "How many hours this week did you spend on homework?"

This is because the question is asking for a numerical response that can be measured and counted. The other options are not statistical questions that can result in numerical data.

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Let's denote the amount that state D spends on tourism as "x" million dollars. According to the given information, state C spends $1.8 million more than state D, so state C would spend "x + 1.8" million dollars on tourism.

The total amount spent by state C and state D combined is $56.8 million. So we can write the equation:

x + (x + 1.8) = 56.8

Now, we can solve this equation to find the values of x and x + 1.8, which represent the amount spent by state D and state C, respectively.

x + x + 1.8 = 56.8

2x + 1.8 = 56.8

2x = 56.8 - 1.8

2x = 55

x = 55 / 2

x = 27.5

So, state D spends $27.5 million on tourism, and state C spends $27.5 + $1.8 = $29.3 million on tourism.

Answer: An even function is a function that satisfies the condition:

f(-x) = f(x)

Let's check which of the given functions satisfies this condition:

f(x) = (x - 1)^2

f(-x) = (-x - 1)^2 = x^2 + 2x + 1

f(x) = (x - 1)^2

The two expressions are not equal, so f(x) is not an even function.

f(x) = 8x

f(-x) = -8x = -f(x)

f(x) = 8x

The two expressions are equal with opposite signs, so f(x) is an odd function.

f(x) = x^2 - x

f(-x) = (-x)^2 - (-x) = x^2 + x

f(x) = x^2 - x

The two expressions are not equal, so f(x) is not an even function.

f(x) = 7

f(-x) = 7 = f(x)

f(x) = 7

The two expressions are equal, so f(x) is an even function.

Therefore, the only even function among the given functions is:

f(x) = 7.

Step-by-step explanation:

The skydiver is in the air for 23 seconds.

A diagram or pictorial representation that organises the depiction of facts or values is known as a graph.  

The relationships between two or more items are frequently represented by the points on a graph.

The skydiver is in the air as long as their height is greater than zero. From the graph, we can see that the skydiver reaches a height of zero at t = 23 seconds. Therefore, the skydiver is in the air for:

t = 23 seconds - 0 seconds = 23 seconds

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Answer:

[tex]81\pi[/tex] [tex]mm^2[/tex]

Step-by-step explanation:

Let's recall the formula for the area of a circle:

[tex]A = \pi r^2[/tex]

We are given the diameter, but the formula uses the radius. Since the radius is equal to one-half of the diameter, we can find the radius by doing this:

[tex]r = \frac{1}{2}d=\\\\r=\frac{1}{2}(18)= \\\\r=9[/tex]

Now that we've found the radius is 9 mm, let's substitute the values into the formula for the area of a circle. We have:

[tex]A = \pi r^2=\\A=\pi (9^2)=\\A=\pi (81)=\\A=81\pi[/tex]

So, we've found that the exact area, in terms of pi, of either face of the coin is [tex]81\pi[/tex] [tex]mm^2[/tex].

To find the area of the coin/a circle use this equation:

(a = area, r = radius, d = diameter)

[tex]\text{a = r}^2[/tex]

So we need to do for the radius.

[tex]\text{r} = \dfrac{\text{d}}{2}[/tex]

[tex]\text{r} = \dfrac{18}{2}[/tex]

[tex]\text{r} = 9[/tex]

Then solve

[tex]\text{a = 9}^2[/tex]

[tex]\boxed{\bold{a = 81}}[/tex]

Answer:

x = 7

Step-by-step explanation:

8x + 5 + 3x + 8 = 90

11x + 5 + 8 = 90

11x + 13 = 90

11x = 77

x = 7

Let's Check

8(7) + 5 + 3(7) + 8 = 90

56 + 5 + 21 + 8 = 90

61 + 21 + 8 = 90

82 + 8 = 90

90 = 90

So, x = 7 is the correct answer!

Answer:

7

Step-by-step explanation:

First, collect common factors. This means put the x's together and the regular numbers together.

8x+3x=11x

5+8=13

11x+13=90

Subtract 13 from both sides

11x+13=90

    -13  -13

11x=77

Divide 77 by 11

x=7

Hope this helps! :)

In 5 minutes, the camel can drink = 1.5 x 5 = 7.5 gallons of water.

So, the camel can drink 7.5 gallons of water in 5 minutes.

The unitary method is a mathematical technique used to solve problems related to proportionality.

It involves finding the value of a single unit and using it to determine the value of a given quantity or multiple quantities.

The unitary method is useful in solving problems that involve direct proportion or inverse proportion.

To find out how much water the camel can drink in 5 minutes, we can use the unitary method.

We know that the camel can drink 15 gallons of water in 10 minutes.

So, in 1 minute, the camel can drink = 15/10 = 1.5 gallons of water.

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Answer:

13m

Step-by-step explanation:

Circumference = 2×3.14.R = 40.82 => R = 40.82÷(2×3.14) = 6.5m

d = 2R = 2×6.5 = 13m

The answers are: A)H0: μ1 − μ2 = 0; Ha: μ1 − μ2 ≠ 0

(b)  Means: Company A___50.6___ min.; Company B___52.75___ min.

c)The t-value is -0.30107., The p-value is 0 .764815.

A hypothesis is a testable statement about the relationship between two or more variables or a proposed explanation for some observed phenomenon

A)H0: μ1 − μ2 = 0

i.e there is no difference between the means of delayed flight for two different airlines

Ha: μ1 − μ2 ≠ 0

i.e there is a difference between the means of delayed flight for two different airlines

(b)

Company A___50.6___ min.

Company B___52.75___ min.

Mean of Company A = x`1= ∑x/n =34+ 59+ 43+ 30+ 3+ 32+ 42+ 85+ 30+ 48+ 110+ 50+ 10+ 26+ 70+ 52+ 83+ 78+ 27+ 70+ 27+ 90+ 38+ 52+ 76/25

= 1265/25= 50.6

Mean of Company B = x`2= ∑x/n =

=46+ 63+ 43+ 33+ 65+ 104+ 45+ 27+ 39+ 84+ 75+ 44+ 34+ 51+ 63+ 42+ 34+ 34+ 65+ 64/20

= 1055/20= 52.75

Difference Scores Calculations

Company A

Sample size for Company A= n1= 25

Degrees of freedom for company A= df1 = n1 - 1 = 25 - 1 = 24

Mean for Company A= x`1=  50.6

Total Squared Difference (x-x`1) for Company A= SS1: 16938

s21 = SS1/(n1 - 1) = 16938/(25-1) = 705.75

Company B

Sample size for Company B= n1= 20

Degrees of freedom for company B= df2 = n2 - 1 = 20 - 1 = 19

Mean for Company B= x`2=  52.75

Total Squared Difference (x-x`2) for Company B= SS2=7427.75

s22 = SS2/(n2 - 1) = 7427.75/(20-1) = 390.93

T-value Calculation

Pooled Variance= Sp²

Sp² = ((df1/(df1 + df2)) * s21) + ((df2/(df2 + df2)) * s22)

Sp²= ((24/43) * 705.75) + ((19/43) * 390.93) = 566.65

s2x`1 = s2p/n1 = 566.65/25 = 22.67

s2x`2 = s2p/n2 = 566.65/20 = 28.33

t = (x`1 - x`2)/√(s2x`1 + s2x`2) = -2.15/√51 = -0.3

The t-value is -0.30107.

The total degrees of freedom is = n1+n2- 2= 25+20-2=43

The critical region for two tailed test at significance level ∝ =0.05 is

t(0.025) (43) = t > ±2.017

Since the calculated value of t=  -0.30107.  does not fall in the critical region t > ±2.017, null hypothesis is not rejected that is there is no difference between the means of delayed flight for two different airlines.

The p-value is 0 .764815. The result is not significant at p < 0.05.

C) Do not reject H0. There is no statistical evidence that one airline does better than the other in terms of their population mean delay time.

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Answer:

2004

Step-by-step explanation:

Answer: 3:7

Step-by-step explanation: since the simplest form of the fraction 36/84 is 3/7 that means 36:84 in simplest form is 3:7.

The inverse function of f(x) = 3x + 5 is given as follows:

C. p(x) = 1/3x - 5/3.

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

f(x) = 3x + 5.

To obtain the inverse function, first we must exchange the variables x and y, hence:

y = 3x + 5

x = 3y + 5.

Now we must isolate the variable y, hence:

3y = x - 5

y = (x - 5)/3.

p(x) = 1/3x - 5/3.

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1. The total amount of your emergency fund will be $11,403.75.

2. $8,552.81 is in the CD, and $2,850.94 is in the regular savings account.

Your FICA deduction is 7.65% of your gross income:

7.65% of $4,520.00 = $345.98

Your federal tax withholding is 11.75% of your gross income:

11.75% of $4,520.00 = $531.40

Your state tax withholding is 8.5% of your gross income:

8.5% of $4,520.00 = $384.40

Your total deductions are:

= $345.98 + $531.40 + $384.40

= $1,261.78

Your monthly income after deductions is:

= $4,520.00 - $1,261.78

= $3,258.22

Your fixed expenses are 30% of your realized income:

= 30% of $3,258.22

= $977.47

Your monthly savings amount is:

= $3,258.22 - $977.47

= $2,280.75

You saved 5 months' worth in an emergency fund, so the total amount in your emergency fund is:

= 5 x $2,280.75

= $11,403.75

Regenerate response

You placed 75% of your emergency fund in a 60-day CD at a 5.25% APR:

= 75% of $11,403.75 = $8,552.81

You placed the remaining 25% of your emergency fund in a regular savings account at a 3.8% APR:

= 25% of $11,403.75

= $2,850.94.

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The amount of taxes owed on a taxable income of $51, 100 is $6,919.00. The correct option is B.

To determine the amount of taxes owed on a taxable income of $51,100, we need to use the federal income tax brackets and rates for the tax year in question.

For the tax year 2021, the federal income tax brackets and rates for single filers are:

10% on taxable income from $0 to $9,950

12% on taxable income from $9,951 to $40,525

22% on taxable income from $40,526 to $86,375

24% on taxable income from $86,376 to $164,925

32% on taxable income from $164,926 to $209,425

35% on taxable income from $209,426 to $523,600

37% on taxable income over $523,600

To calculate the taxes owed on a taxable income of $51,100, we need to determine the amount of income that falls into each tax bracket, and then apply the corresponding tax rate to each portion of income.

Income up to $9,950 is taxed at 10%. This gives us a tax of 0.10 x $9,950 = $995.

Income from $9,951 to $40,525 is taxed at 12%. This gives us a tax of 0.12 x ($40,525 - $9,951) = $3,384.48.

Income from $40,526 to $51,100 is taxed at 22%. This gives us a tax of 0.22 x ($51,100 - $40,526) = $2,312.72.

Adding these three amounts together, we get the total tax owed:

$995 + $3,384.48 + $2,312.72 = $6,692.20

Therefore, the closest answer choice is B) $6,919.00.

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The amount of taxes owned on a taxable income of $51100 is $11242 which is approximately equal to option (c).

An income refers to the money that an individual or organization receives on a regular basis from various sources, such as employment, investments, or business activities. It is typically reported as gross income before taxes and other deductions are taken out.

Tax is a mandatory financial charge imposed by the government on individuals, businesses, and other entities, based on their income or property value. The revenue generated from taxes is used to fund public services and infrastructure.

=$51100* 22/100

=$11242

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Answer:

A.  h'(2) = 5

B.  m'(2) = -24

C.  y = 8x - 31

D.  j'(2) = 3/25 = 0.12

Step-by-step explanation:

When differentiating composite functions, use the chain rule.

[tex]\boxed{\begin{minipage}{5.4 cm}\underline{Chain Rule for Differentiation}\\\\$\left[f\left(g(x)\right)\right]'=f'\left(g(x)\right) \cdot g'(x)$\\\end{minipage}}[/tex]

Chain Rule: The derivative of a composite function is the product of the derivative of the outer function evaluated at the inner function and the derivative of the inner function.

Using the chain rule, if h(x) = g(f(x)) then h'(x) = g'(f(x)) ⋅ f'(x).

To find h'(2), substitute x = 2 into the differentiated equation:

[tex]\begin{aligned}h'(x)& = g'(f(x)) \cdot f'(x)\\\\\implies h'(2)& = g'(f(2)) \cdot f'(2)\\& = g'(5) \cdot 1\\& = 5 \cdot 1\\&=5\end{aligned}[/tex]

Therefore, h'(2) = 5.

Using the chain rule, if m(x) = f(x²) then m'(x) = f'(x²) ⋅ 2x.

To find m'(2), substitute x = 2 into the differentiated equation:

[tex]\begin{aligned}m'(x) &= f'(x^2) \cdot 2x\\\\\implies m'(2) &= f'(2^2) \cdot 2(2)\\&=f'(4) \cdot 4\\&=-6 \cdot 4\\&=-24\end{aligned}[/tex]

Therefore, m'(2) = -24.

To find the slope of the tangent line to the graph of k at x = 4, substitute x = 4 into the derivative of k(x).

If k(x) = f(g(x)) then k'(x) = f'(g(x)) ⋅ g'(x).

Therefore, the slope of the tangent line is:

[tex]\begin{aligned}k'(x) &= f'(g(x)) \cdot g'(x)\\\\\implies k'(4) &= f'(g(4)) \cdot g'(4)\\&= f'(5) \cdot 4\\&= 2 \cdot 4\\&= 8\end{aligned}[/tex]

Now calculate k(x) when x = 4:

[tex]\begin{aligned}k(x)&=f(g(x))\\\\\implies k(4) &= f(g(4))\\&=f(5)\\&=1\end{aligned}[/tex]

To write the equation of the tangent line, substitute the found slope m = 8 and point (4, 1) into the point-slope equation:

[tex]\begin{aligned}y-y_1&=m(x-x_1)\\y-1&=8(x-4)\\y-1&=8x-32\\y&=8x-31\end{aligned}[/tex]

Therefore, an equation for the line tangent to the graph of k at x = 4 is:

To find the derivative of j(x) use the quotient rule.

[tex]\textsf{If\;\;$j(x)=\dfrac{g(x)}{f(x)}$\;\;then:}\\\\\\j'(x)=\dfrac{f(x)g'(x)-g(x)f'(x)}{(f(x))^2}[/tex]

To calculate j'(2), substitute x = 2 into the equation:

[tex]\begin{aligned} \implies j'(2)&=\dfrac{f(2)g'(2)-g(2)f'(2)}{(f(2))^2}\\\\&=\dfrac{5 \cdot 1-2 \cdot 1}{(5)^2}\\\\&=\dfrac{5-2}{25}\\\\&=\dfrac{3}{25}\\\\&=0.12\end{aligned}[/tex]

Therefore, j'(2) = 3/25 = 0.12.

Answer:

20 ..............................

The equation a² + b² = c² represents the Pythagorean theorem.

This is a theorem that  states that in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b).

The Pythagorean theorem is used to find the length of one of the sides of a right-angled triangle when the lengths of the other two sides are known.

To solve the problem, you need to have at least two side lengths given. Then, you can use the equation to find the length of the third side. For example:

If you know the lengths of sides a and b and need to find the length of the hypotenuse (c):

Plug in the known values for a and b into the equation and solve for c.

Example: If a = 3 and b = 4, then 3² + 4² = c², which gives 9 + 16 = c², so c² = 25, and c = sqrt(25) = 5.

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Answer:

1500

Step-by-step explanation:

Number of boxes = 12

Number of pencils in each box = 125

Total number of pencils

= 12 × 125

= 1500 pencils

We can condense and find n's solution: 3n + 24 = 2n - 4

Since n = -14, the unknowable number is also -14.

A mathematical expression called an algebraic expression includes variables, integers, and mathematical operations including addition, subtraction, multiplication, and division. Algebraic expressions can be straightforward, like "2x," or they can be more complicated, like

[tex]3x^2+4y-5[/tex].

Variables are used to represent unknown quantities and have a range of possible values. In problems requiring unknown values or to represent connections between quantities, algebraic expressions are widely used.

A mathematical expression that includes variables, constants, and operations involving algebra (addition, subtraction, etc.) is known as an algebraic expression. Terms comprise expressions.

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the answer to the equation 112+18*14/14-19 is 111.

How to solve the question?

To solve this equation, we need to follow the order of operations (also known as PEMDAS), which is as follows: parentheses, exponents, multiplication and division (performed left to right), and addition and subtraction (also performed left to right).

So let's break down the equation step by step:

18*14 = 252 (multiplication)

252/14 = 18 (division)

112+18 = 130 (addition)

130-19 = 111 (subtraction)

Therefore, the answer to the equation 112+18*14/14-19 is 111.

It's important to note that if we had performed the operations in a different order, we would have gotten a different answer. That's why following the order of operations is crucial in solving mathematical equations.

In general, it's important to have a good understanding of basic arithmetic and algebraic concepts to solve equations like this one. This includes knowing the order of operations, how to perform operations with fractions and decimals, and how to use variables and solve for unknowns. Practicing these skills regularly can help improve your problem-solving abilities in math and other subjects.

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To solve the equation x^2 + 4x - 11 = 0 by completing the square, we can follow these steps:

Move the constant term to the right side of the equation:

x^2 + 4x = 11

Complete the square by adding the square of half the coefficient of x to both sides of the equation:

x^2 + 4x + (4/2)^2 = 11 + (4/2)^2

Simplifying the left side:

x^2 + 4x + 4 = 11 + 4

Factor the perfect square on the left side of the equation:

(x + 2)^2 = 15

Take the square root of both sides of the equation:

x + 2 = ±√15

Solve for x by subtracting 2 from both sides:

x = -2 ± √15

Therefore, the solutions to the equation x^2 + 4x - 11 = 0 by completing the square are x = -2 + √15 and x = -2 - √15.

Step-by-step explanation:

w = width

2w + 2 =  Length

Area = W x L  = 84 = w (2w+2)

                          84 = 2w^2 + 2w

                            0 = 2w^2 + 2w - 84        Use Quadratic Formula

                                                                 a = 2    b=2    c = -84

to find  

W = 6      then     L =  14 inches

The shaded area covers around 0.8664 square feet of space.

The mean and standard deviation of the standard normal distribution are 0 and 1, respectively. The standard deviation shows how much a particular measurement deviates from the mean, and the standard normal distribution is centred at zero.

Using a conventional normal distribution table, we must first determine the areas to the left of z= -1.5 and z=1.5, and then subtract those two areas to determine the area of the shaded zone.

Using a standard normal distribution table, we find that the area to the left of z= -1.5 is 0.0668, and the area to the left of z=1.5 is 0.9332. As a result, the darkened region's area is:

0.9332 - 0.0668 = 0.8664

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The solution to the inequality is x ≤ 10, which means that each row of seats on the floor must have 10 seats or fewer in order to meet the fire safety regulations.

What is inequality?

In mathematics, the inequality of two lines refers to the relationship between the slopes and y-intercepts of two different lines on a coordinate plane. Specifically, if the slope of one line is greater than the slope of another line, and their y-intercepts are not equal, then the inequality symbol (< or >) can be used to represent their relationship. For example, if line A has a slope of 2 and a y-intercept of -3, and line B has a slope of 1 and a y-intercept of 1, we can write A > B to represent that line A is steeper than line B.

To solve this problem, we need to use the information given to us to set up an inequality that represents the total number of seats in the theater and then use that inequality to determine the maximum number of people that can be in the theater while still meeting the fire safety regulations.

Let's start by calculating the total number of seats in the theater. We know that there are 90 seats in the balcony and 15 rows on the floor. We don't know the exact number of seats in each row, but we do know that each row has the same number of seats, which we will call x. Therefore, the total number of seats in the theater is 90 + (15 × x)

Now we can set up an inequality to represent the maximum number of people that can be in the theater while still meeting the fire safety regulations. We know that this number must be less than or equal to 240. Therefore, our inequality is 90 + (15 × x) ≤ 240

Now we can solve for x by first subtracting 90 from both sides of the inequality,

15 × x ≤ 150

Next, we can divide both sides of the inequality by 15,

x ≤ 10

Therefore, the solution to the inequality is x ≤ 10, which means that each row of seats on the floor must have 10 seats or fewer in order to meet the fire safety regulations.

To check this solution, we can plug x = 10 into our expression for the total number of seats,

Total number of seats = 90 + (15 × 10) = 240

This confirms that the maximum number of people in the theater is 240, which is the limit imposed by the fire safety regulations.

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The percentage of females with brown eyes as follows is 25%.

Percentage is a way of expressing a number as a fraction of 100. It is represented by the symbol "%". The word "percent" means "per hundred".

Let's assume that the total population of Math town is 100 people for the sake of simplicity. Then, we can use the following information to create a table:

Population Males Females

Total         60         40

Brown eyes 18         ?

From the table, we can see that 60% of the population are males, so there are 60 x 0.3 = 18 males with brown eyes.

We also know that the total population with brown eyes is 28%, so there are 100 x 0.28 = 28 people with brown eyes. Therefore, there must be 28 - 18 = 10 females with brown eyes.

Finally, we can calculate the percentage of females with brown eyes as follows:

% of females with brown eyes = (10 / 40) x 100% = 25%

Therefore, the answer is (C) 25%.

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