What is the surface area of the triangular prism?


6. 5 ft 8ft 6ft 2. 5ft



115


120


135


159

when running a line, in a right-triangle, from the 90° angle perpendicular to its opposite side, we will end up with three similar triangles, one Small, one Medium and a containing Large one.

Check the picture below.

The correct statement regarding the perimeter of the rectangle is given as follows:

Both are correct.

The perimeter of a polygon is given by the sum of all the lengths of the outer edges of the figure, that is, we must find the length of all the edges of the polygon, and then add these lengths to obtain the perimeter.

The rectangle in this problem has:

Hence the perimeter is given as follows:

2 x 10 + 2 x n = 2 x (10 + n) = 20 + 2n = 2n + 20 cm.

Hence both are correct.

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20 questions subtraction and addition of fractions only like this:

A recipe calls for 2/3 cup of flour and 1/4 cup of sugar. What is the total amount of flour and sugar needed in fraction?

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Producing 0 washing machines is not a practical solution for a company.

To maximize profit, we need to find the difference between revenue and cost functions, which gives us the profit function P(x):

P(x) = R(x) - C(x) = (0.3x²) - (10,000 + 0.7x²)

Simplify the profit function:

P(x) = -0.4x² + 10,000

Now, to maximize profit, we'll find the critical points by taking the first derivative of P(x) with respect to x:

P'(x) = dP(x)/dx = -0.8x

Set P'(x) to zero and solve for x:

-0.8x = 0
x = 0

Since the profit function P(x) is a quadratic with a negative leading coefficient, the maximum value will occur at the critical point x = 0. However, producing 0 washing machines is not a practical solution for a company.

To maximize profit while producing washing machines, the company should consider other factors beyond the given cost and revenue functions, such as market demand and production capacity.

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There are 13.5 cubic meters of water in Mr. Johnson's pool.

Volume is defined as the space occupied within the boundaries of an object in three-dimensional space.

To find the volume of water in Mr. Johnson's pool, we need to multiply the length, width, and depth of the pool. The length is 2.5 meters, the width is 4.5 meters, and the depth of water is 1.2 meters.

So, the volume of water in Mr. Johnson's pool is:

2.5 meters x 4.5 meters x 1.2 meters = 13.5 cubic meters

Therefore, there are 13.5 cubic meters of water in Mr. Johnson's pool.

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The answer is: ∠N ≈ 33°

To find ∠N in ΔLMN, we can use the Law of Cosines which states that c² = a² + b² - 2abcos(C), where c is the side opposite angle C.

In this case, side LM (m) is opposite angle ∠N, side LN (n) is opposite angle ∠L, and side MN (x) is opposite the unknown angle.

So, we can write:
m² = n² + x² - 2nxcos(82°)

Substituting the given values:
x² = 35² + 59² - 2(35)(59)cos(82°)

Solving for x, we get:
x ≈ 64.27

Now, using the Law of Sines which states that a/sin(A) = b/sin(B) = c/sin(C), we can find ∠N:

sin(∠N)/35 = sin(82°)/64.27

sin(∠N) ≈ 0.5392

∠N ≈ sin⁻¹(0.857) ≈ 32.6344°

Therefore, ∠N ≈ 33° to the nearest degree.

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The effective price paid by the company after taking account of hedging would be $63.50, which is the August futures price on July 1. Calculate the profit or loss on the futures contracts and subtract that from the spot price on July 1, to determine the effective.

By entering into futures contracts on March 1, the company was able to lock in the price of $59 for the commodity, when the spot price was $60 and the futures price was $59, the difference between the futures price and the spot price on March 1 was $1 ($60 - $59), so the company had to pay an extra $1 per unit to hedge its purchase.

When the spot price increased to $64 on July 1, the company was still able to purchase the commodity at the lower hedged price of $59, plus the cost of the futures contract, which resulted in an effective price of $63.50. Overall, hedging helped the company mitigate the risk of price volatility and ensured a more predictable cost for the commodity purchase.

Effective price = Spot price - Profit from futures contracts

Effective price = $64 - $0.50(The difference between the futures price and the spot price on July 1 was $0.50 ($64 - $63.50))

Effective price = $63.50 per unit

Therefore, the effective price paid by the company after taking into account hedging was $63.50 per unit.

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Let x be the price of one donut and y be the price of one kolache. Then we have:

6x + 2y = 8.84 4x + y = 5.36

We can solve for y by multiplying the second equation by -2 and adding it to the first equation:

6x + 2y = 8.84 -8x - 2y = -10.72

-2x = -1.88

Dividing both sides by -2, we get:

x = 0.94

This means that one donut costs $0.94

Let's denote the cost of one apple as 'a' and the cost of one banana as 'b'. We can set up a system of two equations to represent the given information:

4a + 9b = 12.70   (equation 1)

8a + b = 17.70    (equation 2)

We can use either substitution or elimination method to solve for 'a' or 'b'. Let's use the elimination method by multiplying equation 2 by 9 and subtracting it from equation 1:

4a + 9b = 12.70

-(72a + 9b = 159.30)   (multiplying equation 2 by 9)

------------------

-68a = -146.60

Dividing both sides by -68, we get:

a ≈ 2.16

Therefore, the cost of one apple is approximately $2.16.

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The measure of angle θ, to the nearest tenth of a degree is 233.1°.

To find the measure of angle θ, we need to use trigonometry. We can see that the point (-5,-6) lies in the third quadrant since both x and y coordinates are negative. We can draw a right-angled triangle with the origin (0,0) as the vertex and the given point (-5,-6) as one of the vertices on the x-y plane.

The hypotenuse of this triangle will be the distance between the origin and the point (-5,-6), which can be calculated using the Pythagorean theorem.

Using the Pythagorean theorem, we get:

√(5²+6²) = √(25+36) = √61

Now we can use trigonometry to find the measure of angle θ. We can see that the sine of θ is equal to the opposite side over the hypotenuse and the cosine of θ is equal to the adjacent side over the hypotenuse. So we have:

sin θ = -6/√61 and cos θ = -5/√61

Using a calculator, we can find that θ is approximately 233.1° to the nearest tenth of a degree.

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A open box without a top 1260 sq. in. wood will Gabriella use.

Since the top of the box is the same area as the base, calculate the base.

B = length × width

Length of the wooden box = 18 in.

Width of the wooden box = 15 in.

B = 18(15) = 270 in.

Calculate the surface area of the box.

Surface Area = 2(B + wh + hl)

h = 15

w × h = 15(15) = 225

h × l = 15(18) = 270

Surface Area of the wooden box = 2(270 + 225 + 270) = 2(765) = 1,530 sq. inches

Subtract the base from the surface area: 1,530 - 270 = 1,260sq. in.

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The given question is incomplete, complete question is:

Gabriella is beauty a wooden box with a rectangular base that is 18 in by 15 in and is 15 in tall if she wants a open box without a top how much wood will Gabriella use

The area of the ring is 1,462.81 square feet, under the condition that a circle is circumscribed around a regular octagon with side lengths of 10 feet.

The area of the ring formed by the two circles can be evaluated using the formula for the area of a ring which is

Area of ring = π(R² - r²)

Here
R = radius of the larger circle
r = smaller circle radius

The radius of the larger circle is equal to half the diagonal of the octagon which is 10 feet. Applying Pythagoras theorem, we can evaluate that the length of one side of the octagon is 10/√2 feet.
Radius of the larger circle is

R = 5(10/√2)
= 25√2/2 feet
≈ 17.68 feet

Staging these values into the formula for the area of a ring,

Area of ring = π(17.68² - 10²) square feet

Area of ring ≈ 1,462.81 square feet
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Surface area of the cylinder in terms of [tex]$\pi$[/tex] is [tex]$5904\pi m^2$[/tex].

The surface area of a cylinder can be calculated by adding the area of the two bases (which are circles) and the lateral area (which is the area of the curved surface).

The radius of the cylinder is given as 36m and the height as 46m. Therefore, the diameter of the cylinder is 72m (twice the radius). Using the formula for the area of a circle, we can calculate the area of each base:

[tex]$A_{base} = \pi r^2 = \pi (36m)^2 = 1296\pi m^2$[/tex]

The lateral area of the cylinder can be calculated using the formula:

[tex]$A_{lateral} = 2\pi r h$[/tex]

Substituting the given values, we get:

[tex]$A_{lateral} = 2\pi (36m) (46m) = 3312\pi m^2$[/tex]

Therefore, the total surface area of the cylinder is:

[tex]$A_{total} = A_{base} + A_{lateral} + A_{base} = 2A_{base} + A_{lateral}$[/tex]

Substituting the values we calculated, we get:

[tex]$A_{total} = 2(1296\pi m^2) + 3312\pi m^2 = 5904\pi m^2$[/tex]

So the surface area of the cylinder in terms of [tex]$\pi$[/tex] is [tex]$5904\pi m^2$[/tex].

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It's actually asking you to find the angles within the circles and match it with the angles it's supposed to be. For example if angle COE is 90° (im taking a fake angle value), you should put arc CE <——> 90

If you are still confused and need me to do it so that you can understand what I mean, reply and I'll help you!

Answer:

See below

Step-by-step explanation:

The objective of the question has been well explained by user vaishub1101.

I am just adding an additional hint and one answer to get you going

Since you just needed one example, I am providing just that
One thing to note in the figure is that segments DEF, ACD and ABF are all tangents to the circle. This fact is important since at the point of tangency (where the tangent touches the circle), the tangent to a circle is always perpendicular to the radius.

Using this knowledge and the given angles we can compute all the other angles but not the arc length [tex]\frown \atop {CE}[/tex] since to find arc length we need the value of the radius

As an example to help you get going,
[tex]\angle{DFA} \longleftrightarrow 58^\circ[/tex]

You would drag the tile with ∠DFA to the top left box and the tile with 58° to the top right box

I am sure you can figure out the rest or else user vaishub1101 can help you out with the rest

Derivative f'(c) equals the average rate of change of f(x) over the interval [1, 4], which is given by (f(4) - f(1))/(4 - 1).

It's not a contradiction of the Mean Value Theorem, as we don't have sufficient information to confirm if the conditions for applying the MVT are met.

A more detailed explanation of the answer.

We need to discuss the Mean Value Theorem and determine if it's a contradiction for the given function.

Let f(x) be a continuous function on the interval [1, 4] and differentiable on the open interval (1, 4). According to the Mean Value Theorem (MVT), if these conditions are met, there exists a value c in the open interval (1, 4) such that the derivative f'(c) equals the average rate of change of f(x) over the interval [1, 4], which is given by (f(4) - f(1))/(4 - 1).

However, in your question, the function f(x) is not specified. We cannot determine whether f(x) is continuous on [1, 4] and differentiable on (1, 4) without knowing its specific form. Therefore, we cannot conclude that the MVT is applicable in this case.

So, it's not a contradiction of the Mean Value Theorem, as we don't have sufficient information to confirm if the conditions for applying the MVT are met. If you could provide the specific function f(x), we could further analyze the situation and determine if the MVT can be applied.

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The volume of the solid generated when the right triangle below is rotated about side IK is: 37.7 units²

The three-dimensional figure that is formed by rotating a triangle about it's height is called a Cone.

Where:

The triangle base length will be seen to become the radius of the cone

The triangle height will be seen to become the height of the cone

The formula for the volume of a cone is expressed as:

V = ¹/₃πr²h

Where:

r refers to the radius

h refers to the height

Therefore, we can say that the volume will be expressed as:

V = ¹/₃ * π * 2² * 9

V = 37.7 units²

Thus, that is the  volume of the solid generated when the right triangle below is rotated about side IK.

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The 99% confidence interval for the population mean is between 39.18 and 62.82, assuming that the population is normally distributed.

To construct a confidence interval for the population mean, we need to make certain assumptions about the distribution of the sample data and the population. In this case, we assume that the population is normally distributed, the sample size is small (less than 30), and the standard deviation of the population is unknown but can be estimated from the sample data.

Using these assumptions, we can calculate the confidence interval as:

CI = X ± tα/2 * (s/√n)

Where X is the sample mean, tα/2 is the critical value of the t-distribution with degrees of freedom (n-1) and a confidence level of 99%, s is the sample standard deviation, and n is the sample size.

Plugging in the values from the provided data, we get:

CI = 51 ± 2.898 * (17/√18)

CI = (39.18, 62.82)

Therefore, with 99% confidence, we can estimate that the population mean is between 39.18 and 62.82 based on the provided data.

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Answer:

Step-by-step explanation:

The volume of the pool can be calculated as:

Volume = length x width x height

Volume = 10 ft x 20 ft x 5 ft

Volume = 1000 cubic feet

The mass of the water in the pool can be calculated as:

Mass = Volume x Density

Mass = 1000 cubic feet x 60 pounds/cubic foot

Mass = 60,000 pounds

Therefore, the approximate mass of water in the pool is 60,000 lb , which corresponds to option D.

The measure of angles a and b is 36 degrees if they are alternate interior angles formed by a transversal intersecting two parallel lines.

To find the measure of angles a and b when angle b has a measure of 36 degrees, we need additional information.

If we assume that angles a and b are adjacent angles formed by two intersecting lines, then we can use the fact that adjacent angles are supplementary, meaning their measures add up to 180 degrees. Since angle b has a measure of 36 degrees, we subtract it from 180 to find angle a.

Thus, angle a = 180 - 36 = 144 degrees. Therefore, angle a has a measure of 144 degrees when angle b has a measure of 36 degrees.

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To find the particular solution to this differential equation using undetermined coefficients, we first need to guess the form of the particular solution. Since the right-hand side of the equation is a sinusoidal function, our guess will be a linear combination of sine and cosine functions with the same frequency:

y_p(t) = A sin(2t) + B cos(2t)

We can then find the derivatives of this guess:

y'_p(t) = 2A cos(2t) - 2B sin(2t)
y''_p(t) = -4A sin(2t) - 4B cos(2t)

Substituting these into the differential equation, we get:

(-4A sin(2t) - 4B cos(2t)) + 41(2A cos(2t) - 2B sin(2t)) - 53(A sin(2t) + B cos(2t)) = -580 sin(2t)

Simplifying and collecting terms, we get:

(-53A + 82B) cos(2t) + (82A + 53B) sin(2t) = -580 sin(2t)

Since the left-hand side and right-hand side of this equation must be equal for all values of t, we can equate the coefficients of each trigonometric function separately:

-53A + 82B = 0
82A + 53B = -580

Solving these equations simultaneously, we get:

A = -23
B = -15

Therefore, the particular solution to the differential equation is:

y_p(t) = -23 sin(2t) - 15 cos(2t)

Adding this to the complementary solution (which is just a constant, since the characteristic equation has no roots), we get the general solution:

y(t) = C - 23 sin(2t) - 15 cos(2t)

where C is a constant determined by the initial conditions.
To solve the given differential equation using the method of undetermined coefficients, we need to identify the correct form of the particular solution.

Given the differential equation:
y'(t) + 41y(t) - 53 = -580sin(2t)

We can rewrite it as:
y'(t) + 41y(t) = 53 + 580sin(2t)

Now, let's assume the particular solution Y_p(t) has the form:
Y_p(t) = A + Bsin(2t) + Ccos(2t)

To find A, B, and C, we will differentiate Y_p(t) with respect to t and substitute it back into the differential equation.

Differentiating Y_p(t):
Y_p'(t) = 0 + 2Bcos(2t) - 2Csin(2t)

Now, substitute Y_p'(t) and Y_p(t) into the given differential equation:
(2Bcos(2t) - 2Csin(2t)) + 41(A + Bsin(2t) + Ccos(2t)) = 53 + 580sin(2t)

Now we can match the coefficients of the similar terms:
41A = 53 (constant term)
41B = 580 (sin(2t) term)
-41C = 0 (cos(2t) term)

Solving for A, B, and C:
A = 53/41
B = 580/41
C = 0

Therefore, the particular solution is:
Y_p(t) = 53/41 + (580/41)sin(2t)

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The mean of the dataset, rounded to the nearest hundredth, is approximately 265.86.

Calculate the mean of the dataset from calculator?

The mean, also known as the average, is a measure of central tendency that represents the typical value of a dataset. It is calculated by summing up all the values in the dataset and dividing the sum by the number of values.

To calculate the mean of the dataset from the calculator output, we need to use the following formula:

mean = Σx / n

where Σx is the sum of all the values in the dataset, and n is the number of values in the dataset.

From the calculator output, we can see that:

Σx = 1861

n = 7

Substituting these values into the formula, we get:

mean = 1861 / 7

mean = 265.857142857

However, the problem asks us to round the mean to the nearest hundredth, so we need to round the answer to two output decimal places. To do this, we look at the third decimal place of the answer, which is 7, and we check the next decimal place, which is 1. Since 1 is less than 5, we leave the third decimal place as it is and drop all the decimal places after it. Therefore, the rounded mean is:

mean  ≈ 265.86

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The length of the base is 16 inches.

To find the length of the base of the triangular pane of glass, we can use the formula for the area of a triangle which is:

Area = (1/2) x base x height

We are given that the height of the pane is 32 inches and the area is 256 square inches. Substituting these values into the formula, we get:

256 = (1/2) x base x 32

To isolate the base, we can divide both sides by (1/2) x 32, which simplifies to 16. This gives us:

256 ÷ 16 = base

Simplifying the left side of the equation, we get:

16 = base

Therefore, the length of the base of the pane is 16 inches.

In summary, the triangular pane of glass has a height of 32 inches and an area of 256 square inches. To find the length of the base, we use the formula for the area of a triangle and solve for the base.

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The volume of the triangular prism is 171 cubic inches.

To find the volume of a triangular prism, you need to multiply the area of the base by the height of the prism. In this case, the base of the prism has an area of 18 square inches and the height is 9.5 inches. So, the volume of the prism can be calculated as follows:

Volume = Base Area x Height
Volume = 18 sq. in. x 9.5 in.
Volume = 171 cubic inches

Therefore, the volume of the triangular prism is 171 cubic inches.

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The values of the variables are:

c = 86 degrees

d = 168 degrees

a = 57 degrees

b = 94 degrees

Since the polygon is inscribed in a circle, the opposite angles of the polygon are supplementary. Thus, we have:

The top and bottom angles of the polygon are supplementary to angle "d":

c + 92 + 123 = 180 + d

The left and right angles of the polygon are supplementary to angle "c":

c + 94 = 180, so c = 86

The angle "a" is supplementary to angle "d":

a + 123 = 180 + d

The angle "b" is supplementary to angle "c":

b + 86 = 180

Substituting the values of "c" and solving the system of equations, we get:

d = 168

a = 57

b = 94

Therefore, the values of the variables are:

c = 86 degrees

d = 168 degrees

a = 57 degrees

b = 94 degrees

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We have shown that if r is both symmetric and antisymmetric, then r is a subset of the diagonal relation on s, i.e., r ⊆ diagonal.

If the relation r on s is both symmetric and antisymmetric, then for any elements a and b in s, we have:

If (a, b) is in r, then (b, a) must also be in r because r is symmetric.

If (a, b) and (b, a) are both in r, then a = b because r is antisymmetric.

Now, we want to show that r is a subset of the diagonal relation on s, which is defined as:

diagonal = {(a, a) | a ∈ s}

To prove this, we need to show that for any pair (a, b) in r, (a, b) must also be in the diagonal relation. Since r is a relation on s, (a, b) ∈ s × s, which means that both a and b are elements of s.

Since (a, b) is in r, we know that (b, a) must also be in r, by the symmetry of r. Therefore, we have:

(a, b) ∈ r and (b, a) ∈ r

By the antisymmetry of r, this implies that a = b. Therefore, (a, b) is of the form (a, a), which is an element of the diagonal relation.

Therefore, we have shown that if r is both symmetric and antisymmetric, then r is a subset of the diagonal relation on s, i.e., r ⊆ diagonal.

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The first derivative is dy/dx = [tex]-20x^3[/tex], and the second derivative is d^2y/dx^2 = -60x^2.

The function you provided is: y =[tex]-5x^4 + 1[/tex]

To find the first derivative (dy/dx), we'll use the power rule which states that if y = x^n, then dy/dx =[tex]n * x^(n-1)[/tex].

Applying this rule to each term, we get: dy/dx = [tex]d(-5x^4)/dx + d(1)/dx[/tex]dy/dx =[tex]-5(4x^(4-1)) + 0[/tex] (since the derivative of a constant is 0) dy/dx = [tex]-20x^3[/tex]

Now, to find the second derivative [tex](d^2y/dx^2)[/tex], we'll differentiate the first derivative again using the power rule: [tex]d^2y/dx^2 = d(-20x^3)/dx d^2y/dx^2 = -20(3x^(3-1)) d^2y/dx^2 = -60x^2[/tex]

So, the first derivative is dy/dx = [tex]-20x^3[/tex], and the second derivative is [tex]d^2y/dx^2 = -60x^2.[/tex]

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Answer:

Part (a):  Because the survey was held at basketball championship.

Part (b): The survey among students should held at school or in any common place.

Step-by-step explanation:

The investment grows to $4,493.29 at 2% interest, $4,558.56 at 3% interest, $4,625.05 at 4% interest, $4,692.79 at 5% interest, and $4,761.81 at 6% interest after 4 years of continuous compounding.

To solve this problem, we need to use the formula for continuous compound interest:
A = Pe^(rt)

Where A is the amount after t years, P is the initial principal, e is the mathematical constant approximately equal to 2.71828, r is the annual interest rate, and t is the time in years.

Using the given information, we can fill in the table as follows:

Interest Rate | Amount after 4 years
--------------|---------------------
2%            | $4,493.29
3%            | $4,558.56
4%            | $4,625.05
5%            | $4,692.79
6%            | $4,761.81

To find the amount after 4 years at each interest rate, we plug in the values of P, r, and t into the formula and simplify:

2%: A = $4000 * e^(0.02*4) = $4,493.29
3%: A = $4000 * e^(0.03*4) = $4,558.56
4%: A = $4000 * e^(0.04*4) = $4,625.05
5%: A = $4000 * e^(0.05*4) = $4,692.79
6%: A = $4000 * e^(0.06*4) = $4,761.81

Therefore, the investment grows to $4,493.29 at 2% interest, $4,558.56 at 3% interest, $4,625.05 at 4% interest, $4,692.79 at 5% interest, and $4,761.81 at 6% interest after 4 years of continuous compounding.

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According to the above, the fishing population is divided into 53% prefer fresh water and 47% prefer salt water.

To find the percentage of people that make up each group, we must find the total number of people who were surveyed:

228 + 245 + 242 + 285 = 1,000

Once we find the total number of people who took the survey, we can find the percentage of each value by making rules of three as shown below:

Age 30 and younger and Saltwater fishing:

1,000 = 100%

228 = ?%

228 * 100 / 1,000 = 22.8%

Age 30 and younger and Freshwater fishing:

1,000 = 100%

245 = ?%

245 * 100 / 1,000 = 24.5%

Over 30 years old and Saltwater fishing:

1,000 = 100%

242 = ?%

242 * 100 / 1,000 = 24.2%

Over 30 years old and Freshwater fishing:

1,000 = 100%

285 = ?%

285 * 100 / 1,000 = 28.5%

To find the other percentages we must find the total number of fishermen by age ranges and by fishing preference:

Age ranges

228 + 245 = 473

242 + 285 = 527

1,000 = 100%

473 = ?%

473 * 100 / 1,000 = 47.3%

1,000 = 100%

527 = ?%

527 * 100 / 1,000 = 52.3%

Fishing mode preferences

228 + 242 = 470

245 + 285 = 530

1,000 = 100%

530 = ?%

530 * 100 / 1,000 = 53%

1,000 = 100%

547 = ?%

470 * 100 / 1,000 = 47%

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Answer:

if Mr. Kamau wants to give each of his children an equal amount of money, he can either:

Buy 1 item for his son (costing sh. 324) and 0 items for his daughter, giving each child sh. 162.

Buy 1 item for his son (costing sh. 324) and 1 item for his daughter (costing sh. 220), giving each child sh. 272.

Step-by-step explanation:

Let x be the number of daughter items that Mr. Kamau will buy for his daughter. Since the son's item costs sh. 324, we know that each child should receive sh. (324 + 220x)/2.

We want to find how many items each child will buy, so we need to solve for x in the equation:

(324 + 220x)/2 = 220

Multiplying both sides by 2, we get:

324 + 220x = 440

Subtracting 324 from both sides, we get:

220x = 116

Dividing both sides by 220, we get:

x = 0.527

Since we can't buy a fraction of an item, Mr. Kamau should buy either 0 or 1 daughter item for his daughter. If he buys 0 daughter items, he can give his son sh. (324 + 2200)/2 = sh. 162. If he buys 1 daughter item, he can give each child sh. (324 + 2201)/2 = sh. 272. Therefore, the possible scenarios are:

Mr. Kamau buys 0 daughter items. His son buys 1 item and his daughter buys 0 items.

Mr. Kamau buys 1 daughter item. His son buys 1 item and his daughter buys 1 item.