The initial population is 4001 and the maximum population is 4000
The given population growth model is [tex]12000/3+e^{-0.02(t)}.[/tex]
To find the initial population, we need to plug in t=0 into the equation.
[tex]12000/3+e^{-0.02(0)}[/tex]
= [tex]12000/3+1[/tex]
= [tex]4000+1[/tex]
= [tex]4001[/tex]
So the initial population is 4001.
To find the maximum population, we need to find the limit of the equation as t approaches infinity.
= [tex]12000/3+0[/tex]
= [tex]4000[/tex]
So the maximum population is 4000.
In conclusion, the initial population is 4001 and the maximum population is 4000.
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Real World Example 1 - Write and Solve an Inequality
a. Of the students surveyed at Madison High School, fewer than eighty-four said they have
never purchased an item online. This is about one-eighth of all those surveyed. How
many students were surveyed?
X < 84
8x < 84 (8)
The answer is 8x < 672
According to the information, the mathematical expression with which the problem is solved is 8x < 672.
How to find the expression that solves this problem?To find the expression that solves this problem we must take into account that it is an inequality. So we must use the symbols greater than > or less than <. Additionally, we must read the information in the statement to identify how it goes to the inequality.
According to the above, there are less than 84 students who answered that they had never bought online (x). Then the expression would start like this:
x < 84Subsequently, they do not say that x equals one eighth of the total number of students. Then the expression would be modified like this:
8x < 84 (8)Finally, if we simplify this expression, it would look like this:
8x < 672So, that would be the expression of this inequality.
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Follow the guided instructions below to rotate the figure 90° clockwise about the point (2, 3).
Answer:
Follow the guided instructions below to rotate the figure 90° clockwise about the point (2, 3).
Step-by-step explanation:
Follow the guided instructions below to rotate the figure 90° clockwise about the point (2, 3).
Answer:15 because it is connected to the line
Step-by-step explanation:
First divide 97.65625 by 2.5. True? Or false
True, 39.0625 is the value of First division .
What is division, and how does it work?
Multiplication is the opposite of division. When you divide 12 into three equal groups, you get four in each group if three groups of four add up to 12, which they do when you multiply. The primary objective of division is to count the number of equal groups that are created or the number of individuals in each group after a fair distribution.
In mathematics, division is the process of dividing a number into equal parts and determining how many of those parts there are in total. For instance, breaking 15 into 3 equal groups of 5 is equivalent to dividing 15 by 3.
= 97.65625 / 2.5
= 39.0625
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Find the area of the right triangle in simplest radical form that has a hypotenuse of 8 ft and a leg of 4 ft. (No decimals)
In its simplest radical form, the area of the right triangle is 8sqrt(3) square feet.
How is area determined?
The length of the other leg of the right triangle can be determined using the Pythagorean theorem:
[tex]a^2 + b^2 = c^2[/tex]
where the hypotenuse is c and the triangle's legs are a and b.
We are aware that the hypotenuse c is 8 feet long and that leg an is 4 feet long. Let's work out the answer for the opposite leg's length, b:
[tex]b^2 = c^2 - a^2\sb^2 = 8^2 - 4^2\sb^2 = 64 - 16\sb[/tex]
[tex]sqrt(48) = 4sqrt(3) foot where 2 = 48 b[/tex]
Given that we know the lengths of both legs, we can use the following formula to get the triangle's area:
[tex](1/2) * Base * Height = Area[/tex]
We may use the 4 ft leg as the base and the 4sqrt(3) ft leg as the height since one leg is 4 ft and the other is 4sqrt(3) ft:
Area: (1/2) * 4 feet * 4 square feet (3)
= 8sqrt(3) square feet
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Im really confused .
Answer:
Triangle A is not a scale drawing
Triangle B is a scale drawing
Triangle C is not a scale drawing
find the surface area of each figure. round answers to the nearest hundredth, if necessary
The surface area of the prism is 224 ft².
What is a prism?Having identical endpoints in three dimensions, a prism is a solid object. This combination consists of flat faces, identical bases, and equal cross-sections.
We are given a figure of a prism having a square base.
We know that
Surface Area of Prism (A) = 2a² + 4ah
We are given the following information:
a = 4 ft
h = 12 ft
On substituting these values in the formula, we get
⇒A = 2(4)² + 4(4)(12)
⇒A = 2(16) + (16)(12)
⇒A = 32 + 192
⇒A = 224 ft²
Hence, the surface area of the prism is 224 ft².
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Since there are multiple questions so the question answered above is attached below
i need helpp pp pp p
Answer:
I CAN NOT SEE THAT OML
Step-by-step explanation:
factor x^3 + 1/8
thank you
[tex]\textit{difference and sum of cubes} \\\\ a^3+b^3 = (a+b)(a^2-ab+b^2) ~\hfill a^3-b^3 = (a-b)(a^2+ab+b^2) \\\\[-0.35em] ~\dotfill\\\\ x^3+\cfrac{1}{8}\implies x^3+\cfrac{1^3}{2^3}\implies x^3+\left( \cfrac{1}{2} \right)^3~\hfill \stackrel{\textit{let's just for a second make}}{\cfrac{1}{2}=a} \\\\\\ x^3+a^3\implies (x+a)(x^2-ax+a^2)\implies \left( x+\frac{1}{2} \right)\left( x^2-\frac{x}{2}+\frac{1}{4} \right)[/tex]
27. For which values of k, if any, are u and v orthogonal? (a) u = (k. 1,3), v = (1,7,K) (b) u = (-2,k,k), v = (k. 5, k) 28. Use vectors to find the cosines of the interior angles of the triangle with vertices A(0,-1), B(1,-2), and C(4,1), 29. Use vectors to show that A(3, 0, 2), B(4,3,0), and C(8, 1.-1) are vertices of a right triangle. At which vertex is the right angle? 30. In each part determine whether the given number is a valid ISBN by computing its check digit. (a) 1-56592-170-7 (b) 0-471-05333-5 31. In each part determine whether the given number is a valid ISBN by computing its check digit. (a) 0-471-06368-1 (b) 0-13-947752-3
For two vectors to be orthogonal, their dot product should be zero.
(a) The dot product of u and v is k+21k=22k. For u and v to be orthogonal, 22k=0, which means k=0.
(b) The dot product of u and v is -2k^2+5k^2+k^2=4k^2. For u and v to be orthogonal, 4k^2=0, which means k=0.
Therefore, in both cases, the vectors are orthogonal when k=0.
Let AB and AC be vectors joining the points A(0,-1), B(1,-2), and C(4,1), respectively. Then,
AB = (1-0, -2-(-1)) = (1,-1)
AC = (4-0, 1-(-1)) = (4,2)
The cosine of the angle between two vectors u and v is given by the dot product of u and v divided by the product of their magnitudes, i.e., cos(theta) = (u.v)/(|u||v|).
(a) Cosine of angle A = cos(BAC) = (AB.AC)/(|AB||AC|) = (1(4) + (-1)(2))/sqrt(2^2+1^2 * 4^2+2^2) = 2/3
Cosine of angle B = cos(CAB) = (AC.AB)/(|AC||AB|) = (4(1) + 2(-1))/sqrt(4^2+2^2 * 2^2+1^2) = 1/3
Cosine of angle C = cos(ABC) = (AB.BC)/(|AB||BC|) = ((1)(3) + (-1)(-1))/sqrt(2^2+1^2 * 2^2+1^2) = 5/9
(b) Let AB and BC be vectors joining the points A(3,0,2), B(4,3,0), and C(8,1,-1), respectively. Then,
AB = (4-3, 3-0, 0-2) = (1, 3, -2)
BC = (8-4, 1-3, -1-0) = (4, -2, -1)
AC = (8-3, 1-0, -1-2) = (5, 1, -3)
The cosine of the angle between two vectors u and v is given by the dot product of u and v divided by the product of their magnitudes, i.e., cos(theta) = (u.v)/(|u||v|).
Cosine of angle A = cos(BAC) = (AB.AC)/(|AB||AC|) = (1(5) + 3(1) + (-2)(-3))/sqrt(1^2+3^2+(-2)^2 * 5^2+1^2+(-3)^2) = 0
Cosine of angle B = cos(CAB) = (AC.AB)/(|AC||AB|) = (5(1) + 1(3) + (-3)(-2))/sqrt(5^2+1^2+(-3)^2 * 1^2+3^2+(-2)^2) = -7/9
Cosine of angle C = cos(ABC) = (AB.BC)/(|AB||BC|) = ((1)(4) + (
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Aliza needs to run at a rate faster than 8.2 feet per second in order to exceed her fastest time in a race. After running for 15 minutes, her coach determines that she is running at an average rate of 5.8 miles per hour. He converts the average rate to feet per second as shown below:
Answer:
8.50667 or approximately 8.51 feet per second
Step-by-step explanation:
The most approximate way to get the feet per second is to multiply the miles per hour by 1.467.
There are 1,000 grams in 1 kilogram. Lucas has a bucket with 2 kilograms of sand. Mac has a bucket with 4 kilograms of sand. How many grams of sand do they have in all?
In total, they have 6000 grams of sand.
What are basic arithmetic operations?
The basic arithmetic operations are the four fundamental mathematical operations used to manipulate numerical values. They are addition, subtraction, multiplication, and division.
To solve the problem, we need to know the conversion factor between kilograms and grams, which is 1 kilogram = 1000 grams.
First, we can find out how many grams of sand Lucas has in his bucket. We are given that he has 2 kilograms of sand, so we can use the conversion factor to convert kilograms to grams:
2 kilograms x 1000 grams/kilogram = 2000 grams
Therefore, Lucas has 2000 grams of sand in his bucket.
Next, we can find out how many grams of sand Mac has in his bucket. We are given that he has 4 kilograms of sand, so we can use the conversion factor again:
4 kilograms x 1000 grams/kilogram = 4000 grams
Therefore, Mac has 4000 grams of sand in his bucket.
To find out the total amount of sand they have in grams, we can add the amount of sand each of them has:
2000 grams + 4000 grams = 6000 grams
Therefore, in total, they have 6000 grams of sand.
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In ΔIJK, i = 2. 1 inches, � m∠J=103° and � m∠K=13°. Find the length of k, to the nearest 10th of an inch
Answer:
k = .5 inches
Step-by-step explanation:
On a piece of paper, graph this system of inequalities. Then determine which
region contains the solution to the system.
y≤x-2
y²-x-4
OA. Region A
B. Region B
OC. Region C
OD. Region D
A
D
10
8
6
4
2
-10-8-04-2 01
2
-8
-8
-10
N
4
'В'
B
C
B
10
The region that contains the solution to the system is region B
How to determine the region with the solutionGiven the following system of inequalities
y ≤ x - 2
y ≥ 1/4x - 4
Next, we analyze each of the inequalities expressions
Inequality 1: y ≤ x - 2
This is a less than or equal to inequalitySo, the bottom part is shadedInequality 2: y ≥ 1/4x - 4
This is a greater than or equal to inequalitySo, the upper part is shadedUsing the above as a guide, we have the following:
This means that the intersection regionn contains the solution
This is represented by the region (b)
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After solving an equation the answer is x=3. What can you say about the solution?
The solution to the equation is x=3, which means that when x is equal to 3, the equation is true.
The solution of an equation is the value of the variable that satisfies the equation.
In this case, the solution is x=3, which means that when x is substituted with 3, the equation is true.
We can say that the solution is unique, as there is only one value of x that satisfies the equation. It is also a real solution, as the value of x is a real number.
Additionally, we can say that the solution is finite, as there is a specific value for x that satisfies the equation.
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Use synthetic division an(d)/(o)r factoring to write f(x)=20x^(3)+44x^(2)-17x-5 in completely factored form, given that (-(5)/(2)) is a zero of f(x).
The function f(x) in completely factored form is (4x+1)(5x-1)(x+5).
To write f(x)=20x^(3)+44x^(2)-17x-5 in completely factored form, we can use synthetic division with the given zero of (-(5)/(2)).
Step 1: Set up the synthetic division with the given zero and the coefficients of the polynomial.
(-(5)/(2)) | 20 44 -17 -5
|______________
Step 2: Bring down the first coefficient, 20, and multiply it by the given zero.
(-(5)/(2)) | 20 44 -17 -5
| -50
|______________
| 20
Step 3: Add the result of the multiplication to the next coefficient and repeat the process until all coefficients have been used.
(-(5)/(2)) | 20 44 -17 -5
| -50 3 10
|______________
| 20 -6 -14 5
Step 4: The last number in the bottom row is the remainder. If it is zero, then the given zero is a factor of the polynomial. In this case, the remainder is 5, so (-(5)/(2)) is not a factor of f(x).
Since (-(5)/(2)) is not a factor of f(x), we cannot use synthetic division to write f(x) in completely factored form. Instead, we can use factoring to find the factors of f(x).
f(x) = 20x^(3)+44x^(2)-17x-5
= (4x+1)(5x-1)(x+5)
Therefore, f(x) in completely factored form is (4x+1)(5x-1)(x+5).
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DUE TODAY HELP!!!!!!!!!!!!
The image shows a circle with radius 5 units. Use the arc length and the radius to calculate the radian measure of 180 degrees.
The radian measure of 180 degrees is [tex]\pi \\[/tex] radians.
How to find the relation between angle subtended by the arc, the radius and the arc length?[tex]2\pi^c = 360^\circ = \text{Full circumference}[/tex]
The superscript 'c' shows angle measured is in radians.
If radius of the circle is of r units, then:
[tex]1^c \: \rm covers \: \dfrac{circumference}{2\pi} = \dfrac{2\pi r}{2\pi} = r\\\\or\\\\\theta^c \: covers \:\:\: r \times \theta \: \rm \text{units of arc}[/tex]
We are given that;
Radius=5units
Radian=180 degrees
Now,
The arc length of a circle is given by the formula:
arc length = (r * theta)
where r is the radius of the circle and theta is the angle in radians subtended by the arc at the center of the circle.
We know that the radius of the circle is 5 units, and we want to find the radian measure of an arc that subtends an angle of 180 degrees.
Since 180 degrees is half of a full circle, the arc length of this arc will be half of the circumference of the circle:
arc length = (1/2) * 2 * pi * r
= pi * r
Plugging in r = 5, we get:
arc length = pi * 5 = 5pi
Now we can use the formula for arc length to find the radian measure of the arc:
arc length = r * theta
5pi = 5 * theta
theta = pi
Therefore, by the arc length the answer will be [tex]\pi[/tex] radians.
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Which answer choice correctly represents the quotient of 28,134 divided by 71?
A.
B.
C.
D.
Answer:
please give brainliest
Step-by-step explanation:
396.253521127
Find the missing degrees in the circle
The missing degrees in the circle are 260 degrees.
What is circle ?
A circle is a geometrical shape that represents a set of points in a plane that are equidistant from a fixed point called the center. The distance from the center to any point on the circle is called the radius, and the diameter of the circle is the distance across its widest point, passing through the center.
To find the missing degrees in the circle, we need to use the fact that the sum of the central angles in a circle is equal to 360 degrees.
In this circle, we have two central angles: one measuring 100 degrees and the other measuring x degrees. We also know that the sum of these two central angles is equal to 360 degrees.
Therefore, we can set up the following equation:
100 + x = 360
To solve for x, we can subtract 100 from both sides:
x = 260
Therefore, the missing degrees in the circle are 260 degrees.
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one of the angles of a parallelogram is 36\deg greater than another one. find the angles of the parallelogram.
The value of the angles of the parallelogram are 72 degree and 108 degree.
What are the characteristics of a parallelogram?A quadrilateral with the opposing sides parallel is known as a parallelogram. It has numerous crucial traits, including:
A parallelogram has equal-length opposite sides. A parallelogram has opposite angles that are equally sized. A parallelogram's diagonals cut each other in half. A parallelogram is divided into four equal-sized triangles by its diagonals. A parallelogram's internal angles add up to 360 degrees. A parallelogram is classified as a rectangle if it also contains four right angles, making it a rectangle-shaped parallelogram.
Let us suppose the smaller angle = x.
The other angle is thus x + 36.
In a parallelogram the opposite angles are equal thus:
x + x + x + 36 + x + 36 = 360
4x + 72 = 360
4x = 288
x = 72
The value of x + 36 = 72 + 36 = 108
Hence, the value of the angles of the parallelogram are 72 degree and 108 degree.
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Write the first five terms of a sequence. Don't make your sequence too simple. Write both an explicit formula and a recursive formula for a general term in the sequence.
For the arithmetic sequence:
f(n) = f(1) + (n - 1)*4
Where the first term of the sequence is f(1) = 2
are:
f(1) = 2
f(2) = 6
f(3) = 10
f(4) = 14
f(5) = 18
How to write the first five terms of a sequence?We want to write the first five terms of a sequence, so first let's define the sequence.
We can define an arithmetic sequence with the recursive formula:
f(n) = f(n) + 4
And the explicit formula.
f(n) = f(1) + (n - 1)*4
Where we can define the first term of the sequence as f(1) = 2
Then the first five terms are:
f(1) = 2
f(2) = 2 + 4 = 6
f(3) = 6 + 4 = 10
f(4) = 10 + 4 = 14
f(5) = 14 + 4 = 18
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Prove that any two consecutive terms in the Fibonacci sequence
are relatively prime. (The Fibonacci sequence is given by f1 = 1,
f2 = 1, fn = fn−2 + fn−1.)
They are relatively prime.
Proof: Let fn and fn-1 be any two consecutive terms in the Fibonacci sequence. By definition, fn = fn-2 + fn-1. Since both fn and fn-1 are integers,
they must have no common factors other than 1,
so they are relatively prime.
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Help needed! Immediately would be very great :)
Answer: 56 inches
Step-by-step explanation:
To find the length of each side, use Pythagorean's Theorem, a² + b² = c²
Note the bottom sides are the same length and the top two are the same length.
Bottom sides:
5² + 12² = c²
25 + 144 = c²
169 = c²
13 = c
Top sides:
9² + 12² = c²
81 + 144 = c²
225 = c²
15 = c
Add it all together
13 + 13 + 15 + 15 = 56
The perimeter is 56 inches.
Hope this helps!
A factory manufactures a metal peice in 32 minutes new technology allowed the factory to cut that time by 8% then another improvement cut the time by 5% how long does it take to manufacture the peice now round your answer to nearest minute
The time is takes to manufacture the piece after two improvements is 28 minutes
Calculating how long it takes to manufacture a pieceFrom the question, we are to calculate how long it takes to manufacture a metal piece
First, we need to find the new time taken to manufacture the metal piece after the two improvements.
The first improvement reduces the time by 8%. This means that the new time is:
32 - (8% of 32)
= 32 - 2.56
= 29.44 minutes
The second improvement reduces the time by 5%. This means that the new time is:
29.44 - (5% of 29)
= 29.44 - 1.45
= 27.99 minutes
We can round this to the nearest minute, which gives us 28 minutes.
Hence, it takes 28 minutes to manufacture the metal piece.
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Marcus found these three ordered pairs for the equation y = 52x + 150: (0, 150), (10,670), and (20,1190).
When he graphs these, what is the best range for the y-axis?
0 to 150
0 to 670
0 to 20
0 to 1190
PLEASE SOLVE FOR ME NEED ANSWER ASAP PLEASE
Using the leg rule and the Pythagorean theorem, we have:
x = 4
y ≈ 4.5
How to Apply the Leg Rule?The leg rule that can be use to solve the missing measures of the right triangle is given as:
hypotenuse/leg = leg/part
We have the following:
Hypotenuse = 9
Leg = 6
Part = x
Plug in the values:
9/6 = 6/x
9x = 36
x = 36/9
x = 4
Use the Pythagorean theorem to find y:
y = √(6² - 4²)
y ≈ 4.5
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Please help I’ll give brainliest!!
25-9x² can be expressed in factor form as (5+3x)(5-3x)
What is Expression?An expression is combination of variables, numbers and operators.
The given expression is 25-9x²
We have to factor it completely
We have an identity that a²-b²=(a+b)(a-b)
25-9x² can be written as 5²-(3x)²
Now apply the identity
(5+3x)(5-3x)
Hence, 25-9x² can be expressed in factor form as (5+3x)(5-3x)
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rio drew two similar rectangles. one rectangle was 9 inches long and 6 inches wide. the second rectangle was 15 inches wide. how long was the second rectangle?
As a result, the length of the second rectangle is 22.5 inches.
Are rectangles always squares?Every square is also a rectangle because a square is a parallelogram with all particular corners at right angles. Yet not all rectangles are squares; for a rectangle to be a square, all of its sides must be the same length.
We can infer that the two rectangles may have a similar shape but differ in size because we can see how similar they are to one another.
By using the fact that the ratio of the adjacent angles of two comparable rectangles is the same, we can determine the length of the following rectangle.
Let x be the second rectangle's length. Then we can establish a ratio:
9/6 = x/15
We can cross-multiply to find x:
9 x 15 = 6 × x
135 = 6x
x = 22.5
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Answer this easy geometry question. And no links, please.
Answer:
Yes, they are equal.
Step-by-step explanation:
Because these are both right triangles, we know that one angle is similar. And seeing that side MO is the hypotenuse of both triangles, by the SA theorem we know that the two are equal. Or because we know that this is a reactangle or square by the four equal angles, we know that because this triangle is split in half, the triangle have to be equal.
-Hope this
helppppp
Suppose the annual interest rate is 7.5% and the interest is compounded annually. How much will an investment of $1,000 be worth after 3 years?
The amount after 3 years with an interest rate of 7.5% will be $1,242.3.
What is compound interest?A loan or deposit's interest is computed using the starting principle and the interest payments from the ago decade as compound interest.
We know that the compound interest is given as
A = P(1 + r)ⁿ
Where A is the amount, P is the initial amount, r is the rate of interest, and n is the number of years.
Assume the yearly interest rate is 7.5% and the interest is compounded once a year.
If the amount of investment is $1,000 and the amount after 3 years is given as,
A = P(1 + r)ⁿ
A = $1,000 × (1 + 0.075)³
A = $1,000 × (1.075)³
A = $1,000 × 1.24229
A = $1,242.3
The amount after 3 years with an interest rate of 7.5% will be $1,242.3.
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Samuel's house is due west of Stafford and due south of Seaside. Stafford is 24 kilometers from Samuel's house and 74 kilometers from Seaside. How far is Seaside from Samuel's house, measured in a straight line? kilometers Submit
The distance between Seaside and Samuel's house is approximately 77.8 kilometers.
Determine The distanceTo find the distance between Seaside and Samuel's house, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the hypotenuse is the distance between Seaside and Samuel's house, and the other two sides are the distances from Stafford to Samuel's house and from Stafford to Seaside.
1. Let x be the distance between Seaside and Samuel's house.
2. According to the Pythagorean theorem, x^2 = 24^2 + 74^2
3. Simplifying the equation gives us x^2 = 576 + 5476
4. Further simplifying gives us x^2 = 6052
5. Taking the square root of both sides gives us x = 77.8
Therefore, the distance between Seaside and Samuel's house is approximately 77.8 kilometers
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