5)


The population of Sanibel, Florida can


be modeled by P = 6191 · 1. 05t,


where t is the number of years since


2016. What was the population in


2016? What percent did the


population increase by each year?

The predicted value of y when x = 3, based on the least-squares regression line equation y = 50 - 15x, is y = 50 - 15(3) = 5.

The given least-squares regression line equation y = 50 - 15x represents a linear relationship between the variables x and y. In this equation, the coefficient of x (-15) represents the slope of the line, and the constant term (50) represents the y-intercept.

To find the predicted value of y when x = 3, we substitute x = 3 into the equation and solve for y. Plugging in x = 3, we have y = 50 - 15(3). Simplifying this expression, we get y = 50 - 45 = 5.

Therefore, when x = 3, the predicted value of y based on the least-squares regression line is 5. This means that according to the regression line, when x is 3, the expected or estimated value of y is 5.

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Answer:

1) f(-2) = -2 + 3

2) f(-2) = 1

Answer:

Aww! Thanks! Have a great day as well!

Step-by-step explanation:

Answer:

Step-by-step explanation:

If you write 1 instead of y, x would be 5/8 so ratio is 1/5:8=8/5

Answer:

\(x^6\)

Step-by-step explanation:

\(\left(\frac{x^5}{x^2}\right)^2\)

\(\frac{\left(x^5\right)^2}{\left(x^2\right)^2}\)

\(\frac{x^{10}}{x^4}\)

\(x^{10-4}\)

\(x^6\)

Answer:

$7700

Step-by-step explanation:

Given data

Rate= 2%

Principal= $7000

Time= 5 years

The simple interest expression is

A=P(1+rt)

substitute

A=7000(1+0.02*5)

A=7000(1+0.1)

A=7000*1.1

A=7700

Hence the amount is $7700

Answer:

241.9026

Step-by-step explanation:

2*pi*r

Answer:

241.9 cm

Step-by-step explanation:

circumference= \(\pi\)d

circumference= \(\pi\)(77)

circumference= 241.9 cm

A script (code) in matlab 1 for the given algorithm is given below.

function x = iterateAlgorithm(D, L, U, B, x0, n)

   % Decompose A into submatrices

   A = D + L + U;

   % Iteration loop

   for iter = 1:n

       % Compute x^n using the given algorithm

       x = inv(D + L) * (B - U * x0);

       % Update x^(n-1) for the next iteration

       x0 = x;

   end

end

This code defines a function called iterateAlgorithm that takes the submatrices D, L, U, the matrix B, the initial vector x0, and the number of iterations n. It performs the specified iteration algorithm to compute xⁿ.

To use this code, you can call the iterateAlgorithm function and provide the appropriate input matrices and variables. For example:

% Define the submatrices D, L, U

D = ...;  % Define the D submatrix

L = ...;  % Define the L submatrix

U = ...;  % Define the U submatrix

% Define the matrix B and initial vector x0

B = ...;  % Define the B matrix

x0 = ...; % Define the initial vector x0

% Specify the number of iterations

n = ...;  % Define the number of iterations

% Call the iterateAlgorithm function

x = iterateAlgorithm(D, L, U, B, x0, n);

Make sure to replace the ... with the actual values for your specific matrices and variables. Running this code will compute the vector x based on the given algorithm and the provided inputs.

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Answer:

C

Step-by-step explanation:

\(\frac{3-\sqrt{3} }{3+\sqrt{3} } *\frac{3-\sqrt{3} }{3-\sqrt{3} } \\\\=\frac{(3-\sqrt{3})^{2} }{(3+\sqrt{3} )(3-\sqrt{3} )} \\\\=\frac{9-2*3\sqrt{3}+3 }{9-3}\\\\=\frac{12-6\sqrt{3} }{6} \\\\=2-\sqrt{3}\)

The area of the sidewalk in square meters is 69π.

To find the area of the sidewalk, we need to subtract the area of the flower bed from the area of the outer circle formed by the sidewalk.

First, we need to find the area of the flower bed. We know that the diameter of the flower bed is 20 m, so the radius is half of that, which is 10 m. We can use the formula for the area of a circle, which is A = πr^2, where A is the area and r is the radius.

Area of flower bed = π(10m)^2 = 100π square meters

Next, we need to find the area of the outer circle formed by the sidewalk. Since the sidewalk is 3 m wide, the radius of the outer circle will be 10 + 3 = 13 m (10 m for the flower bed radius plus 3 m for the width of the sidewalk).

Area of outer circle = π(13m)^2 = 169π square meters

Finally, we can find the area of the sidewalk by subtracting the area of the flower bed from the area of the outer circle:

Area of sidewalk = Area of outer circle - Area of flower bed
Area of sidewalk = (169π) - (100π)
Area of sidewalk = 69π square meters

Therefore, the area of the sidewalk in square meters is 69π, or approximately 216.6 square meters (if we use 3.14 for π).

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The value of the 549 coins in pounds (£) is 305.4 .

What is fraction multiply?

Multiplying fractions is defined as the product of a fraction with a fraction or with an integer or with the variables. The procedure to multiply the fractions are: Multiply the numerator with numerator. Multiply the denominator with the denominator. Simplify the fractions, if required.

Given:

Total coins : 549 coins

one third(1/3) of the coins are £1 coins

164 of the coins are 50p coins

rest of the coins are 20p coins

one third of 549 = 549/3 = 183

Thus ,  

£1 coins = 183

50p coins =  164

20p coins = 549 - (183 + 164) = 202

value of the 549 coins in pounds (£) is given by

\(= 549 * \frac{1}{3} * 1 + 164* 0.5 + (549 *\frac{2}{3} - 164)*0.2\\\\= 183 + 82 +40.4\\\\= 305.4\)

Hence , the value of the 549 coins in pounds (£) is 305.4 .

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Natasha has left with 4.5 inches of oak boards.

What is a simplification?

The act of simplifying something such that it is simpler to carry out or understand, or the thing that is the product of this simplifying process: The group offers suggestions for streamlining trade processes.

Here, we have

120 inches of oak boards

50.75 inches for shelves, 36 1/4 more inches of oak boards, and she didn’t use 401/2 inches for the top and 60.5 inches for the sides.

We have to find how many inches of oak boards Natasha has left.

We use here simplification, we get

= 120 + 36 1/4 - 50.75 - 40 1/2 - 60.5

= 4.5 inches

Hence, Natasha has left with 4.5 inches of oak boards.

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Answer: C

Step-by-step explanation:

The triangle in the picture is an equilateral triangle. We know this is true because all sides are equal, as denoted by the tick marks. In equilateral triangles, each angle is 60° because when you add all the angles, you get 180°.

4x+8=60        [subtract both sides by 8]

4x=52            [divide both sides by 4]

x=13

Now, we know that C is the correct answer.

Answer:

$56.00

Step-by-step explanation:

35+(60/100)

=21

35+21

=$56.00

Points M and N will be located on the number line as:

M is at -15

N is at 3.

Here, we have,

to Find the Coordinate of a Point on a Number Line:

The number line gives us an idea of how real numbers are ordered, where we have the negative numbers to the left, and the positive numbers to the right.

The distance between two points on a number line is the number of units between both points.

Given that point L is at -6 on a number line, thus:

Point M is 9 units away from point L = -6 - 9 = -15

Point N is 9 units away from point L = -6 + 9 = 3

Therefore, points M and N will be located on the number line as:

M is at -15

N is at 3.

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Answer:

-3/2

Step-by-step explanation:

To find:-

Answer:-

We are interested in finding out the slope of the given line . We can see that the line passes through the points (1,0) and (-1,3) . For finding out the slope we can use the formula,

\(:\implies \sf m =\dfrac{y_2-y_1}{x_2-x_1} \\\)

Now on substituting the respective values, we have;

\(:\implies \sf m = \dfrac{0-3}{1-(-1)} \\\)

\(:\implies \sf m = \dfrac{-3}{1+1}\\\)

\(:\implies \sf \pink{m=\dfrac{-3}{2}}\\\)

Hence the slope of the line is -3/2.

Marjorie takes 5 seconds to paint each watermelon seed, while Pembroke takes 4 seconds.  We can calculate their combined rate and divide it by the total number of seeds.

Marjorie takes 5 seconds to paint one seed, so her rate is 1 seed per 5 seconds, which can be expressed as 1/5 seeds per second. Similarly, Pembroke takes 4 seconds to paint one seed, so his rate is 1 seed per 4 seconds or 1/4 seeds per second.

To find their combined rate, we can add their individual rates: 1/5 + 1/4 = 9/20 seeds per second.

Now, to determine the total time it will take for both of them to paint 171 watermelon seeds, we divide the total number of seeds by their combined rate: 171 / (9/20) = 380 seconds.

Therefore, it will take Marjorie and Pembroke together approximately 380 seconds to paint 171 watermelon seeds.

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Step-by-step explanation:

\(x + 76 + 3x + 2 = 90\)

\(4x + 78 = 90\)

\(4x = 12\)

\(x = 3\)

Angle 1 is 79

Angle 2 is 11.

Answer:

x = 1.8

Step-by-step explanation:

2 ( 4x-3) - 8 = 4-2x

Distribute

8x -6 -8 = 4- 2x

Combine like terms

8x - 14 = 4 - 2x

Add 2x to each side

8x - 14 +2x = 4-2x+2x

10x-14 = 4

Add 14 to each side

10x-14+14 = 4+14

10x = 18

Divide by 10

10x/10 = 18/10

x = 1.8

Answer:

\(x=\frac{9}{4}\)

Step-by-step explanation:

Answer:

\(\boxed{\boxed{\sf x=\frac{9}{4} }\:\sf or \:\boxed{x=2.25}}\)

Step-by-step explanation:

\(\sf \cfrac{1}{2}\:x+\cfrac{3}{4}=\:x\cfrac{5}{6}\)

Subtract x (5/6) from both sides:

\(\longmapsto\sf \cfrac{1}{2}\: x+\cfrac{3}{4} -x\left(\cfrac{5}{6}\right)=0\)

Subtract 3/4 from both sides:

** Anything subtracted from zero gives its negation.**

\(\longmapsto\sf -\cfrac{1}{3}\:x=-\cfrac{3}{4}\)

Multiply both sides by -3, reciprocal of - 1/3

\(\longmapsto\sf x=-\cfrac{3}{4} (-3)\)

Express - 3/4 (-3) as single fraction:

\(\longmapsto\sf x=\cfrac{-3(-3)}{4}\)

Multiply -3 and -3 = 9

\(\longmapsto\sf x= \cfrac{9}{4}\)

______________________________________

Answer:

21.21

Step-by-step explanation:

length of arc= 135°÷360×2×π×r

take π=22/7

radius=18/2=9

135°÷360×2×22/7×9

using calculator= 21.21

The angle of depression of the fish from the given height to the bottom of the lake is 60° .

The bird caught the fish at site A, flew it 100 yards to location B, and then dropped it off at location C. (which is horizontally 50 yards from A).

The right angled triangle BAC is equal to the length of the perpendicular and base .

The angle the bird creates with the water piques our interest (horizontal). This angle is BAC. We can claim to be knowledgeable about the "hypotenuse" and "adjacent" side of the right triangle to angle BAC. Since the cosine relationship between the hypotenuse and its neighbors exists, we can write:

cos BAC = 50/100

BAC = cos ⁻¹ 1/2

BAC = 60 °

Here, our goal is to determine the length (distance) of segment BC. We can say that BC is "opposite" to the angle BAC, which we discovered to be 60 degrees. The hypotenuse is known to be 100. So let's utilize sine since sine is the ratio of the hypotenuse's opposite.

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Answer: A good way to get a small standard error is to use a large sample.

Step-by-step explanation:

In order to find the small standard error, there is always need of a complete set which is called the large sample.

If tried to do a small or repeating sample, you will most likely not get an error and you could get a repetition. If you do a population sample, you wont get accurate results at all.

Therefore, a good way to get a small standard error is to use a large sample. Hope this helps!

-From a 5th Grade Honors Student

Answer:

8

Step-by-step explanation:

(1,c) y=5.4321*2^1 or y = 10.8642

(4,d) y=5.4321*2^4 or y = 86.936

Then you plug in the numbers and divide the two...

 \(\frac{86.9136}{10.8642}\)

8

The value of d/c = 8, when the given graph represents the equation f(x) = 5.4321*(2)ˣ, and A (1, c), and B (4, d) pass through the graph.

The graph of an equation passes through all the points that satisfy the given equation. The graph shows a curve joining all those points.

In the question, we are given a graph and its equation f(x) = 5.4321*(2)ˣ.

We are given the coordinates of two points on graphs A: (1, c) and B: (4, d).

We know that any point of the form (x, y) which passes through the graph of the equation, satisfies the equation.

∴ A (1, c) and B (4, d) satisfies the equation f(x) = 5.4321*(2)ˣ.

∴ c = 5.4321*(2)¹ = 5.4321 * 2

d = 5.4321*(2)⁴ = 5.4321 * 16

∴ d/c = (5.4321*16)/(5.4321*2) = 16/2 = 8.

∴ The value of d/c = 8, when the given graph represents the equation f(x) = 5.4321*(2)ˣ, and A (1, c), and B (4, d) pass through the graph.

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Answer:

Max

Step-by-step explanation:

the function given that h = -16t³+64t+10

the general function Equation:

h = at²+bt+c

=> t at the highest point is defined by t = -b/2a

= -64/2(-16) = -64/-32 = 2 second

the total times that the ball hits the ground

= 2× 2 seconds = 4 seconds.

so, Max is right

Answer:

Solution given:

Let h=0=when the ball hit the ground,the height=0.

h= -16t^2 + 64t + 10.

0=16t²-64t-10

8t²-32t-5=0

∆=\( \frac{32±\sqrt{32²+4*5*8}}{2*8}=\frac{8±\sqrt{74}}{4}\)

taking positive

t1=\( \frac{8+\sqrt{74}}{4}=4.15seconds\)

t2=\( \frac{8-\sqrt{74}}{4}(t2<O)(neglected)\)

So

t=4.15seconds closer to 4seconds.So

Max is closer.

A man drinks 5/6 of a gallon on the second day.

Multiplication is an arithmetic operation that involves combining two or more numbers to find their product. It is the process of repeated addition or counting in equal groups.

The man starts with 2 gallons of water. On the first day, he drinks 3/4 of a gallon, leaving him with:

2 - 3/4 = 1 1/4 gallons

On the second day, he drinks 2/3 of what he had left from the first day, which is 1 1/4 gallons. To find out how much he drinks, we can multiply 1 1/4 by 2/3:

1 1/4 * 2/3 = (5/4) * (2/3) = 10/12 = 5/6

Therefore, he drinks 5/6 of a gallon on the second day.

To summarize:

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The cost of a rugby ball is $6.57

The cost of a golf ball is $1.75

Let x represent the cost of a rugby ball and y represent the cost of a golf ball

2x + 3y= 18.39.........equation 1

5x + 7y= 45.10.........equation 2

multiply equation 1 by 5 and equation 2 by 2

10x + 15y= 91.95

-

10x + 14y= 90.2

y= 1.75

Substitute 1.75 for y in equation 2

5x + 7(1.75)= 45.10

5x + 12.25= 45.10

5x= 45.10-12.25

5x= 32.85

x= 32.85/5

x= 6.57

Hence the cost of a rugby ball is $6.57 and the cost of a golf ball is $1.75

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Answer:

1 st year = $320

2nd year $128

320p - 192t = $128

Step-by-step explanation:

Answer:

f.Answer:

K = 3

T = 2

And

H = 12

Step-by-step explanation:

3k = 9

k = 9/3

k = 3.

3k =k + 3t

subtitute value of k

3×3=3+3t

9-3=3t

6/3=t

t=2.

2k + h =18

2×3+h=18

h=18-6

h=12..