Which is the angle of depression from the lighthouse on the boat ?

By the way nice job using Khan Academy, I love it. the answer is the dep. is the numbers of minutes and the ind. is the episodes.

Answer:  The number of episodes you watch → Independent variable

The number of minutes you spend watching anime→ Dependent variable

Step-by-step explanation:

Given : Your favorite anime series has episodes that are 20 minutes long.

In the equation , w is the number of episodes you watch and t is the number of minutes you spend watching anime.

The relationship between these two variables can be expressed by the following equation :-

[tex]t=20w[/tex]

We can see that the time spend on watching anime depends on the number of episodes we watch.

Thus the dependent variable is the number of minutes you spend watching anime i.e. 't'.

The independent variable is the number of episodes you watch i.e. 'w'.

Answer:

Part A) The area of triangle i is [tex]3\ cm^{2}[/tex]

Part B) The total area of triangles i and ii is [tex]6\ cm^{2}[/tex]

Part C) The area of rectangle i is [tex]20\ cm^{2}[/tex]

Part D) The area of rectangle ii is [tex]32\ cm^{2}[/tex]

Part E) The total area of rectangles i and iii is [tex]40\ cm^{2}[/tex]

Part F) The total area of all the rectangles is [tex]72\ cm^{2}[/tex]

Part G) To find the surface area of the prism, we need to know only the area of triangle i and the area of rectangle i and the area of rectangle ii, because the area of triangle ii is equal to the area of triangle i and the area of rectangle iii is equal to the area of rectangle i

Part H) The surface area of the prism is [tex]78\ cm^{2}[/tex]

Part I) The statement is false

Part J) The statement is true

Step-by-step explanation:

Part A) What is the area of triangle i?

we know that

The area of a triangle is equal to

[tex]A=\frac{1}{2} (b)(h)[/tex]

we have

[tex]b=4\ cm[/tex]

[tex]h=1.5\ cm[/tex]

substitute

[tex]A=\frac{1}{2} (4)(1.5)[/tex]

[tex]Ai=3\ cm^{2}[/tex]

Part B) Triangles i and ii are congruent (of the same size and shape). What is the total area of triangles i and ii?

we know that

If Triangles i and ii are congruent

then

Their areas are equal

so

[tex]Aii=Ai[/tex]

The area of triangle ii is equal to

[tex]Aii=3\ cm^{2}[/tex]

The total area of triangles i and ii is equal to

[tex]A=Ai+Aii[/tex]

substitute the values

[tex]A=3+3=6\ cm^{2}[/tex]

Part C) What is the area of rectangle i?

we know that

The area of a rectangle is equal to

[tex]A=(b)(h)[/tex]

we have

[tex]b=2.5\ cm[/tex]

[tex]h=8\ cm[/tex]

substitute

[tex]Ai=(2.5)(8)[/tex]

[tex]Ai=20\ cm^{2}[/tex]

Part D) What is the area of rectangle ii?

we know that

The area of a rectangle is equal to

[tex]A=(b)(h)[/tex]

we have

[tex]b=4\ cm[/tex]

[tex]h=8\ cm[/tex]

substitute

[tex]Aii=(4)(8)[/tex]

[tex]Aii=32\ cm^{2}[/tex]

Part E) Rectangles i and iii have the same size and shape. What is the total area of rectangles i and iii?

we know that

Rectangles i and iii are congruent (have the same size and shape)

If rectangles i and iii are congruent

then

Their areas are equal

so

[tex]Aiii=Ai[/tex]

The area of rectangle iii is equal to

[tex]Aiii=20\ cm^{2}[/tex]

The total area of rectangles i and iii is equal to

[tex]A=Ai+Aiii[/tex]

substitute the values

[tex]A=20+20=40\ cm^{2}[/tex]

Part F) What is the total area of all the rectangles?

we know that

The total area of all the rectangles is

[tex]At=Ai+Aii+Aiii[/tex]

substitute the values

[tex]At=20+32+20=72\ cm^{2}[/tex]

Part G) What areas do you need to know to find the surface area of the prism?

To find the surface area of the prism, we need to know only the area of triangle i and the area of rectangle i and the area of rectangle ii, because the area of triangle ii is equal to the area of triangle i and the area of rectangle iii is equal to the area of rectangle i

Part H) What is the surface area of the prism? Show your calculation

we know that

The surface area of the prism is equal to the area of all the faces of the prism

so

The surface area of the prism is two times the area of triangle i plus two times the area of rectangle i plus the area of rectangle ii

[tex]SA=2(3)+2(20)+32=78\ cm^{2}[/tex]

Part I) Read this statement: “If you multiply the area of one rectangle in the figure by 3, you’ll get the total area of the rectangles.” Is this statement true or false? Why?

The statement is false

Because, the three rectangles are not congruent

The total area of the rectangles is [tex]72\ cm^{2}[/tex] and if you multiply the area of one rectangle by 3 you will get [tex]20*3=60\ cm^{2}[/tex]

[tex]72\ cm^{2}\neq 60\ cm^{2}[/tex]

Part J) Read this statement: “If you multiply the area of one triangle in the figure by 2, you’ll get the total area of the triangles.” Is this statement true or false? Why?

The statement is true

Because, the triangles are congruent

Answer:

Now I am not completely sure but...maybe is it that:

A quadratic regression is the process of finding the equation of the parabola that best fits a set of data. As a result, we get an equation of the form:

y = a x 2 + b x + c where a ≠ 0 .

Cause I think it might be the best way to find this equation manually is by using the least squares method. That is, we need to find the values of a , b ,     and     c such that the squared vertical distance between each point ( x i , y i ) and the quadratic curve y = a x 2 + b x + c is minimal.

The matrix equation for the quadratic curve is given by:

[ ∑ x i 4 ∑ x i 3 ∑ x i 2 ∑ x i 3 ∑ x i 2 ∑ x i ∑ x i 2 ∑ x i n ] [ a b c ] = [ ∑ x i 2 y i ∑ x i y i ∑ y i ]

The quadratic regression equation for the given data set is approximately:

[tex]y \approx -0.043x^2 + 1.333x + 5.895[/tex]

To find the quadratic regression equation for the given data set

Denote the independent variable (x) as x and the dependent variable (y) as y. We want to find the quadratic equation of the form

[tex]y = ax^2 + bx + c[/tex]that best fits the data.

Start by creating a system of equations using the given data points.

Substitute the x and y values into the equation and obtain three equations:

[tex](2^2)a + 2b + c = 10.1\\(4^2)a + 4b + c = 7.3\\(6^2)a + 6b + c = 5.9\\(7^2)a + 7b + c = 5.1\\(11^2)a + 11b + c = 6.3\\(12^2)a + 12b + c = 8.2\\[/tex]

Now, we have a system of three linear equations with three unknowns (a, b, c). We can solve this system to find the values of a, b, and c.

Using a calculator or software,  find the following approximate values:

a ≈ -0.043

b ≈ 1.333

c ≈ 5.895

Therefore, the quadratic regression equation for the given data set is approximately:

[tex]y \approx -0.043x^2 + 1.333x + 5.895[/tex]

Read on Regression on https://brainly.com/question/25987747

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Answer:

[tex]\large\boxed{g\bigg(f(6)\bigg)=-\dfrac{4}{3}}[/tex]

Step-by-step explanation:

[tex]f(a)=-\dfrac{1}{4}(a+8)\\\\g(b)=\dfrac{2}{3}b+1\\\\g\bigg(f(6)\bigg)\\\\\text{calculate}\ f(6)\to\text{put}\ a=6\ \text{to the equation of}\ f(a):\\\\f(6)=-\dfrac{1}{4}(6+8)=-\dfrac{1}{4}(14)=-\dfrac{14}{4}=-\dfrac{7}{2}\\\\g\bigg(f(6)\bigg)\to\text{put}\ b=-\dfrac{7}{2}\ \text{to the equation of}\ g(b):\\\\g\bigg(f(6)\bigg)=\dfrac{2}{3}\left(-\dfrac{7}{2}\right)+1=-\dfrac{7}{3}+1=-\dfrac{7}{3}+\dfrac{3}{3}=-\dfrac{4}{3}[/tex]

Answer:

  1041

Step-by-step explanation:

Among the numbers 1–1000, there are 31 squares, so the sequence will extend to at least 1031. In those added numbers, there is another square (1024), so the sequence must extend to at least 1032.

There are 7 more numbers that are cubes, but not squares, so the sequence must extend to at least 1039.

And there are 2 additional numbers that are 5th powers that are not squares or cubes. Compensating for the removal of these numbers extends the end of the sequence to 1041.

There are no numbers in this range that are both cubes and 5th powers and that have not already been accounted for. (The only 15th power is 1.)

Hence, the 1000th number in the sequence is 1041.

_____

This result is verified by a computer program that listed the numbers.

The 1000th term, 1041, is in the sequence of positive integers that aren't squares, cubes, or fifth powers.

The sequence begins with 2, which is not a perfect square, cube, or fifth power.

It continues with 3, which is also not a perfect square, cube, or fifth power.

It skips numbers like 4, 5 (as 5 is a perfect fifth power), 6, and 7 (as they are squares or cubes).

The sequence picks up with 10 and 11, which are not perfect squares, cubes, or fifth powers.

This pattern continues, with the sequence skipping over numbers that meet any of the three conditions.

When you reach the 1000th term, it should be a number that satisfies these conditions, and that number is 1041.

So, you found the 1000th term by observing the pattern of the sequence and determining that it is neither a perfect square, cube, nor fifth power. Your answer of 1041 is correct for the 1000th term in this sequence.

For similar question on sequence.

https://brainly.com/question/30762797

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Answer:

  opens down; (10, 2); same

Step-by-step explanation:

If the vertex of f(x) is (0, 0) then translating it to (h, k) makes the function look like f(x -h) +k. Changing the sign of f(x) to -f(x) reflects it across the x-axis, so ...

  y = 2 - |x -10|

is the function y = |x| reflected across the x-axis and translated 10 units right and 2 units up. Because there is no horizontal or vertical scale factor, the apparent width of the function is the same as the original.

Final answer:

The graph of the function y = 2 - |x – 10|  a .opens down with a vertex at (10, 2). It has the same width as the graph of y = |x|, meaning it is not stretched or compressed horizontally, but it is shifted upward and to the right.

Explanation:

To determine whether the graph of the function y = 2 - |x – 10| opens up or down, we must understand the behavior of the absolute value function. Since the absolute value function has a V-shape, the negative sign in front of the absolute value in the given function indicates that the graph opens down, creating an upside-down V-shape. Furthermore, the vertex of the graph is at the point where the expression inside the absolute value equals zero. In this case, x – 10 = 0, so x = 10. Plugging this into the function gives us the y-coordinate of the vertex, which is y = 2 - |10 - 10| = 2. Therefore, the vertex is (10, 2).

Comparing the width of the graph to the graph of y = |x|, we notice that there is no multiplication factor affecting the x inside the absolute value, hence the graph of the given function has the same width as the graph of y = |x|. In other words, the graph is neither stretched nor compressed horizontally. Rather, it is vertically shifted upward by 2 units, and horizontally shifted to the right by 10 units due to the x – 10 part of the function.

Answer:

  28

Step-by-step explanation:

It helps to plot the points on a graph. It is easy to see that three of the sides are of length 6, and the remaining two are the hypotenuse of a 3-4-5 triangle, hence length 5.

  3×6 +2×5 = 28

The perimeter of this polygon is 28 units.

Answer:

  a = -3

Step-by-step explanation:

Put the y-intercept values into the equation and solve for a.

  1 = a(0 -1)^2 +4 . . . . with (h, k) filled in, this is y=a(x-1)^2+4

  -3 = a . . . . . . . . . subtract 4, simplify

The value of a is -3.

[tex]|\Omega|=8\cdot7=56\\|A|=3\cdot2=6\\\\P(A)=\dfrac{6}{56}=\dfrac{3}{28}\approx10,7\%[/tex]

Answer:

C.f(2) = 12.6

Step-by-step explanation:

f(n) = 0.4 ⋅ f(n − 1) + 11

f(1) = 4

Let n=2

f(2) = .4 f(1) +11

      = .4 (4) +11

      = 1.6 +11

       = 12.6

Answer:

c-12.6

Step-by-step explanation:

Use the formula and substitute the n for the value and u will find it.

Answer:

$10.5

Step-by-step explanation:

88-4 = $84

84/8 = 10.5

For this case we must find an expression equivalent to:

[tex]8 (-10x + 3.5y-7) =[/tex]

We apply distributive property to each of the terms within the parentheses, then:

[tex]8 * (- 10x) + 8 * (3.5y) +8 * (- 7) =\\-80x + 28y-56[/tex]

Finally, an equivalent expression is:

[tex]-80x + 28y-56[/tex]

Answer:

[tex]-80x + 28y-56[/tex]

Answer:

-80x +28y-56

Step-by-step explanation:

Answer:

For up to 5.5 s after the golf ball is hit, its height is increasing

The golf ball is in the air for 11 s

The maximum height of the golf ball is 150 m.

Step-by-step explanation:

we know that

The graph shown a vertical parabola open downward

The vertex is a maximum

The vertex is the point (5.5,150) ---> that means

For t=5.5 s, the height of a golf ball is h=150 m

Verify each statement

case A) For up to 5.5 s after the golf ball is hit, its height is increasing.

The statement is true

For the interval (0,5.5) ------> the height is increasing

For the interval (5.5,11) ------> the height is decreasing

case B) It takes 11 s for the golf ball to fall to the ground after reaching its maximum height

The statement is false

It takes 5.5 s for the golf ball to fall to the ground after reaching its maximum height

case C) The golf ball is in the air for 11 s

The statement is true

For t=11 s the golf ball fall to the ground (h=0)

case D) The maximum height of the golf ball is 150 m.

The statement is true

The maximum height of the golf ball is at the vertex of the parabola

The vertex is the point (5.5,150)

case E) The golf ball's speed is 11 m/s

The statement is false

The graph is shown below. Then the correct options are B, C, and D.

Functions are found all across mathematics and are required for the creation of complex relationships.

The graph represents the height y, in meters, above the ground of a golf ball x seconds after it is hit.

From the graph, we can conclude some points.

Then the correct options are B, C, and D.

More about the function link is given below.

https://brainly.com/question/5245372

#SPJ5

The time it will take Kelsey to paint the entire room is:

It is given that:

Kelsey painted one fourth of her bedroom in three seventh of an hour.

This means that:

 1/4 of bedroom takes 3/7 of an hour

This means that the whole of the bedroom will take 4 times the time it took to cover 1/4 th of bedroom.

i.e. it will take:

[tex]\dfac{3}{7}\times 4\\\\\\=\dfrac{12}{7}\ hour[/tex]

Hence, the total time it will take to paint the whole room is:

                   twelve over seven hours  

Your answer is C, as it says in the photo below. You can see the amount of points it is worth, and the amount of points it gave me. Hope this helps somebody!

Answer:25≤x≤35

Step-by-step explanation: This statement means that the person can take more than or 25 mg or the can take less 35 or exactly 35 mg.

Answer.

a. Population is the total number of voters in the constituency, that is 10000

b. the parameter is the unknown character of the population, that is 35% of 10000= 3,500

c. Statistics of interest is know character from the sample, that is 40% of 200= 80

d. The two answers are not surprisingly, because the sample is a portion of the population and we expect it to be smaller that the population. Thus, parameter must be bigger than statistics of interest.

d) ii. If another 200 sample was to be taken, we expect to see an increase in a statistics of interest.

Thus my answer, please help by your approval as fast as you can

Answer:

32 oz

Step-by-step explanation:

Assuming the hole in the bottle is not made any bigger as it loses water, it will lose it at a constant rate.  This makes it a linear function.  We can use the 2 points given to find the slope of the line, then use one of the 2 points to write an equation for the line in point-slope form, change it into slope-intercept form, and the amount of water in the bottle originally will be apparent.  Plugging in to the slope formula:

[tex]m=\frac{20-28}{6-2}=-2[/tex]

Now we will choose one point for the x and y values and plug in to the point-slope form of a line:

y - 28 = -2(x - 2) and

y - 28 = -2x + 4 so

y = -2x + 32

That is in y = mx + b form where m is the slope and b is the y-intercept, the initial value of y when x = 0.  x being the time gone by, when x = 0, that means that no time has gone by, and that means that no water has yet to leak out of your bottle.

Answer:

 13.0 feet

Step-by-step explanation:

The circumference of a circle is given by the formula ...

  C = πd . . . . . . where d represents the diameter

Then the diameter is ...

  d = C/π = 40.82 ft/π ≈ 12.9934 ft

Rounded to the nearest tenth foot, the width of the room must be 13.0 ft.

Step-by-step explanation:

add all marbles together:

4 (green) + 3 (red) + 3 (yellow) = 10 marbles total

if we pick a yellow marble out of the bag and do not replace it, then we have 2 yellow marbles left.

we need to add marbles again with one yellow marble subtracted.

4 (green) + 3 (red) + 2 (yellow) =

new Total is 9 marbles.

so then we have 2 yellow marbles out of 9 total marbles.

2:9

or 2/9

or .22 (22%)

is the probability

Answer:

1/15 is the answer guys! Not 2/15 or anything else.

Step-by-step explanation:

Answer:

P = (2,-4)

Q = (3,9)

R = (-4,2)

Step-by-step explanation:

rotation by 180 degrees means that the points are inverted. the answers would be the opposite of the given

To find the triangle's vertices after a 180° rotation about the origin, simply change the sign of each coordinate. P(-2,4) becomes P(2,-4), Q(-3,-9) becomes Q(3,9), and R(4,-2) becomes R(-4,2).

When you rotate a point 180° about the origin, each coordinate (x, y) simply changes its sign to become (-x, -y). Therefore, we can apply this to the vertices of △PQR.

The correct choice for the rotation of △PQR by 180° about the origin will have these new coordinates. Therefore, the answer is:

Answer:

x=-1 is a maximum vaue.

Step-by-step explanation:

To find the minimum and maximum values of the function f(x), we're going to derivate it:

f(x) = –5x^2 – 10x + 6 ⇒ f'(x) = -10x - 10

The points where f'(x) is zero, could be a maximum or a minimum. Then:

f'(x) = -10x - 10 = 0 ⇒ x=-1

Now, to know if x=-1 is a maximum or a minimum, we need to evaluate the original function for x when it tends to -1 from the right and from the left.

Therefore:

For x=-2:

f(x) = 6 (Positive)

For x=0:

f(x) = 6 (Positive)

For x=-1

f(x) = 11 (Positive)

Given that at x=-1, f(x) = 11, and then it goes down to 6 when x=0, we can say that it's a maximum.

Answer:

max at (-1,11)

Step-by-step explanation:

f(x) = –5x^2 – 10x + 6

This parabola opens downward

f(x) = ax^2 + bx+c

The value a is negative, so it opens down.

Because it opens down, it will have a maximum

We can find the x value of the maximum by finding the axis of symmetry

h = -b/2a

h = -(-10)/2(-5)

  = 10/-10

h= -1

The x value of the vertex is -1

To find the y value, substitute this back into the equation

f(-1) = -5( -1)^2 - 10(-1) +6

       =-5(1) +10+6

       =-5 +10+6

     =11

The maximum is at (-1,11)

Answer:

D

Step-by-step explanation:

x=-3 is a zero means x+3 is a factor

x=5/4 (with multiplicity 2) means you have the factor (x-5/4) two times

Now this may be rewritten so you don't have the fraction

like 4x=5 so you have 4x-5 as a factor two times which means you will see (4x-5)^2

So you one factor of (x+3) and two factors of (4x-5)

so you have

(x+3)(4x-5)^2

or

2(x+3)(4x-5)^2

or

41(x+3)(4x-5)^2

You can put whatever constant multiple in front of the whole thing and it will still satisfy the conditions of the problem.

So the answer is D

Final answer:

The factored form of the polynomial p(x) with a simple zero at x=-3 and a double zero at x=5/4 is (x+3)(4x-5)
, which makes option D the correct answer.

Explanation:

If p(x) is a polynomial that has a simple zero at x=-3 and a double zero at x=5/4, then to identify the correct factored form of p(x), we need to determine the factors that correspond to these zeros. A simple zero at x=-3 suggests that (x+3) must be a factor of p(x). A double zero at x=5/4 indicates that the factor corresponding to this zero should be squared in the polynomial, and since 5/4 can be written as 5/4 = 4/4 + 1/4 = 1 + 1/4, thus, the factor is (x-1-1/4), which simplifies to (x - 5/4) or (4x - 5) when multiplied by 4 to clear the fraction.

Looking at the options presented:

A) p(x)=2(x+3)(5x-4) - This has the correct factor for x=-3 but not the squared factor for x=5/4.

B) p(x)=(x+3)(5x-4)
- This has the correct factor for x=-3 but not the squared factor for x=5/4.

C) p(x)=2(x+3)(4x-5) - This has the correct factors but does not square the (4x-5) factor for the double zero at x=5/4.

D) p(x)=(x+3)(4x-5)² - This option correctly includes (x+3) for the simple zero at x=-3 and (4x-5) squared for the double zero at x=5/4.

Therefore, the correct factored form of p(x) is option D.

Step-by-step explanation:

according to the equation, y= mx

Answer:

  D. Factor out 3 from the first two terms.

Step-by-step explanation:

Vertex form is ...

  y = a(x -h)² +k

where (h, k) is the vertex and "a" is the vertical scale factor.

This equation expands to give ...

  y = ax² -2ahx + ah² +k

Factoring "a" from the terms involving x makes it easy to identify h and so finish putting the equation into vertex form. In this equation, that means the most appropriate first step is ...

  factor out 3 from the first two terms

Answer:

D. Factor out 3 from the first two terms.

Step-by-step explanation:

According to the Vertex Formula [y = A(X - H)² + K], -H gives you the OPPOSITE terms of what they really are, but in this case, this would not qualify, since the question is asking something totally unique. So, since 3 is your "A", you factor that out, and since 6 is a multiple of 3, it is easy to work with. Anyway, you get this:

y = 3(x + 1)² - 11

I hope this helps you out alot, and as always, I am joyous to assist anyone at any time.

What does 154 mean in your question?

I assume your room is a square. If so, each corner of the room has a 90 degree angle for a total of 360 degrees.

The angle that is repeated, I assumed based on your obscure question, is 90 degrees.

So, x = 90 degrees.

[tex]\bf (\stackrel{x_1}{8}~,~\stackrel{y_1}{-8})~\hspace{10em} slope = m\implies \cfrac{3}{4} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-8)=\cfrac{3}{4}(x-8)\implies y+8=\cfrac{3}{4}(x-8)[/tex]

Answer:

90 minutes

Step-by-step explanation:

We know that distance = rate * time

We know the distance and the rate, and need to find the time

distance = 60 miles

rate = 40 mile per hour

60 = 40 * t

Divide each side by 40

60/40 = 40t/40

1.5 = t

1.5 hours

Now we need to change it to minutes

1.5 hours * 60 minutes/1 hours = 90 minutes

Answer:

Step-by-step explanation:

Reflection across the line y=x swaps the x- and y-coordinates.

A(-5, 1) becomes A'(1, -5), for example. The coordinates of the other points are swapped in similar fashion.

Answer:

(x,y)→(y,x); A' is at (1, −5)

Step-by-step explanation:

Trapezoid ABCD is shown. A is at negative 5, 1. B is at negative 4, 3. C is at negative 2, 3. D is at negative 1, 1.

(x,y)→(y,−x); A' is at (1, 5)

(x,y)→(y,x); A' is at (1, −5) 

(x,y)→(−x,y); A' is at (5, 1) 

(x,y)→(−x,−y); A' is at (5, −1)

This is the complete question and your answer is :

(x,y)→(y,x); A' is at (1, −5)