1..A message in a bottle is floating on top of the ocean in a periodic manner. The time between periods of maximum heights is 26 seconds, and the average height of the bottle is 12 feet. The bottle moves in a manner such that the distance from the highest and lowest point is 6 feet. A cosine function can model the movement of the message in a bottle in relation to the height.


Part A: Determine the amplitude and period of the function that could model the height of the message in a bottle as a function of time, t. (5 points)


Part B: Assuming that at t = 0 the message in a bottle is at its average height and moves upwards after, what is the equation of the function that could represent the situation? (5 points)


Part C: Based on the graph of the function, after how many seconds will it reach its lowest height? (5 points)


Show/Explain answer for each Part for the answer please

By using the graph and the definition of inverse functions, we will see that:

g⁻¹(1) = 4.

We say that two functions f(x) and g(x) are inverse if:

Now, we know that graph of g(x) and we want to find the value of:

g⁻¹(1)

In the graph, we can see that:

g(4) = 1

Then we can replace it:

g⁻¹(1) = g⁻¹( g(4) ) = 4.

So we can conclude that:

g⁻¹(1) = 4.

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Answer:

-4

Step-by-step explanation:

Khan Academy

Answer:

Since there is 25 students and 8 ounces there you have to do 25 times 8 which equals 200

Answer:

width = 8 ft & length = 32 ft.

Step-by-step explanation:

let the width be x and length be 4x.

we know, Perimeter = 2(l+b)

now,

2(4x + x) = 80

10x = 80

x = 80/10 = 8

x = 8

therefore,

width = x = 8 ft

length = 4x = 4 × 8 = 32 ft.

hope this helps you !

Answer:

[tex]G=(2,\frac{5}{3} ).[/tex]

Step-by-step explanation:

Let the given vertices of a triangle be [tex]A(-2,3)[/tex]and [tex]B (4,-3)[/tex] let the third vertex be[tex]C (4,5)[/tex].

Let Centroid be G = [tex][\frac{x_{1} +x_{2}+x_{3} }{3} , \frac{y_{1}+y_{2}+y_{3} }{3} ][/tex]

⇒ [tex]G=(\frac{-2+4+4}{3} ,\frac{3-3+5}{3})[/tex]

⇒ [tex]G=(\frac{6}{3} ,\frac{5}{3} )\\[/tex]

⇒ [tex]G=(2,\frac{5}{3} ).[/tex]

Answer:

3x+7>34

Step-by-step explanation:

more than means+and the times means multiple

Answer:

1

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

1 is the greatest common factor of 7, 4 and 39

axis of symmetry: x=1.5

vertex: (1.5,-4.75)

Answer:

If this car wash took 4 hours to detail 144. 144/4 = 1/36 meaning that every hour they would detail 36 cars, we can double-check this and multiply 36 by 4 and we will get 144 meaning that this is true and that this car wash detailed 36 cars in an hour.

The amount of stickers bought in the sticker exchange is an illustration of factors

There were 47 people in the sticker exchange

The number of stickers is given as:

Stickers = 141

Next, we list the factors of 141 in pairs

(x,y) = (1,141), (3,47), (47,3) and (141,1)

Each person bought more than 1 sticker.

So, we have:

(x,y) = (3,47) and (47,3)

Hence, we can conclude that there were 47 people in the sticker exchange

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Answer:

4x + 6y + 4

Step-by-step explanation:

–(2x – 3y) + 5x + 2 – 3x + 3y + 2

= -2x + 3y + 5x + 2 - 3x + 3y + 2

= -2x + 5x -3x + 3y + 3y + 2 + 2

= 0 + 6y + 4

= 6y + 4 (C)

Hope it helps ⚜

Answer:

D; 4x+6y+4

Step-by-step explanation:

1. Distribute the negative

2. -2×+3y+5x+2-3×+3y+2

2. combine like terms

answer; 4x+6y+4

Given:

[tex]X = {0,1,2,3,4} \\ Y = {2,4,6,8,10,12} \\ Z = {3,6,9,12,15}[/tex]

So,

[tex]X∪Y = (0,1,2,3,4) \: ∪ \: (2,4,6,8,10,12) \\ = > (0,1,2,3,4,6,8,10,12)[/tex]

[tex]X∩Z = (0,1,2,3,4) \: ∩ \: (3,6,9,12,15) \\ = > (3)[/tex]

[tex](X∪Y)∩Z = (0,1,2,3,4,6,8,10,13) ∩ (3,6,9,12,15) \\ = > (3,6)[/tex]

Using the generic set operations, we will see that:

For two given sets A and B, we define:

A ∪ B as the union of the two sets, this is the set that contains all the elements from both A and B.

A ∩ B is the intersection of A and B, this set contains only the common elements of A and B.

Now we want to complete the given table:

1) X U Y is the union of sets X and Y (we do not repeat elements) so this is equal to:

{0, 1, 2, 3, 4, 6, 8, 10, 12}

2) X ∩ Z is the intersection of X and Z, the only common element between these sets is 3, then:

X ∩ Z = {3}

3) (X U Y)∩ Z

Is the set of the common elements between:

X U Y = {0, 1, 2, 3, 4, 6, 8, 10, 12}

Z = {3, 6, 9, 12, 15}

The common ones are:

3, 6, and 12, then we have:

(X U Y)∩ Z = {3, 6, 12}

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Answer:

70

Step-by-step explanation:

The angle at the bottom right of the triangle is linear with the 105, so it is 180 - 105 = 75

The top angle of the triangle is an alternate interior angle with the 35 degrees, so it is also 35.

75 + 35 = 110

x = 180 - 110 = 70

The angle above x is 35° as alternate interior angles are equal.

Angle aside right to x

Measure of x

Answer:

Step-by-step explanation:

Given system:

Solve by substitution:

We got correct equation without variables.

It means the equation is correct for any value of variables, the lines are same and overlap.

So there are infinitely many solutions.

Answer:

see step-by-step below

Step-by-step explanation:

1)  y - 2 > 3

Add 2 to both sides:   y > 5

2) y ≤ 2

Draw a closed circle at y = 2 then shade the numbers to the left

3) y ≥ 250

where y = savings

4) The image isn't very clear, so I can't tell if it's a closed or open circle on -4.

If it is closed, it will be y ≤ -4

If it is open, it will be y < -4

5) -4 < f

Draw an open circle at f = -4 then shade the numbers to the right

6) x < -3.5

Draw an open circle at x = -3.5 then shade the numbers to the left

7) closed circle ... shade to the left of 8 ... make y  equal to or less than 8.

8) F ≤ 6

C - closed circle at 6 with shaded numbers to the left

9) y > 2.75

Betty saved more than $2.75 every month

10) 1 + x < 5

Subtract 1 from both sides:  x < 4

11) x ≥ -2.5

12) 1 ≤ m means that m is equal to or greater than 1

solutions:  4, 1, 2.3

The value of the apartment in 6 years is $104,527.46.

The value of the apartment appreciates (increase in value) by 6% every year. The formula that can be used to determine the future value of the apartment is:

FV = P (1 + r)^n

Where:

$78,000(1.05)^6 = $104,527.46

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The worth of the apartment after 6 months is =$23,400

The original amount of the apartment(p) = $78,000

The rate of increase of the value of the apartment is(r)= 5%

Time(t) = 6years

But simple interest =

[tex]si = \: \frac{p \times t \times r}{100} [/tex]

[tex]si = \frac{78000 \times 6 \times 5}{100} [/tex]

[tex]si = \frac{2340000}{100} [/tex]

si = $23,400

Therefore, the worth of the apartment after 6 months is =$23,400

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The volume of the triangular prism is 58.32 in³

Volume is the amount of space occupied by a three dimensional object.

The volume of a triangular prism is given by:

V = Area of triangle * height

Area of triangle = (1/2) * 10.8 * 7.2 = 38.88 in²

Volume of prism = 38.88 * 1.5 = 58.32 in³

The volume of the triangular prism is 58.32 in³

Find out more on Volume at: https://brainly.com/question/1972490

Answer:

58.32in3

Step-by-step explanation:

i did the test

Answer:

PS = 7

SQ = 7.125

m<QTR = 115

m<TQR = 32.5

Step-by-step explanation:

To find PS, you need to take the measurement from QR [stated in the problem] which is 7 feet.

To find SQ, you need to take the measurement from RT [stated in the problem as 3 9/16] and then multiply it by 2 as SQ is 2 times longer than RT, which means SQ = 7 1/8 or 7.125 [since it needs to be a decimal]

To find m<QTR, you need to take the measurement from m<RTS, and since those 2 angles together equal 180, you need to subtract 65 degrees [from m<RTS] from 180, resulting in 115 degrees.

To find m<TQR, you need to know that a triangle has 180 degrees within it.  Then you need to find one angle.  We know the wider angle, <T = 115 degrees, so then we have to do 180 - 115, which equals 65 [that is the total for the 2 remaining equal corners], then we just have to divide by 2, which equals 32.5 degrees.

Answer:

false

Step-by-step explanation:

42 is not divisible by 5

Answer:

False

Step-by-step explanation:

5 does not go into 42

Answer:

Rate of change per year = $5300

Step-by-step explanation:

Step 1: Substitute the variable P for the invested amount

    1. A(t) = 5000(1.06)t

    2. A(t) = (5300)t

Step 2: Substitute the variable t for the first 15 years

    1. A(15) = (5300)(15)

    2. A(15) = 79,500

Step 3: Substitute the variable t for the 20 years

    1. A(20) = (5300)(20)

    2. A(20) = 106,000

Step 4: Find your two ordered pairs and relation

    First ordered pair: (15, 79,500)

    Second ordered pair: (20, 106,000)

    Relation: {(15, 79,500), (20, 106,000)}

Step 5: Find the slope or rate of change between 15 and 20 years

    Let (y₁, x₁) = (15, 79,500)

    Let (y₂, x₂) = (20, 106,000)

    1. Use the slope expression: y₂ - y₁/x₂ - x₁

    2. Substitute the correct values into the expression:

         106,000 - 79,500/20 - 15

    3. Simplify: 26500/5 = 5300

    4. Hence, the rate of change in dollars per year is $5300

Answer:

21/50 ,43.7%, 87/200,0.44

Step-by-step explanation:

Answer

$1,004.8

Step-by-step explanation:

hope this helps

[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$12560\\ r=rate\to 2\%\to \frac{2}{100}\dotfill &0.02\\ t=years\dotfill &4 \end{cases} \\\\\\ I = (12560)(0.02)(4)\implies I=1004.80[/tex]

Answer: 153.86 cm²

Ok done. Thank to me :>

Answer is median because aas you can see as the line if divided by its hald angle it equals a median angle.

Answer:

[tex]b=3\sqrt{13}[/tex]

Step-by-step explanation:

Segment Addition Postulate:

[tex]\bar{PY}=\bar{MP}+\bar{MY}[/tex]

Substitute MP = 4, MY = 9 into PY = MP + MY:

[tex]\bar{PY}=4+9[/tex]

Calculate PY = 4 + 9:

[tex]\bar{PY}=13[/tex]

Representing same angles:

[tex]cos A = leg adjacent to <A/hypotenuse:

[tex]cos(Substitute DY = b, PY = 13 into cos (<DYP)=DY/PY:

[tex]cos(Substitute <DYP=<DYM into cos(<DYP)=b/13:

[tex]cos(cos A=leg adjacent to <A/hypotenuse:

[tex]cos\left(Substitute DY=b, MY=9, cos(<DYM)=b/13 into cos (<DYM)=MY/DY:

[tex]\frac{b}{13}=\frac{9}{b}[/tex]

Calculate b/13=9/b:

[tex]b=3\sqrt{13}[/tex]

I hope this helps you :)

Answer:

a: 42%

b: don't have the info for

c: 48%

d: don't have info for

e: don't have info for

f: don't have info for

Step-by-step explanation:

sorry I cant answer everything

Answer: distributive property

Step-by-step explanation:

hope it helps u!!

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