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The equation for the graph above is y = 5sin(2x/3).

In Mathematics and Geometry, a sine wave is sometimes referred to as a sinusoidal wave, or sinusoid and it can be defined as a fundamental waveform that is typically used for the representation of periodic oscillations, in which the amplitude of displacement at each interval is directly proportional to the sine of the displacement's phase angle.

Mathematically, a sine wave can be represented or modelled by this mathematical equation:

y = asin(bx)

Where:

Based on the graph of this sine wave, we have:

Amplitude, a = 5.

Periodicity, b = 2π/period = 2π/(3π) = 2/3

Therefore, the required sine wave function is given by;

y = asin(bx)

y = 5sin(2x/3)

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The value of x is -3 and y is 7 for equilateral triangle having x+1, 2x+4 and 3x+y sides.

We can use the fact that an equilateral triangle has equal lengths on each of its three sides to determine the values of x and y.

Given:

First side=x+y

second side= 2x+4

third side=3x+y

An equilateral triangle has three equal sides, hence the following equations can be constructed:

x + 1 = 2x + 4

2x + 4 = 3x + y

Let's tackle each of these equations separately:

x + 1 = 2x + 4

We will subtract x from both sides and subtract 4 from both sides in order to solve this equation:

x + 1 - x = 2x + 4 - x

1 = x + 4

By taking 4 away from both sides, we arrive at:

1 - 4 = x + 4 - 4 , -3 = x

Therefore, x has been determined to be -3.

Now, substitute the value of x in the second equation:

2x + 4 = 3x + y

2(-3) + 4 = 3(-3) + y

-6 + 4 = -9 + y

-2 = -9 + y

y = -2 + 9

y = 7

So, we determined that y has a value of 7.

As a result, the values of x and y are, respectively, x=-3 and y=7

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Answer:

Step-by-step explanation:

In an equilateral triangle all sides are equal.

So each of these sides (and their equations are equal to each other.)

To find x - set the first two (as they only involve x) equal to each other and solve.

x + 1 = 2x + 4

x -x + 1 = 2x - x + 4

1 = x + 4

1- 4 = x + 4 - 4

-3 = x

Then substitute -3 for x in the last equation to find y, also setting it equal to one of the other equations.

3(x) + y = x + 1

3(-3) + y = -3 + 1

-9 + y = -2

-9 + 9 + y = -2 + 9

y = 7

so x = -3 and y equal 7

Answer:

Step-by-step explanation:

This can happen because of the timestamp on the toll card. When you pass through the initial entrance point the timestamp marks the exact moment you passed. When you pass through the exit toll point the individual subtracts the current time from the time you entered the initial toll entrance. From this, he can easily determine the average speed that you were driving at. If the average speed is higher than the speed limit, it means that at some point between the two toll booths you were speeding and therefore they can give you a speeding ticket.

The principal in this scenario is $ 8000.

Simple Interest can be defined as the sum paid back for using the borrowed money, over a fixed period of time.

Compound Interest can be defined as when the sum principal amount exceeds the due date for payment along with the rate of interest, for a period of time.

It is Given that:

Priscilla invested 20,000 that means the total amount she invested.

Amount= $ 20,000

Rate of interest=12%

Time= 5 year

Interest= $12,000.

By the formula;

Amount =  principal + Interest

Principal = Amount - Interest

Principal= $ 20,000- $12,000

Principal=$ 8000

Hence, the principal in this scenario is $ 8000.

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Answer:

x= -2

y= -4

Step-by-step explanation:

1) solve for y in 5x-y= -6

   which would be y= 5x+6

2) substitute that in for y in the second equation

    which would be 10x+3(5x+6)= -32

3) solve that new equation

    which would be x= -2

4) plug x= -2 into either equation (the shorter equation is the one i chose)

    which would be 5(-2) - y = -6

5) solve that new equation

  which would be y= -4

Answer:

The answer is option

3 and 4

Answer:

The answer is -40

Step-by-step explanation:

Answer:  19x - 216/6

Explanation: Hope this helps!

Answer:

The maximum possible error of in measurement of the angle is  \(d\theta_1 =(14.36p)^o\)

Step-by-step explanation:

From the question we are told that

    The angle of elevation  is  \(\theta_1 = 15 ^o = \frac{\pi}{12}\)

     The height of the tree is  h

      The distance from the base is  D

h is mathematically represented as

            \(h = D tan \theta\)       Note : this evaluated using SOHCAHTOA i,e

                                               \(tan\theta = \frac{h}{D}\)

Generally for small angles the series approximation of  \(tan \theta \ is\)

          \(tan \theta = \theta + \frac{\theta ^3 }{3}\)

So given that \(\theta = 15 \ which \ is \ small\)

       \(h = D (\theta + \frac{\theta^3}{3} )\)

       \(dh = D (1 + \theta^2) d\theta\)

=>        \(\frac{dh}{h} = \frac{1 + \theta ^2}{\theta + \frac{\theta^3}{3} } d \theta\)

Now from the question the relative error of height should be at  most

        \(\pm p\)%

=>    \(\frac{dh}{h} = \pm p\)

=>    \(\frac{1 + \theta ^2}{\theta + \frac{\theta^3}{3} } d \theta = \pm p\)

=>      \(d\theta = \pm \frac{\theta + \frac{\theta^3}{3} }{1+ \theta ^2} * \ p\)

 So  for   \(\theta_1\)

            \(d\theta_1 = \pm \frac{\theta_1 + \frac{\theta^3_1 }{3} }{1+ \theta_1 ^2} * \ p\)

substituting values  

          \(d [\frac{\pi}{12} ] = \pm \frac{[\frac{\pi}{12} ] + \frac{[\frac{\pi}{12} ]^3 }{3} }{1+ [\frac{\pi}{12} ] ^2} * \ p\)

 =>       \(d\theta_1 = 0.25 p\)

Converting to degree

           \(d\theta_1 = (0.25* 57.29) p\)

            \(d\theta_1 =(14.36p)^o\)

Given that 16 families went on a trip and the cost of the trip was Rs. 2,16,352.The amount paid by each family is to be determined by unitary method Hence each family paid Rs.13522

Now, let's solve this by using the method of unitary method. To find the cost of 1 family trip, we will divide the total cost of the trip by the number of families.2,16,352 / 16 = 13,522 So, the cost of the trip per family is Rs. 13,522.Hence, each family paid Rs. 13,522 for the trip.

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Answer:

Step-by-step explanation

1. The total cost of the trip for all 16 families is Rs 2,16,352.
2. To find out how much each family paid, we need to divide the total cost by the number of families: Rs 2,16,352 ÷ 16.
3. When we do the division, we get the result: Rs 13,522.

Now let's check if this result is correct:

1. If each family paid Rs 13,522 for the trip, then the total cost for all 16 families would be: 16 × Rs 13,522 = Rs 2,16,352.
2. This is exactly the same as the total cost given in the problem statement.

So we have shown that each family paid **Rs 13,522** for the trip

-7+(n-1)6

-7 is the starting term

n is the term that you are looking for

6 is the common difference

The formula for the nth term in the arithmetic sequence is:

a(n) = 6n - 13

It is a sequence where the difference between each consecutive term is the same.

We have,

We are given the first four terms of an arithmetic sequence:

a₁ = -7, a₂ = -1, a₃ = 5, a₄ = 11

To find the formula for the nth term, we need to find the common difference (d) first.

We can do this by subtracting any two consecutive terms:

d = a₂ - a₁ = (-1) - (-7) = 6

Now we can use the formula for the nth term of an arithmetic sequence:

a(n) = a₁ + (n - 1)d

Substituting the values we found:

a(n) = (-7) + (n - 1)(6)

Simplifying:

a(n) = -7 + 6n - 6

a(n) = 6n - 13

Therefore,

The formula for the nth term in the arithmetic sequence is:

a(n) = 6n - 13

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Answer:

math is hard

Step-by-step explanation:

a. Monthly payment for the bank's car loan is $407.67

b. Monthly payment for the savings and loan association's car loan is $315.99

c. Total amount paid would be $2,035 less for the bank's car loan than for the savings and loan association's car loan.

The cost of borrowing money, usually expressed as a percentage of the amount borrowed, is what a lender charges a borrower to use their money. This cost is known as an interest rate.

(a) To find the monthly payment for the bank's car loan, we can use the formula for the present value of an annuity:

\(PV = PMT * \frac{1 - (1 + \frac{r}{n})^{(-n*t)}}{\frac{r}{n} }\)

putting the given values,

⇒ \(21000 = PMT * \frac{1 - (1 + \frac{0.065}{12})^{(-12*5)}}{\frac{0.065}{12} }\)

Solving for PMT, we get:

PMT = $407.67

Therefore, the monthly payment for the bank's car loan is $407.67

(b) To find the monthly payment for the savings and loan association's car loan, we can use the same above formula:

where PV is still $21,000, PMT is the monthly payment, r is still 0.065, n is still 12, but t is now 7 years x 12 months/year = 84 payments.

putting the given values,

\(21000 = PMT * \frac{1 - (1 + \frac{0.065}{12})^{(-12*7)}}{\frac{0.065}{12} }\)

Solving for PMT, we get:

PMT = $315.99

Therefore, the monthly payment for the savings and loan association's car loan is $315.99.

(c) Bank's car loan: $407.67 x 60 = $24,460.20

Savings and loan association's car loan: $315.99 x 84 = $26,495.16

Therefore, the bank's car loan would have the lowest total amount to pay off, by: $26,495.16 - $24,460.20 = $2,034.96

Therefore, the total amount paid would be $2,035 less for the bank's car loan than for the savings and loan association's car loan.

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Step-by-step explanation:

a = k/m    or       ma = k    

using 4 and 9     4* 9 = k = 36

then the equation becomes:

    ma = 36    

  using a = 6

      6 * m = 36     shows m = 6 kg

Answer:

Step-by-step explanation:

This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts.

Freddy needs to understand that each member of the group offers their own special talents and viewpoints, and that equation working together can provide better results.

A mathematical equation is a process that links two statements and indicates equality using the equals symbol (=). A mathematical statement that proves the equality of two mathematical expressions is known as an equation in algebra.

Since Freddy is interfering with their chats and insisting that his viewpoint is more relevant than theirs, his group members are likely to find his actions to be both distracting and frustrating. This could lead to an imbalance in the dynamics of the group, making other participants feel unimportant and unheard.

Freddy needs to understand that each member of the group offers their own special talents and viewpoints, and that working together can provide better results than having just one person in charge of the project. All members can contribute to the development of a more inclusive and effective environment by encouraging open conversation and active listening.

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9514 1404 393

Answer:

  20th

Step-by-step explanation:

The person will receive all gifts if the are all of a multiple of 2, a multiple of 4, and a multiple of 5. Since 4 is already a multiple of 2, the person who will receive all is the one who is a multiple of 4 and 5.

20 is 4×5, so is a multiple of both numbers. There is no smaller number that is a multiple of both 4 and 5.

The 20th person will receive all gifts.

_____

The value we have determined here is called the "least common multiple" (LCM). It is the product of the unique prime factors of the numbers of interest, raised to the highest power that appears in any of the numbers.

  2 = 2¹

  4 = 2²

  5 = 5¹

LCM(2, 4 5) = 2² × 5¹ = 20

Answer:

31-6=d

Step-by-step explanation:

it just is

Answer:

ylyiky lio

Step-by-step explanation:

9514 1404 393

Answer:

  (x, y) = (1/2, -√3/2)

Step-by-step explanation:

The coordinates on a unit circle of the intersection of the terminal ray of angle α are ...

  (x, y) = (cos(α), sin(α))

For α = 5π/3, the point on the unit circle is ...

  (x, y) = (cos(5π/3), sin(5π/3)) = (1/2, (-√3)/2)

The area of the triangle is found as 12 unit².

A triangle is a three-sided polygon with three sides that closes a space.

The formula for the area of the triangle is;

Area of triangle= ½ × base × height

The base is given as 6 units and the height is 4 units. (count 1 column of graph as 1 unit).

Put the values in formula.

Area of triangle = ½(6)(4)

Area of triangle = 12 unit.²

Therefore, the area of the triangle is found as 12 unit.²

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Answer: D: 10 and 11

Step-by-step explanation:

The Sq Rt of 111 is 10.5356537529 which falls between 10 and 11

Answer:

D: 10 and 11

Step-by-step explanation:

10.5356537529 10^11

and in standard notation:

105,356,537,529

Option C, One of the weaknesses of quantitative forecasting approaches is the time-series forecast.

Whenever there is no previous data available, businesses utilize qualitative forecasting to predict a certain financial outcome. This method depends on people with knowledge or skill on the potential outcomes. For accurate results, these specialists should draw from trustworthy sources and have relevant expertise.

Making business forecasts using precise figures is known as quantitative forecasting.

Qualitative forecast examples include,

Time-series prediction is an illustration of a quantitative forecasting approach, hence the answer c is the one that is right.

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The question is -

Which of the following is not a qualitative forecast?

A. Executive opinions

B. Sales force opinions

C. Time-series forecast

D. All of the above

Answer:

g = 61.

Step-by-step explanation:

g + 9 = 70             Subtract 9 from both sides of the equation:

g + 9 - 9 = 70 - 9

g = 61.

The required expression represents the Gorans' saving is 9 + g = 70, and his saving is 61.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,
The sum of 9 and Goran's savings is 70.
g is the Goran's saving,
9 + g = 70
g = 70 - 9
g = 61

Thus, the required expression represents the Gorans' saving is 9 + g = 70, and his saving is 61.

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Using the lowest common factor of the shuttles' run times, they will depart again for the campus simultaneously at 10.25 A.M.

We can use the lowest common factor (LCM) of their run time to determine when they depart again for the campus.

The lowest common factor of 30 and 20 is 60 because both 30 and 20 can divide 60 evenly without a remainder, showing that it takes 60 minutes for the two shuttles to depart for the campus at the same time.

We can conclude that every 60 minutes or hour, the two shuttles simultaneously depart for the campus.  Every hour, the shuttle departing from Ball Hall completes 2 runs, while the shuttle departing from Lot A completes 3 runs.

Thus, using the lowest common factor, the next time both shuttles will depart for the campus at the same time is 10:25 A.M.

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Answer:

12*3.25=39

Step-by-step explanation:

u multiply 12 by 3.25 and then u get ure answer witch is 39!!

Answer: b. comma and cola

Step-by-step explanation:

The equation of the line in slope-intercept form is y = (3/5)x + 2. This form allows us to easily identify the slope and y-intercept of the line and to graph it on a coordinate plane.

To write the equation of a line in slope-intercept form, we use the formula:y = mx + b

where:

- y represents the dependent variable (the vertical axis)

- x represents the independent variable (the horizontal axis)

- m represents the slope of the line

- b represents the y-intercept, the point where the line intersects the y-axis.

In this case, we are given the slope as 3/5 and the y-intercept as 2. Plugging these values into the formula, we get:

y = (3/5)x + 2

This equation represents a line with a slope of 3/5, indicating that for every 5 units we move horizontally (along the x-axis), the line moves 3 units vertically (along the y-axis). The y-intercept of 2 tells us that the line intersects the y-axis at the point (0, 2).

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when the scale factor is 1, we have:

(side length of side opposite ∠A) / (length of hypotenuse) = sin A

When the scale factor is 1, the ratio of the side length of the side opposite ∠A to the length of the hypotenuse remains the same as in the original triangle. In a right triangle, the side opposite ∠A is referred to as the "opposite" side, and the hypotenuse is the longest side.

The ratio of the side length of the side opposite ∠A to the length of the hypotenuse is commonly known as the sine of angle A (sin A). So, when the scale factor is 1, the ratio of the side length of the side opposite ∠A to the length of the hypotenuse is equal to sin A.

In mathematical terms, when the scale factor is 1, we have:

(side length of side opposite ∠A) / (length of hypotenuse) = sin A

It's important to note that this ratio holds true for any right triangle, regardless of its size or dimensions, as long as the angle A remains the same.

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Answer:

The range in shelter A is 22, and the range in shelter B is 18.

Subtract 8 from 30 shelter A which gives you 22. Then subtract 10 from 28 which gives you 18 for Shelter B.

Answer:

The range in shelter A is 22, and the range in shelter B is 18.

Subtract 8 from 30 shelter A which gives you 22. Then subtract 10 from 28 which gives you 18 for Shelter B.

Step-by-step explanation: