Harry and Sally both invest $2500 for their school tuition in 3 years. Harry chooses to invest his money at bank A at 2.5%/a compounded monthly while Sally chooses to invest her money at bank B at 2.75%/a compounded quarterly. How much money will Harry and Sally have in their bank account after 3 years? Who made the best investment? Explain your answer.

Answer:

Step-by-step explanation:

40

The domain and the range of a function are the possible input and output values of the function.

The function is given as:

C = 130S + 3500

The domain

This is the possible S values of the function.

S cannot be less than 0, because it represents a physical quantity (i.e. tons of sugar)

The value of S can be any value greater than 0

Hence, the domain of the function is [0, ∞)

The range

This is the possible C values of the function.

The function is given as:

C = 130S + 3500

When S = 0

C = 130(0) + 3500

C = 3500

The above means that:

C cannot be less than 3500

The value of C can be any value greater than 3500

Hence, the range of the function is [3500, ∞)

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Required function y = 2x + 40 to represents linear relationship between number of people and total cost shows following statements are true:

a. Independent variable represents the number of people.

b. Initial value for the picnic is $40.

d. Cost of the picnic increases as per the number of people.

As given in the question,

Let 'x' represents the number of people

And 'y' represents the total cost

Linear relationship between number of people and total cost is:

y = mx + b

Consider two points (x₁ , y₁) = (6, 52) and ( x₂ , y₂ ) = ( 9 , 58)

Slope 'm' = ( y₂ - y₁)/ (x₂ - x₁)

              = (58 - 52)/ (9 -6)

              = 6 / 3

              = 2

y = 2x + b

Now for, (x. y) = ( 12,64)

64 = 2(12) +b

⇒b = 64 - 24

⇒b = 40

Hence, required function is :

y = 2x + 40

a. Independent variable is the number of people.

Here it is x which represents the number of people.

True.

b. Initial value for the picnic is $40

y- intercept when x =0 ⇒ y = $40

True.

c. Rate of change is $8.67 per person.

No, rate of change is $2 per person.

d. Number of people increases as total cost of picnic increases

True .

e. If x = 4

⇒y = 2(4) + 40

     = 48 ≠46

False.

Therefore, function y = 2x + 40 represents that following statements are true:

a. Independent variable represents the number of people.

b. Initial value for the picnic is $40.

d. Cost of the picnic increases as per the number of people.

The above question is incomplete, the complete question :

The table below shows the linear relationship between the number of people at a picnic and the total cost of the picnic. Which statements about the function described by the table are true? Check all that apply. a. The independent variable is the number of people.

b. The initial value (initial fee) for the picnic is $40.

c.  The rate of change is $8.67 per person.

d. As the number of people increases, the total cost of the picnic increases.

e.  If 4 people attended the picnic, the total cost would be $46.

Number of people               Total cost ($)

6                                                 52

9                                                 58

12                                               64

15                                               70

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The number of welcome packets that you will be able to fully complete in the time allotted would be = 14

The time allotted for the refilling of the whole welcome packets = 3 hours

To convert to mins = 3 × 60 = 180 mins.

To run each packet will take the following time:

5 minutes to print,

2 minutes to organize, and

5 minutes to proofread which is a total of 12mins

But for every 5 packets = 5×12+3 = 63 mins.

Therefore X packets = 180 mins.

Make X packets the subject of formula;

X packets = 5 × 180/63

= 900/63

= 14.2

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Answer:

The slope is same for both points.

Step-by-step explanation:

1st set of points: (1, 4) and (7, 2)

m = 2-4/7-1

m = -2/6

m = -1/3

2nd set of points: (7, 2) and (10, 1)

m = 1-2/10-7

m = -1/3

The slope is same for both points.

The total number of fish in the lake would be = 60 fishes

The total of a data set is the addition of the various components that makes up a data set which gives a particular value.

On the first day the number of fish that was marked by the fisher man = 50 fishes.

On the second day the total amount of fishes that was caught = 80 fishes

The number of fishes that where among the 80 fishes that are marked= 20

Therefore the total amount of fishes in the lake = 80 - 20

= 60 fishes.

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The least among all 4 integers such that they sum up to 100 will be 22.

An integer is a whole number irrespective of the sign that the integer is all whole numbers that are going from 0 to infinite or 0 to minus infinite.

Integer; ....-2 , -1 , 0 , 1 , 2 , .....

Integers are non-decimal numbers and all integers are rational numbers.

Suppose the first integer is x.

The next three digits will be, x + 2, x + 4, and x + 6 correspondings.

Sum x + x + 2 + x + 4 + x + 6 = 100

(x + x + x + x) + (2 + 4 + 6) = 100

4x + 12 = 100

4x = 88

x = 22

Hence"The smallest of the four integers that add up to 100 is 22".

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Only point Q is on the ∠MNO because when we connect the point M and O then point R lies outside the ∠MNO. Only point Q remains inside.

In the given question we have to name a point on ∠MNO.

As we know that;

Evaluating the number of points in the curve of the triangle's vertices that are close to the location in question is the easiest method for determining whether a point is inside a triangle. The point on the curve is inside the triangle if it has three points; if it has four, it is outside the triangle.

When we check in the graph then only point Q is on the ∠MNO because when we connect the point M and O then point R lies outside the ∠MNO. Only point Q remains inside.

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The length of the third side is 16.5 for the given right-angle triangle. By using Pythagoras' theorem, the required length is calculated.

The given triangle is a right-angle triangle.

It has two lengths. They are

length of the hypotenuse = 21

length of the adjacent or base = 13

Then, the third side i.e., the opposite side length is calculated by

(hyp)² = (opp)² + (adj)²

⇒ (21)² = (opp)² + (13)²

⇒ 441 = (opp)² + 169

⇒ (opp)² = 441 - 169 = 272

⇒ opposite side length = √272 = 16.49 ≅ 16.5

Therefore, the length of the third side is 16.5.

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Answer:

Step-by-step explanation:

g(x) = 2*[tex]\sqrt{x}[/tex] + 4

Domain is the input  so what limits are there to the input?

for the square root, you are told that you can't not put in negative numbers until you learn about imaginary number in the for m  a+bi,  but for now, just say  the input is  0 to ∞,  for now   The domain is  0 to ∞

Range is the output

so that is from 4 to ∞

Answer:

  a. translation 2 right and up 4

  b. g(x) = √(x -2) +4

  c. domain: x ≥ 2; range: y ≥ 4

Step-by-step explanation:

You have the graph of a square root function with its vertex at (2, 4). You want to know what transformation that represents, the equation of the graph, and the domain and range of the function.

The vertex of the square root function f(x) = √x is located at (0, 0). In the given graph, it has moved to (2, 4). The vertical and horizontal scale factors remain unchanged. This transformation is ...

  translation right 2 units and up 4 units

Translation of function f(x) by h units right and k units up gives you ...

  g(x) = f(x -h) +k

Here, we have (h, k) = (2, 4), and f(x) = √x, so the transformed function is ...

  g(x) = √(x -2) +4

The domain is the horizontal extent of the graph. For a square root function it is the x-value of the vertex, and all points to the right of that.

  domain of g(x): x ≥ 2

The range is the vertical extent of the graph. For a square root function it is the y-value of the vertex, and all points above that.

  range of g(x): y ≥ 4

As a result, if (0,0) is a solution to the system of inequalities above, the connection between a and b is a>b in the xy-plane.

In mathematics, an inequality is a connection between two expressions or values that are not equal to each other. Inequality originates from a lack of equilibrium. To solve an inequality, isolate the variable on one side from the other constants. To do so, use opposing procedures to modify the inequality. To begin, separate the x by multiplying each side by two. Whatever you do on one side must equally be done to the other.

Here,

Given, y<−x+a and y>x+b

As given, (0,0) is a solution to the above inequalities.

0<0+a and 0>0+b

a>0 and b<0

Thus, we can conclude from the above inequalities that a is a positive number and b is a negative quantity.

Therefore, it can be surely said that a>b.

Hence, the relationship between a and b is a>b in the xy-plane, if (0,0) is a solution to the system of inequalities above.

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The balance sheet that correctly represents the engineer's income, expenses and balance is balance number 4.

We should know that balance sheet is a summary of assets and liabilities and income and expenses of a  legal person.

We are told that the the balance sheet shows a bi-weekly net pay

This implies that a month has two bi-weeks.  therefore every income and expenses is multiplied by 2 to get the following figures.

Income                                             Amount

Bi-weekly income                          $2,175.25

Total Monthly Income                   $4,350.50

Expenses                 Percent                              Amount

Housing                      35%                                $1,522.68

Food/Household          10%                               $435.05

Savings                         10%                                $435.05

Transportation              15%                                $652.58

Debt                              5%                                   $217.53

Entertainment              6%                                   $261.03

Medical/Personal Care 5%                                  $217.53

Giving                             5%                                 $217.53

Clothing                        4%                                  $174.02

Miscellaneous              5%                                 $217.53

                                                                           $4,350.50

Balance

Income $4,350.50

Expenses $4,350.50

Balance $0

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We will see that the linear function h(x) is:

h(x) = -21x - 15

The slope is -21, and the y-intercept is -15.

Remember that a general linear function is:

y = a*x + b

Where a is the slope and b is the y-intercept.

Here we start with the linear function:

f(x) = -7x + 9

First, we need to add 2 to the input of f (the input is x) to get function g(x), so we have:

g(x) =f(x + 2)

Replacing the actual function we will get:

g(x) = -7*(x + 2) + 9

Now we multiply the output of function g by 3 to get h(x), then:

h(x) = 3*g(x)

We will get:

h(x) = 3*[-7*(x + 2) + 9]

h(x) = -21*(x + 2) + 27

h(x) = -21x - 42 + 27

h(x) = -21x - 15

So we can see that the slope of function h(x) is -21, while the y-intercept is -15.

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Answer:

5x + 7y = 48 (total number of passengers on the ride)

x + y = 48 (total number of males and females on the ride)

Step-by-step explanation:

To find the number of males and the number of females on the roller coaster ride, you can use the following two linear equations to form a system:

5x + 7y = 48 (total number of passengers on the ride)

x + y = 48 (total number of males and females on the ride)

The first equation states that the total number of passengers on the ride is equal to the sum of the number of males (5x) and the number of females (7y). The second equation states that the total number of males and females on the ride is equal to the sum of the number of males (x) and the number of females (y).

To solve this system, you can use algebraic techniques to eliminate one of the variables and solve for the other. For example, you could multiply the first equation by 5 and the second equation by 7, then subtract the two equations to eliminate the y variable:

5 * 5x + 7 * 7y = 5 * 48

7 * x + 7 * y = 7 * 48

25x + 49y = 240

49x + 49y = 336

24x = 336 - 240

24x = 96

x = 4

Substituting this value for x in the first equation, we can solve for y:

5 * 4 + 7 * y = 48

20 + 7 * y = 48

7 * y = 28

y = 4

Therefore, there are 4 males and 4 females on the roller coaster ride.

Domain of integration is (D) 0 ≤ x ≤ 1, - 2 ≤ y ≤ 0.

Surface S = √21

A surface integral in mathematics is a generalization of multiple integrals to integration over surfaces, particularly in multivariable calculus. It can be viewed as the line integral's double integral equivalent. One can integrate a vector field or a scalar field across a given surface.

Equation of surface (S) is,

x/1 - y/2 + z/4 = 1

From here we get,

z = 4 - 4x + 2y

∫∫(S)xdS = ∫∫ (D)x(1 + (∂z/∂x)² + (∂z/∂y)²)^1/2 dxdy

Here (D) is projection of (S) on xy coordinate plane

so, (D) is triangle with vertices (1, 0, 0), (0, - 2, 0) and  (0,0,0).

∂z/∂x = - 4, ∂z/∂y = 2.

In (D) 0 ≤ x ≤ 1, - 2 ≤ y ≤ 0.

Now we have,

∫∫(S)xdS = ∫∫(D)x(1 + (- 4)² + 2²)^1/2 dxdy

= √21∫₋₂⁰dy ∫₀¹xdx

= √21y₋₂⁰x²/2₀¹

= √21

Hence, Domain of integration is (D) 0 ≤ x ≤ 1, - 2 ≤ y ≤ 0 and Surface S = √21

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The triangle with vertices A(0 , 0), B(0 , 6), and C(10 , 0) has its centroid located at (5 , 3).

Centroid of a triangle refers to the point inside a triangle at which the perpendicular bisectors of the sides of a triangle intersect. This point is also equidistant from the three vertices.

Given the location of the three vertices, there are different methods that can be used to locate the circumcenter of the triangle.

First, try to graph and visualize the triangle formed by the three vertices. (see photo)

From there, we can say that triangle ABC is a right-angled triangle with line BC as the hypotenuse.

One of the properties of the circumcenter of a triangle states that the circumcenter lies in the middle of a hypotenuse if it is a right-angled triangle.

To get the circumcenter, find the midpoint of the line BC.

midpoint = M(xm ,ym) = [(x1 + x2)/2 , (y1 + y2)/2]

M(xm ,ym) = [(0 + 10)/2 , (6 + 0)/2]

M(xm ,ym) = (5 , 3)

Hence, the centroid is located at (5 , 3).

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Answer:

[tex]2+2\sqrt{-1(-7-x)}\\2-2\sqrt{-1(-7-x)}[/tex]

Step-by-step explanation:

The inverse of [tex]2(x-2)^2=8(7+y)[/tex] is

[tex]2+2\sqrt{-1(-7-x)}\\2-2\sqrt{-1(-7-x)}[/tex]

Probability can be used to make predictions or decisions in a variety of situations, such as in gambling, finance, and science. In these situations, probabilities can be calculated based on statistical data or by using mathematical models.

To find the confidence interval for the mean speed (mu) of all cars on this section of the highway, we can use the following formula:

Confidence interval for mu = sample mean +/- z * standard error of the mean

Where:

sample mean is the average speed of the 81 cars in the sample, which is 60 mph

z is the z-score corresponding to the desired confidence level. In this case, the desired confidence level is 86.9%, which corresponds to a z-score of 1.96.

standard error of the mean is the standard deviation of the sampling distribution of the mean, which is calculated as the standard deviation of the population divided by the square root of the sample size.

In this case, the standard error of the mean is 13.5 / sqrt(81) = 2.26 mph.

Plugging these values into the formula, we get:

Confidence interval for mu = 60 +/- 1.96 * 2.26 = 59.131 to 60.869

Therefore, at a confidence level of 86.9%, we can be confident that the interval between 59.131 and 60.869 mph includes the true mean speed of all cars on this section of the highway.

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1. The first step is to determine the sample size. In this case, the sample size is 9 response times.

2. Next, the dispatcher should collect the response times from the log books.

3. After collecting the response times, the dispatcher should calculate the mean or average of the sample. This is known as the sample mean and is represented by the x-bar.

4. To calculate the sample mean, the dispatcher should add together the values of all the response times and divide this sum by the sample size (9). The result of this calculation is the sample mean or x-bar.

5. Finally, the dispatcher can use the value of the x-bar to calculate the standard deviation of the response times. This is done by taking the square root of the sum of the squares of the differences between each response time and the mean, divided by the total number of response times (in this case, 9). This will give us the standard deviation of the response times.

Question: Suppose dispatcher a takes a random sample of 9 response times from the log books in march. dispatcher a calculates x-bar

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a) The Keynesian cross graphs an economy's planned expenditure function,

[tex]$\mathrm{E}=\mathrm{C}(\mathrm{Y}-\mathrm{T})+\mathrm{I}+\mathrm{G}$[/tex],

and the equilibrium condition that actual expenditure equals planned expenditure.

How do you find the expenditure function?

To derive the expenditure function we can either (i) invert V(·) and solve for M, or (ii) set up the dual of the consumer's choice problem, solve for Hicksian demand functions and substitute them into the objective (i.e., expenditure) function.

The amount by which[tex]$\mathrm{Y}$[/tex]falls is given by the product of the tax multiplier and the increase in taxes

[tex]: $\Delta \mathrm{Y}=[-\mathrm{MPC} /(1-\mathrm{MPC})] \Delta \mathrm{T}$.[/tex]

c) We can calculate the effect of an equal increase in government expenditure and taxes by adding the two multiplier effects that we used in parts a and b :

[tex]\Delta \mathrm{Y}=\left[(1 /(1-\mathrm{MPC}))^* \Delta \mathrm{G}\right]-[(\mathrm{MPC} /(1-\mathrm{MPC}))]^* \Delta \mathrm{T}[/tex]

Because government purchases and taxes increase by the same amount, we know that [tex]\Delta \mathrm{G}=\Delta \mathrm{T}$. Therefore we can rewrite the equation as:$$\Delta \mathrm{Y}=[(1 /(1-\mathrm{MPC}))-(\mathrm{MPC} /(1-\mathrm{MPC}))]^* \Delta \mathrm{G}=\Delta \mathrm{G}[/tex]

This expression tells us that an equal increase in government purchases and taxes increases [tex]$\mathrm{Y}$[/tex] by the amount that [tex]$\mathrm{G}$[/tex] increases. That is, the balanced-budget multiplier is exactly 1 .

Complete question: Consider the Keynesian model with a change in the way that taxes are incorporated: (1) PAE = C + IP + G + NX Definition of Planned Aggregate Expenditure (2) C = C+ mpc (1-1) .y Consumption Function (3) PAE = Y Short-run Equilibrium Condition In this case, taxes paid are proportional to income, i.e. taxes paid are t - Y, where t is the tax rate and 0<t< 1. Disposable income is the part of income after taxes, i.e., (1-t). Y. Solve for the PAE spending line with PAE as a function of Y. What is the slope?

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Out of the given choices, we choose 'not enough information given to answer this question' and concluded that  the true slope for the population is equal to zero.

Since, we are given a p-value associated with a test of the slope coefficient equal to 0.028 which leads to 3% level of significance, it means that there is 3% chance of finding difference which is larger than the one given in our study given that the null hypothesis is true. Since, it is less than 5% level of significance, the null hypothesis is rejected and accept an alternative hypothesis. As this hypothesis is not given, we conclude that there is not enough information to give an answer to the question.

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P(D|FS)=.9529

If F and S are conditionally independent given D and ~D, then

P(FSD)= P(D)P(F|D)P(S|D)

P(FS~D) = P(~D)P(F|~D)P(S|~D)

P(F|~D) = 1 - P(~F|~D)

P(S|~D) = 1 - P(~S|~D)

P(~D) = 1 - P(D)

P(D|FS) = P(FSD)/(P(FSD) + P(FS~D))

P(F|D) = P(S|D) = .9

P(~F|~D) = P(~S|~D) = .9

P(D = .2)

Then, P(FSD) = P(D)P(F|D)P(S|D) = .2*.9*.9 = .162

P(FS~D) = P(~D)P(F|~D)P(S|~D) = (1 - .2)(1 - .9)(1 - .9)= .008

P(D|FS) = P(FSD)/(P(FSD) + P(FS~D)) = .162/(.162+.008) = 162/170=81/85 = .9529

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Answer:

[tex]-\frac{2}{3}[/tex]

Step-by-step explanation:

The slope/gradient of a line is defined by this formula:

[tex]\frac{y_{1}-y_{0} }{x_{1}-x_{0} }[/tex]

Where you pick two coordinates, find the change in the [tex]y[/tex] values, and divide it by the change in the [tex]x[/tex] values.

Two coordinates that this line passes through are (3, -2) and (-3, 2).

You can take the second [tex]y[/tex]-value (2) from the first [tex]y[/tex]-value (-2) or vice versa, so long as you do it in the same order the [tex]x[/tex] values.

For this example, I will take the first [tex]y[/tex]-value (-2) from the second [tex]y[/tex]-value (2), and take the first [tex]x[/tex]-value (3) from the second [tex]x[/tex]-value (-3).

The gradient/slope is defined by [tex]m[/tex] in the following:

[tex]m=\frac{2--2}{-3-3}=\frac{4}{-6}=-\frac{4}{6}=-\frac{2}{3}[/tex]

If the response variable y has a correlation coefficient of 0.3 with each of the predictors x1 and x2, it means that there is a weak linear relationship between y and both x1 and x2.

This means that as x1 and x2 increase or decrease, y is likely to change by a small amount. If x1 and x2 are heavily correlated, it means that there is a strong linear relationship between the two variables. This means that as x1 increases or decreases, x2 is likely to change by a large amount in the same direction. When two predictors are highly correlated, it can be difficult to determine the individual contribution of each predictor to the response variable y.

In this situation, it may be useful to use techniques such as multi-collinearity analysis or principal component analysis to understand the relationship between the predictors and the response variable better.

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For 7.45 - 3.029 the reason why they rewrite 7.45 as 7.450 is so as to have both values in three decimal place so the calculation can be easier.

It should be noted that the first digit after the decimal represents the tenths place then the next digit after the decimal  could be reffered to as  hundredths place however the remaining digits continue to fill in the place values until there are no digits left.

It should be noted that Decimal place value  can be described as the place values of all the digits in a given decimal number.

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Answer:

Step-by-step explanation:

Since the domain of the function h is -3 ≤ x ≤ 11 and the range is 1 ≤ h(x) ≤ 25, the possible values of h(x) for a given value of x in the domain will be within the range of 1 to 25. Additionally, we are given that h(8) = 19 and h(-2) = 2, so for the values x = 8 and x = -2, the corresponding values of h(x) are 19 and 2, respectively.

Given this information, the statement that could be true for the function h is: "For every value of x in the domain of h, the corresponding value of h(x) is within the range of 1 to 25." This statement is true because the domain and range of h are such that the possible values of h(x) for any value of x in the domain will be within the range of 1 to 25.

-15 is an integer , rational and a real number

Real numbers are mainly classified into rational and irrational numbers. Rational numbers include all integers and fractions. All negative integers and whole numbers make up the set of integers. Whole numbers comprise of all natural numbers and zero.

A negative number is not a natural number.

This means that -15 is a real number because real number comprises of rational and irrational number and rational numbers include negative numbers and they are called negative integers.

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The sum of the interior angles of a triangle is sometimes, but not always, 180º is false.

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

There are three angles in a triangle.

The sum is always 180 degrees.

Thus,

The sum of the interior angles of a triangle is always 180°.

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Answer:

The approximate period of the wave representing the airplane's path is 0.9 hours.

Step-by-step explanation:

The period of a wave is the time it takes for one complete cycle of the wave to occur. In the case of the airplane's path, this would be the time it takes for the airplane to complete one full oscillation, or "up and down" motion.

To find the period of the wave, we need to determine the value of x that corresponds to one complete cycle of the wave. In this case, the wave is defined by the function h(x) = 10000cos(0.0001x) + 20000.

To find the period, we can use the formula T = 2π/ω, where T is the period, π is the mathematical constant pi, and ω is the angular frequency of the wave. The angular frequency is related to the frequency of the wave, which is the number of cycles per second.

In this case, the angular frequency is given by the coefficient of the x term in the function, which is 0.0001. Plugging this value into the formula above, we get T = 2π/0.0001 = 200000π seconds.

Since one cycle of the wave corresponds to one complete oscillation of the airplane, the period of the wave is approximately 200000π seconds. This is a very large number, so it is usually more useful to express the period in minutes or hours. To convert to minutes, we can divide the period by 60, which gives us a value of about 3334 minutes. To convert to hours, we can divide the period by 3600, which gives us a value of about 0.9 hours.

In summary, the approximate period of the wave representing the airplane's path is 0.9 hours.

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The amount of time it takes for a wave to complete one full cycle is known as the wave's period. This would be the amount of time needed for the plane to perform one full oscillation, or “up and down” motion, in the case of the flight path.

Finding the value of x that represents the wave's full cycle is necessary to calculate the wave's period. The equation h(x) = 10000cos(0.0001x) + 20000 in this instance defines the wave.

The formula T = 2/, where T is the period, is the mathematical constant pi, and is the wave's angular frequency, can be used to determine the period. The wave's frequency, or the number of cycles per second, and the angular frequency are connected.

We may convert the period to hours by dividing it by 3600, which gives us a number of approximately 0.9 hours.

Therefore, The wave that represents the course of the airplane has an approximate period of 0.9 hours.

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Answer:

A

Step-by-step explanation:

5.7(3) can be expressed as a fraction

(573 -57)/90

516/90