0.62, 0.38, 0.35, 0.49, 0.1, 0.21, 0.54, 0.6, 0.51, 0.28 Least to Greatest *

Answer:

144

Step-by-step explanation:

The independent variable in the linear relationship is the number of people.

The dependent variable in the linear relationship is the cost of the dinner.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Cost of dinner for 3 people = $42

Cost of dinner for 7 people = $98

The cost of dinner for one person = $14

Now,

The linear function for this relationship.

f(x) = 14x

Where x is the number of people and f(x) is the cost of the dinner.

Now,

The number of people is the independent variable.

The cost of dinner is the dependent variable.

Thus,

Independent variable = Number of people/

Dependent variable = Cost of the dinner.

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(a) The given differential equation is y'(x) = sin(x) + e^(-x), with initial conditions y(0) = 1. To solve this equation, we can integrate both sides to obtain the general solution. Then, we can use the initial conditions to determine the particular solution that satisfies the given conditions.

(b) In part (b), the differential equation is solved numerically using three different methods: the Euler Method, the Taylor Series Method of order two, and the fourth-order Runge-Kutta Method. These methods approximate the solution by taking small steps and using iterative calculations.

(c) To compare the approximate solutions obtained from the Euler Method with the exact solution, we evaluate the solutions at the given points (0.5 and 1.0) and calculate the corresponding absolute errors. The absolute error is the difference between the approximate solution and the exact solution.

(d) In part (d), we comment on the accuracy of the three methods for solving ordinary differential equations. We analyze the results obtained from each method and compare them to the exact solution. This allows us to assess the accuracy of the methods and determine their effectiveness in approximating the solution to the differential equation.

(a) To solve the given differential equation y'(x) = sin(x) + e^(-x), we can integrate both sides with respect to x. This gives us y(x) = -cos(x) - e^(-x) + C, where C is the constant of integration. Using the initial condition y(0) = 1, we can substitute x = 0 and y = 1 into the equation and solve for C. This gives us C = 2. Therefore, the particular solution to the differential equation with the given initial condition is y(x) = -cos(x) - e^(-x) + 2.

(b) In this part, the differential equation y'(x) = sin(x) + e^(-x) is solved numerically using three different methods: the Euler Method, the Taylor Series Method of order two, and the fourth-order Runge-Kutta Method. These methods involve approximating the derivative and iteratively calculating the values of y at each step. The step size h is given as 0.5.

(c) To compare the approximate solutions obtained from the Euler Method with the exact solution, we evaluate the solutions at the given points (0.5 and 1.0). For each method, we calculate the absolute error by subtracting the approximate solution from the exact solution at each point. The absolute error indicates the difference between the approximation and the true solution.

(d) In part (d), we assess the accuracy of the three methods for solving ordinary differential equations. We compare the results obtained from each method with the exact solution. The accuracy of a method can be determined by examining the magnitude of the absolute errors. If the absolute errors are small, it indicates a higher accuracy of the method in approximating the solution. We analyze the errors and comment on the effectiveness of each method in solving the given differential equation.

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Answer:

y=(2x^2+24x)+25

y=2x(x^2+12x)+25

y=2x(x^2+12x+36)+25-2x(36)

Y=2x(x+6)^2+25-72

Y=2x(X+6)^2-47

Step-by-step explanation:

sorry it was late

Answer: y=2(x+6)²-5

Step-by-step explanation: First you find the coefficient of x^2, which is 2, then take out 2 as a factor, 24/2 which will equal to 12. After that do 47 divided by 2  if you calculate that it will equal to 23.5.  y=2(x²-12+23.5)  y =2(x²-12x+23.5)

Next Step: Figure out the coefficient of x. To make it easier,look what is in front of x as you can see it is 12. Then you divide 12/2 which is 6. Then square 6, which is 36. Then you add and subtract 36. To write the first three terms as a square, you do ( x+6)^2. Then do -36 + 23.5 if you calculate that it will get you wil get -12.5 . Now that you have calculated that distribute 2, then do 2 times -12.5 which is -12.5. This is how it shoud look like y=2(x+6)² -12.5.  

The approximate values triangle for angle B, angle C, and side b are B ≈ 54.4 degrees, C ≈ 96.6 degrees, and b ≈ 36.8 units, respectively, rounded to the nearest 10th.

Given data:

Side a = 18

Side c = 27

Angle A = 29 degrees

Step 1: Find angle B using the law of sines:

sin(B)/c = sin(A)/a

sin(B)/27 = sin(29°)/18

sin(B) = (27sin(29°))/18

B = arcsin((27sin(29°))/18)

Step 2: Find angle C using the fact that the sum of angles in a triangle is 180 degrees:

C = 180° - A - B

C = 180° - 29° - B

Step 3: Find side b using the law of sines:

sin(C)/c = sin(A)/a

sin(C)/27 = sin(29°)/18

sin(C) = (27 × sin(29°))/18

b = (sin(C) × a)/sin(A)

Step 4: Substitute the given values into the equations and calculate the approximate values using a calculator:

B ≈ arcsin((27 × sin(29°))/18) ≈ 54.4 degrees

C ≈ 180° - 29° - 54.4° ≈ 96.6 degrees

b ≈ (sin(96.6°)*18)/sin(29°) ≈ 36.8

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The question is -

Solve the triangle. Angle A is opposite side a, Angle B is opposite side b and Angle C is opposite side c. Round final answers to the nearest 10th

Given data: side a = 18, side c = 27, angle A = 29 degrees.

The appropriate regression model depends on the stationarity properties of both the dependent and independent variables, as well as the error term. The researcher can use a standard OLS regression model with first-order differencing of both Y and X.

In the first scenario, both Y and X are I(0), which means they are stationary time series. In this case, the researcher can perform a standard linear regression analysis, as the stationary series would lead to a stable long-run relationship. The answer from this model will be reliable and less likely to suffer from spurious regressions. In the second scenario, Y is I(2) and X is I(0). This implies that Y is integrated of order 2 and X is stationary. In this case, the researcher should first difference Y twice to make it stationary before performing a regression analysis. However, this approach might not be ideal as the integration orders differ, which can lead to biased results.

In the third scenario, Y and X are both I(1) and the error term is I(0). This indicates that both Y and X are non-stationary time series, but their combination might be stationary. The researcher should employ a co-integration analysis, such as the Engle-Granger method or Johansen test, to identify if there is a stable long-run relationship between Y and X. If co-integration is found, then an error correction model can be used for more accurate predictions.

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Answer:

Center ~ ( -4, 3 ), Radius ~ 2; Option A

Step-by-step explanation:

~ We know that the standard circle equation ( x - a )^2 + ( y - b )^2 = r^2  provided r ⇒ radius of the circle, centered at ( a, b ) ~

1. If we are given the circle formula ( x + 4 )^2 + ( y - 3 )^2 = 4, it would be that the center points ( a, b ) would be the inverse of 4 and -3, provided the formula is -a and -b: center ( -4, 3 )

2. Now the radius in the formula ( x - a )^2 + ( y - b )^2 = r^2, is noted by r such that in ( x + 4 )^2 + ( y - 3 )^2 = 4, r^2 is 4 ⇒ r = √4 = 2

3. We now know that the center of this circle is ( -4, 3 ) with a radius of 2, and the only graph that represents that function is the first graph ~

Answer: Center ~ ( -4, 3 ), Radius ~ 2

Answer: \(2/63, -52/63, 83/63\)

Step-by-step explanation:

\(h(1)=-\frac{6}{7}(1)+\frac{8}{9}=\frac{2}{63}\\\\h(2)=-\frac{6}{7}(2)+\frac{8}{9}=-\frac{52}{63}\\\\h(-1/2)=-\frac{6}{7}(-1/2)+\frac{8}{9}=\frac{83}{63}\)

The inequality representing the number of backpacks, x, that need to be sold each week for the factory to meet the profit goal is:

30x - 12,000 ≥ 980

To represent the situation, we need to consider the revenue and expenses associated with selling backpacks.

Let's break down the components:

Selling price per backpack: $40.00

Cost to make one backpack: $10.00

Operating expenses per week: $12,000.00

Profit goal per week: $980.00

To calculate the profit, we subtract the total cost (including both the cost to make the backpacks and the operating expenses) from the revenue obtained by selling the backpacks. The number of backpacks sold is denoted by 'x.'

Revenue from selling x backpacks: $40.00 × x

Total cost (including operating expenses) for x backpacks: $10.00 ×x + $12,000.00

The profit is given by the difference between revenue and cost:

Profit from selling x backpacks: Revenue - Total Cost

Profit from selling x backpacks: $40.00× x - ($10.00× x + $12,000.00)

To meet the factory's profit goal of at least $980.00, we set up the following inequality:

$40.00× x - ($10.00× x + $12,000.00) ≥ $980.00

Now we simplify the inequality:

$40.00× x - $10.00 × x - $12,000.00 ≥ $980.00

$30.00 × x - $12,000.00 ≥ $980.00

Thus, the inequality representing the number of backpacks, x, that need to be sold each week for the factory to meet the profit goal is:

30x - 12,000 ≥ 980

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Answer:

840 megabytes

Step-by-step explanation:

hope this helps

Answer:

7

Step-by-step explanation:

42/6=7

Answer:

45°

Step-by-step explanation:

-45° would be 360°-45°=315°

Since 315° is in Quadrant IV, then its reference angle is 360°-315°=45°

So really, -45° is just 45° clockwise which is also our reference angle.

Answer:

5/4

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

∠ R = 2x + 5 , ∠ S = x + 1 , ∠ T = 7x - 16

the sum of the 3 angles in a triangle = 180°

sum the 3 angles and equate to 180

2x + 5 + x + 1 + 7x - 16 = 180

10x - 10 = 180 ( add 10 to both sides )

10x = 190 ( divide both sides by 10 )

x = 19

Then

∠ R = 2x + 5 = 2(19) + 5 = 38 + 5 = 43°

∠ S = x + 1 = 19 + 1 = 20°

∠ T = 7x - 16 = 7(19) - 16 = 133 - 16 = 117°

Answer:

238 should be the answer

Step-by-step explanation:

On the interval [0, 2π], the minimum values of f(x) = 12cos^2(x) - 1 are -1, and the maximum values are 11.

To find the minimum and maximum values of the function f(x) = 12cos^2(x) - 1 on the interval [0, 2π], we need to determine the critical points and endpoints within that interval.

First, let's differentiate the function f(x) with respect to x to find the critical points. The derivative of f(x) is f'(x) = -24cos(x)sin(x).

Next, we set f'(x) equal to zero and solve for x:

-24cos(x)sin(x) = 0

This equation is satisfied when cos(x) = 0 or sin(x) = 0.

For cos(x) = 0, we have x = π/2 and x = 3π/2 as critical points.

For sin(x) = 0, we have x = 0 and x = π as critical points.

Now, we evaluate the function f(x) at these critical points and the endpoints of the interval [0, 2π]:

f(0) = 12cos^2(0) - 1 = 11

f(π/2) = 12cos^2(π/2) - 1 = -1

f(π) = 12cos^2(π) - 1 = 11

f(3π/2) = 12cos^2(3π/2) - 1 = -1

f(2π) = 12cos^2(2π) - 1 = 11

From the evaluations, we see that the minimum values of f(x) are -1, occurring at x = π/2 and x = 3π/2, while the maximum values are 11, occurring at x = 0, x = π, and x = 2π.

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The number of movies on which Avery's songs were played is 2 times

From the question, we have the following parameters that can be used in our computation:

Songs played in commercial = $40

Songs played in movie = $140

Total earnings = $480

Number of times played on commercial = 7

The above parameters when represented as an equation is

Total earnings = Songs played in commercial * Number of times played on commercial + Songs played in movie * Number of times played in a movie

Substitute the known values in the above equation, so, we have the following representation

40 * 7 + 140 * Number of times played in a movie = 480

Evaluate the products

280 + 140 * Number of times played in a movie = 480

So, we have

Number of times played in a movie = 200/140

Evaluate

Number of times played in a movie = 2

Hence, the number of times is 2 times

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For a random variable z, its mean and variance are defined as e[z] and e[(z − e[z])2 ], respectively.

What is a random variable?

A random variable is a set of all possible values for which a probability distribution is defined. It is a numerical value assigned to all potential outcomes of a statistical experiment.

What is the mean of a random variable?

The mean, sometimes referred to as the expected value, is the sum of the product of each possible value multiplied by its probability, giving the value that summarizes or represents the center of the distribution of a set of data.

What is the variance of a random variable?

The variance is the expected value of the squared deviation of a random variable from its expected value. It determines how much the values of a variable deviate from the expected value.What is the formula for the mean of a random variable?

The formula for the mean of a random variable is:E(X) = ∑ xi * P(xi)

What is the formula for the variance of a random variable?

The formula for the variance of a random variable is:Variance(X) = ∑ ( xi - mean )² * P(xi)where 'mean' is the expected value.

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Answer:

find AC and BC then check multiply their slopes

Answer: Least common multiple - 2 (m + 2n)

Step-by-step explanation: Evaluate: 2 (m +2n), 2 (m+2n)

-2.05 is the critical value for the left-tailed test .

What is critical z value?

The -1.96 and +1.96 standard deviations are the essential z-score values when adopting a 95 percent confidence level.

                               With a 95 percent confidence level, the uncorrected p-value is equal to 0.05.The critical value for a two-sided test is Z 1-/2, while for a one-sided test, it is Z 1.

                      You reject the null hypothesis if the absolute Z-value is higher than the crucial value. If not, you have not successfully ruled out the null hypothesis.

Given that,

α = 0.02.

left tailed test

Zα = 0.02 = -2.05

critical value = -2.05

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Answer: 3600

Step-by-step explanation: If y = k/x is the formula, solving for k gives xy = k, so 72(50) = 3600; or 30(120) = 3600.

Answer:

1. Given

2. Addition property of inequality

3. Division property of inequality

4. Square root property

Step-by-step explanation:

The first equation is always going to be the given since it hasn't been solved yet, on the next step you had to get rid of the 1 so you had to add 1 to both sides, this is called addition property of inequality, then to isolate the x you had to divide both sides by 4, this is called division property of inequality and lastly you had to do the opposite of squaring a number, which is taking the square root. Hope this helped.

The probability that less than two families out of the random sample of six husband-wife families have life insurance is approximately 0.23.

In this case, the probability of success (a family having life insurance) is 77%, which corresponds to a probability of 0.77. The probability of failure (a family not having life insurance) is the complement of the success probability, which is 1 - 0.77 = 0.23.

To calculate the probability that less than two families have life insurance, we need to find the probability of 0 or 1 success in a sample of six, using the binomial distribution formula. This can be calculated as the sum of the probabilities of these two outcomes.

The calculation involves evaluating the binomial probability function for each outcome and summing them up. The formula for calculating the probability of k successes in a sample of size n is given by: P(X = k) = C(n, k)  p^k  (1 - p)^(n - k), where C(n, k) represents the number of combinations of n items taken k at a time.

In this case, we need to calculate P(X < 2) = P(X = 0) + P(X = 1) = C(6, 0) 0.77^0 x 0.23^6 + C(6, 1)  0.77^1 x 0.23^5. Evaluating this expression will give us the desired probability.

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Answer:

He actually paid a sum of $201.25

Step-by-step explanation:

We simply add the vat value to the cost of the machine

Mathematically, that’s (

175 + 15% of 175

= 175 + (15/100 * 175)

= 175 + 26.25

= $201.25

Answer:

Solve for x by simplifying both sides of the equation, then isolating the variable.

x=17

Step-by-step explanation:

Answer:

115

Step-by-step explanation:

Answer:

Step-by-step explanation:

$86.50

Answer:

Step-by-step explanation:

(x - 3)(x + 6)

=x(x + 6) -3(x + 6)

=x*x + x*6 - 3*x - 3*6

=x^2 + 6x - 3x - 18

=x^2 + 3x - 18

\(\longrightarrow{\green{ \: {x}^{2} + 3x - 18 }}\) 

\(\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}\)

\((x - 3)(x + 6)\)

➼ \( \: x(x + 6) - 3(x + 6)\)

➼ \( \: {x}^{2} + 6x - 3x - 18\)

➼ \( \: {x}^{2} +3x - 18\)

\(\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{❦}}}}}\)

A relation between sets is referred to as a function when there is exactly one output for each input.

To write the equation y = ax + b in function notation, substitute f(x) for y

The only true statement is the last one. A function assigns exactly one output value to each input value. The domain is the set of all input, or x-values. The range is the set of all output, or y-values.

y=ax+b can be written in function notation by replacing y with f(x).

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