An oil tanker and a cruise ship leave port at the same time and travel straight-line at 32 mph and 46 mph, respectively. Two hours later, they are 63 miles apart. What is the angle between their courses?​

The first four nonzero terms are 1 + t - (t^2)/2 - (t^3)/3 + (t^4)/8

To find the first 4 nonzero terms of the Taylor series for the function f(t) = e^(t)cos(t) about 0,

we can use the known Taylor series for e^(t) and cos(t).

The Taylor series for e^(t) is:

e^(t) = 1 + t + (t^2)/2! + (t^3)/3! + ...

And the Taylor series for cos(t) is:

cos(t) = 1 - (t^2)/2! + (t^4)/4! - (t^6)/6! + ...

To find the Taylor series for f(t) = e^(t)cos(t), we can multiply these two series together using the distributive property of multiplication. We get:

f(t) = (1 + t + (t^2)/2! + (t^3)/3! + ...) * (1 - (t^2)/2! + (t^4)/4! - (t^6)/6! + ...)

Expanding this out, we get:

f(t) = 1 + t - (t^2)/2 - (t^3)/3 + (t^4)/8 + (t^5)/15 - (t^6)/72 - ...

The first 4 nonzero terms of this series are:

f(t) = 1 + t - (t^2)/2 - (t^3)/3 + (t^4)/8 + ...

So, the first 4 nonzero terms of the Taylor series for f(t) = e^(t)cos(t) about 0 are:

1 + t - (t^2)/2 - (t^3)/3 + (t^4)/8

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Adding 12 apples to a basket initially containing c apples results in a total of 13.50 apples.

How can a real-world situation be represented by the equation 12 + c = 13.50?

The equation 12 + c = 13.50 can represent a real-world situation of purchasing items at a store and calculating the total cost. In this scenario, let's assume that 12 represents the price of a particular item, and c represents the additional cost, such as taxes or fees.

The equation states that when the additional cost is added to the base price of 12, the total cost becomes 13.50. This can occur when there is a sales tax or an additional charge applied to the base price. By solving the equation for c, we find that the additional cost is 1.50.

Therefore, in this situation, the real-world interpretation is that the item costs 12 dollars, and the additional cost, such as taxes, is 1.50 dollars, resulting in a total cost of 13.50 dollars.

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The radian measure of each angle:

1. π/4

2. 5π/4

The degree measure of each angle:

3. 90°

4. 135°

5. 540°

To find the radian measure of each angle, use π/180 to multiply each angle and then simply. That is:

1.) 45 * π/180 = π/4 radian

2.) 225 * π/180 = 5π/4 radian

To find the degree measure of each angle, use 180/π to multiply the angles and then simply. That is:

3.)  π/2 * 180/π = 90°

4.)  3π/4 * 180/π = 135°

5.)  3π * 180/π = 540°

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Answer:

Step-by-step explanation:

I assume you mean to solve for M in terms of a, b, x, and y.

To solve for M, we can first simplify the given polynomial:

2x^2 - (1/3)ax + by - M = 0

Multiplying through by -1 to isolate M:

M = 2x^2 - (1/3)ax + by

Therefore, the polynomial M is:

M = 2x^2 - (1/3)ax + by

Answer:

Step-by-step explanation:

3x+y = -6

y=-3x-6

The Y-intercept is -6, therefore there is one point (0,-6)

Now go 3 down and one right, so there is your second point (1,-9)

The first four nonzero terms for cos(20x²) are:
1
The first four nonzero terms for ln(1 - 4y) are:
-4y + 8y² - 32y³ +...

To find the first four nonzero terms of the Taylor series for the function cos(20x²) about 0,

we need to find the first few derivatives of the function, and evaluate them at x = 0.

f(x) = cos(20x²)
f'(x) = -40x * sin(20x²)
f''(x) = -40(40x² * cos(20x²) + 20sin(20x²))
f'''(x) = 40(1600x³ * sin(20x²) + 120x * cos(20x²))

Now, evaluate these at x = 0:
f(0) = cos(0) = 1
f'(0) = 0 (since sin(0) = 0
f''(0) = -40(0) = 0
f'''(0) = 0 (since cos(0) = 1

The first four nonzero terms for cos(20x²) are:
1

Now, let's find the first four nonzero terms of the Taylor series for the function f(y) = ln(1 - 4y) about 0.

f(y) = ln(1 - 4y)
f'(y) = -4 / (1 - 4y)
f''(y) = 16 / (1 - 4y)²
f'''(y) = -96 / (1 - 4y)³

Evaluate these at y = 0:
f(0) = ln(1) = 0
f'(0) = -4 / (1) = -4
f''(0) = 16 / (1)² = 16
f'''(0) = -96 / (1)³ = -96

The first four nonzero terms for ln(1 - 4y) are:
-4y + 8y² - 32y³ +...

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The probability of Karmen picking a car with a belge interior and an automatic transmission is 1/6

To find the probability, we need to start by identifying the event or situation for which we want to calculate the probability.

Since Karmen has three choices for the exterior color, two choices for the interior color, and two choices for the transmission, the total number of possible car configurations is:

3 x 2 x 2 = 12

This means there are 12 different cars to choose from.

To find the probability of picking a car that has a black exterior and a belge interior, we need to determine how many cars meet these criteria. There is only one car that has a black exterior and a belge interior, so the probability of picking this car is:

1/12

Therefore, the probability of Karmen picking a car with a black exterior and a belge interior is 1/12.

To find the probability of picking a car with a belge interior and an automatic transmission, we need to determine how many cars meet these criteria. There are two cars that have a belge interior and an automatic transmission, so the probability of picking one of these cars is:

2/12

Simplifying this fraction gives:

1/6

Therefore, the probability of Karmen picking a car with a belge interior and an automatic transmission is 1/6.

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The fare for this flight was $542.50 which is calculated using least-squares regression line equation. Therefore, the correct answer 542.50

To find the fare for this flight, we will first use the provided least-squares regression line equation to predict the fare and then account for the residual.

Step 1: Use the least-squares regression line equation to predict the fare.
ŷ = 102.50 + 0.65x, where ŷ is the predicted fare and x is the distance in miles.

Step 2: Substitute the given distance (x = 500 miles) into the equation.
ŷ = 102.50 + 0.65(500)

Step 3: Calculate the predicted fare.
ŷ = 102.50 + 325
ŷ = 427.50

The predicted fare for a 500-mile flight is $427.50.

Step 4: Adjust for the residual.
The residual for this flight is 115.0, which means the actual fare is $115 higher than the predicted fare.

Step 5: Add the residual to the predicted fare to find the actual fare.
Actual fare = Predicted fare + Residual
Actual fare = 427.50 + 115
Actual fare = 542.50

The fare for this flight was $542.50.

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Answer:

11

Step-by-step explanation:

Because of the parallel lines 5x=6x-11, so x=11.

Step-by-step explanation:

this is the answer being alternate exterior angles

Answer:

I think you get 0.65 inches of pizza for 1 dollar

Step-by-step explanation:

$13 divided by 20 inches = 0.65

The dealer should have sold the article for 103,500 naira to make a profit of 15%.

Let C be the cost price of the composition.  According to the problem, the dealer  vended the composition at a loss of 10, so he  entered 90 of the cost price.  thus, 90 of C is equal to 81,000 naira.

C =  81,000

C =  81,000/0.9

 C =  90,000  

So, the cost price of the composition is 90,000 naira.

  Now, let's find out the selling price  needed to make a profit of 15   Let S be the  needed selling price to make a profit of 15.  We know that profit chance is equal to( profit/ cost price) × 100.

Thus,(15/100) × 90,000 =

S- 90,000 , 500

=  S- 90,000  

S =  90,000 13,500

S =  103,500

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A measure of goodness of fit for the estimated regression equation is the residual standard error (RSE)

It is a measure of goodness of fit for the estimated regression equation. It measures the average amount that the response variable (y) deviates from the estimated regression line, in the units of the response variable.

The RSE is calculated as the square root of the sum of squared residuals divided by the degrees of freedom. A smaller RSE indicates a better fit of the regression line to the data.

It represents the proportion of the variation in the dependent variable that is explained by the independent variable(s) in the model. The value of R-squared ranges from 0 to 1, with higher values indicating a better fit of the model to the data.

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The expression that can be used to find the third number in Mark's pattern is 3[3(5) - 1]. The correct option is C.

In Mark's pattern, the rule is to subtract 1 from the previous number and then multiply the result by 3.

Starting with 5 as the first number, we can apply this rule step by step to find the subsequent numbers.

First step: Subtract 1 from 5, giving us 4.

Second step: Multiply 4 by 3, which equals 12.

So, the second number in Mark's pattern is 12.

Now, to find the third number, we apply the same rule.

First step: Subtract 1 from 12, giving us 11.

Second step: Multiply 11 by 3, which equals 33.

Therefore, the third number in Mark's pattern is 33.

Option C, 3[3(5) - 1], correctly represents this calculation, where 5 is subtracted by 1, multiplied by 3, and then multiplied by 3 again.

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Answer:

A ∪ B = {1, 2, 3, 4, 5, 6, 7, 9}

Step-by-step explanation:

We can find the union of two sets by including all of the numbers in both sets, but without repeating any numbers.

For example:

if A = {1, 2, 3, 4, 5} and B = {4, 5, 6, 7, 8},

then A ∪ B = {1, 2, 3, 4, 5, 6, 7, 8}

We can apply this concept to the problem at hand, but first we need to represent set A as a list of numbers:

They all have to be odd numbers between 0 and 10.

    [tex]\implies A[/tex] = {1, 3, 5, 7, 9}

We are given that B = {2, 3, 4, 5, 6}. So, to find the union of A and B, we can combine both sets of numbers and get rid of copies:

A ∪ B = {1, 2, 3, 4, 5, 6, 7, 9}

Where the above is given, it is correct to state that "Yes; it is a reflection over line y = –1." (Option C)

A reflection is referred to as a flip in geometry. A reflection is the shape's mirror image. The line of reflection is formed when an image reflects through a line. A figure is said to mirror another figure when every point in one figure is equidistant from every point in another figure.

Note that in the above prompt, Since the horiztonal line y = -1 is equidistant between the bases of the trapezoids, ABCD and A'B'C'D and the corresponding coordinates are therefore equidistant from the line.

Hence Option C is correct.

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Out of 25 students in the class, 40% are male is: Descriptive statistics.

Descriptive statistics is the process of summarizing and organizing data from a sample or population in order to provide an overview of the main characteristics. In this case, the data provided tells us that out of 25 students in the class, 40% are male.

This information is a summary of the gender distribution within this specific class, rather than making any predictions or generalizations about a larger population.

In contrast, inferential statistics is the process of using data from a sample to make predictions or draw conclusions about a larger population. If we were given data about a sample of classes and asked to estimate the proportion of male students in all classes, that would be an example of inferential statistics.

To summarize, the situation you provided, which states that out of 25 students in the class, 40% are male, is an example of descriptive statistics as it only provides a summary of the data for that specific class.

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Answer:

Step-by-step explanation:

To solve the equation, we'll need to consider two cases:

Case 1: 2x - 3 is positive or zero

If 2x - 3 is positive or zero, then |2x - 3| = 2x - 3, and the inequality becomes:

2x - 3 < 3 + x - x^2

Rearranging and simplifying:

x^2 - x - 6 < 0

Factoring:

(x - 3)(x + 2) < 0

The solutions to this inequality are:

-2 < x < 3

However, we still need to check that 2x - 3 is indeed positive or zero for this range of x. We can see that this is true for x in the range (-2, 3), so this is a valid solution.

Case 2: 2x - 3 is negative

If 2x - 3 is negative, then |2x - 3| = -(2x - 3), and the inequality becomes:

-(2x - 3) < 3 + x - x^2

Rearranging and simplifying:

x^2 - 3x - 6 < 0

Factoring:

(x - 3)(x + 2) > 0

The solutions to this inequality are:

x < -2 or x > 3

However, we still need to check that 2x - 3 is indeed negative for this range of x. We can see that this is true for x < -2, so this is a valid solution.

Putting these two cases together, we get the solution:

x < -2 or -2 < x < 3

I hope this helps! Let me know if you have any questions.

The minimum square footage of nylon used to make the tent is 168 square feet.

To find the minimum square footage of nylon used to make the tent, we need to calculate the area of each of the four triangular faces and the area of the square base, and then add them up.

The area of each triangular face is given by the formula:

A = 1/2 × base × height

where the base is the side length of the square base (8 feet), and the height is the slant height of the pyramid (6.5 feet).

A = 1/2 × 8 × 6.5

A = 26

So each of the four triangular faces has an area of 26 square feet.

The area of the square base is given by the formula:

A = [tex]side length^{2}[/tex]

A = [tex]8^{2}[/tex]

A = 64

So the square base has an area of 64 square feet.

To find the minimum square footage of nylon used to make the tent, we can add up the areas of the four triangular faces and the square base:

4 × 26 + 64 = 104 + 64 = 168

Therefore, the minimum square footage of nylon used to make the tent is 168 square feet.

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Pedro and Hal will walk 1800 steps staircase and meet after 25 minutes.

Pedro is walking down the longest staircase ever, which contains 4000 steps. She starts from the top and is walking down the staircase at 150 steps a minute. Hal is walking up the staircase, starting at the bottom, at 80 steps a minute. After how many minutes will they meet?

Let's assume that they will meet at point X, which is y steps away from the top and z steps away from the bottom. As Pedro is walking down the staircase, she will cover a distance of y steps, while Hal is walking up the staircase, he will cover a distance of (4000-z) steps.

The time taken by Pedro to cover a distance of y steps is y/150 minutes, while the time taken by Hal to cover a distance of (4000-z) steps is (4000-z)/80 minutes. Since they will meet at the same point X, we can set these two times equal to each other and solve for y and z.

y/150 = (4000-z)/80

Solving this equation, we get y = 1800 and z = 2200. This means that Pedro will have covered 1800 steps in y/150 = 12 minutes and Hal will have covered (4000-2200) = 1800 steps in (4000-2200)/80 = 25 minutes.

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Answer:

The graph on the top right

Step-by-step explanation:

The slope-intercept form is y = mx + b

m = the slope

b = y-intercept

The equation is y = 1/2x + 2

The y-intercept in this equation is 2, meaning the graph has a point (0,2) on it.  Looking at the options, the only graph that has a point (0,2) is the map on the top right, and that is the answer.

To maintain the same ratio of Fuji apple trees to Gala apple trees, the owners of Hillsdale Orchard should: plant 12 new Fuji apple trees when they plant 30 new Gala apple trees.

To find the number of new Fuji apple trees that the owners of Hillsdale Orchard should plant to maintain the same ratio of Fuji apple trees to Gala apple trees, we need to use a ratio table.

First, we need to determine the ratio of Fuji apple trees to Gala apple trees before the new trees are planted. Let's assume that there are currently 40 Fuji apple trees and 100 Gala apple trees. The ratio of Fuji apple trees to Gala apple trees is therefore 40:100, which can be simplified to 2:5.

Next, we need to use this ratio to determine the number of new Fuji apple trees that need to be planted. Since the owners are planting 30 new Gala apple trees, we can use the ratio of 2:5 to find the corresponding number of new Fuji apple trees.

To do this, we need to divide the number of new Gala apple trees by the denominator of the ratio (which represents the number of units of the ratio). In this case, the denominator is 5.

30 (new Gala apple trees) ÷ 5 (denominator) = 6

This means that for every 5 new Gala apple trees, the owners should plant 2 new Fuji apple trees. Therefore, the owners should plant 12 new Fuji apple trees (2 trees for every 5 new Gala apple trees, multiplied by the 30 new Gala apple trees being planted).

In summary, to maintain the same ratio of Fuji apple trees to Gala apple trees, the owners of Hillsdale Orchard should plant 12 new Fuji apple trees when they plant 30 new Gala apple trees.

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The total bill was 520 pesos when the 4 people share the total bill and pay 130 pesos each.

Given data:

Bill paid by each = 130pesos,

Number of people = 4

We have to translate the problem into an equation. Let's assume that the total bill is x. There are a total of 4 people dividing the restaurant bill, Mike and his three friends. Since each of them paid 130 pesos, we need to multiply 130 by the total number of persons involved, we can write the equation as:

x/4 = 130

x = 4 × 130

x = 520

Therefore, the total bill was 520 pesos.

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The slant height of the cone is approximately 5 meters.

We can use the Pythagorean theorem to find the slant height of the cone.

The slant height, denoted by l, the height h and the radius r form a right triangle where l is the hypotenuse:

[tex]l^2 = h^2 + r^2[/tex]

In this case, we are given the height h as 12 m, but we are not given the radius r.

However, we know that the slant height is the distance from the apex of the cone to any point on its circular base.

So, we can draw a line from the apex of the cone to the center of its circular base, which will be perpendicular to the base, and we can use this line as the height of a right triangle that also includes the radius r of the circular base.

Then, we can use the Pythagorean theorem to find the slant height l.

The radius r is half the diameter of the circular base, so we need to find the diameter of the base.

Since we are not given the diameter directly, we need to find it using the height h and the slant height l.

To do this, we can draw a cross section of the cone that includes its circular base and its height, and then draw a line from the apex of the cone to a point on the base that is perpendicular to the diameter of the base.

This line will be the height of a right triangle that also includes the radius r of the base and half the diameter of the base.

Then, we can use the Pythagorean theorem to find the diameter of the base.We have:

[tex]l^2 = h^2 + r^2r = sqrt(l^2 - h^2)d/2 = sqrt(l^2 - r^2)d^2/4 = l^2 - r^2d^2 = 4(l^2 - r^2)[/tex]

Substituting the expression for r that we found above, we get:

[tex]d^2 = 4(l^2 - (l^2 - h^2))d^2 = 4h^2d = 2h[/tex]

Now we can substitute this expression for d into the formula for the volume of a cone:

[tex]V = (1/3) * pi * r^2 * hV = (1/3) * pi * ((2h)/2)^2 * hV = (1/3) * pi * h^2 * 4V = (4/3) * pi * h^3[/tex]

We can solve this formula for h:

[tex]h = (3V)/(4*pi)^(1/3)[/tex]

Substituting the given volume of the cone, which we will assume is in cubic meters:

[tex]V = (1/3) * pi * r^2 * h = (1/3) * pi * r^2 * 12V = 16pih = (3(16pi))/(4*pi)^(1/3)[/tex]

h = 4.819 m

Now we can find the slant height using the Pythagorean theorem:

[tex]l^2 = h^2 + r^2l^2 = (4.819)^2 + ((2(4.819))/2)^2l^2 = 23.187l = 4.815[/tex] [tex]m[/tex]

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Answer:

$9.50

Step-by-step explanation:

Divide the total earnings by total hours.

Entonces, 1/8 de su salario se va en renta, y su salario mensual es de $1200.

Entiendo que deseas saber qué fracción del salario de Edna se va en renta y cuál es su salario mensual si su renta mensual es de $150. Para resolver esto, seguiré estos pasos:

1. Sabemos que Edna gasta la mitad de su salario en renta, utilidades y comida. Esto se puede expresar como 1/2 de su salario.
2. Se nos dice que 1/4 de esos gastos se va en renta. Entonces, para encontrar la fracción de su salario que se va en renta, multiplicamos 1/2 (gastos totales) por 1/4 (fracción de gastos en renta): (1/2) * (1/4) = 1/8.
3. Ahora sabemos que 1/8 de su salario se va en renta. Para hallar su salario mensual, utilizaremos la renta mensual de $150.
4. Si 1/8 de su salario equivale a $150, podemos resolver su salario (S) utilizando la siguiente ecuación: (1/8)S = 150.
5. Para encontrar S, multiplicamos ambos lados de la ecuación por 8: S = 150 * 8.
6. Finalmente, calculamos el valor: S = 1200.

Entonces, 1/8 de su salario se va en renta, y su salario mensual es de $1200.

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The maximum error of estimate is 4.75%.

To calculate the maximum error of estimate for the given problem, we will use the formula for margin of error:

Margin of Error = Z-score * (Standard Deviation / √n)

Where:
- Z-score corresponds to the 90% confidence level, which is 1.645
- Standard Deviation is 0.5 hours
- n is the sample size, which is 300 students

Margin of Error = 1.645 * (0.5 / √300) ≈ 0.0475

To express this as a percentage, multiply by 100:

0.0475 * 100 ≈ 4.75%

Thus, the maximum error of estimate with a 90% confidence level is 4.75%.

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Answer:

(1/2)(6.5 + 12) = x + 4

(1/2)(18.5) = x + 4

9.25 = x + 4

x = 5.25 cm

Answer:3

Step-by-step explanation: We see that 217361.05 =217000+361.05 so our answer is 3

The function f representing the sum of the series for x in the interval (-3, 3). Hi! The given geometric series is 1 - x/3 - x^2/9 - x^3/27...

The common ratio of the series is obtained by dividing a term by its preceding term. Let's consider the first two terms:

(-x/3) / 1 = -x/3

Therefore, the common ratio (r) of the series is -x/3.

For a geometric series to converge, the absolute value of the common ratio must be less than 1, i.e., |r| < 1. In this case:

|-x/3| < 1

To find the values of x for which the series converges, we need to solve the inequality:

-1 < x/3 < 1

Multiplying all sides by 3, we get:

-3 < x < 3

So, the series converges for x in the interval (-3, 3).

Now, let's determine the function f representing the sum of the series. For a converging geometric series, the sum S can be calculated using the formula:

S = a / (1 - r)

where a is the first term and r is the common ratio. In this case, a = 1 and r = -x/3. Therefore:

f(x) = 1 / (1 - (-x/3))
f(x) = 1 / (1 + x/3)

This is the function f representing the sum of the series for x in the interval (-3, 3).

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Solving a direct variation equation to find n gives n = -1

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

A direct variation includes the points (2, –10) and (n,5).

This means that

(2, –10) = (n,5)

Express as an equation

So, we have

-2/10 = n/5

Multiply both sides of the equation by 5

So, we have the following representation

n = -2/10 * 5

Evaluate the product

n = -1

Hence, the value of n in the equation is -1

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