. Divide
6x³+x²+7x+9
2x+1

Hi! To find the orthogonal trajectories of the given curve s = 3a sin θ, we first need to determine its differential equation by eliminating the arbitrary constant, a. The orthogonal trajectories should have slopes that are the negative reciprocal of the original curve's slopes.

1. Differentiate s with respect to θ:
ds/dθ = 3a cos θ

2. Solve for a:
a = (ds/dθ) / (3 cos θ)

3. Substitute the expression for a back into the original equation:
s = 3((ds/dθ) / (3 cos θ)) sin θ

4. Simplify:
s = (ds/dθ) tan θ

5. Find the orthogonal trajectories by taking the negative reciprocal of the original slope:
-1 = -ds/dθ / s

6. Rearrange to find the differential equation for the orthogonal trajectories:
ds/dθ = s

7. Integrate with respect to θ to find the orthogonal trajectories:
s(θ) = c * e^θ, where c is an arbitrary constant.

So, the orthogonal trajectories of the given curve s = 3a sin θ are s(θ) = c * e^θ.

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The height of the kite above the ground is approximately 433.76 feet. Rounded to the nearest foot, the answer is 434 feet.

We can use trigonometry to solve this problem. Let h be the height of the kite above the ground. Then, the opposite side of the triangle formed by the kite string and the ground is h, and the adjacent side is 300 feet. The angle between the ground and the kite string is 52 degrees.

We can use the tangent function to find the value of h:

[tex]tan(52) = h/300[/tex]

Multiplying both sides by 300, we get:

h = 300 t[tex]an(52)[/tex]

Using a calculator, we find:

h ≈ 433.76 feet

Therefore, the height of the kite above the ground is approximately 433.76 feet. Rounded to the nearest foot, the answer is 434 feet.

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The solution of the a) part is 8 x 10⁻⁸ and the solution to the b) part is 2.1 x 10⁰.

Simplify simply means to make an expression simple.

In mathematics, simply or simplification is reducing the expression/fraction/problem in a simpler form.

a. To get the solution of 0.00032 x 500 / 2,000,000, follow these steps:

1. Multiply 0.00032 by 500, which equals 0.16.
2. Divide 0.16 by 2,000,000, which equals 8x10⁻⁸.

So, 0.00032x500 / 2,000,000 = 8 x 10⁻⁸.

b. To solve 15,000 x 0.0000007 / 0.005, follow these steps:

1. Multiply 15,000 by 0.0000007, which equals 0.0105.
2. Divide 0.0105 by 0.005, which equals 2.1.

So, 15,000 x 0.0000007 / 0.005 = 2.1 x 10⁰, since 10⁰ equals 1, and 2.1 remains the same.

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The equivalent expression to 3218y = 8√3y is 4√(15) / 15y when y is not equal to zero. Option C is the correct answer.

To find an equivalent expression to 3218y = 8√3y when y is not equal to zero, we can start by dividing both sides of the equation by 8y, giving us:

3218y / 8y = 8√3y / 8y

Simplifying the right-hand side, we get:

3218 / 8 = √3

Squaring both sides, we get:

(3218 / 8)² = 3

Simplifying the left-hand side, we get:

130071.25 = 3

Dividing both sides by 3, we get:

y = 4√(15) / 15

Therefore, the expression that is equivalent to 3218y = 8√3y when y is not equal to zero is an option (C) 4√(15) / 15y. Option (D) 46y is not equivalent to the original expression because it does not involve the square root of 3. Option (A) 12V / 2y² and option (B) 46 are also not equivalent to the original expression because they involve different values and operations than those in the original expression.

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The account that has the greater principal is account B.

Simple interest is a linear function of the amount invested (the principal), the interest rate and the duration of the investment.

The formula that can be used to determine simple interest is:

Interest = principal x time x interest rate

Principal = interest / (time x interest rate)

Principal in account A = $15.75 / (0.03 x (21/12)) = $300

Principal in account B = $28 / (0.04 x (21/12)) = $400

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We do not have sufficient evidence to support the mayor's claim that the average municipal taxes have fallen by $200 during his term.

Step 1: Hypotheses Set-Up:

H0: The average tax decrease during the mayor's term is not $200 (μ ≠ 200)

Ha: The average tax decrease during the mayor's term is $200 (μ = 200)

Step 2: The significance level α = 0.05

Step 3: Compute the test statistic:

We will use a one-sample t-test since the population standard deviation is unknown and the sample size is less than 30.

The formula for the t-test statistic is:

t = (x - μ) / (s / √n)

Where:

x = sample mean

μ = hypothesized population mean

s = sample standard deviation

n = sample size

Substituting the values, we get:

t = (186.6 - 200) / (43 / √36)

t = -1.98

Step 4: Testing Procedure:

The test is a two-tailed test since we want to determine whether the average tax decrease is significantly different from $200, not just whether it is greater or less than $200.

At a significance level of 0.05 with 35 degrees of freedom, the critical values for a two-tailed test are ±2.03.

The p-value for the test is the probability of getting a t-value as extreme or more extreme than -1.98, given the null hypothesis. From a t-distribution table, we find that the p-value is approximately 0.057.

Step 5: Decision:

Since the calculated t-value (-1.98) is less than the critical value (-2.03) and the p-value (0.057) is greater than the significance level (0.05), we fail to reject the null hypothesis.

Therefore, we do not have sufficient evidence to support the mayor's claim that the average municipal taxes have fallen by $200 during his term.

Step 6: Interpretation:

At a 5% significance level, we do not have enough evidence to reject the null hypothesis that the average tax decrease is not $200.

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Answer:

[tex] {(5x)}^{ \frac{1}{2} } = \sqrt{5x} [/tex]

Bruce can finish the job alone in 5 hours, Bryce can finish the job alone in 8 hours, and Marty can finish the job alone in 10 hours.

Let's assume the job takes x hours for Bruce to complete alone, y hours for Bryce to complete alone, and z hours for Marty to complete alone.

From the first piece of information, we can create the following equation based on the work completed in 1 hour and 20 minutes (4/3 hours):

1/x + 1/y = 3/4

From the second piece of information, we can create the following equation based on the work completed in 1 hour and 36 minutes (8/5 hours):

1/y + 1/z = 5/8

From the third piece of information, we can create the following equation based on the work completed in 2 hours and 40 minutes (8/3 hours):

1/x + 1/z = 3/8

Solving these equations simultaneously, we can find that x = 5, y = 8, and z = 10.

Therefore, Bruce can finish the job alone in 5 hours, Bryce can finish the job alone in 8 hours, and Marty can finish the job alone in 10 hours.

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The probability that z lies between -0.55 and 0.55 is 0.4176. So, the correct option is option OD. 0.4176.

To find the probability that z lies between -0.55 and 0.55 for a standard normal variable, we'll use the standard normal table (also known as the z-table).

Step 1: Look up the z-score of -0.55 in the z-table. This gives us the area to the left of -0.55, which is 0.2912.

Step 2: Look up the z-score of 0.55 in the z-table. This gives us the area to the left of 0.55, which is 0.7088.

Step 3: Subtract the area to the left of -0.55 from the area to the left of 0.55 to find the probability between the two z-scores: 0.7088 - 0.2912 = 0.4176.

Therefore, the probability that z lies between -0.55 and 0.55 for a standard normal variable is approximately 0.4176 (rounded to four decimal places).

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Answer:

-883 - 1

Step-by-step explanation:

Answer:

Step-by-step explanation:

Kathy would like to plan for fiver more guests than she expects to come.

So we have to set the table for 25 guests.

Each guest will need 2 forks.

25x2=50 forks

Step-by-step explanation:

the intersection angles between a line and 2 parallel lines are the same for each parallel line (otherwise they would not be parallel).

and the intersection angles on one side of a line are the same as in the other side - just left-right mirrored.

so,

angle 2 = angle 4 = angle 6 = angle 8 = 60°

All of the above are statistics

Traditional supply chain management (SCM) is ineffective for e-commerce because it is based on manual processes and separation of functions.

4)

We have,

James Lyne mentions that there are:

- 30,000 new infected websites every day

- 8 new internet users join every second

- 250,000 new pieces of malware appear every day.

All the above are statistics.

2)
E-commerce is generally more specialized and requires a more integrated approach to supply chain management. Additionally, traditional SCM is based on manufacturing, whereas e-commerce is mostly retail distribution.

Finally, traditional SCM usually doesn't include e-procurement functions, which are essential for e-commerce supply chain management.

Traditional supply chain management (SCM) is ineffective for e-commerce because it is based on manual processes and separation of functions.

Thus,

All of the above are statistics

Traditional supply chain management (SCM) is ineffective for e-commerce because it is based on manual processes and separation of functions.

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To predict the value of y when x=10 is an example of Extrapolation. So, the correct answer is (b) extrapolation.

Extrapolation involves using a mathematical model, such as a line of best fit, to make predictions outside the range of the original data.

In this case, using the equation y = –3x + 21 to predict the value of y when x = 10 is an example of extrapolation because 10 is outside the range of the original x-values.

Using a line of best fit with the equation y = -3x+21 to predict the value of y when x = 10 is an example of extrapolation in statistics.

Extrapolation involves using a mathematical model, such as a line of best fit, to make predictions outside the range of the original data.

Ricardo's next step to construct the circumscribed circle for △XYZ would be to construct the perpendicular bisector of YZ

In this case, constructing the perpendicular bisector of YZ would give Ricardo the center of the circumscribed circle, which is equidistant from the three vertices of the triangle.

Complete Question:

Ricardo calculates a line of best fit for a data set with integer x-values 1 through 6. Complete the sentence with the correct word.

Using a line of best fit with the equation y = –3x + 21 to predict the value of y when x = 10 is an example of

a) correlation

b) extrapolation

c) causation

d) intrapolation

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Set S has 840 permutations and 70 subsets of 4 elements, and [tex]2^7[/tex] - 7 - 1 = 120 subsets of 2 or more elements an example of a 4-permutation are {b, e, f, c}, and an example of a 4-subset is {a, d, g, e}.

An example of a 4-permutation from the set S would be {a, b, c, d}. An example of a 4-subset from the set S would be {a, c, e, g}.

To find how many subsets of S have two or more elements, we need to subtract the empty set and the singleton sets from the total number of subsets. The total number of subsets of S is [tex]2^7[/tex] = 128. There is only one empty set, and there are seven singleton sets. Therefore, the number of subsets of S with two or more elements is 128 - 1 - 7 = 120.

To find how many subsets of S have 3 or 4 elements, we can use the combination formula. The number of 3-element subsets of S is C(7,3) = 35, and the number of 4-element subsets of S is C(7,4) = 35 as well. Therefore, there are 35 + 35 = 70 subsets of S that have 3 or 4 elements.

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Measurement is the process of obtaining the quantity or size of something, usually expressed in numerical values. It is a crucial aspect in various fields, including science, engineering, and mathematics. When it comes to measuring physical activity or exercise, oxygen consumption measurement is a commonly used method. It involves measuring the amount of oxygen that an individual consumes while exercising, which provides insight into their metabolic rate and energy expenditure.

In the given scenario, the participant's V2 was measured in units of t.min, and their coa was measured in units of Umin. To determine the participant's oxygen consumption rate at that specific point in time, we need to use the formula VO2 = V2/((t2-t1) x (coa-cob)). Here, t1 and t2 represent the start and end time of the measurement, while cob and coa represent the initial and final carbon dioxide levels.

Since we do not have information about the start and end times or the carbon dioxide levels, we cannot accurately determine the participant's oxygen consumption rate. Therefore, we cannot provide a decimal value as requested in the question.

In regards to Question 15, there seems to be incomplete information, and therefore, we cannot provide a response. However, it is essential to note that accurate and precise measurements are crucial in obtaining reliable data and making informed decisions in various fields.

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Answer:

1.5 and 4

Step-by-step explanation:

the scale factor is the ratio of corresponding sides, image to original.

1

scale factor = [tex]\frac{DF}{AC}[/tex] = [tex]\frac{21}{14}[/tex] = [tex]\frac{3}{2}[/tex] = 1.5

2

scale factor = [tex]\frac{8}{2}[/tex] = 4

The solution for the equation ax + by ≡ c (mod 3) does not exist. Hence, it  has no solution.

We need to prove that the equation ax + by ≡ c (mod 3) has no solution.

Since 3 | a and 3 | b, we know that a ≡ 0 (mod 3) and b ≡ 0 (mod 3).

Now let's look at the left side of the equation ax + by. Since a and b are both divisible by 3, their product with any integers x and y will also be divisible by 3.

Therefore, ax + by will always be divisible by 3 and can be written as ax + by ≡ 0 (mod 3).

However, we know that c ≡ 2 (mod 3), which means that c is not divisible by 3. Therefore, we can conclude that ax + by can never be congruent to c (mod 3), as their remainders when divided by 3 are different.

In other words, the equation ax + by ≡ c (mod 3) has no solution.

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Answer:

  x = 3√3

Step-by-step explanation:

You want the middle-length side of a 30°-60°-90° triangle whose short side is 3.

There are two "special" triangles in trigonometry. The ratios of their side lengths are used in many algebra, trig, and geometry problems.

  30°-60°-90° triangle has sides in the ratios 1 : √3 : 2

  45°-45°-90° isosceles right triangle has sides in the ratios 1 : 1 :√2

The triangle shown in this problem is a 30°-60°-90° right triangle with a short side of length 3. You want the middle-length side (x), which the above tells us is √3 times the length of the short side.

  x = 3√3

__

Additional comment

You can use the trig relation ...

  Tan = Opposite/Adjacent   ⇒   Adjacent = Opposite/Tan

For this triangle, this means ...

  x = 3/tan(30°)

  x = 3/(1/√3) = 3√3

A suitable calculator can show this in the desired format.

The null hypothesis and conclude that there is sufficient evidence to support the claim that the percentage of people with genetic markers is less than 1%.

To test whether the percentage of people with genetic markers is less than 1%, we can use a one-tailed hypothesis test with the following null and alternative hypotheses:

H0: p >= 0.01

Ha: p < 0.01

where p is the true proportion of people with the genetic markers.

Using the sample proportion, p-hat = 3/500 = 0.006, and the sample size, n = 500, we can calculate the test statistic z:

z = (p-hat - p) / sqrt(p * (1 - p) / n)

= (0.006 - 0.01) / sqrt(0.01 * 0.99 / 500)

= -1.434

At 75% confidence, the critical value for a one-tailed test is -1.15 (using a standard normal distribution table or calculator). Since our calculated test statistic (-1.434) is less than the critical value (-1.15), we reject the null hypothesis and conclude that there is sufficient evidence to support the claim that the percentage of people with genetic markers is less than 1%.

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It will take the pendulum approximately 0.20 seconds to reach its resting position.

We have,

The resting position of the pendulum is when d(t) = 0.

So we need to solve the equation:

5.5cos(8t) = 0

We know that cos(0) = 1 and that cos(π) = -1, and that the cosine function has a period of 2π.

Therefore, the first time the pendulum will reach its resting position is at

t = 0, and then it will reach its resting position again at t = π/8.

However, we are interested in the time it takes for the pendulum to go from its starting position to its resting position, which is half of its period.

So the time it takes for the pendulum to reach its resting position is:

t = π/8 / 2

t = π/16

Using a calculator, we can approximate this value to the nearest hundredth:

t = 0.20 seconds

Therefore,

It will take the pendulum approximately 0.20 seconds to reach its resting position.

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The sale price of the car is $36,975 and the final cost of the car including 6% sales tax is $39,193.50.

The sale price of the car after a 15% discount can be calculated as:

Sale Price = Original Price - Discount

Sale Price = $43,500 - 0.15($43,500)

Sale Price = $43,500 - $6,525

Sale Price = $36,975

The final cost of the car including 6% sales tax can be calculated as:

Final Cost = Sale Price + Sales Tax

Final Cost = $36,975 + 0.06($36,975)

Final Cost = $36,975 + $2,218.50

Final Cost = $39,193.50

Therefore, the sale price of the car is $36,975 and the final cost of the car including 6% sales tax is $39,193.50.

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The measure of side ZW in rectangle WXYZ is 33.

It is mentioned that rectangle WXYZ is dilated by a scale factor of 3 to form rectangle W'X'Y'Z'. Side Z'W' measures 99. We need to find the measure of side ZW.

To find the measure of side ZW, we need to use the scale factor. Since the rectangle was dilated by a scale factor of 3, we can divide the measure of side Z'W' by the scale factor to find the measure of side ZW.

Identify the scale factor, which is 3.
Identify the measure of side Z'W', which is 99.
Divide the measure of side Z'W' by the scale factor: 99 ÷ 3 = 33.

So, the measure of side ZW in rectangle WXYZ is 33.

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The probabilities and the expected values are calculated below

Next cereal box wll contain blue or yellow

Here, we have

Yellow or blue = 15 + 5 = 20

Total = 50

So, we have

P(Yellow or blue) = 20/50

P(Yellow or blue) = 2/5

Arrival time before 7:30 am

Here, we have

Arrival time before 7:30 am = 7

Total time = 20

So, we have

P(Arrival time before 7:30 am) = 7/20

Team least likely

Convert the probabilities to decimal

So, we have

Nets = 0.67

Rockets = 0.5

Bucks = 0.8

Warriors = 0.375

This means that the team least likely to play in the championship game is 0.375

Section 7 in the game

Here, we have

P(7) = 35/250

In 150 times, we have

n(7) = 35/250 * 150

n(7) = 21

So, the number of times is 21

Expected students to eat chicken nuggets

Here, we have

P(Chicken) = 14/40

In 840 students, we have

n(Chicken) = 14/40 * 840

n(Chicken) = 294

Hence, the expected number of students to eat chicken nuggets is 294

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The mean of the distribution of sample means would be 27 hours, which is the same as the average life of the candles.

This is because the sample means would be expected to be centered around the population mean.

The standard deviation of the distribution of sample means (also known as the standard error of the mean) can be calculated using the formula:

standard deviation of sample means = standard deviation of population / square root of sample size

In this case, the standard deviation of sample means would be:

6 / square root of 4 = 3

So the answer is 3.

So, the mean of the distribution of the sample means would be 3. Your answer: 3.

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The probability that a randomly selected adult has an IQ greater than 134.4 is 0.025.

We have,

To solve this problem, we need to standardize the IQ score using the

z-score formula:

z = (x - μ) / σ

where x is the IQ score, μ is the mean, and σ is the standard deviation.

Substituting the values we have:

z = (134.4 - 101.1) / 17

z = 1.96

We can then use a standard normal distribution table or a calculator to find the probability of a z-score being greater than 1.96.

Using a standard normal distribution table, we find that the probability of a z-score being greater than 1.96 is approximately 0.025.

Therefore,

The probability that a randomly selected adult has an IQ greater than 134.4 is 0.025.

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If 50 students take math and 50 students take art. If there are 280 students enrolled in the school and they all take at least one of these courses then 20  students take both math and art

let A be the set of students taking math, and let B be the set of students taking art.

We know that:

|A| = 250

|B| = 50

|A ∪ B| = 280

We want to find |A ∩ B|, the number of students taking both math and art.

Using the formula above, we can solve for |A ∩ B|:

|A ∩ B| = |A| + |B| - |A ∪ B|

|A ∩ B| = 250 + 50 - 280

|A ∩ B| = 20

Therefore, 20 students take both math and art.

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Using the range rule of thumb:
A. Test scores that are between 10.8 and 32.4 (rounded to one decimal place) are neither significantly low nor significantly high.
B. Test scores that are less than 10.8 (rounded to one decimal place) are significantly low.
C. Test scores that are greater than 32.4 (rounded to one decimal place) are significantly high.

The range rule of thumb states that we can identify significantly low or high values by looking at data points that are more than two standard deviations away from the mean.

In this case, the mean test score is 21.6 and the standard deviation is 5.4.
To find test scores that are significantly low, we need to subtract two standard deviations from the mean:
21.6 - (2 x 5.4) = 10.8
Therefore, test scores that are significantly low are less than 10.8. The answer is B. Test scores that are less than 10.8.

To find test scores that are significantly high, we need to add two standard deviations to the mean:
21.6 + (2 x 5.4) = 32.4
Therefore, test scores that are significantly high are greater than 32.4. The answer is C. Test scores that are greater than 32.4.

Test scores that are neither significantly low nor significantly high are between 10.8 and 32.4. The answer is A. Test scores that are between 10.8 and 32.4.

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The values that are solution of stated inequality expression are -8,-4,0 and 1.

The stated expression represents inequality. Hence, the solution will provide a range rather than a specific number as a resultant value. We will solve it in similar method to inequality.

Rearranging the expression in terms of 4t

4t ≤ 10 - 6

Subtracting the digits on Right Hand Side of the expression

4t ≤ 4

Rewriting the expression

t ≤ 4/4

Dividing the value on Right Hand Side of the equation

t ≤ 1

The values will be 1 or less than 1. Thus, the solution values are -8,-4,0 and 1.

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The complete question is -

Determine which of the values is a solution of 4t+6≤10

Values = -8,-4,0,1,3,7

The numbers that are at a distance of 3 from the number 10 are 7 and 13.

To describe all numbers x that are at a distance of 3 from the number 10, we can use the absolute value notation. The distance between two numbers is given by the absolute value of their difference. So, the numbers x that are 3 units away from 10 can be expressed as:

| x - 10 | = 3

This means that the absolute value of the difference between x and 10 is equal to 3. To find the values of x that satisfy this equation, we can solve for x as follows:

x - 10 = 3 or x - 10 = -3

Adding 10 to both sides of each equation, we get:

x = 13 or x = 7

Therefore, the numbers that are at a distance of 3 from the number 10 are 7 and 13.

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