Find the distance traveled by a particle with position (x, y) as t varies in the given time interval.
x = 4 sin^2(t), y = 4 cos^2(t), 0 ≤ t ≤ 5π
What is the length of the curve?

Using proportional relationships, we can say that They will walk 12 laps and run 20 laps for a total of 32 miles.

In a direct proportional relationship, the output variable is found by the multiplication of the input variable and the constant of proportionality k, as follows:

y = kx.

Given that we know this, they walk 3/8 of the 8 miles that make up the complete distance. Run 5/8 of the route.

The following are the proportional relationships for the distances:

For a total distance of 32 miles, the distances walked and run are given:

therefore, They will walk 12 laps and run 20 laps for a total of 32 miles as per the proportional relation.

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Answer:

y=30°

Step-by-step explanation:

Since the ticks on the sides of the triangle show that the sides are equal, then the triangle must be an equilateral triangle. This means that 2y=60°.

2y=60

Divide both sides by 2:

y=30°

The property that best matches the equation is the associative property.

It should be noted that the associative property simply implies that the way the factors are grouped in a multiplication problem doesn't change the product.

In this case, since it's illustrated that (5 × 3) × 2 = (2 × 3) × 5. They both will give a value of 40.

In this case, the associative property is illustrated.

The complete question is:

Write the property that best matches the following: (5 × 3) × 2 = (2 × 3) × 5.

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Answer:

36.

Step-by-step explanation:

6 plus 3 is 9 and 9 times 4 is 36, hope this helps.

The proof of the congruent sides RU and TS is given below.

What is congruent triangles?

In any orientation, two triangles are said to be congruent if their three sides and three angles are equal.

Therefore, if two triangles have the same number of sides on each side, they are said to be congruent. Additionally, we can determine that they are congruent if we have a side, an angle between the sides, and then another side that is congruent, in that order: side, angle, side.

Let the given figure is a rectangle RSTU.

Since the all four angles of rectangle are of 90 degree.

So, each angle of rectangle RSTU is 90 degree.

Let, US divides the angle RUT and angle RST and form two new triangles, ΔSRU and ΔSTU.

Both the triangles having same measure of angles and sides.

⇒  ΔSRU ≅ ΔSTU

As the triangles are congruent so their sides are congruent.

Hence, RU is congruent to TS.

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The typical margin of error in a sample survey of 1,500 respondents is about 2.5 to 3 percent.

Most surveys provide a margin of error or a confidence interval of some type to quantify the level of accuracy. The margin of error, often represented as a percentage, depicts the range in which the real survey results can fluctuate.

The size of the sample and the degree of variability in the population are the two most crucial elements that influence the margin of error in a survey. It's generally agreed that the bigger the sample size, the lower the margin of error, and the more precise the findings. The margin of error shrinks as the sample size grows. When a sample survey includes 1,500 respondents, the typical margin of error would be around 2.5 to 3 percent.

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Answer:

42.64 mph

Step-by-step explanation:

5 1/3 / 7 1/2 = m/60

see attached for explanation

To form a triangle, the set of line segments must satisfy the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Therefore, we need to check if the given line segments 8 cm, 4 cm, and 3 cm meet this requirement.

We can start by checking if the sum of the two smaller sides (3 cm and 4 cm) is greater than the largest side (8 cm). 3 cm + 4 cm = 7 cm, which is less than 8 cm. Therefore, these three line segments cannot form a triangle.

In general, for a set of line segments to form a triangle, the largest side must be smaller than the sum of the other two sides. In this case, the line segment of 8 cm is too long compared to the other two sides, which makes it impossible to form a triangle.

In conclusion, there are no line segments that meet the requirements to form a triangle with lengths of 8 cm, 4 cm, and 3 cm.

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Answer:

30

Step-by-step explanation:

5 sides Pentagon=540

3x+4x+4x+4x+3x=540

18x=540

x=540/18

x=30

Answer: first blank: jen

second blank: mean

Step-by-step explanation:

N/A

In statistics the sampling method is collecting data based on sample of people who represent a population, whereas the census method involves studying each and every member of the population.

What is statistics?

The gathering, characterization, analysis, and drawing of inferences from quantitative data are all tasks that fall under the purview of statistics, a subfield of applied mathematics. Probability theory, linear algebra, and differential and integral calculus play major roles in the mathematical theories underlying statistics.

The differences between census and sampling method is -

The investigator gathers data using the census method, which asks questions about every component of the population.

The investigator gathers data using the sampling method by selecting a sample of the objects that represent the entire population.

The Census Method of Collecting Data is appropriate when the area under inquiry is rather small. The sampling method is preferred when the investigation region is large.

The Census Method requires more time to gather data. The sampling method requires less time to gather data.

Generally speaking, the Census Method is more accurate than the Sampling Method. This accuracy can be attributed to the Census Method's inclusion of a study of every component of the population. The sampling approach has a lower level of accuracy because it examines a smaller sample of the population. However, since there are fewer elements in the sampling method, errors are simple to find and eliminate. Consequently, if that's the case, the sampling method gives more accuracy than census method.

Therefore, the differences for census and sampling method are pointed out.

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What is the difference between census method and sampling method in statistics?

ok.............

.....

Answer:

nice question bro.....

The number of  subscribers they must  sample to obtain this interval is: b) 385.

How to find the sample?

95% confidence interval for z-score is  1.96

Using this formula to find the number of  subscribers  they must sample to obtain this interval

n≥ (zσ/2 ÷ 2ME)²

Where:

n= Sample

zσ = Z-score

ME = margin of error

Let plug in the formula

n≥ [1.96 / 2(0.05)]²

n≥ [1.96 / 0.1]²

= (19.6)²

= 384.16

=385 (Rounded)

Therefore the correct option is B.

The complete question is:

Netflix would like to estimate the proportion of their current subscribers who would pay extra for a premium membership including access to more movies and TV shows. To do this, they plan to calculate a 95% confidence interval to estimate the proportion. They would like a margin of error of .05. How many subscribers must they sample to obtain this interval?

a) 1537

b) 385

c) 192

d) 10

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The number of additional gifts Jeff can buy with the remaining cost is 1.

Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,

As per the given,

Total cost = $15 + $20 = $35

Total spent = $50

Remaining = $50 - $35 = $15

Since one gift cost $10

Thus, 15/10 = 1.5 since the number of gifts will be the whole number so it will be round to bottom 1 gift.

Hence "With the money still available, Jeff can purchase 1 more present".

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Step-by-step explanation:

remember, the domain is the interval or set of all valid x values, the range is the interval or set of all valid y values (functional result values).

1.

domain : -infinity < x < +infinity

range : -1 <= y < +infinity

due to the x² term that part can never be negative. the minimum is 0, and then -1 gives us a overall minimum -1. and then up ... the sky is the limit ...

2.

domain : every value of x that does not turn (3x + 5) to 0 and therefore does not cause a 1/0 situation.

the only forbidden value of x is therefore

3x + 5 = 0

3x = -5

x = -5/3

so, (-infinity < x < -5/3) OR (-5/3 < x < +infinity)

range : -infinity < y < +infinity

3.

domain : -infinity < x < +infinity

range : 0 <= y < +infinity

due to the x⁴ term (even exponent) all results will be positive starting with 0. similar to 1.

4.

this is 1/(2x) as I understand it.

similar to 2. we must avoid at 1/0 situation.

so, x must not be 0. everything else is possible

domain : (-infinity < x < 0) OR (0 < x < +infinity)

range : -infinity < y < +infinity

5.

everything is allowed and possible.

domain : -infinity < x < +infinity

range : -infinity < y < +infinity

Answer:

hello !!

answer ;

(16 + 5 + 2) - 1

<.........kai.........>

The equation of the tangent line:

y = (-x - sqrt(2)/2) - (π/2)(x - sqrt(2)/2)

To find the equation of the line tangent to the curve at the point corresponding to t = π/4, we need to find the first derivatives of x and y with respect to t, evaluate them at t = π/4, and then use these values to find the slope of the tangent line.

The first derivative of x with respect to t is:

dx/dt = -sint + tcost

The first derivative of y with respect to t is:

dy/dt = cost + tsint

Evaluating these at t = π/4, we get:

dx/dt|t=π/4 = -sqrt(2)/2

dy/dt|t=π/4 = (sqrt(2)/2) + (π/4)(sqrt(2)/2)

The slope of the tangent line is the ratio of the change in y to the change in x. So, the slope of the tangent line at t = π/4 is:

m = dy/dt|t=π/4 / dx/dt|t=π/4 = -1 - π/2

Now, we can use the point-slope form of the equation of a line to find the equation of the tangent line. Using the point (x(π/4), y(π/4)) = (sqrt(2)/2, sqrt(2)/2), we get:

y - (sqrt(2)/2) = (m)(x - sqrt(2)/2)

Substituting the value of m, we get:

y - (sqrt(2)/2) = (-1 - π/2)(x - sqrt(2)/2)

Expanding and simplifying, we get the equation of the tangent line:

y = (-x - sqrt(2)/2) - (π/2)(x - sqrt(2)/2)

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Answer:

126.0000 square units

Step-by-step explanation:

In theory, Option D. All of these stages occurs at prisoner classification.

Prisoner classification occurs during transfer, in preparation for release, and after problems occur. All of these stages are important for assessing an inmate's risk and providing appropriate security.

Prisoner classification involves assessing an inmate's risk level and providing an appropriate security level based on the results. This assessment is conducted during various stages, such as during transfer to another institution, in preparation for release, and after the inmate encounters problems. The classification process may involve evaluating an:

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Throwing a coin until it lands tails is an example of a discrete random variable which does not have a finite expectation.

For the given question,

A discrete random variable is a type of variable whose value depends upon the numerical outcomes of a certain random phenomenon. Discrete random variables are always whole numbers, which are easily countable.

It is a variable that can take on a finite number of distinct values and takes numerous values. It is also known as a stochastic variable. When you consider probabilistic experiments with infinite outcomes, it is easy to find random variables with an infinite expected value.

Let X be a random variable that is equal to 2ⁿ with probability 2⁻ⁿ (for positive integer n). Then,

\(E(X)=\sum_{n:1}^{\infty} |2^{-n}2^{n}|\)

⇒ \(E(X)=\sum_{n:1}^{\infty} (1)\)

⇒ \(E(X)=\infty\)

Consider the following example,

You throw a coin until it lands tails.

Let n be the number of heads

Then number of heads can be found by, 2ⁿ

Now, the expected value function is

\(E(X)=\frac{1}{2}(2^{0} )+ \frac{1}{4}(2^{1} )+....\)

⇒ \(E(X)=\sum_{n:1}^{\infty} |2^{-n}2^{n-1}|\)

⇒ \(E(X)=\sum_{n:1}^{\infty} \frac{1}{2}\)

⇒ \(E(X)=\infty\)

Since the number of outcomes is infinite. The probability of each outcome decreases exponentially.

Hence we can conclude that throwing a coin until it lands tails is an example of a discrete random variable which does not have a finite expectation.

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We should administer 2.05 ml/hr.

A sort of neurotransmitter and hormone is dopamine. It affects a variety of vital bodily processes, such as mobility, memory, rewarding pleasure, and motivation. Dopamine levels are linked to a number of neurological and mental health conditions.

To determine the ml/hr to administer, we first need to calculate the dose of dopamine in mg/kg/min. We can use the following formula:

dose (mg/kg/min) = 4 mcg/kg/min x 10^-3 (to convert from mcg to mg)

dose (mg/kg/min) = 0.004 mg/kg/min

Next, we need to calculate the total dose in mg/min. We can use the following formula:

dose (mg/min) = dose (mg/kg/min) x weight (kg)

dose (mg/min) = 0.004 mg/kg/min x 64 kg = 0.256 mg/min

Now we need to convert the dose from mg/min to ml/hr, using the following formula:

ml/hr = dose (mg/min) x weight (kg) / concentration (mg/ml) x 60 min/hr

ml/hr = 0.256 mg/min x 64 kg / 400 mg/250 ml x 60 min/hr

ml/hr = 2.048 ml/hr

To round to the nearest tenth, we will round 2.048 to 2.05 ml/hr. Therefore, we should administer 2.05 ml/hr.

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(a) product A is increasing.

(b) The highest percentage change in 4th year.

Function is a combination of different types of variable and constants.

A function is denoted by f(x).

The given function is,

f(x) = 72(1.25)ˣ

(a)

At starting when x=0,

f(0)= 72×1 = 72

After 1 year, the price is  

f(1) = 72 × 1.25 = 90

After 2 year, the price is  

f(2) = 72 × (1.25)² = 112.5

After 3 year, the price is  

f(3) = 72 × (1.25)³ = 140.625

After 4 year, the price is  

f(3) = 72 × (1.25)⁴ = 175.78

The function f(x) is in increasing order, implies that product A is increasing.

(b)

The percentage change for 2nd year = 30%

The percentage change for 3rd year = 30 %

The percentage change for 4th year = 30.004

The highest percentage is  4th year.

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Answer:

(x1,y1),(x2,y2)

(x1,y1)=(-5,-1)   (x2,y2)=(1,9)= (1-5/2, 9-1/2)

your answer:

(-2,4)

Step-by-step explanation:

Answer:

Set A : 45, 65, 66, 67 ,68, 68, 69, 70, 70

Median = 68

Set B : 40, 41, 43, 45, 46, 47, 48, 49, 49

Medain = 46

When 45 is removed from both

Set A : 65, 66, 67 ,68, 68, 69, 70, 70

Median = 68

Set B : 40, 41, 43, 46, 47, 48, 49, 49

Medain = 46.5

Set A : 45, 65, 66, 67 ,68, 68, 69, 70, 70

Mean = 65.33

Set B : 40, 41, 43, 45, 46, 47, 48, 49, 49

Mean = 45.33

when 45 is removed from both

Set A :  65, 66, 67 ,68, 68, 69, 70, 70

Mean  = 67.875

Set B : 40, 41, 43, 46, 47, 48, 49, 49

Mean = 45.38

The difference between median of A and B decreases because the median of set B increases.

The difference between mean of A and B increases because the mean of set A increases.

To use Newton's Method, we need to start with an initial approximation, which we can choose as x=1. Then, we can use the formula: x1 = x0 - f(x0)/f'(x0)

where x0 is the initial approximation, f(x0) is the function evaluated at x0, and f'(x0) is the derivative of the function evaluated at x0. In this case, we have:

f(x) = x3 + 9
f'(x) = 3x2

So, we can plug in x0=1 and get:

x1 = 1 - (1^3 + 9)/(3(1^2))
x1 = 1 - 10/3
x1 = -7/3

Now, we can repeat the process using x1 as our new approximation:

x2 = x1 - f(x1)/f'(x1)
x2 = (-7/3) - [(-7/3)^3 + 9]/[3(-7/3)^2]
x2 = (-7/3) - (-754/81)
x2 = 175/81

We can continue this process until two successive approximations differ by less than 0.001:

x3 = 1709/567
x4 = 532082/178605
x5 = 328211562/109735763

Now, we can use a graphing utility to find the zeros to three decimal places. We can see from the graph that there is only one real zero, which is approximately -2.080. This is close to our last approximation using Newton's Method, which was x5 = 2.994. However, our approximation is not accurate to three decimal places, so we need to keep going with Newton's Method.

x6 = -2.082297225
x7 = -2.080083055
x8 = -2.080083823

Now, we have found an approximation that is accurate to three decimal places: -2.080. This is very close to the zero we found using the graphing utility.

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Answer:

-3

Step-by-step explanation:

4a - 2(a + b) + 1 = ?

4(2) - 2(2 + 4) + 1

8 - 2(6) + 1

8 - 12 + 1

-4 + 1 = -3

I hope this helps!

Answer:

The correct answer is "66"

Step-by-step explanation:

P(-2) = 3*16 + 4*4 + 2

P(-2) = 48 + 16 + 2

P(-2) = 66

The y-component of the resultant vector T = 2a + 36 can be found by calculating the y-components of the vectors involved and then adding them together.

The vector a has a y-component of 10, and the vector b does not have a y-component since its second element represents the x-component. Therefore, to find the y-component of T, we need to calculate 2a + 36 and then extract the y-component.

Calculating 2a:

2a = 2(6, 10) = (26, 210) = (12, 20)

Calculating T = 2a + 36:

T = (12, 20) + (36, 0) = (12+36, 20+0) = (48, 20)

The y-component of the resultant vector T is 20.

After calculating the vector T as 2a + 36, we found that its y-component is 20. The y-component represents the vertical component of the resultant vector and is obtained by adding the y-components of the individual vectors involved.

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Answer:

Meaning: If the company sells -2 shirt, they would make a profit of -66 dollars. This interpretation of loss in the context of the problem.

Meaning: If the company sells 6- shirt, they would make a profit of -2 dollars. This interpretation of loss in the context of the problem.

Meaning: If the company sells 9.5shirt, they would make a profit of 26 dollars. This interpretation of profit in the context of the problem.

R(all real numbers)

Step-by-step explanation:

We are given that the profit in dollars when the company sells x shirt is given by

f(x)=8x-50

Substitute x=-2

\(f(-2)=8(-2)-50=-66\)

Meaning: If the company sells -2 shirt, they would make a profit of -66 dollars. This interpretation of loss in the context of the problem.

f(6)=8(6)-50=-2

Meaning: If the company sells 6- shirt, they would make a profit of -2 dollars. This interpretation of loss in the context of the problem.

f(9.5)=8(9.5)-50=26

Meaning: If the company sells 9.5shirt, they would make a profit of 26 dollars. This interpretation of profit in the context of the problem.

The given function is linear function. Therefore, the domain of the function is R(all real numbers).