pls help me understand

Answer:

34

Step-by-step explanation:

The given parametric equations define a relationship between the variable t and the coordinates (x, y) in a two-dimensional plane. The equation x = sin(t) represents the x-coordinate of a point on the graph, while y = csc(t) represents the y-coordinate. The restriction 0 < t < pi ensures that the values of t lie within a specific range.

In more detail, the equation x = sin(t) indicates that the x-coordinate of a point is determined by the sine function of the corresponding value of t. The sine function oscillates between -1 and 1 as t varies, resulting in a periodic pattern for the x-values.

On the other hand, the equation y = csc(t) represents the reciprocal of the sine function, known as the cosecant function. The cosecant function is defined as the inverse of the sine function, so the y-coordinate is the reciprocal of the corresponding sine value. Since the sine function has vertical asymptotes at t = 0 and t = pi, the cosecant function has vertical asymptotes at those same points, restricting the range of y.

Together, these parametric equations describe a curve in the xy-plane that is determined by the values of t. The specific shape of the curve depends on the range of t and the behavior of the sine and cosecant functions.

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The correct statement is c. When marginal utility is positive, an increase in the quantity consumed will increase total utility.

This is because as long as the marginal utility of each additional unit consumed is positive, the total utility will continue to increase with each additional unit consumed. However, when marginal utility starts to decrease, consuming additional units will result in diminishing returns and eventually lead to a decrease in total utility. The statement in option a is incorrect because an increase in the quantity consumed can still increase total utility if the marginal utility is positive. The statement in option b is also incorrect because if the marginal utility is positive, consuming more will increase total utility, not decrease it. Option d is also incorrect because when marginal utility is increasing, it means that the additional units consumed are providing more utility than the previous ones, so decreasing the quantity consumed will result in a decrease in total utility.

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Answer:

It is x2 -4  because it correct

Answer:

  y = (4 -x)e^-2

Step-by-step explanation:

You want an equation of the tangent line to the graph of f(x) = xe^−x at its inflection point.

The inflection point on a curve is the point where the second derivative is zero, where the curve changes from being concave downward to concave upward, or vice versa.

We can use the product rule to differentiate f(x):

  (uv)' = u'v +uv'

  f'(x) = 1·e^-x +x·(-1)(e^-x) = (e^-x)(1 -x)

Then the second derivative is ...

  f''(x) = (-e^-x)(1 -x) +(e^-x)(-1) = (e^-x)(x -2)

The second derivative is zero where one of its factors is zero. e^-x is never zero, so we have ...

  (x -2) = 0   ⇒   x = 2

The point of inflection occurs at x = 2.

The point-slope equation of the line with slope m through point (h, k) is ...

  y -k = m(x -h)

For this problem, we have ...

  m = f'(2) = (e^-2)(1 -(2)) = -e^-2

  (h, k) = (2, f(2)) = (2, 2e^-2)

So, the equation of the tangent line is ...

  y -2e^-2 = -e^-2(x -2)

In slope-intercept form, this is ...

  y = (-e^-2)x +4e^-2

__

Additional comment

We can rearrange the equation to ...

  y = (4 -x)e^-2

Usually a tangent line touches the graph, but does not cross it. The tangent at the point of inflection necessarily crosses the graph.

Answer:

g. 92*

h. 88*

m. 89*

k. 91*

Step-by-step explanation:

To find h and m: All of the angles on a straight line added up equals 180*. So if there are two angles, the sum of them must equal 180* (angle A + angle B = 180*)

So in this case we have angle h + 92* = 180* using algebra, we subtract 92 from both sides and we get angle h = 88*

If you want to check, add 92 + 88 = 180.

Also angle m + 91* = 180*. Same thing as above, subtract 91 from both sides and we get angle m = 89*

If you want to check, add 91 + 89 = 180.

When you have two straight lines intersecting (crossing), the opposing angles at that crossing are going to be equal. So in this case angle g is opposite from the anbgle that we know is 92*, so angle g is also 92*. Same thing for angle k, we know the angle opposite angle k is 91*, so we know that angle k is also 91*.

Student A is wrong and Student B is correct.

How?

The median of the random variable x-bar is 300.The distribution of the sample mean (x-bar) from a normally distributed population follows a normal distribution as well.

For large sample sizes (n ≥ 30), the sample mean will be approximately normally distributed, regardless of the shape of the original population.

Given that x follows a normal distribution with a mean of 300 and a standard deviation of 15, the sample mean x-bar (when sampling 20 observations at a time) will also follow a normal distribution with a mean equal to the population mean (300) and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

The standard deviation of x-bar is given by σ_x-bar = σ_x / √n, where σ_x is the population standard deviation and n is the sample size.

In this case, the standard deviation of x-bar is σ_x-bar = 15 / √20 ≈ 3.3541.

Since the sample mean x-bar follows a normal distribution, its median will be equal to its mean, which is the same as the population mean of 300.

Therefore, the median of the random variable x-bar is 300.

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Answer:

I think ur and is 4140. but I'm not sure, sorry if its incorrect.

Answer:

6

Step-by-step explanation:

2x3= 6 and 4 is 2/3 of 6

It is proved that 1) AB = AC, 2) angle B = angle C fo the given triangles.

A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total.

Here in Delta ADB and Delta ADC.

i) Three pair of equal parts are:

AD = AD ( common side )

BD = CD ( as d is the mid point of BC)

AB = AC (given in the question)

ii) Now,

by SSS Concurrency rule,

Delta ADB\cong \Delta ADC

iii) As both triangles are congruent to each other we can compare them and say

angle B = angle C.

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Complete question:

In figure AB=AC and D is the mid point of BC state the 3 pairs of equal parts in

Triangle ADB and triangle ADC

is ADB= ADC? give reason

is <B = <C? why?

PLEASE ANSWERRR ASAP​

Answer:

0.1

Step-by-step explanation:

Just take 24/24 which is 1 and move the decimal one place to the left because there is an extra 0 on the denominator

Answer:

C

Step-by-step explanation:

Answer:

2.6 kilometers

Step-by-step explanation:

To find the circumference of a circle, we can use the formula:

Circumference = π * diameter

Given that the diameter of the volcanic crater is 840 meters, we can substitute this value into the formula:

Circumference = π * 840

Using the approximate value of π as 3.14159, we can calculate the circumference:

Circumference = 3.14159 * 840

Circumference ≈ 2643.1796 meters

To convert the circumference to kilometers, we divide the value by 1000:

Circumference in kilometers = 2643.1796 / 1000

Circumference ≈ 2.6432 kilometers

Therefore, the circumference of the rim of the volcanic crater is approximately 2.6 kilometers (rounded to 1 decimal place).

Answer:

The solution to the recurrence relation is given by an = 2^(n+1) - 1.

Step-by-step explanation:

(a) To solve the recurrence relation an = an-2 + 4, with initial conditions a1 = 3 and a2 = 5, we'll consider two cases: one for when n is even and one for when n is odd.

For n even:

Substituting n = 2k (where k is a positive integer) into the recurrence relation, we get:

a2k = a2k-2 + 4

Now let's write out a few terms to observe the pattern:

a2 = a0 + 4

a4 = a2 + 4

a6 = a4 + 4

...

We notice that a2k = a0 + 4k for even values of k.

Using the initial condition a2 = 5, we can find a0:

a2 = a0 + 4(1)

5 = a0 + 4

a0 = 1

Therefore, for even values of n, the solution is given by an = 1 + 4k.

For n odd:

Substituting n = 2k + 1 (where k is a non-negative integer) into the recurrence relation, we get:

a2k+1 = a2k-1 + 4

Again, let's write out a few terms to observe the pattern:

a3 = a1 + 4

a5 = a3 + 4

a7 = a5 + 4

...

We see that a2k+1 = a1 + 4k for odd values of k.

Using the initial condition a1 = 3, we find:

a3 = a1 + 4(1)

a3 = 3 + 4

a3 = 7

Therefore, for odd values of n, the solution is given by an = 3 + 4k.

(b) To solve the recurrence relation an = 2an-1 + 1, with initial condition a1 = 1, we'll find a general expression for an.

Let's write out a few terms to observe the pattern:

a2 = 2a1 + 1

a3 = 2a2 + 1

a4 = 2a3 + 1

...

We can see that each term is one more than twice the previous term.

By substituting repeatedly, we can express an in terms of a1:

an = 2(2(2(...2(a1) + 1)...)) + 1

= 2^n * a1 + (2^n - 1)

Using the initial condition a1 = 1, we have:

an = 2^n * 1 + (2^n - 1)

= 2^n + 2^n - 1

= 2 * 2^n - 1

Therefore, the solution to the recurrence relation is given by an = 2^(n+1) - 1.

The required probability of the coin landing tails up at least two times is 15/16.

Given that,
A fair coin is flipped seven times. what is the probability of the coin landing tails up at least two times is to be determined.

Probability can be defined as the ratio of favorable outcomes to the total number of events.

Here,
In the given question,
let's approach inverse operation,
The probability of all tails  = 1 / 2^7 because there is only one way to flip these coins and get no heads.
The probability of getting 1 head = 7 /2^7
Adding both the probability = 8 / 2^7
Probability of the coin landing tails up at least two times = 1 - 8/2^7
                                                                                     = 1 - 8 / 128
                                                                                     = 120 / 128
                                                                                     = 15 / 16

Thus, the required probability of the coin landing tails up at least two times is 15/16.

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We can say with 95% confidence that the average yearly salary of top managers in the private sector is between $6,670 and $13,330 higher than the average yearly salary of top managers in the government sector.

The formula for calculating the confidence interval for the difference between two means where x1 and x2 are the sample means, s1 and s2 are the sample standard deviations, n1 and n2 are the sample sizes, t(a/2,n1+n2−2) is the t-distribution value for the desired confidence level and degrees of freedom, and t is the significance level (in this case, = 0.05).

Plugging in the values from the given data, we get:

(90−80)±(0.025,108)∗(6²/50+8²/60)¹/₂

Simplifying this expression, we get:

10±1.98∗1.634

Therefore, the 95% confidence interval for the difference between the average salaries of top managers in private and governmental organizations is:

(6.67, 13.33)

This means that we can be 95% confident that the true population parameter falls within this range.

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Complete Question:

In order to estimate the difference between the average yearly salaries of top managers in private and governmental organizations, the following information was gathered:

                                                               Private                              Government

Sample size                                                       50                                          60

sample mean                                                     90                                          80

Sample standard deviation                          6                                                8

Develop an interval estimate for the difference between the average salaries of the two sectors. Let alpha = .05.

Answer:

322850405

Step-by-step explanation:

the value of n is 17 and the value of r is 3.

To help account for variability, the pollster used a simple random sample.

Sampling is the selection of a subset (a statistical sample) of people from within a statistical population in statistics, assurance, and survey procedures. the population's characteristics that were sampled. Obtaining samples that are typical of the population being researched is the objective of statisticians.

In situations where it is not practical to evaluate the complete population, sampling offers insights and is more cost-effective and time-efficient than doing so.

Each observation gives a number for one or more characteristics of certain things or people, including their size, location, color, or weight.

In survey sampling, especially in stratified sampling, ratings can be added to the results to take into consideration the sample design. The practice is guided by conclusions from statistical theory and probability theory.

Since 1000 people are randomly selected , hence we can say that the preference is simple random sample.

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Answer:

3

Step-by-step explanation:

HJ = 9 and IJ = 6.

HJ = HI + IJ

9 = HI + 6

HI = 9-6=3

Every polynomial function of odd degree with real coefficients will have at least one real root or zero.

This statement is known as the Fundamental Theorem of Algebra. It states that a polynomial of degree n, where n is a positive odd integer, will have at least one real root or zero.

The reason behind this is that when a polynomial of odd degree is graphed, it exhibits behavior where the graph crosses the x-axis at least once. This implies the existence of at least one real root.

For example, a polynomial function of degree 3 (cubic polynomial) with real coefficients will always have at least one real root. Similarly, a polynomial function of degree 5 (quintic polynomial) with real coefficients will also have at least one real root.

It's important to note that while a polynomial of odd degree is guaranteed to have at least one real root, it may also have additional complex roots.

The Fundamental Theorem of Algebra ensures the existence of at least one real root but does not specify the total number of roots.

In summary, every polynomial function of odd degree with real coefficients will have at least one real root or zero, as guaranteed by the Fundamental Theorem of Algebra.

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Answer: Y=-5

Step-by-step explanation:

The reason is because if you look down the y axis from the origin you can see the location where the line crosses over the y axis in this case it was at (0,-5)

The p-value of the given hypothesis is; 0.9999

The formula for the z-score of proportions is;

z = (p^ - p)/√(p(1 - p)/n)

where;

p^ is sample proportion

p is population proportion

n is sample size

We are given;

p^ = 15% = 0.15

p = 20% = 0.2

n = 5000

Thus;

z = (0.15 - 0.2)/√(0.2(1 - 0.2)/5000)

z = -8.8388

From p-value from z-score calculator, we have;

P(Z < -8.8388) = 1 - 0.0001 = 0.9999

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The length of top enclose r s end enclose = √(4² + 5²) = √(16 + 25) = √(41) = approximately 6.4 inches.

The length of top enclose r s end enclose can be determined using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Since top enclose p s end enclose is a diameter of the circle, it is the hypotenuse of a right triangle formed by top enclose p s end enclose, top enclose p q end enclose and top enclose p r end enclose. Thus, the length of top enclose r s end enclose is the square root of the sum of the squares of the lengths of the other two sides, which are 4 inches and 5 inches.

In other words, the length of top enclose r s end enclose = √(4² + 5²) = √(16 + 25) = √(41) = approximately 6.4 inches.

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The smallest positive integer y such that the product xy is a perfect cube is 3.

To find the value of y, we need to factorize x, which is 7 * 24 * 48.

We can then find the prime factorization of xy, which will help us determine the smallest integer y that will make the product a perfect cube.

Since 7, 24, and 48 are already factored, we can express x as:

x = 2⁴ * 3 * 7²

To make xy a perfect cube, we need to ensure that the exponents of all the prime factors are multiples of 3.

Therefore, we need to add a factor of 3 to the exponent of 2 in x to make it a multiple of 3. This gives us:

xy = 2⁷ * 3² * 7²

The smallest integer y that can make this product a perfect cube is 3, because we need to add a factor of 1 to the exponent of 2 in xy to make it a multiple of 3, and the smallest integer that can achieve this is 3.

Thus, the smallest positive integer y such that the product xy is a perfect cube is 3.


The question is: A number x is equal to \($7\cdot24\cdot48$\). What is the smallest positive integer y such that the product xy is a perfect cube

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Given the lengths of the two sides and the angle between them, only one triangle can be created under the given circumstances.

1. Given that angle B is 32.5°, side AB is 37 cm, side AC is 26 cm, etc.

2. Calculate side BC using the Law of Cosines:

BC = (2(AB)(AC)cosB) + (AB)(AC)2

3. Input the values that are known: BC = (37 2 + 26 2 - 2(37)(26)cos32.5°)

4. Condense: BC = (1369 plus 676 minus 1848 cos 32.5 °)

5. Determine BC =. (2095 - 1539.07)

6. Condense: BC = 556.93

7. Determine BC as 23.701 cm.

8. Since the lengths of the two sides and the angle between them are specified, only one triangle can be formed under the current circumstances.

By applying the Law of Cosines, we can determine the length of the third side, BC, given that side AB is 37 cm, side AC is 26 cm, and angle B is 32.5°. In order to perform this, we must first determine the cosine of angle B, which comes out to be 32.5°. Then, we enter this value, together with the lengths of AB and AC, into the Law of Cosines equation to obtain BC.BC = (AB2 + AC2 - 2(AB)(AC)cosB) is the equation. BC is then calculated by plugging in the known variables to obtain (37 + 26 - 2(37)(26)cos32.5°). By condensing this formula, we arrive at BC = (1369 + 676 - 1848cos32.5°). Then, we calculate BC as BC = (2095 - 1539.07), and finally, we simplify to obtain BC = 556.93. Finally, we determine that BC is 23.701 cm. Given the lengths of the two sides and the angle between them.

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The official is approximately \(\sqrt{(13)\)  meters from the center of the discus circle.

The official is standing 2 meters from the edge of the discus circle and 3 meters from a point of tangency. To find how far the official is from the center of the discus circle, we can use the properties of a tangent line.

First, let's draw a diagram. We have a discus circle with a center, a point of tangency, and the official standing outside the circle.

The official is standing 2 meters from the edge of the circle, so we can draw a line from the official to the point of tangency. This line is a tangent line, and it is perpendicular to the radius of the circle that passes through the point of tangency.

We also know that the official is 3 meters from the point of tangency.

To find the distance from the official to the center of the discus circle, we can form a right triangle. One leg of the triangle is the radius of the circle, and the other leg is the distance from the official to the point of tangency.

Using the Pythagorean theorem, we can find the length of the hypotenuse of the right triangle, which is the distance from the official to the center of the circle.

Let's call the distance from the official to the center of the circle x.

Using the Pythagorean theorem: \(x^2 = 2^2 + 3^2\)
Simplifying the equation: \(x^2 = 4 + 9\)

Combining like terms: \(x^2 = 13\)

Taking the square root of both sides: \(x = \sqrt{(13)\)

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