find the area inside one loop of the curve. r2 = 8 sin(8), r ≥ 0

The improper integral ∫ 1/x dx from 0 to ∞ is divergent. The improper integral ∫ 1/x dx from 0 to ∞ represents the integral of the function 1/x with respect to x over the interval from 0 to positive infinity.

To determine whether this integral is convergent or divergent, we need to evaluate it.

Let's split the integral into two parts: from 0 to 1 and from 1 to ∞.

∫(0 to 1) 1/x dx

This part of the integral is a finite integral, and it can be evaluated as:

∫(0 to 1) 1/x dx = [ln|x|] (0 to 1) = ln(1) - ln(0)

However, ln(0) is undefined, so this part of the integral does not converge.

Now let's evaluate the second part of the integral:

∫(1 to ∞) 1/x dx

This integral represents the area under the curve of the function 1/x from 1 to ∞. This is a well-known integral and is known to diverge. As x approaches infinity, the value of 1/x approaches 0, but it never reaches 0. Therefore, the area under the curve keeps increasing indefinitely, and the integral diverges.

Since either part of the integral diverges, the overall integral ∫ 1/x dx from 0 to ∞ is divergent.

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After answering the presented question, we can conclude that  it will function take 36 months for the total cost to reach $2005.

In mathematics, a function appears to be a link between two sets of numbers in which each member of the first set (known as the domain) corresponds to a specific member of the second set (called the range). In other words, a function takes input from one collection and creates output from another. The variable x has frequently been used to represent inputs, whereas the variable y has been used to represent outputs. A formula or a graph can be used to represent a function. For example, the formula y = 2x + 1 depicts a functional form in which each value of x generates a unique value of y.

inverse function

\(c(x) = 55x + 25\\c(x) - 25 = 55x\\x = (c(x) - 25) / 55\\c^(-1)(x) = (x - 25) / 55\\c(x) = 55x + 25 = 2005\\55x = 1980\\x = 36\\\)

it will take 36 months for the total cost to reach $2005.

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Answer:

1: Given

2: Verical angles are always congruent

3: Angle Angle theorem

Answer:

- 7

Step-by-step explanation:

Given

t < - 6

Then t = - 7 is less than - 6 and is a solution

Answer:

-1/125

Step-by-step explanation:

1/(-5)^3

evaluate

1/-125

By using the definition of second order polynomials and the discriminant from quadratic formula, we conclude that the values of k must be less than 1/4.

In this question we must determine the set of values of k such that the function g(x), a linear function, intersects a quadratic function f(x) at two points. In this case, we must solve the following second order polynomial:

k · x² + 4 · x - 3 - g(x) = 0

k · x² + 4 · x - 3 - 2 · x + 7 = 0

k · x² + 2 · x + 4 = 0

In this case, the discriminant of the equation described above must be positive:

2² - 4 · k · 4 > 0

4 - 16 · k > 0

4 > 16 · k

16 · k < 4

k < 1/4

By using the definition of second order polynomials and the discriminant from quadratic formula, we conclude that the values of k must be less than 1/4.

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Answer:

..

Step-by-step explanation:

no the correct point would be (7,12)

7x1=7

7+5=12

Answer:

nop0e

Step-by-step explanation:

Based on mathematical models, it appears that there is a positive correlation between height and weight. This means that as height increases, weight also tends to increase. However, it is important to note that correlation does not necessarily imply causation and there may be other factors at play that affect weight independent of height.

It appears that there is a positive correlation between height and weight. As height increases, weight generally increases as well, and vice versa. The relationship is the relationship between two variables that tend to move in the same direction. A relationship occurs when one variable decreases while the other decreases, or when one variable increases while the variable increases. In statistics, a perfect correlation is indicated by a correlation coefficient of +1.0, while 0 indicates no correlation and -1.0 indicates a perfect (negative) difference.

This relationship can be observed in various mathematical models and real-life data sets. However, it is important to note that individual variations and other factors can also influence this correlation.

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Answer:

Answer:

The function describes the motorboat's distance from the shore  

Step-by-step explanation:

A motorboat moves across a lake as a constant speed. when it begins, it is 50 km from the shore

After 9 minutes, it is 14 km from the shore.

So, rate of change =  

Negative sign shows that there is decrease in distance per minute

The rate of change of distance is 4 km / minutes

General equation : y = mx+c

Where m is the slope and c is the constant

Substitute the values in the equation :

y=-4x+50

Where y is the final distance and x is the minutes

So, Option C is true

Hence The function describes the motorboat's distance from the shore

Step-by-step explanation:

Answer:

(Hope this helps can I pls have brainlist (crown)☺️)

Step-by-step explanation:

Graph in pic

(Credits: Symbolab)

The correct solutions about holiday is:

a. $1250

b. c = 200 + 150n

The expression that will be formed based on the information will be -

Total cost = travel cost + cost per night for a hotel × number of nights

Now, representing total cost with c, travel cost with t and nights with n. The resultant expression will be -:

c = t + 150n

c = 200 + 150n

This will be function of c in terms of n.

Keeping the value of n as 7 in the mentioned expression

c = 200 + 150×7

Performing multiplication on Right Hand Side of the equation

c = 200 + 1050

Performing addition on Right Hand Side of the equation

c = $1250

The solution of a is $1250 and b is c = 200 + 150n.

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the probability that at least seven customers arrive in three minutes, given that exactly two arrive in the first minute, is approximately 0.081 or 8.1%.

How to solve?

To solve this problem, we can use the Poisson distribution, which models the probability of a certain number of events occurring in a fixed interval of time or space, given the expected rate of occurrence.

Let lambda be the expected rate of customer arrivals per minute. If exactly two customers arrive in the first minute, then the expected number of customers to arrive in three minutes is lambda ×3. We can use this expected value to calculate the probability of at least seven customers arriving in three minutes:

P(X ≥ 7 | X ~ ∝(λ×3))

= 1 - P(X ≤ 6 | X ~ ∝(λ×3))

= 1 - ∑[k=0 to 6] (e²(-λ3) ×(lλ3)²k / k!)

where e is the mathematical constant approximately equal to 2.71828, and k! denotes the factorial of k.

To find lambda, we can use the fact that exactly two customers arrive in the first minute. The Poisson distribution assumes that the number of events in a fixed interval of time or space follows a Poisson distribution with parameter lambda, which represents the expected rate of occurrence. Therefore, lambda is equal to the number of customers arriving per minute, which is 2.

Substituting lambda = 2 into the formula, we get:

P(X ≥ 7 | X ~ ∝(2×3))

= 1 - P(X ≤ 6 | X ~ ∝(6))

= 1 - ∑[k=0 to 6] (e²(-6) ×6²k / k!)

Using a calculator or computer software, we can evaluate this expression to get:

P(X ≥ 7 | X ~ ∝(6)) ≈ 0.081

Therefore, the probability that at least seven customers arrive in three minutes, given that exactly two arrive in the first minute, is approximately 0.081 or 8.1%.

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Answer: The length of First piece = 6

The length of second piece = 18

The length of third piece = 30  

Step-by-step explanation:

Given data,

A 54-inch board is to be cut into three pieces.

so that the second piece is 3 times as long as the first piece and the third piece is 5 times as long as the first piece.

So, we can write,

Let us assume, first piece is represented by = x

Then,

second piece is 3 times as long as the first piece

So, we can write,

second piece is represented by = 3 ( first piece )

second piece is represented by = 3x

Then,

third piece is 5 times as long as the first piece

So, we can write,

third piece is represented by = 5 ( first piece )

third piece is represented by = 5x

So, we can find the all 3 pieces length,

we can solve it :
combine all three pieces = x + 3x + 5x

length of all three pieces = x + 8x

                                          = 9x

 Total board is to be cut into three pieces = 54

Hence,

                         9 x = 54

                          x = 54/9

                          x = 6

Now we know that the base length, x, is equal to 6.

From there, we can find the length of the all three pieces is :

The length of First piece = x = 6

The length of second piece = 3x

                                         = 3(6)

                                         = 18

The length of third piece = 5x

                                         = 5(6)

                                         = 30

Therefore,

The length of First piece = 6

The length of second piece = 18

The length of third piece = 30  

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The better survey would be when the possibility of adults in favour of fee and not in favour of fee is same that is 50% each.

Everything in surveys revolves around asking the appropriate questions in the right ways since they are meant to elicit feedback. Many polls purposefully and unintentionally ask one-sided questions.

An objective question attempts to avoid using leading language and is fact-based rather than judgmental.

Biased questionnaire items use word choice and sentence structure in a way that affects how respondents react. This is sometimes done on purpose. This usually happens as a result of inadequate survey planning and assessment.

Here are a few advices.

Given query:

Thus, the better survey would be when the possibility of adults in favour of fee and not in favour of fee is same that is 50% each.

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Answer:

your answer will be A

Step-by-step explanation:

Answer:

Step-by-step explanation:

Solve for x:

As we know an absolute value is always positive

So there is no solution to this equation as | x + 0.5 | ≥ 0 and the right side is negative

Correct option is C

There are 1,120 different ways to order an egg, a pancake with a choice of syrup, and a beverage.

Given data: 4 different ways to have an egg cooked, 7 different choices of pancakes, 5 different types of syrups and 8 different beverages.The total number of different ways are there to order an egg, a pancake with a choice of syrup, and a beverage can be calculated as follows: Multiplying the number of choices for each item together.

That is 4 ways to have an egg cooked x 7 choices of pancakes x 5 choices of syrup x 8 beverages= 4 x 7 x 5 x 8= 1120 Thus, there are 1,120 different ways to order an egg, a pancake with a choice of syrup, and a beverage.

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Answer:

perpendicular

Step-by-step explanation:

Parallel lines have equal slopes

The product of the slopes of perpendicular lines = - 1

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - 4x + 3 ← is in slope- intercept form

with slope m = - 4

x - 4y =  8 ( subtract x from both sides )

- 4y = - x + 8 ( divide through by - 4 )

y = \(\frac{1}{4}\) x + 2 ← in slope- intercept form

with slope m = \(\frac{1}{4}\)

Since the slopes are not equal the lines are not parallel

- 4 × \(\frac{1}{4}\) = - 1

Then the lines are perpendicular

Answer:

To find the measure of angle KOM without repositioning the protractor, you can follow these steps:

1. Place the protractor on the vertex of the angle, which is point O.

2. Align the base of the protractor with one of the rays of the angle, which is ray OK. Make sure that the zero degree mark of the protractor lines up with the ray.

3. Read the measure of the angle from the protractor. In this case, the measure of angle KOM is the same as the measure of angle KOB, which is 75 degrees.

4. If necessary, you can check your measurement by aligning the protractor with the other ray of the angle, which is ray OM. The measure of angle KOM should be the same as the measure of angle KOM

Step-by-step explanation:

1. Place the protractor on point O, which is the vertex of the angle.

2. Align the base of the protractor with ray OK. Make sure that the zero degree mark on the protractor is lined up with ray OK.

3. Read the measure of the angle from the protractor. In this example, the measure of angle KOB is 75 degrees.

4. Since the measure of angle KOM is the same as the measure of angle KOB, we can use 75 degrees as the measure of angle KOM.

5. If you need to verify your measurement, you can align the protractor with ray OM. The measure of angle KOM should be the same as the measure of angle KOB, which is 75 degrees

The simple average of the given data set is 3.72 g, and the weighted average cannot be determined without knowing the weights assigned to each data point.

To calculate the simple average, we sum up all the data points and divide the sum by the number of data points. In this case, the sum of the data points (3.50 g + 3.72 g + 3.72 g + 3.50 g + 3.72 g + 3.72 g + 3.50 g + 3.72 g) is 29.1 g. Dividing this sum by the number of data points (8), we get the simple average of 3.72 g.

The weighted average requires the weights assigned to each data point. Without knowing the weights, we cannot calculate the weighted average.

The weighted average takes into account the importance or significance of each data point by multiplying the data point by its corresponding weight, summing up the weighted data points, and dividing by the sum of the weights.

Since the question does not provide any information about the weights assigned to each data point, we cannot determine the weighted average in this case. So B is correct.

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The box is totally submersed in paint, how many square cm of painted surface will there be = 2216 cm^2

Having four right angles makes a rectangle a quadrilateral. It can alternatively be explained in terms of an equiangular quadrilateral—a term that refers to a quadrilateral whose angles are all equal—or a parallelogram with a right angle. A square is a rectangle with four equally long sides.

The external dimensions of the

base are 16 cm by 24 cm,

the external height is 10 cm

So , finding the area of A1 , A2 , A3

A1 = 2* 16* 10 + 2* 24 * 10 + 1 * 16 * 24

   = 1184

A2 = 2 * 14 * 9 + 2 * 22 * 9 + 1 * 14 * 22

    =  956

A3 = 16 *24 - 14 * 22

     = 76

Total area will be :

A = 1184 + 956 + 76

   = 2216 cm^2

The box is totally submersed in paint, how many square cm of painted surface will there be = 2216 cm^2

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Given the initial number 814,593, notice that it is equivalent to

Therefore, the number 4 is in the one thousands place.

Answer:

x=6

Step-by-step explanation:

Simplifying

x + 15 = 21

Reorder the terms:

15 + x = 21

Solving

15 + x = 21

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-15' to each side of the equation.

15 + -15 + x = 21 + -15

Combine like terms: 15 + -15 = 0

0 + x = 21 + -15

x = 21 + -15

Combine like terms: 21 + -15 = 6

x = 6

Simplifying

x = 6

HOPE THIS HELPS :)

The assumption necessary to apply a goodness-of-fit test is that the data are measured with a nominal or ordinal scale.

Goodness-of-fit tests are used to determine whether an observed frequency distribution of categorical data fits an expected theoretical distribution. They compare the observed frequencies with the expected frequencies based on a specified distribution. The data being analyzed using a goodness-of-fit test are typically categorical, such as counts or proportions in different categories or groups.

Therefore, the correct answer is: The data are measured with a nominal or ordinal scale.

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Answer:

20 cm.

Step-by-step explanation:

In order to find the height, we need the volume and the base area first. We are already given the volume so we need to find the base area.

A = 18 · 5 = 90

Now that we know the base area is 90 cm², we can substitute the information into the equation to solve for the height.

V = 1/3(A)(h)

600 = 1/3(90)(h) (Given)

600 = 30h (Simplified)

20 = h (Divided 30 on both sides)

Therefore, the height is 20 cm.

Answer:

it would take around 10 hours to grade all 30 papers

Step-by-step explanation:

if for one student it takes 20 minutes that means you would have to do 20 minutes 30 times which is 600 minutes. to convert that to hours you divide total minutes (600) by 60 which gives you 10 hours. no need for thanks

We have to find the value of  `(sinθ+cosθ−tanθ)/(secθ+cscθ−cotθ)`

Let's find all trigonometric ratios:

We can say that:

\($$\tan \theta= \frac{opp}{adj}= \frac{-4}{3}$$$$\text\)

{Using the Pythagorean Theorem we can find the hypotenuse }

\($$$$\text{Hypotenuse = } \sqrt{(-4)^2+(3)^2}\)

\(= \sqrt{16+9}\)

= \(\sqrt{25}\)

=\(5$$$$\)

Substituting the values of sinθ, cosθ and tanθ in `

\(= \frac{\frac{3}{5} + \frac{-4}{5} - \frac{-4}{3}}{\frac{-4}{5} + \frac{5}{3} - \frac{-3}{4}}$$$$\)

\(=\frac{\frac{9}{15} + \frac{-12}{15} + \frac{20}{15}}{\frac{-16}{20} + \frac{25}{12} + \frac{3}{4}}$$$$\)

\(=\frac{\frac{17}{15}}{\frac{-14}{15}}$$$$\)

\(=-\frac{17}{14}$$\)

Therefore, \(`(sinθ+cosθ−tanθ)/(secθ+cscθ−cotθ)\)` is equal to

`-17/14` when `tanθ=−43` (Quadrant II).

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Answer:

5.8 × 10^(6) is greater.

Step-by-step explanation:

The 2 numbers she wants to compare are;

5.8 × 10^(6) and 2.32 x 10^(7)

Now,for her to compare easily both numbers will need to have the same powers of 10.

To this effect, let's convert the power of ten of the second number to the power of 6.

We will divide by 10 to get it.

Thus; 2.32 x 10^(7) ÷ 10 = 0.232 × 10^(6)

Comparing 0.232 × 10^(6) to 5.8 × 10^(6), we can see that they have same power of 10 but the greater number that precedes the power of 10 is 5.8.

Thus, 5.8 × 10^(6) is greater.