how to tell if an integral is convergent or divergent

In the image line segment SE is the tangent. The secant line making an angle with tangent line SE is NS. So the angle is ∠GSE. So option B is the correct answer.

Tangent is a line which intersect with only a single point on the curve. The point where the line meets is the point of tangency. Tangent line is always perpendicular to the radius drawn to the point of tangency. Here the tangent line is SE, point of tangency is S.

Secant lines are the lines which passes through two points of a curve. A chord drawn to the circle is a secant line. Here there are two secant lines NS and NA. Here only NS makes an angle with the tangent line.

So the angle made by a tangent and secant line is ∠GSE.

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The image for the question is attached below.

The original coordinates are P(-x, y), and it is on the second quadrant.

Remember that for a general point (a, b), a reflection about the x-axis changes the sign of the y-component, so we will get the image (a, -b)

Here we know that the image after the refection is P' = (-x, -y), then the coordinates of point P are (-x, y)

If we assume both x and y to be positive, then point P would be on the second quadrant.

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Graph of y = cosec x is attached below.

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.

Given function,

y = cosecx

when x = (π/2)

y = cosec (π/2)

y = 1

when x = π

y = cosec π

y = ∞

when x = 3π/2

y = cosec 3π/2

y = -1

By the calculation, graph of y = cosecx is drawn as follows.

Hence, graph of y = cosecx is attached below.

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The two figures (i.e. triangles) are similar triangles

Let's create a triangle with the following coordinates:

A = (0, 0)

B = (3, 0)

C = (0, 4)

To get the new coordinates, we need to multiply the y-coordinate of each point by 4:

A' = (0, 0 * 4)

B' = (3, 0 * 4)

C' = (0, 4 * 4)

So the new points are:

A' = (0, 0)

B' = (3, 0)

C' = (0, 16)

To determine if the two figures are similar, we need to check if they have the same shape but different sizes.

Specifically, the new triangle is four times larger in the vertical direction but has the same shape and angles as the original triangle.

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The measure of angle B is given as follows:

<B = 295º.

Angles A and B in the context of this problem are reflex angles, meaning that the sum of their measures is of 360º.

The measures are given as follows:

Hence the measure of angle B is obtained as follows:

65 + <B = 360

<B = 360 - 65

<B = 295º.

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Answer:

y = -3x + 10

where y = Value and x = Position

or

Value = - 3(Position) + 10

Step-by-step explanation:

We can determine a linear equation for this table in slope-intercept form

The slope intercept form of a linear equation is

y = mx + b

y is referred to as the dependent variable and x the independent variable

Here m is the slope which is the rate of change of y with respect to x

b = y-intercept which is the value of y when x = 0

For the given table it appears that the value is dependent on the position

So the independent variable, let's call it x, is position

The dependent variable, y, is value

Plugging values of x, y into the generalized equation

y = mx + b

At x(position) = 1, we get y = 7
==> 7 = m(1) + b  
==> 7 = m + b
== m + b = 7         ............................. (1)

At x = 3, y = 1

==> 1 = m(3) + b
==> 1 = 3m + b
==> 3m + b = 1       ..............................(2)

If we subtract  equation 1 from equation (2) we get
(3m + b) - (m + b) = 1 - 7

3m - m + b - b = -6

2m + 0 = -6

2m = -6

m = -6/2 = -3

So we now know m = -3 we can write the equation as

y = -3m + b

To find b, plug in any value of x and corresponding y from the table and solve for b. remember that x is position and y is value

Let's choose the last entry x = 9, y = -17

Plugging these into y = -3x + b gives

-17 = -3(9) + b

-17 = -27 + b

Switch sides:
- 27 + b = -17

Add 27 to both sides:
- 27 + 27 + b = -17 + 27

b = 10

So the equation for the table is

y = - 3x + 10

or in terms of the table
Value = - 3(Position) + 10

You can check this is correct by choosing a value for position from the table and seeing the equation value is consistent with the given value

We are are 95% confident that the true proportion of wins using the new strategy will be between 0.1812 and 0.242895 in first simulation and between 0.1948 and 0.2732 in second simulation.

A chess player ran a simulation twice to estimate the proportion of wins to expect using a new game strategy. Each time, the simulation ran a trial of 1,000 games. The first simulation returned 212 wins, and the second simulation returned 235 wins. Construct and interpret 95% confidence intervals for the outcomes of each simulation.

A 95% confidence interval gives us a range of values that we are 95% confident contains the true proportion of wins that the new game strategy will produce in the long run. To construct the confidence interval for each simulation, we can use the following formula:

CI = p ± 1.96 * sqrt(p * (1 - p) / n)

where p is the sample proportion of wins, n is the number of trials, and 1.96 is the z-score corresponding to a 95% confidence level.

For the first simulation, p = 212 / 1000 = 0.212 and n = 1000, so the confidence interval is:

CI = 0.212 ± 1.96 * sqrt(0.212 * (1 - 0.212) / 1000)

CI = (0.1812, 0.2428)

This means that we are 95% confident that the true proportion of wins using the new strategy will be between 0.1812 and 0.2428.

For the second simulation, p = 235 / 1000 = 0.235 and n = 1000, so the confidence interval is:

CI = 0.235 ± 1.96 * sqrt(0.235 * (1 - 0.235) / 1000)

CI = (0.1948, 0.2732)

This means that we are 95% confident that the true proportion of wins using the new strategy will be between 0.1948 and 0.2732.

In general, larger sample sizes lead to narrower confidence intervals. In this case, both confidence intervals overlap, indicating that the two simulations are consistent with each other. This gives us additional confidence in the estimated proportion of wins using the new strategy.

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Answer:

the confidence interval for the first simulation is (0.187, 0.237), and the confidence interval from the second simulation is (0.209, 0.261). For the first trial, we are 95% confident the true proportion of wins with the new game strategy is between 0.187 and 0.237. For the second trial, we are 95% confident the true proportion of wins with the new game strategy is between 0.209 and 0.261.

Step-by-step explanation:

got it right on the test :)

The length of line FG is 16 units

The length of FG is equal to length GH that is to say

line FG = line GH

From the problem, we have that

FG = x  + 11

GH = 3x + 1

Equation both lines

x + 11 = 3x + 1

collecting like terms

11 - 1 = 3x - 1

10 = 2x

rearranging and isolating x

2x = 10

x = 5

The line FG = x + 11 = 5 + 11 = 16 units

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The brand that is the better buy based on their unit price is; Brand A

A unit price is defined as the price for one item or measurement, such as a pound, a kilogram, or a pint, which can be used to compare the same type of goods sold in varying weights and amounts.

It is also referred to as a product's average price which is the result of dividing the product's total sales revenue by the total units sold.

Thus;

Unit price of Brand A = 8.77/24 =$0.365 per pencil

Unit price of Brand B = 9.84/26 = $0.378 per pencil

The cheaper one is the better buy which is Brand A.

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The total area of the composite figure can be found to be 24. 52 cm ²

First, find the area of the first triangle :

= 1 / 2 x base x height

= 1 / 2 x 3 x 2. 7

= 4. 05 cm ²

The area of the second triangle :

= 1 / 2 x 3 . 4 x ( 6. 8 - 2 . 7 )

= 6. 97 cm ²

Then the area of the rectangle :

= 5 x 2. 7

= 13. 5 cm ²

The total area of the composite shape is :

= 13.5 + 6.97 + 4. 05

= 24. 52 cm ²

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Answer: 8y=2h

Step-by-step explanation: you have to subtract the first 2 numbers then add the others and then add letters and boom

With the sequence having sum of four consecutive integers as 198 , the fourth integer in the sequence is calculated to be 51.

Let's call the first integer in the sequence "x". Since the integers are consecutive, the next three integers in the sequence would be "x + 1", "x + 2", and "x + 3". The sum of these four integers can be represented as:

x + (x + 1) + (x + 2) + (x + 3) = 198

Expanding and simplifying the left side of the equation, we get:

4x + 6 = 198

Subtracting 6 from both sides of the equation, we get:

4x = 192

Dividing both sides of the equation by 4, we get:

x = 48

So the first integer in the sequence is 48. To find the fourth integer in the sequence, we add 3 to the first integer:

x + 3 = 48 + 3 = 51

So the fourth integer in the sequence is 51.

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The value of m∠J in the triangle is 65°

Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.

We have triangle HIJ and m∠H = (4x + 1)°, m∠I = (2x-6)° and m∠J = (6x-7)°.

Since the sum of angle in a triangle is 180°. We can say:

m∠H +  m∠I +  m∠J = 180°

(4x + 1)° + (2x-6)° + (6x-7)° = 180°

4x + 1 + 2x-6 + 6x-7 = 180

12x - 12 = 180

12x = 180 + 12

12x = 192

x = 192/12

x = 16

To find m∠J = (6x-7)°, put x = 12 into  m∠J = (6x-7)°. That:

m∠J = 6(12) - 7

m∠J = 72 - 7

m∠J = 65°

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Carol pays a 10% deposit, it means the amount of deposit she pays is £234,900.

To work out the amount of deposit paid by Carol, we need to find 10% of the house price. We can do this by multiplying the house price by 10/100 or 0.10.

Here are the steps to find the amount of deposit paid by Carol:

1. Start with the house price: £2349000
2. Multiply by 0.10 to find 10% of the house price: £2,349,000 x 0.10 = £234,900
3. The amount of deposit paid by Carol is £234,900.

So, the answer is £234,900.

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The requried expression that describes the cost of a talk-and-texting plan for one month, given x minutes over 600 is 35 + 0.35(x) + 20.

The expression model is described as the model of the given situation in the form of an equation using variables and constants.

here,
The cost of a talk-and-texting plan for one month can be expressed as:

= 35 + 0.35(x) + 20

where x is the number of minutes over the 600 minutes included in the plan. The first two terms represent the cost of talk time, while the last term represents the cost of unlimited texting.

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The equation which represents the number of tickets sold in advance is 0.35 × 800

Total tickets sold for a play = 800

Percentage of tickets sold in advance= 35%

Number of tickets sold in advance= Percentage of tickets sold in advance × Total tickets sold for a play

= 35% × 800

= 0.35 × 800

= 280 tickets

In conclusion, 280 tickets were sold in advance.

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Answer:

Step-by-step explanation:

The best estimate of the speed Morris is traveling will be 48 miles per hour.

What is conversion?

Conversion means to convert the same thing into different units.

Aneesha travels at a rate of 50 miles per hour. Morris is traveling 3 feet per second less than Aneesha.

We know that 1 mile = 5,280 feet.

Then convert the feet per second to miles per hour. Then the speed of the Morries will be

⇒ 3 feet / 1 second

⇒ (3 / 5285) miles / (1 / 3600) hour

⇒ (3 / 5285) x (3600)

⇒ 2 miles per hour

Then the best estimate of the speed Morris is traveling will be

⇒ 50 - 2

⇒ 48 miles per hour

The best estimate of the speed Morris is traveling will be 48 miles per hour.

Answer: The empirical rule states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.

In this case, the mean of Xochitl's finishing times is 84 seconds and the standard deviation is 2.5 seconds, so the interval that represents the middle 68% of her finishing times is:

[84 - 2.5, 84 + 2.5] = [81.5, 86.5]

So, we can conclude that the middle 68% of Xochitl's finishing times in the 400 meter race fall between 81.5 and 86.5 seconds.

Step-by-step explanation:

To properly measure the volume of water in a calibrated glass device such as a graduated cylinder, follow these steps:

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The four consecutive numbers which adds to give 130, are 31, 32, 33, 34

Numbers that follow each other continuously in the order from smallest to largest are called consecutive numbers.

Given that, there are four consecutive numbers which adds to give 130,

According to the definition of consecutive numbers, we add 1 to each previous integer to get the successive integer,

Therefore, let us consider x, x+1, x+2, x+3 be the four consecutive numbers,

Therefore,

x+x+1+x+2+x+3 = 130

4x + 6 = 130

4x = 124

x = 31

Therefore, the required consecutive integers are, 31, 32, 33, 34

Hence, the four consecutive numbers which adds to give 130, are 31, 32, 33, 34

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Answer:

23 degrees

Step-by-step explanation:

Sum of interior angles in a triangle = 180°

∴Sum of interior angles in the right- angled triangle in the question:
    67° + 90° + ? = 180°

= ? = 180° - 90° - 67°

∴ ? = Missing angle measurement = 23°

                                                           = 23 degrees

The value of length WZ is 7.5 in and angle Y is 45°

Similar shapes are enlargements of each other using a scale factor. All the corresponding angles in the similar shapes are equal and the corresponding lengths are in the same ratio. E.g. These two rectangles are similar shapes.

therefore;

WZ /QT =WX/QR

represent WZ by x

x/3 = 5/2

2x = 15

x = 15/2

x = 7.5

therefore the value of WZ = 7.5 in

Since the two quadrilaterals are similar angle Y is 45°

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Answer:

[tex]\sin A=\frac{a}{b}[/tex]

[tex]\cos A=\frac{c}{b}[/tex]

[tex]\tan A=\frac{a}{c}[/tex]

[tex]\csc A=\frac{b}{a}[/tex]

[tex]\sec A=\frac{b}{c}[/tex]

[tex]\cot A=\frac{c}{a}[/tex]

Step-by-step explanation:

Here are the definitions of the trig functions listed in the picture

[tex]\sin x=\frac{O}{H}[/tex]

[tex]\cos x=\frac{A}{H}[/tex]

[tex]\tan x=\frac{O}{A}[/tex]

[tex]\csc x=\frac{H}{O}[/tex]

[tex]\sec x=\frac{H}{A}[/tex]

[tex]\cot x=\frac{A}{O}[/tex]

Note:

[tex]A[/tex] = side adjacent to angle

[tex]O[/tex] = side opposite to angle

[tex]H[/tex] = hypotenuse

All 6 questions are about angle A.

The side adjacent to angle A is side c.

The side opposite to angle A is side a.

The hypotenuse is side b.

Therefore we can write

[tex]A=c\\O=a\\H=b[/tex]

Knowing that we can fill out the table.

[tex]\sin A=\frac{a}{b}[/tex]

[tex]\cos A=\frac{c}{b}[/tex]

[tex]\tan A=\frac{a}{c}[/tex]

[tex]\csc A=\frac{b}{a}[/tex]

[tex]\sec A=\frac{b}{c}[/tex]

[tex]\cot A=\frac{c}{a}[/tex]

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A frequency distribution usually has equal bin widths is the true statement.

All the line charts are not used for the purpose of cross-sectional data. A scatter plot is very useful in this process of visualizing trends over time. A scatter plot essentially requires two quantitative variables (i.e., not categorical data).

The difference of the maximum and minimum values is divided by the number of bins.

1. Identify the maximum and minimum values of the quantitative data.

2. Subtract the minimum value from the maximum value to get the difference

3. Divide the difference by the number of bins to get the approximate width of each bin

The width of the bins in a frequency distribution of quantitative data can be estimated by dividing the difference between the maximum and minimum values of the data by the desired number of bins. This will provide an approximate size for each bin, that can then be used to construct the frequency distribution.

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Answer:

Answer is 1/2. Box plot is split into quarters. So 1/4 + 1/4 = 1/2

The only coordinate solution in the table is (8, -9), the other coordinates are not a solution.

A linear equation is an equation that has a leading degree of 1.  Given the linear equation below:

4x + 5y = -13.

We are to determine the coordinates that form a solution.

For (8, -9)

4(8) + 5(-9) = 32 - 45

4(8) + 5(-9) = 13

Hence the coordinate (8, -9) is a solution

The other given coordinates are not a solution since the result on substituting their coordinate will not result in. -13

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Answer:

ranalllldooo

Step-by-step explanation:

suiiiiiii

Answer: y = 6x

Step-by-step explanation:

Answer:

y = 6x

In real-world terms
x = number of sandwiches

y = total cost of x sandwiches in dollar amounts

Step-by-step explanation:

The first piece of advice I have for you is to have confidence in yourself that you will succeed. That is what learners and tutors here at brainly are for. To help out.

Now to explanation of the problem and solution
The linear equation of a graph can be written in a couple of ways. On ios the standard form which is of the form
Ax + By = C where A, B and C are constants

The other is in slope-intercept form which is written as
y = mx + b

Here m is the slope which is also referred to as rise/run. I will explain these terms as we solve the problem

b is the y-intercept. This is the y-value at which the line crosses the y-axis. It corresponds to the value of y when x = 0

Sometimes the graph will not show the complete line so we cannot determine where the line crosses the y-axis. In this case this determination is a cinch

Looking at the graph, we see the line crosses the y-axis at (0,0) which is the origin

Therefore the y-intercept is 0 and hence b=0

Hence we get the line equation as

y = mx + b
==> y = mx + 0
==> y = mx

Let's find m, the slope:
Take any two points on the line. Here two points have been identified as (1, 6) and (4, 24)

The difference in y-values for these two points is 24 - 6 = 18.
This difference in y-values is known as the rise since it is measured vertically

The corresponding difference in x values is 4  - 1 = 3
This is referred to as run because it is measured horizontally

The slope m = rise/run
Here m = 18/3 = 6

Therefore plugging in m = 6 the equation in slope-intercept form is
y = 6x

Slope has another meaning. It signifies the rate of change
In this particular case in real-world terms it means that the cost of sandwiches is proportional to the number of sandwiches

Every sandwich you purchase will cost you $6 more

So the cost per sandwich is $6

For 1 sandwich -→ $6,

For 2 sandwiches → $12

For 7 sandwiches → $42

and all this is clearly evident in the graph

Hope that helps you and good luck on all your subjects

Answer

linear

nonproportional

Step-by-step explanation:

Since for each equal change in time (1 week), there is an equal change in weight (5 lb), the situation is linear.

At time zero, the first week, the weight was not zero. It was 60 lb, so it is not proportional.

Answer:

linear

nonproportional

The measure of angle X is given as follows:

40º.

We have two secants in this problem, and point C is the intersection of the two secants, hence the angle measure of x is half the difference between the angle measure of the largest arc by the angle measure of the smallest arc.

The arc angles are given as follows:

125º and 45º.

Hence the value of x is given as follows:

X = 0.5 x (125 - 45)

x = 40º.

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