What is the integral of 1/(1-x^2)?

The given triangles are similar by SSS theorem

The given figures are similar triangles with 3 sides and angles. There are several ways triangles can be proved to be similar such as the AAS, SSS, SAS etc theorems.

For the given triangles, if the ratio of their similar sides is equivalent  to the same constant, then the triangles are similar.

AC/HF = AB/HG = CB/GF = k

84/14 = 72/12 = 48/8

84/14 = 6

72/12 = 6

48/8 = 6

Since the ratios are all equal, hence the triangles are similar

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To find 10 percent of 20000, you can multiply 20000 by 0.1, which gives you the answer of 2000.

0.1 × 20000 = 2000.

Here's the explanation of the calculation: When we want to find a certain percentage of a number, we can convert the percentage into a decimal by dividing it by 100. In this case, 10% is equivalent to 10/100, which simplifies to 0.1. Then, we can multiply 20000 by 0.1 to find the answer, which is 2000. In summary, to find 10% of a number, we can convert the percentage into a decimal by dividing it by 100, and then multiply the decimal by the original number.

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IQR =  16.5

The range = 31

Mean absolute deviation = 9.5

The median is the value that splits the mathematical numbers or expressions in the half. The median value is the middle number of data points. to find the median first arrange the data points in ascending order.

Given:

A data set:

15, 22, 16, 13, 14, 20, 40, 44.

The lower half of median Q1 = (14 + 15)/2 = 14.5

The upper half of median Q3 = (40 + 22)/2 = 31

So IQR = Q3 - Q1 = 31 - 14.5 = 16.5

The range = 44 - 13 = 31

Mean absolute deviation = 9.5

Therefore, MAD = 9.5.

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the probability P(X<-2), we use the cumulative distribution function F(x) = 0 for x < -2. We plug in -2 for x in the function to get F(-2) = 0.

a. P(X<1.8) = .25(1.8) + .5 = .95

b. P(X>-1.5) = .25(-1.5) + .5 = .375

c. P(X<-2) = 0

d. P(-1.5<X<2) = .25(2) + .5 - (.25(-1.5) + .5) = .875

a. For the probability P(X<1.8), we use the cumulative distribution function F(x) = 0.25x + 0.5 for -2 <= x < 2. We plug in 1.8 for x in the function to get F(1.8) = 0.25(1.8) + 0.5 = 0.95. Therefore, P(X<1.8) = 0.95.

b. For the probability P(X>-1.5), we use the cumulative distribution function F(x) = 0.25x + 0.5 for -2 <= x < 2. We plug in -1.5 for x in the function to get F(-1.5) = 0.25(-1.5) + 0.5 = 0.375. Therefore, P(X>-1.5) = 0.375.

c. For the probability P(X<-2), we use the cumulative distribution function F(x) = 0 for x < -2. We plug in -2 for x in the function to get F(-2) = 0. Therefore, P(X<-2) = 0.

d. For the probability P(-1.5<X<2), we use the cumulative distribution function F(x) = 0.25x + 0.5 for -2 <= x < 2. We plug in -1.5 and 2 for x in the function to get F(-1.5) = 0.25(-1.5) + 0.5 = 0.375 and F(2) = 0.25(2) + 0.5 = 0.95. Therefore, P(-1.5<X<2) = 0.95 - 0.375 = 0.875.

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Answer: The graph of y = 3/4 is a horizontal line with y-intercept at 3/4. When this graph is translated, its y-intercept changes, while its slope remains the same.

Since the new graph has asymptotes at x = -5 and y = 14, the new equation must be of the form y = m(x + 5) + 14, where m is the slope of the original line, which is 3/4. Substituting the values, we get:

y = (3/4)(x + 5) + 14

So the equation of the translated graph is y = (3/4)(x + 5) + 14.

Step-by-step explanation:

The height of the cylindrical package is 6 inches.

The new volume of the package is 88.26 cubic inches.

A cylinder is a 3-D figure that has a radius and a height.

The volume of a cylinder is given as πr²h.

Example:

The volume of a cup with a height of 5 cm and a radius of 2 cm is

Volume.

= 3.14 x 2 x 2 x 5

= 62.8 cm³

We have,

Part A:

The formula for the volume of a cylinder is V = Bh, where B is the area of the base of the cylinder and h is its height.

For a cylinder with radius r and height h, the base area B is given by

B = πr².

Substituting the given values, we have:

V = Bh

87.92 = π(2²)h

h = 87.92 / (4π)

h ≈ 5.57

Rounding to the nearest inch, the height of the cylindrical package is 6 inches.

Part B:

If the company doubles the height of the cylinder while keeping the radius the same, the new height will be 2h = 2(5.57) = 11.14 inches.

The new volume can be calculated using the same formula:

V = Bh

V = π(2²)(11.14)

V ≈ 88.26 cubic inches

Rounding to the nearest hundredth, the new volume of the package is 88.26 cubic inches.

Thus,

The height of the cylindrical package is 6 inches.

The new volume of the package is 88.26 cubic inches.

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Answers:

(12, 7)

(20, 11)

(32, 17)

There are infinitely many possible answers.

=======================================================

Explanation:

The equation given to us is the same as y = 0.5x+1 because 1/2 = 0.5

If we replace x with even numbers, then we'll get whole number outputs for y.

Example: if x = 12, then y = 0.5x+1 = 0.5*12+1 = 7

This leads to (12,7) as one solution to this equation. A solution is a point that is on the line. Use graphing software like Desmos or GeoGebra to confirm.

Another example: if x = 20, then y  = 0.5x+1 = 0.5*20+1 = 11. Therefore, another solution point is (20, 11)

Final example: If x = 32, then y = 0.5x+1 = 0.5*32+1 = 17. This gives the point (32,17)

There are infinitely many possible answers since we can replace x with infinitely many real numbers.

Answer:

The total cost of putting on the play is $500 for theater rental + $500 for actors + $750 for set decorations and costumes = $1750.

To reach the break-even point, the revenue from ticket sales needs to equal the total cost, so $1750 = $25 x (number of tickets sold).

Solving for the number of tickets sold, we can divide both sides by $25: $1750 / $25 = (number of tickets sold).

This gives us: 70 = number of tickets sold.

Therefore, Mr. Curry needs to sell 70 tickets to reach the break-even point.

Step-by-step explanation:

Answer:

indicates the relationship of two variables whenever one variable changes.

Step-by-step explanation:

Answer:

23736 x 2858

= 67837488

Step-by-step explanation:

You're welcome.

Answer:

67837488

Step-by-step explanation:

24 X 3 X 23 X 43 X 1429

The area of the field is 900√10 m².

Pythagorean theorem states that for a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

We can apply this theorem only in a right triangle.

Example:

The hypotenuse side of a triangle with the two sides as 4 cm and 3 cm.

Hypotenuse side = √(4² + 3²) = √(16 + 9) = √25 = 5 cm

We have,

Quadrilateral ABCD.

The longer diagonal connects vertices A and C, and let E and F be the feet of the perpendiculars from vertices B and D to the longer diagonal AC.

From the figure,

BE = 20 m

DF = 30 m

AE = EC = 120/2 = 60 m

Now,

The area of the quadrilateral.

The area of a trapezoid.

= (sum of parallel sides) x (height) / 2

Using the Pythagorean theorem,

AB² = AE² + BE²

60² + 20² = 4000

AB = √(4000)

AB = 20 √10

And,

CD² = CE² + DF²

CD² = 60² + 30²

CD² = 4500

CD = √(4500)

CD = 15 √20

Now,

Area = AB + CD x 1/2 x AC

= 20√10 + 15√20 x 1/2 x 120

= 900√10

Therefore,

The area of the field is 900√10 m².

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The correct response is C. 0.0036 Square degrees The field of vision of the Hubble Space Telescope is only 0.006 degrees, which is around 100 times less than that of the Micro Observatory telescopes. But it has a 100 times better angular resolution!

Skywatchers can readily view planets with just a modest or medium-sized telescope. How much of our solar system is visible will wow you! Additionally, you don't need a completely dark sky to see all of the planets in our solar system; a telescope can still make Venus, Mars, Jupiter, and Saturn easily visible even when viewed in a city. From $100 to well over $10,000, a telescope can be purchased. In 2022, you can anticipate that a good telescope for visual observing will start around $300 and a telescope capable of deep-sky astrophotography would start around $800. With a 25x telescope, even the tiniest telescope should be able to see Saturn's rings.

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Large telescopes often have small fields of view. For example, the Hubble Space Telescope's (HST's) advanced camera has a field of view that is roughly square and about 0.06 degree on a side. Calculate the angular area of the HST's field of view in square degrees.

A. 0.006 Square degrees

B. 0.36 Square degrees

C. 0.0036 Square degrees

D. 0.06 Square degrees

Julie is correct. If n=0 then you would get the fraction [tex]\frac{0}{0}[/tex] which is indeterminant (or undefined) since a zero is present in the denominator.

Answer:

(3,4)

k is 4

Step-by-step explanation:

See attached graph.

Answer:

yes

Step-by-step explanation:

if i did the math right marcy should have enough

To calculate the arc length of a circle, you need to use the formula: arc length = (central angle in radians) x (radius)

where the central angle is measured in radians and the radius is the distance from the center of the circle to the edge. To use this formula, first convert the central angle from degrees to radians by multiplying it by π/180. Then, multiply the result by the radius to find the arc length. For example, if you have a circle with a radius of 5 units and a central angle of 45 degrees, you can calculate the arc length as follows: Convert the central angle to radians: 45 x π/180 = 0.7854 radians. Multiply the central angle in radians by the radius: 0.7854 x 5 = 3.927 unit. Therefore, the arc length of a circle with a radius of 5 units and a central angle of 45 degrees is 3.927 units.

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Answer: 16.8 miles

Step-by-step explanation:

Multiply 2.8 miles by 6 to find the number of miles jogged after 6 days.

Answer:

16.8 miles!

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Using the formula for compound interest:

A = P(1 + r/n)^(nt)

where:

A = final amount

P = principal (starting amount)

r = annual interest rate (as a decimal)

n = number of times interest is compounded per year

t = time (in years)

We can plug in the given values:

P = $1,500

r = 0.0825 (8.25% expressed as a decimal)

n = 1 (compounded annually)

t = 2

A = $1,500(1 + 0.0825/1)^(1*2)

A = $1,500(1.0825)^2

A = $1,757.71

Therefore, the total balance after 2 years will be $1,757.71. Answer choice B is correct.

The solution to the equations have the coordinates of (-6.61, 9.91) and (0.61, -0.91)

From the question, we have the following parameters that can be used in our computation:

f(x) = − ³/2 x and g(x) = (½)² – 1

Express the equation properly

So, we have

f(x) = -3/2x

g(x) = (1/2x)^2 - 1

Next, we make a plot of the system to determine the solution

The point of intersection in the plot represent the solution to the equations

In this case, the point of intersection has a coordinate of (-6.61, 9.91) and (0.61, -0.91)

Hence, the solution is (-6.61, 9.91) and (0.61, -0.91)

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The value of r is 2.134

in the equation, we would first

add 2.4

to both sides:

5.2r - 2.4 + 2.4 = 8.7+ 2.4

5.2r = 11.1

now we will

divide both sides by 5.2

to isolate the variable "r"

[tex]\frac{5.2r}{5.2} = \frac{11.1}{5.2}[/tex]

1r = 2.13461538

thus, the value of r = 2.134 approximately

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A) An algebraic expression that could be used to model the situation where a horse's weight decreases by ¹/₂ pounds weekly is w/r, where w is the total weight lost and r is the constant rate of weight loss.

B) Using division operation and decreasing rate, if a horse's weight decreases by ¹/₂ pounds weekly, it will take the horse 11 weeks to lose a total of 5¹/₂ pounds.

An algebraic expression combines constants, variables, and mathematical operations (+, -, ×, ÷) without the equal sign (=) found in equations.

While equations show the equality of expressions, algebraic expressions merely state values.

Division operation is one of the four basic mathematical expressions, including addition, subtraction, and multiplication.

Division operations involve the dividend, the divisor, the equal sign (=), the division operand (÷), and the result called the quotient.

The total weight loss over time = 5¹/₂ pounds

The constant rate of weight loss = ¹/₂ pounds per week

The number of weeks for the horse to lose 5¹/₂ pounds = 11 weeks (5¹/₂ ÷ ¹/₂).

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An alpha value of 0.05 means that there is a 5% chance of incorrectly rejecting the null hypothesis.

In statistics, "alpha" is used to represent the significance level in a hypothesis test. The significance level, denoted by α, is the probability of rejecting the null hypothesis when it is actually true.

In other words, if the p-value in a hypothesis test is less than or equal to 0.05, we can reject the null hypothesis and conclude that there is a statistically significant difference between the groups or variables being tested.

An alpha value of 0.05 is commonly used in research studies, but other values such as 0.01 or 0.10 may also be used depending on the desired level of significance.

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The sum of deviations of the individual observations from their sample mean is always equal to zero.

The sum of deviations of the individual observations from their sample mean is always equal to zero. This is because the sum of all the deviations is the sum of a positive and a negative value. When we add the negative value to the positive value, the net result is always zero.To illustrate this, let's take an example. Suppose we have a sample of 5 observations: 2, 4, 6, 8, 10. The mean of the sample is 6. The deviations of the individual observations from the sample mean can be calculated as follows:

2-6=-4

4-6=-2

6-6= 0

8-6= 2

10-6=4

When we add the deviations, we get: -4+(-2)+0+2+4=0. The sum of all the deviations is always equal to zero.

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The diameter of the circle is 396 units

The diameter is the length of the line through the center that touches two points on the edge of the circle.

A diameter is twice the radius of a circle.All diameters are segment but not all segments are diameter.

length of an arc = tetha/360 × πd

l = 80/360 × π d

88π = 80/360 × π d

80d = 88× 360

80d = 31680

divide both sides by 80

d = 31680/ 80

d = 396 units

therefore the diameter of the circle is 396 units

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The system of equations can be written as:-

10x + 4y = 42

6x + 8y = 14

A system of equations, also known as a set of simultaneous equations or an equation system, is a finite set of equations for which we sought common solutions in mathematics. A system of equations can be classified in the same way that a single equation can.

Given that in an online quiz, positive points are awarded for a correct answer, and negative points are awarded for an incorrect answer. Elena answers 10 questions correctly and 4 incorrectly and scores 42 points. Kiran answers 6 questions correctly and 8 incorrectly and scores 14 points.

The system of equations can be written as:-

10x + 4y = 42

6x + 8y = 14

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The linear equation represented by the graph is y = 8x.

A linear equation is a mathematical equation that describes a straight line in a two-dimensional space. It can be written in the form of:

y = mx + b

where y and x are variables, m is the slope of the line, and b is the y-intercept of the line (the point where the line crosses the y-axis).

The slope, represented by "m", describes the steepness of the line, while the y-intercept, represented by "b", is the point where the line intersects with the y-axis.

Linear equations can also be written in other forms, such as the standard form:

Ax + By = C

where A, B, and C are constants, and x and y are variables. In this form, the equation describes a line in terms of its x and y intercepts.

Linear equations are used in a variety of fields, including mathematics, physics, engineering, economics, and more. They are useful for describing and predicting relationships between variables that exhibit a linear pattern.

The equation represented by the graph is a linear equation in the form of y = mx + b, where m is the slope and b is the y-intercept.

To find the slope, we can use the formula:

m = (y2 - y1)/(x2 - x1)

Let's choose the first two points (0.5, 4) and (1, 8):

m = (8 - 4)/(1 - 0.5) = 8

So, the slope is 8.

To find the y-intercept, we can use the point-slope form of the equation:

y - y1 = m(x - x1)

Let's choose the point (0.5, 4) and the slope we just found:

y - 4 = 8(x - 0.5)

y - 4 = 8x - 4

y = 8x

So, the linear equation represented by the graph is y = 8x.

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The percentage error made by the person is 25%.

To get the percentage error, multiply the relative error by 100%. In other words, first, calculate the difference between the true value and the measured value. Then, divide the obtained difference by the true value. Then take the absolute value of the obtained result and multiply it by 100%.

The measured value is 4 feet.

The true value is 3.2 feet.

So, the difference between the true value and the measured value is (4 feet - 3.2 feet), that is, 0.8 feet.

Now, divide the obtained difference by the true value.

(0.8 feet)/(3.2 feet) = 1/4

= 0.25

To get the percentage error, take the absolute value of the obtained result and multiply it by 100%.

|0.25|×100% = 0.25×100%

= 25%

Therefore, the obtained answer is 25%.

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d)  whenther there the limit is going to infinity like that

take the large term on the top and the largest one on the bottom

so;

4x^5/12x^2 =

basically if you continued to plug it in it would give you

4x^5/12x^2

eventually 12x^2 would = 24 because you would get 12x^2 to 24x^1, take the dervative = 24

for the top it would go from 4x^5; 20x^4; 80x^3

then you would have 80x^3/24

plug in infinity for x

infinity/24

The distance is decreasing at a rate of 1028.30 miles/hour.

An indicator of how one quantity changes in proportion to another is called a rate of change. If x and y are the independent and dependent variables, respectively, then rate of change is equal to y-to-x conversions. Positive or negative change rates are possible.

Plane X: The first plane is due west of you, or at x = -280

traveling towards you at 560 mph

Plane Y: The second plane is due south of you, or at y = -450

traveling towards you at 900 mph.

D = Distance between the two planes.

D = √( x² + y² )

d/dt [ D ] = d/dt [ √( x² + y² ) ]

dD/dt = 1 / 2√( x² + y² ) (2XX' + 2YY')

dD/ dt = 1/2 √(-280)² + (-450)² (2 (-280)(560) + 2(-450)(900)

dD/ dt = 1/2 √(-280)² + (-450)² (2 (-280)(560) + 2(-450)(900))

dD/ dt = 1/ 530 (-140,000 - 405, 000)

dD/ dt = -1028.30

Thus, The distance is decreasing at a rate of 500 miles/hour  

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