How many types of fraction names are there?

The cot(θ) is positive in the first and the third quadrants and negative in the second and the fourth quadrants

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

Function: cot(θ)

Mathematically, this can be represented as

cot(θ) = 1/tan(θ)

This is the same for the cotangent function

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The slope of the line which passes through the given points (-9, -7) and (-11, -6) is calculated as: 1/2.

To find the slope of a line, we use the formula:

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

where m is the slope, and (x1, y1) and (x2, y2) are the coordinates of two points on the line.

In this case, the two points are (-9, -7) and (-11, -6), so we can plug them into the formula:

m = (-6 - (-7)) / (-11 - (-9))

Simplifying this, we get:

m = 1 / 2

So, the slope of the line that passes through (-9,-7) and (-11,-6) is 1/2.

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The slope of the line which passes through the given points (-9, -7) and (-11, -6) is calculated as: 1/2.

To find the slope of a line, we use the formula:

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

where m is the slope, and (x1, y1) and (x2, y2) are the coordinates of two points on the line.

In this case, the two points are (-9, -7) and (-11, -6), so we can plug them into the formula:

m = (-6 - (-7)) / (-11 - (-9))

Simplifying this, we get:

m = 1 / 2

So, the slope of the line that passes through (-9,-7) and (-11,-6) is 1/2.

∑ (-1)ⁿ xⁿ/n   is convergent for  x ∈ (−1,1].

Given the series ∑ (-1)ⁿ xⁿ/n

we can use the ratio test by evaluating:

n/(n+1) |x|

So we get two cases,

i) x = 1

∑ (-1)ⁿ xⁿ/n  = (-1)ⁿ/n which is the alternate harmonic series and is convergent.

ii) ∑ (-1)ⁿ xⁿ/n = ∑ (-1)ⁿ  (-1)ⁿ/n = ∑ 1/n which is the harmonic series and is divergent.

In conclusion the series is convergent for x ∈ ( -1, 1].

A power series' radius of convergence is equal to the diameter of the biggest disk at the series' convergence point. A non-negative real number or are both possible. When it is positive, the power series converges to the Taylor series of the analytical function absolutely and evenly on compact sets inside the open disk with radius equal to the radius of convergence.

The radius of convergence is the shortest or smallest of all the estimated distances from the center of the disk of convergence to each individual singularity of a function in the event of multiple singularities (singularities are those values of the argument for which the function is not defined).

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The provided polygon is a quadrilateral, and by solving it, we discovered that x is, [tex]x = 23.5^\circ[/tex]

Used the concept of angle as a quadrilateral,

The total of the angles on two adjacent sides equals 180° when there are two additional angles on the same side.

Given that,

A polygon is shown in the image.

Now from the property of the quadrilateral, the equation is,

[tex](6x+3)^\circ + (x + 12.5)^\circ = 180^\circ[/tex]

[tex]7x + 15.5 = 180[/tex]

Subtract 15.5 on both sides,

[tex]7x= 164.5[/tex]

Divide 7 on both sides,

[tex]x= 23.5^ \circ[/tex]

Therefore, the value of x is 23.5°.

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Answer:

  d.  5% decrease

Step-by-step explanation:

You want the change in price of coins bought for x dollars and sold for 0.95x dollars.

The percent change in price is given by ...

  % change = ((new price)/(old price) -1) × 100%

  % change = (0.95x/x -1) × 100% = (0.95 -1) × 100%

  % change = -0.05 × 100% = -5%

The change in the price of the coins is described as a 5% decrease.

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For a membership to be worth it to Stewart, the number of days he will have to go to the gym would be 20 days

Assuming the number of days that would make the gym membership worth it is x, the formula for finding the total cost of gyming with the membership fee is:

= 50 + 5. 50 x

The number of days as a nonmember would be:

= 8 x

The number of days till the membership is worth it is therefore:

8x = 50 + 5.50 x

8x - 5.50 x = 50

2. 50x = 50

x = 50 / 2. 50

x = 20 days

Stewart has to for for at least 20 days

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In other words,

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

Explanation:

Factor 63 and 27 such that the GCF 9 is involved.

So,

63 - 27 = 9*7 - 9*3 = 9(7 - 3)

I used the distributive rule.

A secant is a straight line that intersects a curve at two points.

For example, consider the curve y = x^2. If we draw a secant line through the points (1,1) and (3,9), the secant line will intersect the curve at those two points.

Secants are often used to approximate the slope of a curve at a particular point. For example, if you want to find the slope of the tangent line to a curve at a point x = a, you can draw a secant line through that point and another point nearby, and use the slope of the secant line to approximate the slope of the tangent line.

To find the slope of the tangent line using a secant line, you can use the following formula:

where (x1, y1) and (x2, y2) are points on the secant line.

By taking the limit of this formula as x2 approaches x1, we can find the slope of the tangent line at the point where x = x1. This is known as the limit definition of the derivative.

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Answer:

x = 18

Step-by-step explanation:

Solve for x:

6.2 = x - 11.8

6.2 = x - 11.8 is equivalent to x - 11.8 = 6.2:

x - 11.8 = 6.2

Add 11.8 to both sides:

x + (-11.8 + 11.8) = 11.8 + 6.2

11.8 - 11.8 = 0:

x = 6.2 + 11.8

6.2 + 11.8 = 18:

Answer: x = 18

Answer:

x-11.8=6.2

Step-by-step explanation:

add 11.8 for both sides

then x=11.8+6.2

the result of adding is 18

x=18.0

S.S={18.0}

The data set that could be represented by the box plot would be = 32,36,27,30,35,39,28,34. That is option D.

The box plot is defined as the type of data representation that is used in descriptive statistics to show the distribution of numerical data such as the number of hours Judy takes to complete a quilt.

The characteristics of the box plot is that is shows the outliers, the median, and the mode of the given numerical data.

Therefore, the data set that could be represented by the box plot would be = 32,36,27,30,35,39,28,34.

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Answer:

See below

Step-by-step explanation:

[tex]f(x)=|x-2|\\f'(x)=\frac{x-2}{|x-2|}\\f'(2)=\frac{2-2}{|2-2|}=\frac{0}{0}[/tex]

So, the function is not differentiable at x=2.

The range of the function represented by the graph is 1 ≤ y ≤4. The correct option is c.

These visual representations include tables and graphs. They are employed to arrange data in order to highlight patterns and correlations. This information is displayed as a shape on a graph.

To present the results of their research, scientists and researchers frequently employ tables and graphs. Graphs present information to you as a picture or visual representation. This knowledge is referred to as "data." When you put data into a picture, it can appear lean or bulky, lengthy or short.

Therefore, the correct option is c, 1 ≤ y ≤4.

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Answer:

First option:
1.2076

Step-by-step explanation:

Just use the standard deviation functionality of any scientific/statistical calculator.

The answer is 1.2076 which is the first option

The percent error of the measurement is -1.2%, to the nearest tenth of a percent.

To calculate the percent error, we need to use the following formula:

Percent Error = (Actual Value - Measured Value) / Actual Value x 100

In this example, the actual value is 8.6 inches and the measured value is 8.7 inches. Plugging these values into the formula, we get:

Percent Error = (8.6 - 8.7) / 8.6 x 100

Simplifying, this gives us:

Percent Error = -0.1 / 8.6 x 100

Finally, we can calculate the percent error to the nearest tenth of a percent:

Percent Error = -1.2%

Therefore, we can conclude that the percent error of the measurement is -1.2%, to the nearest tenth of a percent.

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Considering the figure the height of  the tree is calculated to be 97.7 feet

The height of the tree is calculated using the trigonometry relation having the pneumonic SOH CAH TOA this is a short form for

Sin = opposite / hypotenuse - SOH

Cos = adjacent / hypotenuse - CAH

Tan = opposite / adjacent - TOA

The image describes a right angle triangle of

opposite = height of the tree

adjacent = distance from the tree

The bearing is calculated using tan, TOA

tan 60 = h / WX

h = WX tan 60

Also, tan 40 = h / (60 + WX)

h = (60 + WX) tan 40

hence, equating both h

WX tan 60 = (60 + WX) tan 40

WX tan 60 = 60 tan 40 + WX tan 40

make WX the subject of the formula

WX tan 60 - WX tan 40 = 60 tan 40

WX (tan 60 - tan 40) = 60 tan 40

WX = 60 tan 40 / (tan 60 - tan 40)

substituting WX to h = WX tan 60

h = (60 tan 40 / (tan 60 - tan 40) ) * tan 60

h = 97.6557 feet

h = 97.7 feet to the nearest tenth

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The wavelength of the given speed and frequency would be = 0.062m

Speed is defined as the distance a wave travels in a given amount of time, such that it is measured in meters per second.

The frequency of a wave is defined as the number of cycles that can be completed in a given time. This is measured in Hertz (Hz).

The wavelength is defined as the distance if a wave which can be measured in meters.

The formula for wave speed = v = fλ

Where v = Speed = 5.410x10⁴

f = 872khz = 872000hz

λ = ?

make λ the subject of formula;

λ = 5.410x10⁴/872000

λ = 54100/872000

λ = 0.062m

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Answer:

[tex]10a-4[/tex]

Step-by-step explanation:

[tex]2(3a-2)+4a=(6a-4)+4a=10a-4[/tex]

The number of pre-sale tickets must she sell to make her goal is (c) 200

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

These parameters can be represented using the following system of equations

10x + 15y = 3500

x + y = 300

The graph that completes the question is added as an attachment

From the graph, we have

(x, y) = (200, 100)

The variable y represents the number of pre-sale ticket

So, we have

x = 200

Hence, the number of pre-sale ticket is (c) 200

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Answer:

C, 200

Step-by-step explanation:

An easier way to get the answer in this case would be to see where the 2 lines meet, which is at 200 pre-sale tickets :))

Numbers greater than 500 can be obtained using the digits 2345 is 30.

A number is an arithmetic value used for representing the quantity and used in making calculations. A written symbol like “3” which represents a number is known as a numeral. A number system is a writing system for denoting numbers using digits or symbols in a logical manner.

The following numbers can be formed using the given numbers that are greater than 500:

523, 532, 542, 543, 524, 534, 2345, 2435, 2354, 2453, 2543, 2534, 3245, 3254, 3425, 3452, 3542, 3524, 4235, 4253, 4325, 4352, 4523, 4532, 5234, 5243, 5432, 5423, 5342 and 5324.

Thus, Numbers greater than 500 can be obtained using the digits 2345 is 30.

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There are numbers greater than 500 can be obtained using the digits 2345 is 30

The combination method is defined as the way of selecting objects or numbers from a group of objects or collections, in such a way that the order of the objects does not matter.

Here we have to find the numbers that are greater than 500 can be obtained using the digits 2345.

By using the given digits, we have created the following number that are greater that 500 as listed as follows:

=> 523, 532, 542, 543, 524, 534, 2345, 2435, 2354, 2453, 2543, 2534, 3245, 3254, 3425, 3452, 3542, 3524, 4235, 4253, 4325, 4352, 4523, 4532, 5234, 5243, 5432, 5423, 5342 and 5324.

Therefore, the total resulting number is 30.

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The Third Angles Theorem states that if two angles of a triangle are equal, then the third angle must also be equal to the other two.

This theorem can also be stated as "the measure of the third angle of a triangle is equal to the sum of the measures of the two known angles." This theorem can help solve for missing angles in a triangle and can also be used to determine if the given triangle is right-angled, obtuse-angled, or acute-angled. Additionally, this theorem is related to the Triangle Inequality Theorem which states that the sum of any two sides of a triangle must be greater than the third side.

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The expression x⁻². x⁻¹.x⁶ can be simplified as x³.

An algebraic expression is consists of variables, numbers with various mathematical operations,

The given expression is,

x⁻². x⁻¹.x⁶

Simplify the expression,

By using multiplying property,

x⁻²⁺⁽⁻¹⁾⁺⁶

x ⁻²⁻¹⁺⁶

x⁻³ ⁺ ⁶

x³

The simplified form of the expression x⁻². x⁻¹.x⁶ is x³.

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Answer: 181.61

Step-by-step explanation:

130 x 139.7

----------------    =181.61

100

Teaching angles to 5th graders can be a fun and engaging process.

Here are a few strategies that you can use to help students understand angles:

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The ratio of the given conversion units is; 24:5

Conversion of units is defined as the conversion between different units of measurement for the same quantity, and this is typically done through multiplicative conversion factors that change the measured quantity value without changing its effects.

Now, we are given a ratio of yards to inches but to get an effective ratio without units, we need to convert them to the same units.

Now, from conversion of units, we know that;

1 yard = 36 inches

Thus;

4 yards = 4 * 36 = 144 inches.

Thus;

The ratio = 144:30

This can be simplified to 24:5

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The coordinate (x, y) of the midpoint is (2, 15)

The midpoint of a line is a point halfway between the two endpoints of the line, such that the line is divided into two equal segments. The coordinates of the midpoint can be found by taking the average of the x-coordinates of the endpoints and the average of the y-coordinates of the endpoints.

The formula of midpoint of a line is given as;

M = [(x₂ + x₁) / 2], [(y₂ + y₁) / 2]

The coordinates given are;

M = [(-9 + 3) / 2], [(11 + 19) / 2]

M = (6/3) , (30/2)

M = 2, 15

The midpoint is (2, 15)

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In the 7th year, Marco will get compounded interest greater than $5, so he will have to keep money in the bank without withdrawing for 6 years.

Simple Interest: is the interest based on the principal amount.

Compound Interest: is the interest based on the principal amount and the interest  that accumulates on it every year.

So 5% simple interest on $100 =   *100 =$5

So the compound interest needs to be greater than $5 .

Lets calculate the  compound interest over the years.

1st Year:   *100 =$4

2nd Year: Now to calculate the interest in second year the interest in first year will be accumulated. So interest will be calculated on 100 +4 =$104

4/100*104 =$4.16

3rd Year: Again interest from 2nd year will be added

4/100*108.16 =$4.33

4th Year: Again interest from 3rd year will be added

4/100*112.49 =$4.49

5th Year:

4/400*116.99 =$4.68

6th Year:

*121.67 =$4.87

7th Year:

*126.54 =$5.06

In the 7th year, Marco will get compounded interest greater than $5, so he will have to keep money in the bank without withdrawing for 6 years.

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In the given situation we have to drive at the speed of 75 miles per hour.

The speed at which an object's location changes in any direction.

The distance traveled in relation to the time it took to travel that distance is how speed is defined.

Since speed simply has a direction and no magnitude, it is a scalar quantity.

The speed of an item, which is a scalar quantity in everyday usage and kinematics, is the size of the change in that object's position over time or the size of the change in that object's position per unit of time.

So, we know that:
We must drive the first 25 miles at 40 miles per hour.

We have a time of 20 minutes.

20 minutes = 1/3 hour

Then our speed will be:

25 ÷ (1/3)

25 * 3/1

75 miles per hour

Therefore, in the given situation we have to drive at the speed of 75 miles per hour.

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The pair of angles 30⁰ and 30⁰ are supplementary angles.

Examples of additional angles

Angles with a supplementary sum are those whose sum is 180 degrees. For instance, the sum of angle 130° and angle 50° is 180°, hence they are supplementary angles. In the same way, complimentary angles sum to 90 degrees.

Supplementary angles may have three angles.

Three angles can't be added together. Two angles whose sum of the measures is exactly 180 degrees are supplementary angles, according to the definition. Even if three angles, such as 60 degrees, 30 degrees, and 90 degrees, sum up to 180 degrees, they would not be referred to as supplementary angles.

Supplementary angles add up to 180 degrees. An angle is supplementary to another angle if the sum of the measures of the two angles is 180 degrees. So, 30 + 30 = 60 which is supplementary.

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Let's consider what the question asks for:

 --> find the value of 'x'

The function gives us a quadrilateral

  --> separated into two triangles

In the triangle that has one angle with measure 65 degrees

 -->it is an isosceles triangle thus the top most angle in that triangle is also

     65 degrees

      --> the other unknown angle is, therefore:

                [tex]\text{unknown angle} + 65 + 65 = 180\\\text{unknown angle}+130=180\\\text{unknown angle}=180-130=50\\\text{unknown angle}=50[/tex]

Now that unknown angle forms a complementary relationship with the angle of the other triangle.

   [tex]50 + \text{bottom most angle of other triangle}=90\\\text{bottom most angle of other triangle}=90-50\\\text{bottom most angle of other triangle}=40[/tex]

Now that the bottom triangle

  --> has an angle with measure 'x'

    --> that triangle is also an isosceles

      --> meaning that our triangle's angle looks like this

              [tex]40 + x+x+180\\2x+40=180\\2x=140\\x=70[/tex]

Answer: 70

Waiter is given $10.52 and total bill including tax and tip = $67.33

Tip is the amount of money given by the customer himself so as to express the gratitude towards the hospitality from a particular service sector.

before tax paying cost for food = $52.60

sales tax rate is 8%

so, the amount of tax = $52.60 × 8/100 = $ 4.21

If 20% tip is given by customer, then the amount of tip =$52.60 × 20/100

amount of tip = $10.52

Waiter is given $ 10.52.

total bill including tax and tip = $52.60 + $4.21 + $10.52

                                               = $67.33

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