Two different decimals that are the same value when rounded to the nearest tenth.

The value of the trigonometric functions cos 2θ and cos 0.5θ for the given angle are - 7 / 25 and - 2√5 / 5, respectively.

In this problem we must determine the cosine of the double angle and half angle based on the exact values of the cosine of an angle and the quadrant location of the angle.

Cosine is a function between - 1 and 1 and whose period is 2π (360°), positive when angle is either on first quadrant (0 < θ < 0.5π) or on fourth quadrant (1.5π < θ < 2π). In addition, sine function is positive on first quadrant and negative on fourth quadrant.

The required trigonometric formulas in terms of trigonometric function cos θ are described below:

sin θ = √(1 - cos² θ)

cos 2θ = cos² θ - sin² θ

cos 0.5θ = ± √ [(1 + cos θ) / 2]

First, determine the exact value of sine:

sin θ = - √[1 - (3 / 5)²]

sin θ = 4 / 5

Second, determine the exact value of cosine of the double angle:

cos 2θ = (3 /  5)² - (4 / 5)²

cos 2θ = - 7 / 25

Third, determine the exact value of cosine of the half angle:

cos 0.5θ = - √[(1 + 3 / 5) / 2]

cos 0.5θ = - 2√5 / 5

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Answer:

6

Step-by-step explanation:

Answer: 15% of 40 is 6.

Let's find 15% of 40.

Explanation:

15% of 40 can be written as 15% × 40

= 15/100 × 40

= 6

Thus, 15% of 40 is 6.

Answer:28

Step-by-step explanation:

Answer:

Step-by-step explanation:

Fraction: 3/10 decimal: 0.30

Answer:

Fraction: 3/10; Decimal: 0.3

Step-by-step explanation:

A). When trying to find the fraction of percent, the denominator is always 100 since the word percent itself states "per-cent," meaning per 100 as a cent can go up to a maximum of 100 before being converted into a dollar. Therefore, the fraction then becomes 30/100, however, we need to simplify it as stated by the question and we can easily do that by canceling out one zero on the numerator and the denominator, giving us the simplified fraction of 3/10.

B). Now, to find the decimal, we just have to divide the numerator by the denominator and dividing 3 by 10 gives us a decimal of 0.3. This decimal has already been rounded to the nearest hundredth since it is in the tenths place, so thus, there is a continuation of zeroes after the 3 infinitely. Therefore, the decimal rounded to the nearest hundredth is 0.3.

Hope this helped!  :D

A function is defined as a relation that assigns exactly one output to each input. Since each input in this set is paired with exactly one output, the set is a function.

A. (1,2), (3,4), (5,6)

Yes, this set of ordered pairs is a function. A function is defined as a relation that assigns exactly one output to each input. Since each input in this set is paired with exactly one output, the set is a function.

B. (1,2), (2,4), (3,6)Yes, this set of ordered pairs is a function. A function is defined as a relation that assigns exactly one output to each input. Since each input in this set is paired with exactly one output, the set is a function.

The key features of a function include: (1) It is a relation that assigns exactly one output to each input; (2) The input values must be distinct from each other (no repeated values); (3) The output values can be the same as one another (so there can be repeated values); and (4) It has a domain (set of input values) and a range (set of output values).

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Answer: 57

Step-by-step explanation:

The five number summary of the given data is the minimum value = 20, maximum value = 100, median = 69.5, Q1 = 48, and Q3 = 89.

A number summary consists of five values: the most extreme values in the data set (the maximum and minimum values), the lower and upper quartiles, and the median. In order to find the five number summary,

1. Arrange the given data in ascending order. In the given case, the data is already in ascending order.

2. Determine the minimum and maximum value for the data set. In the given case, the minimum value is 20 and maximum value is 100.

3. Determine the median of the data set. The median refers to the middle number of the data set. If the data is an even set of numbers, the middle two terms are averaged. In the given case, there are 14 numbers, hence the median is an average of 7th and 8th term.

Median = (69 + 70)/2 = 69.5

4. Determine the lower quartile (Q1) and upper quartile (Q3). The Q1 and Q3 are the middle term of the lower and upper range respectively.

For the lower range, 20, 33, 43, 48, 64, 68, 69, the middle term is 48. Hence Q1 = 48.

For the upper range, 70, 72, 83, 89, 96, 99, 100, the middle term is 89. Hence Q3 = 89.

Note: The question is incomplete. The complete question probably is: Find the 5 number summary for the data shown. 20, 33, 43, 48, 64, 68, 69, 70, 72, 83, 89, 96, 99, 100

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Mathematically, a line is a group of infinite points. In another word, a line expands endlessly in both directions. It is a one-dimensional figure with no limit, both to the left and to the right.

Types of lines: There are various types of lines used in everyday life.

1) Curved Lines: A line that is not straight is a curved line. If a point does not proceed in one direction, get a curve.

2) Straight Lines: The shortest line joining any two points is a straight line.

3) Horizontal Lines: A horizontal line is a line that passes from left to right in a straight line.

4)Vertical Lines: Vertical lines move up and down from top to bottom or bottom to up.

5) Parallel Lines: In geometry, parallel lines can be determined as two lines in the same plane that are at an equal distance from each other and never meet.

6) Intersecting Lines: When two or more lines cross each other in a plane, they are called intersecting lines. The intersecting lines share an ordinary point, which lies on all the intersecting lines.

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The cost for 3 feet of lace based on the information provided is 9 dollars.

Based on the information given, a foot of lace costs $3 (3 dollars).

In this case, the mathematical operation that needs to be applied is multiplication as were are given the price for 1 unit and we need to calculate the equivalent price for 3 units.

Multiplication implies adding equal groups, in this case we will need to add 3 times the initial price to find the final price. Based on this, we need to multiply the price by 3 as it is shown below:

Price for 1 foot = $3

Price for 3 feet=

$3 per feet x 3 = $9

This means that for 3 feet of lace Cheryl will need to pay a total of $9 (nine dollars).

Note: This question is incomplete; here is the complete question:

Cheryl is buying lace for her dance costume.  of lace costs . How much does each length of lace cost?

3 feet

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The cost of each length of the lace is 7.2 dollars.

Cheryl is buying lace for her dance costume. One foot of lace cost 3 dollars. The length of each lace is 2 2 / 5 feet.

The cost of each length of lace can be calculated as follows:

Therefore, using proportion.

1 feet = 3 dollars

2 2 / 5 feet(12 / 5 feet)  =  ?

cross multiply

cost of the length of a lace = 12 / 5 × 3

cost of the length of a lace = 36 / 5

cost of the length of a lace = 7.2 dollars.

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It will take to complete the entire order of sneakers in 8 days.

To find out how long it will take to complete the entire order of sneakers, you need to multiply the time it takes to complete 1/10 of the order by the total number of orders. Since there are 10 orders in the entire order of sneakers, it will take 10 times as long to complete the entire order as it does to complete 1/10 of the order.

Since it takes 4/5 of a day to complete 1/10 of the order, it will take 4/5 * 10 = 8 days to complete the entire order. Therefore, the answer is 8 days.

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At given rate, it will take 8 days to complete the entire order of sneakers

In this questiion we have been given at Sami's Shoe Warehouse, it takes 4/5 day to complete 1/10 of an order of sneakers.

We need to find the number of days it will take to complete the entire order of sneakers, at this rate.

It takes 4/5 day to complete 1/10 of an order of sneakers.

If we multiply a fraction by 10 then it would be 10/10

This means, 10/10 represents the complete order of sneakers.

4/5 days are required to complete 1 of 10 order of sneakers.

For 10 of 10 order of sneakers:

By unitary method,

10 × 4/5

= 2 × 4

= 8 days

So, it will take 8 days to complete the order.

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Answer:

it's 290

Step-by-step explanation:

[tex] \frac{290}{29} + 156[/tex]

[tex]10 + 156 = 166[/tex]

The kind of triangle does the Third Angle Theorem work on include all Triangles that have sum of 180°.

The Third Angle Theorem states that if in a triangle, one angle is known, the other two angles can be determined. So, this theorem works on any triangle, regardless of its shape or size. As long as the triangle has three angles, the theorem can be applied.

It states that the sum of the three angles in a triangle is always 180 degrees. So if you know the measure of one angle, you can use the theorem to find the measure of the other two angles by subtracting the measure of the known angle from 180 degrees.

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The amount of time that it would take Jordan to be able to complete the go cart is 5. 5 weeks

It would be best to convert the mixed fractions to decimals, for easier calculations.

85 1/5 hours :

= 85 + 1/5

= 85 + 0.2

= 85 .2 hours

15 1/2 hours :

= 15 + 1 / 2

= 15 + 0.5

= 15.5 hours

If it takes 85.2 hours to make the go cart and 15 .5 hours is what Jordan can complete per week, the number of weeks it would take is :

= 85 . 2 / 15. 5

= 5. 5 weeks

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Three mathematical concepts Sets, relation, function a strong tool for storing and analysing data is relational data.It is based on three crucial mathematical ideas. The correct answer is b. a domain a tuple

Relation and functions what they do Understanding the ideas in Mathematics a strong tool for storing and analysing data is relational data. It is built on sets, relations, and functions, three fundamental ideas in mathematics. In a relational database, sets are collections of items like tables, columns, and rows.

Relations are the connections between items in a set, such as the connections between database columns and rows. Functions are the rules that specify how objects and the connections between them interact, such as the rules that specify how a query behaves. Relational data can be arranged and managed with the use of these mathematical ideas in order to store and analyse data effectively.

Complete question:

On which three mathematical concepts is the relational data structure based? Select all that apply.

a. a variable

b. a domain a tuple

c. a relation

d. a table

e. an equation

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The percentage by which the price of the car went up from the original price is 60% (third option)

The first step is to determine the price of the car after the percentage increase. Percentage is the fraction of a number as a value out of 100. The sign that is used to represent percentage is %.

Price of the car after the percentage increase = (1 + percent increase/100) x original cost of the car

Price of the car after the percentage increase = (1 + 20/100) x 20,000

Price of the car after the percentage increase = (1 + 0.2) x 20,000

Price of the car after the percentage increase = 1.2 x 20,000 = $24,000

Price after the $8,000 increase = $24,000 + 8,000 = $32,000

Percentage of the original price = (32,000 / 20,000) - 1 = 0.60 = 60%

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Answer: The purpose of this research is to explore the potential relationship between traditional religious beliefs and authoritarian tendencies. We are administering a questionnaire that will measure your views on various topics and ask about your religious beliefs. It is important to note that this research is not intended to judge or stereotype individuals based on their religious beliefs, but rather to gain a better understanding of how these beliefs may be related to certain personality traits. Your participation in this study is completely voluntary and your responses will be kept confidential. We understand that some of the questions may be sensitive in nature, and we want to assure you that your personal beliefs will not be used in any negative way. Your participation in this research will help us to better understand the relationship between religious beliefs and personality traits, and will contribute to the field of psychology.

The first option, A BC^2 - AB^2 = AC^2, is true. This is a special case of the Pythagorean Theorem, which states that for a right triangle, the sum of the squares of the two shorter sides (A and B) is equal to the square of the longest side (C). In this case, BC^2 - AB^2 = AC^2.

The first option, A BC^2 - AB^2 = AC^2, is true. This special case of the Pythagorean Theorem states that for any right triangle, the sum of the squares of the two shorter sides (A and B) is equal to the square of the longest side (C). In other words, BC^2 - AB^2 = AC^2. This theorem has been used for centuries by mathematicians and builders, as it is a reliable way to measure and construct the sides of a triangle. The theorem is also useful in applications such as computer graphics, where it is used to calculate the dimensions of a triangle on a two-dimensional plane. By understanding the principles of the Pythagorean Theorem, one can accurately measure and construct triangles of any size and shape.

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The first option, A BC^2 - AB^2 = AC^2, is true. This is a special case of the Pythagorean Theorem, which states that for a right triangle, the sum of the squares of the two shorter sides (A and B) is equal to the square of the longest side (C). In this case, BC^2 - AB^2 = AC^2.

The first option, A BC^2 - AB^2 = AC^2, is true. This special case of the Pythagorean Theorem states that for any right triangle, the sum of the squares of the two shorter sides (A and B) is equal to the square of the longest side (C). In other words, BC^2 - AB^2 = AC^2. This theorem has been used for centuries by mathematicians and builders, as it is a reliable way to measure and construct the sides of a triangle. The theorem is also useful in applications such as computer graphics, where it is used to calculate the dimensions of a triangle on a two-dimensional plane. By understanding the principles of the Pythagorean Theorem, one can accurately measure and construct triangles of any size and shape.

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Answer:

  Kate is 16

  Leo is 20

Step-by-step explanation:

You want to know Kate's and Leo's ages if Kate is 4 years younger and twice Kate's age less 3 is the same as Leo's plus nine.

We can let K and L represent Kate's and Leo's ages, respectively. The given relations can be written as ...

  K = L -4

  2K -3 = L +9

Subtracting the first equation from the second gives ...

  (2K -3) -(K) = (L +9) -(L -4)

  K -3 = 13 . . . . . . . . . . . . . . . . . simplify

  K = 16 . . . . . . . . . . . . . add 3

  L = K +4 = 20

Kate is 16 and Leo is 20.

__

Check

Twice Kate's age, minus 3 is 2(16) -3 = 29.

Leo's age plus 9 is 20 +9 = 29, the same.

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Answer:

5 1/2 units

Step-by-step explanation:

area = 4 1/8 units²

width = =3/4 units

Assume shape is rectangle.

area = length × width

length = area/width

length = 4 1/8 units² ÷ 3/4 units

length = 33/8 units² × 4/3 units

length = 33/2 units² × 1/3 units

length = 33/6 units

length = 11/5 units

length = 5 1/2 units

The quadratic function answer for 2(x^2-3x+6) is 4x^2 - 6x + 12.

I believe that is correct

Answer:

.lol

Step-by-step explanation:

The tomato plant population was likely homogenous, meaning that all the plants were genetically identical and therefore more susceptible to the same disease.

1. A plant nursery only grew one type of tomato.

2. All of their tomatoes died from the same disease.

3. Therefore, the tomato plant population was likely homogenous, meaning that all the plants were genetically identical and therefore more susceptible to the same disease.

The plant nursery only grew one type of tomato and all of the tomatoes died from the same disease. This suggests that the tomato plant population was likely homogenous, meaning that all of the plants were genetically identical. This homogeneity made them more susceptible to the same disease, as all of the plants would have been affected by the same pathogens and environmental conditions. Furthermore, the same genetic makeup of the tomato plants would have made them unable to resist the disease. This lack of genetic variation within the population likely led to the death of all of the tomatoes.

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The most likely true statement to represent the population of the tomato plantation died with the same disease is given by option d. they had very little variation in the tomato plants genes.

As given in the question,

Type of tomato plants grew by a plant nursery = one or same type

Given condition of the plant infected by the disease is :

All the tomatoes plant planted by nursery died that is also from same disease.

Explanation of all options:

a. If they had resistance to disease many of the plants could survive.

False statement.

b. Few of the tomato plant resistant to the disease then few of the plants among the given plants may survive for few days.

False statement.

c. Variation is very high in their genes then plants will not infected by the same disease at the same time.

False statement.

d. Little variation in the genes of the plants.

Due to little variation all the plants get infected by the same disease and died.

True statement.

Therefore, the most likely true statement for the tomato plantation disease is given by option d. the tomato plants had little variation in their genes.

The above question is incomplete , the complete question is :

A plant nursery only grew one type of tomato plant. All of their tomato plants died from the same disease. What was most likely true of the tomato plant population?

a) They had a lot of resistance to disease.

b) They had a few plants that were resistant to the disease.

c) They had too much variation in their genes.

d) They had little variation in their genes.

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The surface whose equation is given. [tex]rho2(sin2(φ) sin2(θ) + cos2(φ)) = 4[/tex] is a cylinder with radius 2.

The cylinder has two key characteristics, namely surface area and volume, because it is a three-dimensional form. The combined curved surface area of the cylinder and the areas of the two circular bases make up its whole surface area. A cylinder's volume is the term used to describe the three-dimensional space it takes up.

A surface is a representation of a surface in mathematics. Similar to how a curve generalizes a straight line, it is a generalization of a plane but unlike a plane, it may be curved.

A thing or body's top or outer limit. on the water's surface. the surface of the earth. a two-dimensional locus of points that can be flat or curvy (such as the boundary of a three-dimensional region).

The equation of the surface is

[tex]$$\rho^2\left(\sin ^2 \phi+\sin ^2 \theta+\cos ^2 \phi\right)=4[/tex]

equation of a cylindrical surface is [tex]$y^2+z^2=r^2$$$[/tex]

[tex]\begin{aligned}& y^2=\rho^2 \sin ^2 \phi \sin ^2 \theta \\& \mathrm{y}=\rho \sin \phi \sin \theta\end{aligned}$$[/tex]

and, [tex]$\mathrm{z}=\rho \cos \phi$[/tex]

and, Radius of the cylinder is

[tex]$$r=2 \text {. }$$[/tex]

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Based on the quantity equation, if m = 8,000, p = 3, and y = 12,000, then v = 0.22

B. The Quantity Equation is a relationship between the money supply (m), the price level (p), and the level of economic activity (y), represented as m = py.

In this case, since we know that m = 8,000, p = 3, and y = 12,000, we can use this equation to solve for v. By dividing both sides of the equation by y, we get m/y = pv. Now we know m/y=8,000/12,000=0.66, and p=3, so we can solve for v by dividing m/y by p, which results in v=0.66/3=0.22 (when rounded) .

This means that the velocity of money (v) is .22, it means that each unit of money is used 0.22 times per year to purchase goods and services.

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Vertical and horizontal asymptotes are the two different forms of asymptotes. In order to help us comprehend the horizontal asymptotes fully, we provide an example. We just assess the function's limit as it approaches infinity and again as it approaches negative infinity to discover horizontal asymptotes.

the equation  limx→cf(x)=L , both  c  and  L  were numbers. In this section we relax that definition a bit by considering situations when it makes sense to let  c  and/or  L  be "infinity.''

consider  f(x)=1/x2 , as shown in Figure 1.30. Note how, as  x  approaches 0,  f(x)  grows very, very large. It seems appropriate, and descriptive, to state that

[tex]\lim_{x \to \infty} \frac{1}{x^{2} }[/tex]

If the limit of  f(x)  as  x  approaches  c  from either the left or right (or both) is  ∞  or  −∞ , we say the function has a vertical asymptote at  c .

When a rational function has a Vertical asymptote at  x=c , we can conclude that the denominator is 0 at  x=c . However, just because the denominator is 0 at a certain point does not mean there is a vertical asymptote there. For instance,  f(x)=(x2−1)/(x−1)  does not have a vertical asymptote at  x=1 , . While the denominator does get small near  x=1 , the numerator gets small too, matching the denominator step for step. In fact, factoring the numerator, we get

f(x)=(x−1)(x+1)/x−1.

If either limxf(x)=L or limxf(x)=L, then a function f(x) will have a horizontal asymptote of the form y=L.

Because "x" approaches to infinity and negative infinity, we must thus determine the limit value.

Take the formula f(x)=3x+7/2x5 as an example.

Now that "x" approaches to infinity, we must first determine the limit value.

In other words, [tex]\lim_{x\to \infty}f(x)[/tex]= [tex]\lim_{x\to \infty} \frac{3x+7}{2x-5}[/tex]

Using 'x' as the common denominator and numerator, we obtain

= [tex]\lim_{n \to \infty} \frac{x(3+\frac{7}{x} )}{x(2-\frac{5}{x} )}[/tex]

=[tex]\lim_{x \to \infty} \frac{(3+\frac{7}{x} )}{(2-\frac{5}{x} )}[/tex]

putting the cap on. As x → ∞, we will have 7/x → 0 and 5/x→0, giving us =3/2.

In other words, [tex]\lim_{x \to \infty} f(x)[/tex] = 3/2

Similarly, when "x" approaches toward negative infinity, calculate the limit value.

In other words,[tex]\lim_{x \to \infty} f(x)[/tex] = [tex]\lim_{n \to -\infty} \frac{3x+7}{2x-5}[/tex]

Applying the limit,

we get = [tex]\lim_{x \to -\infty} \frac{x(3+\frac{7}{x} )}{x(2-\frac{5}{x} )}[/tex]

           =[tex]\lim_{x \to -\infty} \frac{(3+\frac{7}{x} )}{(2-\frac{5}{x} )}[/tex]

by taking the 'x' common to the numerator and denominator. As x, we will have 7/x→ 0 and 5/x→ 0; this gives us 3/2.

i.e., [tex]\lim_{x\to- \infty}f(x)[/tex]  = 3/2

Therefore, the function has horizontal asymptote at y=3/2

There is just one horizontal asymptote for this function because the two limits were the same. Since asymptotes are lines, equations rather than merely numbers are used to describe them. There can only be two horizontal asymptotes in a function, one in each direction. When 'x' approaches any constant value 'c,' parallel to the y-axis, this is known as the vertical asymptote. The x-axis is parallel to flat lines known as horizontal asymptotes.

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Answer:

[tex]4^{4}[/tex] and [tex]6^{2}[/tex]

Step-by-step explanation:

1. The base numbers are 4 and six in this question

2. There are four #4s and two #6

3. 4 and 2 would be the exponents

a. The percent of Benny's mom's age to his age is 400%.

b.  Benny's mom's age is 400% of his age.

What is a percent of numbers?

The percent of a number is its fraction that is expressed as percentage. Thus the percentage of a number or part of a number can be determined.

Considering the given question, the years of Benny and that of his mom were given as;

Benny's age = 12 years

His mom's age = 48 years

Thus we can deduce that;

a. The percent of his mom's age to that of Benny's = 48/ 12 * 100%

                                            = 400%

b. Benny's mom's age is 400% of his age.

Therefore, the correct option to be selected is D.

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Answer:

The three sides 9 in, 12 in, and 15 do represent a right triangle.

Step-by-step explanation:

Hope it helps!

The following ordered pairs represent the correct mapping.

(0,1), (2,7), (3,4), (-4,1), (-6,7)

Mapping, any prescribed way of assigning to each object in one set a particular object in another (or the same) set. Mapping applies to any set: a collection of objects, such as all whole numbers, all the points on a line, or all those inside a circle.

From the diagram, we have both one-to-one and one-to-many mapping, so we first of all, list all of them.

one-to-one mapping ordered pairs include; (3,4)

one-to-many mapping ordered pairs include: (0,1), (2,7), (-4,1), (-6,7)

Therefore, the correct ordered pairs for the mapping will be both one-to-one and one-to-many mapping all put together, which is: (0,1), (2,7), (3,4), (-4,1), (-6,7)

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