can someone explain interval and set notation (algebra 2)

Answer:

Solve the problems. a) The number a is 4/5 of the number b. What part of number a is number b?

Step-by-step explanation:

a) If a is 4/5 of b, then b is 5/4 of a.

To find what part of a is b, we divide b by a:

b/a = 5/4

This means that b is 5/4 times larger than a, or b is 125% of a.

To find what part of a is b, we subtract 1 from this fraction:

b/a - 1 = 5/4 - 1

b/a - 1 = 1/4

So, b is 1/4 of a, or b is 25% of a.

Answer:

The number x that is midway between x and 27, and has a midpoint of -3, is -33

midpoint = (x + 27) / 2

We also know that the midpoint is equal to -3, so we can set these two expressions equal to each other and solve for x:

-3 = (x + 27) / 2

Multiplying both sides by 2 gives:

-6 = x + 27

Subtracting 27 from both sides gives:

x = -33

Answer:

576 books.

Step-by-step explanation:

134+254+188=576 books in total.

Answer:

576

Step-by-step explanation:

This is literally easy!

Checked books are 134 + 254 + 188 = 576

The simplified form of the given expression as required to be determined in the task content is; 2x⁴√5.

It follows from the task content that the Simon form of the given expression √20x⁸ is required to be determined from the task content.

On this note, since the given expression is; √20x⁸.

We have that; = √ (4 × 5 × x⁸)

Therefore, since 4 and x⁸ are perfect squares; it follows that we have;

= 2x⁴ √5.

Ultimately, the simplified form of the given expression as required to be determined is; 2x⁴ √5.

Complete question; The correct expression is; √20x⁸.

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Net rendering is a method of rendering a computer-generated animation or image on multiple computers over a network.

Net rendering is a method of rendering a computer-generated animation or image on multiple computers over a network. This technique allows a user to take advantage of the computing power of multiple computers to render a scene. To do this, the user would divide the scene into several parts, assigning each part to a different computer. The computers would then render each part of the scene independently, and then the results are combined into a single image. This process can significantly reduce the time required to render a scene, as the workload is distributed over multiple computers. For example, if it would normally take a single computer 10 minutes to render a scene, net rendering could reduce that time to 2 minutes.

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(a) Dataset with mean substantially less than median:

9, 10, 11, 12, 90

The mean of this dataset is (9+10+11+12+90)/5 = 26.4, while the median is 11, which is substantially greater than the mean. The last data value is 90, which is a positive integer less than 100.

(b) Dataset with mean substantially more than median:

98, 99, 100, 101, 200

The mean of this dataset is (98+99+100+101+200)/5 = 119.6, while the median is 100, which is substantially less than the mean. The last data value is 200, which is a positive integer less than 100.

(c) Dataset with mean equal to median:

2, 3, 4, 4, 5

The mean of this dataset is (2+3+4+4+5)/5 = 3.6, which is equal to the median (the middle value of the dataset). The last data value is 5, which is a positive integer less than 100.

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Answer:

Step-by-step explanation:

Based on the exponential decay equation, the number of employees for the company that has been decreasing yearly by 5%, will in 10 years be approximately 515.

The exponential decay equation or function gives the value in t years that has a constant ratio of decrease.

Exponential decay equation is one of the two exponential functions.  The other is the exponential growth equation.

The annual decrease in the number of employees = 5%

The current number of employees in the company = 860

The expected time = 10 years.

The exponential decay equation is as follows, y = 860 x 0.95^10.

y = 860 x 0.95^10 = 515

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The dimensions of the open rectangular box of maximum volume that can be made from a sheet of cardboard 19 in. by 11 in. by cutting congruent squares from the corners and folding up the sides are 6.33 in. x 3.33 in. x 5.33 in. The volume of the box is 113.78 in³.

The dimensions of the box can be found with the following steps:

First, determine the side length of the square that is to be removed from each corner of the cardboard box. Since this will be done uniformly on all four corners, let the side length be x. The dimensions of the cardboard box can then be written as:

Length = 19 in. - 2x

Breadth = 11 in. - 2x

Height = x

After folding the cardboard along the creases, the base of the rectangular box will be (19 - 2x) in. by (11 - 2x) in. with the height of the box being x in. The volume of the box can then be found by multiplying the base and height of the box, i.e.,

Volume = (19 - 2x) (11 - 2x) x

Let V(x) be the volume of the rectangular box in terms of x. Then:

V(x) = (19 - 2x) (11 - 2x) x

Simplifying,

V(x) = 4x³ - 60x² + 209x

The maximum value of V(x) can be found by differentiating V(x) with respect to x and equating the result to zero. Therefore,

V'(x) = 12x² - 120x + 209 = 0

Solving, V(x) has a maximum value when x = 19/3 - 2(2/3)√14 or x = 19/3 + 2(2/3)√14. The value x = 19/3 - 2(2/3)√14 is the maximum value because x must be less than 5.5, which is the minimum of 11/2 and 19/2 divided by 3, the upper bound for x. Therefore, the dimensions of the box are

Length = 19 - 2(19/3 - 2(2/3)√14) = 6.33 in.

Breadth = 11 - 2(19/3 - 2(2/3)√14) = 3.33 in.

Height = 19/3 - 2(2/3)√14 = 5.33 in.

Thus, the dimensions of the box are 6.33 in. x 3.33 in. x 5.33 in. The volume of the box is:

V = 6.33 x 3.33 x 5.33 = 113.78 in³.

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Answer: 4.5

Step-by-step explanation:

A^2 +B^2 =C^2

A^2 + 6^2 =7.5^2

A^2 + 36= 56.25

A^2= 20.25

A= square root of 20.25

A= 4.5

Answer:

the numbers are

[tex] \sqrt{10} + 5 \\ - \sqrt{10} + 5[/tex]

Step-by-step explanation:

then there difference is

square root of 10 + 5 -(- square root of 10 +5)

=

[tex]2 \sqrt{10} [/tex]

and the cube of there sum is 15^3 = 15* 15* 15

= 3375

The total weight of the granola bars in the box is 6.7 ounces.

To calculate the total weight of the granola bars with the correct number of significant digits, we need to multiply the weight of a single bar by the number of bars in the box.

Given parameters:

Total weight of the granola bars

= Weight of a single bar x Number of bars in the box

= 0.84 ounces x 8

= 6.72 ounces

Since the weight of a single bar is given with two significant digits, and we have multiplied it by a whole number, the answer should be reported with two significant digits.

so we can say that, the total weight of the granola bars is 6.7 ounces.

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In the given system of equations one taco costs $0.80 and one burrito costs $0.72.

An equation system is a finite collection of equations for which we searched for the common solutions. It is sometimes referred to as a set of simultaneous equations or an equation set. The classification of a system of equations is similar to that of a single equation. In modelling issues where the unknown values may be expressed in the form of variables, a system of equations finds use in everyday life.

Let us suppose the cost of one taco = x.

Let us suppose the cost of one burrito = y.

Then, for Emma we have:

3x + y = 3.65

For Cooper we have:

x + 2y = 3.30

Using elimination, multiply the first equation by 2 and subtract it from the second equation:

(2)(3x + y = 3.65)

6x + 2y = 7.30

x + 2y = 3.30

-5x = -4

x = 4/5

Substituting this value of x into either equation:

3(4/5) + y = 3.65

y = 2.15/3 ≈ 0.72

Therefore, one taco costs $0.80 and one burrito costs $0.72.

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If f(x,y) > 0 and is a continuous function defined over a rectangle R=[a,b]x[c,d], then the double integral over R of f(x,y) can be interpreted as the volume of a solid that lies in the first octant and under the graph of the function f(x,y) over the region R.

The geometric interpretation of the double integral over R of f(x,y) if f(x,y) > 0, where f is a continuous function defined on a rectangle R = [a,b] × [c,d] is given as follows:

The double integral of f(x,y) over R, if f(x,y) > 0, gives the volume under the graph of the function f(x,y) over the region R in the first octant.

Consider a point P (x, y, z) on the graph of f(x, y) that is over the region R, and let us say that z = f(x,y). If f(x,y) > 0, then P is in the first octant (i.e. all its coordinates are positive).

As a result, the volume of the solid that lies under the graph of f(x,y) over the region R in the first octant can be found by integrating the function f(x,y) over the rectangle R in the xy-plane, which yields the double integral.

The following formula represents the double integral over R of f(x,y) if f(x,y) > 0:

∬Rf(x,y)dydx

The geometric interpretation of the double integral over R of f(x,y) if f(x,y) > 0 is given by the volume of the solid that lies under the graph of the function f(x,y) over the region R in the first octant.

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Answer: 100:3

Step-by-step explanation:

Answer:

the ratio of first-year college basketball players to high school seniors playing basketball is 3:100.

Step-by-step explanation:

The problem states that for every 75,000 high school seniors playing basketball, about 2,250 play college basketball as first-year students. To write the ratio of first-year college basketball players to high school seniors playing basketball, we need to compare the two quantities.

The ratio is a way of expressing the relationship between two numbers as a fraction or a pair of numbers separated by a colon (:). In this case, we want to express the ratio of the number of first-year college basketball players to the number of high school seniors playing basketball.

To write the ratio, we start by putting the number of first-year college basketball players (2,250) in the numerator of a fraction. We put the number of high school seniors playing basketball (75,000) in the denominator of the same fraction.

So the ratio can be expressed as:

2,250/75,000

To simplify this fraction, we can divide both the numerator and denominator by a common factor. In this case, both 2,250 and 75,000 are divisible by 750. Dividing both numbers by 750 gives:

2,250/75,000 = 3/100

Smallest number in the data set that is not an outlier is 15, Median of the first half is 17, Median of the entire data set is 20.5. Median of the second half is 22. Largest number in the data set that is not an outlier is 35.

Give a short note on Median?

In statistics, the median is a measure of central tendency that represents the middle value in a dataset. To find the median, the data must first be sorted in ascending or descending order. If the dataset contains an odd number of values, the median is the middle value. If the dataset contains an even number of values, the median is the average of the two middle values.

The median is a useful measure of central tendency in datasets that are skewed or have outliers, as it is less sensitive to extreme values than the mean. It is also useful in datasets with non-numeric values, such as rankings or survey responses.

To create a modified box plot, we need the following values:

The smallest number in the data set that is not an outlier: 15

The median of the first half of the data set: 17

The median of the entire data set: 20.5

The median of the second half of the data set: 22

The largest number in the data set that is not an outlier: 35

So the values needed to create a modified box plot for this data set are: 15, 17, 20.5, 22, 35.

Each pair of children gets to bat for 7.5 minutes.

To find out how much time each pair gets to bat, we need to divide the total session time by the number of pairs of children who bat.

Number of pairs of children who bat = 6 groups x 1 pair/group = 6 pairs

Total time for the session = 45 minutes

Time per pair of children who bat = Total time / Number of pairs of children who bat

= 45 minutes / 6 pairs

= 7.5 minutes per pair

Therefore, each pair of children gets to bat for 7.5 minutes.

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Answer: $15.25

Step-by-step explanation:

Let x be the number of apples purchased and y be the number of mangos purchased. Then we have the following constraints:

2.25x + 1.25y ≤ 20 (Jose has $20 to spend)

x + y ≥ 9 (Jose must buy at least 9 apples and mangos altogether)

x ≥ 3 (Jose must buy at least 3 apples)

y ≤ 9 (Jose can buy at most 9 mangos)

To solve this system of inequalities graphically, we can plot the relevant lines and shade the feasible region.

First, we graph the line 2.25x + 1.25y = 20 by finding its intercepts:

When x = 0, we have 1.25y = 20, so y = 16.

When y = 0, we have 2.25x = 20, so x = 8.89 (rounded to two decimal places).

Plotting these intercepts and connecting them with a line, we get:

     |       *

 16  |   *    

     |      

     |  /    

     | /      

     |/      

 0   *--------*

      0    8.89

Next, we graph the line x + y = 9 by finding its intercepts:

When x = 0, we have y = 9.

When y = 0, we have x = 9.

Plotting these intercepts and connecting them with a line, we get:

    |      

 9   |   *    

     |      

     |  /    

     | /      

     |/      

 0   *--------*

      0    9  

Finally, we shade the feasible region by considering the remaining constraints:

x ≥ 3: This means we shade to the right of the line x = 3.

y ≤ 9: This means we shade below the line y = 9.

Shading these regions and finding their intersection, we get:

   |       *

 16  |   *    |

     |       |

     |  /    |

     | /     |

     |/      |

 9   *--------*---

     |       | /

     |       |/

     |       *

 0   *--------*

      3    8.89

The feasible region is the shaded triangle bounded by the lines 2.25x + 1.25y = 20, x + y = 9, and x = 3.

To find one possible solution, we can pick any point within the feasible region. For example, the point (4, 5) satisfies all the constraints and represents buying 4 apples and 5 mangos, which costs 4(2.25) + 5(1.25) = $15.25.

The height of an open cylinder of radius of 8cm given that it has a curved surface area of 1000 cm² is equals to the 159.24 cm.

The area obtained after substracting the circular area from the total area of the cylinder is called as curved surface area. Curved surface area is calculated by formula, 2πrh

where r --> radius of cylinder

h --> height of cylinder

π --> math special constant

We have an open cylinder with the following dimensions,

Radius of cylinder, r = 8 cm

Curved surface area of cylinder, A = 1000 cm². We have to calculate the height of this open cylinder. Let the height of an open cylinder be 'h cm' . Using the above formula, height of cylinder, h = curved Area/ 2πr

=> h = A/2π

=> h = 1000/2 ( 3.14)

=> h = 1000/6.28

=> h = 159.24

Hence, required value of height is 159.24 cm.

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The smallest value of `n` for which `S_n` has an element of order greater than or equal to 100 is 101.

To determine the smallest value of n for which S_n has an element of order greater than or equal to 100, we can use the formula

S_n = n!/r!(n - r)!,

where n is the number of elements in the set, and r is the number of elements being chosen at a time.

Given, S_n has an element of order greater than or equal to 100. The smallest value of n should be determined.

The formula for the number of permutations in a set with n elements is given by, `S_n = n!/r!(n - r)!`

where `n` is the number of elements in the set and `r` is the number of elements being chosen at a time.

The element of order `n` in `S_n` is an `n` cycle. For `n = 100`, we have an element of order 100.

This element can be expressed as `(1 2 3 ... 99 100)`. Thus, `r = 100`.

Substituting these values in the formula of S_n we get, S_n = n!/r!(n - r)! => n!/(100!(n - 100)!)

Now, we have to find the smallest value of n for which S_n has an element of order greater than or equal to 100. If we substitute `n = 100`, then we will have an element of order 100. But the question asks for the smallest value of n. So, if we substitute `n = 101`, we will have an element of order `101`. Hence, the smallest value of `n` for which `S_n` has an element of order greater than or equal to 100 is 101.

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As a result, the percentage of adults who selected math is different from the percentage of kids who did.

As a number out of 100, a percentage is a method to express a proportion or a fraction. It is symbolized by the number %. If there are 25 boys in a class of 100 pupils, for instance, then there are 25% of boys in the class. It is a helpful method to compare quantities and to express changes in values over time.

given

120 80

Total    200

Women Overall Party A Party B

70 60

Overall    130

Therefore, there are 130 ladies in the group.

b) The chart indicates that 70 women plan to support Party A.

Thus, the percentage of adults who selected English was 40% of 48, which is equal to 0.4 times 48 and 19.2 when rounded to the closest whole number.

b) Reeshma is not accurate. The percentage of adults who selected math is 35%, while for children it is 40%, according to the pie chart.

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The complete question is:-   complete the two-way table, which shows the voting intentions of a group of men and women. a How many women are in the group?

Men

Party A Party B 120

Total    200

Women   130

Total       380

b How many women intend to vote for Party A?

2 A group of 48 adults are asked what their favourite subject was at school. They can choose from

maths, English and science.

A group of 32 school children are asked the

same question.

The total resistance of the circuit is  6 + 2i.

Resistance is a unit of measurement for the resistance to current flow in an electrical circuit. The Greek letter omega () represents the unit of measurement for resistance, which is ohms.

Georg Simon Ohm (1784–1854), a German physicist who investigated the connection between voltage, current, and resistance, is the name given to the unit of resistance known as an ohm.

The amount of opposition any object applies to the flow of electric current is known as resistance. A resistor is an electrical component utilised in the circuit to provide that particular level of resistance. R = V I is a formula used to calculate an object's resistance.

given :

R1 =  (4 + 6i)

R2 = (2 - 4i)

total resistance of the circuit is

R = R1 + R2

= (4 + 6i) + (2 - 4i)

= 6 + 2i

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The equation RT = + R1 = 4 + 6i ohms and R2 = 2 4i ohms, RT = 6 - 2i ohms, determines the circuit's total resistance.

R1 and R2 are added to determine RT: RT = R1 + R2.

The actual components added together give us 4 + 2 = 6.

When we add the fictitious parts, we obtain 6i - 4i = 2i.

RT is thus equal to 6 - 2i ohms.

To put it another way, the circuit's total resistance is a complex number containing a real component of 6 ohms and an imaginary component of -2 ohms. This shows the combined impact of the circuit's resistances R1 and R2. When a constant voltage differential of one volt (V) is supplied to two conductor points and a current of one ampere (A) results, the resistance between those points is measured in ohms. It is comparable to one volt for every ampere (V/A), to put it simply.

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Using the mean formula we know that the new mean height of 14 people is 159.7 cm.

A mean in math is the average of a data set, calculated by adding all numbers together and then dividing the total of the numbers by the number of numbers.

For illustration, with the dataset containing: 8, 9, 5, 6, 7, the mean is 7, as 8 + 9 + 5 + 6 + 7 = 35, 35/5 = 7.

The mean height given is 159 cm.

Let, x1, x2, x3 ..... x15 be the height of 15 people.

x1+x2+x3 ..... x15/15 = 159

x1+x2+x3 ..... x15 = 159 * 15 = 2385 cm ...(1)

Let, x1 = 148 cm, who leaves the group.

148+x2+x3 ..... x15 = 2385 cm

x2+x3 ..... x15 = 2237 cm

Now, we have 14 people.

New mean = x2+x3 ..... x15/14

= 2237/14

= 159.7 cm

Therefore, using the mean formula we know that the new mean height of 14 people is 159.7 cm.

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To create opposite x terms, we need to multiply the first equation by -5.

How to choose what term to multiply the first equation?

To choose what term to multiply the first equation, we need to consider the coefficients of the variable that we want to eliminate (in this case, the x variable) in both equations. Our goal is to create opposite terms for that variable in the two equations, so that when we add or subtract the equations, that variable will be eliminated.

Determining the number to multiply the first equation by to form opposite terms for the x-variable :

In this case, the coefficient of x in the first equation is 2/5, and the coefficient of x in the second equation is -2.

To create opposite terms for x, we need to find a constant that, when multiplied by the first equation, will result in a coefficient of x that is the negative of the coefficient of x in the second equation (i.e., -2).

To do this, we can divide the coefficient of x in the second equation by the coefficient of x in the first equation, and then multiply the entire first equation by the resulting constant.

In this case, we have:

[tex](-2)/(2/5) = -5[/tex]

Multiplying the first equation by -5 gives:

[tex]-5(2/5)x + (-5)6y = -5(-10)[/tex]

which simplifies to:

[tex]-2x - 30y = 50[/tex]

Now we have two equations with opposite x terms:

[tex]-2x - 4y = 40[/tex]

[tex]-2x - 30y = 50[/tex]

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Answer: 4 batches of fudge brownies and 1 batch of peanut butter brownies were made.

Step-by-step explanation:

Let x be the number of batches of fudge brownies made, and y be the number of batches of peanut butter brownies made.

From the problem, we can write two equations based on the information given:

   Each batch of fudge brownies makes 1 pan: x = number of pans of fudge brownies.

   Each batch of peanut butter brownies makes 9 pans: 9y = number of pans of peanut butter brownies.

We also know that the class made 5 batches in total, and ended up with 29 pans:

x + 9y = 29 (total number of pans)

We can now solve for x and y by using a system of two equations:

x + 9y = 29 (equation 1)

x + y = 5 (equation 2)

Solving for x in equation 2 and substituting into equation 1, we get:

(5 - y) + 9y = 29

Simplifying and solving for y:

8y = 24

y = 3

Substituting y = 3 into equation 2, we get:

x + 3 = 5

x = 2

Therefore, the class made 2 batches of fudge brownies (2 pans) and 1 batch of peanut butter brownies (9 pans), for a total of 29 pans. Alternatively, we can say that the class made 4 batches of fudge brownies (4 pans) and 1 batch of peanut butter brownies (9 pans) for a total of 29 pans.

Answer:

[tex]5x {}^{3} - x + 5x + 2[/tex]

Step-by-step explanation:

Greetings!!!

So to find the sum of (f+g)(x) just simply add these two functions

Add like terms together

If you have any questions tag it on comments

Hope it helps!!!

It would cost €27 to buy a sheet of area 4 meters by 75 centimeters.

We solve this problem easily by employing the unitary method. To answer this question, we need to first calculate the area of the metal sheet being sold and the area of the metal sheet being purchased.

The area of the metal sheet being sold is:

5 meters × 2 meters = 10 square meters

The area of the metal sheet being purchased is:

4 meters × 0.75 meters = 3 square meters

Now we can calculate the price per square meter of the metal sheet being sold:

€90 ÷ 10 square meters = €9 per square meter

Finally, we can calculate the cost of the metal sheet being purchased:

3 square meters × €9 per square meter = €27. Therefore, the cost to buy a sheet of area 4 meters by 75 centimeters which costs €90 to a metal of area 5 meters by 2 meters would be €27.

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To understand why b = d = 0 if the function is even, we need to consider the definition of an even function.Therefore If P(x) is an even function, then b = d = 0.

A polynomial is a mathematical expression that consists of variables and coefficients, combined using the operations of addition, subtraction, and multiplication. It can have one or more terms and can be of any degree.

An even function is a function that satisfies the condition f(x) = f(-x) for all x in the domain of the function.

If P(x) is an even function, then we have P(x) = P(-x) for all x. Substituting -x for x in the expression for P(x), we get:

P(-x) = a(-x)⁴ + b(-x)³ + c(-x)² + d(-x) + e

= a(x⁴) - b(x³) + c(x²) - d(x) + e

Since P(x) = P(-x), we can equate the two expressions for P(x) and P(-x) to get:

a(x⁴) + b(x⁴) + c(x²) + d(x) + e = a(x⁴) - b(x³) + c(x²) - d(x) + e

Simplifying this equation, we get:

2b(x³) + 2d(x) = 0

Since this equation holds for all values of x, we can set x = 0 to get:

2d(0) = 0

which implies that d = 0. Similarly, setting x = 1, we get:

2b(1³) + 2d(1) = 0

2b = 0

b = 0

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