What do we mean by integral?

The mean for a given set of observations is 10.

The mean is the average of a set of variables in mathematics and statistics. The mean may be calculated in a variety of methods, including the simple arithmetic mean (add the numbers and divide the total by the number of observations), geometric mean, and harmonic mean. A data set's mean (average) is calculated by summing all of the numbers in the set and then dividing by the number of values in the set. When a data collection is arranged from least to largest, the median is the midway value. The mode is the number that appears the most frequently in a data collection.

Here,

given set of observation,

=2,4,6,8,10,30

=(2+4+6+8+10+30)/6

=10

The mean for given set of observation is 10.

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Answer: w = 4

Step-by-step explanation:

To solve the equation 10(w+3) = 70, we will work to get w by itself:

1. Divide by 10. This will get us closer to w.

(10( w + 3))/10 = 70/10

w + 3 = 7

2. We now have the equation w + 3 = 7. All we need to do now to get w by itself (or isolate it) is to subtract 3.

(w + 3) - 3 = 7 - 3

w = 7 - 3

w = 4

3. We can check our solution by inputting our found value, w = 4, into the equation.

10( 4 + 3 ) = 70

10(7) = 70

70=70

Because both sides of the equation are true, our solution of w = 4 is correct.

Answer: w = 4

Step-by-step explanation:

10(w+3)=70

10w + 30 = 70

10w = 40

w = 4

The slope of the line is  [tex]m = \frac{4}{5}[/tex]

slope using standard form:

[tex]m = \frac{4}{5}[/tex]

slope m of a line of the form Ax + By = C, equals -[tex]\frac{A}{B}[/tex]

A = 4 , B = -5

[tex]m = - \frac{4}{-5}[/tex]

Therefore;

[tex]m = \frac{4}{5}[/tex]

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The extent of the variations that could occur or the dividing lines between them several styles and prices across the steel spectrum. the scale or extent of a procedure, move, or activity.

The statistical range for a certain data collection is the range of values between the highest and lowest values. Comparing the top and lowest observational values also allows one to visualize the range. By deducting the greatest value from the lowest, the sample interval is determined. The sample range is a critical indicator of variability for variables with continuous variation.

here ,

There is a range of values between the lowest and highest. The lowest and greatest values in the example are 2 and 9, respectively.

Therefore, the range is 9 x 2 = 8.

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Linear equations are easy to solve .They are a type of mathematical equation that involve one or more variables, in which all terms are of the first degree.

The general form of a linear equation is Ax + B = C, where A, B and C are numerical coefficients and x is a variable. Linear equations can be solved by first rewriting the equation in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. Then, the y-intercept can be determined by substituting in a value for x and solving for y. To find the slope, two points on the line must be chosen, and the formula            m = (y2 - y1)/(x2 - x1) is used to calculate the slope. Once the slope and y-intercept are known, the equation can be written in its slope-intercept form and solved for x.

Linear equations can also be solved using the substitution method, where one of the variables is substituted with a numerical value. This method can be used when the equation is already written in its standard form, Ax + B = C. By solving for x, the value of x can be found and substituted back into the equation to find the value of C.

Finally, linear equations can also be solved using the elimination method, which is used when there are two linear equations with two unknowns. The two equations are added together, and the coefficients of one of the variables are eliminated. This method is useful for solving systems of linear equations.

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Answer:D

Step-by-step explanation:

A unit rate's component is always 1. To find the unit rate, divide the fraction by the fraction such that the denominator is equal to one.

The meaning of math units:

Of mathematics, a unit can be thought of as the right side point in a number or the number one. In this instance, the unit number in the number 6713 is 3. A unit is also a term that may be used to describe the common measurement units.

The dimensions of a unit:

The area of a unit as depicted on the subdivision or annexation map that created the unit is referred to as its size. The lot, tract, or parcel size divided by the number of dwellings is the unit size for two-family and multiple-family homes on a single unit.

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Three commonly used types of graphs are bar graphs, Pie Chart, and line graphs. Every sort of graph is appropriate for displaying a one-of-a-kind kind of records.

Graph:

The term graph is a pictorial illustration of facts in an organized way. Charts are normally fashioned from different data factors that represent the link among two or more matters.

Bar Graph:

A bar graph is a chart that displays complete data in rectangular bars, with the height of the bars proportional to the values ​​they represent. Chart bars can be displayed vertically or horizontally. A bar chart, also called a bar chart, is a graphical representation of grouped data. It is a method of data processing. Bar Graph are great for displaying data independent of each other and do not need to be in any particular order when displayed. Bars provide a visual indicator for comparing amounts in different categories. A bar chart has two lines, the horizontal and vertical axes (also called x-axis and y-axis), a title, labels, and a scale range.

Pie Chart:

Pie Chart is a chart type that visually represents data in a pie chart. It is one of the most commonly used charts for representing data with attributes of circle, sphere, and angle data to represent real-world information. The shape of the pie chart is circular, the circle represents all the data and the slices of the pie represent portions of the data and are plotted separately.

For Example: A full circle represents a value of 100. Divided into 10 slices or sectors. Different colors represent the ingredients used to prepare the cake. What is the exact amount of each component represented by a particular color in the pie chart below?

Solution: As you can see, the pie he is divided into 10 segments or sectors. To calculate the exact amount of ingredients added to the cake, divide the value across sectors.

H. 100 in sectors. So 100 ÷ 10 = 10.

Line graph:

A line chart is a graphical representation of changes that occur over a period of time. A line chart has a horizontal axis called the x-axis and a vertical axis called the y-axis. The x-axis usually has a period of time that measures the quantity of a particular thing or item on the y-axis. Line charts are useful for analyzing trends, whether the quantity on the y-axis is increasing or decreasing over time. A line chart clearly shows an uptrend or a downtrend.

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By applying concepts of Quadratic Inequality and applying on graphs option C is correct.

A quadratic inequality of the form

y>ax^2+bx+c

(or substitute <,≥ or ≤ for > ) denotes a section of the plane enclosed by a parabola.

Graphing the parabola is the first step in graphing a quadratic inequality. Then, depending on the inequality, fill in the area either above or below it.

If the inequality symbol is ≤ or ≥ , then the region includes the parabola, so it should be graphed with a solid line.

Otherwise, a dotted line should be drawn around the parabola to show that the region excludes the border if the inequality symbol is either <or >.

If it is > then the region above the dotted line is taken and if it is < the region below it is taken.

In the given question

y>(x-3)^2-1;

So the region above the dotted line should be taken which is option C.

By applying concepts of Quadratic Inequality and applying on graphs option C is correct.

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Answer: 3.6

Step-by-step explanation:

20/100= 1/5

1/5*18=18/5 or 3.6

Answer:

Twenty percent of 18 is 3.6. To find 20% of a number, simply multiply the number by 0.20. For example, 20% of 18 can be calculated by multiplying 18 by 0.20, which gives us 3.6.

Step-by-step explanation:

The true equations among the given expression are

True equation has same value at the left hand side and the right hand side of the equations after simplifying

The true equation is shown below

48 ÷ 8 + 2³ = 5 + 3²

applying PEMDAS

Exponents

48 ÷ 8 + 8 = 5 + 9

Division

6 + 8 = 5 + 9

Addition

14 = 14

(8 * 7) / 2 − 12 = 22 − 2 * 3

Parenthesis

56/2 - 12 = 22 - 2 * 3

Division

28 - 12 = 22 - 2 * 3

Multiplication

28 - 12 = 22 - 6

Subtraction

16 = 16

since the values in LHS = RHS the both equation are true

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The total cost before the sales tax was 19.828 pounds.

For a party, Jordan purchased 3.8 pounds of turkey, 2.2 pounds of cheese, and 3.6 pounds of egg salad.

We have to determine the total cost before sales tax.

As per the question, we have prices as:

cost of turkey = 3.95 per pound

cost of egg cheese = 1.3 per pound

cost of egg salad = 0.89 per pound

The total cost of turkey = 3.8 × 3.95  = 15.01 pounds

The total cost of cheese = 2.2 × 1.3 = 2.86 pounds

The total cost of egg salad = 2.2 × 0.89 = 1.958 pounds

The total cost before sales tax = 15.01 + 1.958 +2.86

Apply the addition operation, and we get

The total cost before sales tax = 19.828 pounds

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The question seems to be incomplete the correct question would be:

Jordan bought 3.8 pounds of turkey, 2.2 pounds of cheese, and 3.6 pounds of egg salad for a party. If prices are 3.95 per pound turkey, 1.3 per pound cheese and 0.89 per pound egg salad What was the total cost before sales tax?

[tex]{\huge{G = \frac{P-2M}{2} }}[/tex]

Simplifying 3 to the 3rd power gives 27.

Raising a base number to an exponent is referred to as "power" in mathematics. It indicates that "base number" and "exponent" are the two fundamental components of powers. The exponent shows how many times the base number has been multiplied, whereas the base number is defined as a number that is multiplied by itself. In a nutshell, power is a number that has exponents used to express it. It means that the same element has been multiplied repeatedly. In the context of powers, the following specific terminology may be used:

Whenever a number:

Squared – power is 2

cubed – Power is 3

“to the power of” – used for powers more than 3

3 to power 3= [tex]3*3*3=27[/tex]

Simplifying 3 to the 3rd power gives 27.

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Answer:

Step-by-step explanation:

If you're wondering about what percent of 212 is 400, the answer is 189.3%. This means that 400 is 89.3% higher than 212. It’s easy to see that, when compared side by side, 400 is a much bigger number, almost twice as great as 212. Put another way, if you divide 400 by 212, you get 1.89—that’s your answer! Clearly, 400 is a great deal larger than 212 and this difference in size can be expressed as a percentage increase of 189.3%.

Approximately 19.05% of 212 is 400.

Answer:

Step-by-step explanation:

Solution for 212 is what percent of 400:

212:400*100 =

(212*100):400 =

21200:400 = 53

Now we have: 212 is what percent of 400 = 53

Question: 212 is what percent of 400?

Percentage solution with steps:

Step 1: We make the assumption that 400 is 100% since it is our output value.

Step 2: We next represent the value we seek with $x$.

Step 3: From step 1, it follows that $100\%=400$.

Step 4: In the same vein, $x\%=212$.

Step 5: This gives us a pair of simple equations:

$100\%=400(1)$.

$x\%=212(2)$.

Step 6: By simply dividing equation 1 by equation 2 and taking note of the fact that both the LHS

(left hand side) of both equations have the same unit (%); we have

$\frac{100\%}{x\%}=\frac{400}{212}$

Step 7: Taking the inverse (or reciprocal) of both sides yields

$\frac{x\%}{100\%}=\frac{212}{400}$

$\Rightarrow x=53\%$

Therefore, $212$ is $53\%$ of $400$.  

the answer is 53 or 188.68%

1. Always (by definition)

2. Always (triangle inequality)

3. Always (Pythagorean theorem)

4. Sometimes (take x=y=1 and x=4, y=3)

5. Never (by definition)

6. Sometimes (Only if area = circumference)

7. Sometimes (Consider when scale factor = 1)

8. Never (Lines extend infinitely)

9. Sometimes (Only if both angles are right angles)

10. Always (Angle-angle similarity)

Answer:

[tex]x=5[/tex]

Step-by-step explanation:

[tex]x+3=8\\x=8-3\\x=5[/tex]

Answer:

[tex]y=\frac{1}{2}x+4[/tex]

Step-by-step explanation:

[tex]y-3=\frac{1}{2}(x+2) \\ \\ y-3=\frac{1}{2}x+1 \\ \\ y=\frac{1}{2}x+4[/tex]

Answer: y = 1/2 x + 4

Step-by-step explanation:

1) They gave you the slope so: y= 1/2x + b

2) Goes through point (-2,3) so: 3 = 1/2(-2) + b

3) 3 = -1 + b

4) b = 4

5) answer: y = 1/2x + 4

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Yes, a function can have no holes when it has no common factor at both numerator and denominator.

In Mathematics, a function can be defined as a mathematical expression which is typically used for defining and representing the relationship that exists between two or more variables.

This ultimately implies that, a function is typically used in mathematics for uniquely mapping an input variable (domain) to an output variable (range).

In Mathematics, a hole can be defined as a point on the graph wherein the input value of a given function is undefined or not defined. This ultimately implies that, a hole is a point on the graph of a rational function where the input value causes both its numerator and denominator to be equal to zero (0).

In conclusion, we can reasonably infer and logically deduce that it is very possible for a function to have no holes.

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The total balance he will have in the accounts at the end of 2 years will be $870.88. The correct option is D.

In most cases, simple interest paid or received over a specific time period is a fixed percentage of the principal amount borrowed or lent. Borrowers must pay interest on interest as well as principal because compound interest accrues and is added to the accumulated interest from previous periods.

Given that Thomas deposited $450 into an account that pays 4.5% simple interest and deposited $350 into an account that pays 4.25% compounded annually.

The simple interest is calculated as,

SI = ( 450 x 4.5 x 2 )

SI = $40.5

Amount = 450 + 40.5

Amount = $490.5

The compound interest will be calculated as,

A = 350 ( 1 + 0.0425 )²

A = $380.38

The total balance in the account after 2 years will be,

Total balance = $490.5 + $ 380.38

Total balance = $870.88

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Answer:

  22098

Step-by-step explanation:

You want the difference between the largest and smallest 5-digit numbers whose digits are from the set {1, 2, 3} and include each of these at least once. The numbers cannot be divisible by 2 or 3.

The number will be divisible by 3 when its sum of digits is a multiple of 3. Since 1, 2, and 3 are prescribed digits, the remaining two digits must not have a total of 3 or 6. The largest possible remaining digits are {2, 3}, and the smallest remaining digits are {1, 1}. (Using {3, 3} for the largest digits would give a number divisible by 3.)

The number will be divisible by 2 if the least significant digit is 2. The largest and smallest digits are not 2, so that will not be an issue.

The largest number will place the largest available digit in the place with the highest place value: 33221.

The smallest number will place the smallest available digit in the place with the highest place value: 11123.

The desired difference is the difference of these numbers:

  33221 -11123 = 22098 . . . . difference of largest and smallest

The difference between the two numbers will be 1998.

A numeral system is a writing system for expressing numbers; that is, a mathematical notation for representing numbers of a given set in a consistent manner using digits or other symbols. In different numeral systems, the same sequence of symbols can represent different numbers.

Given that Consider five-digit integers that have the following properties. Each of the digits is 1, 2 or 3, and each of 1, 2, 3 occurs at least once as a digit; also, the number is not divisible by 2 nor divisible by 3.

The largest number will be 3211.

The smallest number will be 1213.

The difference between the largest and the smallest number will be calculated as,

D = 3211 - 1213

D = 1998

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Answer:

222222222222222222222%

Answer: A = 67%

Step-by-step explanation:

Answer:

See explanation

Step-by-step explanation:

the probability that the two cards dealt to Satara (without replacement) will both be hearts is 7%

Total Number of cards left in the deck = 10

Number of hearts left in the deck = 3

Probability = (required outcome / Total possible outcomes)

Required outcome = hearts card in the deck

Without replacement, deal Satara two cards as follows:

The chance that the first card is a heart:

P(first card being hearts) = necessary result / all possible results

P(first card is a heart) equals 3/10.

The probability that the second card is a heart:

It cannot be replaced because:

Required result = (3 - 1). = 2

The total number of outcomes is (10 - 1) = 9 P(the second card is a heart) = 2 /9

The likelihood that the two cards are hearts is (3/10 x 2/9) = 6/90 = 0.0666 x 100% = 6.66%

= 7% (nearest whole number)

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The coefficient of variation is 200%.

The coefficient of variation is the ratio of the standard deviation to the mean. One form of measure of dispersion is the coefficient of variation. A number called a measure of dispersion is used to assess the degree of data variability. As a result, the coefficient of variation is used to assess how much data deviate from the mean or average value. The acronym CV stands for coefficient of variation.

Given that,

Arithmetic mean = 10
Standard deviation = 20

Therefore of coefficient of variation is SD/AM*100 = 20/10*100 = 200%

Hence, the coefficient of variation is 200%.

Correct question: If the arithmetic mean is 10 and the standard deviation is 20 then what is the coefficient of variation?

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The system of equations has "no solution" because they are parallel lines.

The equation is defined as a mathematical statement that has a minimum of two terms containing variables or numbers that are equal.

In general, any equation of the form y = k, where k is a constant, represents a horizontal line that extends indefinitely in both directions.

The system of equations y = 0 and y = -5 describes two lines in the coordinate plane.

The first equation, y=0, is the x-axis.

The second equation, y=-5, is a horizontal line 5 units below the x-axis.

As we know, y = 0 and y = -5 are two parallel lines.

Therefore, no solution exists.

Hence, the system of equations has no solution.

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Since, The given line is the line which is parallel to the y-axis that is a vertical line, It makes 90 degree with the positive x-axis, The slope is undefined that is tan(90).

A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is used. A formula that expresses the connection between two expressions on each side of a sign. Typically, it has a single variable and an equal sign. Like this: 2x - 4 Equals 2.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction. Divide the difference in elevation between two points by the distance between them to find the percent slope, then multiply the result by 100. The term "rise" refers to the difference in elevation between two sites. The run is the separation between the points. Percent slope is therefore equal to (rise / run) x 100.

x=-4

This is a vertical line parallel to y-axis.

It makes 90 degree with positive x-axis in anti-clockwise direction.

slope = tan(90) = undefined.

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No, two equilateral triangles need not to be always congruent with one another .

Justification of answer:

The reason is that although an equilateral triangle's angles are all 60 degrees, their corresponding sides are not necessarily the same .

1. All 3 side of an equilateral triangles have same length .

2. All 3 angles of an equilateral triangles have same measure.

3. Each angles of an equilateral triangles is 60 degree .

4. Area of equilateral triangles = [tex]\frac{\sqrt{3} }{4} *a^2[/tex]

5 . Perimeter of an equilateral triangles = 3*a

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Volume of the rectangle is estimated as;

Volume =  length x width x height

A three-dimensional object's volume is a measurement of the amount of space it occupies. We'll look at the procedure for calculate a box's volume on this page.

The size of a box:

View the box illustration below:

As you can see, there are three dimensions to take into account when dealing with a box or other three-dimensional object: length, width, and height.

Thus, the volume is calculated using the formula length x width x height:

V = l x w x h

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