4. The 6th term of an arithmetic series is 13, the sum of the first 40 terms is 3420. Find
the sum of the first 30 terms.

Using concept of linear inequality, number of least deliveries is 30 and value of freight is $60000.

What are linear inequalities?

Inequality represents the mathematical expression in which both sides are not equal. If the relationship makes the non-equal comparison between two expressions or two numbers, then it is known as inequality in Maths. In this case, the equal sign “=” in the expression is replaced by any of the inequality symbols such as greater than symbol (>), less than symbol (<), greater than or equal to symbol (≥), less than or equal to symbol (≤) or not equal to symbol (≠). The different types of inequalities in Maths are polynomial inequality, rational inequality, absolute value inequality.

The symbols ‘<‘ and ‘>’ express the strict inequalities and the symbols ‘≤’ and ‘≥’ denote slack inequalities. A linear inequality seems exactly like a linear equation but there is a change in the symbol that relates two expressions.

e.g. y>x+2

Now,

Given charge of $70 per delivery and A charge of 6.5% of the total value of the freight for each delivery and least amount is $102,000.

Let only one delivery is possible per day and no. of deliveries=n

amount of each freight=x

Therefore,

Linear inequality will be n(6.5/100**x+70)>102000

So least values of n and x will be

n=30 and x=$60000

Hence,

          number of least deliveries is 30 and value of freight is $60000.

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The predicted population would be 5,250,00 in the year 2011.

An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.

The population in Austin is growing at a rate of 5% per year in 2010 the population was 500,000.

The exponential function for the prediction of the population can be written as:

ABˣ

Where A represents the population in 2010, B is a growth factor, and x is the year

As per the question, we have

(500,000)(1.05)¹

5,250,00

This is the predicted population in the year 2011.

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

The population in Austin is growing at a rate of 5% per year in 2010 the population was 500,000. what would be the predicted population year in 2011?

The equivalent expressions are  (b+3c)+(b+3c) and 2(b)+2(3c) or 2b+6c. Options B and C

An algebraic expression is simply described as an expression consisting of variables, coefficients, terms, constants, and factors.

Algebraic expressions are also made up of mathematical operations, such as;

Given the expression;

2(b+3c)

expand the bracket

2(b)+ 2(3c)

2b + 2×3×c

Multiply the values, we get;

= 2b +6c

It can also  be written as the sum of b+3c as (b+3c)+(b+3c)

Hence, the expressions are (b+3c)+(b+3c) and 2(b)+2(3c) or 2b+6c

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The complete question:

Which expressions are equivalent to 2(b+3c)2(b+3c)2, left parenthesis, b, plus, 3, c, right parenthesis ?

Choose all answers that apply:

A 3(b+2c)3(b+2c)3, left parenthesis, b, plus, 2, c, right parenthesis

B (b+3c)+(b+3c)(b+3c)+(b+3c)left parenthesis, b, plus, 3, c, right parenthesis, plus, left parenthesis, b, plus, 3, c, right parenthesis

C 2(b)+2(3c)2(b)+2(3c)2,

The ratios do not form a proportion. The cross-products are not equal.

To find ratios 8 : 4 and 12 : 8 are proportional or not, we are using cross products.

First, we write an equation with the ratios given:

[tex]\frac{8}{4}[/tex] = [tex]\frac{12}{8}[/tex]

Next, we cross-multiply the equation to find the cross products:

8×8 = 12×4

Simplifying both sides we get:

64 ≠ 48

we get our cross products 64 and 48 which are not equal. Thus the ratios 8 : 4 and 12 : 8 are not in proportion.

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The mean of the distribution of the given data set is equal to 273.33.

As given in the question,

Given distribution of the data set is :

388, 217, 317, 361, 350, 298, 400, 147, 254, 101, 336, 387, 14, 256.

Mean of the given data set

= ( Sum of all the distribution of the data set ) / ( number of observations)

= [tex]\sum x_{i}[/tex] / n

Where x represents the value of each distribution of the given data set.

and 'n' represents the number of data set

Here n = 14

Mean

=(388+217+317+361+350+298+400+147+254+101+ 336+387+14+ 256)/ 14

= 3826/ 14

=273.328

=273.33

Therefore, the mean of the given data set is equal to 273.33.

The given question is incomplete, I answer the question in general according to my knowledge:

Calculate the mean of the distribution of the following data set.

388, 217, 317, 361, 350, 298, 400, 147, 254, 101, 336, 387, 14, 256.

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Answer:

$24.46

Explanation:

$6.85÷7= 1 pint

you times the answer by 25 = $24.46

Answer:

Hi!

We will solve this using proportions, like this:

4 pints cost 10,08

30 pints cost x

__________________

x = (30 * 10,08)/4

x = 302,4/4

x = 75,6

30 pints of ice cream cost 75,6$.

Hope this helps!

Step-by-step explanation:

The relation {(3, 2),(6, 4),(9, 6),(12, 8)} is a function.

The relation {(2, 3),(2, 5),(3, 6),(9, 4)} is not a function.

The relation {(2, 4),(6, 3),(4, 8),(6, 6)} is not a function.

The relation {(3, 4),(5, 2),(6, 8),(6, 4)} is not a function.

A relation between a set of inputs having one output each is called a function.

Now,

In first option,

The relation is,

⇒ {(3, 2),(6, 4),(9, 6),(12, 8)

Clearly, Every inputs having one output each.

Hence, It is a function.

In second option,

The relation is,

{(2, 3),(2, 5),(3, 6),(9, 4)}

Clearly, Two Outputs 3 and 5 have same input 2.

Hence, It is not a function.

In third option,

{(2, 4),(6, 3),(4, 8),(6, 6)}

Clearly, Two Outputs 3 and 6 have same input 6.

Hence, It is not a function.

In fourth option,

{(3, 4),(5, 2),(6, 8),(6, 4)}

Clearly, Two Outputs 8 and 4 have same input 6.

Hence, It is not a function.

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The base of an exponent is a number that is increased to a definite power. So, the base of an exponent defines the number that is multiplied by itself.

The exponent means how many times the base number is multiplied.

The power can be expressed as the number obtained by increasing the base number to the exponent.

So, in the power [tex]a^{n}[/tex], the letter “a” is the base. The letter n is the exponent.

It says, a is multiplied by itself n number of times.

Example - (-5) ² = (-5) × (-5) = 25

Example: (-5)³ = (-5) × (-5)× (-5) = -125

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Abby can make 26 tie-dyed T-shirts.

We can start by setting up a linear equation to represent the total cost of making the tie-dyed T-shirts.

What is a linear equation?

First-order equations include linear equations. In the coordinate system, linear equations are defined for lines. A linear equation in one variable is one in which there is a homogeneous variable of degree 1 (i.e., just one variable).

Multiple variables may be present in a linear equation. Linear equations with two variables, for example, are used when a linear equation contains two variables.

Let x be the number of T-shirts Abby makes

The cost for each T-shirt is $3.95 + $0.50 = $4.45

The cost of the two boxes of salt is $4.50 * 2 = $9

So the total cost for x T-shirts is $4.45x + $9

We know that the total cost is 124.70 and we want to find the value of x, so we can set up the equation as:

$4.45x + $9 = 124.70

Solving for x:

$4.45x = 115.70

x = 115.70 / 4.45

x = 26

Therefore, Abby can make 26 tie-dyed T-shirts.

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Answer:

c = number of chimes

12c = amount gotten from the sale of the chimes.

To make a profit what she gets from the sales must be greater than her expenses.

12c > 530

c > 44.166666

She must sell each chime for more than 44 an one-sixth cent.

Step-by-step explanation:

The equation for the slant asymptote of the given function is y = 2x - 4.

Option (B) is correct.

What is the slant asymptote of the function?

A slant asymptote of a function is a line that the function approaches, but never touches or crosses. It is a type of asymptote that occurs when the degree of the numerator of a rational function (a function that can be written as the ratio of two polynomials) is greater than the degree of the denominator.

To determine the equation for the slant asymptote of a rational function (a function that can be written as the ratio of two polynomials), we need to look at the degree (the highest power of x) of the numerator and the degree of the denominator.

The function g(x) = (2x^2 + 4x + 6) / (x + 4)

The degree of the numerator is 2 and the degree of the denominator is 1, since the x^2 is the highest power of x in numerator and x is the highest power of x in denominator.

Since the degree of the numerator is greater than the degree of the denominator, the slant asymptote will have the same degree as the numerator, which is 2.

To find the equation of the slant asymptote, we divide the numerator by the denominator using the long division method and get

2x + 2 - (x + 2)/(x + 4)

The equation of the slant asymptote will be the result of the long division, which is 2x - 4

Hence, the equation for the slant asymptote of the given function is y = 2x - 4

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The value of x, in the triangle shown is: C. 5.25.

In the image given, the triangles shown are similar to each other, which means that their corresponding side lengths are proportional to each other.

Therefore, we would have the following proportion:

x / 2 = 16.8 / 6.4

Cross multiply:

6.4 * x = 16.8 * 2

6.4x = 33.6

6.4x/6.4 = 33.6/6.4

x = 5.25

The correct value of x is: C. 5.25.

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Answer:

[tex]8y^3+32y[/tex]

Step-by-step explanation:

[tex]8y(y^2+4)\\= (8y)(y^2)+(8y)(4)\\= 8y^3 + 32y[/tex]

The number of rentals would  be 20 so that both plans cost the same amount.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

It costs $30 to join and each video game rental for members costs $2.

Non-members pay a rental fee of $3.50 per rental.

let the number of rentals they both pay same amount be x.

So, 30 + 2x = 3.5x

30 = 3.5x - 2x

30 = 1.5x

x= 30/1.5

x = 20

Hence, number of rentals should be 20.

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4 real solutions does the system x² + y² = 25 and xy = 10 have.

The main distinction between an ideal solution and a non-ideal solution (real solutions) is that in an ideal solution, all molecules interact uniformly, but in a non-ideal solution, there are various forces acting on the molecules of the solute and solvent.

A real solution is one that has all the necessary constituent particles in the right ratio and has undergone the necessary dissolution. A solution is therefore referred to as a real solution.

Given that,

x² + y² = 25 .......... (i)

xy = 10 ............(ii)

or, y = 10/x

Now, putting the value of x in equation (i) we get-

x² + (10/x)² = 25

or, x⁴ + 100 = 25 x²

or, x⁴ - 25 x² + 100 = 0

or,  x⁴ - 20 x² - 5 x² + 100 = 0

or, x² (x² - 20) - 5 (x² - 20) = 0

or, (x² - 20) (x² - 5)

therefore, x = ±√20 and ±√5

Thus, there are 4 real solutions of these systems.

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The separation of two numerical values, regardless of whether they are positive or negative. Thus, the absolute difference offers little insight into the relative magnitude.

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The degree value, when rounded to the nearest decimal, is 6. Therefore, the slope's angle of 1 in 10 is 6 degrees.

1 in 10 in geometry refers to the ratio of one unit of vertical drop or rise for every ten units of horizontal distance crossed. This slope's value is calculated using the angle of tan. Let x represent the tan-using angle.

tan x = horizontal distance/vertical distance

tan x = 1/10

tan x = 0.1

Now taking the inverse

x = [tex]\tan^{-1}(0.1)[/tex]

x = 5.71 degree

The degree value, when rounded to the nearest decimal, is 6.

Therefore, the slope's angle of 1 in 10 is 6 degrees.

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The right question is:

How many degrees angle is a 1 in 10 slope?

Allele are alternative forms of genes found on chromosomes. Humans are known to be diploid organisms because they have two alleles at each genetic locus, with one allele inherited from each parent.

Chromosomes are long molecules of DNA that contain some or all of an organism's genetic material. In most chromosomes, very long, thin strands of DNA are coated with packaging proteins. In eukaryotic cells, the histones are the most important of all proteins. These proteins, with the help of chaperone proteins, bind and condense DNA molecules to maintain their integrity. These chromosomes have complex three-dimensional structures that play important roles in transcriptional regulation.

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Answer:

Step-by-step explanation:

−6−8÷2x−6(9−7)

3

Divide 8 by 2 to get 4.

−6−4x−6(9−7)

3

Subtract 7 from 9 to get 2.

−6−4x−6×2

3

Calculate 2 to the power of 3 and get 8.

−6−4x−6×8

Multiply 6 and 8 to get 48.

−6−4x−48

Subtract 48 from −6 to get −54.

−54−4x

By using the correlation coefficients, it is found that the two conclusions which the researcher can make from the given data are:

The correlation coefficient is a statistical measure of the strength of a linear relationship among two variables. Its assuming values can range from -1 to 1. If it is positive, the relation is positive, which is, they are direct proportional. And if it is negative, they are inverse proportional. If the absolute value of the correlation coefficient is greater than 0.6, it means the relationship is strong.

In this case, since the correlation is 0.486, thus, the conclusion is that the relation among the variables is positive, that means the higher the proportion of calories from sweeteners in the diets, the higher the mortality. And the other conclusion is that the relationship between the variables is not strong enough.

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Although part of your question is missing, you might be referring to this full question: A researcher found a study relating the mortality rates for women aged 65 to 74, y, to the proportion of calories from sweeteners in their diets, x. When researchers looked at the association of x and y, they found that the coefficient of determination was r squared equals 0.486. Select two conclusions that the researcher can make from this data.

Yes, 73 is a mirror prime number.

A prime number is a positive integer greater than 1 that has no positive integer divisors other than 1 and itself. Prime numbers play an important role in number theory and have many applications in mathematics and computer science.

A "mirror prime" or "emirp" is a prime number that remains prime when its digits are reversed. For example, the number 73 is prime, but if we reverse its digits, we get 37, which is also prime, so 73 is a mirror prime.

Mirror primes are relatively rare, and finding them requires a lot of computation power. They have been studied in number theory and have been found to have some interesting properties, for example, some researchers have found that the density of mirror primes are similar to the density of regular primes.

In the case of 73, it is a prime number, and it's not a "mirror prime" because when its digits are reversed, 37 is not a prime number, it is divisible by 37.

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The value of 'k' for the given system of equation kx−y=2, 6x−2y=3 has :

a. no solution is k = 3.

b. Infinitely many solution : no such value of 'k' exist.

As given in the question,

Given system of equations are :

kx−y=2

6x−2y=3

Standard form of system of equations are:

a₁x + b₁y + c₁ = 0

a₂x + b₂y + c₂ =0

a. Condition for the no solution is given by :

( a₁ /a₂ ) = (b₁ / b₂) ≠  (c₁ /c₂ )

(k/6) = ( -1/-2)≠( -2/-3)

⇒k/6 = 1/2

⇒k = 3

b. For infinitely many solution:

( a₁ /a₂ ) = (b₁ / b₂) =  (c₁ /c₂ )

⇒(k/6) = ( -1/-2)=( -2/-3)

We know that ( 1/2 ) ≠ ( 2/3)

Condition does not hold true.

No such value of 'k' exist.

Therefore, the value of 'k' for the given system of equation is given by :

a. no solution is k = 3.

b. Infinitely many solution : no such value of 'k' exist.

The above question is incomplete , the complete question is :

Find the value of k for which the system of equations

kx−y=2

6x−2y=3

has no solution. Is there a value of k for which the system has infinitely many solution?

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Answer: Teo is 9 years old and Richard is 27 years old.

Step-by-step explanation:

First of all, create expressions which represents Teo's and Richard's age:

x = Teo's Age

2x + 9 = Richard's Age

Now create an equation which can be used to find Teo's age and Richard's Age:

(x) + (2x)+9 = 33

(x) + (2x) = 24

3x = 24

x = 9

From this, we can conclude that Teo is 9 years old.

Now substitute 9 into Richard's Age expression which is 2x+9

2*9+9 = 27

From this, we can conclude that Richard is 36 years old.

The transformation of the graph of f to obtain g is described as follows:

The graph of g is a vertical compression of the graph of f by a factor of 6 units.

The object must be dropped at a height of 1.66 feet from the moon so it hits the ground at the same time as on Earth,

The functions in the context of this problem are given as follows:

The multiplier that was applied to function f(t) to obtain function g(t) is given as follows:

-16x = -8/3

16x = 8/3.

x = 8/48

x = 1/6.

The leading coefficient was divided by 6, meaning that the graph of g is a vertical compression of the graph of f by a factor of 6 units.

The object hits the ground when the output of the quadratic function assumes a value of zero.

For the Earth, we have that the time to hit the ground is obtained as follows:

-16t² + 10 = 0

16t² = 10

t² = 5/8

[tex]t = \sqrt{\frac{5}{8}}[/tex]

t = 0.79 seconds.

For the Moon, the function is given as follows:

g(t) = -8/3t² + h.

In which h is the initial height.

We want that g(t) = 0 when t = 0.79, hence the initial height is obtained as follows:

0 = -8/3(0.79)² + h

h = 8/3(0.79)²

h = 1.66 feet.

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Therefore , the solution to the given problem of linear equation comes out to be  x = -2.9.

Any function that can be expressed algebraically as y=mx+b is referred to as linear. The slope is B, and the y-intercept is m. The previous statement is sometimes referred to as a two-variable equation system because both y and x are factors. Bivariate equations are linear equations with two variables. There are numerous uses for linear equations, two of which are x + z = 2 and 3z - y + z = 3. A mathematical equation is said to be linear if its formula is y=mx+b, where m denotes the slope and b the y-intercept. Y=mx+b is how the equation is written, where m stands for the slope and b for the y-intercept.

Here,

Given : 8x-4 = -27.2

To find the x value

We do,

=>8x-4= -27.2

=> 8x = -27.2 +4

=>8x = -23.2

=> x = -23.2/8

=> x = -2.9

Therefore , the solution to the given problem of linear equation comes out to be  x = -2.9.

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The average rate of change of the function over the interval -1≤x≤8 is -3.22.

The average rate of change of a function over an interval is given by the formula (f(b) - f(a)) / (b - a) where f(x) is the function, a is the starting point of the interval, and b is the ending point of the interval.

In this case, the function is h(x) = -x² + 4x + 12, the interval is -1≤x≤8.

Plugging in the values we have:

Average rate of change = (h(8) - h(-1)) / (8 - (-1)) = (h(8) - h(-1)) / 9

h(8) = -8² + 4(8) + 12 = -64 + 32 + 12 = -20

h(-1) = -1² + 4(-1) + 12 = 1 - 4 + 12 = 9

So the average rate of change = (-20 - 9) / 9 = -29/9 = -3.22

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Answer:

ttt

Step-by-step explanation:

Answer: To find the length of the hypotenuse of a right triangle, you can use the Pythagorean theorem. The theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides (the legs).

So, if the legs of the right triangle measure 2 cm and 5 cm, the hypotenuse c can be calculated as follows:

c² = a² + b²

c² = 2² + 5²

c² = 4 + 25

c² = 29

Therefore, the length of the hypotenuse c is the square root of 29.

c = √29

The answer is c = √29 which is the only one that is not squared, So the answer is (C) 29.

Step-by-step explanation:

Answer:

The slope intercept form in math is one of the forms used to calculate the equation of a straight line, given the slope of the line and intercept it forms with the y-axis. The slope intercept form is given as, y = mx + b, where 'm' is the slope of the straight line and 'b' is the y-intercept.

Answer:

The line parallel to y=2x +3 is

y=2x + k---(1)

Since,st.line (1) passes through point (5,-4) then,

-4=2(5)+k

or,k=-4-10

:.k= -14

Putting value of k in eqn(1) we get

y=2x -14

Hence, y=2x -14 is the line parallel to y=2x +3 and passes through point (5,-4)

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