At the student store, pencils are sold in either packs of three or packs of eight.
Without opening any packages, which numbers of pencils is it possible to buy?
Which numbers are impossible?

Answer:

[tex]\huge\boxed{\sf Yes.}[/tex]

Step-by-step explanation:

y = 6x - 9 ---------------(1)

y = 2x + 3 --------------(2)

So,

x = 3, y = 9

Put this in Eq. (1) to verify.

9 = 6(3) - 9

9 = 18 - 9

9 = 9 [Equation satisfied]

Now, put x = 3, y = 9 in Eq. (2)

9 = 2(3) + 3

9 = 6 + 3

9 = 9 [Equation satisfied]

Since, both the equations are satisfied by the values of x and y, we can say that x = 3 and y = 9 is the solution to the system.

[tex]\rule[225]{225}{2}[/tex]

Answer: Yes, it is a solution

Step-by-step explanation:

Plug (x,y) values into the equations.

Plug in (3,9)

y=6x-9  ---->.  (9)=6(3)-9 ----> 9=18-9 ----->   9=9

y=2x+3 ------>.  (9)=2(3)+3 ----> 9=6+3 ----> 9=9

When know (3,9) is a solution because each side has the same value.

Example:

8=9 Not a solution

5=5 A solution

A rate is a ratio comparing quantities of different items. A unit rate is a rate with 1 in the denominator.

A rate is a ratio comparing quantities of different items. A unit rate is a rate with 1 in the denominator. If you have a rate, such as price per some number of items, and the quantity in the denominator is not 1, you can calculate unit rate or price per unit by completing the division operation: numerator divided by denominator.

Examples of How to Find Unit Rate or Unit Price

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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.

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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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 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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The solution of the given inequality is x < –5 or x > 2

Equations are not always balanced on both sides using an "equal to" symbol in mathematics. Sometimes it can be about a "not equal to" relationship, meaning that something is greater than or lower than another.

In mathematics, an inequality is a relationship between two numbers or other mathematical expressions that results in an unequal comparison. Inequalities are the name given to certain algebraic mathematical expressions.

Here we have

|2x + 3| < 7  

=> 2x + 3 > 7  or 2x + 3 < - 7

Take 2x + 3 > 7

Add  - 3 on both sides    

=> 2x + 3 - 3  > 7 - 3

=> 2x  > 4

Divide by 2 into both sides

=>  2x/2 > 4/2

=> x > 2

Take 2x + 3 < - 7  

Add  - 3 on both sides  

=> 2x + 3 - 3  < - 7 - 3

=> 2x  < -10

Divide by 2 into both sides

=> 2x/2 < -10/2

=> x < -5    

Therefore,

The solution of the given inequality is x < –5 or x > 2

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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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Answer:

How can you tell if a function is an exponential function? If your function can be written in the form y = a b x , where and are constants, a ≠ 0 , b > 0 , and b ≠ 1 , then it must be exponential. In quadratic equations, your functions were always to the 2nd power. In exponential functions, the exponent is a variable.

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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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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Substitution refers to the process of replacing one group with another. We can say that it refers to replacing a variable with another given value.

For example, given that x = 17, we can substitute the value of 17 in for x and evaluate the obtained expression to get the value of x.

We can name the expression: F (x) = 17 + 3x - 4.

here , let's say x = 2

then , F (x) = 17 + 6 + 2 = 25

The algebraic method which is used for solving simultaneous linear equations is known as the substitution method. The value of one variable from one equation is substituted in the second equation, as the name implies.

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The measures of the missing angles are given as follows:

First we consider that when two angles form a ray, they are supplementary, meaning that the sum of their measures is of 180º.

Then the measures of angles 3 and 5 are given as follows:

The sum of the internal angles of triangle is of:

S(3) = (3 - 2) x 180º = 180º.

Hence the measure of angle 4 is obtained as follows:

m < 4 + 36 + 56 = 180

m < 4 = 180 - (36 + 56)

m < 4 = 88º.

Angles 2 and 4 are congruent, hence the measure of angle 2 is given as follows:

m < 2 = m < 4 = 88º.

The sum of the internal angles of a quadrilateral is of:

S(4) = (4 - 2) x 180º = 360º.

Hence the measure of angle 1 is obtained as follows:

m < 1 + 88 + 144 + 124 = 360

m < 1 = 360 - (88 + 144 + 124)

m < 1 = 4º.

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Answer:

BY = 9.90 cm

Step-by-step explanation:

AY = 7cm

AB = 7cm

BY = ?

BY = [tex]\sqrt{7^2+7^2}[/tex]

BY = [tex]\sqrt{98}[/tex]

BY = 9.89cm (round to 9.90cm)

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 linear equation for the relationship between the weight and number of months is y = 5.55x + 78.95.

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.

We know that the sumo wrestler's weight is 140 kilograms after 11 months and he gained weight at a rate of 5.55 kilograms per month.

The equation for the relationship between the weight and number of months can be represented as:

y = 5.55x + b

Where y is the sumo wrestler's weight (in kilogram) after x month, 5.55 is the rate at which he gained weight per month, x is the number of months and b is the y-intercept.

To find the value of b, we can use the point (11, 140) which represents that after 11 months the sumo wrestler's weight is 140 kg, and substitute it into the equation:

y = 5.55x + b

140 = 5.55(11) + b

Solving for b:

b = 140 - (5.55 * 11)

b = 140 - 61.05

b = 78.95

So the complete equation is:

y = 5.55x + 78.95

Where y is the sumo wrestler's weight (in kilogram) after x months.

Therefore, The linear equation for the relationship between the weight and number of months is y = 5.55x + 78.95.

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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

Both statement by Lorene and Maria is correct because it has a common factor is "1/4".

Both fraction are called proper fraction. Basically, a fractions represent the parts of a whole or collection of objects.

Under fraction, proper fraction is one in which the numerator is less than the denominator. It is in contrast to improper fraction, that numerator equals or exceeds the denominator. Proper fractions are 3/4, 2/11, and 7/19, while improper fractions are 5/2, 8/5, and 12/11.

The statements of Laurie and Maria can be compared as follows:

It can be written as,

3/12 = (3 ÷ 3)/(12 ÷ 3)

= 1/4

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Answer:

B. 7

Step-by-step explanation:

[tex]I=Prt \\ \\ 196=700(0.04)t \\ \\ 196=28t \\ \\ t=7[/tex]

Answer:  x [tex]\leq[/tex] 52 inches.

Step-by-step explanation:

The solution set of the following equation (- 8x +  x + 15) = ( - 7x + 12) is zero i.e this equation does not have any solution.

Equation is (- 8x + x + 15) = (-7x + 12)

Now solving

(-8x + x  + 7x ) = ( 12 - 15 )

( - 7x +7x) = (-3)

( 0 )= ( - 3)

Since 0 = -3 is not correct, therefore, the equation does not have any solution.

So it is stated that the equation (- 8x +  x + 15) = ( - 7x + 12) does not have any solution in its solution set.

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A statement of an order relationship between two numbers or algebraic expressions is known as an inequality in mathematics. It can be greater than, greater than or equal to, less than, or less than or equal to.

Using the inequality symbol, a mathematical statement known as an inequality depicts the relationship between two expressions. An inequality symbol denotes that the terms on each side are not equal.

It indicates that the expressions on the left and right should be bigger or less than one another, or vice versa. Literal inequalities are those where the relationship between two algebraic expressions is described by the inequality symbols.

According to the definition, a relationship is considered to be an inequality if it involves two real numbers or algebraic expressions and uses the symbols “>”, “<”, “≥”, “≤”.

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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: MMDCCLXXXIX

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

f(x)=a(b)^x

Step-by-step explanation:

exponential functions are usually growth or decay,

a represents the base, b is the change, and x is how much time (depending on the question). if b is larger than 1 ex: 1.08, it is growth. if it is less than 1 ex: 0.4, it is decay

The exponential form formula is a^b = c, where a is the base, b is the exponent, and c is the result. In this formula, a is raised to the power of b, resulting in the value c.

By setting each factor to 0, you can get the roots, or solutions, of the polynomial equation P(x) = 0 by figuring out what x is. Factor the polynomial equation to find the solution.

Constants and indeterminates are parts of polynomial algebraic expressions.

One could consider polynomials to be a subset of mathematics.

They are used to express numbers in almost all areas of mathematics, and calculus is one of those areas where they are particularly important.

A polynomial is a specific sort of expression.

An expression is a mathematical statement that does not contain the equals sign (=). Let's look at the following descriptions of polynomials' definition and applications.

All the exponents of an algebraic expression called a polynomial must be whole numbers.

Any polynomial must have non-negative integer variable exponents. We cannot divide a polynomial by a variable even though it contains variables and constants.

Hence, By setting each factor to 0, you can get the roots, or solutions, of the polynomial equation P(x) = 0 by figuring out what x is. Factor the polynomial equation to find the solution.

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we can see that the function C(x) = 25x + 75 represents the labor cost (in dollars) for Bob's Auto Repair to replace your alternator, where x is the number of hours. We can use this function to find the cost of replacing an alternator that is estimated to take 5 hours of labor.

C(5) = 25(5) + 75 = 125 + 75 = 200

We also have the labor cost for the main competitor, Budget Auto Repair, in a table format.

Hours Cost

1          $90

2         $130

3         $170

We can see that the cost of labor increases as the number of hours increases. From the information provided it's hard to say which company would be cheaper to hire, however the company with the function C(x) = 25x + 75 would be cheaper if the alternator takes more than 4 hours of labor, otherwise Budget Auto Repair would be cheaper.

It's important to check the warranty, prices of parts, and reputation of both companies. If a company has a good reputation and a good warranty, it may be worth paying a little more for labor.

It's also a good idea to get a second opinion or ask for a quote from both companies before making a decision.

In conclusion, it's hard to say which company would be cheaper to hire based on the information provided, but it's recommended to check the warranty, prices of parts, and reputation of both companies, and to get a second opinion or quote from both companies before making a decision.

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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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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,