Write Expressions Word Problems 1.
You run a small business and would like to print some business cards.
Staples offers color business cards for a small fee.
The cost is $.75 per card.
A) Write an expression for the total cost (in dollars) if you print b business cards. B) How much does it cost you to print 50 business cards?

The volume of the rectangular block in this problem is given as follows:

1300 cm³.

The block is a rectangular prism, hence it's volume is given by the multiplication of it's dimensions, as follows:

V = length x width x height.

The dimensions for this block are given as follows:

However, there is a small rectangular block that is removed from the prism, with the dimensions given as follows:

Hence the volume of the rectangular block can be calculated as follows:

V = 16 x 10² - 6 x 5 x 10 = 1300 cm³.

(total volume subtracted by the removed volume from the empty space at the middle).

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The null and different hypotheses for hypothesis test are

[tex]H_{0}[/tex] : P =0.63 against [tex]H_{1}[/tex] p [tex]\neq[/tex] 0.63

Null hypotheses

Given that:

sample size (η)= 196

sample proposition (p^) = 114/196

Let p denote the population proportion of people who use a loyalty card.

The percentage of shoppers use loyalty cards in their stores has remittent from sixty-three in 2014. [That is, whether or not the proportion has shifted from zero to 1] .63]

Hence, the null and alternative hypothesis are

[tex]H_{0}[/tex] : P =0.63 against [tex]H_{1}[/tex] p [tex]\neq[/tex] 0.63

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the area of the generic rectangle will be x²-2x-15.

What is a rectangle?

Rectangles are quadrilaterals having four right angles in the Euclidean plane of geometry. Various definitions include an equiangular quadrilateral, A quadrilateral with equal angles and parallel opposite sides is referred to as a rectangle. Around us, there are a lot of rectangle items. The length and width of any rectangle form serve as its two distinguishing attributes. The width and length of a rectangle, respectively, are its longer and shorter sides.

Area of rectangle is A = a*b

(x + 3)(x - 5) in a generic rectangle

The product will give the area

x²-2x-15

hence the area of the generic rectangle will be x²-2x-15.

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The solution to the equation f(x)=g(x) are x=-2 and x=1.

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

The given functions are f(x)=-x+6 and g(x)=-x²-2x+8.

Now, f(x)=g(x)

-x+6=-x²-2x+8

⇒ x²+x-2=0

⇒ x²+2x-x-2=0 (Splitting middle term method)

⇒ x(x+2)-1(x+2)=0

⇒ (x+2)(x-1)=0

⇒ x+2=0 and x-1=0

⇒ x=-2 and x=1

Therefore, the solution for the obtained equation are x=-2 and x=1.

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Answer:

D.  b + c = 68

    0.08b + 0.15c = 6.00

Step-by-step explanation:

The total cost is $6.00

The total amount of copies is 68

To find the total cost, we multiply the amount of copies by the individual price. So we get

0.08b + 0.15c = 6.00

We add the amount of copies bought to get a total of 68, so we get this equation:

b + 6 = 68

The rocket's height after 3 seconds is 6.3 sec.

The quadratic equation y = -x2 - 12x, where y is the height of the rocket in metres at time x seconds after launch, may be used to describe the trajectory of a model rocket. The rocket's highest point should be noted, along with the time it was at that height.

A rocket's height is a function of time, h(t), where h is measured in metres and t is measured in seconds. 9.8 m/s2 is the rate of change of velocity (d2h dt2 - t). The rocket is catapulted into the air, reaching a speed of 50 m/s at time t0.

To find the rocket's height at t = 2 sec, we just have to substitute 2 into the equation for t and then solve for h:

h = -5*t2 + 30*t + 10

h = -5(2)2 + 30(2) + 10

h = -5(4) + 30(2) + 10

h = -20 + 60 +10

h = 50 m

The height of the rocket 2 seconds after launching it is 50 meters.

To find the x-coordinate of the vertex of a parabola, we use the formula:

[tex]xvertex = -b / 2a[/tex]

t - 3 = ± √(11)

t = 3 ± √(11)

t = 3 ± 3.3

Solving for t, we get two solutions:

t = 3 - 3.3

t = -0.3 sec

and

t = 3 + 3.3

t = 6.3 sec

Remember that the rocket takes off from an elevated platform (the roof of a building), not from the ground, in order to comprehend the two alternatives we came up with. Even though we have two x-intercepts, only one of them, tground = 6.3 seconds, is related to when the rocket touches down. The other x-intercept, t = -0.3 sec, only has theoretical significance and is therefore irrelevant in our actual situation.

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Answer:

D

Step-by-step explanation:

(7+-6)/2

(7-6)/2

1/2

(-6+(-8)/2

(-6-8)/2

-14/2

-7

(.5,-7)

True, is it possible for the results of a study to show a non-zero correlation, even though the correlation for the general population is zero.

When a correlation is statistically significant, it is a significant and strong correlation. Even a very slight association can be statistically significant with a very large sample size.

                   While the correlation for the entire population is zero, it is nevertheless feasible for a sample to have a true, non-zero correlation.

When there is no association in a correlational analysis, what happens?

The variables fluctuate in opposite directions when there is a negative correlation. There is no association between the variables if there is zero correlation.

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A car manufacturer wants to lean about the brand preferences, then the company should survey a sample of all electric car owners.

A survey is a set of questions used in human subject research with the goal of gathering specific information from a particular population. Surveys can be carried out via the phone, by mail, online, at street corners, and even in shopping centers. Surveys are employed to collect data or learn more in areas like demography and social research.

Survey research is frequently used to evaluate ideas, beliefs, and emotions. Surveys may have narrow, specialized objectives, or they may have more general, extensive objectives.

As the manufacturer wants to learn about the brand preferences of electric car owners that what type of things people like nowadays, or what kind of improvement he can do in his model or design or other things, he should prefer a sample of all electric car owners.

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The value of x will be 1.17 inches and the maximum volume of the box is 1.6 cubic inches.

Volume is a measurement of three-dimensional space that is occupied. It is frequently numerically quantified using SI-derived units or various imperial or US customary units. The definition of length is linked to the definition of volume.

Given that the rectangular box is made from cardboard the thickness is x.

The length of the box will be,

L = 4.5 - 3x

The width of the box will be,

W = 4 - 2x

The thickness of the box is,

H = x

The volume of the box will be calculated as,

V = ( 4.5 - 3x) ( 4 - 2x ) (x)

V = ( 4.5 - 3x) ( 4 - 2x ) (x)

V = ( 18 - 12x - 9x + 6x² ) x

V = 6x³ -21x² + 18x

For maximum volume differentiate the volume with respect to x and get the value of x,

dV / dx = d / dx (  6x³ -21x² + 18x ) = 0

d / dx (  6x³ -21x² + 18x ) = 0

18x² - 42x + 12 = 0

3x² - 7x + 6 = 0

Solve the above quadratic equation as,

x = [ -b ±√(b² - 4ac) ] / 2a

x = [ -7 ± √ (-7² - 4 x 3 x 6 ) ] / ( 2 x 3 )

x = 1.17

The value of x is 1.17 inches by solving the above quadratic equation. The maximum volume will be calculated as,

V = 6x³ -21x² + 18x

V = 6(1.17)³ -21(1.17)² + 18(1.17)

V = 9.6 - 28.7 + 21.06

V = 1.96 cubic inches

The maximum volume is 1.96 cubic inches and the value of x is 1.17 inches.

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1. f(x) - cubic function -- polynomial , g(x) - linear function

similar

The function f(x) = x³+x²-3x+4 is a polynomial function and g(x) = 2ˣ-4 is an exponential function.

Domain: -∞ < x < ∞

Range: -∞ < y < ∞

y-intercept = 4

x - intercepts = -2.68

Function g(x)

Domain: x > 0

Range: -4 < y < ∞

y - intercept = -4

x - intercepts = none

By comparing the key features above, we can conclude that the common features in both functions are their range

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Answer:

i think that answer is correct

Step-by-step explanation:

Answer:

Step-by-step explanation:

The point of the compass located in order to make the arcs is points X and Y.

An "arc" in mathematics is a straight line that connects two endpoints. An arc is typically one of a circle's parts. In essence, it is a portion of a circle's circumference. A curve contains an arc. A circle contains an arc. For instance, a quarter-circle and a semicircle are both examples of arcs. A minor arc is one that is smaller than half of the circle it is a part of, or less than a semicircle, whereas a major arc is one that is more than half of its circle.

Given

The following figure was drawn using a straightedge and a compass.

The point of the compass located in order to make the arcs:

1. points X and Y

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The number of quizzes still need to be graded is 17quizzes.

There are many different ways to define an equation. In terms of algebra, an equation is a claim that demonstrates the equality of two mathematical expressions.

For instance, the two equations 5x + 4 and 16, which are separated by the 'equal' sign, make up the equation 5x + 4 = 16.

Algebraic equations in mathematics frequently have one or more variables.

It is given that,

grades of the teacher out of 48 quizzes before school = 16

grades of the teacher of the remaining quizzes after school = 15

Let us assume 'X' as the number of quizzes still need to be graded.

then X= 48-16+15

          =48-31

          =17

Hence, The number of quizzes still need to be graded is 17quizzes.

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The number of quizzes still need to be graded is 17 quizzes.

   then X= 48-=48-31

    =17

Hence, The number of quizzes still need to be graded is 17 quizzes.

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The value of the x would be 9.

Option (A) is correct.

What is a complementary angle?

A complementary angle is an angle that, when added to another angle, forms a right angle (90 degrees). Complementary angles are pairs of angles that add up to 90 degrees.

Angle JKM and angle MKN are complementary angles

so

   (3x + 2) + (6x + 7) = 90

  9x + 9 = 90

  9(x + 1) = 90

     x + 1 = 10

    x = 9

Hence, the value of the x would be 9.

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After solving the equation the value of the x would be 9. Therefore, the correct option is A.

What is a complementary angle?

A complementary angle is a pair of angles that add up to 90 degrees. Complementary angles can be adjacent angles, or angles that share a common vertex and side, or they can be nonadjacent angles that have no common points or sides. Complementary angles are usually referred to by their sum, such as "90-degree angles" or "angles that add up to 90 degrees." Complementary angles can also be called supplementary angles when they add up to 180 degrees.

Angle JKM and angle MKN are complementary angles

so   (3x + 2) + (6x + 7) = 90

 9x + 9 = 90

 9(x + 1) = 90

    x + 1 = 10

   x = 9

Hence, the value of the x would be 9.

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Answer:

x + x - x = x

explanation:

give us the actual formula lol

The equations found for the number of tickets sold when 22 tickets are sold on Monday and 30 per day after are sold by Madelyn, and 53 tickets are sold on Monday and 20 per day after that are;

Tickets sold by Madelyn is; y = 22 + 30·x

Tickets sold by Kaia is; y = 53 + 20·x

A system of equation obtained from the details in the question can be presented as follows

y = 22 + 30·x...(1)

y = 53 + 20·x...(2)

The appropriate method for solving the system is to equate equivalent values of one of the variable obtained from each equation in the system.

The solution of the system of equation is; x = 3.1, which indicates that it takes about 3.1 days for the number of tickets sold by Madelyn and Kaia to be equivalent.

An equation consists of two expressions that are joined by the 'equals to' (=) sign.

The number of tickets for the Winter Dance Madelyn sold = 22

Number of tickets per day Madelyn sold after that = 30 per day

Number of tickets Kaia sold on Monday = 53

Number of tickets per day Kaia sold after that = 20 per day

Let x represent the number of days since Monday, and let y represent the number of tickets sold

Therefore;

The number of tickets Madelyn sold, y = 22 + 30·x

The number of tickets Kaia sold, y = 53 + 20·x

The system of equations from the specified information is the equation for the number of tickets Madelyn sold and the number of tickets Kaia sold combined, which can be presented as follows;

y = 22 + 30·x...(1)

y = 53 + 20·x...(2)

The method of solving the equations is by plugging in the value of y from equation (1) in equation (2), as follows;
22 + 30·x = 53 + 20·x

30·x - 20·x = 53 - 22 = 31

10·x = 31

x = 31 ÷ 10 = 3.1

The meaning of the solution of the system of equation, x = 3.1, is that the number of days for the number of tickets sold by Madelyn and Kaia to be the same is about 3 days

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Answer:

-2

Step-by-step explanation:

Given,

g(x) = f(4)

or, 2 - 4x = 3*4 - 2

or, 2 - 4x = 10

or, 2 - 10 = 4x

or, -8 = 4x

or, x = -2

Answer:

144cm²

Step-by-step explanation:

If the square is perfectly even on all sides, the you first need to divide 48 by 4, as a square has 4 sides.

48/4 = 12cm

Then, to find the area, you need to multiply 12 by 12.

12 cm x 12 cm = 144cm²

Hope this helps :)

Answer:

D

Step-by-step explanation:

when we have the zeroes, we can build the polynomial by multiplying factors that will turn the functional value to 0 at exactly these points.

f(x) = (x - 3)(x + 6)(x - 1)

we don't need to do the full multiplications to see that the constant term of the polynomial is the result of the multiplication of all 3 constant terms of the factors :

-3 × +6 × -1 = +18

and therefore, D is the correct answer (as it is the only answer option with +18 as constant term).

According to Euclidean geometry, the geometric system consisting in isosceles triangle has an angle x whose measure is equal to 74°.

In this problem we find a geometric system consisting in a triangle, where two sides are congruent and the measure of an angle equals 74°.

According to Euclidean geometry, a triangle represented by the geometric system, with such features represents an isosceles triangle, that is, a triangle with two congruent sides and two congruent angles between the base side and each of the two congruent sides. Thus:

m ∠ x = 74°

x = 74°

Therefore, the measure of angle x, opposite to the angle whose measure is 74°, must be also equal to 74°.

The measure of angle x associated with the geometric system consisting in an isosceles triangle is equal to 74°.

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The remainder of polynomial g(x) divides (x - 3) that is  g(x) / (x - 3) is 0.

What is polynomial?

A polynomial is a mathematical expression made up of variables, constants, and exponents that are combined using addition, subtraction, multiplication, and division operations.

Given: g(x) = 2x^3 + 5x^2 - 28x - 15

(x - 3) is a factor of g(x).

We have to find the remainder of g(x) / (x - 3).

Consider,

                 2x^2 + 11x + 5

         [tex]\sqrt[(x-3)]{2x^3+5x^2 -28x -15}[/tex]

          -    2x^3 -6x^2

____________________________

                      11x^2 - 28x

               -      11x^2 - 33x

____________________________

                               5x - 15

                          -    5x - 15

_______________________________

                                      0

Hence, the remainder of polynomial g(x) divides (x - 3) that is

g(x) / (x - 3) is 0.

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In the given relation, 1 is not a domain.

The domain of a function is the set of all possible inputs for the function. or we can that in an ordered pair, all the values of x are called domain.

All the values that go into a function. The output values are called the range.

The domain of a function is the set of all possible inputs for the function.

If a function f provides a way to successfully produce a single value y using for that purpose a value for x than that chosen x-value is said to belong to the domain of f.

Given that, a function,

{(5, 1), (4, -3), (3, -1)}

We know, a domain is the set of all "x" values.

Therefore, domain of the function are, 5, 4 and 3

But, if we see, 1 is one of the values of y.

Hence, 1 is not a domain.

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The proposition ststement is: the only prime number that is odd is 2.

The correct answer is an option (d)

In this question we have been given some statements.

we need to identify the proposition statement.

We know that a proposition is a declarative statement. In mathematics proposition gives a clear inference of whether a sentence is true or false. The proposition statement cannot be stated in two ways. The statement must be either correct or incorrect.

a) get me a glass of milkshake.

It is a commanding statement.

b) god bless you!

It is a type of optative statement.

c) what is the time now?

It is a question sentence.

d) the only odd prime number is 2.

It is a false proposition statement.

Therefore, option (d) is a proposition statement.

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Parent function is represented by the graph is

B. The quadratic parent function

What is Parent function?

A parent function in mathematics is the most basic function within a family of functions that nonetheless upholds the definition of the entire family. For instance, displaystyle y=x2 is the simplest function in the family of quadratic functions with the general form displaystyle y=ax2+bx+c.

A parent function is an equation in the simplest form of a family of functions. There are many forms of parent functions such as: Linear functions: f(x)=x f ( x ) = x , where the degree of the function is 1 and represents a straight line.

The simplest parabola is y = x2, whose graph is shown at the right. The graph passes through the origin (0,0), and is contained in Quadrants I and II. This graph is known as the "Parent Function" for parabolas, or quadratic functions.

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Answer:

2/3 or 0.667

Step-by-step explanation:

5/9 ÷ 5/6

5/9 * 6/5

1/3 * 2/1 (after cancelling off)

= 2/3

Answer:

New price = 0.06 x Original price

New price $1,968