A television was originally priced at $522, but Sam waited to buy it until the television was on sale for 50% off. If he paid 8% sales tax on the sale price, how much did he pay in total?

Answer:

y = - 2x + 7

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given m = - 2 , then

y = - 2x + c ← is the partial equation

to find c substitute (4, - 1 ) into the partial equation

- 1 = - 2(4) + c = - 8 + c ( add 8 to both sides )

7 = c

y = - 2x + 7 ← equation of line

Mathematical induction, .∴ Pn+1 follows if Pn is true. For all positive integers of n, Pn holds true because P1 is true.

Assume that Pn is 4 + 9 + 14 +... + (n/2)(5n + 3)=(5n -1).

First, establish that P1 is accurate when n equals 1.

LHS= 4

RHS

= 1/2(5 + 3)

= 1/2(8)

= 4

= LHS

Is P1 true.

2) Assume Pn to be accurate, i.e., 4 + 9 + 14 +... + ( 5n -1)= (n/2)(5n +3)

3) Establish Pn+1 as true in the induction stage.

Replace (n+1) on both sides of n to obtain Pn+1.

Pₙ₊₁: 4 +9 +14 +...+(5n -1)+ [5(n+1) -1]=

Establish the RHS and LHS's parity.

LHS = 4 +9 +14 +...+(5n -1)+ [5n +5-1]

Bold expression in (2) should be replaced with the value of Pn:

.∴ Pn+1 follows if Pn is true. For all positive integers of n, Pn holds true because P1 is true.

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To ascertain an element's molar mass, use the periodic table. Calculate the quantity of moles by dividing the supplied mass in grammes by the molar mass.

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The value of C in the table will be 24.

the property of having suitable proportions in terms of size, number, degree, harshness, etc.: If a defensive action against an unfair attack results in the destruction that contravenes the proportionality criterion, it may even go far beyond a justifiable defense.

Given, a table of proportional data below,

Part      8    B    D

Part     10   15   45

Whole  A    C    72

Since the two-part will be proportional to the whole.

thus,

=> c /72 = 15/45

=> C = 72/3

=> C = 24

Therefore, the value of C  in the given table will be 24 as pe the proportionality.

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The function is decreasing on the interval (0, [infinity])

The function h of x equals negative 2 times the square root of x is a decreasing function on the interval (0, ∞). This means that as the value of x increases, the value of h(x) decreases. On the interval (-∞, 0), the function is increasing. This means that as the value of x decreases, the value of h(x) increases. The graph of the function looks like a parabola that opens downward and is symmetric around the y-axis. The graph is a concave down curve, and the y-intercept is at (0, 0). As the value of x gets closer to 0, h(x) approaches negative infinity. As x approaches infinity, h(x) approaches 0. This means that the range of h(x) is (-∞, 0].In order to determine if the function is increasing or decreasing on a given interval, we need to look at the sign of the derivative of the function on the interval.

The derivative of h(x) is -2/sqrt(x).

For the interval (0, [infinity]), the derivative of h(x) is negative, indicating that the function is decreasing.

For the interval (–[infinity], 0), the derivative of h(x) is positive, indicating that the function is increasing.

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Answer:

9/-7

Step-by-step explanation:

the reason is all you have to do is reverse the fraction

Answer:

-9/7

Step-by-step explanation:

The multiplicative inverse of -7/9 is_____?

-7/9 × (- 9/7) = 1

Answer:

Step-by-step explanation:

x-​4/​5+​9

Picking a king from a deck of cards, swapping it out for a queen, then continuing. These occurrences would constitute Dependent events.

'What is dependent probability?'

A dependent variable is precisely what it sounds like, just like an independent variable. It is something on which other elements depend.

A test score, for instance, may be a dependent variable because it could vary based on a number of variables, including how much you studied, how much sleep you got the night before the test, and even how hungry you were. Typically, when attempting to establish a connection between two variables, the goal is to determine what causes the dependant variable to vary in the manner that it does.

Many people struggle to recall which variable is the independent variable and which variable is the dependent variable.

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Answer: 14 boys & 28 girls

Step-by-step explanation:

the number of girls= 2x

the number of boys= x

now create an algebraic equation:

x + 2x = 42

     3x = 42

        x = 14 (boys)

multiply 14 by 2 as the number of girls is two times the number of boys.

14 x 2 = 28 girls

The equivalent way to write the expression is 12x-15. The solution has been obtained by simplifying the expression.

What is simplified expression?

Simplified expression is that expression which does not contains any like terms. When in an expression, all the like terms are combined and all of the specified brackets are solved, then only unlike terms are left in the simplified expression which cannot be further reduced.

We are given 3(4x-5).

There are no like terms in the given expression.

Therefore, as the next step, we  need to solve the bracket for simplifying the expression.

Thus, we obtain

⇒ 3*4x - 5*3

⇒ 12x -15

Hence, the equivalent way to write the given expression is 12x-15.

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Answer:

Perimeter = 8π cm

Area = (32π - 64) cm²

Step-by-step explanation:

ABCD is a square.

Therefore:

The perimeter of the shaded part is the sum of two congruent quarter circles, i.e. half the length of the circumference.

The arcs AC are quarter circles of a circle with radius 8 cm.

Therefore the perimeter of the shaded area is:

[tex]\implies \sf Perimeter=Half\;circumference=\dfrac{1}{2} \cdot 2\pi r=\pi r=8\pi\;cm[/tex]

To find the area of the shaded area, subtract the two unshaded areas from the area of the square.

As the two unshaded areas are congruent we only need to find the area of one unshaded area.

The area of one unshaded area is the area of the square minus the area of the sector ADC (which is a quarter of a circle with radius 8 cm).

[tex]\begin{aligned}\implies \textsf{Area of one unshaded area}&=\textsf{Area of square}-\textsf{Area of $\frac{1}{4}$ circle}\\&=64-\dfrac{1}{4} \pi r^2\\&=64-\dfrac{1}{4} \pi \cdot 8^2\\&=64-\dfrac{1}{4} \pi \cdot 64\\&=(64-16 \pi)\; \sf cm^2\end{aligned}[/tex]

Now we have found the area of one unshaded area, to calculate the area of the shaded area simply subtract two unshaded areas from the area of the square:

[tex]\begin{aligned}\implies \textsf{Shaded area}&=64-2(64-16\pi)\\&=64-128+32\pi\\&=(32\pi-64)\; \sf cm^2 \end{aligned}[/tex]

The conceptual schema and the E-R diagram are attached.

(i) Before making the E-R diagram we discuss the entity relational model for the given problem. So the E-R diagram is the graphical representation of different entities and attributes.

Assumptions for the given problem:

(i) University: a university has its name, address, email id, and mobile number

the university gives admission to students and also university and different departments.

(ii) Student: a student has attributes name, contact number, and social security number as the primary number, address, student number, birth date has its name, department, sex, class, department, and degree program.

(iii) Department: the department has its name, department code, office number, phone

(iv) Courses: each course has its name, description, course number, number of semester hours, level, and offering department.

(v) Section: section has an instructor, semester, year, course, section number

(vi) Grade report: a grade report contain a student section, letter grade, and numeric grade

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For the system of equations, there are infinitely many solutions exist.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The system of equations are,

⇒ - 2x + 2y = 10  .. (i)

⇒ y = x + 5  .. (ii)

Here, From (i) equation,

⇒ - 2x + 2y = 10

Take 2 as common,

⇒ 2 (- x + y) = 10

⇒ - x + y = 5

⇒ y = x + 5

Which is same as equation (ii).

Hence, There are infinitely many solutions exist.

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The c1 and c2 are arbitrary constants.

What is the arbitrary constant?

y=mx+c is the general equation of a straight line in two dimensions, where m and c are arbitrary constants that represent the gradient of the line and the y-intercept. And ∫2x dx=x 2+c where c is an arbitrary constant whose value can be determined by a boundary condition.

y = c1ekx + c2e-kx is a general solution to the homogeneous linear differential equation y' + ky = 0. This means that any specific solution to this equation can be obtained by plugging in appropriate values for c1 and c2.

The general solution y = c1ekx + c2e-kx is a linear combination of ekx and e-kx.

The differential equation y' + ky = 0 is a first-order, linear differential equation.

The general solution y = c1ekx + c2e-kx is valid for all values of x.

The general solution y = c1ekx + c2e-kx is a sum of two linearly independent solutions to the differential equation.

The general solution y = c1ekx + c2e-kx is a particular solution if c1 and c2 are determined by initial or boundary conditions.

The general solution y = c1ekx + c2e-kx is a general solution if c1 and c2 are arbitrary constants.

The general solution y = c1ekx + c2e-kx is a unique solution if c1 and c2 are determined by initial or boundary conditions, otherwise, it is not unique.

The general solution y = c1ekx + c2e-kx is a solution to the homogeneous differential equation y' + ky = 0, it does not contain any particular solution for the non-homogeneous differential equation.

Hence,  The c1 and c2 are arbitrary constants.

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Integers higher than or equal to -3 and less than or equal to 0 make up the set of numbers (-3 , -2 , -1, 0)

The collection of whole numbers and negative numbers is known as an integer in mathematics. Integers, like whole numbers, do not include the fractional portion. Integers can therefore be defined as numbers that can be positive, negative, or zero but not as fractions.

The formal definition of the set Z of integers is as follows: Z = {..., -3, -2, -1, 0, 1, 2, 3, ...} Unknown or unidentified integers are denoted in mathematical equations by lowercase, italicised letters from the "late middle" of the alphabet. P, q, r, and s are the most prevalent.

The category of whole numbers and the negative of natural numbers is known as integers. Thus, integers can be either positive or negative, including 0.

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The chain rule tells us where to search the derivative of a composite function.

d/dx[f(g(x))] =f'[f[g(x)g'(x).

A function is composite if you can write it as f(g(x)) In other words, it is a function within a function, or a function of a function.

Following steps should be followed to find chain rule:

1: Recognize the chain rule: The function needs to be a composite function, which implies one function is nested over the other one.

2: Know the inner function and the outer function respectively.

3: Determine the derivative of the outer function, dropping the inner function

4: Obtain the derivative of the inner function Step

5: Multiply the outcomes from step 4 and step 5 respectively.

6: Simplify the obtained chain rule derivative.

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The reference angles are given as -

The radian is the unit of angle in the International System of Units and is the standard unit of angular measure used in many areas of mathematics

Given are the angles as shown in the figure.

We can write the reference angles as -

- 34π/3 → -34 x π/3 → π/3

- 34π/3 → π/3

- 5π/12 → -5x π/12 → π/12

- 5π/12 → π/12

17π/6 → 17 x π/6 → π/6

17π/6 → π/6

Therefore, the reference angles are given as -

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The total cost of the nuts that Chris and Emily buy can be found using the expression: (1.6a) + (2.8c) + (0.7a) + (1.5c) You can also use the expression (10.6a) + (2.8c) for the total cost of nuts that Chris buy.

pound, unit of avoirdupois weight, equal to 16 ounces, 7,000 grains, or 0.45359237 kg, and of troy and apothecaries’ weight, equal to 12 ounces, 5,760 grains, or 0.3732417216 kg. The Roman ancestor of the modern pound, the libra, is the source of the abbreviation lb. In medieval England several derivations of the libra vied for general acceptance.

Among the earliest of these, the Tower pound, so called because its standard was kept in the Royal Mint in the Tower of London, was applied to precious metals and drugs and contained 5,400 grains, or 0.350 kg, whereas the mercantile pound contained 6,750 grains, or 0.437 kg. The troy pound, believed to have originated in Troyes, France, superseded the lighter Tower pound in 1527 as the gold and silver standard. Increased trade with France led also to the adoption of the 16-ounce avoirdupois pound in the 16th century to replace the mercantile pound.

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Graphical techniques are widely used to assess whether the data support the fractionation of a single source or the mixture of two putative sources.

For 210 items in total there will be 140 number of hats and 70 number of pairs of sunglasses.

To determine if the data support the mixing of two potential sources or the fractionation of a single source, graphical approaches are frequently used.

To better interpret their data, researchers now employ a variety of graphical tools, including scatterplots, box plots, and histograms. Graphs are excellent for illustrating trends, patterns, and correlations between variables as well as for displaying and summarizing vast volumes of numerical data.

We generate a graph for each equation in order to solve systems of equations or simultaneous equations graphically. Then, we search for the intersection of the two graphs. The system of equations would have a solution at the coordinates of the point of intersection.

Let x be the number of hats and y be the number of pairs of sunglasses.

The constraints exists:

2y = x (because for every 2 hats sold, 1 pair of sunglasses is sold)

y <= 100 (because the supplier can only provide 100 pairs of sunglasses)

x + y >= 210 (because you want to sell at least 210 items in total)

x, y >= 0 (because the number of items sold cannot be negative)

Lose in every hat is $3 and in Pair of Sunglasses is $ 2

Total loss in promotion or cost of promotion is

3x + 2y

For least purchase,

x + y = 210

⇒ x + x/2 = 210

⇒3x/2 = 210

⇒ x =140

y = 140/2 = 70

So, for 210 items in total there will be 140 number of hats and 70 number of pairs of sunglasses.

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For 210 items in total there will be 140 number of hats and 70 number of pairs of sunglasses.

What is meant by total?

Let x be the number of hats and y be the number of pairs of sunglasses.

The constraints exists:

2y = x (because for every 2 hats sold, 1 pair of sunglasses is sold)

y <= 100 (because the supplier can only provide 100 pairs of sunglasses)

x + y >= 210 (because you want to sell at least 210 items in total)

x, y >= 0 (because the number of items sold cannot be negative)

Lose in every hat is $3 and in Pair of Sunglasses is $ 2

Total loss in promotion or cost of promotion is

3x + 2y

For least purchase,

x + y = 210

⇒ x + x/2 = 210

⇒3x/2 = 210

⇒ x =140

y = 140/2 = 70

So, for 210 items in total there will be 140 number of hats and 70 number of pairs of sunglasses.

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Answer:

69

Step-by-step explanation:

The x-intercepts will be at x = 0 , -2 A line crosses the x-axis at the x-intercept, and the y-intercept is where the line crosses the y-axis.

Given

f(x) = x²(x+2)

To find the x-intercepts ⇒ f(x) = 0

∴ x²(x+2) = 0

∴ x² = 0  OR   x+ 2 = 0

∴ x = 0  or   x = -2

So, the x-intercepts will be at x = 0 , -2

We must graph the function f in order to determine whether the graph crosses the x-axis, hits the x-axis, and then reverses at each intercept (x)

The attached figure represents the graph of f(x)

As shown in the figure:

1)  The graph crosses the x-axis at x = -2

2) The graph touches the x-axis and turns around at x = 0

The complete question is,

Find the x-intercepts. State whether the graph crosses the x-axis or touches the x-axis and turns around at each intercept. Show your work.

f(x) = x2(x + 2)

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Transitivity: Assume that for some a, b, xRSy and yRSz, or xRaSy and yRbSz, exist. After that, aSRb, abbreviated as aSyRb. In light of the fact that SoR=RoS, we obtain aRSb, or, to use an example, aRcSb.

R and S should be two equivalence relations on X.

I want to demonstrate that the relationship RS is equivalent, but I am unable to demonstrate that it is transitive and reflexive.

regarding transitivity

There are random x and y with (x,y)RS, z with (x,z)R and (z,y)S, and what else?

Do I need to use R=S=S=R somewhere else?

As opposed to (x,y)R, I use the notation xRy. For some a, the term "xRSy" specifically refers to "xRaSy." Additionally, writing (xRy and yRz) is more convenient than writing xRySz. I would generally suggest drawing these relationships as graphs, with the vertices representing the points and the edges denoting the relationship.

assumption R=S=R.

Transitivity: Assume that for some a, b, xRSy and yRSz, or xRaSy and yRbSz, exist. After that, aSRb, abbreviated as aSyRb. In light of the fact that SoR=RoS, we obtain aRSb, or, to use an example, aRcSb. Then, as R,S are equivalence relations, xRcSz follows from xRaRcSbSz, and xRSz follows.

I'm sure you can now independently demonstrate reflexivity.

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You want to know the opinions of American school teachers about establishing a national test for high school graduation then correct option is  D) all American school teachers.

In statistics,  A population is a very large set of individuals or values that belong to a specified group established by researcher.

A sample is a subset of population that represents the entire population in research.

Given : We want to know the opinions of American school teachers about establishing a national test for high school graduation.

Clearly , by the above definition

Population =   all American school teachers.

You obtain a list of the members of the National Education Association and mail a questionnaire to 2500 teachers chosen at random from this list.

sample = 2500 teachers chosen at random from this list.

Hence, the intended population is all American school teachers.

Thus , the correct answer is D) all American school teachers.

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The fixed point of the function f(x) = x^2 + 1 is c = 0.

f(x) = x^2 + 1

c = 0

To find the fixed point of the function f, we can set the equation f(x) = x^2 + 1 equal to x, since the fixed point is when f(x) is equal to x.

Therefore, we can solve for x by setting x^2 + 1 = x. Re-arranging the equation, we get x^2 - x + 1 = 0.

Using the quadratic formula, x = (-(-1) ± √(1 - 4(1)(1))/(2(1))

Simplifying this expression, x = (-1 ± √3)/2.

Since we are looking for a real number, we can eliminate the negative solution and set x = (1 + √3)/2.

Therefore, the fixed point of the function f is c = 0.

The fixed point of the function f(x) = x^2 + 1 is c = 0.

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The number of students in the population would be:

The sample is directly related to the population of students so parts of the students can be found using the sample.

Students in population who wear glasses :

= Sample who wear glasses / Total sample x Total population

= 11 / 50 x 750

= 165 students

Students who wear contacts:

= 4 / 50 x 750

= 60 students

Students with no vision problems :

= 35 / 50 x 750

= 525 students

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Part A: The path of the ball in relation to the curved path of the thrower

Part A: The path the ball takes is perpendicular to the hand, bat, or feet  at the point of last contact

Part A:

A real-world example of tangents is the direction of a ball immediately after it is released and the circular path of the motion, that provides the force input that is given to the ball to cause it to move in the required direction

The tangent is the path the ball takes immediately after it is moving without contact with the bat, hand, or feet that causes it to move.

The circular path is the motion of the hand, leg, bat, or feet that makes before the ball is released.

The radius is the hand, leg, or bat that rotates in a circular path, so as to move the ball

Part B:

The radius, such as the leg kicking a ball is perpendicular to the tangent which is the path of the ball because a kick sends the ball into the air, the orientation of the leg at the point the ball leaves is perpendicular to the angle of elevation with which the ball is launched.

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Step-by-step explanation:

[tex]x = \frac{13}{8} \\ y = \frac{ - 7}{8} \\ 2y + x = - \frac{14}{8} + \frac{13}{8} = - \frac{1}{8} [/tex]

Answer:

-1/8

Step-by-step explanation:

x + y = 3/4

x -y = 5/2

2x = 13/4       3/4 + 5/2 = 3/4 + 10/4 = 13/4  Next divide both sides by 2

[tex]\frac{2x}{2}[/tex] = [tex]\frac{\frac{13}{4} }{2}[/tex]      [tex]\frac{13}{4}[/tex] ÷[tex]\frac{2}{1}[/tex] = [tex]\frac{13}{4}[/tex] x [tex]\frac{1}{2}[/tex] = [tex]\frac{13}{8}[/tex]

x = [tex]\frac{13}{8}[/tex]

plug in 13/8 for x in either of the two original equations.

x + y = 3/4

13/8 + y = 3/4  Subtract 13/8 from both sides

y = -7/8        3/4 - 13/8 = 6/8 - 13/8 = -7/8

Check:

substitute x = 13/8 and y = -7/8 back into the original two equations to see if the equations ae true

x + y = 34

13/8 - 7/8 = 3/4

6/8 = 3/4

3/4 = 3/4  Checks

x - y = 5/2

13/8 - (-7/8) = 5/2

13/8 + 7/8 = 5/2

20/8 = 5/2

5/2 = 5/2 Checks

Find the value of 2y + x

2(-7/8) + 13/8

-14/8 + 13/8

-1/8

The value of the probability of event C is 0.30.

The law of total probability states that

P(A U B U C) = P(A) + P(B) + P(C) - P(A n B) - P(A n C) - P(B n C) + P(A n B n C).

Substitute the known values in the above equation, so, we have the following representation

P(A U B U C) = 0.24 + 0.26 + P(C) - 0.05 - 0.05 - 0.05 + 0.02.

Also are given:

P(A U B U C)' = 0.33,

This implies that

P(A U B U C) = 1 - 0.33 = 0.67.

Substituting the values, we get:

0.67 = 0.24 + 0.26 + P(C) - 0.05 - 0.05 - 0.05 + 0.02

0.67 = 0.24 + 0.26 + P(C) - 0.15 + 0.02

0.67 = 0.50 + P(C) - 0.13

0.80 = 0.50 + P(C)

P(C) = 0.80 - 0.50 = 0.30.

Hence, the probability is 0.30

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