The manager of a store increases the price of a popular product by 7%. Let t be the original
price of the product. The new price is t + 0.07t.

If the original price was $19.99, estimate the new price by first rounding the original price
to the nearest dollar.

Since this journalist writes n articles and gets 200(n + 7) for each article. If he gets N52000 altogether, the number of articles which he wrote is equal to 253 articles.

In order to determine the number of articles that was written by this journalist, we would simplify the expression and then determine the value of n as follows;

52,000 = 200(n + 7)

Opening the bracket through expansion, we have the following:

52,000 = 200n + 1,400

Subtracting 1,400 from both sides of the expression, we have the following:

52,000 - 1,400 = 200n + 1,400 - 1,400

Rearranging the expression, we have the following:

200n = 52,000 - 1,400

200n = 50,600

Dividing both sides of the expression by 200, we have the following:

n = 50,600/200

n = 253 articles.

In this context, we can reasonably infer and logically deduce that the total number of articles that was written by this journalist is equal to 253 articles.

Read more on expression here: https://brainly.com/question/25767785

#SPJ1

The volume of 3 cones = The volume of one cylinder.

The volume of 2 cones = The volume of one sphere.

The volume of 1 sphere = 2/3 the volume of one cylinder.

The volume of one cone = 1/3 the volume of one cylinder.

It is a shape of a Christmas tree where there is a base of radius r and a top point called the apex.

The volume of a cone is 1/3πr²h.

We have,

Volume of a cylinder = πr²h

Volume of a cone = 1/3 πr²h

Volume of a sphere = 4/3 πr³

Now,

The radius is the same.

Height of cone and cylinder = 2r

The new volume:

Volume of a cylinder = 2πr³

Volume of a cone = 2/3 πr³

Volume of a sphere = 4/3 πr³

Thus,

Volume of 3 cones = 2πr³ = volume of one cylinder

Volume of 2 cones = 4/3 πr³ = volume of one sphere

Volume of 1 sphere = 4/3 πr³ = 2/3 x volume of a cylinder

Volume of one cone = 2/3 πr³ = 1/3 x volume of cylinder

Learn more about cones here:

https://brainly.com/question/13798146

#SPJ1

Answer:

b = 8

Step-by-step explanation:

cosΘ = 4/7 = adjacent/hypotenuse

Therefore:

4/7 = b/14

7b = 56

b = 56/7 = 8

The amount received after 3 years is ₹12950.

Compound interest is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.

The formula used to find the compound interest = [tex]A=P(1+\frac{r}{100})^{nt}[/tex]

Given that, principal = ₹10,000, rate of interest =9% and time period = 3 years.

Now, amount =10000(1+9/100)³

= 10000(1.09)³

= 10000×1.295

= ₹12950

Therefore, the amount is ₹12950.

To learn more about the compound interest visit:

https://brainly.com/question/14295570.

#SPJ1

The probability that each guest got one roll of each type is 3/1, which is a fraction with a numerator of 3 and a denominator of 1. Since the numerator and denominator are relatively prime integers, the value of m + n is 3

The equation for the probability that each guest got one roll of each type is m/n, where m and n are relatively prime integers.

We can expand this equation to

m/n

= 3/1.

Since the numerator and denominator are relatively prime integers, we can solve for m + n by multiplying both sides of the equation by 1.

Multiplying both sides of the equation by 1 gives us

m + n = 3.

Therefore, the value of

m + n is 3.

Let m = numerator and n = denominator in the probability of m/n.

Given that each guest got one roll of each type, the probability is m/n.

The numerator and denominator are relatively prime integers, so m and n have no common factors.

Therefore,

m + n = 3.

Learn more about probability here

https://brainly.com/question/11234923

#SPJ4

Answer:

To find the x-intercepts and y-intercepts of a function, we need to find the values of x and y at which the function crosses the x-axis or y-axis.

X-intercepts:

The x-intercepts occur when y = 0, so we can set f(x) = 0 and solve for x:

3x³-12x²-15x = 0

This is a cubic equation, we can use factoring, synthetic division or use a numerical method like the Newton-Raphson method to solve for x.

Y-intercepts:

The y-intercepts occur when x = 0, so we can substitute x = 0 into the function to find the y-intercept:

f(0) = 3(0)³ - 12(0)² - 15(0) = 0

So the y-intercept of the graph is at the point (0,0)

In summary, the x-intercepts are the solutions of the equation 3x³-12x²-15x = 0 and the y-intercept is (0,0)

Please note that, if the equation has complex roots, the graph will not cross the x-axis and hence it will not have any real x-intercepts.

Step-by-step explanation:

A 3rd degree polynomial function with real coefficients satisfying the given condition. 2 and -3 +3i are zeros; leading coefficients is 1, is:

f(x) = x³ + 4x² + 6x - 36

An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).

A polynomial function is one that uses only non-negative integer powers or positive number coefficients of such a variables in such an expression like the quadratic function, cubic equation, and so on.

we have to find third degree polynomial, so, n = 3

Since 2 is its zero ,so, x - 2 is its factor

As complex zeros occur in conjugate pairs .

So,other factors are (x + (3 + 3i)) and (x + (3 - 3i)) ,

Firstly, we find the product of these two factors:

= x² + 6x + 9 - 9i²

= x² +6x +9 - 9(-1)

= (x² +6x + 18)

Now multiply (x² +6x + 18) with (x - 2) we get f(x):

= (x² +6x + 18) (x - 2)

= x³ - 2x² + 6x² - 12x + 18x - 36

= x³ + 4x² + 6x - 36

Correct option: b

To know more about polynomial function refer to:

https://brainly.com/question/7693326

#SPJ1

Answer:

Read below

Step-by-step explanation:

) To find the percentage loss on the sale of the refrigerator, we need to subtract the selling price from the cost price and divide that number by the cost price. Then, multiply the result by 100% to express the answer as a percentage.

(280 - 224) / 280 * 100% = 57.14% loss

b) To find the selling price if the profit is 15% of the cost price, we need to add 15% of the cost price to the cost price.

280 + (15% * 280) = 280 + 42 = $322

c) To find the new price of the refrigerator after a 43% discount, we need to subtract 43% of the cost price from the cost price.

280 - (43% * 280) = 280 - 120.4 = $159.60

The average change in the price per mp3 download was a decrease of $0.06 per year because 0.3/5 is 0.06

A division is a process of splitting a specific amount into equal parts.

Given that price per mp3 download 5 years ago was $0.99.

Now, each mp3 download costs $1.29.

We have to find the difference between cost 5 years back and now

1.29-0.99

Which is 0.3

The change is 0.3 for five years.

Now we have to find the change per year.

To find this we have to divide 0.3 by 5.

0.3/5

0.06

Hence, option C is correct. The average change in the price per mp3 download was a decrease of $0.06 per year because 0.3/5 is 0.06

To learn more on Division click:

https://brainly.com/question/21416852

#SPJ1

The total number of students in the school is 1100

From the question, we have the following parameters that can be used in our computation:

Number of students that play a sport = 528

Proportion of students that play a sport = 48%

Using the above as a guide, we have the following:

Number of students that play a sport = Proportion of students that play a sport * number of students in the school

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

48% * number of students in the school = 528

Express as decimal

This gives

0.48 * number of students in the school = 528

Divide both sides by 0.48

number of students in the school = 528/0.48

Evaluate

number of students in the school = 1100

Hence, the students are 1100

Read more about proportion at

https://brainly.com/question/12535721

#SPJ1

The triangles are congruent with SAS property.

In mathematics, the term "congruent" refers to figures and shapes that can be flipped or rearranged to match up with other ones. These forms can be mirrored to produce related shapes.

A triangle is a closed polygon with three line segments that intersect at each of its three angles.

When the sides and angles of two triangles match, the triangles are said to be congruent. Thus, two triangles can be placed side by side and angle by angle on top of one another.

Given  question shows ΔABC and ΔADC

AD is parallel to AB,

AD = AB (equal sides)

∠DAC equal to ∠BAC

∠DAC = ∠BAC (angle equal)

and AC is common

AC =AC common side

so ΔABC ≅ ΔADC

by SAS (side angle side) property

B: since both triangles are congruent,

so BC = DC

∠BCA = ∠DCA

and ∠B = ∠D

because of congruency.

Hence, triangles are congruent by SAS property and and all remaining angles and sides are equal.

Learn more about  congruent triangles;

https://brainly.com/question/12413243

#SPJ1

On solving the provided question, we can say that in the line, The value of x is 5; the length of in inches is 5; the length of ec in inches is 15

A line is an endlessly long object without breadth, depth, or curvature in geometry. Consequently, a line is a one-dimensional entity, while it may also exist in two-, three-, and more-dimensional regions. In common use, a line segment with two points serving as its ends is referred to as a line. A line is a single-dimensional, straight form with no thickness that can go on forever in both directions. To indicate that a line has no "wobble" anywhere along its length, it is frequently referred to as a straight line or an ancient accurate line.

here,

The value of x is 5

The length of in inches is 5

The length of ec in inches is 15

To know more about line visit:

https://brainly.com/question/2696693

#SPJ1

Answer:D

Step-by-step explanation:i think

You can prove the difference of two cubes identity. a³ – b³ = (a – b)(a² + ab + b²) based on the following responses:

A. Use the distributive property to multiply the factors on the right side of the equation.

B. Simplify the product by combining like terms.

C. Show that the right side of the equation can be written exactly the same as the left side.

D. Show that the right side of the equation simplifies to a cubed minus b cubed.

In Mathematics, the distributive property of multiplication states that when the sum of two (2) or more addends are multiplied by a particular numerical value, the same result and output would be obtained as when each addend is multiplied respectively by the same numerical value, and the products are added together.

By applying the distributive property of multiplication to the given mathematical expression, we have the following:

a³ – b³ = (a - b)(a² + ab + b²)

a³ – b³ = a(a² + ab + b²) - b(a² + ab + b²)

Next, we would combine like terms:

a³ – b³ = a³ + a²b + ab² - a²b - ab² - b³

a³ - b³ = a³ - b³.

Read more on distributive property here; https://brainly.com/question/18706722

#SPJ1

Complete Question:

Explain how you can prove the difference of two cubes identity. a³ – b³ = (a – b)(a² + ab + b²)

Which of the following did you include in your response? Check all of the boxes that apply.

Use the distributive property to multiply the factors on the right side of the equation.

Simplify the product by combining like terms.

Show that the right side of the equation can be written exactly the same as the left side.

Show that the right side of the equation simplifies to a cubed minus b cubed.

The equation of an exponential function is y = a * b^x, where a and b are constants, and x is the independent variable.

A function is a block of organized, reusable code that is used to perform a single, related action. It is used to make a program easier to read, debug, and maintain. Functions are key to programming languages as they allow code to be broken into smaller, more manageable parts that can be easily reused, updated, and modified. Functions can also be used to pass data between different parts of a program.

From the graph, the equation of the function can be determined by finding the values of a and b. To do this, we need to identify two points on the graph and then calculate a and b using those points. For example, if we choose the points (0,2) and (2,8),

we can calculate a and b using the equation y = a * b^x, such that 2 = a * b^0 and 8 = a * b^2.

Using these equations, we can solve for a and b, yielding a = 2 and b = 2.

Therefore, the equation of the exponential function in the graph is y = 2 * 2^x.

To know more about function click-
https://brainly.com/question/25638609
#SPJ1

We may conclude from the stated answer that: (here on the graph, we have on solving equation =[tex]x^2 + 3y^2 = > 7[/tex]

A mathematical equation is a formula that connects two assertions using the equal sign (=) to signify equivalence. A mathematical statement demonstrating the equivalence of two mathematical expressions is the definition of an equation in algebra. For instance, the variables 3x + 5 and 14 are separated by an equal sign in the equation 3x + 5 = 14. Mathematically, the connection between two sentences on each side of a letter is stated. The symbol doubles as the sole variable most of the time. for illustration, 2x - 4 = 2.

here-

Graph shows that x=2.

y = 1

[tex]x^2 + 3y^2\\7[/tex]

To know more about equation visit:

brainly.com/question/649785

#SPJ1

On solving the provided question, we can say that -the  given graph is a starlight lined .

Graphs are visual representations or charts used in mathematics to methodically express data or values. A relationship between two or more objects is frequently represented by a point on a graph. A non-linear data structure called a graph is made up of nodes, or vertices, and edges. Connect the nodes, also known as vertices. This graph comprises a set of vertices V= 1, 2, 3, 5, and a set of edges E= 1, 2, 1, 3, 2, 4, and (2.5), (3.5), (4.5). Statistics graphs (bar charts, pie charts, line charts, etc.) Exponential diagrams. triangle graph, a logarithmic graph

here,

in the graphs we have been given a straight line,

so its a straight line graphs

To know more about graphs visit:

https://brainly.com/question/11950136

#SPJ1

For constant A to be -4 (option 1) the system of equations have exactly one real solution.

NOTE: We are working with the problem statement: Y=-3 Y=Ax2+4x-4 In the system of equations above, a is constant. For which of the following values of a does the system of equations have exactly one real solution?

We have given, y=-3

y= Ax^2+4x-4

Therefore, -3= Ax^2+4x-4

or, Ax^2+4x-1=0

For second order equation of ax^2+bx+c=0 have a solution for

x= [-b± (√b^2-4ac)]/2a]   [Ax2 + Bx + C = 0 is the Sridharacharya equation, where a, b, and c are real values and a 0. The Sridharacharya formula, which is stated as x = (-b (b2 - 4ac)) / 2a, provides the answer to the Sridharacharya equation.]

For single solution b^2-4ac=0

here, Ax^2+4x-1=0

4^2 - 4a(-1)=0

16+4a=0

a= -(16)/4

a= -4

option A is correct .

For more quadratic equation problem here:

https://brainly.com/question/1863222#

#SPJ4

This is only true equation when A is equal to -2. Therefore, the correct answer is B) -2.

B) -2

The given system of equations can be written as:

Y = A*x^2 + 4*x - 4

We can solve this equation by using the Quadratic Formula. The Quadratic Formula states that the solutions to the equation are given by:

x = [-b +/- sqrt(b^2-4ac)]/2a

where a, b, and c are the coefficients of the equation. In this case, a = A, b = 4, and c = -4.

Substituting these values into the equation, we get:

x = [-4 +/- sqrt(4^2-4*A*(-4))]/2A

Simplifying this, we get:

x = [-4 +/- sqrt(16 + 16A)]/2A

For the system of equations to have two real solutions, the value of the square root must be greater than or equal to zero. This means that 16 + 16A must be greater than or equal to zero.

This is only true when A is equal to -2. Therefore, the correct answer is B) -2.

Learn more about equation here

https://brainly.com/question/29657992

#SPJ4

The mean price of a loaf of bread at five supermarket is 1.71.

From the information, yesterday the price of a loaf of bread at five supermarkets was 1.54, 1.69, 1.79, 1.57, and 1.71, but today each supermarket raised its price by 0.05.

The mean price of a loaf of bread at five supermarket will be:

(1.54 + 1.69 + 1.79 + 1.57 + 1.71) + (0.05 × 5) / 5

= 8.55 / 5

= 1.71

The mean price is 1.71.

Learn more about mean on:

brainly.com/question/1136789

#SPJ1

Answer: Write properties of function:

vertex form:

vertex form:

vertex:

vertex:

Answer:

See the graph below

Step-by-step explanation:

Answer:

A)  Exponential function

[tex]\textsf{B)} \quad y = 2(2)^x[/tex]

C)   12

Step-by-step explanation:

Given points:

In a linear function, the y-values have equal differences.  

In an exponential function, the y-values have equal ratios.

From inspection of the given points, we can see that y doubles each time x increases by 1 unit, therefore the data models an exponential function.

[tex]\boxed{\begin{minipage}{9 cm}\underline{General form of an Exponential Function}\\\\$y=ab^x$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the initial value ($y$-intercept). \\ \phantom{ww}$\bullet$ $b$ is the base (growth/decay factor) in decimal form.\\\end{minipage}}[/tex]

As the function doubles, the base is 2.

Substitute one of the points (1, 4) and b = 2 into the formula and solve for a:

[tex]\implies 4=a \cdot 2^1[/tex]

[tex]\implies 4=2a[/tex]

[tex]\implies a = 2[/tex]

Substitute the found values of a and b into the formula to create the exponential function to represent the given data:

[tex]y=2(2)^x[/tex]

[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Average rate of change of function $f(x)$}\\\\$\dfrac{f(b)-f(a)}{b-a}$\\\\over the interval $a \leq x \leq b$\\\end{minipage}}[/tex]

Station 2:  (2, 8)

Station 4:  (4, 32)

To determine the average rate of change between station 2 and station 4 find the average rate of change over the interval 2 ≤ x ≤ 4.

Therefore, a = 2 and b = 4:

[tex]\implies \textsf{Rate of change}=\dfrac{f(4)-f(2)}{4-2}=\dfrac{32-8}{4-2}=\dfrac{24}{2}=12[/tex]

Answer:Answer: (i) The capacity of the bucket in litres = π × 30 × 30 × 0.4 = 113.04 litres.

(ii) The volume of water required to fill the tank in litres = π × 1.2 × 1.2 × 1.35 × 0.8 = 4.72 m3.

(iii) The number of buckets that must be drawn to fill the tank = 4.72 m3 / 113.04 litres = 41.76 = 42 buckets.

Step-by-step explanation:

Answer: add 2 to the input to have the output.

Step-by-step explanation: X=The Input and you have to mulitiply the input by the positive number then add it to the original number to get the output.

Answer:

a) There is only one hole in a whole.

b) There are five fifths in a whole. In four wholes, there would be 5 x 4 = 20 fifths.

c) There are eight fourths in two wholes. In five wholes, there would be 8 x 5 = 40 fourths.

Give me a harder one lol

Step-by-step explanation:

Answer:

A bag of almonds that weighs 1.6 ounces will cost $0.51 x 1.6 = $<<0.51*1.6=0.816>>0.816.

Step-by-step explanation:

Answer:

3x + 1

Step-by-step explanation:

1/5/2023

7:25PM

answer........................

3x +1

Answer:

Yes he did finish the book on the second day as 1/4=2/8  so 5/8-2/8=3/8 so he read 5/8 on the first day and 3/8 on the second day and 5/8+3/8=8/8=1

Step-by-step explanation:

1/4=2/8  so 5/8-2/8=3/8 so he read 5/8 on the first day and 3/8 on the second day and 5/8+3/8=8/8=1