1. The Daily Statesman newspaper costs $6. 00 per week. The newspaper currently has 700


subscribers. The newspaper wants to increase its revenue and estimates that it will lose 40


customers for every $0. 75 increase in price. What weekly subscription price will maximize the


newspaper's weekly income? Round the answer to the nearest hundredth.

Answer:

28 is the total surface area!!

Step-by-step explanation:

A = 2(wl + hl + hw)

Answer:

\(\dfrac{2^3•5^2}{2^5•3•5^4}\)

=\(\dfrac{1}{2^2•3•5^2}\)

Fourth option is the right answer.

The independent variable in this experiment is the highly nutritious supplement.

The independent variable in this experiment is the highly nutritious supplement. The teacher is manipulating this variable by providing it to one group while not providing it to the other group. The dependent variable is the academic performance of the students. The teacher measures the performance of the students to see how it changes depending on whether or not they are given the supplement. The two groups of students and the same diet are controlled variables – variables that are kept the same, as they are not directly related to the experiment and the related hypothesized effect.

Therefore, the independent variable in this experiment is the highly nutritious supplement.

Learn more about the independent variable here:

brainly.com/question/29430246.

#SPJ4

Disclaimer: The shapes were missing. I have provided the required diagram.

The area of the given shape is 46.26cm².

Area of a triangle = (1/2)*base*height.

For a right-angled triangle, the base and height are the two sides making the right angle, that is, the base and the perpendicular.

∴ Area of a right-angled triangle = (1/2)*base*perpendicular.

We know the formula for the area of a circle is πr².

A semi-circle is half of the circle, so the area will also be its half.

∴ Area of a semi-circle = (πr²)/2

According to the Pythagoras theorem, the square of the hypotenuse is the sum of the squares of the other two sides. If we say the hypotenuse is 'c' and the other two sides are 'a' and 'b', then by the theorem:

a² + b² = c².

The given shape consists of one right-angled triangle and a semi-circle. To calculate its area, we first find the area of the right-angled triangle and the semi-circle individually and then add them to calculate the area of the shape.

Area of a right-angled triangle = (1/2)*base*perpendicular,

or, Area of a right-angled triangle = (1/2)*6*6 = 18cm².

We find AC using the Pythagoras theorem,

AC² = AB² + BC² = 6² + 6² = 72.

or, AC = √72 = √(36*2) = 6√2cm

The radius of the semi-circle (r)= (1/2)*diameter = (1/2)*6√2 = 3√2cm.

Area of a semi-circle = (πr²)/2,

or, Area of the semi-circle = (π*(3√2)²)/2 = 18π/2 = 9π.

Now, we can find the total area, by adding the two areas.

Area of the shape = Area of a right-angled triangle + Area of the semi-circle.

or, Area of the shape = 18 + 9π = 18 + 9*3.14 = 18 + 28.26 = 46.26cm²

Learn more about Area of shapes at

https://brainly.com/question/23848962

#SPJ2

Michael’s child is going to college in 13 years. If he saves $ 7,000 a year at 9% compounded annually. Therefore,  the amount available for Peter's child education will be $147,330.55.

Given that Michael is saving $7,000 per year for his child's education which will occur in 13 years. If the interest rate is 9% compounded annually,

The problem of finding the amount of money Michael will have saved in 13 years is a compound interest problem.

In this case, the formula for calculating the future value of the annuity is: $FV = A[(1 + r)n - 1] / r

where: FV is the future value of the annuity, A is the annual payment,r is the annual interest rate, and n is the number of payments.

Using the above formula; the future value of Michael's savings is:

FV = 7000[(1 + 0.09)^13 - 1] / 0.09= 7000(1.09^13 - 1) / 0.09= 147,330.55

Therefore, the amount available for Peter's child education will be $147,330.55.

Learn more about interest rate here:

https://brainly.com/question/27743950

#SPJ11

The area, in square units, bounded by f(x)= − 6x−13 and g(x)= − 7x+5 over the interval [33,34] is 1172.5

Area of bounded lines

f(x) = y₁ and g(x) = y₂

Area  = \(\int\limits^a_ b{y_{2} - y_{1} } \, dx\)

y₂ - y₁ = -7x + 5 - (-6x-13)

y₂ - y₁ = -7x + 5 + 6x + 13

y₂ - y₁ = -x + 18

Area = \(\int\limits^a_b {-x+18} \, dx\)

Area = [- x²/2 + 18x ]\(\left \{ {{a=34} \atop {b=33}} \right.\)

Area = [-(34)²/2 + 18 × 34 - (-(33)²/2 + 18 × 33]

Area = [ -578 + 612 + 544.5 +594]

Area = 1172.5

Area of the bounded region is 1172.5 sq. units

To know more about bounded click here :

https://brainly.com/question/32067810

#SPJ4

Answer:

the answer and explanation is in the picture

please like and Mark as brainliest

hope this helps

The coordinates of a vertex of the hyperbola are (0, a) and (0, -a) for the hyperbola \(y^2/a^2 - x^2/b^2 = 1\), where "a" and "b" are constants.

the given answer is provided below:Given, the coordinates of a vertex of the hyperbola are (0, −4), (−3, 0), (0, 0), and (0, 5).In order to determine which of these coordinates represents the vertex, we need to identify the value of a, which is the distance from the center of the hyperbola to the vertex, for the hyperbola equation.If a hyperbola is expressed in the form of\(y^2/a^2 - x^2/b^2 = 1\), where "a" and "b" are constants, then the center of the hyperbola is the origin (0, 0), and the distance between the center and the vertex along the y-axis is "a".Let's go over each point:1. (0, −4)Since this coordinate is four units below the origin, the value of "a" should be 4. Hence, the coordinates of the vertex would be (0, 4) and (0, -4).2. (−3, 0)

Since this coordinate is three units to the left of the origin, it is not a vertex.3. (0, 0)Since this coordinate is at the center of the hyperbola, it is not a vertex.4. (0, 5)Since this coordinate is five units above the origin, the value of "a" should be 5. Hence, the coordinates of the vertex would be (0, 5) and (0, -5).Therefore, the coordinates of the vertices are (0, 4) and (0, -4), and (0, 5) and (0, -5) respectively.

To know more about BODMAS visit:

https://brainly.com/question/29626866

#SPJ11

If Abby deposited $3000 and has $3600 at the end of 8 years, then the interest-rate is 2.5%.

The "Simple-Interest" is the interest which is calculated based only on principle amount of a loan or investment, without taking into account any additional interest earned on previous periods.

We can use the simple interest formula to find the annual interest rate:

⇒ Simple Interest = Principle × Rate × Time,

Where: Principle is = initial deposit of $3000,

Rate = annual interest rate (what we need to find)

Time = number of years the money was invested = 8,

The Simple Interest earned over 8 years : $3600 - $3000 = $600,

Substituting the values,

We get,

⇒ $600 = $3000 × Rate × 8,

⇒ Rate = 600/(3000 × 8),

⇒ Rate = 0.025, or 2.5%.

Therefore, the annual interest rate on the account is 2.5%.

Learn more about Simple Interest here

https://brainly.com/question/30964674

#SPJ1

To prove that 3 divides n^3 + 2n for any positive integer n, we need to show that there exists an integer k such that n^3 + 2n = 3k.

Let's proceed with the proof using mathematical induction:

Base case:

For n = 1, we have 1^3 + 2(1) = 1 + 2 = 3, which is divisible by 3. So the statement holds true for n = 1.

Inductive hypothesis:

Assume that the statement holds true for some positive integer k, i.e., k^3 + 2k = 3m, where m is an integer.

Inductive step:

We need to prove that the statement holds true for k + 1, i.e., (k + 1)^3 + 2(k + 1) = 3p, where p is an integer.

Expanding the expression (k + 1)^3 + 2(k + 1):

= k^3 + 3k^2 + 3k + 1 + 2k + 2

= (k^3 + 2k) + 3k^2 + 3k + 3

= 3m + 3k^2 + 3k + 3

= 3(m + k^2 + k + 1)

From the inductive hypothesis, we know that k^3 + 2k = 3m. Substituting this in the above expression:

= 3m + 3k^2 + 3k + 3

= 3(m + k^2 + k + 1)

We can see that the expression is a multiple of 3, with (m + k^2 + k + 1) as the coefficient.

Since m, k, and 1 are integers, (m + k^2 + k + 1) is also an integer. Therefore, (k + 1)^3 + 2(k + 1) is divisible by 3.

By using mathematical induction, we have proved that for any positive integer n, 3 divides n^3 + 2n.

To learn more about mathematical induction click here:

brainly.com/question/29503103

#SPJ11

The medicine bottle has 120 doses of 100 miligram each.

As per the known fact, 1000 miligram is 1 gram. So, the amount of medicine in the bottle in milligrams = 12×1000

Performing multiplication on Right Hand Side of the equation

Amount of medicine in bottle = 12000 milligrams.

Now, number of dose of 100 miligram medicine = 1

Amount of dose of 12000 miligram medicine = (1/100)×12000

Performing division and multiplication on Right Hand Side of the equation

Amount of doses in 12000 miligram medicine = 120

Thus, there are 120 doses in a medicine.

Learn more about dosage calculations -

https://brainly.com/question/24793154

#SPJ4

Answer:

$5 is the answer.......

Answer:

one box cost is $5

Step-by-step explanation:

$25 - $5 = $20 - this is the cos of four cereal boxes

$20 / 4 = $5 each box cost

The advantages of the superposition theorem compared to other circuit theorems are its simplicity and modularity in circuit analysis, as well as its applicability to linear circuits.

Superposition theorem is a powerful tool in circuit analysis that allows us to simplify complex circuits and analyze them in a more systematic manner. When compared to other circuit theorems, such as Ohm's Law or Kirchhoff's laws, the superposition theorem offers several advantages. Here are two key advantages of the superposition theorem:

Simplicity and Modularity: One major advantage of the superposition theorem is its simplicity and modular approach to circuit analysis. The theorem states that in a linear circuit with multiple independent sources, the response (current or voltage) across any component can be determined by considering each source individually while the other sources are turned off. This approach allows us to break down complex circuits into simpler sub-circuits and analyze them independently. By solving these individual sub-circuits and then superposing the results, we can determine the overall response of the circuit. This modular nature of the superposition theorem simplifies the analysis process, making it easier to understand and apply.

Applicability to Linear Circuits: Another advantage of the superposition theorem is its applicability to linear circuits. The theorem holds true for circuits that follow the principles of linearity, which means that the circuit components (resistors, capacitors, inductors, etc.) behave proportionally to the applied voltage or current. Linearity is a fundamental characteristic of many practical circuits, making the superposition theorem widely applicable in real-world scenarios. This advantage distinguishes the superposition theorem from other circuit theorems that may have limitations or restrictions on their application, depending on the circuit's characteristics.

It's important to note that the superposition theorem has its limitations as well. It assumes linearity and works only with independent sources, neglecting any nonlinear or dependent sources present in the circuit. Additionally, the superposition theorem can become time-consuming when dealing with a large number of sources. Despite these limitations, the advantages of simplicity and applicability to linear circuits make the superposition theorem a valuable tool in circuit analysis.

To learn more about superposition theorem visit : https://brainly.com/question/25329462

#SPJ11

Answer:

He is charged 5% simple interest per year. How much interest, in dollars, will Nate pay after 2 years? The interest after 2 years will be 0.05*300*2 = 30 dollars.

Answer:

0.1  exponent2  ( x − 2 y )  exponent 2

Step-by-step explanation:

The first step to solve this exercise is to write the Mixed number as a decimal number. You can do it by dividing the numerator by the denominator of the fractional part and adding the quotient to the Whole number part, as follows:

So:

Knowing that Positive numbers are greater than zero and knowing that Negatives numbers are less than zero, we can order the given numbers from greatest to least, as you can see below:

Yes, there are many rational numbers that can be plotted between 1/2 and 2/3 on the number line. Here are a few examples:

1/2 + 1/6 = 5/6: This rational number is greater than 1/2 and less than 2/3.

2/5: This rational number is also greater than 1/2 and less than 2/3.

1/3: This rational number is halfway between 1/2 and 2/3.

To plot a rational number on a number line, you can start by drawing the number line and marking off the positions of 1/2 and 2/3. Then, you can locate the position of the rational number you are trying to plot by dividing the distance between 1/2 and 2/3 into equal segments and finding the position of the rational number within those segments. For example, if you wanted to plot 5/6, you could divide the distance between 1/2 and 2/3 into six equal segments, and then mark the fifth segment as the position of 5/6 on the number line.

Therefore, the area of the quarter circle of radius 8 cm is 16π square centimeters (or approximately 50.2655 square centimeters if we use a decimal approximation for π).

A circle is a two-dimensional shape that is defined as the set of all points that are a fixed distance (called the radius) from a central point (called the center) in a plane. It is one of the most basic geometric shapes and is often used in a variety of mathematical and scientific contexts. One important thing to note about circles is that they are symmetrical: any line passing through the center of a circle divides the circle into two halves that are mirror images of each other. Circles are commonly used in a variety of contexts, including geometry, trigonometry, physics, engineering, and many other fields. They are also used in everyday life, such as in the design of wheels and other circular objects, the calculation of the areas of circular fields or gardens, and the measurement of circular objects like plates and bowls.

Here,

The formula for the area of a quarter circle is given by:

A = (1/4)πr²

where A is the area of the quarter circle, r is the radius of the circle, and π is the mathematical constant pi (approximately 3.14159).

In this case, the radius of the quarter circle is 8 cm, so we can substitute this value into the formula and simplify as follows:

A = (1/4)π(8 cm)²

A = (1/4)π(64 cm²)

A = 16π cm²

To know more about circle,

https://brainly.com/question/27802544

#SPJ1

Answer:

8 inches

Step-by-step explanation:

The coordinates of point E is (-2, -1.5)

How to determine the coordinates of point E?

see in the file attached below

The given parameters are

C = (1, 6)

D = (-3, -4)

The ratio 3/4 can be represented as:

m : n = 3 : 1

So, the coordinate of point E is

E = 1/(m + n) * (mx2 + nx1, my2 + ny1)

So, we have:

E = 1/(3 + 1) * (3 * -3 + 1 * 1, 3 * -4 + 1 * 6)

Evaluate

E = 1/(4) * (-8, -6)

This gives

E = (-2, -1.5)

Hence, the coordinates of point E is (-2, -1.5 )

learn more about line segments here

https://brainly.com/question/28243354

#SPJ4

27-1= 26 (the one book beside her bed)

26/8= 3.25, but there isn’t .25 of a shelf, so she needs 4 shelves to fit all of her books

The inability to recall the original random letters in the Peterson and Peterson (1959) experiment was due in part to the decay of information in short-term memory (STM).

STM has a limited capacity and duration, which means that information can be lost over time if it is not rehearsed or refreshed.

Know more about the short-term memory (STM).

https://brainly.com/question/12121626

#SPJ11

Answer:

30°

Step-by-step explanation:

We know that the angles in triangles always add up to 180°. There is also a right angle in this triangle, which is 90°.

Using this policy, we can assume that:

(3x - 30) + x + 90 = 180

First, we need to combine like terms. We can combine the 3x and the x, and the -30 and the 90.

4x + 60 = 180

Subtract 60 from both sides.

4x = 120

Divide by 4 on both sides.

x = 30

Answer:

Step-by-step explanation:

Mae Ling has  a salary of 340 dollars, plus 6.0% commission

she sold 4300 worth of merchandise, this will add to her

4300*6/100=258 dollars

Her salary in that week will be:

340+258=598 dollars

Answer:

It is not because the half the perimeter is not only one side but another half side of the triangle, and the distence between two points in a triangle can never become longer then the length of one side.

Step-by-step explanation:

The math part I am unsure of because you did say prove but let me know if this helps. Thanks!