A storekeeper increased the price of hats by `5\%`. If the price of a hat (after the increase) is `\$33. 60`, what is the original price?

False. In the given scenario, the statement "the cost function is always greater than the revenue function" is unrelated to the question about drawing three numbers whose sum is 13.

The truth or falsity of the statement does not affect the calculation of the number of ways three numbers can be drawn with a sum of 13.

To determine the number of ways three numbers can be drawn with a sum of 13, we can use a combinatorial approach. We need to find the number of combinations of three numbers from the set {1, 2, 3, ..., 10} that add up to 13. This can be done by considering different cases and using combinations or counting techniques.

Note: If you have any further questions regarding the cost and revenue functions or any other topic, please let me know, and I'll be happy to assist you.

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Answer:

Each will receive \(\frac{1}{6}th\) of the cake.

Step-by-step explanation:

Let the amount of cake = c

Lisa, Juan and Isaac are the persons who are sharing half of a cake equally.

Number of persons = 3

Part of the cake shared = \(\frac{c}{2}\)

Fraction of the cake shared by each = \(\frac{\text{Amount of cake shared}}{\text{Number of persons who shared}}\)

                                                             = \(\frac{\frac{1}{2}c}{3}\)

                                                             = \(\frac{1}{6}c\)

Therefore, fraction of total cake shared by each member will be \(\frac{1}{6}\) of the total amount of cake.

By using a maclaurin series to obtain the maclaurin series for the given function is  F(x) = x cos(5x) = \(1 - 25x^2/2! + 625x^4/4! - 15625x^6/6! + ...\)

To obtain the Maclaurin series for the function f(x) = x cos(5x), we need to write the Maclaurin series for cos(5x). The Maclaurin series for cos(x) is: \(cos(x) = 1 - x^2/2! + x^4/4! - x^6/6! + ...\)

Using this formula, we can substitute 5x for x and obtain the Maclaurin series for cos(5x): cos(5x) =\(1 - (5x)^2/2! + (5x)^4/4! - (5x)^6/6! + ...\)

\(= 1 - 25x^2/2! + 625x^4/4! - 15625x^6/6! + ...\)

We can substitute this series into the original function f(x) = x cos(5x) and obtain its Maclaurin series: f(x) = x cos(5x)

\(= x[1 - 25x^2/2! + 625x^4/4! - 15625x^6/6! + ...]\)

\(= x - 25x^3/2! + 625x^5/4! - 15625x^7/6! + ...\)

This is the Maclaurin series for the function f(x) = x cos(5x). It is obtained by substituting the Maclaurin series for cos(5x) into the original function and simplifying the resulting series. Maclaurin series are useful for approximating functions using polynomials. By truncating the series after a certain number of terms, we can obtain a polynomial that approximates the original function to a certain degree of accuracy. The accuracy of the approximation depends on the number of terms in the series that are used. The more terms we include, the more accurate the approximation will be.

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Answer: 5

Step-by-step explanation:

Answer: 650

Step-by-step explanation:

25/13.7 = x/360

[cross multiply] : (360)(25)/(13.7)(x)

= 9000/13.7

X=656.9

which is closest to 650

Answer choice for 650

Kyla will hike close to 650 meters in 6 minutes if she maintains the same speed.

Proportions are defined as the statement when two or more ratios are made to be equal to each other.

Two quantities are said to be directly proportional is they decrease or increase in the same ratio.

If a : b = c : d, then we can write a/b = c/d.

Distance Kyla hikes in 13.7 seconds = 25 meters

We have to find the distance Kyla hikes in 6 minutes.

Here, as the distance increases or decreases, time also increases or decreases. Hence the quantities distance and time are directly proportional.

Let x be the distance covered by Kyla in 6 minutes

Also 6 minutes = 360 seconds

We can write,

25 : 13.7 = x : 360

25/13.7 = x/360

x = (25 × 360) / 13.7

x = 9000 / 13.7

x = 656.9 ≈ 650 meters

Hence Kyla will hike close to 650 meters in 6 minutes.

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The two polygons are similar if the corresponding angles are congruent and the corresponding sides are proportional,the value of x is 8.

The two polygons are similar if the corresponding angles are congruent and the corresponding sides are proportional. Therefore, the ratio of the lengths of the sides of the two polygons is equal to the ratio of the measures of the corresponding angles.

In this case, the ratio of the corresponding side lengths of the two polygons is equal to the ratio of the measures of the corresponding angles. The ratio of the lengths of the two sides of the larger polygon (x-3 , 8 and 16) is (x-3)/8 : 8/16. This ratio is equal to the ratio of the measures of the corresponding angles of the two polygons, which is 2.5/2 : 2/4.

Equating these two ratios, we get (x-3)/8 = 2.5/2 and 8/16 = 2/4. Solving these two equations, we get x-3 = 5 and 8 = 4. Adding 3 to both sides, we get x = 8. Hence, the value of x is 8.Therefore, the value of x is 8.

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The demand function can be derived from the marginal revenue function. To find the demand function, we need to integrate the marginal revenue function to obtain the revenue function and then solve for the price function. We can then obtain the demand function by solving for the quantity demanded at each price point. The integral that is needed to solve the problem is: \[R(x) = \int R'(x) \, dx = \int (499 - 0.15\sqrt{x}) \, dx\].

Given that the revenue is zero when no items are sold, the revenue function can be found by integrating the marginal revenue function as follows:

\[R(x) = \int R'(x) \, dx = \int (499 - 0.15\sqrt{x}) \, dx\]

\[R(x) = 499x - \frac{0.3}{2/3} x^{3/2} + C\]

where C is the constant of integration. Since the revenue is zero when no items are sold, we can solve for C as follows:

\[R(0) = 0 = C\]

Therefore, the revenue function is:

\[R(x) = 499x - \frac{0.3}{2/3} x^{3/2}\]

To find the price function, we need to solve for the price at each quantity demanded. The price is equal to the marginal revenue, which is the derivative of the revenue function with respect to the quantity demanded. Therefore, the price function is:

\[P(x) = R'(x) = 499 - 0.15\sqrt{x}\]

To find the demand function, we need to solve for the quantity demanded at each price point. The demand function is the inverse of the price function. Therefore, we need to solve for x in terms of P as follows:

\[P = 499 - 0.15\sqrt{x}\]

\[0.15\sqrt{x} = 499 - P\]

\[\sqrt{x} = \frac{499 - P}{0.15}\]

\[x = \left(\frac{499 - P}{0.15}\right)^2\]

Therefore, the demand function is:

\[x = \left(\frac{499 - P}{0.15}\right)^2\]

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Let's start by finding the length of one edge of the original cube.

The surface area of a cube can be expressed as 6s^2, where s is the length of one edge.

So we have:

6s^2 = 2400

Solving for s, we get:

s = sqrt(2400/6)

s = 20

Therefore, the original cube has an edge length of 20 cm.

To find the volume of the similar box enlarged by a scale factor of 1.5, we need to multiply the volume of the original cube by (1.5)^3, since the scale factor applies to all three dimensions (length, width, and height).

The volume of the original cube is:

V = s^3 = 20^3 = 8000 cm³

So the volume of the similar box is:

V' = V x (1.5)^3 = 8000 x 1.5^3 = 8000 x 3.375 = 27000 cm³

Therefore, the volume of the similar box enlarged by a scale factor of 1.5 is 27,000 cm³.

Answer:

21.8

Step-by-step explanation:

The equation 2 + 3 = 3 + x has an infinite number of solutions.

A value of x that makes the equation true is -1, which when substituted into the equation and simplified makes the equation turn into 2 + 3 = 3 - 1 = 2.

Another value of x that makes the equation true is -4, which when substituted into the equation and simplified makes the equation turn into 2 + 3 = 3 - 4 = -1.

Therefore, the equation 2 + 3 = 3 + x has an infinite number of solutions.

A quadratic equation is a polynomial equation of degree 2, written in the form:

ax^2 + bx + c = 0

where a, b, and c are constants and x is an unknown variable. The equation can be solved to find the values of x that satisfy the equation, known as the roots or solutions. These solutions can be found using methods such as factoring, the quadratic formula, or completing the square.

Quadratic equations are commonly used in mathematics, science, and engineering to model and solve a wide range of real-world problems, such as modeling the trajectory of a projectile or finding the minimum or maximum value of a function.

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5 is pushed to the stack.63- : 3 and 6 are pushed to the stack.  (10+5)/(6−3) is the equivalent infix expression.

Given postfix (reverse Polish notation) 105+63−/ is to be converted to its equivalent infix expression which is: (10+5)/(6−3).Explanation:Postfix notation (also known as Reverse Polish notation) is a way of representing expressions in which the operator follows the operands. So, first operand comes first followed by second operand and then operator.So, the given postfix (reverse Polish notation) can be explained as below:105+ : First, 1 and 0 are pushed to the stack. When the operator + is encountered, the top two operands are popped from the stack and added. Therefore, 5 is pushed to the stack.63- : 3 and 6 are pushed to the stack. When the operator - is encountered, the top two operands are popped from the stack and subtracted. Therefore, 3 is pushed to the stack./ : When the operator / is encountered, the top two operands are popped from the stack and divided. Therefore, the final result is 1.Now, let's convert it to the infix notation as below:(10+5)/(6−3)Hence, (10+5)/(6−3) is the equivalent infix expression.

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Answer:

t=17.36951

so the answer would be 17.4 mins

John initially had Php 132 and Mary initially had Php 252 (384 - 132).

Let's start by setting up the equations to solve for this problem.

Let x be the amount of money John had initially.

Then, Mary had (384 - x) initially.

After John gave Php 36 to Mary, John had (x - 36) left and Mary had (384 - x + 36) = (420 - x).

We are told that Mary had three times as much money as John after this transaction, so we can write:

3(x - 36) = 420 - x

Simplifying this equation gives:

3x - 108 = 420 - x

4x = 528

x = 132

Therefore, John initially had Php 132 and Mary initially had Php 252 (384 - 132).

Answer: Mary had Php 252 at first.

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Answer:

L=2v/n -c n and -c is seperated.

Answer:

$18,480

Step-by-step explanation:

so rate of the car, increases annually by 14%

so in 4 years time it will be 14×4= 56%

new car purchased is $42,000

to find the car's value in 4 years time it would be

100%-56%,which is 44%

then 44% of $ 42,000 will give you

$18,480

According to the given statement 5 men and 12 boys finish a piece of work in 4 days, 7 men and 6 boys do it in 5 days. The ratio between the efficiencies of a man and a boy is 1 : 3.

To find the ratio between the efficiencies of a man and a boy, we need to compare the amount of work each man and each boy can do in a given time.

Let's assume that the efficiency of a man is M and the efficiency of a boy is B.

From the first scenario, we know that 5 men and 12 boys finish the work in 4 days.

This means that the combined efficiency of the 5 men is 5M and the combined efficiency of the 12 boys is 12B.

So, in 4 days, we have:
5M + 12B = 1

From the second scenario, we know that 7 men and 6 boys finish the work in 5 days.

This means that the combined efficiency of the 7 men is 7M and the combined efficiency of the 6 boys is 6B.

So, in 5 days, we have:
7M + 6B = 1

Now, we can solve these two equations simultaneously to find the values of M and B.

Multiply the first equation by 7 and the second equation by 5 to eliminate M:

35M + 84B = 7
35M + 30B = 5

Subtract the second equation from the first equation:

54B = 2

Divide both sides by 54:

B = 1/27

Now, substitute the value of B into any of the original equations to find M.

Let's use the first equation:

5M + 12(1/27) = 1
5M + 4/9 = 1
5M = 5/9
M = 1/9

Therefore, the ratio between the efficiencies of a man and a boy is:
M : B = (1/9) : (1/27)

To simplify the ratio, we can multiply both the numerator and denominator of the boy's efficiency by 3:

M : B = (1/9) : (3/27)
        = 1 : 3

So, the ratio between the efficiencies of a man and a boy is 1 : 3.

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For every 12 boy-days of work, a man completes 5 days in the first scenario. And in the second scenario, for every 6 boy-days of work, a man completes 7 days. The efficiency ratio between a man and a boy is:
First scenario: 5 men-days / 12 boy-days
Second scenario: 7 men-days / 6 boy-days

The efficiency of a person is measured by the amount of work they can complete in a given time. Let's find the efficiency ratio between a man and a boy.

In the first scenario, 5 men and 12 boys finish the work in 4 days. To find the total work done, we multiply the number of people by the number of days: (5 men + 12 boys) x 4 days = 20 men-days + 48 boy-days.

In the second scenario, 7 men and 6 boys finish the work in 5 days. Using the same logic, we get: (7 men + 6 boys) x 5 days = 35 men-days + 30 boy-days.

To find the efficiency ratio between a man and a boy, we can compare the work done by men to the work done by boys in both scenarios.

In the first scenario, the ratio of men's work to boys' work is 20 men-days : 48 boy-days.
In the second scenario, the ratio of men's work to boys' work is 35 men-days : 30 boy-days.

To simplify the ratios, we can divide the number of men-days and boy-days by their greatest common divisor (GCD). The GCD of 20 and 48 is 4, and the GCD of 35 and 30 is 5.

After dividing, we get the simplified ratio of men's work to boys' work:
First scenario: 5 men-days : 12 boy-days
Second scenario: 7 men-days : 6 boy-days

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Step-by-step explanation:

the correct answer is option a 6a-7

The argument presented is an example of a fallacy known as affirming the consequent, which incorrectly assumes that if the consequent of a conditional statement is true, then the antecedent must also be true. It fails to consider other possibilities and overlooks the fact that not all square shapes are cubes.

The argument presented is an example of a fallacy known as affirming the consequent, which is a formal logical fallacy. This fallacy occurs when one assumes that if the consequent (the "then" part) of a conditional statement is true, then the antecedent (the "if" part) must also be true.

In this case, the argument incorrectly assumes that because all cubes are square (if cube, then square) and a dice is a cube, then the dice must be square. However, this reasoning is flawed. While it is true that all cubes are square, not all square shapes are cubes. Therefore, even though a dice is a cube, it does not necessarily mean that it must be square.

The argument fails to consider other possibilities, such as the fact that cubes can have other shapes besides squares, like rectangular cubes. This logical error highlights the importance of careful reasoning and avoiding fallacies when making arguments.

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Answer:

2.95

Step-by-step explanation:

When we have a problem like this (-2.05)-(-5)

It becomes -2.05+5 because two negatives make a positive, then we add them and we get 2.95

A set of reflections that would carry hexagon ABCDEF onto itself would be "x-axis, y=x, x-axis" or "y=x, x-axis, y-axis".

What is a combination of reflections?

Combination of Two Reflections. A point or object once reflected can further be reflected to form a new image. The axes of these reflections may be parallel to each other or they intersect each other at a point.

Given the coordinates of hexagon ABCDEF, it can be determined that a set of reflections that would carry the hexagon onto itself would be a combination of reflections over the x-axis and y-axis.

One possibility would be to reflect over the x-axis, then reflect over the y=x line, and finally reflect over the x-axis again.

This would take the hexagon from its original position to itself.

Another possibility would be to reflect over the y = x line, then reflect over the x-axis, and finally reflect over the y-axis.

This would also take the hexagon from its original position to itself.

Hence, a set of reflections that would carry hexagon ABCDEF onto itself would be "x-axis, y=x, x-axis" or "y=x, x-axis, y-axis".

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7x-4 and 6x-4+x, Both the equations are equivalent

Given two equations i.e. 7x-4 and 6x-4+x, and asked whether these equations are equivalent or not

Equivalent equations :

Equivalent equations are algebraic equations with the same solution or roots. Equivalent equations are created by adding or subtracting the same number or expression from both sides of an equation. An equivalent equation is produced by multiplying or dividing both sides of an equation by the same non-zero number.

⇒6x-4+x, This is the equation. This can be reducible to simplest form i.e.

⇒7x-4 ( addition of like terms)

when both the equations reduced, final equation's are 7x-4 , 7x-4

so,they are equivalent

Therefore, both the equations are equivalent

Hence,7x-4 and 6x-4+x, Both the equations are equivalent.

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Answer:

Sample Respons:  6x − x = 5x. The new expression is now 5x − 4. This is not equivalent to 7x − 4.

Step-by-step explanation:

took a test in edg

Answer:

a) 2 * 8 = 16

b) (-2.5)(-2.5) = 6.25 = \(\frac{625}{1000} = \frac{5}{8}\)

Step-by-step explanation:

discriminant = b * 2 - 4 * a * c   the formula for computing the discriminant .

What is quadratic equation?

quadratic equation ax^2 }+ bx+  c = 0

a = 3 b = 4 c = 5  discriminant = b * 2 - 4 * a * c  print("discriminant is", discriminant)

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Dr. Ellison's equation that f(2) = 5/3 is wrong

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

y = -3x + 7

This equation can be expressed as a function

So, we have

f(x) = -3x + 7

In Dr. Ellison's equation, we have

f(2) = 5/3

This means that

x = 2

So, we have

f(2) = -3 * 2 + 7

Evaluate

f(2) = 1

The calculated value is different from Dr. Ellison's equation

Hence, the solution is wrong

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Answer:C

Step-by-step explanation:

Answer:

It is C. Yes, Paul used stratified random sampling.

Step-by-step explanation:

The surface area of the rectangular prism is 18 sq cm greater than the surface area of the cube.

Here, we are given a rectangular prism and a cube as shown in the figure below.

The three sides of the prism are- 2, 3 and 6

Thus, the total surface area of the cube will be-

2 [(2*3) + (3*6) + (6*2)]

= 2[6 + 18 + 12]

= 2*36

= 72 cm square

Now, the side of the cube is 3 cm

Thus, the total surface area of the cube will be-

6( 3*3 )

= 6*9

= 54 cm square

Thus, the difference between the surface area of prism and cube is = 72 - 54

= 18 cm square.

Thus, the surface area of the rectangular prism is 18 sq cm greater than the surface area of the cube.

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Your question was incomplete. Check for the missing figure below.

Answer:-9

Step-by-step explanation: Divide each term by -25 and simplify

To calculate the marginal cost, find the change in total cost when one additional unit is produced.

Variable Fixed Total Average Variable Average Total Marginal Cost

Cost Cost Cost

0 $30 $30 - - -

2 $30 $34 $17 $17 $4

5 $30 $47 $9.4 $9.4 $13

6 $30 $56 $9.3 $9.3 $9

8 $30 $78 $9.75 $9.75 $22

10 $30 $100 $10 $10 $22

12 $30 $132 $11 $11 $32

Note: To calculate the average variable cost, divide the total variable cost by the quantity produced. To calculate the average total cost, add the total variable cost and the total fixed cost and divide by the quantity produced. To calculate the marginal cost, find the change in total cost when one additional unit is produced.

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Answer:

I think its m=3/2

Step-by-step explanation:

If it right can I please have brainliest :)

Answer:

here is how to figure this out

Step-by-step explanation:

point 1 = (9,8)  =  (x1,y1)

point 2 =(7,5)  = (x2,y2)

slope= y2-y1 / x2-x1

slope = 5-8 / 7-9

slope = -3 / -2

slope = 3/2  :)