Find the three consecutive integers such that the smallest and three times the largest is 330. What is the smallest integer?

Answer:

x is equal to 2

Step-by-step explanation:

simplify the equation

distribute the 0.3

0.3*4-0.3x=x-1.4

1.2-0.3x=x-1.4

get x by itself on one side

1.2+1.4=x+0.3x

simplify

2.6=1.3x

2=x

The dividend is represented by synthetic division is 2x³+10x²+x+5.

Synthetic division can be defined as a simplified way of dividing a polynomial with another polynomial equation of degree 1.

Here,

A vertical line and a horizontal line combine to make an L shape.

There are two rows of entries within the shape.

Row 1 has entries 2, 10, 1, 5.

Row 2 has entries blank, -10, 0, -5.

Entry -5 is on the outside to the left of the shape.

The entry represents the zero of the divisor.

This entry to the variable (assume the variable is x) is; 2x³+10x²+x+5.

Hence, the dividend is represented by synthetic division is 2x³+10x²+x+5.

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Answer:

2

Step-by-step explanation:

Answer:

x^2 - x

=

x(x-1)

Step-by-step explanation:

(a) The firm's output supply function is given by q = (p + 199) / 2.

(b) The market-equilibrium price is $32.56, and the equilibrium number of firms is 10.

(c) Each firm sells 70 computers in the long run.

(39 - 0.009q) = (2q - 2) / q

Simplifying the equation, we find:

q = (p + 199) / 2

This represents the firm's output supply function.

p = 39 - 0.009((p + 199) / 2)

Simplifying and solving for p, we get:

p ≈ $32.56

Substituting this price back into the output supply function, we find:

q = (32.56 + 199) / 2 ≈ 115.78

Given that each firm produces 70 computers in the long run, we can calculate the equilibrium number of firms:

Number of firms = q / 70 ≈ 10

70 * 10 = 700

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The formula to calculate energy consumption is power * time

Energy is the ability to do work

Multiplying the power in kW by the number of hours the devices are used per day, per week, or per month gives the energy consumption.

For instance, looking at the consumption in A B and C house:

The TV has a 200 W, or 0.2 kW, power output. It was used for 2 hours each day hence the energy consumed is

= power * time

= 0.2 kW * 2 hours

= 0.4 kWh every day since they leave it on for the day

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Amanda would use 3 planks of lengths 3 feet, 5 feet, and 6 feet.

To determine which planks Amanda should use to build the triangular-shaped kennel:

Therefore, Amanda would use 3 planks of lengths 3 feet, 5 feet, and 6 feet.

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Answer:

p(not blue) = 11/13 = 0.8461538462 = approx 0.85 = approx 85%

Step-by-step explanation:

65-10 = 55 are not blue, so 55 out of 65 cars are not blue.

p(not blue) = 55/65 = 11/13 = 0.8461538462 = approx 0.85 = approx 85%

Answer: I think the answer is 4.

Step-by-step explanation:

I am not sure because i am just in 5th grade (10) so might be wrong and i am so sorry if its wrong.

The parent function of a parabola is y = x².

A function is said to be a parent function if it is expressed in the simplest form and satisfies the definition of a particular type of function.

The simplest function that satisfies the definition of a parabola is given by y = x². It is also called quadratic function.

Its graph passes through the origin (0,0) and lies in first and second quadrant.

One or more parabolas can be easily obtained by transforming the parent function of the parabola.

Therefore, the parent function of parabola is given by y = x².

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Answer:

  a = -5

Step-by-step explanation:

You want the solution to the equation a -6/3 = -7.

The improper fraction -6/3 can be written as -2, so the equation is ...

  a -2 = -7

  a = -5 . . . . . . . add 2 to both sides

__

Additional comment

If you intend the equation to be ...

  (a -6)/3 = -7

The first step can be multiplication by 3:

  a -6 = -21

  a = -15 . . . . . . . add 6 to both sides

If the equation is typeset as ...

  \(\dfrac{a-6}{3}=-7\)

the fraction bar serves the purpose of grouping the terms of the numerator. When this is written in plain text, the typographic grouping clues are lost, and parentheses are needed.

<95141404393>

The cash balance in Mr. Steven's account five years from now will be £2,761.50.

The cash balance in Mr. Steven's account five years from now, we can use the formula for compound interest:

Future Value = Principal * (1 + Interest Rate)^Number of Periods

Principal = £2,500

Interest Rate = 2% per year

Number of Periods = 5 years

Let's substitute these values into the formula to calculate the future value:

Future Value = £2,500 * (1 + 0.02)^5

Calculating this expression will give us the cash balance in Mr. Steven's account five years from now.

To calculate the cash balance in Mr. Steven's account five years from now, we use the compound interest formula:

Future Value = Principal * (1 + Interest Rate)^Number of Periods

In this case, the principal amount is £2,500, the interest rate is 2% per year, and the number of periods is 5 years.

Substituting the values into the formula, we have:

Future Value = £2,500 * (1 + 0.02)^5

Simplifying the expression, we get:

Future Value = £2,500 * (1.02)^5

Calculating this expression gives us the cash balance in Mr. Steven's account five years from now.

Please note that the interest rate is in decimal form (0.02) and we assume annual compounding.

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Answer:

3x + 2x

Step-by-step explanation:

Pretty sure its the first one because its the only thing that could come next.

A sequence is (recursively) defined as a1 = 0, a2 = 1, n>2, \(a_n = a_{n-1} - 3a_{n-2}\). The first seven terms are 0, 1, 1, -2, -5, 1, 16.

A recursive sequence is a sequence in which terms are defined using one or more previous terms which are given.

a1 = 0

a2 = 1

\(a_n = a_{n-1} - 3a_{n-2}\)

a3 = a2 - 3*a1 = 1 - 0 = 1

a4 = a3 - 3*a2 = 1 - 3 = -2

a5 = a4 - 3*a3 = -2 - 3 = -5

a6 = a5 - 3*a4 = -5 + 6 = 1

a7 = a6 - 3*a5 = 1 +15 = 16

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Answer:

\(x^{3}\)= 36 = \(\sqrt[3]{36}\)

\(x^{2}\) = \(\sqrt{42}\)

\(x^{3}\) = 55 = \(\sqrt[3]{55}\)

Hope it helps. =D

Have a great day!

According to the information we can infer that participants are likely to make more accurate decisions about which cards to flip over in the new version, likely because the new content makes the problem more concrete and relatable to everyday life (option B).

In the new version of the Wason four-card task, the content involves a familiar scenario of reading a textbook and receiving an exam grade. This scenario is more relatable to everyday life compared to the original version with abstract numbers and letters.

When a problem is relatable and has real-life context, participants tend to have a better understanding of the situation and are more likely to make accurate decisions. The content of the new version provides participants with a clearer mental model, allowing them to relate the "if-then" conditional statement to their own experiences.

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Se trata de 12.6. Espero que esto haya ayudado!

Based on table shown above, we have that: B. No, because one x-value corresponds to two different y-values.

A function can be defined as a mathematical expression which is used to define and represent the relationship that exists between two or more variables. This ultimately implies that, a function is typically used for mapping an input variable to an output variable.

Based on table shown above, we can reasonably infer and logically deduce that this table does not represent a function because one x-value corresponds to two different y-values.

In conclusion, this table is not a function because no function can have the same x-values (3) for different y-values (5 and 6).

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The following are the zeros for the function h (x) = x2 + 3x - 8: - x= -4 and x=2.

Given a collection of inputs X (domain) and a set of potential outputs Y (codomain), a function is more technically defined as a set of ordered pairings (x,y) where xX and yY with the caveat that there can only be one ordered pair with the same value of x. The function notation f:XY can be used to express that f is a function from X to Y.

The function's zero is a value of x that makes it equal to zero. In other words, the equation f(x) = 0 leads to a zero.

By putting h(x) equal to zero and figuring out x, we may determine the zeroes for the function h(x) = x2 + 3x - 8.

h(x) = x² + 3x - 8 = 0

We may factor the left side of the equation to find x:

x² + 3x - 8 = (x-2)(x+4) = 0

We set each factor to zero and solve for x to discover the zeroes:

x-2 = 0 or x+4 = 0

x = 2 or x = -4

Consequently, the function's zeros are x = 2 and x = -4.

So, A is the right response. x = -4 and x = 2

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The complete question is

What are the zeros of the function h (x) = x² + 3x - 8?

A. x = -4 and x = -2

B. x= -8 and x = 2

C. x = -2 and x = 8

D. x = 2 and x = 8

From the graph,

\(y = \frac{1}{2}x + 2\)

But this one is inequality so you gotta remember this:

When y > x/2+2

- The shade/region is above the graph itself.

When y < x/2+2

- The shade/region is below the graph.

Therefore, the inequality as shown in the picture is

\(y > \frac{1}{2} x + 2\)

That the constant of integration C cancels out when we evaluate the definite integral, so we do not need to include it in the final answer.

We can evaluate the definite integral using the power rule of integration, which states that

∫ \(x^n dx = (x^(n+1))/(n+1) + C\)

where C is the constant of integration.

So, for the given definite integral, we have:

∫ \((1/(5^(50)x^3)) dx\)

\(= (-1/2) * (1/(5^(50))) * (1/x^2) + C\)

Evaluating this from x = 1 to x = 1/5, we get:

\(= (-1/2) * (1/(5^(50))) * (1/(1/5)^2) - (-1/2) * (1/(5^(50))) * (1/1^2)\)

\(= (-1/2) * (5^2) * (5^(50)) + (1/2) * (5^(50))\)

\(= - (1/2) * (5^(52)) + (1/2) * (5^(50))\)

\(= (1/2) * (5^(50)) * (1 - 5^2)\)

\(= (1/2) * (5^(50)) * (-24)\)

\(= -12 * (5^(50))\)

So, the value of the definite integral is \(-12 * (5^(50))\). Note that the constant of integration C cancels out when we evaluate the definite integral, so we do not need to include it in the final answer.

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The DWL falls when the monopolist receives the subsidy because it leads to an increase in output and a decrease in price.

The cost function and demand function of a monopolist can be found in the question. These can be used to derive the marginal revenue and marginal cost.

The optimal level of output and profit can be derived using the marginal revenue and marginal cost equations. After that, you can confirm that the demand is elastic at the optimal output.

After that, you need to calculate the markup and the DWL associated with the monopoly output. Finally, you need to find the new optimal output and determine if the DWL increases or decreases.

Given:Cost Function C(Q) = ¼ Q2 Marginal cost MC(Q) = ½ Q Demand P = 100 – ¼ Q. a.

Sketch the market demand, marginal costs, and marginal revenues.

Market demand:Marginal cost:Marginal revenue: b. What is the monopolist’s optimal level of output and profits?In the monopolistic market, the optimal level of output and profits are given by the condition that Marginal Revenue = Marginal Cost.

Marginal Revenue is the derivative of Total Revenue with respect to Quantity, which can be found by using the demand equation and solving for Q:TR(Q) = P × Q = (100 – ¼ Q)Q = 100Q – ¼ Q2MR(Q) = dTR(Q)/dQ = 100 – ½ QMarginal Cost is given by the question as MC(Q) = ½ Q.

The monopolist's optimal level of output and profits can be found by equating MR and MC:100 – ½ Q = ½ Q => Q = 66.67 units of outputWhen Q = 66.67, the price is given by the demand equation:P = 100 – ¼ Q => P = 83.33.

Therefore, the monopolist's optimal output is 66.67 and optimal profits are (P – MC) × Q = (83.33 – 33.33) × 66.67 = $2,000.

Confirm that demand is elastic at the optimal output.The demand is elastic at the optimal output if the absolute value of the price elasticity of demand is greater than one.

The price elasticity of demand is given by:Ed = (% Change in Quantity Demanded)/(% Change in Price) = (dQ/Q)/(dP/P) × P/QSince MR = P(1 - 1/Ed), MR is greater than MC if Ed is less than 1 and less than MC if Ed is greater than 1. Therefore, the optimal output occurs where Ed is equal to
Substituting the values of P and Q, we get:Ed = (dQ/Q)/(dP/P) × P/Q = -1.47Therefore, demand is elastic at the optimal output.

Calculate the firm’s markup.The markup is given by the formula (P - MC)/P.Substituting the values of P and MC, we get:(83.33 - 33.33)/83.33 = 0.6 = 60% markup .

What is the DWL associated with the monopoly output?DWL (Deadweight Loss) is the difference between the total surplus in a competitive market and the total surplus in a monopoly market.

The formula for DWL is:DWL = (1/2)(Pmon - Pcomp)(Qcomp - Qmon)DWL can be calculated by using the demand equation and finding the quantity demanded at the monopoly price and the competitive price. At the monopoly price of $83.33, the quantity demanded is 66.67.

At the competitive price of $66.67, the quantity demanded is 100. Therefore, DWL can be calculated as follows:DWL = (1/2)(83.33 - 66.67)(100 - 66.67) = $1,111.1 f.

Suppose the government offered a $10 production subsidy to the monopolist. What is their new optimal output?The new optimal output will be where the new marginal cost equals the original marginal revenue.

The subsidy reduces the marginal cost to (1/2) Q - $10.

Therefore, the monopolist's new optimal output can be found by solving for Q:100 - 1/2 Q + 10 = 1/2 Q => Q = 74.07 units of outputWhen Q = 74.07, the price is given by the demand equation:P = 100 - 1/4 Q => P = $81.48 g. Does the DWL fall or rise?The DWL falls when the monopolist receives the subsidy because it leads to an increase in output and a decrease in price.

Therefore, the deadweight loss falls.

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hello! :p

area of shape one is 12

and area of shape to is 36

In not 100% sure but I thought I could try to help! Don't take my word for it though. :) Have a wonderful day!

Answer: The radii of atomic nuclei are of the order of 50×10^-15 to the negative 15th power.

Answer:

hope it helps..

Step-by-step explanation:

If this helped please comment..

The volume of a cube is given by V = s^3, where s is the edge length.

Given V = 116, we can solve for s as follows:

s^3 = 116

Taking the cube root of both sides, we get:

s = ∛116

This is the exact value of the edge of the cube in cube root notation. We can simplify it further as follows:

116 can be factored as 2 × 2 × 29. Taking the cube root of each factor, we get:

∛2 × ∛2 × ∛29

This can be simplified as:

2∛29

Therefore, the exact value of the edge of the cube in cube root notation is 2∛29 units.

The domain and range are the set of x and values of the function are in the table.

the function as a table,

Input (x) | Output (y)

-3         |        -4

-1          |         2

0         |         0

-3         |         5

2         |         4

What is the domain and range?

The domain and range are fundamental concepts in mathematics that are used to describe the input and output values of a function or relation.

The domain of a function refers to the set of all possible input values, or x-values, for which the function is defined.

The range of a function refers to the set of all possible output values, or y-values.

To find the domain and range of functions and represent them in different formats.

To find the domain and range of a function:

The domain refers to the set of all possible input values (x-values) for the function.

The range refers to the set of all possible output values (y-values) for the function.

To represent the function as a table, you would list the input-output pairs. For example:

Input (x) | Output (y)

-3         |        -4

-1          |         2

0         |         0

-3         |         5

2         |         4

To represent the function as a mapping, you would indicate the correspondence between the input and output values.

For example:

-3     ->   -4

-1     ->     2

0     ->     0

-3    ->     5

2     ->     4

To represent the function as a graph, The x-values would be on the horizontal axis, and the y-values would be on the vertical axis.

The points (-3, -4), (-1, 2), (0, 0), (-3, 5), and (2, 4) would be plotted accordingly.

Hence, The domain and range are the set of x and values of the function are in the table.

the function as a table,

Input (x) | Output (y)

-3         |        -4

-1          |         2

0         |         0

-3         |         5

2         |         4

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Answer:

Perimeter of XYZ is 33

Step-by-step explanation:

The Midpoint Theorem states that the segment joining two sides of a triangle at the midpoints of those sides is parallel to the third side and is half the length of the third side.

So XZ = 24/2 = 12

P = XZ + ZY + XY = 12 + 11 + 10 = 33

Answer:

im not sure im really sorry

Step-by-step explanation:

im answering this because i have the same question