An AP has 15 terms and a common
difference of - 3. Find its first and last terms
if its sum is
b 15
d -120
a 120
​

Answer:

157.07963

Step-by-step explanation:

2πr²

2π(5)²

2π(25)

50π

157.07963

Answer: the answer is C

The formula that models the ratio y is:

y = 6 / (6 + x)

Let y be the ratio of the number of gallons of acid in the container compared to the total volume of liquid in the container, and let x be the number of gallons of water added to the container.

Initially, the container has 6 gallons of acid and 0 gallons of water, for a total volume of 6 gallons. When x gallons of water is added, the total volume of liquid becomes 6 + x gallons, and the amount of acid remains at 6 gallons.

Therefore, the formula that models the ratio y is:

y = 6 / (6 + x)

This formula gives the ratio of the number of gallons of acid in the container compared to the total volume of liquid in the container when x gallons of water is added.

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The correct answer is (d) The price must be replaced with a relative price, and the marginal values must be replaced with the corresponding Marginal Rates of Substitution.

When the value of a public good cannot be expressed in monetary terms, the Samuelson condition still holds, but some modifications are required. In this case, the per-unit price (p) used in the Samuelson condition needs to be replaced with a relative price, which represents the trade-off between the public good and other goods or services. Additionally, the marginal values (MV) of the public good need to be replaced with the Marginal Rates of Substitution (MRS), which measure the rate at which one person is willing to substitute the public good for another good.

Therefore, to determine the efficient level of the public good, the modified Samuelson condition uses a relative price and the corresponding Marginal Rates of Substitution.

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Nοn hοmοgenοus equatiοn are οften fοrm dy/dx +P(y)=  Q(x) dy/dx=y²+cοs(x)

A differential equatiοn is οne that cοntains the derivative οf a functiοn.

1. Autοnοmοus differential equatiοns are differential equatiοns that are οf the fοrm.

dy/dx = f(y)

οur equatiοn is dy/dx = y² + cοs(x) and its nοt οf the abοve fοrm .Sο (A)  is ruled οut

2. lοgistic differential equatiοn are οf the fοrm :

y=r[1-(y/k)]y

οptiοn (C) is ruled οut as well

3. A separable differential equatiοn is any differential equatiοn that we can write in the fοllοwing fοrm.

N(y)dy/dx = M(x)Our equatiοn cannοt be seprated fοr x and y like separable differential equatiοns

sο οptiοn B is ruled οut as well.

4. Nοn hοmοgenοus equatiοn are οften fοrm dy/dx +P(y)=  Q(x) dy/dx=y²+cοs(x)

this cοuld be written as dy/dx - y²=  cοs(x) the fοrm matches

=> οptiοn (D) nοn hοmοgenοues is cοrrect

5.fequatiοns are like dy/dx + P(y) = 0 , the x term is missing

sο οptiοn (E) is nοt valid

6. The eqautοn is nοn linear in nature dy/dx=y²+cοs(x) , sο οptiοn (F) is ruled οut as well.

Optiοn (D) is cοrrect.

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Answer:

18yrds n 8 inches

From the information given,

BA is congruent to AC

AD is common to triangle ABD and ACD

Since the two sides of triangle ABC are congruent, it means that the triangle is an isosceles triangle. Thus,

angle ABD = angle ACD

Triangle ABD and ACD are congruent. Thus, the corresponding sides are congruent

If BD = 3, then

CD = 3

The percent change in height after the second bounce would be:

Percent change = [(h_2 - h_1) / h_1] * 100%

The expression \(25(0.93)^x\)represents the height of the ball after x bounces. To find the percent change in height after each bounce, we need to calculate the ratio of the change in height to the original height and express it as a percentage.

Let's denote the height after the first bounce as h_1, the height after the second bounce as h_2, and so on.

The percent change in height after the first bounce is given by:

Percent change = [(h_1 - original height) / original height] * 100%

Using the given expression, we can substitute x = 1 to find h_1:

h_1 = \(25(0.93)^1\) = 23.25

Therefore, the percent change in height after the first bounce is:

Percent change = [(23.25 - original height) / original height] * 100%

To find the percent change after subsequent bounces, we can continue this process. For example, after the second bounce:

h_2 = \(25(0.93)^2\)

And the percent change in height after the second bounce would be:

Percent change = [(h_2 - h_1) / h_1] * 100%

You can repeat this process for each subsequent bounce to find the percent change in height after each bounce using the given expression.

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Answer:

x = 9

Step-by-step explanation:

Rearrange

\(\sf \rightarrow x^3 - 729 = 0\)

Factor using (a-b) × (a^2 +ab +b^2)

a^3 + a^2b + ab^2 - ba^2 - b^2a - b^3 =

           a^3 + (a^2b-ba^2) + (ab^2-b^2a) - b^3 =

           a^3 + 0 + 0 - b^3 =

           a^3 - b^3

x^3 = x^1

Rearrange(Using polynomial/cube roots)

(x - 9) × (x2 + 9x + 81)  = 0

Subtract/Add

x - 9 = 0 = 9

x^2 + 9x = -81

-81 + 81/4

-243/4

x^2 + 9x + (81/4) = -243/4

(x + (9/2)) × (x + (9/2)) = (x + (9/2)) × 2

(x + (9/2))2 = -243/4

x^2 + 9x + 81 = 0

√243 = 3 × 3 × 3 × 3 × 3 = 3 × 3 × √3 = ±9 × √3

= ±9x  =  (-9 ± 9 × 1.732(i)) / 2

= ±9x

Divide by 9 (Absolute value: positive)

|9/9| = x

Reverse, re-arranging x (Assuming x = 1)

x = |9/x|

Thus,

x = 9

Hope this helped, let me know if anything confuses you, and I will try my best to address that. Have a good day!

If Arianna decides to sell the rental property in the future, the gain or loss will be calculated based on the $270,405 gain basis.

The gain basis for Arianna's converted personal residence to rental property can be calculated by determining the lower value between the adjusted basis and the fair market value.

In this case, the adjusted basis is $300,450 and the fair market value is $270,405.

The gain basis is the lower of the two values, which in this case is $270,405. This means that the gain basis for Arianna's rental property is $270,405.

The gain basis is important for tax purposes as it is used to calculate the taxable gain or loss when the property is eventually sold.

If the property is sold for a higher price than the gain basis, there will be a taxable gain.

On the other hand, if the property is sold for a lower price than the gain basis, there will be a deductible loss.

In Arianna's case, if she decides to sell the rental property in the future, the gain or loss will be calculated based on the $270,405 gain basis.

It is important to note that there may be additional factors and adjustments that could affect the final tax calculations, such as depreciation deductions and any improvements made to the property.

Consulting a tax professional would provide more accurate and detailed information regarding the tax implications of selling the rental property.

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Answer:1.345299 = -1/3

Step-by-step explanation:

Answer:

0.5 ; 0.34458

Step-by-step explanation:

Given that:

Mean (m) = 28

Standard deviation, s = 5

To obtain the Zscore :

Z = (x - m) / s

1.) P(x > 28)

Z = (28 - 28) / 5

Z = 0

P(Z > 0) = 0.5 (Z probability calculator)

2.) P(x < 26)

Z = (26 - 28) / 5

Z = - 0.4

P(Z > -0.4) = 0.34458 (Z probability calculator)

\(\textsf {Let the variables for the people be V, R, and S respectively.}\)

\(\textsf {1) R = V + 30}\)

\(\textsf {2) S = R - 20}\)

\(\textsf {3) S = 150}\)

\(\textsf {Substitute the value of S in Equation 2 :}\)

\(\implies \mathsf {150 = R - 20}\)

\(\implies \textsf {R = 170}\)

\(\textsf {Substitute the value of R in Equation 1 : }\)

\(\implies \textsf {170 = V + 30}\)

\(\implies \mathsf {V = 140}\)

\(\textsf {Therefore, Vinu collected 140 stamps.}\)

Vinu collected some stamps. Rahul collected 30 more than Vinu. Shaan collected 20 less than Rahul. Shaan had 150 stamps..Solving for x, we find that Vinu collected 140 stamps.

To find out how many stamps Vinu collected, we can follow the information given step by step. First, we know that Rahul collected 30 more stamps than Vinu. Let's represent the number of stamps Vinu collected as "x."

Therefore, Rahul collected x + 30 stamps. Next, we are told that Shaan collected 20 less stamps than Rahul. So, the number of stamps Shaan collected can be represented as (x + 30) - 20. We are also given that Shaan had 150 stamps.

Therefore, we can set up the equation: (x + 30) - 20 = 150. To solve this equation, we need to simplify it by combining like terms. (x + 30) - 20 simplifies to x + 10. Now we have the equation x + 10 = 150. To isolate x, we need to subtract 10 from both sides of the equation. Subtracting 10 from both sides gives us x = 140. Therefore, Vinu collected 140 stamps. In summary: - Rahul collected x + 30 stamps. - Shaan collected (x + 30) - 20 stamps. - The equation is (x + 30) - 20 = 150. - Simplifying, we get x + 10 = 150. - Solving for x, we find that Vinu collected 140 stamps.

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Answer:

producers Will grow more chocolate.

To solve this problem, we can use the method of Lagrange multipliers. This method allows us to find the maximum or minimum of a function subject to constraints.

In this case, the function we want to maximize is Z = 2x + 3y and the constraints are x = 24, y = 25, and 3x + 2y = 52.We begin by setting up the Lagrangian function, which is given by:L(x, y, λ) = Z - λ(3x + 2y - 52)where λ is the Lagrange multiplier. We then take the partial derivatives of the Lagrangian with respect to x, y, and λ and set them equal to zero.∂L/∂x = 2 - 3λ = 0∂L/∂y = 3 - 2λ = 0∂L/∂λ = 3x + 2y - 52 = 0Solving for λ, we get λ = 2/3 and λ = 3/2. However, only one of these values satisfies all three equations. Substituting λ = 2/3 into the first two equations gives x = 20 and y = 22. Substituting these values into the third equation confirms that they satisfy all three equations. Therefore, the maximum value of Z subject to the given constraints is Z = 2x + 3y = 2(20) + 3(22) = 84.

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The maximum value of Z = 2x + 3y, subject to the conditions x ≤ 24, y ≤ 25, and 3x + 2y = 52, is 96.

To maximize the function Z = 2x + 3y, subject to the conditions x ≤ 24, y ≤ 25, and 3x + 2y = 52, we will use the method of linear programming.

Let us first graph the equation 3x + 2y = 52.

The intercepts of the equation 3x + 2y = 52 are (0, 26) and (17.33, 0).

Since the feasible region is restricted by x ≤ 24 and y ≤ 25, we get the following graph.

We observe that the feasible region is bounded and consists of four vertices:

A(0, 26), B(8, 20), C(16, 13), and D(24, 0).

Next, we construct a table of values of Z = 2x + 3y for the vertices A, B, C, and D.

We observe that the maximum value of Z is 96, which occurs at the vertex B(8, 20).

Therefore, the maximum value of Z = 2x + 3y, subject to the conditions x ≤ 24, y ≤ 25, and 3x + 2y = 52, is 96.

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The ways in which the linear systems are similar to quadratic systems includes:

The linear system means the model based on the use of a linear operator and, they exhibit features and properties that are much simpler than the nonlinear case. The quadratic system of equations consists of only quadratic equations.

The linear & quadratic systems are solved by graphing and substitution. In the linear systems, we get the lines and in quadratic systems, we get curves. In conclusion, the point of intersection of two lines or curves are the solutions of the respectively system.

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The probability (to the nearest percent) of a randomly thrown dart landing somewhere in the red shaded regions is approximately 2%.

To find the probability of a randomly thrown dart landing somewhere in the red shaded regions, we need to determine the ratio of the area of the red shaded regions to the total area.

Let's break down the problem step by step:

We are given that the area of the inner circle is 256π. Let's denote this area as A_inner.

The area of a circle is calculated using the formula A = πr^2, where A is the area and r is the radius. From the given information, we can determine the radius of the inner circle.

A_inner = πr^2

256π = πr^2

r^2 = 256

r = 16

So, the radius of the inner circle is 16 units.

Now, let's consider the area of the red shaded regions. These regions consist of the area between the inner circle and the outer circle, as well as the five triangular regions formed by the sides of the pentagon.

The area between the two circles can be calculated as the difference between the areas of the two circles:

A_red = A_outer - A_inner

To find the area of the outer circle, we need to determine its radius. Since the outer circle is inscribed in the pentagon, the distance from the center of the circle to any vertex of the pentagon is the radius.

Let's denote the radius of the outer circle as R. The distance from the center of the circle to a vertex of the pentagon is also the apothem (a) of the pentagon.

Using trigonometry, we can calculate the apothem of a regular pentagon:

a = Rcos(36°)

Since the pentagon is regular, each interior angle is 108°, and the central angle of the isosceles triangle formed by the radius, apothem, and one side of the pentagon is 36°.

From the given information, we know that the apothem (a) is equal to the radius of the inner circle, which is 16 units.

16 = Rcos(36°)

Solving for R:

R = 16 / cos(36°)

R ≈ 19.82

The radius of the outer circle is approximately 19.82 units.

Now, we can calculate the area of the red shaded regions:

A_red = πR^2 - A_inner

= π(19.82)^2 - 256π

= 1238.22π - 256π

= 982.22π

Finally, we can calculate the probability of a randomly thrown dart landing somewhere in the red shaded regions by dividing the area of the red shaded regions by the total area, which is the area of the outer circle:

Probability = (A_red / A_outer) * 100

Plugging in the values:

Probability = (982.22π / πR^2) * 100

= (982.22 / 19.82^2) * 100

≈ 2.51%

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4 by the power 2 is 16.

The number of times a number has been multiplied by itself is shown by its exponent.

Problems involving exponents can be resolved using either the laws or properties of exponents. When a number is repeated many times by itself, writing the product becomes extremely challenging without the use of exponents. These properties are also regarded as major exponentiation rules.

Given to find 4 by the power of 2,

means 4 x 4

= 4²

where 4 is base and 3 is exponent,

4² = 4 x 4

4² = 16

Hence 16 is 4 by power 2.

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Answer: 6.71, and 6.7

Step-by-step explanation:

In order to write to two decimal places, we must first calculate the square root of 45.

The square root of 45 is 6.708

Therefore, when we round, we get 6.71

In order to write to two sig figs, we remember that sig figs are the number digits without zeros on the end.

Therefore, all we take is the 6.7

Answer:

a) 6.71

b) 6.7

Answer:

Step-by-step explanation:

5.33

To find the marginal density of X/Y, we need to integrate the joint density function fXY(x, y) over the range of Y. By performing the integration, we obtain the marginal density of X/Y as a function of X. The resulting marginal density provides information about the distribution of the ratio X/Y.

The marginal density of X/Y can be obtained by integrating the joint density function fXY(x, y) over the range of Y. In this case, the joint density function is given by:

fXY(x, y) =

  24xy    if x >= 0, y >= 0, and x + y <= 1

  0       otherwise

To find the marginal density of X/Y, we integrate fXY(x, y) with respect to y, while keeping x as a constant. The integration limits for y can be determined based on the given conditions x >= 0, y >= 0, and x + y <= 1. Since y must be non-negative, the lower limit of integration is 0. The upper limit of integration can be determined by the constraint x + y <= 1, which implies y <= 1 - x.

Integrating fXY(x, y) over the range of y, we obtain the marginal density of X/Y as follows:

fX/Y(x) = ∫[0 to (1 - x)] 24xy dy

Evaluating the integral, we have:

fX/Y(x) = 24x * ∫[0 to (1 - x)] y dy

       = 24x * [(y^2)/2] evaluated from 0 to (1 - x)

       = 12x * (1 - x)^2

The resulting marginal density fX/Y(x) represents the distribution of the ratio X/Y. It provides information about the likelihood of different values of X/Y occurring. The shape of the distribution can be further analyzed to understand the characteristics of the random variable X/Y.

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Solution:

We want to estimate the population when the population exceed 1455

Set p(t) = 1455 and solve for t

Thus, the population will exceed 14551 after 6.99 years

Answer:

So, every one inch in the real dog house would be equal to .4 on the scale drawing.

So,

8/.4= 20

10/.4= 25

So, the dog house is 20 by 25 inches.

The question asked for the area.

20*25= 500

The real dog house has an area of 500 in^2.

I hope this helps!

Step-by-step explanation:

Answer:

$8000

Step-by-step explanation:

profit = selling price - Cost Price

P = 35000-27500

P= 8000

The number of collections of 50 coins that can be chosen from this pile is: C(125, 25) = 177,100,565,136,000
This is a very large number, which shows that there are many possible collections of 50 coins that can be chosen from the pile.

If the pile contains only 25 quarters but at least 50 of each other kind of coin, then the total number of coins in the pile must be at least 50 + 50 + 50 = 150. Let's assume that there are 150 coins in the pile, including the 25 quarters.
To choose a collection of 50 coins from this pile, we need to exclude the 25 quarters and choose 25 coins from the remaining 125 coins. We can do this in C(125, 25) ways, which is the number of combinations of 25 items chosen from a set of 125 items.
Therefore, the number of collections of 50 coins that can be chosen from this pile is:
C(125, 25) = 177,100,565,136,000

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There are 351 possible collections of 50 coins that can be chosen, considering the given conditions.

To find the number of collections of 50 coins that can be chosen, we will consider the given conditions:
The pile contains only 25 quarters.

There are at least 50 of each other kind of coin (pennies, nickels, and dimes).
Now, let's break this down step by step:
Determine the minimum number of coins from each kind required to make a collection of 50 coins.
- 25 quarters (as it's the maximum available)
- The remaining 25 coins must be a combination of pennies, nickels, and dimes.
Find the different combinations of pennies, nickels, and dimes that can be chosen to make a collection of 50 coins.
- We need 25 more coins, so we can divide them into three groups:
 a) Pennies (P)
 b) Nickels (N)
 c) Dimes (D)
Calculate the combinations for the remaining 25 coins.
- Using the formula for combinations with repetitions: C(n+r-1, r) = C(n-1, r-1)
 Where n is the number of types of coins (3) and r is the number of remaining coins (25)
- C(3+25-1, 25) = C(27, 25) = 27! / (25! * 2!) = 351.

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You can approximate the probability using the standard normal distribution table by looking up the closest values for Φ(2) and Φ(1).

To calculate the probability P(1 < z < 2) for a standard normal random variable, we can use the cumulative distribution function (CDF) of the standard normal distribution.

The CDF gives us the probability that a standard normal random variable is less than or equal to a given value. We can use this information to calculate the probability between two values.

Let's denote the CDF of the standard normal distribution as Φ(z). The probability P(1 < z < 2) can be calculated as follows:

P(1 < z < 2) = Φ(2) - Φ(1)

To calculate this, we need to look up the values of Φ(2) and Φ(1) from a standard normal distribution table or use a calculator/computer software. However, since I don't have access to real-time computations in this environment, I am unable to provide the exact numerical value.

But you can use statistical software or online calculators to find the precise value. Alternatively, you can approximate the probability using the standard normal distribution table by looking up the closest values for Φ(2) and Φ(1).

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Answer:

a. yes

b. no

c. yes

d. yes

e. yes

f. no

Step-by-step explanation:

a regular polygon must be equiangular (all angles are same) and equilateral (all sides are same)

A. equilateral triangle, regular

B. is a rectangle and the sides of rectangle are not all equal, thus, not regular

C. octagon, regular

D. flipped pentagon, regular

E. square, regular

F. not normal pentagon, not regular

Answer:

a. yes  

b. no  

c. yes  

d. yes  

e. yes  

f. no

Step-by-step explanation:

a regular polygon must be equiangular (all angles are same) and equilateral (all sides are same)

A. equilateral triangle, regular

B. is a rectangle and the sides of rectangle are not all equal, thus, not regular

C. octagon, regular

D. flipped pentagon, regular

E. square, regular

F. not normal pentagon, not regular

After solving the given expression the values for x will be equal to x = 1 and x = 13.

Mathematical actions are called expressions if they have at least two terms that are related by an operator and include either numbers, variables, or both. Adding, subtraction, multiplying, and division are all reflection coefficient operations. A mathematical operation such as reduction, addition, multiplication, or division is used to integrate terms into an expression.

As per the given information in the question,

The given equation is,

(x - 7)² = 36

x - 7 = √36

x = ±6

Then the values for x will be,

x1 = 6 + 7 = 17

x2 = -6 + 7 = -1

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Answer:

Option B is the best way to write the underlined parts of sentences 2 and 3.

Sentence 2: They have a special finish that helps.

Sentence 3: The finish helps the swimmer glide through the water.

Option B provides a clear and concise way to connect the two sentences and convey the idea that the special finish of the swimsuits helps the swimmer glide through the water. It avoids any ambiguity or redundancy in the language.

Answer:

x = -1

General Formulas and Concepts:

Pre-Alg

Step-by-step explanation:

Step 1: Define equation

5x - (x + 4) + 1 = 3 - 2(x + 6)

Step 2: Solve for x

Step 3: Check

Plug in x to verify it's a solution.