Conny's favorite pencil, Ticonderoga, come in packages of 24, while cap erasers come in packages of 10. Conny wants to purchase the smallest number of pencils and erasers so that se have exactly one eraser for each pencil, with none left over. How many packages of pencils and erasers should Conny buy?

The explicit formula for the given sequence is Fn = ((1 + sqrt(5))^n - (1 - sqrt(5))^n) / (2^n * sqrt(5))

To find an explicit formula for the given recurrence relation and initial conditions, we first need to understand the sequence and its behavior. The recurrence relation provided indicates that the next term in the sequence is equal to the sum of the two preceding terms. This type of sequence is commonly known as a Fibonacci sequence.

Now, let's find the explicit formula for the sequence. We can start by writing out the first few terms of the sequence to see if we can notice a pattern:

0, 1, 1, 2, 3, 5, 8, 13, 21, ...

We can see that the first two terms of the sequence are 0 and 1, respectively. Using the recurrence relation, we can find the third term by adding the previous two terms, which gives us 1. We can continue this process to find the fourth term (2), fifth term (3), and so on.

To find the explicit formula, we can use Binet's formula for Fibonacci numbers:

Fn = ((1 + sqrt(5))^n - (1 - sqrt(5))^n) / (2^n * sqrt(5))

where n is the nth term in the sequence. Using this formula, we can find any term in the sequence without having to calculate each preceding term.

In summary, the explicit formula for the given sequence is Fn = ((1 + sqrt(5))^n - (1 - sqrt(5))^n) / (2^n * sqrt(5)). This formula can be used to find any term in the sequence without having to calculate each preceding term.

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The RTS of the isoquant is 1000K, indicating the rate at which labor can be substituted for capital while maintaining constant production. The labor to capital cost ratio is 0.5. To minimize the cost of producing q units per hour, the specific value of q is needed to find the optimal combination of K and L along the expansion path, represented by the cost function C(K, L) = 40K + 20L.

The RTS (Rate of Technical Substitution) measures the rate at which one input can be substituted for another while keeping the production level constant. To determine the RTS, we need to calculate the derivative of the production function with respect to L, holding q constant.

Given the production function q = 1000KL, we can differentiate it with respect to L:

d(q)/d(L) = 1000K

Therefore, the RTS of the isoquant for production level q is 1000K.

The ratio of labor to capital cost can be calculated by dividing the labor cost by the capital cost.

Labor cost = $20/hour

Capital cost = $40/machine/hour

Ratio of labor to capital cost = Labor cost / Capital cost

                              = $20/hour / $40/machine/hour

                              = 0.5

The ratio of labor to capital cost is 0.5.

To find the combination of K and L that minimizes the cost of producing q units per hour, we need to set up the cost function and take its derivative with respect to both K and L.

Let C(K, L) be the total cost function.

The cost of capital is $40 per machine per hour, and the cost of labor is $20 per hour. Therefore, the total cost function can be expressed as:

C(K, L) = 40K + 20L

To produce q units per hour at minimal cost, we need to find the values of K and L that minimize the total cost function while satisfying the production constraint q = 1000KL.

The expansion path of the firm represents the combinations of K and L that minimize the cost at different production levels q.

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The ordered pair which is the solution to the system of equations is  (3,-1)

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

y=3x-10 and 2x+3y=3    

                   putting y=3x-10 in 2x+3y=3

          ⇒      2x+3(3x-10)=3

          ⇒      2x+9x-30=3

          ⇒      11x=33

          ⇒       x=33/11

          ⇒       x=3

Putting x=3 in y=3x-10 ,we get

                          y=3×3-10

                      ⇒    y=9-10

                      ⇒    y=-1

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unbiased

If the expected value of a sample statistic is equal to the parameter it is estimating, we can call the sample statistic:

a. unbiased.

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Answer:

1/2 × |AB| × |OE|

Step-by-step explanation:

use the formula for finding the area of a triangle.

Answer:

If the sum of the digits is divisible 3 and 9

Step-by-step explanation:

Answer:

Step-by-step explanation:

c: x=32

d: all real numbers are solution

e: there are no solutions

Answer:

J

Step-by-step explanation:

Given

5(y + 2) + 4 ← note 4 is outside the parenthesis

Each term in the parenthesis is multiplied by 5, that is

5 • y + 5 • 2 + 4 → J

Answer:

regular price

Step-by-step explanation:

regular price

Answer:

P represents the usual price of a sandwich

The constant (1.5) represents the discount

Step-by-step explanation:

Answer:

\(y=4x+1\)

Step-by-step explanation:

The equation of a line with slope \(m\) and \(y\)-intercept \(b\) in slope-intercept form is \(y=4x+1\).

The time required for the deposit to double at 3.1% interest rate is 22.4 years.

The formula for calculating compound interest can expressed as;

A = Pe^( rt )

Where A is the accrued amount, P is principal, r is interest and t is time.

Given the data in the question;

Let the deposit be represented by x

Since the deposit doubled

Plug the values into the above compound interest formula and solve for time t.  

A = Pe^( rt )

t = ( In( A / p ) ) / r

t = ( In( 2x / x ) ) / 3.1%

t = ( In( 2 ) ) / 0.031

t = ( In( 2 ) ) / 0.031

t = 22.3595

t = 22.4 years.

Therefore, the time needed is 22.4 years.

Option C is the correct answer.

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The domain of the function \(f(x) = \sqrt{\frac{1}{3}x + 2\) is (d) x  ≥ -6

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

\(f(x) = \sqrt{\frac{1}{3}x + 2\)

Set the radicand greater than or equal to 0

So, we have

1/3x + 2 ≥ 0

Next, we have

1/3x  ≥ -2

So, we have

x  ≥ -6

Hence, the domain of the function is (d) x  ≥ -6

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The equation of the line through \((1,2)\) which make equal intercepts on the axis \(x+y=3\)

The equation of the line through (1,2) makes an equal intercept on the axis

The formula of the intercept form is

\(\frac{x}{a} +\frac{y}{b} =1\)

If they make an equal intercept

\(a=b\\\frac{x}{a} +\frac{y}{a} =1\\x+y=a\)

Put the value of the point in the axis, and we get.

\(1+2=a\\a=3\)

Put the value in the equation, and we get.

\(x+y=3\)

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Answer:

Yes, there is enough paint to cover the table top.

Step-by-step explanation:

We are told in the above question that the table top is round = circular

The area of a circle = πr²

Diameter = 6 feet

Radius = Diameter/2 = 6 feet/2 = 3 feet

Area of the table top= π × 3²

= 28.27 square feet

We are told that the a sample jar will cover 30 square feet.

Therefore, yes, there is enough paint to cover the table top.

Answer:

x=1/4

Step-by-step explanation:

x12=3 (I would treat it as 12x=3 since the 12 is still attached with multiplication)

x=3/12 (simplify your fraction)

x=1/4

Answer:

sorry it doesn't make sense

Step-by-step explanation:

Answer:

-3.7

Step-by-step explanation:

1.  More = Addition

2. 0.65 + -4.35 = -3.7

\(\Large\maltese\underline{\textsf{A. What is Asked}}\)

0.65 more than -4.35

\(\Large\maltese\underline{\textsf{B. This problem has been solved!}}\)

The word more means addition, thus

-4.35+0.65=

\(\bf{-3.7}\)

\(\cline{1-2}\)

\(\bf{Result:}\)

            \(\bf{=-3.7}\)

\(\LARGE\boxed{\bf{aesthetic\not1\theta\ell}}\)

The estimated salary for an employee with 18 years of experience is $65,856.46.

To find the estimated salary for an employee with 18 years of experience using the given regression equation, follow these steps:

1. Identify the regression equation: Estimated Salary = 21,640.90 + 2456.42 (Years of Experience)

2. Substitute the given years of experience (18 years) into the equation:

Estimated Salary = 21,640.90 + 2456.42(18)

3. Multiply 2456.42 by 18: 2456.42(18) = 44,215.56

4. Add 21,640.90 to the result from step 3: 21,640.90 + 44,215.56 = 65,856.46

The estimated salary for an employee with 18 years of experience is $65,856.46.

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This is an experimental study. In an experimental study, the researcher actively manipulates the independent variable, which in this case is the type of instructional method .

The students are randomly assigned to different groups, with one group using the animation and the other group studying the textbook. The researcher then measures and compares the increase in biology test scores between the two groups. By randomly assigning the students to different instructional methods, the researcher has control over the independent variable and can make causal inferences about the effectiveness of the different teaching approaches.

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Answer:

8

Step-by-step explanation:

In 2 hours

1 cook makes 10 large cakes

24/10 = 2.4

You need 3 cooks to make the large cakes.

In 2 hours

1 cook makes 28 small cakes

130/28 = 4.64

You need 5 cooks to make the small cakes.

3 + 5 = 8

Answer: 8

The domain will be the integer numbers between 8 and 12 using the limits in other words 8 ≤ u ≤ 12

this is considering every player will bought only one uniform for the season

Hope this helped!

if thats not it read this and see if this works out

The domain of the function is

Step-by-step explanation:

Given : The total cost in dollars to buy uniforms for the players on a volleyball team can be found using the function c= 34.95u +6.25, where u is the number of uniforms bought.

If there are at least 8 players but not more than 12 players on the volleyball team.

To find : What is the domain of the function for this situation ?

Solution :

The total cost in dollars  c= 34.95u +6.25

Where, u is the number of uniforms bought.

Now, The number of uniforms bought depend on the number of players.

We have given that, there are at least 8 players but not more than 12 players on the volleyball team.

i.e, The number of players are between 8 to 12.

So, The domain of the function is

8< u < 12  

hope this helped

The equation that represents this situation is: y = 10x, where y represents the amount charged and x represents the number of rooms painted.

This is a linear equation in slope-intercept form, where the slope is the cost per room, which is $10, and the y-intercept is 0, since there is no charge for zero rooms painted. The equation allows us to calculate the cost of painting any number of rooms by simply plugging in the value of x. For example, if Samuel painted 6 rooms, the equation would be y = 10(6) = $60. The y-intercept of the equation is 0, indicating that if Samuel doesn't paint any rooms, he doesn't earn any money. Thus, this equation can be used to calculate the total amount of money Samuel will earn based on the number of rooms he paints.

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The equation that represents this situation is: y = 10x, where y represents the amount charged and x represents the number of rooms painted.

This is a linear equation in slope-intercept form, where the slope is the cost per room, which is $10, and the y-intercept is 0, since there is no charge for zero rooms painted. The equation allows us to calculate the cost of painting any number of rooms by simply plugging in the value of x. For example, if Samuel painted 6 rooms, the equation would be y = 10(6) = $60. The y-intercept of the equation is 0, indicating that if Samuel doesn't paint any rooms, he doesn't earn any money. Thus, this equation can be used to calculate the total amount of money Samuel will earn based on the number of rooms he paints.

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Answer:

just draw a line like that one on the other side and put 2 letters like e and f on each end

Step-by-step explanation:

Answer:

u basically draw the same thing

Step-by-step explanation:

congruent mean identical hope this helps... points

To determine the horizontal asymptotes of the graph of the function y = (5 + 2^x) / (1 - 2^x), we need to analyze the behavior of the function as x approaches positive infinity and negative infinity.

As x approaches positive infinity (x → +∞), both the numerator and the denominator of the function approach infinity. In this case, we can use the concept of limits to determine the horizontal asymptote. By taking the limit of the function as x approaches positive infinity, we have:

lim (x → +∞) [(5 + 2^x) / (1 - 2^x)]

The limit of the numerator (5 + 2^x) as x approaches positive infinity is positive infinity, and the limit of the denominator (1 - 2^x) as x approaches positive infinity is negative infinity. Therefore, the overall limit approaches negative infinity:

lim (x → +∞) [(5 + 2^x) / (1 - 2^x)] = -∞

This implies that there is a horizontal asymptote at y = -∞ as x approaches positive infinity.

Similarly, as x approaches negative infinity (x → -∞), both the numerator and the denominator of the function also approach infinity. By taking the limit of the function as x approaches negative infinity, we have:

lim (x → -∞) [(5 + 2^x) / (1 - 2^x)]

The limit of the numerator (5 + 2^x) as x approaches negative infinity is positive infinity, and the limit of the denominator (1 - 2^x) as x approaches negative infinity is positive infinity. Therefore, the overall limit approaches positive infinity:

lim (x → -∞) [(5 + 2^x) / (1 - 2^x)] = +∞

This implies that there is no horizontal asymptote at y = +∞ as x approaches negative infinity.

Therefore, the correct answer is (a) y = -1 only.

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These special prime pairs are best known as "twin primes."

The question is about the unproven conjecture that there exist infinitely many pairs of prime numbers that differ by two, which are best known as a specific term. These special prime numbers, such as (17 and 19) or (1019 and 1021), are sometimes called "prime pairs" but they are best known as "twin primes."

Twin primes are the pairs of prime numbers that differ by a number of two, such as (3, 5), (5, 7), (11, 13), (17, 19), and so on. The conjecture that there are infinitely many twin primes is one of the oldest unsolved problems in number theory.

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Answer:

Step-by-step explanation:

This is a linear relationship. We know this because as the number of songs increases by 10,000 the amount of money increases $2500. We can use that relationship in a proportion, which is a method used to solve problems involving directly proportional numbers.

If we arrange our information such that the dollars earned are on the top of the fraction and the number of songs that need to be downloaded to earn that amount of money is on the bottom of the fraction, here is what we have:

\(\frac{2500}{10,000}\). This means that the artist receives $2500 for every 10,000 downloads. Keeping in that pattern, we can find out how much money he will earn when 500,000 downloads are completed, assuming that the amount he earns per 10,000 songs doesn't change.

\(\frac{2500}{10000}=\frac{x}{500000}\) and cross multiply to get

10,000x = 1250000000 and divide to get

x = 125,000

That is the amount that he will earn from 500,000 downloads.

\(\frac{$}{#}\)

Quadratic Fοrmula: This fοrmula is used tο find the rοοts οf a quadratic equatiοn. It is calculated as:

\($ \rm x = \frac{(-b \pm \sqrt{(b^2 - 4ac)}}{ 2a}\)

it's a secοnd-degree quadratic equatiοn which is an algebraic equatiοn in x. Ax² + bx + c = 0, where a and b are the cοefficients, x is the variable, and c is the cοnstant term, is the quadratic equatiοn in its standard fοrm.

1. Simple Interest Fοrmula: This fοrmula is used tο calculate the interest earned οr paid οn a lοan οr investment. It is calculated as:

\(\rm I = P \times r \times t\)

Where I is the interest earned οr paid, P is the principal amοunt, r is the interest rate, and t is the time periοd.

2. Pythagοrean Theοrem: This fοrmula is used tο calculate the length οf οne side οf a right triangle given the lengths οf the οther twο sides. It is calculated as:

\(\rm a^2 + b^2 = c^2\)

Where a and b are the lengths οf the twο legs οf the right triangle, and c is the length οf the hypοtenuse.

3. Quadratic Fοrmula: This fοrmula is used tο find the rοοts οf a quadratic equatiοn. It is calculated as:

\($ \rm x = \frac{(-b \pm \sqrt{(b^2 - 4ac)}}{ 2a}\)

Where a, b, and c are cοefficients οf the quadratic equatiοn ax² + bx + c = 0, and x is the sοlutiοn.

4. Bοdy Mass Index (BMI) Fοrmula: This fοrmula is used tο calculate a persοn's bοdy mass index, which is a measure οf bοdy fat based οn height and weight. It is calculated as:

BMI = (weight in kilοgrams) / (height in meters)²

A BMI οf 18.5 tο 24.9 is cοnsidered healthy, while a BMI οf 25 tο 29.9 is cοnsidered οverweight, and a BMI οf 30 οr higher is cοnsidered οbese.

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Complete question:

Describe some common or unique mathematical formulas that you use in your life.

Answer:

x=3 y=1 is the answer if that is what you were looking for :)

Answer:

x = 3 and y = 1

Step-by-step explanation:

x + y = 4

2x - y = 5

We know x must be greater than y.

Let's try x = 3 and y = 1

3 + 1 = 4

6 - 1 = 5