please help me with this precalc question?

Answer:

52/82

Step-by-step explanation:

6-9+15-52

15-81+82

52/82

The general solution of the given recurrence equation is Qn = (-1/4)(-1)n + (1/4)n(-1)n + (1/2)(3)n.

The given recurrence equation is

Qn-1 + 5Qn-2 + 3Qn-3 = 3

Let's find the characteristic equation of the given recurrence equation:

By assuming Qn = rn,

the characteristic equation can be derived as:

r3 - r2 - 5r - 3 = 0

So, the characteristic polynomial is

(r + 1)(r - 3)2

Let α = -1 and β = 3 (repeated roots)

Now, the solution of the given recurrence equation is:

Qn = Arn + Bnαn + Cnβn

As α = -1 and β = 3 are the roots of the characteristic equation, substitute these values in the above equation.

We have

A(-1)n + Bn(-1)n + Cn(3)n ... (1)

As we are going to find the general solution of Qn, the constants A, B, and C need to be determined.

Let's solve for A, B, and C by considering the first few terms of the given recurrence equation.

Suppose n = 3 in the recurrence equation Qn-1 + 5Qn-2 + 3Qn-3 = 3, we have

Q2 + 5Q1 + 3Q0 = 3 ... (2)

Now, substitute n = 2 in the general solution (1), we have

Q2 = A(-1)2 + B2(-1)2 + C23 ... (3)

Now, substitute n = 1 in the general solution (1), we have

Q1 = A(-1)1 + B1(-1)1 + C31 ... (4)

Now, substitute n = 0 in the general solution (1), we have

Q0 = A(-1)0 + B0(-1)0 + C30 ... (5)

Now, let's solve for A, B, and C using equations (2), (3), (4), and (5).

Q2 + 5Q1 + 3Q0 = 3:

2A + 5B + 3C = 3A(-1)2 + B2(-1)2 + C23:

A - B + 9C = 3A(-1)1 + B1(-1)1 + C31:

-A - B + 3C = 1A(-1)0 + B0(-1)0 + C30:

A + B + C = 1

On solving the above equations,

we get A = -1/4, B = 1/4, and C = 1/2

So, the general solution of the given recurrence equation is  

Qn = (-1/4)(-1)n + (1/4)n(-1)n + (1/2)(3)n

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The number of bacteria  After 3 hours, in the petri dish would be approximately 823,542,481.

To calculate the number of bacteria in the petri dish after a certain number of hours, you can use the formula:

Number of bacteria = Initial number of bacteria × (growth factor)^(number of hours)

In this case, the initial number of bacteria is 500,500,500 and the growth factor is 1.21.21, point, 2.

Let's calculate the number of bacteria after 1 hour:

Number of bacteria after 1 hour = 500,500,500 × (1.21.21, point, 2)^1

Number of bacteria after 1 hour ≈ 500,500,500 × 1.21.21, point, 2 ≈ 605,662,605

After 1 hour, the number of bacteria in the petri dish would be approximately 605,662,605.

If you want to calculate the number of bacteria after multiple hours, you can simply raise the growth factor to the power of the number of hours. For example, to calculate the number of bacteria after 3 hours:

Number of bacteria after 3 hours = 500,500,500 × (1.21.21, point, 2)^3 ≈ 500,500,500 × 1.21.21, point, 2 × 1.21.21, point, 2 × 1.21.21, point, 2 ≈ 500,500,500 × 1.64642042 ≈ 823,542,481

After 3 hours, the number of bacteria in the petri dish would be approximately 823,542,481.

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We are given the polynomial

Find the roots:

To find the roots of this polynomial, we want to solve the following equation

On the left side, we can factor the polynomial as follows

This leads to the following two equations

with solution x=0, and the equation

by subtracting -2 from both sides , we get

Finally, by dividing both sides by -7, we get

So, the roots of this polynomial are x=0 and x=2/7.

Describe the end behavior:

To describe the end behavior of a polynomial we should first see how the polynomial is written

In here, we see that we have a power of 4 and a power of 3. Consider that the power of 4, as x grows bigger and bigger (or smaller and smaller) the power of 4 will dominate the behavior of the polynomial as x⁴ grow bigger and bigger than x³. So, we can forget the other part and focus on the polynomial

Note that as x is a positive number, then x^4 is also a positive number. So as x grows bigger and bigger, we would get a more negative number, since we are multiplying -7 (a negative number) with a really big positive number (x^4). Then this polynomial will go to - infinity as x grows bigger and bigger.

Also, to understand the end behaviour, we should see how the polynomial behaves as x becomes a really negative number. As before, we can only focus on the polynomial

note that if x is a negative number, x^4 is again a positive number. So, as x becomes more negative (approaching - infinity) the number -7x^4 would once again be a negative number. So, the end behavior as x goes - infinity is also - infinity.

Sketch:

For the sketching, we will use a sketchin software, so the polynomial would look like this

Answer:

8 hundredths

Step-by-step explanation:

2 + 6 = 8

Answer: 430 cm

Step-by-step explanation:

Answer:

430 cm

Step-by-step explanation:

43 multiplied by 10 is 430

The possible coordinates for point B could be (12, 4) if each coordinate increment is 1.

To find the coordinates of point B given that there are 10 equally spaced points between point A and point B, we need to determine the distance between the two points and divide it by 10 to find the increment for each coordinate.

Let's assume the coordinates of point B are (x, y).

The x-coordinate increment would be the difference between the x-coordinates of point B and A divided by 10:

Δx = (xB - xA) / 10

The y-coordinate increment would be the difference between the y-coordinates of point B and A divided by 10:

Δy = (yB - yA) / 10

Substituting the known values:

Δx = (xB - 2) / 10

Δy = (yB - (-3)) / 10

Since we have 10 equally spaced points between A and B, we can calculate the coordinates of point B by multiplying the increments by the number of points from A:

xB = 2 + 10 * Δx

yB = -3 + 10 * Δy

Now we can calculate the possible coordinates for point B using these formulas.

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Answer:

Step-by-step explanation:

it shows the center

or the center of an angle

A consumer loan of $40,000 with a 15.8% interest rate will require monthly payments over a period of 2 years. The total amount to be paid, including both principal and interest, will be approximately $45,380.

To calculate the monthly payments, we need to determine the total amount to be paid over the loan period, including the principal amount and the interest. The formula used for calculating equal monthly installments is:

M = P * (r * (1 + r)^n) / ((1 + r)^n - 1)

Where:

M = Monthly payment

P = Principal amount

r = Monthly interest rate

n = Number of monthly payments

In this case, the principal amount (P) is $40,000, the interest rate (r) is 15.8% per year, and the loan duration (n) is 2 years (24 months).

First, we convert the annual interest rate to a monthly rate by dividing it by 12: 15.8% / 12 = 0.0132.

Next, we substitute the values into the formula:

M = 40,000 * (0.0132 * (1 + 0.0132)^24) / ((1 + 0.0132)^24 - 1)

Calculating this formula gives us the monthly payment (M) of approximately $1,907.42.

To find the total amount to be paid, we multiply the monthly payment by the number of payments: $1,907.42 * 24 = $45,778.08. However, this includes both the principal and the interest. Subtracting the principal amount ($40,000) gives us the total interest paid: $45,778.08 - $40,000 = $5,778.08.

Therefore, the total amount to be paid, including both principal and interest, will be approximately $45,778.08.

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The largest area that can be enclosed if 88 feet of fencing material is available is 484 feet².

Given, a barn has a perimeter of 88 feet.

Now, the perimeter of the rectangle i.e. Barn is 88 feet.

Perimeter = 2(l + b)

88 = 2(l + b)

l + b = 44

b = 44 - l

Now, area = l × b

Area = l × (44 - l)

Area = 44l - l²

On differentiating both the sides, we get

A' = 44 - 2l

On putting A' = 0

44 - 2l = 0

l = 22

Now, for l = 22 the area will be the largest.

if l = 22

then, 22 + b = 44

b = 22

So, the largest area will be 22×22 = 484

Hence, the largest area that can be enclosed if 88 feet of fencing material is available is 484 feet².

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The probability that a randomly selected adult has an IQ less than 140 is approximately 0.9772 or 97.72%.

To find the probability that a randomly selected adult has an IQ less than 140, we need to calculate the z-score and then use the standard normal distribution table.

The z-score can be calculated using the formula:

z = (x - μ) / σ

In this case, x = 140, μ = 100, and σ = 20.

z = (140 - 100) / 20

z = 40 / 20

z = 2

Now, we can use the standard normal distribution table or a calculator to find the probability associated with a z-score of 2. Looking up the z-score of 2 in the table, we find that the probability is approximately 0.9772.

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The percent of attendance figures that differs from the mean by 1500 persons or more is 6.68%.

From the question above, Mean μ = 10,000

Standard Deviation σ = 1,000

The formula for z-score is :

z = (x-μ) / σ

Where, x = observation

z = z-score

Mean μ = 10,000

Standard Deviation σ = 1,000

From the above formula, let's calculate z-score for x = 11,500

z = (x-μ) / σ

z = (11,500 - 10,000) / 1000

z = 1.5

Now, find the probability of attendance figures that differs from the mean by 1500 persons or more.

P(z ≥ 1.5) = 0.0668

To find the percentage, we need to multiply the above value by 100.

P(z ≥ 1.5) × 100 = 0.0668 × 100 = 6.68%

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Anna would need to invest approximately $23,175, rounded to the nearest hundred dollars, to reach a value of $47,000 in 14 years with continuous compounding at an interest rate of 5.1%.

We can use the formula for continuous compounding to solve this problem. The formula is:

A = Pe^(rt)

where A is the amount of money in the account after t years, P is the initial principal (the amount Anna needs to invest), r is the annual interest rate as a decimal, and e is the mathematical constant approximately equal to 2.71828.

Substituting the given values, we get:

47000 = Pe^(0.051*14)

Solving for P, we first divide both sides by e^(0.051*14):

P = 47000 / e^(0.051*14)

Using a calculator, we get:

P ≈ $23,175

Therefore, Anna would need to invest approximately $23,175, rounded to the nearest hundred dollars, to reach a value of $47,000 in 14 years with continuous compounding at an interest rate of 5.1%.

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To translate the given English statements into logical expressions using the provided predicates, here are the translations:

1. Everyone who was well went to work yesterday.

  - ∀x [(W(x) ∧ ¬P(x)) → W(x)]

2. Someone who was sick yesterday did not go to work yesterday.

  - ∃x (P(x) ∧ ¬W(x))

3. Someone who missed work was neither sick nor on vacation.

  - ∃x (¬(P(x) ∨ Q(x)) ∧ ¬W(x))

4. Joshua was on vacation yesterday and he did not go to work.

  - Q(Joshua) ∧ ¬W(Joshua)

5. Everyone was well and went to work yesterday.

  - ∀x (W(x) → W(x) ∧ ¬P(x))

Please note that these translations assume that the domain consists of all employees of the company, including Joshua. Also, the logical expressions are based on the provided predicates and their interpretations.

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The tax amount to the nearest cent:$6.478

What is Tax?

Tax is the sum of money that citizens hand up to the government in exchange for goods and services. A taxpayer and a tax collector are both partners in any tax transaction. An entity that pays taxes to the government is referred to as a taxpayer. Any middleman that collects taxes on the government's behalf, including the government, is a tax collector.

Given,

The price of Rare gem = $82.00

The  sales tax = 7.9%

Converting percent into decimal

7.9 / 100 = 0.079

The amount of sales tax = 82 x 0.079

                                        = $6.478

The Total amount of the gem before the sales tax:

82 - 6.478 = $75.522

Hence, The tax amount to the nearest cent is $6.478

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Answer: If you look at the x axis 1 is less than $1 so if you follow the x axis to the right until you find a number of minutes that meets the y axis of $1 so x4, y1 that means  $.25 per minute if you divide 1 by 4. So 1 is the correct answer.

Step-by-step explanation:

1. Follow the x axis until the x and y axis meet. This is $1.00 on the y axis.

2. Then you would divide 1 by 4 and you get .25. Each minute would be $.25.

Answer:

dont b lazy googIe it

Step-by-step explanation:

Based on the given information, we know that x must be 2 since it is the only even prime number. We also know that y must be either 11, 13, 17, or 19 since those are the only prime numbers between 10 and 20.

So, the sum of x and y can be 2 + 11 = 13, 2 + 13 = 15, 2 + 17 = 19, or 2 + 19 = 21.

Out of these four possible sums, only 13, 17, and 19 are prime numbers. Therefore, we can say that the sum of x and y may or may not be a prime number, depending on the specific values of x and y.

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Factor when dividing the function the remainder is zero. The factorized form of the function \(f(x)=-3x^3+12x^2\) is -3x²(x-4).

A factor of a function is a factor which when multiplied by another the result is the function itself.

We know that in order to factorize a function of the third-order, we need to take the common terms out from the expression,

\(f(x)=-3x^3+12x^2\)

Taking -3x² as the common terms out of the entire function,

\(\begin{aligned}f(x)&=-3x^3+12x^2\\\\&=-3x^2(x-4)\end{aligned}\)

Hence, the factorized function \(f(x)=-3x^3+12x^2\) is -3x²(x-4).

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Answer:

Yes, all 3 are correct.

Step-by-step explanation:

Answer:no it is not right

Step-by-step explanation:so to get the answer right, you have to add a one as the denominator of the five. Next you have to switch the one and the five to make it a multiplication also called the keep change flip then, you multiply and you are done hope this helps!!!!

Answer:

A quadratic polynomial is a type of polynomial that cannot be factored

Examples are;

x^2 + 3x + 5

x^2 + 5x + 7

Step-by-step explanation:

A quadratic polynomial is a type of polynomial which cannot be factored. Just like prime numbers, it only has two factors, 1 and itself.

Hence, a quadratic polynomial does not have rational roots. Its roots are complex and not real

Example are as follows;

(i) x^2 + 3x + 5

(ii) x^2 + 5x + 7

\(\huge\sf\underline{\purple{❥}\pink{Q}\orange{U}\blue{E}\red{S}\green{T}\purple{I}\pink{O}\red{N}}\)

# What does it mean if a quadratic polynomial

is prime? Give two examples of quadratic

polynomials that are prime. Now, find a quadratic

polynomial that is prime.

\(\huge\sf\underline{\purple{❥}\pink{A}\orange {N}\blue{S}\red{W}\green{E}\purple{R}}\)

\(\color{red}{About \:Quadratic \: polynomials\: :-}\)

➯ A polynomial having degree 2 is called a quadratic polynomial.

➯ The form of quadratic polynomial is

\(p(x) = a {x}^{2} + bx + c\)

➯ Degree of the quadratic polynomial will be 2.

➯ Variable of the quadratic polynomial will be 1.

\(\color{red}{For \:example :-}\)

\(p(x) = 2 {x}^{2} + 5x + 3 \\ 3 \:➝ \: constant \\ 2 \: and \: 5 \: ➝ \: coefficient \\ {}^{2} \: ➝ \: degree \\ x \:➝ \: variable \:\)

➯ In a quadratic polynomial there are 2 zeros because it has degree 2.

\(\color{red}{➯ The \: 2\: zeros \:are :-}\)

\(i) \: \: alpha( \alpha ) \: \\ ii) \: beta \: ( \beta )\)

\(\color{red}{For \:example :-}\)

\(p(x) = 2 {x}^{2} + 5 + 3 \\ = 2 {x}^{2} + 2x + 3x + 3 \\ = 2x(x + 1) + 3(x + 1) \\ = (x + 1)(2x + 3) \\ \\ As, \: \: p(x) = 0 \\ \\ ❥∴ \: (x + 1)(2x + 3) = 0 \\ x + 1 = 0 \\ x = - 1 \\ \\ ❥ \: 2x + 3 = 0 \\ 2x = - 3 \\ x = \frac{ - 3}{2} \\ \\ Here, \: \alpha = - 1 \\ \beta = \frac{ - 3}{2} \)

Answer:

I am pretty sure that it is 4.

Step-by-step explanation: Got it right on edge2020

Answer:

4

Step-by-step explanation:

i took on edge

The value of x and y are 4.24 units and 4.24 units respectively in the right angled triangle.

An equation is an expression that shows the relationship between two or more numbers and variables.

Trigonometric ratio shows the relationship between the sides and angles of a right angled triangle.

For the triangle shown, using trigonometric ratio:

sin(45) = x / 6

x = 4.24 units

Also:

cos(45) = y / 6

y = 4.24 units

The value of x and y are 4.24 units and 4.24 units respectively

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Answer:

g(x) = (2x)²

Step-by-step explanation:

To find the 4th order Newton's divided-difference interpolating polynomial for f(x)=ln(x) with x=1,4,5,6,8, we first need to calculate the divided differences:

A. (a) The 4th order Newton's divided-difference interpolating polynomial for the function f(x) = ln(x) using the given data points is:

P(x) = ln(1) + (x - 1)[(ln(4) - ln(1))/(4 - 1)] + (x - 1)(x - 4)[(ln(5) - ln(4))/(5 - 4)(5 - 1)] + (x - 1)(x - 4)(x - 5)[(ln(6) - ln(5))/(6 - 5)(6 - 1)] + (x - 1)(x - 4)(x - 5)(x - 6)[(ln(8) - ln(6))/(8 - 6)(8 - 1)]

B. (a) To find f(x) at x = 7 and x = 9 using the interpolating polynomial, substitute the respective values into the polynomial expression P(x) obtained in the previous part.

Explanation:

A. (a) The 4th order Newton's divided-difference interpolating polynomial can be constructed using the divided-difference formula and the given data points. In this case, we have five data points: (1, ln(1)), (4, ln(4)), (5, ln(5)), (6, ln(6)), and (8, ln(8)). We apply the formula to calculate the polynomial.

B. (a) To find the value of f(x) at x = 7 and x = 9, we substitute these values into the polynomial P(x) obtained in the previous part. For x = 7, substitute 7 into P(x) and evaluate the expression. Similarly, for x = 9, substitute 9 into P(x) and evaluate the expression.

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To reconstruct the ANOVA display for Laura's experiment conducted as a random complete block design with a sum of squares for blocks (SSB) equal to 12, we will add a new row for the "Blocks" factor and redistribute the sum of squares accordingly.

step-by-step explanation:
1. Add a row for "Blocks" in the ANOVA table.
2. Place the given sum of squares for blocks (SSB) value, 12, in the appropriate cell.
3. Calculate the degrees of freedom for blocks (dfB) by subtracting 1 from the number of blocks (assuming the number of blocks is given or can be inferred from the context).
4. Calculate the mean square for blocks (MSB) by dividing the sum of squares for blocks (SSB) by the degrees of freedom for blocks (dfB).
5. Adjust the sum of squares for error (SSE) by subtracting the sum of squares for blocks (SSB) from the original sum of squares total (SST). This will give the new SSE.
6. Adjust the degrees of freedom for error (dfE) by subtracting the degrees of freedom for blocks (dfB) from the original total degrees of freedom (dfT). This will give the new dfE.
7. Calculate the new mean square for error (MSE) by dividing the new sum of squares for error (SSE) by the new degrees of freedom for error (dfE).
8. Recalculate the F-ratio if necessary.
The blocking has reduced the estimate of the experimental error by the difference between the original sum of squares for error (SSE) and the new sum of squares for error (SSE) after accounting for the blocking factor. To find this reduction, subtract the new SSE from the original SSE.

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Answer:

X = 74

Step-by-step explanation:

106 + x = 180

X = 180 - 106

X = 74