Hank paid $16,780 for a used car 5 years ago. Because he did not properly maintain the car, he sold it for $4,280. What was his average annual depreciation?

Answer:

1/9?

Step-by-step explanation:

Quadratic Form : \(y = 5x^2 - 5x - 30\)

What is quadratic form?

Any equation in the form \(ax^2+bx+c = 0\) is said to be in quadratic form. This equation then can be solved by using the quadratic formula, by completing the square, or by factoring if it is factorable.

Given,

⇒ \(y = 5 (x+2) (x-3)\\ \\y = 5 (x^2-x-6)\\\\y = 5x^2 - 5x - 30\)

Hence,

Quadratic Form : \(y = 5x^2 - 5x - 30\)

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Answer:

1³ = 1

2³ = 8

3³ = 27

4³ = 64

5³ = 125

6³ = 216

Step-by-step explanation:

Answer:

The cube of first six natural numbers are

1, 8, 27, 65, 125, 216

Step-by-step explanation:

Natural Numbers are known as 1, 2, 3, 4, ..., ∞

Now,

For Cube of first six natural numbers

1³ = 1

2³ = 8

3³ = 27

4³ = 64

5³ = 125

6³ = 216

Thus, The cube of first six natural numbers are

1, 8, 27, 65, 125, 216

-TheUnknownScientist

To find the probability that strictly more than 5 customers arrive in a given hour, we can use the Poisson distribution with a mean rate of 11 customers per hour.

The probability mass function of the Poisson distribution is given by:

P(X = k) = (e^(-λ) * λ^k) / k!

Where X is the random variable representing the number of arrivals, λ is the mean rate, and k is the desired number of arrivals.

In this case, λ = 11 (mean rate of 11 customers per hour). We want to find the probability that strictly more than 5 customers arrive, which is equivalent to finding the probability that 6, 7, 8, 9, 10, 11, and so on, customers arrive.

Let's calculate the probability using the complement rule, which states that the probability of an event happening is equal to 1 minus the probability of the event not happening.

P(X > 5) = 1 - P(X ≤ 5)

To find P(X ≤ 5), we sum the probabilities for k = 0, 1, 2, 3, 4, and 5:

P(X ≤ 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)

Using the Poisson distribution formula, we can calculate each term:

P(X = k) = (e^(-λ) * λ^k) / k!

P(X = 0) = (e^(-11) * 11^0) / 0! = e^(-11)

P(X = 1) = (e^(-11) * 11^1) / 1! = 11e^(-11)

P(X = 2) = (e^(-11) * 11^2) / 2!

P(X = 3) = (e^(-11) * 11^3) / 3!

P(X = 4) = (e^(-11) * 11^4) / 4!

P(X = 5) = (e^(-11) * 11^5) / 5!

Now we can calculate P(X ≤ 5):

P(X ≤ 5) = e^(-11) + 11e^(-11) + (11^2 * e^(-11)) / 2! + (11^3 * e^(-11)) / 3! + (11^4 * e^(-11)) / 4! + (11^5 * e^(-11)) / 5!

Finally, we can find P(X > 5) by subtracting P(X ≤ 5) from 1:

P(X > 5) = 1 - P(X ≤ 5)

You can calculate this value using a calculator or software that supports mathematical functions.

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Step-by-step explanation:

ab = (x - 3)(x + 3)

multiply

ab = x² + 3x - 3x - 9

Simplify

ab = x² - 9

---------------------------

2ab = 2(x² - 9)

Distribute

2ab = 2x² - 18

Answer:

5 hours

Step-by-step explanation:

Let x represent the amount of hours that ralph can do.

Let y represent the money he earned.

Let m represent how much he earns per hour.

Let b represent the initial fee

y=mx+b

y=33x + 24

189=33x+24

Solve for x:

189=33x+24

165 = 33x

x=5

Answer:

6.00150024e+14

Step-by-step explanation:

i am sorry if im wrong

Answer:

\( {(a + b + c)}^{2} = {(5 + 4 + 3)}^{2} \\ = {12}^{2} \\ = \boxed{144}\)

Answer:

B. Symmetric

Step-by-step explanation:

Using the Pigeonhole Principle, we can prove that in any set of n consecutive integers, there is exactly one integer that is divisible by n.

The Pigeonhole Principle states that if you have more pigeons than pigeonholes, at least one pigeonhole must contain more than one pigeon. I

n this case, the pigeons represent the consecutive integers and the pigeonholes represent the possible remainders when dividing the integers by n.

Consider a set of n consecutive integers, starting from some integer k. The n integers can be written as k, k+1, k+2, ..., k+n-1. To show that there is exactly one integer divisible by n, we will assign each integer to a pigeonhole based on its remainder when divided by n.

Since there are n possible remainders when dividing an integer by n (0, 1, 2, ..., n-1), and we have n consecutive integers, by the Pigeonhole Principle, there must be at least two integers that have the same remainder when divided by n.

Let's say two integers, k+i and k+j, have the same remainder r when divided by n, where i < j.

Then we have (k+i) ≡ r (mod n) and (k+j) ≡ r (mod n).

Subtracting these two congruences, we get (k+j) - (k+i) ≡ 0 (mod n), which simplifies to j - i ≡ 0 (mod n). This implies that n divides (j - i).

Since j > i, we have j - i > 0, and since n divides (j - i), we conclude that n must divide (j - i), which means that one of the integers between k+i and k+j is divisible by n.

Therefore, in any set of n consecutive integers, there is exactly one integer that is divisible by n.

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Ally will be able to cover 285 miles for the trip

Ally wants to rent the car for one day

The rents costs $35 and $0.35 per mile

Ally has $134.75 to spend for the trip

The number of miles Ally can drive for the trip can be calculated as follows

134.75 - 35

= 99.75

99.75/0.35

= 285

Hence Ally will be able to drive 285 miles for the trip  

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The demand equation is given to be:

where p is the price and x is the number of units sold.

If the price per unit is $14.75, the number of units will be calculated as follows:

Subtracting 32 from both sides, we have:

Multiply both sides by -1:

Square both sides:

Subtract 1 from both sides:

Divide both sides by 0.0001:

The number of units sold will be 2,965,625 units.

Answer:

The third one (parabola)

Step-by-step explanation:

Do a vertical line test.

Basically draw vertical lines over the function. If the x-value has more than one y-value then it is a relation and not a function

Answer:

8*12=96

Step-by-step explanation:

Answer:

8 newspapers in one pile

Step-by-step explanation:

\(\frac{96}{12} = \frac{8}{x} \\\\96x=8*12\\\\96x=96\\x=1\)

All correct proportions include the following:

A. \(\frac{AC}{CE} =\frac{BD}{DF}\)

D. \(\frac{CE}{DF} =\frac{AE}{BF}\)

In Mathematics and Geometry, two geometric figures are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.

Hence, the lengths of the pairs of corresponding sides or corresponding side lengths are proportional to one another when two (2) geometric figures are similar.

Since line segment AB is parallel to line segment CD and parallel to line segment EF, we can logically deduce that they are congruent because they can undergo rigid motions. Therefore, we have the following proportional side lengths;

\(\frac{AC}{CE} =\frac{BD}{DF}\)

\(\frac{CE}{DF} =\frac{AE}{BF}\)

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The values of a and b that make f(x) continuous everywhere are a = 2x and b = 2a - 3/2 = 2(2x) - 3/2 = 4x - 3/2.

The limit is a concept in mathematics that describes the behavior of a function near a particular value, called the limit point. The limit of a function gives the value that the function approaches as the input (variable) approaches the limit point.

For f(x) to be continuous everywhere, the function must have the same value and the same limit as x approaches 2 from the left and the right. In other words, f(2-) = f(2+) and the limit of f(x) as x approaches 2 from the left and the right must be equal.

Let's start by finding f(2-), which is the value of f(x) as x approaches 2 from the left. In this case, f(x) = (x2 - 4)/(x - 2) for x < 2, so as x approaches 2 from the left, f(x) approaches (2^2 - 4)/(2 - 2) = 0.

Next, let's find f(2+), which is the value of f(x) as x approaches 2 from the right. In this case, f(x) = ax^2 - bx + 3 for 2 <= x < 3, so as x approaches 2 from the right, f(x) approaches a(2^2) - b(2) + 3 = 4a - 2b + 3.

Since f(x) must be continuous at x = 2, we need to have f(2-) = f(2+), so we can set f(2-) = f(2+) and solve for a and b:

0 = 4a - 2b + 3

2b = 4a - 3

b = 2a - 3/2

Now that we have an expression for b in terms of a, we can substitute b = 2a - 3/2 into the expression for f(x) for x >= 3 to find the value of a that makes f(x) continuous everywhere:

f(x) = 2x - a + b for x >= 3

f(x) = 2x - a + (2a - 3/2) for x >= 3

f(x) = 2x + 3/2 - a for x >= 3

Since f(x) must be continuous at x = 2, we need to have f(2+) = f(2+), so we can set f(2+) = f(2+) and solve for a:

4a - 2b + 3 = 2x + 3/2 - a for x >= 3

4a - 2(2a - 3/2) + 3 = 2x + 3/2 - a

4a - 4a + 3 + 3/2 = 2x + 3/2 - a

3/2 = 2x + 3/2 - a

a = 2x

So, the values of a and b that make f(x) continuous everywhere are a = 2x and b = 2a - 3/2 = 2(2x) - 3/2 = 4x - 3/2.

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The surface area of revolution of y = 4\(x^3\) about the x-axis over the interval [4, 5] is approximately 806.259 square units.

To find the surface area of revolution of the curve y = 4\(x^3\) about the x-axis over the interval [4, 5], we can use the formula:

S = 2π ∫ [a,b] y √(1 + \((dy/dx)^2\)) dx

where a = 4, b = 5, and dy/dx = 12\(x^2\).

Substituting these values, we get:

S = 2π ∫[4,5] 4x \(\sqrt{(1 + (12x^2)^2)}\) dx

Simplifying the expression inside the square root:

1 + \((12x^2)^2\) = 1 + 144\(x^4\)

= 144\(x^4\)  + 1

The integral becomes:

S = 2π ∫[4,5] 4x √(144\(x^4\) + 1) dx

To evaluate this integral, we can make the substitution u = 144\(x^4\) + 1. Then, du/dx = 576\(x^3\), and dx = du/576\(x^3\).

Substituting these values, we get:

S = 2π ∫[577, 11521] 4x √u du / (576x^3)

Simplifying:

S = π/36 ∫[577, 11521] √u du

S = π/36 x (2/3) x  \((11521^{(3/2)} - 577^{(3/2)})\)

S = π/54 x \((11521^{(3/2)} - 577^{(3/2)})\)

Using a calculator, we can approximate this value to be:

S ≈ 806.259

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hello

from the table given, we can establish a relationship bewteen the number of dozens to the cost in dollars

if 2 dozens costs $17

8 dozens costs x

cross multiply and solve for x

what i did above was test if the relationship is correct

now let's find for 24 dozens

if 2 dozens = $17

24 dozen = ?

24 dozens of muffins would cost $204

Answer:

803.84 bc radius is half of diameter which is 16

Area of circle is (pi)r^2 = (3.14)16^2= 3.14 x 256 = 803.84

Step-by-step explanation:

Answer:

The answer is 804.25

Step-by-step explanation:

\(\frac{32}{2}=16\)

\(Area = 3.14 * 16^2\)

A=3.141592654×16×16

804.2477193mm^2

Area 804.248

Answer:

$14.70

Step-by-step explanation:

191.10/13= 14.70

Answer: 14.70

Step-by-step explanation:  you're supposed to divide 191.10 by 13. you get 14.7 so that's the answer.

There are total 30 positive 3-digit palindromes are multiples of 3.

The numbers are as follows,

111, 141, 171, 222, 252, 282, 303, 333, 363, 393, 414, 444, 474, 525, 555, 585, 606, 636, 666, 696, 717, 747, 777, 828, 858, 888, 909, 939, 969, 999.

Palindrome numbers

A palindromic number is a number that remains the same when its digits are reversed. In other words, it has reflectional symmetry across a vertical axis.

A palindrome number is a number that is same after reverse.

For example - 121, 34543, 343, 131, 48984 are the palindrome numbers.

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The probability of picking a cast member who sold more than 30 tickets is 2/5

Given that one cast member will be picked at random from the 20 cast members who sold tickets to receive a prize. We have to determine the probability of picking a cast member who sold more than 30 tickets.

To find the probability of picking a cast member who sold more than 30 tickets, we need to count the number of cast members who sold more than 30 tickets. Let A be the event of picking a cast member who sold more than 30 tickets. The number of cast members who sold more than 30 tickets is 8. Therefore, P(A) = 8/20 = 2/5.

The probability of picking a cast member who sold more than 30 tickets is 2/5.Answer: 2/5.

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The confidence interval and critical value methods are equivalent in providing an interval estimate, the p-value method is used for hypothesis testing and evaluates the strength of evidence against the null hypothesis.

What is the confidence interval?

A confidence interval is a range of values that is likely to contain the true value of an unknown population parameter, such as the population mean or population proportion. It is based on a sample from the population and the level of confidence chosen by the researcher.

In general, when dealing with inferences for two population proportions, the confidence interval method and the critical value method are equivalent. These two methods provide a range of plausible values (confidence interval) for the difference between two population proportions and involve the calculation of critical values to determine the margin of error.

On the other hand, the p-value method is not equivalent to the confidence interval and critical value methods. The p-value method involves calculating the probability of observing a test statistic as extreme as, or more extreme than, the one obtained from the sample data, assuming the null hypothesis is true. It is used in hypothesis testing to determine the statistical significance of the difference between two population proportions.

To summarize:

- Confidence interval method: Provides a range of plausible values for the difference between two population proportions.

- Critical value method: Uses critical values to determine the margin of error in estimating the difference between two population proportions.

- P-value method: Determines the statistical significance of the observed difference between two population proportions based on the calculated p-value.

Hence, the confidence interval and critical value methods are equivalent in providing an interval estimate, the p-value method is used for hypothesis testing and evaluates the strength of evidence against the null hypothesis.

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Answer:

Gustavo used a simulation where the data is quantitative’

Answer:

y = - 72

Step-by-step explanation:

Given

\(\frac{y}{9}\) = - 8 ( multiply both sides by 9 to clear the fraction )

y = - 72

Answer:

y/9=-8

y=-8*[multiply]9

y=-72

answer is negative 72

Answer:

B) 1

Plot A range is 4 and plot b is 5

Answer:

1

Step-by-step explanation:

Particular solution with the determined constants is:
y(t) = 4*cos(7t) - (5/7)*sin(7t)

To solve the given initial-value problem y'' + 49y = 0 with initial conditions y(0) = 4 and y'(0) = -5, follow these steps:

Step 1: Identify the type of problem.
This is a second-order linear homogeneous differential equation with constant coefficients.

Step 2: Write down the characteristic equation.
The characteristic equation for this problem is \(r^2\) + 49 = 0.

Step 3: Solve the characteristic equation.
\(r^2\) = -49
r = ±√(-49) = ±7i

Since the roots are complex conjugates, the general solution of the differential equation is in the form:
y(t) = C1*cos(7t) + C2*sin(7t)

Step 4: Apply the initial conditions to find the constants.
Apply the initial condition y(0) = 4:
4 = C1*cos(0) + C2*sin(0)
4 = C1
So, C1 = 4

Next, find the first derivative of y(t):
y'(t) = -7*C1*sin(7t) + 7*C2*cos(7t)

Apply the initial condition y'(0) = -5:
-5 = -7*4*sin(0) + 7*C2*cos(0)
-5 = 7*C2
So, C2 = -5/7

Step 5: Write the particular solution.
The particular solution with the determined constants is:
y(t) = 4*cos(7t) - (5/7)*sin(7t)

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The simplified form of the expression 2x^2 - 3x - 2 remains as 2x^2 - 3x - 2.

To simplify the expression 8x - 2x - x^2, we can combine like terms by adding or subtracting coefficients.

8x - 2x - x^2

First, let's combine the x terms:

(8x - 2x) - x^2

This simplifies to:

6x - x^2

Therefore, the simplified form of the expression 8x - 2x - x^2 is 6x - x^2.

Now, let's simplify the expression 2x^2 - 3x - 2:

The expression is already in simplified form, and no further simplification is possible.

Therefore, the simplified form of the expression 2x^2 - 3x - 2 remains as 2x^2 - 3x - 2.

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The error involved in approximating the sum of the given series by the sum of the first five terms of the series is `R5 = 1/6³ + 1/7³ + ...`.

To estimate the error that is made by approximating the sum of the given series by the series the first 5 terms 1/k³, we can use the remainder term of a convergent series.

The given series is ∑ 1/k³ from k = 1 to infinity.We have to find the error involved in approximating the sum of the given series by the sum of the first five terms of the series.

That is, we need to find the difference between the actual sum of the series and the sum of the first five terms of the series.

The sum of the series is given by: `S = 1/1³ + 1/2³ + 1/3³ + 1/4³ + ... + 1/n³ + ...` We can use the remainder term of the series to find the error in approximation.

The remainder term `Rn` is given by: `Rn = Sn - S` where `Sn` is the sum of the first `n` terms of the series. Thus, we have to find the remainder term for `n = 5`.

The remainder term `Rn` is given by: `Rn = S - Sn = 1/6³ + 1/7³ + ...` Since the given series is convergent, the remainder term `Rn` tends to zero as `n` tends to infinity.

So, if we take the sum of the first five terms of the series, the error involved in approximation is given by the remainder term `R5`.

The error involved in this approximation is very small and can be neglected.

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