A house was purchased for $175,000. Due to a crash in the market, it is depreciating at a rate of 2.5% each year. Write a function to represent the situation: And how much was the house after 5 years

Answer:

A. 2x(x+1)(x-6);x=0,-1,6

Step-by-step explanation:

Take out 2x and factorise:

2x(x² - 5x - 6)

We can factorise (x² - 5x - 6)

What two numbers multiply to make -6 and add to give -5? That is -6 and 1 which is written as:

(x - 6)(x + 1)

Now the fully factorised polynomial is:

2x(x - 6)(x + 1)

Equate each of them to 0

2x = 0, x - 6 = 0, x + 1 = 0

Solve for x

x = 0, x = 6, x = -1

Answer:

1. \(y=-\frac{1}{4}x + 3\frac{1}{4}\)

2. (See picture)

3a. \(y=-\frac{300}{4}x + 700\)

3b. Jerry returning $300 back to his father per 4 months

3c. the amount of money Jerry owes to his father

4. \(y+8=\frac{1}{4} (x-4)\)

5. \(y=-3x+6\)

Step-by-step explanation:

This is going to take a while to explain...

1. Firstly, identify the slope. We can see that the line lands on (1, 3) and (5, 2) (not sure because the graph is off), using the definition of slope, we get:

\(m=\frac{3-2}{1-5} \\m=\frac{1}{-4} \\m=-\frac{1}{4}\)

Next, we can replace everything into a point-slope formula:

\(y-3=-\frac{1}{4} (x-1)\\y-3=-\frac{1}{4}x + \frac{1}{4} \\y=-\frac{1}{4}x +3\frac{1}{4}\)

That's question 1 done.

2. Start by locating the y-intercept, in this case, is 6. Draw a dot on (0, 6), and then draw the next point using the slope -5/2, go down 5 grids and go 2 grids to the right. Use a ruler to connect both points and draw a straight line across them. It should look something like this:

(See picture)

3a. Using the same method in the first question, we can write down the equation:

\(y=-\frac{300}{4}x + 700\)

3b. Since slope means "change in y over change in x", then the change in y means the amount of money that Jerry gives back to his father, and change in x means the time that passes per month. Thus, we can express the slope as "Jerry returning $300 back to his father per 4 months".

3c. The y-intercept is 700, and looking at the parameter at the left, it says "amount owed", thus, it means "the amount of money Jerry owes to his father".

4. We have a point and the slope, enough information to write down a point-slope form equation:

\(y-(-8)=\frac{1}{4} (x-4)\\y+8=\frac{1}{4} (x-4)\)

5. We have two points, so we can find the slope of the line, and (0, 6) tells us that the y-intercept is 6:

\(m=\frac{-3-6}{3-0} \\m=\frac{-9}{3} \\m=-3\)

With the following information, we can fill in the variables into the point-slope form equation:

\(y-6=-3(x-0)\\y-6=-3x\\y=-3x+6\)

Whoosh! I hope everything in number 3 is correct.

a) The probability histogram of pmf for the number of students who show up for a professor's office hour on a particular day is shown below.

b) The probability that at least two students show up = 0.55 and the probability that more than two students show up = 0.25

c) The probability that between one and three students show up = 0.7

d) The probability that the professor shows up = 0.20

First we write the number of students who show up for a professor's office hour on a particular day and their pmf in tabular form.

x        p(x)

0       0.20

1       0.25

2       0.30

3       0.15

4       0.10

The probability histogram of this data is shown below.

The probability that at least two students show up would be,

P(x ≥ 2) = p(2) + p(3) + p(4)

P(x ≥ 2) = 0.30 + 0.15 + 0.10

P(x ≥ 2) = 0.55

Now the probbability that more than two students show up:

P(x > 2) = p(3) + p(4)

P(x > 2) = 0.15 + 0.10

P(x > 2) = 0.25

The probability that between one and three students show up would be:

P(1 ≤ x ≤ 3) = p(1) + p(2) + p(3)

P(1 ≤ x ≤ 3) = 0.25 + 0.30 + 0.15

P(1 ≤ x ≤ 3) = 0.7

And the probability that the professor shows up would be: p = 0.20

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Answer:

For easy way

convert to decimals first

3.5h - 3 (5h - 3.5)

Open brackets

3.5h - 15h + 10.5

Answer = 10.5 - 11.5h

Answer:

I can't read is so blurry -0_0-

Step-by-step explanation:

Rounding to the nearest whole number, she will have run a total distance of 13 kilometers after 16 days.

To find out how far she will have run in total after 16 days, we can use the formula for calculating compound interest:

A = P(1 + r/100)^n

Where:

A = Total distance run after n days

P = Initial distance (4.8 kilometers)

r = Rate of increase per day (6.9%)

n = Number of days (16)

Plugging in the given values, we can calculate the total distance:

A = 4.8(1 + 6.9/100)^16

Using a calculator or performing the calculations step by step, we get:

A ≈ 4.8(1.069)^16 ≈ 4.8(2.092473)^16 ≈ 4.8(2.628)

A ≈ 12.6144

Rounding to the nearest whole number, she will have run a total distance of 13 kilometers after 16 days.

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Answer:

The given matrix equation can be written as:

[1 1; 10 20] * [c; a] = [30,000; 500,000]

Multiplying the matrices on the left side of the equation gives us the system of equations:

c + a = 30,000 10c + 20a = 500,000

To solve for c and a using matrices, we can use the inverse matrix method. First, we need to find the inverse of the coefficient matrix [1 1; 10 20]. The inverse of a 2x2 matrix [a b; c d] can be calculated using the formula: (1/(ad-bc)) * [d -b; -c a].

Let’s apply this formula to our coefficient matrix:

The determinant of [1 1; 10 20] is (120) - (110) = 10. Since the determinant is not equal to zero, the inverse of the matrix exists and can be calculated as:

(1/10) * [20 -1; -10 1] = [2 -0.1; -1 0.1]

Now we can use this inverse matrix to solve for c and a. Multiplying both sides of our matrix equation by the inverse matrix gives us:

[2 -0.1; -1 0.1] * [c + a; 10c + 20a] = [2 -0.1; -1 0.1] * [30,000; 500,000]

Solving this equation gives us:

[c; a] = [25,000; 5,000]

So, on that particular day, there were 25,000 children’s tickets sold.

12 1/2 years

Step-by-step explanation:

Let the unknown be n. Then 40+n = 3(5+n).

Performing the multiplication:

40+n = 15+3n

Isolate n and combine the constant terms:

25=2n, so n= 25/2 years

The given question is related to a regression line, where the equation is given as y = 1425 + 19.87x.

Slope of the equation is 19.87 and the intercept of the equation is 1425.

In part (a), step 2, we can explain that the slope in the least square regression equation is the coefficient of x and represents the average increase or decrease in y per unit of x.

Therefore, the slope value here is b = 19.87, which means that the average consumption of natural gas per day by Joan will decrease by 19.87 cubic feet per degree Fahrenheit over a month.

In part (b), step 1, we can explain that the y-intercept is a constant value in the least square regression equation that represents the average value of y when x is 0. Here, the intercept value is m = 1425, which means that when the temperature is 0 degrees Fahrenheit, the average consumption of natural gas per day is 1425 cubic feet.

This value has significance in this scenario because it indicates that a temperature of 0 degrees Fahrenheit is a possible temperature for which the natural gas consumption has been calculated.

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Answer:

Step-by-step explanation:

Pythagorean Theorem

(AB)² = 5.6² + 3.9² = 46.57

radius r = (√46.57)/2 cm

area = πr² = π46.57/4 ≈ 36.5759925 cm l²

Answer:

Answer:

22801

Step-by-step explanation:

#40

No. of terms = (301 + 1)/2

No. of terms = 302/2

No. of terms = 151

Now,

Sum = n²

Sum = (151)²

Sum = 22801

The first equation, 3^x = 12, is an exponential equation. To solve for x, we would take the logarithm of both sides with base 3:

x = log3(12)

The second equation, x^3 = 12, is a polynomial equation of degree 3. To solve for x, we would take the cube root of both sides:

x = ∛12

The similarity between these two equations is that both are equations with one variable and are looking for the value of that variable.

The main difference between these two equations is the type of function they represent. The first equation is an exponential function, represented by 3^x, while the second equation is a polynomial function, represented by x^3.

As a result, the methods used to solve these equations are also different. The first equation is solved by taking the logarithm of both sides and the second equation is solved by taking the cube root of both sides.

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Answer:

Step-by-step explanation:

a.

5kg = 5000 g

5000 ÷ 125 = 40

Mary can make 40 packets

b. 40 x 99 = 3960

3960 ÷ 100 = 39.60

39.6 - 25 = 14.6

Therefore, Mary makes a profit of £14.6

When a trouble ticket is initiated, the first step that should be taken according to the customer support topology is to reassure the caller as to your intention and interest in addressing the issue. Option C is the correct answer.

This step is crucial in customer support as it helps build rapport and trust with the caller. Reassuring the caller shows empathy and demonstrates that their concern is being taken seriously. It also sets the stage for effective problem-solving and ensures the caller feels valued and heard. By addressing the caller's concerns and expressing a genuine interest in resolving the issue, the customer support representative can lay a solid foundation for providing satisfactory assistance.

Option C is the correct answer.

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Answer:

64 people

Step-by-step explanation:

multiply the number by of people the precentage who have genetic mutation (divide percentage by 100 before multiplying) 0.08 x 800 = 64

Answer: as per question statement

we need to set up an equation first

p(t)=1200e(0.052*t)

they have given that it is relative to 1200 that means it starts to increase from 1200 at t=0 initially 1200 bacteria were present

we need to find population at t=6

we need to plug t=6 in p(t).

P(6)=1200e(0.052*6)=1639.38

1638.38 bacteria were present at that time t=6

Step-by-step explanation: I hope this helps.

The prime factorization of 15 is 3 × 5. The correct option is the second option 3 × 5

From the question, we are to determine which of the given options is the prime factorization of 15

First, we will list the factors of 15

The factors of 15 are

15: 1, 3, 5, and 15

Among the given options, 3 and 5 are prime factors

Thus,

Prime factorization of 15 = 3 × 5

Hence, the prime factorization of 15 is 3 × 5. The correct option is the second option 3 × 5

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Answer:

3/8+8/11= 97/88

Step-by-step explanation:

This is how you add

\(\frac{3}{8}\)   + \(\frac{8}{11}\)

Step 1

Of course, you can't add two fractions if the denominators (bottom numbers) don't match. To get a common denominator, multiply the denominators together. Then we fix the numerators by multiplying each one by their other term's denominator.

Now you multiply 3 by 11, and get 33, then we multiply 8 by 11 and get 88.

Do the same for the second term. We multiply 8 by 8, and get 64, then multiply 8 by 11 and get 88.

The problem now has new fractions to add:

33/88 + 64/88

Step 2

Since our denominators match, we can add the numerators.

33 + 64 = 97

The sum we get is: 97/88

The last step is to reduce the fraction if we can.

To find out, we try dividing it by 2...

Nope! So now we try the next greatest prime number, 3...

Nope! So now we try the next greatest prime number, 5...

Nope! So now we try the next greatest prime number, 7...

Nope! So now we try the next greatest prime number, 11...

And finally after we reduce we get 89

89 is larger than 88. So we're done reducing.

There you have it! Here's the final answer to 3/8 + 8/11

3/8+8/11= 97/88

Can I plss get brainly i worked so hard!

Answer:

7

Step-by-step explanation:

Answer:

7 dollars per pound

Explanation:

divide 42 by 6 and your answer is 7 dollars per pound

Answer:

C,D

Step-by-step explanation:

Recursive algorithm for computing n²: 1. If n equals 0, return 0 (base case), 2. Otherwise, recursively compute (n-1)², 3. Compute n² by using the formula: n² = (n-1)² + 2n - 1.

What is recursive algorithm?

A recursive algorithm is a problem-solving approach where a function calls itself to solve smaller instances of the same problem until a base case is reached.

To prove the correctness of the recursive algorithm for computing n², we will use mathematical induction.

Base case: For n = 0, the algorithm returns 0, which is correct since 0² equals 0.

Inductive step: Assume that the algorithm correctly computes n² for a given nonnegative integer k, i.e., n² = k². Now, we will show that it also computes (k+1)² correctly.

According to the algorithm, (k+1)² is computed by first calculating k² using the recursive step, and then applying the formula n² = (n-1)² + 2n - 1.

Using the assumption, we have k² = (k-1)² + 2k - 1.

Expanding (k-1)², we get k² - 2k + 1 + 2k - 1 = k².

Therefore, (k+1)² = k² + 2(k+1) - 1, which simplifies to (k+1)² = k² + 2k + 1.

This matches the definition of (k+1)², so the algorithm correctly computes (k+1)².

By induction, we have proven that the algorithm correctly computes n² for any nonnegative integer n.

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A population has a mean of 180 and a standard deviation of 36. A sample of 84 observations will be taken. The probability that the sample mean will be between 181 and 185 is

Given n(sample size) = 84

Population mean(μ) = 180

Standard Deviation(σ) = 36

Standard error of the mean = σx-bar = σ/√n = 36/√84 = 36/9.165 = 3.927

Standardizing the sample mean we have

Z = (x-bar - μ)/σx-bar = (x-bar - μ)/σ/√n

x-bar = 180

Z(x-bar=185 at point C) = (185 - 180)/3.927 = 5/3.927 = 1.273

Z(x-bar=181 at point D) = (181 - 180)/3.927 = 1/3.927 = 0.254

The area ABCD is the probability that the sample mean will lie between 181 and 185.

The shaded Area ABCD = (Area corresponding to Z = 2 or x-bar = 185) - (Area corresponding to Z = 1 or x-bar = 181)

Area corresponding to Z = 1.273 = 0.898

Area corresponding to Z = 0.254 = 0.598

The shaded Area ABCD = 0.898-0.598 = 0.300

Therefore the probability that the sample mean will lie between 181 and 185 is 0.300.

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Step 1:

Write the given data

Step 2:

Write the z-score formula

Step 3

Substitute the values in the z score equation

Step 4:

Draw the z-curve

Step 5

Probability that scores greater than 1979 id Pr (z > -1.677)

Final answer

= 95.4%

Answer:

The oval is a line and rotational symmetry.

The line shapes rectangle has no symmetry.

The smiling face is a line symmetry.

Step-by-step explanation:

Answer:

The first oval - line symmetry, rotational symmetry

The L shape - no symmetry

The smiley face - line symmetry

Step-by-step explanation:

I just took the quiz on egde2020

9t + 4t can be simplified by combining the like terms (terms with the same variable and exponent). The coefficients of the two terms (9 and 4) are added to get the coefficient of the simplified term:

9t + 4t = (9 + 4)t = 13t

Therefore, the expression that is equivalent to 9t + 4t is 13t.

Apply the Binomial Probability Distribution, The Answer is 0.044.

The discrete probability distribution of the number of successes in a series of n independent experiments, each asking a yes-or-no question and each with its own Boolean-valued outcome is known as the binomial distribution with parameters n and p in probability theory and statistics.

The required formula is:

\(P(x)= C(n,x) p^{x}q^{n-x}\)

n=10

x=8

p(8)= \(C(10,8) * 0.5 ^ {8} *0.5 ^{2}\)

=0.044

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Answer:

(-2,4)

Explanation:

Given the inequality:

The solution set is graphed on the number line below:

The value of the triple integral is 72π.

To evaluate this triple integral in cylindrical coordinates, we first need to express the region E using cylindrical coordinates.

The cylinder x² + y² = 16 can be expressed in cylindrical coordinates as r² = 16, or r = 4. The planes z = -5 and z = 4 define a region of height 9.

So, the region E can be expressed in cylindrical coordinates as:

4 ≤ r ≤ 4

-5 ≤ z ≤ 4

0 ≤ θ ≤ 2π

The integrand √(x² + y²) can be expressed in cylindrical coordinates as r, so the integral becomes:

∭E√x²+y²dV = ∫0²π ∫4⁴ ∫-5⁴ r dz dr dθ

Note that the limits of integration for r are from 0 to 4, which means we are only integrating over the positive x-axis. Since the integrand is an even function of x and y, we can multiply the result by 2 to get the total volume.

The integral with respect to z is easy to evaluate:

∫₋₅⁴ r dz = r(4 - (-5))

= 9r

So the triple integral becomes:

∭E√x²+y²dV = 2 ∫0^2π ∫4⁴ 9r dr dθ

= 2(9) ∫0^²π 4 dθ

= 72π

Therefore, the value of the triple integral is 72π.

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