Mandy bought a desktop computer system to start her business from home for $4,995. It is expected to depreciate at a rate of 10% per year. How much will her home computer system be worth after 9 years? Round to the nearest hundredth

The absolute maximum will be at (11, 10373).
The absolute minimum is at (-1.963, -25.294).

What in are the absolute maximum maxime off on the given interval?

To determine the location and value of the absolute extreme values of the function f(x) = 8x³+ 22x² - 24x on the interval (-7, 11), follow these steps:

Find the critical points by taking the derivative of the function and setting it equal to zero:
f'(x) = 24x² + 44x - 24

Solve for x:
Factor the equation: 4(6x² + 11x - 6) = 0
Using the quadratic formula, x = (-11 ± √(121 + 144))/12
x ≈ -1.963, 0.630

Check the endpoints and the critical points to find the absolute maximum and minimum:
f(-7) ≈ 461
f(-1.963) ≈ -25.294
f(0.630) ≈ -16.102
f(11) ≈ 10373

Compare the values:
The absolute maximum is at x = 11, with a value of 10373.
The absolute minimum is at x ≈ -1.963, with a value of ≈ -25.294.

Answer:
The absolute maximum is at (11, 10373).
The absolute minimum is at (-1.963, -25.294).

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Answer:..

Step-by-step explanation:Use the distance formula to find the length of each side and then add the lengths.

Use the slope formula to find the slope of each of side, and then determine if the opposite sides are parallel.

Use the slope formula to find the slope of each of side, and then determine if the consecutive sides are perpendicular.

Use the distance formula to find the length of the sides, and then multiply two of the side lengths.

The amount each of them pays when their electricity bill is $110, $165, and $352 respectively, in the ratio 2:4:5, are:

1) $20, $40, $50

2) $30, $60, $75

3) $64, $128, $160

To find out how much each of them pays, we'll use the given ratio of 2:4:5 and divide the total bill among them accordingly.

Total bill: $110

The total ratio is 2+4+5=11.

Greg's share: (2/11) * $110 = $20

Harry's share: (4/11) * $110 = $40

Ian's share: (5/11) * $110 = $50

Therefore, Greg pays $20, Harry pays $40, and Ian pays $50.

Total bill: $165

The total ratio is still 2+4+5=11.

Greg's share: (2/11) * $165 = $30

Harry's share: (4/11) * $165 = $60

Ian's share: (5/11) * $165 = $75

Therefore, Greg pays $30, Harry pays $60, and Ian pays $75.

Total bill: $352

The total ratio remains the same: 2+4+5=11.

Greg's share: (2/11) * $352 = $64

Harry's share: (4/11) * $352 = $128

Ian's share: (5/11) * $352 = $160

Therefore, Greg pays $64, Harry pays $128, and Ian pays $160.

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A 16-inch radius tire would require 75 revolutions to travel the same distance as a 12-inch radius tire that made 100 revolutions.

Let's start by defining some variables. Let "r" represent the radius of the tire and "n" represent the number of revolutions it makes over a fixed distance. We are given that the number of revolutions is inversely proportional to the radius of the tire. This means that as the radius increases, the number of revolutions decreases, and vice versa. We can express this relationship mathematically as follows:

n = k/r

Here, "k" is the constant of variation, which remains the same for any given tire traveling over the same distance. To solve the problem, we need to find the value of "k" first. We know that a 12-inch radius tire makes 100 revolutions to travel a certain distance. Substituting these values into the equation, we get:

100 = k/12

Solving for "k," we get k = 1200. Now we can use this value to find the number of revolutions required by a 16-inch radius tire to travel the same distance:

n = 1200/16 = 75

Therefore, a 16-inch radius tire would require 75 revolutions to travel the same distance as a 12-inch radius tire that made 100 revolutions.

In summary, we defined the variables, identified the constant of variation, wrote the equation (n=k/r), found the value of the constant by using the given information, and used it to solve the problem by finding the number of revolutions required by a tire with a different radius.

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It will take Josh about 66.67 minutes to easy the cafeteria alone.

Let's anticipate that the amount of work required to easy the cafeteria is 1 unit.

In a single minute, Josh can easy 1/x of the cafeteria (in which x is the number of mins it takes Josh to do the task alone), and Draven can clean 1/40 of the cafeteria in one minute.

When they work together, they could easy the cafeteria in 25 minutes, so in one minute they are able to easy 1/25 of the cafeteria.

The use of the fact that their combined rate is the sum in their individual rates, we are able to installation an equation:

1/x + 1/40 = 1/25

Multiplying each facets through the least common more than one of the denominators (40 * 25 * x), we get:

25 * 40 + x * 40 = x * 25

1000 + 40x = 25x

15x = 1000

x = 66.67

Therefore, it'd take Josh about 66.67 minutes to easy the cafeteria alone.

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The mean of the fifth-grade jump distance data set.

To determine the mean of the data set for fifth-grade jump distances, we need the actual data values. Without the specific data set, it is not possible to calculate the mean.

The mean is the sum of all the values in a data set divided by the number of values. Therefore, we would need the individual jump distances for each fifth-grade student to calculate the mean accurately.

Once we have the complete data set, we can add up all the distances and divide by the total number of students to find the mean. Without the specific data, we cannot provide a numerical answer for the mean of the fifth-grade jump distance.

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Answer: A. 2 ways; FG, GF

Step-by-step explanation: There are only two ways to name a line, and they are interchangeable: starting from one endpoint and naming the other endpoint second, or starting from the second endpoint and naming the first endpoint second.

The monthly rent for the apartment would be $1238.84 in the fifth year.

The problem states that the monthly rent for an apartment is $925. To calculate the rent for the second year, we need to increase this amount by 6%.

To do this, we first need to calculate 6% of $925. We can do this by multiplying 0.06 (which is equivalent to 6%) by $925:

6% of $925 = 0.06 × $925 = $55.50

So, the rent for the second year would be:

$925 + $55.50 = $980.50

To find the rent for the third year, we need to increase the rent for the second year by 6%. We can follow the same process:

6% of $980.50 = 0.06 × $980.50 = $58.83

So, the rent for the third year would be:

$980.50 + $58.83 = $1039.33

To find the rent for any year n, we use the formula:

Rent for year n = $925 × (1 + 0.06)^n

In this formula, (1 + 0.06) represents the multiplier used to calculate the new rent each year.

For example, the multiplier for the second year is 1 + 0.06 = 1.06, and the multiplier for the third year is 1.06 × 1.06 = 1.1236 (rounded to four decimal places).

To find the rent for the fifth year, we plug in n = 5:

Rent for year 5 = $925 × (1 + 0.06)^5 = $925 × 1.3382 = $1238.84 (rounded to the nearest cent)

So, the monthly rent for the apartment would be $1238.84 in the fifth year.

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The company's profit in the year 2005 would be approximately $10.5 million.

Let's calculate the company's profit for the year 2005 using the given information.

Initial profit in 2001: $7.2 million
Annual profit increase: 11%

We need to find the profit for 2005, which is 4 years after 2001.

Step 1: Identify the formula for compound interest, which can be applied to profit increase:
Future Profit = Initial Profit * (1 + Profit Increase Rate)^Number of Years

Step 2: Plug in the values:
Future Profit [tex]= $7.2 million * (1.11)^4[/tex]
Step 3: Calculate the result:
Future Profit [tex]= $7.2 million * (1.11)^4[/tex]
Future Profit = $7.2 million [tex]* 1.4641[/tex]
Future Profit = $10.54152 million

Step 4: Round the result to the nearest tenth of a million dollars:
Future Profit ≈ $10.5 million

So, the company's profit in the year 2005 would be approximately $10.5 million.

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The reasoning behind this is that the initial amount (h(x)) is multiplied by the interest growth factor (s(x)) to calculate the total amount with interest over time.

To model the total amount of money Victoria will have in her bank account as interest accrues after depositing her $200, you can combine the two functions h(x) and s(x). The given functions are h(x) = 200 and s(x) = (1.05)^x−1.

First, note that s(x) represents the growth factor of the interest, which is 5% (1.05) compounded annually. To find the total amount after x years, you need to multiply the initial amount by the growth factor raised to the power of x.

So, the combined function T(x) can be written as T(x) = h(x) * s(x).

Substitute the given functions into the combined function:

T(x) = (200) * ((1.05)^x−1)

This function, T(x), models the total amount of money Victoria will have in her bank account after x years with interest accrued on her $200 deposit. The reasoning behind this is that the initial amount (h(x)) is multiplied by the interest growth factor (s(x)) to calculate the total amount with interest over time.

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There are 252 different combinations of shirts, the correct option is B.

Remember that if you have N elements, and you want to select K of these, the number of combinations is given by:

[tex]C(N, K) = \frac{N!}{(N - K)!*K!}[/tex]

Here we have 10 shirts and we want to select 5 of these, so the number of combinations is given by:

[tex]C(10, 5) = \frac{10!}{(10 - 5)!*5!} \\\\C(10, 5) = \frac{10*9*8*7*6}{5*4*3*2} = 252[/tex]

There are 252 different combinations, so the correct option is B.

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1. This is not an example of a quasi-experimental design because the researcher randomly assigned participants to the two groups. In a quasi-experimental design, the researcher does not have full control over the assignment of participants to groups.

2. The dependent variable in this study is the word recall. It is the variable that the researcher is interested in measuring and is expected to be affected by the independent variable.

3. The independent variable in this study is sugar consumption. It is the variable that the researcher manipulated by assigning participants to one of two groups, sugar vs. no sugar.

The purpose of manipulating the independent variable is to examine its effect on the dependent variable, word recall.

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Answer:

$1.01

Step-by-step explanation:

We Know

A 2-quart carton of pineapple juice costs $8.08

1 quart = 4 cups

2 quarts = 8 cups

So, 8 cups of pineapple juice cost $8.08.

What is the price per cup?

We Take

8.08 / 8 = $1.01

So, the price per cup is $1.01

There is 20% decrease in scholars number who went to the morning homework help.

To get the scholar's percent decrease, we need to calculate the difference between them on Thursday and Friday and theb divide that by the number of scholars on Thursday.

Data:

Number of scholars on Thursday = 30

Number of scholars on Friday = 24

Difference = 30 - 24 = 6

The percent decrease = (6/30) x 100%

The percent decrease = 0.2 * 100%

The percent decrease = 20%

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To find the maximum height of the soccer ball, we need to determine the vertex of the quadratic function. The vertex is given by the formula:

t = -b/2a

where a = -16 and b = 27 from the given equation:

H = -16t^2 + 27t + 3

Substituting these values into the formula, we get:

t = -27/(2(-16)) = 0.84375

Now that we have the value of t at the vertex, we can find the maximum height by substituting it back into the original equation:

H = -16(0.84375)^2 + 27(0.84375) + 3 = 12.65625

Therefore, the maximum height of the soccer ball is approximately 12.65625 units.

h = -16t^2 + 27t + 3 = -(4t - 27/8)^2 + 921/64

With every number t, h [tex]\leq[/tex] 921/64.

Therefore, the maximum height of the soccer ball is 921/64, or aprroximately 14.4(units)

"=" when 4t = 27/8, or t = 27/32.

There would be   1.302 x 10¹² cells in koala, and  there are  3.04 x 10^17 cells in the average hippo.

To find the number of cells in the average koala, we first need to find the volume of the koala in cubic centimeters, since we know the density of the cell and can use that to find the mass of the koala in grams.

The average weight of a koala is 6 kilograms, which is equivalent to 6,000 grams. We can use the density of the cell to find the volume of the koala:

Density = Mass / Volume

1.1 g/cm³ = 6,000 g / Volume

Volume = 6,000 g / 1.1 g/cm³

Volume = 5,454.54 cm³

Next, we need to find the volume of one cell:

Volume of cell = 4/3 * π * (0.001 cm)³

Volume of cell = 4.188 x 10⁻⁹ cm³

Finally, we can divide the volume of the koala by the volume of one cell to find the number of cells in the average koala:

Number of cells = 5,454.54 cm³ / (4.188 x 10⁻⁹ cm³)

Number of cells = 1.302 x 10¹²

Therefore, there are approximately 1.302 x 10¹² cells in the average koala.

To find the number of cells in the average hippo, we can follow the same process. The average weight of a hippo is 1,400 kilograms, which is equivalent to 1,400,000 grams. Using the density of the cell, we can find the volume of the hippo:

Density = Mass / Volume

1.1 g/cm^3 = 1,400,000 g / Volume

Volume = 1,400,000 g / 1.1 g/cm³

Volume = 1,272,727.27 cm³

Dividing the volume of the hippo by the volume of one cell, we get:

Number of cells = 1,272,727.27 cm³ / (4.188 x 10⁻⁹ cm³)

Number of cells = 3.04 x 10¹⁷

Therefore, there are approximately 3.04 x 10¹⁷ cells in the average hippo.

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The value 78 inches best describes the tallest player on the Bulldogs baseball team. This height is an outlier within the data set and may affect statistical analyses.

The Bulldogs, a baseball team, consists of nine starting players with varying heights. Their heights are as follows: 72 in, 71 in, 78 in, 70 in, 72 in, 72 in, 73 in, 70 in, and 72 in. To describe the data, we can analyze the presence of the 78 in height value.

In this case, the value 78 in represents the tallest player on the team. When examining this data set, it is important to understand how this value affects the overall distribution of heights among the players. One way to determine this is by calculating the mean, median, and mode of the height data.

The mean (average) height for the team is 71.22 inches, and the median (middle) value is 72 inches. The mode (most frequent) height is also 72 inches. The value 78 inches is above the mean and median values, indicating that it is an outlier, or a value that is significantly different from the majority of the other data points.

In conclusion, the value 78 inches best describes the tallest player on the Bulldogs baseball team. This height is an outlier within the data set and may affect statistical analyses. However, it provides valuable information about the diversity of heights among the starting players on the team.

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Answer:

7/5

Step-by-step explanation:

Lily's age in months: 2×12+4=28mo

Hugo's age in months=12+8=20

Lily's age over Hugo's age: 28/20

Simplify:

28/20=14/10=7/5

Answer: 344cm²

Step-by-step explanation:

7x7=49

49x5=245

3x2=6

49-6=43

245+43=288

5x2=10 10x2=20

5x3=15 15x2=30

288+30+20+6=344

Answer: Diffusion

Step-by-step explanation:

The system of equations is.

x + y = 80

12x + 10y = 900

And the solutions are y = 30 and x = 50

Let's define the two variables:

x = number of calculators.

y = number of calendars.

With the given information we can write two equations, then the system will be:

x + y = 80

12x + 10y = 900

Now let's solve it.

We can isolate x on the first equation to get:

x = 80 - y

Replace that in the other equation to get:

12*(80 - y) + 10y = 900

-2y = 900 - 960

-2y = -60

y = -60/-2 = 30

Then x = 50

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The predicted populations of rabbits in the warren in 2008 and 2022 are 2909 and 9933, respectively.

To predict the population of rabbits in the warren in 2008 and 2022, we can use the formula for exponential growth:
P(t) = P₀ (1 + r)ᵗ

Where P(t) is the population at time t, P₀ is the initial population, r is the growth rate, and t is the time elapsed.

For this problem, we know that P₀ = 1500, r = 0.07 (since the growth rate is 7%), and we want to find P(8) and P(22) (since we're predicting the population in 2008 and 2022, respectively).

Using the formula, we get:
[tex]P(8) = 1500( 1 + 0.07)^{8}  = 2909[/tex]

So we can predict that there will be about 2909 rabbits in the warren in 2008.

To find P(22), we simply plug in t = 22:
[tex]P(22) = 1500 (1 + 0.07)^{22}  = 9933[/tex]

So we can predict that there will be about 9933 rabbits in the warren in 2022.

Therefore, the predicted populations of rabbits in the warren in 2008 and 2022 are 2909 and 9933, respectively.

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Answer:

Step-by-step explanation:

a) Let x be the cost of each ticket. Then the total cost of the tickets for the 6 friends is 6x. The total cost, including the popcorn, is $54.50. So we can set up an equation:

6x + $9.50 = $54.50

Solving for x, we get:

6x = $45.00

x = $7.50

So each ticket costs $7.50.

b) To find the cost per person, we need to add up the cost of each ticket and divide by the number of people. The cost of all 6 tickets is:

6 tickets × $7.50/ticket = $45.00

Adding the cost of the popcorn, we get:

$45.00 + $9.50 = $54.50

So the total cost for the 6 friends is $54.50, and the cost per person is:

$54.50 ÷ 6 people = $9.08 per person.

Therefore, each person contributed $9.08 towards the total cost of the tickets and popcorn.

If the cake is in the shape of a rectangular prism, the total surface area of the cake that will be covered in frosting is 314 sq. inches.

To find the total surface area of the cake that will be covered in frosting, we need to calculate the area of all sides except the bottom. A rectangular prism has 6 sides, and we will be considering 5 of them.

Surface area of top: length × width = 13 × 8 = 104 sq. inches
Surface area of front: length × height = 13 × 5 = 65 sq. inches
Surface area of back: length × height = 13 × 5 = 65 sq. inches
Surface area of left side: width × height = 8 × 5 = 40 sq. inches
Surface area of right side: width × height = 8 × 5 = 40 sq. inches

Now, we will sum the areas of all these sides:
104 + 65 + 65 + 40 + 40 = 314 sq. inches

So, the total surface area of the cake that will be covered in frosting is 314 sq. inches. None of the provided options match this answer, so it is important to double-check the question for any discrepancies.

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Answer:

275 miles

Step-by-step explanation:

Samantha determines the answer as cos(θ) = -√(3/4).

Based on the information given, I can help you with this problem. Samantha is correct in using the Pythagorean identity and substitution, but she made an error in identifying the quadrant. Here's the correct process:

1. Given sin(θ) = 1/2 and tan(θ) < 0.
2. The correct quadrant where sin(θ) is positive and tan(θ) is negative is the second quadrant, not the first.
3. Using the Pythagorean identity: sin^2(θ) + cos^2(θ) = 1.
4. Substitute sin(θ) = 1/2 into the equation: (1/2)^2 + cos^2(θ) = 1.
5. Simplify: 1/4 + cos^2(θ) = 1.
6. Solve for cos^2(θ): cos^2(θ) = 3/4.
7. Since we are in the second quadrant, cos(θ) is negative: cos(θ) = -√(3/4).

Your answer: cos(θ) = -√(3/4).

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Answer:

Step-by-step explanation:

I assume the question is what trig function do you use to find x?  If that's correct then answers, from TOP to BOTTOM, are:

tan

cos

sin

Answer:

Triangle 1: tangent

Triangle 2: cosine

Triangle 3: sine

Step-by-step explanation:

First, some definitions before working the problem:

The three standard trigonometric functions, cosine, tangent, and sine, are defined as follows for right triangles:

[tex]sin(\theta)=\dfrac{opposite}{hypotenuse}[/tex]

[tex]tan(\theta)=\dfrac{opposite}{adjacent}[/tex]

[tex]cos(\theta)=\dfrac{adjacent}{hypotenuse}[/tex]

One memorization tactic is "Soh Cah Toa" where the first capital letter represents one of those three trigonometric functions, and the "o" "a" and "h" represent the "opposite" "adjacent" and "hypotenuse" respectively.

The triangle must be a right triangle, or there wouldn't be a "hypotenuse", because the hypotenuse is always across from the right angle.  

Triangle 1

For the first triangle, the known acute angle is in the bottom left.  The two sides of the triangle that are known or are a "goal to find" are not the hypotenuse, so they are the "opposite" & "adjacent".

Specifically, the side of length "13" is touching the known acute angle AND the right angle, so it is the adjacent side.  The unknown side of length "x" is is touching the right angle but is NOT touching the known acute angle, so it is the "opposite" (across from the angle).

Out of "Soh Cah Toa," the part that uses o & a is "Toa".  The "T" in "Toa" stands for Tangent.  So, the desired function to use for the first triangle is the Tangent function.

Triangle 2

For the second triangle, the known acute angle is in the top left.  This time, the "adjacent" side is unknown, labeled as x, so it is the "goal to find" side.  The "hypotenuse" is known.

Therefore, the two sides of the triangle that are known or are a "goal to find" are the "adjacent" & "hypotenuse".

Out of "Soh Cah Toa," the part that uses "a" & "h" is "Cah".  So, the desired function to use for the first triangle is the Cosine function.

Triangle 3

For the third triangle, the known acute angle is in the top right.

This time, the side (at the bottom) across from the angle (at the top right) is known -- the "opposite" leg.  Additionally, the "hypotenuse" is unknown and is our "goal to find" side.  

Therefore, the two sides of the triangle that are known or are a "goal to find" are the "opposite" & "hypotenuse".

Out of "Soh Cah Toa," the part that uses "o" & "h" is "Soh".  So, the desired function to use for the first triangle is the Sine function.

The volume of the larger rectangular box is 125 times the volume of the smaller box.

To compare the volume of the larger rectangular box to the smaller box, we need to consider how the dimensions have changed.

Since the larger box has dimensions 5 times those of the smaller box, let's represent the dimensions of the smaller box as length (L), width (W), and height (H). Therefore, the dimensions of the larger box would be 5L, 5W, and 5H.

Now, let's calculate the volume of both boxes:

1. Volume of the smaller box: V_small = L * W * H
2. Volume of the larger box: V_large = (5L) * (5W) * (5H)

To find the ratio of the larger box's volume to the smaller box's volume, we can divide the volumes:

V_large / V_small = ((5L)*(5W)*(5H)) / (L * W * H)

Notice that L, W, and H can be canceled out:

(5 * 5 * 5) = 125

So, the volume of the larger rectangular box is 125 times the volume of the smaller box.

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