The points (9, 9) and (5, 1) fall on a particular line. What is its equation in slope-intercept form?

The present value of the cash flows is approximately $1,586.2.

The appropriate discount rate for the given cash flows is 12 percent compounded quarterly. The cash flows and their respective years are as follows:

Year 1 Cash flow = $800

Year 2 Cash flow = $500

Year 3 Cash flow = $0

Year 4 Cash flow = $1,100

To find the present value of these cash flows, we can use the present value formula:

Present value = Cash flow / (1 + r/n)^(n*t)

Where:

r = Rate of interest

n = Number of times compounded annually

t = Number of years

Cash Flow 1:

The present value of Cash flow 1 is given by:

PV1 = $800 / (1 + 0.12/4)^(1*4)

PV1 = $800 / (1.03)^4

PV1 = $626.31 (approx)

Cash Flow 2:

The present value of Cash flow 2 is given by:

PV2 = $500 / (1 + 0.12/4)^(2*4)

PV2 = $500 / (1.03)^8

PV2 = $348.56 (approx)

Cash Flow 3:

The present value of Cash flow 3 is given by:

PV3 = $0 / (1 + 0.12/4)^(3*4)

PV3 = $0 / (1.03)^12

PV3 = $0 (approx)

Cash Flow 4:

The present value of Cash flow 4 is given by:

PV4 = $1,100 / (1 + 0.12/4)^(4*4)

PV4 = $1,100 / (1.03)^16

PV4 = $611.33 (approx)

Hence, the total present value of the given cash flows is:

PV = $626.31 + $348.56 + $0 + $611.33

PV = $1,586.2

Thus, the present value of the cash flows is approximately $1,586.2.

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According to the question For ( a ) the amount and concentration of salt at any time \(\(t\)\) can be \(\[S(t) = 10 + 11 - 44 \times C(t) \text{ kg}\]\)\(\[C(t) = \frac{S(t)}{100}\text{ kg/L}\]\) . For ( b ) the limiting concentration of salt in the tank is 0.25 kg/L.

To determine the amount and concentration of salt at any time in the tank, we need to consider the inflow of saltwater, outflow of water, and evaporation. Let's denote the time as \(\(t\)\) in hours.

a. Amount and Concentration of Salt at any time:

Let's denote the amount of salt in the tank at time \(\(t\) as \(S(t)\)\) in kg and the concentration of salt in the tank at time \(\(t\) as \(C(t)\) in kg/L.\)

Initially, the tank contains 100 L of water with a salt concentration of 0.1 kg/L. Therefore, at \(\(t = 0\)\), we have:

\(\[S(0) = 100 \times 0.1 = 10 \text{ kg}\]\)

\(\[C(0) = 0.1 \text{ kg/L}\]\)

Considering the inflow, outflow, and evaporation rates, the amount of salt in the tank at any time \(\(t\)\) can be calculated as:

\(\[S(t) = S(0) + \text{Inflow} - \text{Outflow} - \text{Evaporation}\]\)

The inflow rate of saltwater is 55 L/h with a concentration of 0.2 kg/L. Thus, the amount of salt entering the tank per hour is:

\(\[\text{Inflow} = \text{Inflow rate} \times \text{Concentration} = 55 \times 0.2 = 11 \text{ kg/h}\]\)

The outflow rate is 44 L/h, so the amount of salt leaving the tank per hour is:

\(\[\text{Outflow} = \text{Outflow rate} \times C(t) = 44 \times C(t) \text{ kg/h}\]\)

The evaporation rate is 11 L/h, and as only water evaporates, it does not affect the salt concentration in the tank.

Therefore, the amount and concentration of salt at any time \(\(t\)\) can be expressed as follows:

\(\[S(t) = 10 + 11 - 44 \times C(t) \text{ kg}\]\)

\(\[C(t) = \frac{S(t)}{100}\text{ kg/L}\]\)

b. Limiting Concentration:

The limiting concentration refers to the concentration reached when the inflow and outflow rates balance each other, resulting in a stable concentration. In this case, the inflow rate of saltwater is 55 L/h with a concentration of 0.2 kg/L, and the outflow rate is 44 L/h. To find the limiting concentration, we equate the inflow and outflow rates:

\(\[\text{Inflow rate} \times \text{Concentration} = \text{Outflow rate} \times C_{\text{limiting}}\]\)

\(\[55 \times 0.2 = 44 \times C_{\text{limiting}}\]\)

\(\[C_{\text{limiting}} = \frac{55 \times 0.2}{44} = 0.25 \text{ kg/L}\]\)

Therefore, the limiting concentration of salt in the tank is 0.25 kg/L.

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Using the monthly payments formula, it is found that a car with a value of at most $25,293.

It is given by:

\(A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}\)

In which:

In this problem, we have that the parameters are given as follows:

A = 400, n = 70, r = 0.035.

Hence:

r/12 = 0.035/12 = 0.002917.

Then we have to solve for P to find the maximum value of the car.

\(A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}\)

\(400 = P\frac{0.002917(1.002917)^{70}}{(1.002917)^{70}-1}\)

\(P = \frac{400[(1.002917)^{70}-1]}{0.002917(1.002917)^{70}}\)

P = $25,293.

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The rules of the calculation are:

The complete question is added as an attachment

The equation is given as:

0.738 × 0.28 = 0.20664

When approximated, we have:

0.738 × 0.28 ≈ 0.21

The above approximation can mean any of the following:

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Answer:

D

Step-by-step explanation:

8n = 32

32/8n

n=4

Answer:

There ya go

Step-by-step explanation:

Hope this helped!

The area of each triangle should be rounded to the nearest hundredth.

The area of a triangle can be calculated using the formula A = (1/2)bh, where A represents the area, b represents the length of the base, and h represents the height of the triangle. To find the area, we need to know the values of the base and height.

For example, let's consider a triangle with a base of 5 units and a height of 8 units. Using the formula A = (1/2)bh, we can substitute the given values to calculate the area:

A = (1/2) * 5 * 8

A = (1/2) * 40

A = 20

Therefore, the area of the triangle is 20 square units.

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Answer:

305$

Step-by-step explanation:

305 because if it costs 61 dollars for 2 tickets and 61/2 30.5. 30.5*10=305

Answer:

\(y = \frac{5}{2} x^{2}\)

Step-by-step explanation:

When you scale a parabola vertically, you multiply the \(x^{2}\) by what you are scaling it vertically by.

For example, say you have  \(y = 8x^{2}\). That means that  \(y = x^{2}\) was scaled vertically by a factor of 8.

I hope this helps!

Answer:

-8

Step-by-step explanation:

-21-(-13)

=-21+13

=-8 is the answer......

Answer:

\(-8\)

Step-by-step explanation:

\(-21 - (-13)\)is the same as \(-21+13\), so the answer is \(-8\).

Answer:

y = -3x - 5

Step-by-step explanation:

The answer might be 433.5. I'm not quite for sure

Step-by-step explanation:

1734 divided by 4 = 433.5

Answer:

$3185

Step-by-step explanation:

Multiply the number of grade 6 students by the money needed ($3.50) and you get 318x3.50=1113

Multiply the number of grade 7 students by the money needed ($3.50) and you get  286x3.50=1001

Multiply the number of grade 8 students by the money needed ($3.50) and you get 306x3.50=1071

Add all the total amounts together and you get $3185

Equation f(x) = x² + 6x + 16 represents the quadratic function, and the table provides various instances of the quadratic function. Hence, the A, C, and E proposition are true.

What are some examples of quadratic functions?

f(x) = ax² + bx + c, in which a, b, and c are integers and an is not equal to zero, is a quadratic function. The diagram for a quadratic function has the form of an arc.

What method of solving quadratic equations is the simplest?

There are three main methods for resolving quadratic equations: factoring, the cubic formula, and completing the square. to solve a quadratic issue via factoring.

The y- intercept of f(x) is f(0) = 16, while the y-intercept of g(x) is g(0) = 8. Therefore, statement A is true.

The  x-coordinate of the vertex of f(x) is given by -b/2a = -6/(2 x 1) = -3 , which is less than the x-coordinate of the vertex of g(x), which is 1. Therefore, statement C is true.

The y-coordinate of the vertex of f(x) is given by f(-b/2a) = f(-3) = (-3)² + 6(-3) + 16 = 1, while the y-coordinate of the vertex of g(x) is 5. Therefore, statement E is true.

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Answer:

1.15 dollars

Step-by-step explanation:

To calculate the cost of 1 pound of apples, we can divide the total cost of 4 pounds of apples by 4.

The total cost of 4 pounds of apples is 4.60 dollars.

So, the cost of 1 pound of apples would be 4.60 / 4 = 1.15 dollars.

The cost in dollars of 1 pound apples is $1.15

Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers.

The process of dividing a number up into equal parts, and finding how many equal parts can be made. It is represented by the symbol "÷" or sometimes "/"

Division is breaking a number up into an equal number of parts.

Given that, a shopper buys 4 pounds of apples for 4.60, we need to find the cost in dollars of 1 pound of apples,

To calculate the cost of 1 pound of apples, we can divide the total cost of 4 pounds of apples by 4.

The total cost of 4 pounds of apples is 4.60 dollars.

So, the cost of 1 pound of apples would be 4.60 / 4 = 1.15 dollars.

Hence, the cost in dollars of 1 pound apples is $1.15

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Answer:

(-3/2, -13/2)

Step-by-step explanation:

To solve the system of equations graphically, we need to plot the two equations on the same set of axes and find the point of intersection.

To plot the first equation y = x - 5, we can start by finding the y-intercept, which is -5. Then, we can use the slope of 1 (since the coefficient of x is 1) to find other points on the line. For example, if we move one unit to the right (in the positive x direction), we will move one unit up (in the positive y direction) and get the point (1, -4). Similarly, if we move two units to the left (in the negative x direction), we will move two units down (in the negative y direction) and get the point (-2, -7). We can plot these points and connect them with a straight line to get the graph of the first equation.

To plot the second equation y = -x - 8, we can follow a similar process. The y-intercept is -8, and the slope is -1 (since the coefficient of x is -1). If we move one unit to the right, we will move one unit down and get the point (1, -9). If we move two units to the left, we will move two units up and get the point (-2, -6). We can plot these points and connect them with a straight line to get the graph of the second equation.

The point of intersection of these two lines is the solution to the system of equations. We can estimate the coordinates of this point by looking at the graph, or we can use algebraic methods to find the exact solution. One way to do this is to set the two equations equal to each other and solve for x:

x - 5 = -x - 8 2x = -3 x = -3/2

Then, we can plug this value of x into either equation to find the corresponding value of y:

y = (-3/2) - 5 y = -13/2

So the solution to the system of equations is (-3/2, -13/2).

Answer:

58 million = .16a

a = 362.5 million square miles

Answer: C

Step-by-step explanation:

Answer:

3[c(0.07)]+c=? [3(c)]1.07=?

Step-by-step explanation:

The expression that is used to represent the total cost of ink supplies is 3c + 3c(0.07) and 3c(1.07).

Given that,

Based on the above information, the calculation is as follows:

= 3c + 3c(0.07)

And

3c(1.07)

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Answer:

I think the answer is 5 hours and 15 minutes or 5.25 hours. Sorry if I'm wrong

Step-by-step explanation:

Answer:

5.25 Hours

Step-by-step explanation:

To find the time, you would divide 4200 kilometers by 800 kilometers per hour because the kilometers would cancel each other out giving only hours which is 5.25 hours

Answer:

1 hour or 60 minutes later

the fraction of four-digit positive integers containing only digits from the set {2,4,6,8} that have at least one of their digits repeated is 29/32.

First, let's determine the total number of four-digit positive integers using digits from the set {2,4,6,8}. Since there are 4 choices for each of the 4 digits, there are a total of 4^4 = 256 possible integers.

Next, we'll count the number of four-digit integers without any repeating digits. Since there are 4 choices for the first digit, 3 choices for the second digit, 2 choices for the third digit, and 1 choice for the last digit, there are a total of 4! (4 factorial) = 4 x 3 x 2 x 1 = 24 integers without any repeating digits.

Now, to find the number of integers with at least one repeating digit, we can subtract the number of integers without any repeating digits from the total number of integers: 256 - 24 = 232 integers.

Finally, to find the fraction of these integers with at least one repeating digit, we'll divide the number of integers with at least one repeating digit by the total number of integers: 232/256 = 29/32.

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Answer:

The perimeter is 72 inches

Step-by-step explanation:

using the pythagorean theorem we can solve for the missing leg by plugging in the values we know.

\(a^{2} + b^{2} = c^{2} \\18^{2} + b^{2} = 30^{2} \\324 + b^{2} = 900\\ b^{2} = 900-324\\b^{2} = \sqrt{576} \\b= 24\)

now you just add the values, 30 + 24 + 18

Answer:This is 69

Step by step explanation:67 +2 is 69

Answer:

The ramainder is equal -86

Step-by-step explanation:

Since the polynomial degree Q(x) is 1, the remainder of the division must be a number. Therefore we only need to calculate the value of polynomial for x = -2

Answer:

14.7460317

Step-by-step explanation:

you just divide 464.5 by 31.5