The explicit formula for the value of the truck after [tex]\(n\)[/tex] years is:
[tex]\[V(n) = -2,500n + 32,000\][/tex]
Where [tex]\(V(n)\)[/tex] represents the value of the truck after [tex]\(n\)[/tex] years.
To write an explicit formula for the value of the truck after n years with linear depreciation, we can use the formula for the equation of a straight line:
[tex]\[y = mx + b\][/tex]
Where:
- [tex]\(y\)[/tex] is the value of the truck after [tex]\(n\)[/tex] years.
- [tex]\(m\)[/tex] is the slope of the line, which represents the rate of depreciation per year.
- [tex]\(x\)[/tex] is the number of years.
-[tex]\(b\)[/tex] is the initial value of the truck.
Given:
- Initial value [tex](\(b\)): $32,000[/tex]
- Value after 3 years [tex](\(y\)): $24,500[/tex]
We can use these values to find the slope [tex](\(m\))[/tex]:
[tex]\[m = \frac{y_2 - y_1}{x_2 - x_1}\][/tex]
Substituting the given values:
[tex]\[m = \frac{24,500 - 32,000}{3 - 0}\]\[m = \frac{-7,500}{3}\]\[m = -2,500\][/tex]
Now, we have [tex]\(m = -2,500\)[/tex]. We can substitute this slope and the initial value into the equation:
[tex]\[y = -2,500x + 32,000\][/tex]
The explicit formula for the value of the truck after [tex]\(n\)[/tex] years is:
[tex]\[V(n) = -2,500n + 32,000\][/tex]
Where [tex]\(V(n)\)[/tex] represents the value of the truck after [tex]\(n\)[/tex] years.
Two accounts each begin with a deposit of $5000. Both accounts have rates of 5.7%, but one account compounds interest once a year while the other account compounds interest continuously. Show the amount in each account and the interest earned after one year, five years, ten years, and 20 years.
A certain component is critical to the operation of an electrical system and must be replaced immediately upon failure. If the mean lifetime of this type of component is 100 hours and its standard deviation is 30 hours, how many of the components must be in stock so that the probability that the system is in continual operation for the next 2000 hours is at least .95?
To calculate the stock required for continuous operation for 2000 hours with components having a mean lifetime of 100 hours and a standard deviation of 30 hours, use the Z-score for a 0.95 probability and solve for the number of components. This involves applying the normal distribution.
Explanation:Calculating Stock Quantity for Component ReplacementThe given problem requires calculating the number of electrical components that must be in stock to ensure continuous operation of an electrical system for 2000 hours. We are to assume that the components have a mean lifetime of 100 hours and a standard deviation of 30 hours. The aim is to keep the probability of the system running without interruption at 0.95 or higher.
Firstly, determine the number of lifetimes within the 2000-hour period:
2000 hours / 100 hours = 20 lifetimes.
Next, apply the concept of the normal distribution to find the z-score that corresponds to the 0.95 cumulative probability. Looking at z-tables or using statistical software, we find that the z-score for 0.95 is approximately 1.645.
Now, calculate the stock required using this z-score. The formula for the z-score in this context is:
Z = (X - mean) / (standard deviation / sqrt(n))
where X is the total hours (2000), mean is 100, standard deviation is 30, and n is the number of components.
Rearrange the formula to solve for n:
1.645 = (2000 - (100n)) / (30 / sqrt(n))
Solve for n to get the required number of components in stock.
This is a complex statistics problem that requires knowledge of z-scores and the normal distribution to solve. Given that this requires more complex calculations and potentially the use of calculators or software, a more detailed step-by-step calculation may go beyond the scope of this platform.
Final answer:
To ensure the probability of continuous operation for the next 2000 hours is at least 0.95, at least one component must be in stock.
Explanation:
To calculate the number of components that must be in stock to ensure the probability of continuous operation for the next 2000 hours is at least 0.95, we need to use the concept of the normal distribution. Given that the mean lifetime of the component is 100 hours and the standard deviation is 30 hours, we can calculate the Z-score for 2000 hours.
Z-score = (X - mean) / standard deviation = (2000 - 100) / 30 = 63.33
Using a Z-table or calculator, we can find that the probability of the component lasting for 2000 hours or more is approximately 1. With a probability of 1, we can say that the system is guaranteed to be in continual operation for the next 2000 hours. Therefore, at least one component must be in stock.
Sherry had an ending balance of $125.36, outstanding deposits of $153.53, and outstanding checks of $100.19. What was her checkbook balance?
Answer: $178.70
Step-by-step explanation: $125.36 + $153.53 = $278.89
$278.89 - $100.19 = $178.70
There were 3,905 more hits on the school’s website in January than February. February had 9,854 hits.
How many hits did the school’s website have during both months?
Factor out the GCF from each term in the expression
3. 30w5 + 25w3
4. 3x(7x + 1) – 2(7x + 1)
June Elloy makes a 22 percent down payment on a home in Rockford, Illinois. What is the purchase price of the home assuming her down payment is $35,200?
Answer:
Total purchase price of of the home is $160000
Step-by-step explanation:
We know that
Percent of down payment June Elloy makes = 22 %
Down payment is = $35200
Let x be the total purchase price.
Therefore,
22 % of x = 35200
( 22 / 100 ) times x = 35200
0.22 times x =35200
x = 35200 / 0.22
= 160000
Thus, total purchase price of of the home is $160000
what is 3400 as a decimal answer asap
A box contains
4
plain pencils and
4
pens. A second box contains
5
color pencils and
7
crayons. One item from each box is chosen at random. What is the probability that a pen from the first box and a crayon from the second box are selected?
Write your answer as a fraction in simplest form.
Population of the world was 5.7 billion in 1995 and the observed growth rate was 2% per year. By what year will the population triple?
21/24 reduced fraction
In a fraternity with 37 members,18 take math 5 take both math and chemistry and 8 take neither math nor chemistry. How many take chemistry but not math
Answer:
its 11 members
Step-by-step explanation:
You are building a chair. The plans call for 1/2 inch nails. Your nails are 3/4 inch long. Are your nails too long are too short
The plans call for 1/2 inch nails, but the nails you have are 3/4 inch. Therefore, your nails are too long.
Explanation:The chair plans call for 1/2 inch nails, but the nails you have are 3/4 inch long. When comparing these lengths, you can see that 3/4 is greater than 1/2. Therefore, your nails are too long for what the plans call for.
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how do you write 84,052 in word form
suppose f(x)=33.3+1.4 log (x+1) models salinity of ocean water to depths of 1000 meters at a certain latitude. x is the depth in meters and f(x) is in grams of salt per kilogram of seawater. Approximate the salinity to the nearest hundredth when the depth is 785 meters
The ratio of the sum of two numbers to the difference of the two numbers is 9. The product of the two numbers is 80. Find the numbers.
Find the future value and interest earned if $8904.56 is invested for 8 years at 6% compounded (a) semiannually and (b) continuously.
The Future value is $ 15162.80 and Interest is $6258.26
What is Future Value?The worth of a current asset at some point in the future based on an estimated rate of growth is known as future value (FV). For investors and financial planners, the future value is crucial because they use it to predict how much an investment made now will be worth in the future.
Investors can make wise investment choices based on their projected demands by knowing the future worth. However, external economic forces that depreciate an asset's value, such inflation, might have a negative impact on the asset's future worth.
Given:
P = $8904.56
R= 6%
T= 9
n= 2
Now, Future Value = P [tex](1 + r/n)^ {(nt)}\\[/tex]
FV= 8904.56 [tex](1 + 0.06/2)^ {(2)(9)}\\[/tex]
FV = 8904. 56 [tex]( 1+ 0.03)^{18[/tex]
FV= 8904.56[tex](1.03)^{18}[/tex]
FV = $15162.80
And Interest = FV - P
Interest = 15162. 80 - 8906.4
Interest = $6258.26
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how do you turn a fraction into a whole number
"lucy owns a bakery in 2006 she sold pies for $9.50 each in 2010 she sold pies for $17.50. Find the rate of change for the price of a pie from 2006 to 2010"
Applying it's concept, it is found that the rate of change for the price of a pie from 2006 to 2010 is of $2 a year.
What is the rate of change?It is given by the change in the output divided by the change in the input.
In this problem, in 4 years, from 2006 to 2010, the price increased $8, from $9.50 to $17.50. Hence, the rate of change is given by:
r = 8/4 = 2.
Thus, the rate of change for the price of a pie from 2006 to 2010 is of $2 a year.
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When 50% of a number is added to the number, the result is 225. What is the number?
The unknown number in the problem is 150. This was determined by creating an equation based on the information given, simplifying it, and solving for the unknown variable 'n'.
Explanation:This is a math problem that involves working with percentages and algebraic equations. Let the unknown number we're trying to find be 'n'. The problem says that 50% of the number, which is 0.5*n, is added to the number (n), resulting in 225. This situation can be represented with the equation: n + 0.5*n = 225.
Combining like terms on the left side of the equation, we get 1.5*n = 225. To isolate 'n', divide both sides of the equation by 1.5. So, n = 225 / 1.5, which gives us the number 150. Therefore, the unknown number is 150.
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What is -2 3/10 as a improper fraction?.
1. The purpose of this exercise is to provide practice using the LINGO or Excel solvers. Find the values of X and Y that minimize the function
Min X 2 - 4X + Y 2 + 8Y + 20
Do not assume nonnegativity of the X and Y variables. Recall that by default LINGO assumes nonnegative variables. In order to allow the variables to take on negative values you can add
@FREE(X); @FREE(Y);
Alternatively, if you want LINGO to allow for negative values by default, in the LINGO menu select Options and then click General Solver, and then uncheck the Variables assumed nonnegative tab.
A machine starts dumping sand at the rate of 20 m3/min, forming a pile in the shape of a cone. The height of the pile is always twice the length of the base diameter. After 5 minutes, how fast is the area of the base increasing?
Final answer:
The area of the base is increasing at a rate of 200π m²/min after 5 minutes.
Explanation:
To find how fast the area of the base is increasing, we first need to calculate the rate at which the height and radius of the cone are changing. Given that the height of the pile is always twice the length of the base diameter, we can write the equation h = 2r, where h is the height and r is the radius of the cone. Differentiating both sides with respect to time, we get dh/dt = 2dr/dt. Since the height is changing at a constant rate of 20 m³/min, dh/dt = 20 m³/min. Using this information, we can find the rate at which the radius is changing, dr/dt. Since the base diameter is equal to 2r, the base radius changes at a rate of dr/dt = 10 m/min. Now, we can find the rate of change of the area A of the base using the formula A = πr². Differentiating both sides with respect to time, we get dA/dt = 2πr(dr/dt). Plugging in the values, we have dA/dt = 2π(10)(10) = 200π m²/min. Therefore, the area of the base is increasing at a rate of 200π m²/min after 5 minutes.
Kohl's sells casual shirts for $9 and Poles shirts for $18. Total sales $1080, and customers bought 4 times as many casual as polo shirts. How many casual shirts did kohl sells?
Karen works for 85 hours throughout a two-week period. She earns $1,891.25 throughout this period. how much does she earn for 8 hours to work?
the speed of the stream is 4 mph. a boat travels 4 miles upstream in the same time it takes to travel 12 miles downstream. what is the speed of the boat in still water?
You can ride your bike around your block twice and the whole neighborhood once in 15 minutes. You can ride your bike around your block twice and the whole neighborhood 5 times in 55 minutes. How long does it take you to ride around the neighborhood?
To determine the time it takes to ride around the neighborhood, equations are set up from the given scenarios and solved algebraically, resulting in 10 minutes for one neighborhood lap.
To solve the problem, we need to set up equations based on the information provided. Let's let N represent the time it takes to ride around the neighborhood once and B represent the time it takes to ride around the block twice. The first scenario gives us:
B + N = 15 minutes
In the second scenario, the only difference is the number of neighborhood laps, so:
B + 5N = 55 minutes
Subtracting the first equation from the second gives us:
4N = 40 minutes
Dividing both sides by 4, we find:
N = 10 minutes
Therefore, it takes 10 minutes to ride around the neighborhood once.
The temperature decreased overnight by 15.2°C to a temperature of –12.8°C. Suppose t represents the temperature before it decreased.
Which equation can be used to represent this situation?
A.
t – 15.2 = –12.8
B.
t + 12.8 = –15.2
C.
t – 12.8 = 15.2
D.
t – (–15.2) = –12.8
Answer:
12.8
Step-by-step explanation:
if N/8+6=58, then N equals?
Suppose a carpet for an 8ft by 12 ft room cost $500. How much would an 16 ft by 24ft cost
To determine the cost of carpeting for a room that is twice the length and width of another, calculate the cost per square foot of the smaller room and then multiply that by the area of the larger room.
Explanation:The question is asking how much a carpet would cost for a room that is twice as long and twice as wide as an 8 ft by 12 ft room, given that the carpet for the smaller room costs $500.
To solve this, we first find the area of the smaller room, which is 8 ft multiplied by 12 ft, resulting in an area of 96 square feet.
The cost per square foot for the carpet is then $500 divided by 96 square feet, which equals approximately $5.21 per square foot.
Next, we calculate the area of the larger room.
Since both dimensions are doubled, the area will be 16 ft by 24 ft, which equals 384 square feet.
To find the cost for the larger room's carpet, we multiply the area of the larger room by the cost per square foot previously calculated.
Therefore, 384 square feet multiplied by $5.21 per square foot results in a cost of approximately $2,000 for the larger carpet.
A researcher is studying the effects of caffine on exam scores of college students. In this study what would be the population and sample of this research?