The rate at which the value of the computer system is changing 4 years after it was purchased is "Declining at the rate of $8,803.21 per year". The correct option is D.
We can use the exponential decay formula \(V(t) = V0 * e^{-kt}\), where V(t) is the value of the computer system after t years, V0 is the initial value, and k is the decay rate.
We know that V(1) = $15,700 and V(0) = $28,000, so we can solve for k:
\($15,700 = $28,000 * e^{-k*1}\)
\(e^{-k} = 0.5607\)
-k = ln(0.5607) ≈ -0.5797
k ≈ 0.5797
Therefore, the decay rate is approximately 0.5797 per year.
To find the rate of change of the value of the computer system 4 years after it was purchased, we can take the derivative of V(t) with respect to t:
dV/dt = -k * V0 * \(e^{-kt}\)
Substituting t = 4, V0 = $28,000, and k ≈ 0.5797, we get:
dV/dt = -0.5797 * $28,000 * \(e^{-0.5797*4}\) ≈ -$8,803.21 per year
Therefore, the value of the computer system is declining at the rate of approximately $8,803.21 per year 4 years after it was purchased.
The correct answer is (D) Declining at the rate of $8,803.21 per year.
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what is the vertex of this graph?
Is the vertex a minimum or a maximum?
Answer:
Maximum
Step-by-step explanation:
Answer:
(-2, -3)
Maximum
Step-by-step explanation:
The vertex of a parabola is the highest or lowest point,
(-2, -3)
Maximum
let f{o) = 0, /(1) = 1, /(2) = 22 , /(3) = 333 = 327, etc. in general, f(n) is written as a stack n high, of n's as exponents. show that f is primitive recursive.
So, g(n) is primitive recursive, as required.
In order to show that f is primitive recursive, we must first show that the function which outputs a stack n high of n's as exponents is primitive recursive.
Let's call this function g(n). Here's the definition:g(0) = 1g(n+1) = n ^ g(n)This can be translated into a recursive function using the successor and exponentiation functions:
g(0) = 1 g(n+1) = (n)^(g(n))
To show that g(n) is primitive recursive, we need to show that it can be constructed from the basic primitive recursive functions using composition, primitive recursion, and projection.
First, we'll need to define the basic primitive recursive functions.
Here's the list:
Successor: S(x) = x+1
Projection: pi_k^n(x1, ..., xn) = xk
Zero: Z(x) = 0
Here are the composition and primitive recursion rules:
Composition: If f: k_1 x ... x k_n -> m and g_1: m -> p_1 and ... and g_n:
m -> p_n are primitive recursive functions, then h:
k_1 x ... x k_n -> p_1 x ... x p_n defined by
h(x1, ..., xn) = (g_1(f(x1, ..., xn)), ..., g_n(f(x1, ..., xn)))
is a primitive recursive function.Primitive recursion:
If f: k_1 x ... x k_n x m -> m and
g: k_1 x ... x k_n -> m and
h: k_1 x ... x k_n x m x p -> p
are primitive recursive functions such that for all x1, ..., xn, we have f(x1, ..., xn, 0) = g(x1, ..., xn) and f(x1, ..., xn, m+1)
= h(x1, ..., xn, m, f(x1, ..., xn, m)), then k:
k_1 x ... x k_n x m -> m defined by k(x1, ..., xn, m) = f(x1, ..., xn, m) is a primitive recursive function.
Now we can show that g(n) is primitive recursive using these tools.
We'll use primitive recursion with base case Z(x) = 1 and recursive case f(n, g(n)). We define f as follows:
f(n, 0) = 1f(n, m+1)
=\(n ^ m\) (using the exponentiation function)
Then we define g(n) = f(n, n).
It's clear that g(n) is the same function we defined earlier, and that f(n, m) is primitive recursive.
Therefore, g(n) is primitive recursive, as required.
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g(n) is the same function we defined earlier, and that f(n, m) is primitive recursive. Therefore, g(n) is primitive recursive, as required.
In order to show that f is primitive recursive, we must first show that the function which outputs a stack n high of n's as exponents is primitive recursive.
Let's call this function g(n). Here's the definition: \(g(0) = 1g(n+1) = n ^ g(n)\).
This can be translated into a recursive function using the successor and exponentiation functions: \(g(0) = 1g(n+1) = n ^ g(n)\\\).
To show that g(n) is primitive recursive, we need to show that it can be constructed from the basic primitive recursive functions using composition, primitive recursion, and projection.
First, we'll need to define the basic primitive recursive functions. Here's the list:
Successor: S(x) = x+1
Projection: \(pi_k^n(x1, ..., xn) = xk\)
Zero: Z(x) = 0,
Here are the composition and primitive recursion rules:
Composition: If f: k_1 x ... x k_n -> m and g_1: m -> p_1 and ... and g_n: m -> p_n are primitive recursive functions,
then h: k_1 x ... x k_n -> p_1 x ... x p_n defined by
h(x1, ..., xn) = \((g_1(f(x1, ..., xn)), ..., g_n(f(x1, ..., xn)))\)is a primitive recursive function.
Primitive recursion: If f: k_1 x ... x k_n x m -> m and
g: k_1 x ... x k_n -> m and
h: k_1 x ... x k_n x m x p -> p are primitive recursive functions such that for all x1, ..., xn,
we have \(f(x1, ..., xn, 0) = g(x1, ..., xn)\)and \(f(x1, ..., xn, m+1) = h(x1, ..., xn, m, f(x1, ..., xn, m))\), then
k: k_1 x ... x k_n x m -> m defined by
k(x1, ..., xn, m) = f(x1, ..., xn, m) is a primitive recursive function.
Now we can show that g(n) is primitive recursive using these tools. We'll use primitive recursion with base case Z(x) = 1 and recursive case f(n, g(n)). We define f as follows: \(f(n, 0) = 1f(n, m+1) = n ^ m\) (using the exponentiation function).
Then we define g(n) = f(n, n).
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100 points!! The question and graph is provided with the attached image.
A. {a=2, b=3}
B. {a=3, b=2}
C. {a=−3, b=2}
D. {a=2, b=−3}
Answer:
b its b im pretty sure if not d okk!!
16-2k=14. what is the value of k
Answer:
k = 1
Step-by-step explanation:
16 - 2k = 14
- 16 - 16
-2k = -2
-2 -2
k = 1
35/48*100 fraction into percentage.
Answer:
729167
Step-by-step explanation:
Now we can see that our fraction is 72.916666666667/100, which means that 35/48 as a percentage is 72.9167%.
television retails for $4,500. What is the purchase price in dollars of the television if it has been marked up 25% of the retail price
The purchase price in dollars of the television that has been marked up 25% of the retail price of $4,500 would be $5,625.
To find the purchase price of the television in dollars, follow these steps:
1. Determine the markup amount: 25% of the retail price ($4,500).
2. Subtract the markup amount from the retail price to find the purchase price.
Step 1: Calculate the markup amount:
25% of $4,500 = 0.25 × 4,500 = $1,125
Step 2: Subtract the markup amount from the retail price:
$4,500 (retail price) - $1,125 (markup) = $3,375
The purchase price of the television in dollars is $3,375.
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Mira picked two numbers from a bowl. The difference of the two numbers was 4, and the sum of one-half of each number was 18. The system that represents Mira’s numbers is below.
Last month, a basketball team scored 83, 84, 85, 87, 89, 88, 67, 79, and 81 points in their games. Which data value(s) are outliers? Select all that apply.
The data value that is an outlier is 67
How to determine the outlier?The dataset is given as:
83, 84, 85, 87, 89, 88, 67, 79, and 81
To determine the outlier, we select the data values that are relatively far from others
In the above dataset, the data element 67 is far from other data values
Hence, the data value that is an outlier is 67
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What is the first 5 terms for 40-3n
=================================================
Explanation:
The variable n represents the term number.
Plug n = 1 into the expression to get 40-3n = 40-3*1 = 37.
Therefore, 37 is the first term.
The second term is 34 because 40-3n = 40-3*2 = 34.
This process is repeated for values n = 3, n = 4, and n = 5. You should get 31, 28, and 25 for the third, fourth, and fifth terms in that order.
--------
An alternative is to subtract 3 from each term to get the next term.
37-3 = 3434-3 = 3131-3 = 2828-3 = 25This alternative method will only be useful once you find the first term is 37.
Which polynomial is in standard form?
If the simple interest on a sum of a money invested at 3. 5% per annum for 44 years is birr 420, find the principal
As per the given simple interest, the principal amount is $165.35.
The term simple interest in math is defined as the interest charge on borrowing that's calculated using an original principal amount only and an interest rate that never changes.
Here we have given that If the simple interest on a sum of a money invested at 3. 5% per annum for 44 years is birr 420.
Therefore, through the given question we have identified the value of
interest rate = 3.5%
time period = 44
sum amount = 420.
Then the principal amount is calculated by using the formula of simple interest as,
P = A / (1 + rt)
Here first we have to convert R percent to r a decimal, then we get
r = R/100 = 3.5%/100 = 0.035 per year.
Now, we have to apply the values on the equation and then we have to solve our equation, then we get
P = 420 / ( 1 + (0.035 × 44)) = 165.35433070866
P = $165.35
Therefore, the principal investment required to get a total amount, principal plus interest, of $420.00 from simple interest at a rate of 3.5% per year for 44 years is $165.35.
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7. -4y = 48 what is the answer for y? To get 48
Answer:
Y= -12
Step-by-step explanation:
to get the answer to Y you just have to divided the number beside the variable to get just one itself.
so divide both sides by -4 to get
y=-12
Answer:
-12 lol I just got out of school and we did this exact type of math
Step-by-step explanation:
Let's say you have this data: 25, 26, 24, 26, 25, 7, 8, 8, 15, 10, 25, 24, 26 What should your bin size be if you want to have 10 bins
are the fractions 2/2 and 8/8 equivalent fractions?
Answer:
Yes
Step-by-step explanation:
2/2 can be simplified to 1. 8/8 can be simplified to 1. 1=1 so the fractions are equivalent.
Answer:
Yes
Step-by-step explanation:
2 is the same as 2 so it equals 1 same thing with 8/8because 8=8 and one and one are the same thing
This is long and complex, may you please get some help?
Answer:
Step-by-step explanation:
a = -4 , b = 16 and c = -17
\(x =\dfrac{-b}{2a}\\\\x = \dfrac{-16}{2*(-4)}\\\\\\ =\dfrac{-16}{-8}\\\\\\\\\)
x = 2
y = -4(2)² + 16*2 - 17
= -4*4 + 32 - 17
= -16 + 32 - 17
y = -1
Vertex (2, -1)
axis of symmetry: x = 2
The average third grade student can read
80 words in 5 minutes. What is the average
reading rate per minute?
write an expression to represent the problem.
Answer:
16x
Step-by-step explanation:
80 divided by 5 is 16, so the student can read 16 words per minute. X is the number of minutes.
The average reading rate per minute is 16 words/ min.
and its expression will be \(16x\)
where, \(x\) represents the minutes
What is proportion ?
A proportion is an equation based on the equality of two ratios.
It is given that the average third grade student can read 80 words in 5 minutes and it is to calculate the average words read by the student per minute :
\(\begin{aligned}5 \text{\:min}&\rightarrow 80 \text{\:words}\\1 \text{\:min}&\rightarrow \frac{80}{5}\text{\:words} \\&\rightarrow 16 \text{\:words}\end{aligned}\)
Therefore, the average reading rate per minute is 16 words/ min.
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Write a statement and reason proof. Number each statement and each reason. Give the line numbers of the lines used to determine which lines were used to arrive at each conclusion. Let A= apples are red C= cherries are black M= melons are yellow P= peaches are ripe. S= strawberries are sweet The following premises are given to be true. Either strawberries are sweet or melons are not yellow. If peaches are ripe and strawberries are sweet then apples are not red. Apples are red. Peaches are ripe. PROVE: Melons are not yellow.
Melons are not yellow due to the given premises and logical deductions.This is the statement and the proof.
Either strawberries are sweet or melons are not yellow. (Premise)
If peaches are ripe and strawberries are sweet, then apples are not red. (Premise)
Apples are red. (Premise)
Peaches are ripe. (Premise)
Assume that melons are yellow (for contradiction).
Since melons are yellow and apples are red, the statement "If peaches are ripe and strawberries are sweet, then apples are not red" is false, contradicting premise 2.
Therefore, our assumption that melons are yellow is false, and hence, melons are not yellow. (Contradiction)
Thus, we have proven that melons are not yellow.
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Answer these correct and ill give 500 pts!!
1. Agricultural policy made it cheaper for Americans to buy food that can be bad for our health.
False
True
2. Which option identifies the concept represented in the following scenario?
A rural cherry-growing co-op in northern Michigan contracts with a company in Wisconsin to process dried cherries.
vertical integration
monocropping
sustainability
horizontal consolidation
3. Which option identifies the agency most likely to be involved in monitoring in the following scenario?
Forest fires have caused contamination of a river in southern Colorado. Fish from the river are found to contain high levels of mercury.
Food and Drug Administration
Environmental Protection Agency
Department of Agriculture
Forest Service
Answer:
ture
Step-by-step explanation:
Answer:
1.True
2.Monocropping
3.Food and Drug administration
Step-by-step explanation:
explain, giving two reasons,when a person is entitled to claim for UIF benefits
Two reasons when a person is entitled too access the Unemployed Insurance Fund are:
When a worker becomes unemployed within 6 months of losing their job.Dependents of a deceased contributor.What is the Unemployed Insurance Fund (UIF)?The unemployed insurance fund (UIF) is described as a short-term relief given to workers who are unable to work or when they become unemployed due to several reasons. In addition, the fund (UIF), can also be accessed by dependents of a deceased contributor.
Therefore, two reasons when a person is entitled too access the Unemployed Insurance Fund are:
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NEED ASAP . 19 MINUTES LEFT GIVNG BRAINLIEST PLZZZZ
Answer:
9
Step-by-step explanation:
so sorry if im too late...
Type the correct answer in the box. Round off your answer to the nearest integer.
ZA and ZC are right angles. mZp=
D
6
A
degrees.
P
5
C
B
Answer:
59°
Step-by-step explanation:
in ∆abd according to Pythagorean theorem:
(bd)²=√(ad)²+(ab)²
= √25+36
= 61
abcd. cosld= cd/bd
=4/√61
= 61. _~0.512
so lp = arc cos 0.512
_~59°
What is the simplest form of 8(5k+7)−10(6k−7)
The simplest form of the given expression is -20k + 126.
To find the simplest form of the expression 8(5k+7)−10(6k−7), follow these steps:
1. Distribute the numbers outside the parentheses to the terms inside the parentheses:
8 × 5k + 8 × 7 - 10 × 6k + 10 × 7
2. Perform the multiplication:
40k + 56 - 60k + 70
3. Combine like terms (terms with the same variable and exponent):
(40k - 60k) + (56 + 70)
4. Simplify the expression by performing the subtraction and addition:
-20k + 126
The simplest form of the given expression is -20k + 126.
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reflect the point worksheet
Answer:
I don't know the answer I thinkA cone-shaped container has a height of 240 in. And a radius of 150 in. The cone is filled with a liquid chemical. The chemical evaporates at a rate of 12,000 in³ per week. How many weeks will it take for all of the chemical to evaporate? use 3. 14 to approximate pi. Enter your answer in the box.
Therefore, it will take approximately 1415.7 weeks for all of the chemical to evaporate.
To calculate the volume of a cone, we can use the formula:
\(Volume = (1/3) * π * r^2 * h\)
Given that the height (h) of the cone is 240 inches and the radius (r) is 150 inches, we can substitute these values into the formula:
\(Volume = (1/3) * 3.14 * 150^2 * 240\)
Simplifying the equation:
Volume = 3.14 * 22500 * 240
Volume ≈ 16988400 cubic inches
Now, we know that the liquid chemical evaporates at a rate of 12,000 cubic inches per week. To find out how many weeks it will take for all the chemical to evaporate, we can divide the total volume of the chemical by the evaporation rate:
Number of weeks = Volume / Evaporation rate
Number of weeks = 16988400 / 12000
Number of weeks ≈ 1415.7 weeks
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simplify the expression x · ¡ [x > 0] − [x < 0] ¢ .
Putting it all together, we have:
- If x is greater than 0, then [x > 0] is 1 and [x < 0] is 0, so the expression becomes x · ¡0¢, which simplifies to x · 1, or simply x.
- If x is less than 0, then [x > 0] is 0 and [x < 0] is 1, so the expression becomes x · ¡1¢, which simplifies to x · (-1), or -x.
- If x is equal to 0, then both [x > 0] and [x < 0] are 0, so the expression becomes x · ¡0¢, which simplifies to 0.
Therefore, the simplified expression is:
x · ¡ [x > 0] − [x < 0] ¢ = { x, if x > 0; -x, if x < 0; 0, if x = 0 }
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What type of graph is this
Answer:
Its a graph to find out the median. Or can be called a box plot
Step-by-step explanation:
Mr. Martinez is buying food for a party. Hamburger patties are sold in packages of 6 and hamburger buns are sold in packages of 8. If he wants to have an equal number of each, what is the LEAST number of hamburger patties and buns that Mr. Martinez will have to buy?
Enter the correct answer in the box.
Answer:
24 is the least number of hamburger patties and buns Mr. Martinez will have to buy.
Step-by-step explanation:
You need to find the LCM of 6 and 8. The number they have first have common is 24
simplify the following
\( \frac{5 {ab } ^{2} + 10 {a}^{4} {b}^{3} - 15 {ab}^{3} }{5ab} \)
Scale Factor: 1/2; Center: point N
The new coordinates of points M and O is determined as;
M = (0.5, - 1)
O = (2.5, -2).
What is the new coordinate of points of M and O?The new coordinate of points M and O after applying the scale factor is calculated as follows;
The given scale factor = 1/2
The current coordinates of point M and O is;
M = (1, - 2)
O = (5, - 4)
A scale factor can be used to either enlarge a figure or decrease a figure.
When the scale factor is less than 1, it means the new figure will be smaller than the original figure.
However, if the scale factor is greater than 1, the new figure will be greater than the original figure.
The new coordinates of points M and O is determined as follows;
M = (1 x 1/2, -2 x 1/2) = (0.5, - 1)
O = (5 x 1/2, -4 x 1/2) = (2.5, -2)
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Identify the initial amount a and the rate of decay r (as a percent) of the exponential function f(t)=475(0.5)t. Evaluate the function when t=3. Round your answer to the nearest tenth.
The function when t=3 to the nearest tenth is 59.4.
How did we get the value?The initial amount is a = 475, and the rate of decay r is 50%.
To evaluate the function when t=3, we plug in t=3:
f(3) = 475(0.5)^3 = 475 * (0.125) = 59.375
Rounding to the nearest tenth, f(3) = 59.4.
Therefore, the correct answer is as given above. It could be concluded that the rounded answer to the nearest tenth is 59.4
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