. The value V of a computer
depreciates exponentially and is
represented by V = 2,750(0.93)t
,
where t is the number of months
since the computer is purchased.
What is the purchase price of the
computer?

Scroll down for answer!

Step-by-step explanation:

123.51/2.3 = 53.7

Two options = 53.7 or 53.1

a) The recurrence T(n) = T(n/2) + 1 has an asymptotic complexity of O(log(n)).   b) The recurrence T(n) = 2T(n/2) + n has an asymptotic complexity of Ω(nlog(n)).



a) To analyze the recurrence T(n) = T(n/2) + 1, we make a guess that T(n) = O(log(n)). Assuming this guess is correct, we substitute T(n/2) with O(log(n/2)) = O(log(n)) in the recurrence relation. We get T(n) = O(log(n)) + 1. Since O(log(n)) + 1 is dominated by O(log(n)), our guess holds true, and we conclude that T(n) = O(log(n)).

b) For the recurrence T(n) = 2T(n/2) + n, we make a guess that T(n) = Ω(nlog(n)). Assuming this guess is correct, we substitute T(n/2) with Ω((n/2)log(n/2)) = Ω(nlog(n) - nlog(2)) in the recurrence relation. We get T(n) = Ω(nlog(n) - nlog(2)) + n. Simplifying, we have T(n) = Ω(nlog(n) + n - nlog(2)). Since nlog(n) dominates nlog(2), T(n) is Ω(nlog(n)), confirming our guess.

In both cases, the substitution validates our initial guesses for the asymptotic complexity of the recurrences.Therefore, The recurrence T(n) = T(n/2) + 1 has an asymptotic complexity of O(log(n)).   The recurrence T(n) = 2T(n/2) + n has an asymptotic complexity of Ω(nlog(n)).

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Answer:

15 students on each bus!

Step-by-step explanation:

100-10(with parents)

90÷6(how many busses)

15 students on each

The students travelling on each bus are 15.

The arithmetic operations are the fundamentals of all mathematical operations. The example of these operators are addition, subtraction, multiplication and division.

Total number of students is given as 100.

The students to travel on car are 10.

Then, the students to travel on bus are given by following operation as,

Total students - Students to travel on car

⇒ 100 - 10 = 90

Now, the students on each bus can be obtained by using the division operation as below,

Students to travel on bus ÷ Total number of bus

⇒ 90 ÷ 6 = 15

Hence, the number of students on each bus is obtained as 15.

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The relation S={(a,b)∈R×R:a²+b²=1} is not an equivalence relation on the set of real numbers R.

To show that S is not an equivalence relation, we need to demonstrate that it fails to satisfy one or more of the properties of an equivalence relation: reflexivity, symmetry, and transitivity.

Reflexivity: For a relation to be reflexive, every element of the set should be related to itself. However, in the case of S, there are no real numbers (a, b) that satisfy the equation a² + b² = 1 for both a and b being the same number. Therefore, S is not reflexive.

Symmetry: For a relation to be symmetric, if (a, b) is related to (c, d), then (c, d) must also be related to (a, b). However, in S, if (a, b) satisfies a² + b² = 1, it does not necessarily mean that (b, a) also satisfies the equation. Thus, S is not symmetric.

Transitivity: For a relation to be transitive, if (a, b) is related to (c, d), and (c, d) is related to (e, f), then (a, b) must also be related to (e, f). However, in S, it is not true that if (a, b) and (c, d) satisfy a² + b² = 1 and c² + d² = 1 respectively, then (a, b) and (e, f) satisfy a² + b² = 1. Hence, S is not transitive.

Since S fails to satisfy the properties of reflexivity, symmetry, and transitivity, it is not an equivalence relation on the set of real numbers R.

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2n^3 + 3n + 10 can be written as a polynomial of the form Q(n^3), where Q(n^3) represents the set of polynomials of the form a(n^3).

To prove that the expression 2n^3 + 3n + 10 is in the set Q(n^3), where Q(n^3) represents the set of polynomials of the form a(n^3), we need to show that the expression can be written in the form a(n^3) for some constant "a".

Let's start by factoring out the common factor of n^3 from each term:

2n^3 + 3n + 10 = n^3(2 + 3/n^2 + 10/n^3)

Now, let's rewrite the expression as a single term multiplied by n^3:

2n^3 + 3n + 10 = (2 + 3/n^2 + 10/n^3)n^3

Simplifying the expression inside the parentheses:

= (2n^3 + 3n^2 + 10n^3)/n^3

= (12n^3 + 3n^2)/n^3

= 12 + 3/n

ow, we can see that the expression can be written in the form a(n^3), where a = 12 and n^3 = 3/n.

Therefore, we have shown that 2n^3 + 3n + 10 can be written as a polynomial of the form Q(n^3), where Q(n^3) represents the set of polynomials of the form a(n^3).

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Answer:

False

Step-by-step explanation:

Factorise means to carry over the common number or letter to the outside of a set of brackets, whilst keeping the rest of the equation inside the brackets.

Answer:

Carry f to the outside, meaning that you would be left with f(4f +1).

Answer:

6.5

Step-by-step explanation:

In this question, we are tasked with calculating the mean temperature for the first 8 days.

since we we have the mean temperature for the first 7 days, the total temperature is thus 7 * 6 = 42

Now, on the 8th day, temperature is 10, this brings total temperature to 42 + 10 = 52

The mean temperature for the first 8 days ys therefore; 52/8 = 6.5

The equation \(x^{2} \sqrt{x} \leq \alpha \pi \sqrt[n]{x}\) is a mathematical inequality that relates the values of x, alpha, pi, and n.

The equation is an inequality because it uses the less than or equal to symbol (≤). This means that there is a range of possible values for x that will satisfy the inequality.

Breaking down the terms in the inequality:

- x² is x raised to the power of 2.
- √x is the square root of x.
- α is a variable that represents a constant value.
- π (pi) is a mathematical constant that represents the ratio of a circle's circumference to its diameter.
- √[n]x is the nth root of x.

So, the inequality is saying that the product of x² and the square root of x must be less than or equal to the product of alpha, pi, and the nth root of x. This is true for some values of x, alpha, pi, and n, but not necessarily for all possible values.

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We can be 80% confident that the true average medical deduction for the population is between $9,496.84 and $10,187.16.

We can construct confidence intervals for the population mean using the following formula:

Confidence interval = sample mean ± z*(standard error)

where z is the critical value from the standard normal distribution, which depends on the level of significance and the type of hypothesis test (one-tailed or two-tailed), and the standard error is calculated as:

standard error = population standard deviation / sqrt(sample size)

(a) For a 5% level of significance, we need to find the critical value z such that the area to the right of z is 0.025 in the standard normal distribution. Using a table or a calculator, we find that z = 1.96. The standard error is:

standard error = 2409 / sqrt(46) = 355.65

The confidence interval is therefore:

Confidence interval = 9842 ± 1.96*(355.65) = (9151.09, 10532.91)

We can be 95% confident that the true average medical deduction for the population is between $9,151.09 and $10,532.91.

(b) For a 10% level of significance, we need to find the critical value z such that the area to the right of z is 0.05 in the standard normal distribution. Using a table or a calculator, we find that z = 1.645. The standard error is the same as before:

standard error = 2409 / sqrt(46) = 355.65

The confidence interval is therefore:

Confidence interval = 9842 ± 1.645*(355.65) = (9327.14, 10356.86)

We can be 90% confident that the true average medical deduction for the population is between $9,327.14 and $10,356.86.

(c) For a 20% level of significance, we need to find the critical value z such that the area to the right of z is 0.1 in the standard normal distribution. Using a table or a calculator, we find that z = 1.282. The standard error is the same as before:

standard error = 2409 / sqrt(46) = 355.65

The confidence interval is therefore:

Confidence interval = 9842 ± 1.282*(355.65) = (9496.84, 10187.16)

We can be 80% confident that the true average medical deduction for the population is between $9,496.84 and $10,187.16.

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The critical value of the function \(\(y = 3x^2 - 12x - 15\)\)    is \(\(x = 2\)\). To find the critical values, we need to determine the values of \(\(x\)\) where the derivative of the function is equal to zero or undefined.

First, we find the derivative of the function with respect to x,

\(\(y' = 6x - 12\).\)

Next, we set the derivative equal to zero and solve for x:

\(\(6x - 12 = 0\)\\\(6x = 12\)\\\(x = 2\).\)

The critical value is \(\(x = 2\)\).

Therefore, the correct answer is option C: \(\(x = 2\)\).

To verify this, we can substitute the given values of x into the derivative equation:

For option A: \(\(y'(-1) = 6(-1) - 12 = -6 - 12 = -18\)\) (not equal to zero).

For option B: \(\(y'(1) = 6(1) - 12 = 6 - 12 = -6\)\) (not equal to zero).

For option D: \(\(y'(-2) = 6(-2) - 12 = -12 - 12 = -24\)\) (not equal to zero).

Options A, B, and D are incorrect because they do not represent the values where the derivative is equal to zero.

Therefore, the critical value of the function is \(\(x = 2\)\).

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There is nothing inherently wrong with any of the statements in question 21. Sampling rate and sound frequency both use hertz (Hz) as their unit of measurement.

The sample rate is a setting that can be adjusted during the digitization process, as is the sound frequency. It is also true that a higher sampling rate does not necessarily result in a higher pitch.

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Answer:

B) 48

Step-by-step explanation:

16 x 3 = 48

Answer:

20100???

Step-by-step explanation:

Im not sure if thats right but i hope it helps

Answer:

\( \frac{6}{8} \\ \\ \\ \frac{2}{8} \)

Answer:

382.5?????

Step-by-step explanation:

because 850×45% its that

Answer:

Step-by-step explanation:

I am not sure what your first inequality is saying y≤2x +7 or y≥2x+7

-the equation y> -3x-2 , has a negative slope m= -3 (the line is going down from left to right if is a negative slope) and it has to be a dotted line( <, or > is a dotted line, ≤, or ≥ is a solid line) so the answer must be either A or D

-if the second equation is y≤2x +7 then the answer is D because y has to be less than 2x+7 the area under the line will be include in the solution

--if the second equation is y≤2x +7 then the answer is A because y has to be greater than 2x+7 the area above the line will be include in the solution

Answer:

1 4/5

Step-by-step explanation:

2x+7>-3x-2

2x+3x>-2-7

5x/5>-9/5

=1 4/5

Thanks Hope It Help

To find f'(3) (f prime of 3), you must find f' first.  f' is the derivative of the function f(x).

Finding the derivative of f(x) = 2x⁴ requires the use of the power rule.

The power rule for derivatives is \(\frac{d}{dx} [x^{n} ] =nx^{n-1}\).  In other words, you bring the exponent forward and multiply it by the coefficient of the term, and then you subtract 1 from the original exponent.

f'(x) = \(\frac{d}{dx}\)(2x⁴)

f'(x) = 2(4)x³

f'(x) = 8x³

Now, to find f'(3), plug 3 into your derivative.

f'(3) = 8(3)³

f'(3) = 216

f'(3) = 216

Answer:

http://www.easternlocal.com/userfiles/251/Classes/6779/7th%20grade%205.1%20notes0001.pdf  this is the link for the answer

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let sharma age be S and Ankit age be A

S = 3a

(s-10) = 5(a-10)

substitute 1 in 2

3a-10 = 5a -50

40 = 2a

a = 20

s = 3 * 20 = 60

Hello!

To evaluate the expression \(\sf{\cfrac{y+xz}{2}}\), we should plug in the values of every variable:

\(\begin{aligned} \sf{\frac{8+6\cdot3}{2}}\\\sf{\frac{8+18}{2}} \\\sf{\frac{26}{2}} \\\bf{13}\end{aligned}\)

Therefore the answer is 13.

Hope that helps! :)

-art lover

Answer:

The second bag (4.75)

Step-by-step explanation:

Answer:

hi

Step-by-step explanation:

Answer:

42 degrees

Step-by-step explanation:

the other angles are 90 and 48

Answer: Reject \(H_0\) if the confidence interval does not contain the value of the hypothesized mean \(\mu_0\).

Step-by-step explanation:

In the case of Confidence Intervals and Two-Tailed Hypothesis Tests,

Null hypothesis : \(H_0:\mu=\mu_0\)  [There is no change in mean.]

Alternative hypothesis: \(H_a:\mu\neq\mu_0\)  [There is some difference.]

Since confidence intervals contain the true population parameter ( mean).

So, Decision rule states that

Answer:

The answer should be line B!^^

Have a great day/night, let me know it that was right or not!

Yes, the equation implicitly determines z as a function f(x,y) near (1,1), with f(1,1) = 1. The formula for ∂x f(x,y) is -1, and when evaluated at (1,1), ∂x f(x,y) = -1.

To determine if the equation implicitly determines z as a function f(x,y), we need to calculate ∂F/∂z and check if it is nonzero. Taking the partial derivative, we have ∂F/∂z = xln(yz) + xz(1/z) = xln(yz) + x. Evaluating this at (1,1,1), we get ∂F/∂z = 1ln(1*1) + 1 = 1. Since ∂F/∂z is nonzero, z can be determined as a function f(x,y) near (1,1).

To find a formula for ∂x f(x,y), we differentiate F(x,y,f(x,y)) = 1 with respect to x. Using the chain rule, we have ∂F/∂x + ∂F/∂z * ∂f/∂x = 0. Since ∂F/∂z = 1 (as calculated earlier), we can solve for ∂f/∂x: ∂f/∂x = -∂F/∂x. Differentiating F(x,y,z) = xy + xzln(yz) = 1 with respect to x gives ∂F/∂x = y + zln(yz). Evaluating this at (1,1,1), we obtain ∂F/∂x = 1 + 1ln(1*1) = 1. Therefore, ∂x f(x,y) = -∂F/∂x = -1.

In conclusion, the equation implicitly determines z as a function f(x,y) for (x,y) near (1,1), with f(1,1) = 1. The formula for ∂x f(x,y) is -1, and when evaluated at (1,1), it yields ∂x f(x,y) = -1.

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Answer:

2 faces, 0 edges, and 0 vertices

Step-by-step explanation:

D. three more than Sam's age doubled

Answer:

D) three more than his age doubled

Step-by-step explanation:

Answer:

7x - 8y

Step-by-step explanation:

Lol is this delta math