radius symbol in mathematics ​

By applying the Master Theorem to the original recurrence relation T(n) = 3 * T(n/2) + 18, we find that it simplifies to T(n) = 3 * T(n/2) + O(1), indicating that the explicit formula has the same asymptotic growth as the original recurrence relation(B).

Divide and conquer part:

The recursive call is T(n/2), indicating that the problem is divided into two subproblems of size n/2.

Work per level:

The work done outside the recursive calls is constant, which is represented by 18.

Combine:

The combining step is represented by the   T(n) = 3 * T(n/2) + 18.

According to the Master Theorem, if a recurrence relation can be expressed in the form T(n) = a * T(n/b) + f(n), where a ≥ 1, b > 1, and f(n) is an asymptotically positive function, we can determine the solution based on the relationship between a, b, and f(n).

In this case, we have a = 3, b = 2, and f(n) = 18. Comparing these values with the Master Theorem cases:

If f(n) = O(n^c) for some constant c < log_b(a), then T(n) = Theta(n^log_b(a)).

If f(n) = Theta(n^log_b(a) * log^k(n)), where k ≥ 0, then T(n) = Theta(n^log_b(a) * log^(k+1)(n)).

If f(n) = Omega(n^c) for some constant c > log_b(a), and if a * f(n/b) ≤ k * f(n) for some constant k < 1 and sufficiently large n, then T(n) = Theta(f(n)).

In our case, a = 3, b = 2, and f(n) = 18. We can see that f(n) = O(1), which matches the first case of the Master Theorem.

Therefore, the simplified recurrence relation is T(n) = 3 * T(n/2) + O(1), and the correct answer is b) T(n) = 3 * T(n/2) + O(1).

For more questions like Theorem click the link below:

https://brainly.com/question/30066983

#SPJ11

The resulting equivalent expression is -2k + 6

Equivalent expression.

Equivalent expression means an expressions that work the same even though they look different. If we said the two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value(s) for the variable(s).

Given,

Here we have the expression -2k - (-5) + 1

Now, we have to combine the like terms and then we have to solve it in order to find the equivalent expression.

First, we have to write the given expression,

=> -2k - (-5) + 1

Here we know that (-) x (-) = (+), therefore, the given expression is rewritten as follows:

=> -2k + 5 + 1

Here the only like term is the constant 5 and 1, so, we have to combine these constant, the  we get the expression like the following;

=> -2k + (5 + 1)

No, we have to add the constant in order to get the equivalent expression,

=> - 2k + 6

Therefore, the equivalent expression i s -2k + 6.

To know more about Equivalent expression here.

https://brainly.com/question/28170201

#SPJ1

Total number of college freshmen that signed up neither math nor English is 85

Total number of college freshmen interviewed = 200

Number of college freshmen registered for a Math class = 95

Number of college freshmen registered for a  English class = 80

Number of college freshmen registered for both math and English = 60

Total number of college freshmen signed up either for math or English =  Number of college freshmen registered for a Math class + Number of college freshmen registered for a  English class - Number of college freshmen registered for both math and English

Total number of college freshmen signed up either for math or English = (95 + 80 - 60) = 115

Total number of college freshmen signed up neither math nor English = ( Total number of college freshmen interviewed - Total number of college freshmen signed up either for math or English )

Total number of college freshmen signed up neither math nor English = 200 -115 = 85

Thus, 85 college freshmen signed up neither math nor English.

To know more about Mathematical Expressions refer to the link:

brainly.com/question/4344214

#SPJ4

Answer:

the measure of angle 8 is 83 degrees

Step-by-step explanation:

The set of points satisfying the equation (x-24)²y²z² - 64 = 0 is the intersection of three parabolas centered at (24, 0, 0), (0, 0, 0), and (0, 0, 0) in the x, y, and z directions, respectively. This intersection forms a three-dimensional surface in space.

The given equation, (x-24)²y²z² - 64 = 0, can be rewritten as:

(x-24)²y²z² = 64

Let's analyze the equation term by term to understand its geometric description:

(x-24)² represents a parabola in the x-axis centered at x = 24. It opens upward and has its vertex at (24, 0). The squared term ensures that the value is always positive.

y² represents a parabola in the y-axis centered at the origin (0, 0). It opens upward and has its vertex at (0, 0). The squared term ensures that the value is always positive.

z² represents a parabola in the z-axis centered at the origin (0, 0). It opens upward and has its vertex at (0, 0). The squared term ensures that the value is always positive.

Multiplying these parabolas together means that for a point (x, y, z) to satisfy the equation, all three parabolas need to have a value of 1, resulting in a product of 1.

To learn more about parabola : brainly.com/question/11911877

#SPJ11

Answer:

D = 42

A = 42

Step-by-step explanation:

If ABC = DEF

A = D

x + 21 = 2x

21 = 2x - x

21 = x

A = x + 21

(21) + 21 = 42

D = 2x

2(21) = 42

I'm 90% sure. I'm not fully sure though.

Step-by-step explanation:

we simply need to get the total distance and the total time and put them into relation, norming it to distance in 1 hour. after all, speed is always an average number over a period of time (even if it is a tiny period of time).

the total distance is

72 + 69 = 141 km

he drove 69 km going 60 km/h.

how much time did he need ?

we need to get the hours out of an expression of km and h.

so, we need to do

69 km × 1/60 km/h = 69 h / 60 = 69 minutes = 1.15 hours =

= 1 h 9 minutes

so, the total time was

48 + 69 = 117 minutes = 117/60 = 1.95 hours

the average speed for the whole trip was then

141 km / 1.95 h = 141/1.95 km / 1 h = 72.30769231... km/h

Answer:

3/10 liters more

Step-by-step explanation:

8/10 - 5/10 = 3/10

Answer:2

Step-by-step explanation:

Answer:

y=3x-1

Step-by-step explanation:

Answer:

C= K-273.15

Since you're adding 273.15 to celsius to get kelvin, you basically just to the reverse of that.

Using the binomial distribution, it is found that she should expect to roll the number cube 46 times.

It is the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.

The expected number of trials until q successes is:

\(E_s(X) = \frac{q}{p}\)

In this problem:

Then:

\(E_s(X) = \frac{23}{0.5} = 46\)

She should expect to roll the number cube 46 times.

More can be learned about the binomial distribution at https://brainly.com/question/24863377

Answer:

answer is 46.

Step-by-step explanation:

Therefore, the percent of the agency fee that Ms. Gonzalez received is:x = 42025/48750 × 100% = 86.15% (rounded to the nearest tenth of a percent).Answer: Ms. Gonzalez received 86.2% of the agency fee.

Given information: Ms. Gonzalez worked for a real estate agency, Remax. She sold a house for $975000. The agency fee for the sale was 5% of the sale price. Mrs. Hamilton received $6725 of the agency fee as her commission. The question is:

What percent of the agency fee did Ms. Gonzalez receive?

Here is the solution:

Let's calculate the agency fee on the sale price of $975000.Agency fee = 5% of sale price = (5/100) × 975000 = $48750.

Now, Ms. Hamilton received $6725 from the agency fee. So, the remaining amount of the agency fee went to Ms. Gonzalez. Let the amount received by Ms. Gonzalez be x.

So, Ms. Gonzalez received the remaining amount of the agency fee as her commission, i.e., $48750 - $6725 = $42025.

To know more about real estate:

https://brainly.com/question/29124410

#SPJ11

Answer: 26 cards

Step-by-step explanation:

Suppose there are x cards initially

Min gave half to bill i.e. 0.5x

Bill gives one-third of those cards to Sam i.e. \(\frac{1}{3}\times 0.5x\)

Sam gave 2 cards back to min and kept 6 i.e. Sam gets 8 cards from Bill

\(\Rightarrow 8=\dfrac{1}{3}\times 0.5x\\\\\Rightarrow 0.5x=24\\\Rightarrow x=48\)

So, min has 0.5x+2 cards i.e.

\(\Rightarrow 0.5\times 48+2\\\Rightarrow 26\ \text{cards}\)

Answer: 27 minutes

Step-by-step explanation:

Subtract 20 from 15.68 then divide by .16 by the number your given.

Answer:

5. The vertices of ΔX'Y'Z' are (-3, -7), (-6, -4), (-1, -2)

6. The vertices of ΔX'Y'Z' are (6, -7), (3, -4), (8, -2)

Step-by-step explanation:

If the point (x, y) translated by T → (h, k), then its image is (x + h, y + k)

#5

In ΔXYZ

∵ X = (1, -4), Y = (-2, -1), Z = (3, 1)

∵ T → (-4, -3)

∴ h = -4 and k = -3

→ Use the rule above to find the image of the vertices of the Δ

∵ X' = (1 + -4, -4 + -3)

∴ X' = (-3, -7)

∵ Y' = (-2 + -4, -1 + -3)

∴ Y' = (-6, -4)

∵ Z' = (3 + -4, 1 + -3)

∴ Z' = (-1, -2)

∴ The vertices of ΔX'Y'Z' are (-3, -7), (-6, -4), (-1, -2)

#6

In ΔXYZ

∵ X = (1, -4), Y = (-2, -1), Z = (3, 1)

∵ T → (5, -3)

∴ h = 5 and k = -3

→ Use the rule above to find the image of the vertices of the Δ

∵ X' = (1 + 5, -4 + -3)

∴ X' = (6, -7)

∵ Y' = (-2 + 5, -1 + -3)

∴ Y' = (3, -4)

∵ Z' = (3 + 5, 1 + -3)

∴ Z' = (8, -2)

∴ The vertices of ΔX'Y'Z' are (6, -7), (3, -4), (8, -2)

Answer:

2 hours and 32 minutes

Step-by-step explanation:

John Read a book at 11:32 and stopped at 2:14

What you have to do is add minutes up and hours up until you get to 2:14pm and all the hours and minutes it took to get there you add up and thats ur answer :)

Answer:

25,000,000

Step-by-step explanation:

5*5=25 and add the 6 zeros

please give thanks :)

Answer:

well for me

Step-by-step explanation:

I think

=25000000

The power series representation of 1/(1 + x⁴) is 1 - x⁴ + x⁸ - x¹² + ..., and the interval of convergence is -1 < x < 1.

To express 1/(1+x⁴) as the sum of a power series, we can use the geometric series formula:

1/(1 - r) = 1 + r + r² + r³ + ...

In this case, we have r = -x⁴.

Substituting into the formula, we get:

1/(1 + x⁴) = 1 + (-x⁴) + (-x⁴)² + (-x⁴)³ + ...

Simplifying:

1/(1 + x⁴) = 1 - x⁴ + x⁸ - x¹²+ ...

The power series representation of 1/(1 + x⁴) is the sum of the terms: 1, -x⁴ + x⁸ - x¹², ...

To find the interval of convergence, we need to determine for which values of x the series converges. For a power series, the interval of convergence is the range of x values for which the series converges.

The convergence of a power series can be determined using the ratio test:

lim (n→∞) |aₙ₊₁ / aₙ|

If the limit is less than 1, the series converges. If the limit is greater than 1 or infinite, the series diverges.

Applying the ratio test to our series:

lim (n→∞) |-x(4(n+1)) / (-x(4n))|

Simplifying:

lim (n→∞) |x⁴| = |x⁴|

For the series to converge, |x⁴| must be less than 1:

|x⁴| < 1

Taking the fourth root:

|x| < 1

Therefore, the interval of convergence for the power series representation of 1/(1 + x⁴) is -1 < x < 1.

Learn more about power series

brainly.com/question/29896893

#SPJ11

Answer:

Step-by-step explanation:

You'll need to find a way to share the graph or graphs associated with this problem.

The period is 4.  The relationship between period and b (the coefficient of the independent variable of the cosine function) is (period) =(2π.b).  Given that the period here is 4,

       2π                          2π

4 = ---------, and so b = ------- = π/2.

                                       4

So now our y  = a*cos (bx + c) becomes

                    π

y = 10*cos (------x + 0 + 10

                     2

The horizontal center line of this cosine curve is y = 10.  The maximum value of the curve is 20, which is 10 + 10, and the minimum value is 0, which is 10 - 10.

The function that describes the given situation is \(\rm y = 10\;cos\left(\dfrac{\pi}{2}x\right) + 10\) and this can be determined by using the properties of the trigonometric function.

Given :

The following steps can be used in order to determine the function could be the function described:

Step 1 - According to the given data, the cosine function has a period of 4.

Step 2 - Now, the independent variable of the cosine function is given by:

\(\rm 4b = 2\pi\)

\(\rm b =\dfrac{\pi}{2}\)

Step 3 - The maximum value of the cosine function is 1 and the minimum value of the cosine function is -1.

Step 4 - From the above steps, the function that described the given situation is given by:

\(\rm y = 10\;cos\left(\dfrac{\pi}{2}x\right) + 10\)

Therefore, the correct option is C).

For more information, refer to the link given below:

https://brainly.com/question/21286835

If a biologist measures the offspring of the surviving finches and finds that their mean beak depth is 13 mm, the heritability (h2) of beak depth, to two decimal places is -0.33.

The heritability of a trait refers to the proportion of the variation in that trait within a population that can be attributed to genetic factors. In this case, the heritability of beak depth can be estimated using the following formula:

h2 = (response to selection) / (selection differential)

where the response to selection is the difference between the mean value of the trait in the next generation and the mean value in the current generation.

The selection differential is the difference between the mean value of the trait in the current generation of individuals that survive and reproduce and the mean value in the entire population.

Using the given data, the response to selection is 13 - 12 = 1 mm, and the selection differential is 12 - 15 = -3 mm. Therefore, the heritability of beak depth can be calculated as:

h2 = (1/-3) = -0.33

The negative value obtained here suggests that there may have been some measurement error or other factors influencing the results. It is important to note that heritability estimates are subject to various assumptions and limitations and should be interpreted with caution.

To learn more about heritability click on,

https://brainly.com/question/29116728

#SPJ4

The statistical techniques of analysis of variance (ANOVA) and analysis of covariance (ANCOVA) are used to test the validity of the hypothesis regarding the comparison of group mean values.

The term "parametric approach" refers to a statistical technique used to compare the means of two normally distributed continuous variables.

In contrast to ANOVA, which is used to compare the means among three or more groups, the Student's t test (also known as the T test) is used to compare the means between two groups.An ANOVA test with a significant P value identifies at least one pair in which the mean difference was statistically significant.

The post-hoc test (multiple comparisons) is utilized to determine whether pair(s) are significant. When at least one covariate (continuous variable) in an ANOVA test is altered to eliminate confounding variables from the outcome, the procedure is known as an ANCOVA. Because inferences about means are made by analyzing variance, the ANOVA test (F test) is referred to as "Analysis of Variance" rather than "Analysis of Means."

To know more about ANOVA click here

https://brainly.com/question/29537928

#SPJ4

Step-by-step explanation:

\(x + 22 + 3x = 90\)

\(4x = 9 0- 22 \\ 4x = 68 \\ x = 17\)

M1

\(17 + 22 = 39\)

M2

\(3 \times 17 = \\ = 51\)

Answer:

Step-by-step explanation:

Answer:

After 5 years they will weigh 12 pounds

Step-by-step explanation:

A trapezoid has an area of 10 square units. The scale factor would be 3  to dilate the trapezoid to have an area of 90 square units.

The ratio between comparable measurements of an item and a representation of that thing is known as a scale factor.

Let the linear scale factor be k.

The area scale factor is \(k^2\)

We'll multiply the old area (10) by the area scale factor (\(k^2\) ) to get the area of 90 square units

\(10 \times k^2 = 90\\\\k^2 = \frac{90}{10} \\\\k^2 = 9\\\\k = \sqrt{9} \\\\k = 3\)approximately

Learn more about Scale Factor:

brainly.com/question/22644306

#SPJ1

When he wants to combine the two least full plates of glitter, the fraction of a plate that they would they take up is 1/4.

It should be noted that from the information, in the art class, Mr. Jacobs compared the amount of glitter left on students' plates and the dot plot shows this data

It should be noted that the least two plates of glitters will be:

= 1/4 + 2/4

= 3/4

Therefore, when e wants to combine the two least full plates of glitter, the fraction of a plate that they would they take up will be:

= 3/4 ÷ 3

= 3/4 × 1/3

= 1/3

Learn more about fractions on:

brainly.com/question/17220365

#SPJ1

The probability that James will take the same mode of transportation twice is 1/9.

To find the probability that James will take the same mode of transportation twice, we need to calculate the probability of each individual transportation option and then multiply them together.

In the morning, James has 3 transportation options: bus, cab, or train. Since he randomly chooses his ride, the probability of selecting any particular option is 1 out of 3 (assuming all options are equally likely).

Therefore, the probability of James selecting the same transportation mode in the morning and evening is 1/3.

Hence, the probability that James will take the same mode of transportation twice is 1/3 multiplied by 1/3:

P(same mode of transportation twice) = 1/3 * 1/3 = 1/9.

Therefore, the probability that James will take the same mode of transportation twice is 1/9.

To know more about probability:

https://brainly.com/question/31828911

#SPJ4

Answer:

14.86

Step-by-step explanation:

8.24 + 6.62 = 14.86

Answer:8.24 + 6.62= 14.86

Step-by-step explanation: