Evaluating the function for the given value of x

If the 1/12 scale model of the rocket stood 48 inches high. The height of the actual rocket is 576 inches.

A ratio box can be defined as a tool that can be used to set up and solve proportion problems.

In order to use a ratio box to solve this problem, we can set up the following proportion:

Scale model height / Actual rocket height = 1/12

48 inches / actual rocket height = 1/12

To solve for the actual rocket height, we can cross-multiply and divide:

48 inches××12 = actual rocket height

Actual rocket height = 576 inches

Therefore the height of the actual rocket is 576 inches.

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By providing the c and k values in the formal definition when asserting a big O, Ω or θ relationship, we have

(i) [tex]3^{n/2}[/tex] = O(2^n)

(ii) [tex]8^{\log n}[/tex] = θ([tex]n^2(\log n)^4[/tex] ≤ 3n^3)

(iii) √n + (log n)^5 = O([tex](2)^{1/2\times\log n}[/tex])

We have to compare the following function pairs by providing the c and k values in the formal definition when asserting a big O, Ω or θ relationship

i) The first function is [tex]3^{n/2}[/tex] vs. 2^n

We can write  [tex]3^{n/2}[/tex] as

[tex]3^{n/2}[/tex] = [tex](\sqrt{3})^n[/tex]

[tex]3^{n/2}[/tex] = (1.732)^n

Clearly, we get for c = 1 and n ≥ 0, then

0 ≤ 1.732n ≤ 2n

Hence, [tex]3^{n/2}[/tex] = O(2^n)

ii) The second function is [tex]8^{\log n}[/tex] vs. n^2(log n)^4 + 2n^3

We can write it as

[tex]8^{\log n}[/tex] = [tex]n^{\log 8}[/tex]

[tex]8^{\log n}[/tex] = [tex]n^{\log 2^3}[/tex]

[tex]8^{\log n}[/tex] = n^3

For n ≥ 0, c(1) = 1 and c(2) = 3, we have

0 ≤ n^3 ≤ [tex]n^2(\log n)^4[/tex] ≤ 3n^3

Hence, [tex]8^{\log n}[/tex] = θ([tex]n^2(\log n)^4[/tex] ≤ 3n^3)

iii) The third function is  [tex](\sqrt{2})^{\log n}[/tex] vs. √n + (log n)^5

We can write [tex](\sqrt{2})^{\log n}[/tex] as

[tex](\sqrt{2})^{\log n}[/tex] =  [tex](2)^{1/2\times\log n}[/tex]

For c = 2 and n ≥ 2, we have

0 ≤ √n + (log n)^5 ≤ [tex](2)^{1/2\times\log n}[/tex]

Hence, √n + (log n)^5 = O([tex](2)^{1/2\times\log n}[/tex])

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The complete question is:

Show your complete work when comparing the following function pairs. provide the c and k values in the formal definition when asserting a big O, Ω or θ relationship(e.g. f(n) is O(g(n)) if there exists C>0 and k≥0 such that f(n)≤Cg(n) for all n≥k).

(i) [tex]3^{n/2}[/tex] vs. 2^n

(ii) [tex]8^{\log n}[/tex] vs. n^2(log n)^4 + 2n^3

(iii) [tex](\sqrt{2})^{\log n}[/tex] vs. √n + (log n)^5

The equivalent expression to 7/8+3/8x-3/4y-1/2 is given as follows:

3x/8 - 3y/4 + 3/8.

Equivalent expressions are expressions that have the same result when they are simplified.

The expression for this problem is defined as follows:

7/8+3/8x-3/4y-1/2.

The expression is simplified combining the like terms.

The like terms are given as follows:

Combining(adding) the like terms, the simplified expression is given as follows:

3x/8 - 3y/4 + 3/8.

As none of the options are this one, I suppose that there was a typing mistake either in the expression or in the options.

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Answer:

The number of those line segments which have endpoints of different colors is 47.

(a) Total 288 different arrangements of the committee are possible if the rowers and basketballers both sit together in groups, but no rower sits next to a basketballer.

(b) If the conditions in a apply, 1/24 is the probability that these two members of the committee will sit next to one another.

(a) Considering the four rowers as a single person, the three basketball players as a single person, and the cricketers as two unique people (So, a total of 4 persons).

Number of configurations for a round table of n people = (n-1)!

Number of configurations for a round table of n people = (4-1)!

Number of configurations for a round table of n people = 6 ways

Let's leave out the number of arrangements that the basketball players and rowers will have.

Assuming that a basketball player and a rower are one person, they will sit together = (3-1)! × 2!

Assuming that a basketball player and a rower are one person, they will sit together = 4

There are therefore numerous arrangements for the groups where basketball players and rowers sit together = 2

No. of ways to arrange basketball players in a group = 3!

No. of ways to arrange basketball players in a group = 6

There are numerous number of methods to arrange rowers within a group = 4!

There are numerous number of methods to arrange rowers within a group = 24

Hence, total number of ways = 2×6×24

Total number of ways = 288

No. of ways are 288

b) The definition of an event's probability is as follows:

Probability = No. of Successful Outcomes / Total no. of Outcomes

Number of ways a cricketer can take a seat = 2! = 2 ways

Number of arrangements for the remaining rowers when he is seated next to the cricket player = 3!

Number of arrangements for the remaining rowers when he is seated next to the cricket player = 6 ways

Total number of possible ways = 6×2

Total number of possible ways = 12 ways

Probability = 12/288

Probability = 1/24

Hence, the required probability is 1/24.

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The number of round beads in the glitz jewelry kit are 25

An equation is the equality between two algebraic expressions, which have at least one unknown or variable.

Let x be the number of round beads in the glitz jewelry kit. Then the equation is written as,

6x + 100 = 250

Simplify the equation, then the value of 'x' is given as,

6x + 100 = 250

6x  = 250 - 100

6x = 150

x = 150/6

x = 25

The number of round beads there in each color will be 25.

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Answer:

A

Step-by-step explanation:

x² - 12x + 35

consider the factors of the constant term (+ 35) which sum to give the coefficient of the x- term (- 12)

the factors are - 5 and - 7 , since

- 5 × - 7 = + 35 and - 5 - 7 = - 12 , then

x² - 12x + 35 = (x - 5)(x - 7) ← in factored form

Answer:

  C, D

Step-by-step explanation:

You want to know possible rational roots of x⁴-6x³-19x² +84x+180.

The rational root theorem tells you any rational roots will be fractions of the form ...

  ±(divisor of the constant)/(divisor of the leading coefficient)

Here, the coefficient of x⁴, the leading coefficient, is 1. So any rational roots will be divisors of ±180. Those divisors are (plus or minus) ...

  1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180

The highlighted values are ones that are answer choices.

__

Additional comment

An estimate of the upper bound of the magnitude of the roots would be ...

  [tex]2\max(\sqrt[4]{180},\sqrt[3]{84},\sqrt{19},6)=12[/tex]

The rational root theorem allows roots larger than this.

The roots of this polynomial are actually {-3, -2, 5, 6}.

The variance of the difference of two independent random variables is equal to the sum of the variances, not the difference.

False. So, var(x - z) = var(x) + var(z).

False. If x ~ n(0,0°), then z = 2x ~ n(0,2°), not n(0,4°). This is because the variance of the difference of two variables is the sum of the variance of the individual variables plus twice the covariance between the two variables. Since x and z are independent, the covariance between them is 0, and so the variance of x - z is equal to the sum of the variances of x and z.

If x ~ n(0,0°), then z = 2x ~ n(0,2°). This is because the mean of a random variable multiplied by a constant is equal to the original mean multiplied by the same constant, and the variance of a random variable multiplied by a constant is equal to the square of the constant multiplied by the original variance. So, if x has mean 0 and variance 0°, then z has mean 0 and variance 2°.

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Father:28

Son: 4

filler since

i need 20 characters

The average monthly pay for 150 employees was Rs 22500; however, after two employees' salaries were incorrectly inputted, the actual average monthly pay for employees was Rs 22532.

150 x 22,500 equals the total salary before correction, or Rs.

After rectification, the total salary equals

(150-2)*22500 + 25760 + 18590, or Rs. 339060.

Correct mean pay is equal to Rs. 339060 / 150, or Rs. 22532.

Initial reports stated that the mean wage for 150 workers was Rs. 22500 per month. Further examination revealed, however, that two employees' salary had been put incorrectly as Rs 25760 and Rs 19590, respectively. The two employees' actual pay were Rs. 27760 and Rs. 18590. The total salary before rectification was therefore 150*22,500, or Rs. 337,000. After two employees' pay were adjusted, the total salary was (150-2)*22500.The average monthly pay for 150 employees was Rs 22500; however, after two employees' salaries were incorrectly inputted, the actual average monthly pay for employees was Rs 22532 (150-2)*22500 + 25760 + 18590 = Rs339060. Consequently, it was determined that Rs339060 / 150 = Rs22532 was the proper mean wage paid to employees. After correcting the two incorrectly reported salaries, the average monthly wage for the organization's employees came to Rs22532.

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The measure of angle SQR for the given set of supplementary angles is found as 72°.

By the definition of supplementary angles:

6x + 4x = 180

10x = 180

x = 18

measure of angle SQR : 4x

4x = 4*18

measure of angle SQR = 72°

Thus, the measure of angle SQR for the given set of supplementary angles is found as 72°.

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Answer: h= -4

Step-by-step explanation:

To solve the equation 2(h+3.5)=-1, we can use the following steps:

Distribute the 2 on the left side of the equation: 2h + 7 = -1

Subtract 7 from both sides of the equation: 2h = -8

Divide both sides of the equation by 2: h = -4

Therefore, the solution to the equation is h = -4

By dividing a person's height in meters by their weight in kilograms (or pounds), the body mass index (BMI) is determined (or feet).

Body Mass Index (BMI) is calculated by dividing a person's height in meters squared by their weight in kilograms (or pounds) (or feet). A high BMI may be a sign of high body fat.

A person's body mass index (BMI) is calculated by dividing their weight in kilograms by their height in meters squared. Underweight, healthy weight, overweight, and obesity can all be detected using the BMI, which is a low-cost and simple screening approach.

Your risk of developing diseases that can be brought on by having a higher body fat percentage can be determined by your BMI. Your chance of developing certain conditions, including breathing difficulties, heart disease, high blood pressure, type 2 diabetes, gallstones, and some malignancies, increases with your BMI.

a) The formula for the rate of change of the BMI in relation to weight at a constant height is [tex]$B_w=\frac{1}{h^2}$[/tex].

b) Since [tex]$B_w=\frac{1}{h^2}$[/tex] exists always positive, we see that for fixed h, the BMI exists an increasing function of w.

c) Given a fixed weight and height, the rate of change in the BMI is given by  [tex]$B_w=\frac{-2 w}{h^3}$[/tex].

d) Since [tex]$B_w=\frac{-2 w}{h^3}$[/tex] exists always negative, we see that for fixed w, the BMI exists a decreasing function of h

The complete question is:

The body mass index (BMI) for an adult human is given by the function [tex]$B=\frac{w}{h^2}$[/tex], where w is the weight measured in kilograms and h is the height measured in meters. (The BMI for units of pounds and inches is [tex]$B=703 \frac{w}{h^2}$[/tex].)

a) Find the rate of change of the BMI with respect to weight at a constant height.

b) For fixed h, is the BMI an increasing or decreasing function of w?

c) Find the rate of change of the BMI with respect to height at a constant weight.

d) For fixed w, is the BMI an increasing or decreasing function of h?

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The significance of the intercept and the coefficient of performance rating is defined below.

The significance level is used to determine the strength of evidence for the relationship between the variables.

A significance level of .01 means that there is only a 1% chance that the relationship between the variables is due to chance. A significance level of .05 means that there is a 5% chance that the relationship is due to chance, and a significance level of .10 means that there is a 10% chance that the relationship is due to chance.

If the significance level is .01, the relationship between the variables is considered to be strictly significant, meaning that there is a very low probability that the relationship is due to chance.

If the significance level is .05, the relationship is considered to be regularly significant, meaning that there is a moderate probability that the relationship is due to chance.

If the significance level is .10, the relationship is considered to be weakly significant, meaning that there is a relatively high probability that the relationship is due to chance.

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In the trapezoid ABCD , when AB || DC and M, N are the midpoint of AD and BC then the value of AB , DC , and MN is equal to 26, 10, and 18 respectively.

In trapezoid ABCD,

AB || DC

AB = 7x + 5

DC = 4x -2

MN = 5x + 3

Using midpoint segment of two parallel lines in a trapezoid we have,

( AB + DC ) / 2 = MN

Substitute the value of AB, DC, and MN we get,

⇒ ( 7x + 5 + 4x -2 )/ 2 = 5x + 3

⇒11x + 3 = 10x + 6

⇒x = 3

⇒ AB = 7(3) + 5

         = 26

DC = 4(3) -2

      = 10

MN = 5(3) + 3

      = 18

Therefore, the value of AB, DC, and MN in the trapezoid ABCD is equal to 26, 10, and 18 respectively.

The above question is incomplete, the complete question is :

The drawing shows trapezoid ABCD with AB||DC; also, M and N are midpoints of AD and BC, respectively. Given: AB=7x+5, DC=4x−2, and MN=5x+3 find the value of AB, DC, and MN for the calculated value of  x.

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Answer:

54 square feet

Step-by-step explanation:

First get the area of both rectangles.

The bigger one is 8 by 9

8 times 9 is 72

the smaller one is 3 times 6 which is 18

Now you subtract both of them

72-18 = 54

The coordinates of the point S after translation will be -

S'(0, - 2).

Given is that triangle ΔRST is translated so that point R (-2, 1) is mapped to point R’ (2, -4).

The triangle is translated according to the rule as follows -

(x, y) → (x + 4, y - 5)

For the point S(-4, 3), we can write -

S(-4, 3) → S'(0, - 2)

Therefore, the coordinates of the point S after translation will be -

S'(0, - 2).

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The sequence after the first iteration of a radix sort is radixgoxt (arr) [03,10,15,20,26,32,47,53].

The sequence will not be one of the given sequences after the first iteration of a radix sort.

In radix sort, the elements are sorted based on the digits in their least significant position and then moving towards the most significant position. After each iteration, the elements will be rearranged based on the current significant position being considered.

For example, in the first iteration, the elements could be sorted based on the unit's place (i.e., the least significant position) in the following order: [03,10,15,20,26,32,47,53].

In the next iteration, the elements could be sorted based on the tens placed in the following order: [03,10,15,20,26,32,47,53].

And so on, until all the significant positions have been considered and the elements have been rearranged into their final sorted order.

Therefore, the sequence after the first iteration of a radix sort will depend on the sorting method used and the specific implementation of the algorithm

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Answer:

0.28 meters per second

Step-by-step explanation:

1 hour = 3600 seconds

1km = 1000 meters

1000 divided by 3600 = 0.28 meters per second

So, the speed of the train is 0.28 meters per second.

Answer:

The speed of the train is 22.22 meters per second.

Step-by-step explanation:

1 hour = 3600 seconds

1km = 1000 meters

80KM=80000

80000/3600 = 22.22

So, the speed of the train is 22.22 meters per second.

The answer of the  given question based on cryptarithm the answer is ,

958870 - 214803 = 744067, so the solution is correct.

Alphametics, also known as verbal arithmetic or cryptarithm, is a type of mathematical puzzle where letters or symbols are used to represent digits or numbers, and the puzzle solver must determine the correct digit or number to replace each letter or symbol in order to solve the puzzle.

The objective of an alphametic puzzle is to find a unique solution, where each letter or symbol represents a different digit or number, and the arithmetic equation is correct. In some alphametic puzzles, there may be additional constraints, such as leading zeros not being allowed, or certain digits being constrained to specific values.

One possible solution to this cryptarithm is:

 9 5 8 8 7 0

- 2 1 4 8 0 3

_________

7 4 4 0 6 7

In this solution, P=9, E=5, R=8, S=7, A=0, L=4, and Y=6.

To check:

PEPPER = 958870

SALT = 214803

YUMMY = 744067

And 958870 - 214803 = 744067, so the solution is correct.

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To find the unit rate, we need to divide the price of the chips by the number of ounces:  for every ounce of chips, it cost $0.08

The denominator of a unit rate is always 1. Divide the denominator by the numerator such that the denominator equals one in order to calculate the unit rate.

For instance, the unit rate is 50 km/5.5 = 9.09 km/hour if 50 km are traveled in 5.5 hours. An item's unit rate is its price for one of it. This is expressed as a ratio with a one as the denominator. For instance, if you covered 70 yards in 10 seconds, you covered 7 yards on average every second. 70 yards in 10 seconds and 7 yards in 1 second are both ratios, although only the latter is a unit rate.

Unit rate = Price / Number of ounces

Unit rate = $1.20 / 15 ounces = $0.08 per ounce

So the unit rate is $0.08 per ounce. This means that for every ounce of chips, it cost $0.08

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There is no relation between the number of people living and the number of pets. The correct option is D.

Scatter plots are used to visually observe and plot relationships between two numerical variables. The values of each individual data point are represented by the dots in a scatter plot.

The scatter plot is showing the data between the number of people living and the number of pets.

In the scatter plot, there is not any perfect relation between the number of people living in a room and the number of pets.

The correct option is D.

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Answer:

To find (f•g)(-2), we need to first calculate f(-2) and g(-2).

f(-2)=-3(-2)-1=-7

g(-2)=(-2)^2+5=9

Then, we can calculate (f•g)(-2) as follows:

(f•g)(-2)=f(-2)g(-2)=-7*9=-63

Answer:

To calculate Tom's new average, you need to know the total number of runs he scored in the three matches and the total number of runs he scored in the recent two matches.

You can use the following formula to calculate the new average:

New Average = (Total Runs + Recent Runs) / Total Matches

First you need to find the total runs he scored in the first 3 matches:

74 (average) * 3 (number of matches) = 222 runs

Then you need to find the total runs he scored in the recent two matches:

42 (runs in match 1) + 31 (runs in match 2) = 73 runs

Now you can find the new average by adding the total runs in recent two matches and total runs in the first 3 matches and divide it by the total number of matches:

(222 + 73) / 5 = 295 / 5 = 59

So, Tom's new average is 59 runs.

Answer: 59

Step-by-step explanation:

Please refer to the image below:

When the  expression [tex]log_b{32} - log_b{7}[/tex], b > 1, is written in the form [tex]log_b{a}[/tex], the value of a is 25

We know that a logarithm of a number is nothing but the power to which a number must be raised to get some other values.

We know that the rules for the addition or subtraction (basic algebraic operations)

When the base od logarithms are same, then only we can add or subtract logarithms.

Consider logartithemic numbers : log₂7 , log₃8 and log₂5

Her we can observe that the base of  logartithemic numbers  log₂7 , log₃8  is different.

Here, the expression [tex]log_b{32} - log_b{7}[/tex]

The base of logartithemic numbers  [tex]log_b{32} , log_b{7}[/tex] is equal.

so, we can perform algebraic operation.

[tex]log_b{32} - log_b{7}\\\\=log_b{32-7}\\\\=log_b{25}[/tex]

Comparing above expression with [tex]log_b{a}[/tex] we have,

a = 25

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Answer:

29

Step-by-step explanation:

w = # william laps

 then  w-2 = gabby's laps    together they sum to 56

w   +    w-2 = 56      add 2 to both sides of the equation

2w =58

w = 29   <=====william's laps

Answer: 29

Step-by-step explanation:

Gabriela went w -2 ( 2 lengths less than william)

William went w

Total is 56

So w - 2 + w = 56

Combine like terms: 2w - 2 = 56

Add the two ro both sides: 2 + 2 - 2w  = 56 + 2

2w / 2 = 58 / 2

w = 29

May or may not be correct

If Bentonville Police Department confiscated 10(5/7) kg of cocaine from a drug but sealed in 25 plastic bag , the Kilogram of cocaine in each bag is  0.43 Kg .

The amount of cocaine confiscated by Police = 10(5/7) = 75/7 kilograms

The number of plastic bags in which the cocaine was found is = 25 .

To determine the weight of cocaine in each bag, the total amount of cocaine was divided by the number of bags.

substituting the required value ,

we get ;

⇒ [75/7]/25 = 3/7 = 0.428571 ≈ 0.43 .

Therefore , there was 0.43 Kg of Cocaine present in each bag .

The given question is incomplete , the complete question is

The Bentonville Police Department confiscated 10(5/7) kg of cocaine from a drug but . If the cocaine was found in 25 sealed, plastic bag, how many kilogram of cocaine was in each bag .

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The statement A is correct option.

The vertex of a quadratic equation is the minimum or maximum point of the equation.

Given that, the quadratic function f(x) has a vertex at (1, 6) and opens downward and g(x) = (x - 7)² + 1,

The vertex of f(x) is at (1, 6), we know that a vertical line passing through the vertex is called the axis of symmetry for the parabola.

That mean, axis of symmetry will pass through (1, 6)

Therefore, the axis of symmetry for f(x) is x = 1

And, g(x) = (x - 7)² + 1

= x²+49-14x+1

= x²-14x+50

Vertex = -b / 2a

here, b = -14 and a = 1

Vertex (h, k) = 14 / 2 = 7

To find k, put x = 7 in the equation,

(7-7)²+1 = 1

Therefore, point of the vertex = (7, 1)

That mean axis of the symmetry will pass through (7, 1)

Therefore, axis of the symmetry for g(x) = 7

Hence, the statement A is correct option.

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