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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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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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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 value of x in the continued proportion is 6

From the question, we have the following parameters that can be used in our computation:

3,x,12 are in continued proportion

This means that

x/3 = 12/x

So, we have

x^2 = 36

Take the square roots

x = 6

Hence, the solution is 6

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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

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

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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The probability of a core of the two odd number be 1/4.

A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.

The outcome of one die has no bearing on the outcome of the other since the two dice are independent.

In this instance, a complex event's probability is calculated by adding its component simple event probabilities.

Three odd and three even results occur from each roll of the dice. So, the probability of getting an odd number exists [tex]$\frac{3}{6}=\frac{1}{2}$[/tex]

The probability that this happens with both dice exists [tex]$\frac{1}{2} \cdot \frac{1}{2}=\frac{1}{4}$[/tex]

It is relatively simple to list the "excellent" possibilities in this situation because there are a total of 36 outcomes (all numbers from 1 to 6 for one die and the same for the other die). The positive results are

(1, 1), (1, 3), (1, 5)

(3, 1), (3, 3), (3, 5)

(5, 1), (5, 3), (5, 5)

And in fact, 9 good outcomes over 36 total outcomes means

[tex]$\frac{9}{36}=\frac{1}{4}$$[/tex]

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It will take 8.8 years for the initial deposit to reach $7,500.

The formula to calculate the number of years it takes for an initial deposit to reach a certain amount with compounding interest is A = P(1+r/n)^nt, where A is the final amount, P is the principal, r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years. In this example, P = $6,000, r = 3, n = 12 (monthly compounding of interest) and A = $7,500. We can solve for t, the number of years, by rearranging the equation to t = log(A/P)/log(1+r/n). When we plug in the numbers, we find that it will take 8.8 years for the initial deposit to reach $7,500.

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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

Answer:

x = 3.  y = 11

Step-by-step explanation:

The two equations are two simultaneous equations, which can be solved by substitution, elimination or graphical method.

Elimination method:

The coefficients of 'x’ or ‘y’ need to be the same with opposite signs. The coefficients of ‘y’ will be focused:

                  (17x - y = 40) Multiplied by 4

                  (2x + 4y = 50) Multiplied by 1

                  68x - 4y = 160

                   2x + 4y = 50

In the net total, the ‘y’ terms will cancel each other out:

                 70x = 210

                     x = [tex]\frac{210}{70}[/tex]

                     x = 3

The calculated value of x is substituted in any of the equations to determine the value of y:

                 17(3) - y = 40

                    51  - y = 40

                   51 - y - 40 = 0

                   51 - 40 - y = 0

                   11 - y = 0

                   y = 11

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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Point U would be (1, 1)

(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 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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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

Father:28

Son: 4

filler since

i need 20 characters

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 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:

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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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 slope, y-intercept, and equation of each of the lines are:

a. m = 2, b = -1.

y = 2x - 1

b. m = -1; b = 2.

y = -x + 2

c. m = -2/3; b = 1

y = -2/3x + 1

d. m = 1/2; b = -2.

y = 1/2x - 2

The slope-intercept form is y = mx + b, where b equals the y-intercept and m is the slope.

a. Slope (m) = change in y/change in x = (3 -(-1))/(2 - 0) = 4/2 = 2

y-intercept (b) = -1.

The equation is: y = 2x - 1

b. Slope (m) = change in y/change in x = (2 -(-2))/(0 - 4) = 4/-4 = -1

y-intercept (b) = 2.

The equation is: y = -x + 2

c. Slope (m) = change in y/change in x = (3 -(-1))/(-3 - 3) = 4/-6 = -2/3

Substitute m = -2/3 and (x, y) = (3, -1) into y = mx + b to find the y-intercept (b):

-1 = -2/3(3) + b

-1 = -2 + b

-1 + 2 = b

1 = b

b = 1

The equation is: y = -2/3x + 1

d. Slope (m) = change in y/change in x = (0 -(-1))/(4 - 2) = 1/2 = 1/2

y-intercept (b) = -2.

The equation is: y = 1/2x - 2

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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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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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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:

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

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:

9

Step-by-step explanation:

g(h(2))= 2(x3-x2)+1 = 2(2^3-2^2)+1 = 2(8-4)+1

=2*4+1 = 9

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.