Prove (n + 6)² – (n + 2)² is always a multiple of 8​

The mean and standard deviation of the sampling distribution of the difference in sample means xF − xM is 1.5 minutes(mean) and 1.533 minutes(std. dev) approx The probability of getting a difference in sample means xF − xM that is less than 0 is 0.0239 approx.

Suppose that a random variable X is formed by n mutually independent and normally distributed random variables such that:

Xi = N(μi, σ²) ; i = 1, 2,......, n

And if

X = X1 + X2 +........+ Xₙ

Then, its distribution is given as:

X ≈ N (μ1 + μ2+........+ μₙ)

For this case, it's given that

Distribution of time taken for distance ran by lady is Normal distribution and had a mean handling time of = 8.8 minutes with standard divagation of = 3.3 minutes.

Distribution of time taken for distance ran by joker is Normal distribution and had a mean handling time of = 7.3 minutes with standard divagation of = 2.9 minutes.

Samples of size n = 8 are taken from both population.

Estimated sample mean = population mean

Estimated sample standard deviation = population std. dev / √n

where n = sample size

For sample of females, the distribution is

For sample of males, the distribution is

Also, if we take distribution of difference between sample means(, then it would be normal with mean = 8.8-7.3 = 1.5 minutes (as mean for  will be -7.3 but same standard deviation) as factor gets squared for affecting standard deviation and variance)

and standard deviation is:

\(\sqrt{s^2f + s^2m } = \sqrt{3.3^2/8 + 2.9^2/8}\)

≈ 1.553 minutes.

The distribution of difference between sample means is  approximately

We need \(P(Xf - Xm < 0)\)

Thus, the mean and standard deviation of the sampling distribution of the difference in sample means xF − xM is 1.5 minutes(mean) and 1.533 minutes(std. dev) approx The probability of getting a difference in sample means xF − xM that is less than 0 is 0.0239 approx.

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Answer:

B,C,E

Step-by-step explanation:

because a unite rate is a number over one

Answer:

183.25 or 183 remainder 1

Step-by-step explanation:

733 is not divided by 4 fully it have remainder

Answer:

15-23x

Step-by-step explanation:

The solution to the given differential equation is y = 4sin(2x+C), where C is a constant determined by the initial condition y(-4).

The differential equation dy/dx = 8x√(16-y^2), we can separate the variables and integrate both sides. We rearrange the equation as √(16-y^2) dy = 8x dx.

Integrating both sides, we have ∫√(16-y^2) dy = ∫8x dx.

On the left-hand side, we can use a trigonometric substitution to evaluate the integral. Let y = 4sin(u), then dy = 4cos(u) du. Substituting these values, the integral becomes ∫4cos(u) (4cos(u)) du = ∫16cos^2(u) du.

Using the trigonometric identity cos^2(u) = (1 + cos(2u))/2, we rewrite the integral as ∫8(1 + cos(2u))/2 du.

Integrating both sides, we get y = 4sin(u) = 4sin(2x + C), where C is the constant of integration.

To determine the value of the constant C, we use the initial condition y(-4). Plugging x = -4 into the solution equation, we have y(-4) = 4sin(-8 + C) = -4. Solving for C, we find C = -π/2.

Therefore, the solution to the differential equation is y = 4sin(2x - π/2), where C = -π/2.

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500 lol

thanks for the free points!

have a great day!

The maximum value of the data is given as follows:

75.

A box and whisker plot shows these five metrics from a data-set, listed and explained as follows:

The maximum value on the box plot is the end of the plot, hence it is of 75.

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Answer:

B

Step-by-step explanation:

When a polynomial is in standard form, it is arranged in the order of largest power first, followed by the next largest, and then so on. The only polynomial here that follows this rule is the second one, or choice B. Hope this helps!

Answer:

Slope = 4

Step-by-step explanation:

Answer:

1, Find the mean of all values

2. Find the distance of each value from that mean (subtract the mean from each value, ignore minus signs)

3. Then find the mean of those distances

Answer: Find the mean of all values

Find the distance of each value from that mean (subtract the mean from each value, ignore minus signs)

Then find the mean of those distances

Explanation: Example: the Mean Deviation of 3, 6, 6, 7, 8, 11, 15, 16

Step 1: Find the mean:

Mean =   3 + 6 + 6 + 7 + 8 + 11 + 15 + 168   =   728   = 9

Find the mean of those distances:

Mean Deviation =   6 + 3 + 3 + 2 + 1 + 2 + 6 + 78   =   308   = 3.75

So, the mean = 9, and the mean deviation = 3.75

Hope this helped! :)

Answer:

The volume of the hemisphere is 2/3 of the volume of the cone.

Step-by-step explanation:

pa brainly po and thanks

The amount of money in Iris's checking account can be modeled by a linear function of the form:

y = mt + b

where y is the amount of money in the account, t is the time (measured in years), m is the rate of interest, and b is the initial amount in the account.

In this case, we have m = 0.04 (since the interest rate is 4% per year) and b = 180 (since that's the initial amount in the account). Therefore, the linear function that models the amount of money in Iris's checking account at any time t is:

y = 0.04t + 180

For example, if t = 5 (years), then the amount of money in Iris's checking account is 0.04 * 5 + 180 = 198 dollars.

Answer:

6g+42

To be certain, expand the brackets; (6×g) (6×7)

Step-by-step explanation:

A cheerful teen willing to help,

have a splendiferous day/night ahead!

stay salty...

Answer:

6g + 42

Step-by-step explanation:

\(6(g + 7)\\\rule{150}{0.5}\\\rightarrow 6 * g = 6g\\\\\rightarrow 6 * 7 = 42\\\\\rightarrow 6(g+7) = \boxed{6g + 42}\)

Answer:

7:8 also means 7/8.

Hope it helps ;)

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Answer: Approximately 0.0003047

As a fraction, it is equal to exactly 792/(2,598,960)

===========================================================

Explanation:

The king of spades must be in the hand, and we can pick any other king. There are 3 ways to pick the other king. Then there are 4 C 2 = 6 ways to pick the two queens. The 4C2 refers to the nCr notation. Or you could use Pascal's Triangle.

Overall, there are 3*6 = 18 ways to pick the king of spades, another king, and exactly 2 queens.

Then we have one more card to pick that isn't a king nor a queen. There are 4+4 = 8 cards that are either a king or queen, leaving 52-8 = 44 cards that are neither.

So there are 18*44 = 792 ways to pick a king of spades, another king, exactly 2 queens, and some other card that isn't a king nor queen.

This is out of 52C5 = 2,598,960 possible five card hands.

The probability we're after is roughly 792/(2,598,960) = 0.0003047

Side note: order does not matter with card hands.

Hunter and three friends spent a total $41 of money.

Addition is the process used to combine things and count them as a single, large group. Addition in mathematics is the process of combining two or more numbers. The term "sum" refers to the result of the process, and "addends" refers to the numbers that are added.

Given, Hunter and three friends were going to the movies.

The movie tickets cost $10 each.

So, cost of movie ticket is 3 times $10 = $30.

And they bought three popcorn at $7.25, and three drinks at $2.75.

That means, the expenditure other than movie is;

$7.25 + $2.75 = $11

To find the total money they spent:

Add all the expenditures,

$30 + $11 = $41.

Therefore, they spent $41.

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There is only 1 power of 7 contained in 10.

Students use powers of numbers to solve this problem and learn what is occurring to the numbers as a result.

Students also learn how to divide a seemingly vast and challenging equation into smaller, more accessible components. The pupils should understand that raising 7 to a power only produces a finite number of unit digits. Furthermore, as the power of 7 rises, these particular numbers "circle round." 7, 9, 3, and 1 make up this cycle.

The digit in the tens place is the same.

The total number of times we multiply a number is known as its exponent or power. For instance, 2 to the power 3 denotes a 3x3 multiplication of 2.

The largest power of 7 that is less than 10 is 7^1 = 7, therefore there is only 1 power of 7 contained in 10.

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There is only 1 power of 7 contained in 10.

Students use powers of numbers to solve this problem and learn what is occurring to the numbers as a result.

Students also learn how to divide a seemingly vast and challenging equation into smaller, more accessible components. The pupils should understand that raising 7 to a power only produces a finite number of unit digits. Furthermore, as the power of 7 rises, these particular numbers "circle round." 7, 9, 3, and 1 make up this cycle.

The digit in the tens place is the same.

The total number of times we multiply a number is known as its exponent or power. For instance, 2 to the power 3 denotes a 3x3 multiplication of 2.

The largest power of 7 that is less than 10 is 7^1 = 7, therefore there is only 1 power of 7 contained in 10.

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• Let's call A the event of a bow tie designed with swirls (P(A)=0.3).

• Let's call B the event of a bow made of velvet (P(B)=0.1).

It is important to know that the events are mutually exclusive because bows can be made of two different materials at the same time. which means there's no intersection between A and B. So, the probability is

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▹ Answer

C = 3215.36

▹ Step-by-Step Explanation

A = πr²

A = 3.14(32)²

A = 3215.36

Hope this helps!

- CloutAnswers ❁

Brainliest is greatly appreciated!

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Answer:

Susie reaches the store first being ahead by 0.06 hours.

Step-by-step explanation:

20 miles going 45 miles/hour.

20 miles / (45 miles / hour) = 20 miles hours / 45 miles =

= 20 hours / 45 = 4/9 hours = 0.44 hours

25 miles going 50 miles/hour.

25 miles / (50 miles / hour) = 25 miles hours / 50 miles =

= 25 hours / 50 = 1/2 hours = 0.5 hours

So Susie needs less time (= arrives first).

the difference is 0.5 - 0.44 = 0.50-0.44 = 0.06 hours

as additional practice :

0.06 hours is 60 × 0.06 minutes.

60 × 0.06 = 60 × 6 / 100 = 360 / 100 = 3.6 minutes.

Answer: 82

Step-by-step explanation:

You add them all

Answer: The answer is C and D

Step-by-step explanation:

Answer

0. Horizontal translation 5 units.

1. Reflection over the x-axis

2. Vertical compression 2 units

3. Vertical translation down 3 units

Explanation

• Writing the function in completed-square form.

As a ≠ 1, where a is the coefficient of the leading term, to write it in the completed-square form we have to make a = 1:

Now we have to take half of the x term and square it and add it to the function as follows:

Finally, we have a Perfect Squared Trinomial in the left side that we can rewrite as follows, obtaining our function g(x):

As our parent function is:

Then, the transformations that suffered were:

• Horizontal translation to the left 5 units

• Reflection over the x-axis

• Vertical compression 2 units

• Vertical translation down 3 units

Answer:

We have the proportion: 8/10 = 100/y

We can solve for y by cross-multiplying.

That is, 8y = 100 * 10 Simplifying the right-hand side, 8y = 1000

Dividing both sides by 8 to solve for y, y = 125

Hence, the value of y is 125.

Finally, we have the expression: y = √80We can simplify this expression by factoring 80 into its prime factors:80 = 2 * 2 * 2 * 2 * 5

Taking the square root of 2 * 2 * 2 * 2, we have:√(2 * 2 * 2 * 2) = 2 * 2 = 4

Therefore, y = 4√5The value of y is 4√5.

Step-by-step explanation:

Hope this helps!! Have a good day/night!!

To calculate the residual for observation 6, we first need to find the forecast for observation 6. Based on the given information, the forecast for observation 6 is 34. Therefore, the residual for observation 6 would be:

Residual = Actual Demand - Forecast
Residual = 38 - 34
Residual = 4

So the residual for observation 6 is 4.
Hi! To find the residual for observation 6, we need to subtract the forecast (F) from the actual demand (A). In this case, the observation 6 values are:

Actual Demand (A): 38
Forecast (F): 28

Now, we'll calculate the residual:

Residual = Actual Demand (A) - Forecast (F)
Residual = 38 - 28
Residual = 10

So, the residual for observation 6 is 10.

The number of one-to-one functions from a set with five elements to sets with one, two, three, four, and five elements are 1, 20, 60, 120, and 1, respectively.To answer this question, we need to use the concept of one-to-one functions.

A one-to-one function is a function where each element in the domain corresponds to a unique element in the range. In other words, no two elements in the domain can have the same image in the range.

Let's consider each case separately.

1. Set with one element: In this case, there is only one possible function since there is only one element in the range that needs to be mapped to.

2. Set with two elements: There are a total of 20 possible one-to-one functions from a set with five elements to a set with two elements. To see why, we can think of it as choosing two distinct elements from the domain to map to the two elements in the range. There are 5 choices for the first element, and 4 choices for the second element (since we can't choose the same element twice). So the total number of possible functions is 5 x 4 = 20.

3. Set with three elements: There are a total of 60 possible one-to-one functions from a set with five elements to a set with three elements. To see why, we can think of it as choosing three distinct elements from the domain to map to the three elements in the range. There are 5 choices for the first element, 4 choices for the second element, and 3 choices for the third element. So the total number of possible functions is 5 x 4 x 3 = 60.

4. Set with four elements: There are a total of 120 possible one-to-one functions from a set with five elements to a set with four elements. To see why, we can think of it as choosing four distinct elements from the domain to map to the four elements in the range. There are 5 choices for the first element, 4 choices for the second element, 3 choices for the third element, and 2 choices for the fourth element. So the total number of possible functions is 5 x 4 x 3 x 2 = 120.

5. Set with five elements: In this case, there is only one possible function since there are five elements in both the domain and the range, and every element in the domain must be mapped to a unique element in the range.

In summary, the number of one-to-one functions from a set with five elements to sets with one, two, three, four, and five elements are 1, 20, 60, 120, and 1, respectively.

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Answer: Bigger X = 17       Smaller X = 1/3

Step-by-step explanation:

for the larger number

1x - 8 = 9 (equation)

X = 17 (the result)

for the smaller number

9x - 2 = 1 (equation)

X = 1/3 (the result)

Therefore , the solution of the given problem of equation comes out to be value of g is 12 .

In a math equation, the comparable symbol (=) is used to denote equality between two propositions. It is demonstrated that by using mathematical formulas, which have been expressions of reality, different numerical factors can be compared. The equal sign, for instance, splits the integer 12 or the equation y + 6 = 12 to 2 different halves. It is possible to determine how many characters each side of such a symbol has. It's common for symbols to have conflicting meanings.

Here,

Given :

=> g -3 = 9

To find the value of g :

=> g = 9 + 3

=> g = 12

Thus , value of g is 12.

Therefore , the solution of the given problem of equation comes out to be value of g is 12 .

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Answer:

1330.5 cm³

Step-by-step explanation:

The volume of a cylinder is: V = πr²h

Substitute the values for those variables.

V = π(5.5)²(14)

V = π(30.25)(14)

V = 1330.5

Here, x = 6 is a vertical asymptote of f, so the function approaches infinity as x approaches 6 from both sides.

Let's start by integrating f'(x) to get f(x). We have:

f'(x) = 16(x+2)(6-x)³ - 32(x+6)

Integrating both sides with respect to x:

f(x) = ∫[16(x+2)(6-x)³ - 32(x+6)] dx

Simplifying the integral, we get:

f(x) = -2(x+2)²(6-x)⁴ + 16(x+6) + C

where C is the constant of integration.

Next, we can find the critical points of f(x) by setting f'(x) = 0:

f'(x) = 16(x+2)(6-x)³ - 32(x+6) = 0

Solving for x, we get x = -2 and x = 6 as critical points.

Now, we can use the second derivative f''(x) to determine the concavity of the function. We have:

f''(x) = (6x-x)⁴ = x⁴

Since the second derivative is always positive for x > 0, the function is concave up on the interval (6, ∞).

Similarly, since the second derivative is always negative for x < 0, the function is concave down on the interval (-∞, -2).

At x = -2 and x = 6, the function has an inflection point.

Finally, we know that x = 6 is a vertical asymptote of f, so the function approaches infinity as x approaches 6 from both sides.

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