In testing for differences between the means of two (2) related populations where the
variance of the differences is unknown, the degrees of freedom are
a. n - 1
b. n1 + n2 - 1
c. n1 + n2 - 2
d. n - 2

for the following integrals, we can evaluate the change the coordinate system to either cylindrical or sperical so that the integrals as follows:

a) We want to employ the coordinate system that best utilizes axial symmetry, which is cylindrical coordinates, when we have it.

x=rcos

y=rsinθ

z=z

r2=x2+y2

θ=tan−1y/x

dV=r dz dr dθ

The portion of the circle with radius 2 that is located in the first quadrant is described by the constraints on x and y, as you will see. Thus, r2 and [0, 2]. The paraboloid that is the lower bound on zvis z=r2 is then obtained (the upper bound clearly does not change). The integral in cylindrical coordinates is hence we get the answer as shown in image.

b) We wish to utilize spherical coordinates when we have spherical symmetry.

x=ρcosθsinϕ

y=ρsinθsinϕ

z=ρcosϕ

ρ2=x2+y2+z2

√x2+y2=ρsinϕ

dV=ρ2sinϕ dρ dϕ dθ

This one is actually simpler because a portion of the unit sphere is precisely described by the limits of integration. Any value for x is acceptable, but y and z must be positive. Therefore, we have 1-1, [0, 2] (to maintain positive zz), and [0,] (to maintain positive y). hence, we get the answer as shown in image.

To learn more about integrals: https://brainly.com/question/27419605

#SPJ4

Answer:

14+14 + 4pi= 28 + 4pi

\(\pi\)

Answer:

it's 10

Step-by-step explanation:

don't know the steps

Answer:

3 minutes

Step-by-step explanation:

there are many ways to answer this question you can on it later but im going to write the easiest here

4 plates is 2 minutes

find how many minutes for one plate and times it by 6

2 ÷ 4 = 1/2 minutes or 30 seconds

therefore;

1/2 × 6 = 3 minutes

please rate brainliest if helps

The standard normal distribution has a mean of 0 and a standard deviation of 1. M ≈ 30.935. The median of the distribution is also 25.

(a) To find M, we first need to convert the given values of mean and standard deviation to the standard normal distribution. This can be done by using the formula Z = (X - μ) / σ, where Z is the Z-score, X is the value of interest, μ is the mean, and σ is the standard deviation. In this case, we have X ~ N(25, 9). Substituting the values into the formula, we get Z = (X - 25) / 3. Now we need to find the Z-score that corresponds to the desired probability of 0.95. Using a standard normal distribution table or a calculator, we find that the Z-score corresponding to a cumulative probability of 0.95 is approximately 1.645. Setting Z equal to 1.645, we can solve for X: (X - 25) / 3 = 1.645. Solving for X, we get X ≈ 30.935. Therefore, M ≈ 30.935.

(b) The median is the value that divides the distribution into two equal halves. In a normal distribution, the median is equal to the mean. In this case, the mean is given as 25. Therefore, the median of the distribution is also 25.

Learn more about Z-score here: brainly.com/question/30557336

#SPJ11

Answer:

7g-13

Step-by-step explanation:

Answer:

-13 +17g

Step-by-step explanation:

−3 + 6g + 11g −10

-13 + 6g + 11g

-13 + 17g

Answer:

6.93 cm

Step-by-step explanation:

You have a right triangle (90°), so you do as follow:

If I understand correctly, you are looking for the hypotenuse so

\(cos(30) = \frac{PQ}{QR} = \frac{8 cm}{QR}\)

That is equal to \(QR = cos(30)*8 cm = 6.928 cm\)

The linear relationship between time and distance can be considered proportional. The constant of proportionality in this case is 4.

In a proportional relationship, the ratio between the two quantities remains constant. Here, as time increases by 2 hours, the distance also increases by 8 miles. Let's calculate the ratio of distance to time for each pair of values:

For the first pair (2 hours, 8 miles):

Ratio = distance / time = 8 miles / 2 hours = 4 miles/hour

For the second pair (4 hours, 16 miles):

Ratio = distance / time = 16 miles / 4 hours = 4 miles/hour

For the third pair (6 hours, 24 miles):

Ratio = distance / time = 24 miles / 6 hours = 4 miles/hour

For the fourth pair (8 hours, 32 miles):

Ratio = distance / time = 32 miles / 8 hours = 4 miles/hour

As we can see, the ratio of distance to time remains constant at 4 miles per hour for all the pairs. This indicates a proportional relationship between time and distance.

Therefore, the linear relationship is also proportional, and the constant of proportionality is 4.

To know more about proportional relationships, refer here:

https://brainly.com/question/29765554#

#SPJ11

They have to sell D. 75 shirts to make a profit of $300.

The total cost of buying and printing the shirts was $600.

In order to make a profit of $300, they would therefore have to raise:

= Cost + profit

= 600 + 300

= $900

As they are selling each shirt $12, the number of shirts they would have to sell to get to $900 is:

= 900 / 12

= 75 shirts

They would therefore have to sell 75 shirts in order to make a profit of $300.

Find out more at https://brainly.com/question/18477566.

Answer:

$339.00

Step-by-step explanation:

If you put $25 each month into a savings account that paid a simple interest rate of 6.5% each year, how much would you have in your account at the end of two years?

We solve the above question using the Equation:

A = P(1 + rt)

P = Principal = Amount deposited each month = $25

The amount deposited in a year = $25 × 12 months = 300

Calculation:

First, converting R percent to r a decimal

r = R/100 = 6.5%/100 = 0.065 per year.

Solving our equation:

A = 300(1 + (0.065 × 2)) = 339

A = $339.00

Therefore, you would have $339 in your account after 2 years

Answer:

6

Step-by-step explanation:

Answer:

52 is the cost of the snowboard rental per day.

s represents the day(s) that the equipment is rented out.

So, 52s is the cost for the snowboard times s days.

Approximately 304,657,600 Americans were there in July 2009 based on the estimated 2008 growth rate of 0.88%.

To find the approximate US population in July 2009, we need to apply the growth rate of 0.88% to the initial population in July 2008.

Convert the growth rate from percentage to decimal:

0.88% = 0.0088
Calculate the number of people added to the population in 2008: 302,000,000 * 0.0088 = 2,657,600
Add this number to the initial population to find the population in July 2009:

302,000,000 + 2,657,600 = 304,657,600.

For similar question on growth rate.

https://brainly.com/question/29334875

#SPJ11

Answer:

angle 2= 110

angle 3= 70

angle 4=  70

Step-by-step explanation:

because angle 2 is parallel and a line is 180

Answer:

Angle 2-110

Angle 3- 70

Angle 4- 70

Step-by-step explanation:

9514 1404 393

Answer:

  ∠Z = 34°

  ∠T = 56°

Step-by-step explanation:

You can solve for x using the measure of the right angle:

  90 = 3x +6

  30 = x +2 . . . . . divide by 3

  28 = x . . . . . . . . subtract 2

Then the measure of T is ...

  ∠T = 2x° = 2(28)° = 56°

  ∠Z is its complement: 90° -56° = 34°

The angle measures are ...

  m∠Z = 34°

  m∠T = 56°

Answer:

13 2/15

Step-by-step explanation:

The combination formula can be used to calculate the number of ways that a group of people can be divided into teams of a certain size. In this case, there are 48,620 ways that the 18 people can be divided into 2 teams of 9 people.

To find out how many ways 18 people can be divided into 2 teams of 9 people, we need to use the combination formula. The formula for combination is nCr = n!/r!(n-r)!, where n is the total number of people and r is the number of people in each team.
In this case, n=18 and r=9. Plugging in the values into the formula, we get:
18C9 = 18!/9!(18-9)! = (18x17x16x15x14x13x12x11x10)/(9x8x7x6x5x4x3x2x1)
Simplifying the expression, we get:
18C9 = 48,620
Therefore, there are 48,620 ways that the 18 people can be divided into 2 teams of 9 people.
It is important to note that the order of the teams does not matter. For example, team A consisting of 9 people and team B consisting of the remaining 9 people is the same as team B consisting of 9 people and team A consisting of the remaining 9 people.
In conclusion, the combination formula can be used to calculate the number of ways that a group of people can be divided into teams of a certain size. In this case, there are 48,620 ways that the 18 people can be divided into 2 teams of 9 people.

for more questions on combination

https://brainly.com/question/11732255

#SPJ11

Answer:

D' (-6, -2)

Step-by-step explanation:

3 units up means y will increase by 3

y = -5 + 3 = -2

x will stay the same

x = -6

New coordinate

D' (-6, -2)

Answer:

5.75, you have to multiply the height and width and then divide the total volume by that product

Answer:5.75

Step-by-step explanation:

Just multiply multiply the numbers

A consumer loan of $40,000 with a 15.8% interest rate will require monthly payments over a period of 2 years. The total amount to be paid, including both principal and interest, will be approximately $45,380.

To calculate the monthly payments, we need to determine the total amount to be paid over the loan period, including the principal amount and the interest. The formula used for calculating equal monthly installments is:

M = P * (r * (1 + r)^n) / ((1 + r)^n - 1)

Where:

M = Monthly payment

P = Principal amount

r = Monthly interest rate

n = Number of monthly payments

In this case, the principal amount (P) is $40,000, the interest rate (r) is 15.8% per year, and the loan duration (n) is 2 years (24 months).

First, we convert the annual interest rate to a monthly rate by dividing it by 12: 15.8% / 12 = 0.0132.

Next, we substitute the values into the formula:

M = 40,000 * (0.0132 * (1 + 0.0132)^24) / ((1 + 0.0132)^24 - 1)

Calculating this formula gives us the monthly payment (M) of approximately $1,907.42.

To find the total amount to be paid, we multiply the monthly payment by the number of payments: $1,907.42 * 24 = $45,778.08. However, this includes both the principal and the interest. Subtracting the principal amount ($40,000) gives us the total interest paid: $45,778.08 - $40,000 = $5,778.08.

Therefore, the total amount to be paid, including both principal and interest, will be approximately $45,778.08.

To learn more about interest click here: brainly.com/question/30393144

#SPJ11

What is true about ΔXWZ is that the ratio of its altitude to the corresponding altitude in ΔYWZ is equal to the ratio of the length of XW to the length of YZ.

If ΔYWZ is similar to ΔYXW, it means that these two triangles have corresponding angles that are equal and corresponding sides that are proportional. In this case, we are specifically interested in the altitude of ΔWXZ, which we will denote as h.

Since ΔYWZ is similar to ΔYXW, we can establish the following proportion based on their corresponding sides:

YZ/YX = YW/YW

Let's denote the length of YZ as a and the length of YW as b. We can rewrite the proportion as:

a/YX = b/YW

Now, let's consider ΔXWZ. Since XW is common to both triangles, we can conclude that the altitude of ΔXWZ, which we will denote as k, is also proportional to the altitude of ΔYWZ (h). Therefore, we can express this proportion as:

k/h = XZ/YZ

To establish a relationship between k and h, we need to find a way to relate XZ to YZ. Using the proportion established earlier, we can substitute a for YZ:

k/h = XZ/a

To relate XZ to YZ, we need to find a relationship between XZ and YX. Again, using the similarity of the triangles, we have:

XZ/YZ = XW/YW

Substituting the value of YZ (a) from the earlier proportion, we have:

XZ/a = XW/YW

Now, we can combine the two proportions to find the relationship between k and h:

k/h = (XW/YW) * (YW/a)

Simplifying further, we get:

k/h = (XW/a)

From this equation, we can conclude that the ratio of the altitudes k/h in ΔXWZ and h in ΔYWZ is equal to the ratio of XW to YZ. In other words, the ratio of the altitudes is equal to the ratio of the corresponding sides in the similar triangles.

Learn more about altitude at: brainly.com/question/31017444

#SPJ11

Answer:

92/3 acres

Step-by-step explanation:

Size of one section = \(3\frac{5}{6}\) acres = 23/6 acres

No. of sections = 8

Total land owned by the owner = 23/6 * 8

= 92/3 acres or 3 \(\frac{2}{3}\) acres

Jim will take 3.6 hours to climb the same hill, assuming he walks at a constant speed of 5 miles/hour.

We can start by using the formula: distance = speed x time

Let's assume that the distance of the hill is 'd' miles. Jerry walks at a speed of 6 miles/hour and walked for 3 hours to climb the hill, so the distance he covered is: distance = speed x time

distance = 6 x 3

distance = 18 miles

Now, we can use the same formula to find out how long Jim will take to climb the same hill. We know that Jim walks at a speed of 5 miles/hour, so: distance = speed x time

d = 5t

where 't' is the time it takes for Jim to climb the hill in hours. We can set the distance that Jim covers equal to the distance that Jerry covered, since they both climbed the same hill: 5t = 18

Solving for 't':

t = 18/5

t = 3.6 hours

Therefore, Jim will take 3.6 hours to climb the same hill, assuming he walks at a constant speed of 5 miles/hour.

To learn more about distance click here

brainly.com/question/25841655

#SPJ4

Answer:

x=4 so d

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

Simplify the following:

(2 sqrt(5))^2

Multiply each exponent in 2 sqrt(5) by 2:

2^2×5^(2/2)

2/2 = 1:

2^2×5

2^2 = 4:

4×5

4×5 = 20:

Answer:  20

The top stores based on sales and the top stores based on the cost of goods sold may not be the same, and several factors can cause differences like Marketing campaigns, Geographical location, Product mix.

A company’s performance can be measured in terms of sales and cost of goods sold.

Cost of goods sold is the expense incurred in manufacturing or acquiring products to be sold, while sales refer to the revenue generated from selling those goods. These two metrics are used by businesses to determine the success or failure of their operations.

A company's 5 largest/smallest stores based on sales may not be the same as its 5 largest/smallest based on the cost of goods sold. Because if sales are high, it doesn't necessarily imply that the cost of goods sold would be high.

When the cost of goods sold is low, profit margins are higher and when the cost of goods sold is high, profit margins are lower. In such circumstances, the top stores based on sales and the top stores based on cost of goods sold may vary.

The following are some of the factors that could cause differences:

Marketing Campaigns:

Large retail chains use marketing campaigns to raise brand awareness, attract new consumers, and increase sales. Since this is not a production cost, it does not affect the cost of goods sold and has no bearing on the company's manufacturing process.

Geographical location:

If a company has a number of shops located in different areas, their cost of goods sold may differ, depending on location, as transportation costs and import duties can have an effect on production expenses.

Product mix:

Businesses that sell a variety of items may have different costs of goods sold. Certain goods are sold at a higher margin, while others are sold at a lower margin. This ensures that the cost of goods sold differs significantly between various items.

To conclude, the top stores based on sales and the top stores based on the cost of goods sold may not be the same, and several factors can cause differences.

Learn more about the sales and the cost of goods from the given link-

https://brainly.com/question/24561653

#SPJ11

Answer:

(x+4)(x+3)

Step-by-step explanation:

x^2+4x+3x+12

take x out of each

x(x+4)+3x+12

take 3 out

x(x+4)+3(x+4)

(x+3)(x+4)

The approximate 95% confidence interval is (14.69, 18.51).

What is the confidence interval?

A confidence interval is a range of estimates for an unknown parameter in frequentist statistics. The 95% confidence level is the most popular, however other levels, such as 90% or 99%, are occasionally used when computing confidence intervals.

Here, we have

Given:

H₀ : μ = 15

H₁ : μ > 15

The test statistic t = ( x - μ) /(s/√n)

= (16.6 - 15)/(8√70/))

= 1.67

P-value = P(T > 1.67)

= 1 - P(T < 1.67)

= 1 - 0.9503

= 0.0497

At a 5% significance level, since the P-value < α (0.0497 < 0.05), so we should reject H₀.

So at a 5% significance level, there is sufficient evidence to conclude that employees spend more than 15 minutes on average on non-business activities.

The point estimate for the population mean (x) = 16.6

SE = (s/√n) = 8/√70 = 0.9562

At a 95% confidence interval, the critical value is t* = 1.995

The 95% confidence interval for the population mean is

x± t* (s/√n)

= 16.6 ± 1.995 × (8/√70)

= 16.6 ± 1.91

= 14.69, 18.51

Hence, the approximate 95% confidence interval is (14.69, 18.51).

To learn more about the confidence interval  from the given link

https://brainly.com/question/17097944

#SPJ4