Suppose​ that, for two​ populations, the distributions of the variable under consideration have the same shape. Further suppose that you want to perform a hypothesis test based on independent random samples to compare the two population means. In each​ case, decide whether you would use the pooled​ t-test or the​ Mann-Whitney test and give a reason for your answer.
a. You know that the distributions of the variable are normal.
b. You know that the distributions of the variable are not normal.
a. Choose the correct answer below.
A. Use the​ Mann-Whitney test. It is slightly more powerful than the pooled​ t-test when the conditions of normal distributions and equal standard deviations are met.
B. Use the pooled​ t-test, because the​ Mann-Whitney test cannot be used on normally distributed data.
C. Use the​ Mann-Whitney test, because the pooled​ t-test cannot be used on normally distributed data.
D. Use the pooled​ t-test. It is slightly more powerful than the​ Mann-Whitney when the conditions of normal distributions and equal standard deviations are met.
b. Choose the correct answer below.
A. Use the pooled​ t-test test, since the​ Mann-Whitney test cannot be used on data that are not normally distributed.
B. Use the​ Mann-Whitney test, since the distributions have the same​ shape, and the distributions are not normal.
C. Use the​ Mann-Whitney test, since the distributions have the same​ shape, and the pooled​ t-test cannot be used on data with equal standard deviations.
D. Use the pooled​ t-test test, since the distributions have the same​ shape, and the distributions are not normal.

Answer:

x = \(\frac{19}{12}\)     y = \((-\frac{9}{4} )\)   z = \(\frac{8}{3}\)    One solution for each variable.

Step-by-step explanation:

5x + y − z = 6

x + y + z = 2

12x + 4y = 10

The first thing we need to do is solve for x in the 3rd equation because it inly have 2 variables, x and y.

12x + 4y = 10   Subtract 4y from each side

12x + 4y - 4y = 10 - 4y

12x = 10 - 4y    Pull 2 out on the right side

12x = 2(5 - 2y)    Divide each side by 12

12x/12 = 2(5 - 2y)/12

x = 2(5 - 2y)/12

x = (5 - 2y)/6

Now we plug in our x value into the 2nd equation and solve for z

x + y + z = 2

\(\frac{5-2y}{6}\) + y + z = 2    Multiply each side by 6

6(\(\frac{5-2y}{6}\) + y + z) = 2 * 6

6(\(\frac{5-2y}{6}\) + y + z) = 12

5 - 2y + 6y + 6z = 12  Combine like terms

5 + 4y + 6z = 12   Subtract 5 from each side

5 - 5 + 4y + 6z = 12 - 5

4y + 6z = 7    Subtract 4y from each side

4y - 4y + 6z = 7 - 4y

6z = 7 - 4y  Divide each side by 6

6z/6 =  (7 - 4y)/6

z =  (7 - 4y)/6

Now we solved for z and x, so in the 1st equation we plug in x and z.

5x + y − z = 6

5(\(\frac{5-2y}{6}\)) + y - \(\frac{7-4y}{6}\) = 6     Multiply each side by 6

6*(5(\(\frac{5-2y}{6}\)) ) + 6y - 6(\(\frac{7-4y}{6}\)) = 6*6

6*(5(\(\frac{5-2y}{6}\)) ) + 6y - 6(\(\frac{7-4y}{6}\)) = 36

5(5 - 2y) + 6y - 7 - 4y = 36

25 - 10y + 6y - 7 - 4y = 36  Rearrange to make it easier to combine terms.

25 - 7 - 10y + 6y - 4y = 36

18 - 8y = 36   Subtract 18 from each side.

18 - 18 - 8y = 36 - 18

- 8y = 36 - 18

- 8y = 18  Divide each side by -8

- 8y/-8 = 18/- 8

y = 18/- 8

y = - 9/4

Now we plug our answer for y back into the 3rd equation and solve for the value of x.

12x + 4y = 10

12x + 4\((-\frac{9}{4} )\) = 10

12x - 9 = 10  Add 9 to each side

12x - 9 + 9 = 10 + 9

12x = 10 + 9

12x = 19 Divide each side by 12

12x/12 = 19/12

x = 19/12

Now we have a value for x and y so plug these into the 2nd equation to sovle for z.

x + y + z = 2

\(\frac{19}{12}\) + \((-\frac{9}{4} )\) + z = 2      We need to find the common denominator in order to add.

\((-\frac{9}{4} )\) * \(\frac{3}{3}\) = \(-\frac{27}{12}\)

\(\frac{19}{12}\) \(-\frac{27}{12}\) + z = 2

\(-\frac{8}{12}\) + z = 2   Add \(-\frac{8}{12}\) to each side

\(-\frac{8}{12}\)  \(+ \frac{8}{12}\) + z = 2 \(+ \frac{8}{12}\)

z =  2 \(+ \frac{8}{12}\)       Reduce   \(+ \frac{8}{12}\)  to \(\frac{2}{3}\)

z = 2 + \(\frac{2}{3}\)    To add find a common denominator.

\(2 * \frac{3}{3} = \frac{6}{3}\)

z = \(\frac{6}{3}\) + \(\frac{2}{3}\)

z = \(\frac{8}{3}\)

So there is 1 solution for each variable.

Answer:

Step-by-step explanation:

Answer:

960 foxes after 24 years

Step-by-step explanation:

given

y = 60 × \(4^{x}\) models the situation

there are 2 12- year periods in 24 years , then x = 2 , so

y = 60 × 4² = 60 × 16 = 960

there will be 960 foxes after 24 years

The requried equivalent fraction is 7/4. Option B is correct.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Fraction is defined as the number of compositions that constitutes the Whole.

here,
7/6 divided by 2/3
= 7/6 ÷ 2/3
= 7/6 × 3/2
= 7/4

Thus, the requried equivalent fraction is 7/4. Option B is correct.

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Answer:

C. Total Points = 10 • Months + 100

The completed table that has a slope of -5 is illustrated below.

Let's choose two points on the line: (0, y-intercept) and (1, y). We don't know the values of y-intercept or y yet, but we can use the slope (-5) to find them. The change in the y-coordinate between these two points is y - y-intercept, and the change in the x-coordinate is 1 - 0 = 1.

So we have:

slope = vertical change / horizontal change

-5 = (y - y-intercept) / 1

To solve for y, we can multiply both sides by 1:

-5 * 1 = y - y-intercept

Simplifying:

-5 = y - y-intercept

Now, we have one equation and two unknowns. But remember that the problem tells us to circle the y-intercept, so we can assume that it's a known value. Let's say the y-intercept is -3.

Substituting -3 for y-intercept, we have:

-5 = y + 3

Simplifying:

y = -8

So now we know that when x is 0, y is -3 (the y-intercept), and when x is 1, y is -8. We can use the same process to fill in the rest of the table.

If we choose the points (1, -8) and (2, y), we have:

slope = vertical change / horizontal change

-5 = (y - (-8)) / (2 - 1)

Simplifying:

-5 = y + 8

y = -13

So now we know that when x is 2, y is -13. We can continue this process for the remaining values of x to fill in the rest of the table.

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Answer:

\(xy=wz\)

Step-by-step explanation:

Given that:

Speed of Wilmer up the hill = \(y\) km/min

Time taken up the hill = \(x\) minutes

Speed of Wilmer down the hill = \(z\)  km/min

Time taken up the hill = \(w\) minutes

Distance can be calculated by multiplying the Speed with Time i.e.

The formula for distance is given as:

\(Distance = Speed \times Time\)

Distance up the hill = \(y\times x =xy\ kilometers\)

Distance down the hill = \(z\times w =wz\ kilometers\)

It is well known that, the distance up the hill and down the hill will be same.

Putting both the values equal, we get:

\(xy=wz\)

Answer:

xy=wz

Step-by-step explanation:

Answer:

\(\frac{x}{4}+ \frac{x}{6}=1\frac{1}{2}\)

Step-by-step explanation:

Speed is the ratio of distance traveled to the total time taken. It is given by the equation:

speed = distance / time.

Given that the distance to the park = x miles.

On his way to the park, he averages 4 miles per hour. Let the time taken be \(t_1\) therefore:

speed = distance / time.

4 = x /  \(t_1\)

\(t_1\) = x / 4

On his way home, he averages 6 miles per hour Let the time taken be \(t_2\) therefore:

speed = distance / time.

6 = x /  \(t_2\)

\(t_2\) = x / 6

The total trip takes 1 and one-half hours, therefore:

\(t_1+t_2=1\frac{1}{2}\\\\ substituting\ t_1 \ and\ t_2:\\\\\frac{x}{4}+ \frac{x}{6}=1\frac{1}{2}\)

Answer:

B

Step-by-step explanation:

Edg. 2020

Answer:

slope: -5

y-intercept: -3

Step-by-step explanation:

Answer:

Step-by-step explanation:

y=mx+b is the slope intercept form

m is your slope, b is your y-intercept

so we have y=-5x-3

your slope would be -5 and your y-intercept would be -3

The probability that one of the dice has the number 3 or less facing up given that the other has at least the number 3 facing up is 3/16.

To find the probability that one of the dice has the number 3 or less facing up given that the other has at least the number 3 facing up, we can use conditional probability.

First, let's consider the possible outcomes when rolling a pair of fair dice.

There are a total of 36 possible outcomes, since each die has 6 possible outcomes (numbers 1 to 6)

and there are 6 possibilities for the second die for each outcome of the first die.

Next, let's consider the outcomes where one of the dice has the number 3 or less facing up and the other has at least the number 3 facing up.

If the first die has the number 3 or less, there are 3 possible outcomes:

(1,3), (2,3), (3,3). If the second die has at least the number 3 facing up, there are 16 possible outcomes:

(3,1), (3,2), (3,3), (3,4), (3,5), (3,6), (4,3), (5,3), (6,3), (4,4), (4,5), (4,6), (5,4), (5,5), (5,6), (6,4), (6,5), (6,6).

Out of these 16 outcomes, 3 outcomes also satisfy the condition that the first die has the number 3 or less facing up: (3,3), (4,3), (5,3).

Therefore, the probability that one of the dice has the number 3 or less facing up given that the other has at least the number 3 facing up is 3/16.


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Answer:

the correct percentage is 28.5

Answer:

in explanation

Step-by-step explanation:

Input to output so for the input when it is 1=6 because it starts at 5 and then 8 what I mean is when the input comes out the output is going to be 3 more greater than last time.

So 1=6 so 6 is 5 more then

2 to 10=8 so 5 more went to 8 more.

Next is 3 and 14 so 3 more again because 8 + 3=11 so in that case that next number is 4 it will be 14 more

So 14 more than 4=18 and that is the output.

Also for the output it adds 4 for the numbers 6 + 4=10 + 4=14+ another 4=18.

And input is just plus 1.

Hope it helps have a great day:)

The four points on the lemniscate where the tangent is horizontal are (0, ±a/sqrt(2)) and (±sqrt(a^2 - x^2), ±sqrt(a^2 - x^2)), where x is a solution of the equation x(x^2 + y^2 - 2a^2) = 0

Explanation: The lemniscate is given by the equation (x^2 + y^2)^2 = 2a^2(x^2 - y^2), where a is a positive constant. To find the points on the lemniscate where the tangent is horizontal, we differentiate this equation with respect to x:

d/dx [(x^2 + y^2)^2] = d/dx [2a^2(x^2 - y^2)]

2(x^2 + y^2)(2x + 2y dy/dx) = 4a^2x

To find the values of x where the tangent is horizontal, we set the derivative dy/dx equal to zero, since a horizontal tangent has zero slope. This gives:

2(x^2 + y^2)(2x) = 4a^2x

(x^2 + y^2)(2x) = 2a^2x

x(x^2 + y^2 - 2a^2) = 0

Thus, we have two possible values of x: x = 0 and x^2 + y^2 = 2a^2. To obtain the corresponding values of y, we substitute these values of x into the equation of the lemniscate:

When x = 0, we have y = ±a/sqrt(2), corresponding to the two points (0, ±a/sqrt(2)) on the lemniscate where the tangent is horizontal.

When x^2 + y^2 = 2a^2, we have y = ±sqrt(2a^2 - x^2), corresponding to the two pairs of points on the lemniscate where the tangent is horizontal: (±sqrt(a^2 - x^2), sqrt(a^2 - x^2)) and (±sqrt(a^2 - x^2), -sqrt(a^2 - x^2)).

Therefore, the four points on the lemniscate where the tangent is horizontal are (0, ±a/sqrt(2)) and (±sqrt(a^2 - x^2), ±sqrt(a^2 - x^2)), where x is a solution of the equation x(x^2 + y^2 - 2a^2) = 0.

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To calculate the angles of a figure there are different strategies

In this case we can divide into different geometric shapes for example a square and a right triangle

The total expenses and sales at this point is $234

When she breaks even, the number of necklaces is 26

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

Initial amount for advertising and materials = $78

Necklace  = $6

Selling price = $9

Represent the total expense with f(x) and the total sales with g(x)

Where the number of necklace is x

So, we have the following representation

f(x) = 78 + 6x

g(x) = 9x

When she breaks even, we have

f(x) = g(x)

Substitute the known values in the above equation, so, we have the following representation

9x = 78 + 6x

This gives

3x = 78

Divide

x = 26

Substitute x = 26 in g(x) = 9x

g(x) = 9 * 26

Evaluate

g(x) = 234

In (a), we have

x = 26

This means that the number of necklaces is 26

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Answer:

n=2.56

Step-by-step explanation:

the probability that 50 or more requests are made for pop songs is  0.0967, or about 9.67%.

The binomial distribution is a probability distribution that describes the number of successes in a fixed number of independent trials, where each trial has the same probability of success.

We can use the binomial distribution to model this situation, where the number of trials is 120 (the number of people at the party), and the probability of success (making a request for a pop song) is 0.37. Let X be the number of requests for pop songs. Then:

The mean of X is μ = np = 120 x 0.37 = 44.4

The standard deviation of X is σ = sqrt(np(1-p)) = sqrt(120 x 0.37 x 0.63) = 4.32

To find the probability that 50 or more requests are made for pop songs, we can use the normal approximation to the binomial distribution, which applies when np >= 10 and n(1-p) >= 10.

Let Z be a standard normal random variable, then:

P(X >= 50) = P((X - μ)/σ >= (50 - μ)/σ)

= P(Z >= (50 - 44.4)/4.32)

= P(Z >= 1.2963)

= 1 - P(Z < 1.2963)

= 1 - 0.9033

= 0.0967

Therefore, the probability that 50 or more requests are made for pop songs is approximately 0.0967, or about 9.67%.

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Answer:

6

Step-by-step explanation:

2 times the difference of a number and 1 = 4 plus that number

In other to express the word problem Mathematically ; let the number = x

2(x - 1) = 4 + x

Expand

2x - 2 = 4 + x

Collect like terms

2x - x = 4 + 2

x = 6

Hence, the number is 6

Answer:

3 feet

Step-by-step explanation:

All 4 sides are equal so 12/4=3

Answer:

I) Y=5x

II) Y=50

III)X=12

Step-by-step explanation :

I) Y=5x

II) Y=5(10)

Y=50 when x=10

III)Y=5x

60=5x

X=60/5

X=12 when y=60

Hope this helps..

Answer:48.125

Step-by-step explanation:

Answer and Step-by-step explanation:

To graph the equation with a slope of -2 and a y-intercept of 6, we can use the slope-intercept form of the equation of a line, which is:

y = mx + b

where m is the slope and b is the y-intercept.

Substituting in the given values, we get:

y = -2x + 6

To graph this line, we can start by plotting the y-intercept, which is the point (0, 6). Then, we can use the slope to find additional points on the line. The slope of -2 means that for every increase of 1 in the x-direction, the y-value decreases by 2. So, we can plot another point by starting at the y-intercept and moving down 2 units and to the right 1 unit. This gives us the point (1, 4). We can continue this pattern to plot more points and draw the line.

Here's what the graph looks like:

Step-by-step explanation:

We are given the slope -2 and the y intercept -6. So we can create a linear equation using this data:

\(y=-2x+6\)

Now all we have to do is graph it.

(graph below)

To solve the expression -25 x (84/21) + (-3) x (-6), follow these steps:

Step 1: Perform the division inside the parentheses.
(84/21) = 4

Step 2: Replace the terms and rewrite the expression.
-25 x (4) + (-3) x (-6)

Step 3: Perform the multiplications.
-25 x 4 = -100
-3 x -6 = 18

Step 4: Rewrite the expression and perform the addition.
-100 + 18

Step 5: Calculate the final result.
-100 + 18 = -82

Your answer is -82.

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Answer: r+7

Whatever his age is now, we add 7 to it. So we simply add 7 to r getting r+7.

Example: Say he is 10 years old now

r = 10

r+7 = 10+7 = 17

meaning he will be 17 seven years from now

Answer:

The true statements are B, D, A

Step-by-step explanation:

A source of money that allows individuals to pay for goods and services later is called consumer credit and an advantage of this source of money is that there are no interest charges.

Consumer credit, also known as consumer debt, enables the consumers to incur debt or borrow money and to defer repayment of that money over time. It allows consumers to buy goods without having to pay for them in cash at the time of purchase. Examples of consumer credit include credit cards, student loans, etc. Among the advantages of using consumer credit is that there is no interest charge to borrow the money for a certain period of time until the due date.

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