1. At a party there are four different types of soft drinks and from each type there are seven cans available. How many drinks have to be chosen so that we are guaranteed to have three cans chosen from the same type of soft drink? Explain your answer in details.

Once you have obtained the area, you can round it to four decimal places as needed.

To find the area of a shaded region under the standard normal curve, you can use a standard normal distribution table or a statistical software package, such as Excel or R.

If using a standard normal distribution table, you need to first determine the z-scores that correspond to the boundaries of the shaded region. Then, you look up the corresponding probabilities in the standard normal distribution table and subtract them to find the area of the shaded region.

If using a statistical software package, you can use the functions or commands that calculate the area under the standard normal curve between the boundaries of the shaded region.

Once you have obtained the area, you can round it to four decimal places as needed.

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Plot the points (0, -20) and (10, 5) on a graph, and draw a line connecting them to represent the gross sales function S(x) = -20 + 2.5x.

To draw the graph of the gross sales function S(x) = -20 + 2.5x, we need to plot two points: the S-intercept and another point.

First, let's find the S-intercept. The S-intercept is the value of S when x = 0. Substituting x = 0 into the function, we get:

S(0) = -20 + 2.5(0) = -20

So the S-intercept is -20, which means that when the production facility produces 0 curtains, they will not make any sales.

Now, let's find another point. We can choose any value of x and calculate the corresponding value of S. Let's choose x = 8 (you can choose any other value if you prefer). Substituting x = 8 into the function, we get:

S(8) = -20 + 2.5(8) = 0

So when the production facility produces 8 curtains, their gross sales will be $0. This means that the break-even point is at x = 8, where the revenue from selling the curtains covers the production costs.

To plot the graph, we can use these two points: the S-intercept (-20, 0) and the point (8, 0). The graph should look like this:

```
        |
        |
        |
        |         *
        |      *
        |   *
        |*_______
        0   8    x-axis
              S-axis
```

The x-axis represents the number of curtains produced, and the S-axis represents the gross sales in hundreds of dollars. The graph shows that the gross sales function is a linear function that increases as the number of curtains produced increases. The break-even point is at x = 8, and after that, the production facility starts making a profit.

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Answer:

Deon drove 270 miles.

Let x be the number of miles driven.

The total cost is 20.95 + 0.74x = 221.49

Subtracting 20.95 from both sides gives 0.74x = 200.54

Dividing both sides by 0.74 gives x = 270 miles

So the answer is 270

Answer:

271 miles

Step-by-step explanation:

The equation to find the total cost is

C = 20.95 + .74 m  where m is the number of miles

221.49 = 20.95 +.74m

Subtract 20.95 from each side

221.49 -20.95 = 20.95-20.95 +.74m

200.54 = .74m

Divide each side by .74

200.74/.74 = m

271 = m

Answer: 82

Step-by-step explanation:

               82

            35   47

       15     20     27

   7      8        12    15

2     5      3        9        6

puzzle two numbers add up to one above

2 numbers under a number add up to make that number

2+5=7

5+3=8 etc

Why don't you and Julián eat? Why not have something to eat?

How old am I? You have come nine years.

In the first sentence, Mario's answer is using the auxiliary verb "have" to suggest that they should eat something. The phrase "have something to eat" is a common way to express this idea.

In the second sentence, Mario's answer is using the verb "come" in the sense of "reach" or "attain". So, he is saying that his little sister has reached the age of nine years old. This is a colloquial way of answering the question about age, rather than saying "you are nine years old".

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Full Question: Mario's little sister is very curious and always wants to know why people do certain things. Complete Mario's answers with have and come. 1. Why don't you and Julián eat? Why not ______ hungry. 2. How old am I? You ____ nine years

We first calculate the z-score:

z = (0.517 - 0.61) / sqrt((0.61 * (1 - 0

To solve these probability questions, we need to use the central limit theorem, which states that if we have a large enough sample size, the sampling distribution of the sample proportion will be approximately normal, regardless of the population distribution.

For a sample of size n, the mean of the sample proportion (p) is equal to the population proportion (p), and the standard deviation of the sample proportion (σp) is equal to:

σp = sqrt((p(1-p))/n)

Using this information, we can standardize the sample proportion using z-score:

z = (p - p) / σp

Then, we can use the standard normal distribution table (such as Appendix A Statistical Tables) to find the probabilities.

a) What is the probability that the sample proportion is greater than 0.643?

We first calculate the z-score:

z = (0.643 - 0.61) / sqrt((0.61 * (1 - 0.61)) / 656) = 3.17

Using the standard normal distribution table, the probability of getting a z-score greater than 3.17 is approximately 0.0008.

Therefore, the probability that the sample proportion is greater than 0.643 is 0.0008.

b) What is the probability that the sample proportion is between 0.60 and 0.647?

We need to calculate the z-scores for both values:

z1 = (0.60 - 0.61) / sqrt((0.61 * (1 - 0.61)) / 656) = -1.23

z2 = (0.647 - 0.61) / sqrt((0.61 * (1 - 0.61)) / 656) = 1.79

Using the standard normal distribution table, the probability of getting a z-score between -1.23 and 1.79 is approximately 0.8438.

Therefore, the probability that the sample proportion is between 0.60 and 0.647 is 0.8438.

c) What is the probability that the sample proportion is greater than 0.607?

We first calculate the z-score:

z = (0.607 - 0.61) / sqrt((0.61 * (1 - 0.61)) / 656) = -0.73

Using the standard normal distribution table, the probability of getting a z-score greater than -0.73 is approximately 0.7665.

Therefore, the probability that the sample proportion is greater than 0.607 is 0.7665.

d) What is the probability that the sample proportion is between 0.57 and 0.597?

We need to calculate the z-scores for both values:

z1 = (0.57 - 0.61) / sqrt((0.61 * (1 - 0.61)) / 656) = -4.13

z2 = (0.597 - 0.61) / sqrt((0.61 * (1 - 0.61)) / 656) = -1.08

Using the standard normal distribution table, the probability of getting a z-score between -4.13 and -1.08 is approximately 0.0361.

Therefore, the probability that the sample proportion is between 0.57 and 0.597 is 0.0361.

e) What is the probability that the sample proportion is less than 0.517?

We first calculate the z-score:

z = (0.517 - 0.61) / sqrt((0.61 * (1 - 0

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The images of the coordinates of the quadrilateral are A'(x, y) = (0, 0), B'(x, y) = (2, - 5), C'(x, y) = (- 5, - 5) and D'(x, y) = (- 3, 0). (Correct choice: B)

In this problem we have the coordinates of the four ends of a quadrilateral, whose images must be found by rotation formula:

P'(x, y) = (x · cos θ - y · sin θ, x · sin θ + y · cos θ)

Where:

If we know that A(x, y) = (0, 0), B(x, y) = (5, 2), C(x, y) = (5, - 5), D(x, y) = (0, - 3) and θ = 270°, then the coordinates of the images are, respectively:

A'(x, y) = (0 · cos 270° - 0 · sin 270°, 0 · sin 270° + 0 · cos 270°)

A'(x, y) = (0, 0)

B'(x, y) = (5 · cos 270° - 2 · sin 270°, 5 · sin 270° + 2 · cos 270°)

B'(x, y) = (2, - 5)

C'(x, y) = (5 · cos 270° + 5 · sin 270°, 5 · sin 270° - 5 · cos 270°)

C'(x, y) = (- 5, - 5)

D'(x, y) = (0 · cos 270° + 3 · sin 270°, 0 · sin 270° - 3 · cos 270°)

D'(x, y) = (- 3, 0)

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The equation of the linear relationship that represents the table given is: y = 6x + 4.

The linear relationship between x and y can be represented as an equation which can be expressed in slope-intercept form as:

y = mx + b [m is the slope and b is the y-intercept]

The y-intercept of the equation is the value of y, when x = 0, which is b = 4.

Using any two points, (0, 4) and (2, 16), we have:

Slope (m) = change in y / change in x = 16 - 4 / 2 - 0

Slope (m) = 12/2 = 6

Substitute m = 6 and b = 4 into y = mx + b:

y = 6x + 4.

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In most countries, including the United States, income tax is a tax imposed on an individual's income by the government. The amount of income tax paid typically depends on the amount of income earned and any deductions or credits that apply to the individual's tax situation.

A typical pay stub includes information such as the employee's gross pay (the amount earned before any deductions), the net pay (the amount received after deductions), and various taxes and deductions taken out of the employee's pay, such as federal income tax, state income tax, Social Security tax, and Medicare tax.

To complete the missing pieces on a pay stub, you will need to know the employee's gross pay and any deductions that apply to their tax situation. The amount of income tax withheld from an employee's pay depends on several factors, including their tax bracket, filing status, and any exemptions or deductions they are eligible for.

It's important to note that tax laws and regulations vary by country and even by state or province within a country, so the specific rules and calculations for income tax can differ depending on your location.

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3. Each of the following pay stubs represents two different employees. Use your understanding of income tax to complete the missing pieces.

LILY'S PAY STUB

GROSS INCOME

$865.00

FEDERAL TAXES

$110.32

=

MEDICARE (6%)

FEDERAL TAXES

$80.32

MEDICARE (6%)

SOCIAL SECURITY (1%)

SOCIAL SECURITY (1%)

$6.65

NET INCOME

MARK'S PAY STUB

GROSS INCOME

NET INCOME

Answer: 9.2

Step-by-step explanation:

Pythagorean theorem = A^2+B^2=C^2

x^2+6^2=11^2…. Putting the equation into math-way. com

x=9.2159444

Rounded 9.2

There are multiple expressions that equal 4 x 10^6, but here are some possible options: Note that all of these expressions simplify to [tex]4 * 10^6.[/tex]

A group of words coupled with the operations +, -, x, or form an expression, such as 4 x 3 or 5 x 2 3 x y + 17. A statement with an equals sign, such as 4 b 2 = 6, asserts that two expressions are equal in value and is known as an equation. Monomial Expression is one of the three primary categories of algebraic expressions.

Binary Expression. Expression of a polynomial.

Expressions:

4,000,000

[tex]40 * 10^5\\400 * 10^4\\0.4 * 10^7\\0.04 * 10^8[/tex]

Note that all of these expressions simplify to [tex]4 * 10^6[/tex].

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Answer:

3.8

Step-by-step explanation:

Using a 0.05 significance level, a hypothesis test was conducted to determine if polygraph results are correct less than 80% of the time. So null hypothesis is not rejected by test results due to insufficiency of evidence to support the claim.

Null hypothesis, The polygraph results are correct 80% of the time or more.

Alternative hypothesis, The results given by polygraph are correct as they are less than 80% of the time.

Since the sample size is large and the success-failure condition is satisfied, we can use the normal distribution as an approximation of the binomial distribution. we can calculate the test statistic from formula

z = (p - P) / √(P(1-P)/n)

where p is the sample proportion of correct results, P is the hypothesized proportion of correct results (0.80), and n is the sample size.

p = 77/99 = 0.7778

z = (0.7778 - 0.80) / √(0.80(1-0.80)/99) = -0.6318

Using a standard normal distribution table, the p-value is found to be 0.2646.

Since the p-value (0.2646) is greater than the significance level (0.05), we fail to reject the null hypothesis. There is not enough evidence to conclude that the polygraph results are correct less than 80% of the time.

Therefore, we can conclude that at a 0.05 significance level, there is not enough evidence to support the claim that such polygraph results are correct less than 80% of the time.

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1. The volume of the box is given by:

Volume = length x width x height = 9 in. x 2 in. x 12 in. = 216 cubic inches

So, the answer is 216 cubic inches.

2. The surface area of the box is given by:

Surface Area = 2lw + 2lh + 2wh = 2(9)(12) + 2(9)(2) + 2(2)(12) = 216 + 36 + 48 = 300 square inches

So, the answer is 300 square inches.

3. The surface area of the cereal box is 300 sq. in.

If cardboard costs $0.01 per square inch, then the cost of manufacturing this cereal box would be:

300 sq. in. x $0.01/sq. in. = $3.00

Therefore, the correct answer is -3.00.

4. The volume of the rectangular prism is given by:

Volume = length x width x height = 9 in. x 2 in. x 12 in. = 216 cubic inches

To find the surface area of the sphere, use the formula:

A = 4πr²

Plugging in r = 3.7 in.:

A = 4π(3.7 in.)² ≈ 172.11 square inches

Rounding this to the nearest square inch gives us:

A ≈ 172 square inches

5. The rectangular prism with dimensions of 9 in. x 2 in. x 12 in. would cost less in packaging.

6. The volume of the cylinder is given by:

Volume = πr²h = 390 cubic inches

Solving for r:

r ≈ 4 inches

Therefore, the approximate radius of the cylinder should be 4 inches to hold the same volume of cereal as the rectangular prism.

7. The surface area of the travel-size cereal box is given by:

Surface Area = 2lw + 2lh + 2wh = 2(3)(1.5) + 2(3)(4.5) + 2(1.5)(4.5) = 9 + 27 + 13.5 = 49.5 square inches

To find the length of each side in the cube with the same surface area, we use the formula:

Surface Area of Cube = 6s²

49.5 = 6s²

s ≈ 2.2 inches

So, the length of each side in the cube would be approximately 2.2 inches.

8. The rectangular prism with dimensions of 3 in. x 1.5 in. x 4.5 in. holds more volume than the cube with a side length of approximately 2.2 inches.

9. Some factors that a cereal company may consider in creating their packaging include how well it stacks for shipping and storing on shelves, how easy it is to hold and pour, and how much advertising space there is on the front of the design.

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The values of the variables for the parallelogram include the following;

In Mathematics and Geometry, a parallelogram is a geometrical figure (shape) and it can be defined as a type of quadrilateral and two-dimensional geometrical figure that has two (2) equal and parallel opposite sides.

In this context, we can reasonably infer and logically deduce that this parallelogram has both pairs of opposite sides parallel to each other and the opposite angles (vertical angles) are equal and congruent.

By CPCTC, the variable x can be calculated as follows;

15x = 45°

x = 45°/15

x = 3

Since the diagonals of a parallelogram are perpendicular to each other, we have:

m<1 = 3y - 9 = 90

3y = 99

y = 33

15x = 18z

15(3) = 18z

45 = 18z

z = 45/18

z = 2.5

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

a.  The probability distribution of the test statistic is approximately a standard normal distribution.

b. The p-value for the test of  factors that affect the prevalence of tuberculosis among intravenous drug users is 0.0202.  

c. We can conclude that there is a statistically significant difference between the two groups in terms of their proportions of positive skin test results.

d. The 95% confidence interval does not contain zero, so there is a statistically significant difference between the two groups in terms of their proportions of positive skin test results.

To estimate the common value of p assuming that the population proportions of positive skin test results are equal, we can compute the pooled proportion:

p-hat = (x1 + x2) / (n1 + n2)

= (24.7 + 17.4) / (97 + 161)

= 0.195

where x1 and x2 are the number of individuals with positive skin test results in the two groups, and n1 and n2 are the sample sizes.

a. To test the null hypothesis that the proportions of intravenous drug users who have positive tuberculin skin test results are identical for those who share needles and those who do not, we can use a two-sample z-test for proportions. The test statistic is:

z = (p1 - p2) / sqrt(phat * (1 - phat) * (1/n1 + 1/n2))

where p1 and p2 are the sample proportions, phat is the pooled proportion, and n1 and n2 are the sample sizes.

Plugging in the values, we get:

z = (0.247 - 0.174) / sqrt(0.195 * (1 - 0.195) * (1/97 + 1/161))

= 2.05

The probability distribution of the test statistic is approximately a standard normal distribution, since the sample sizes are large enough (both n1 and n2 are greater than 30).

b. The p-value for the test is the probability of observing a z-value of 2.05 or more extreme under the null hypothesis. From a standard normal distribution table or calculator, we find that the p-value is approximately 0.0202 (or 0.0404 for a two-tailed test).

Since the p-value is less than the significance level of 0.05, we reject the null hypothesis and conclude that the proportions of intravenous drug users who have positive tuberculin skin test results are not identical for those who share needles and those who do not.

c. To construct a 95% confidence interval for the true difference in proportions, we can use the formula:

(p1 - p2) ± z* sqrt(phat * (1 - phat) * (1/n1 + 1/n2))

where z is the critical value for a 95% confidence interval from a standard normal distribution (z = 1.96).

Plugging in the values, we get:

(0.247 - 0.174) ± 1.96 * sqrt(0.195 * (1 - 0.195) * (1/97 + 1/161))

= 0.073 ± 0.090

Therefore, we can be 95% confident that the true difference in proportions of intravenous drug users who have positive tuberculin skin test results between those who share needles and those who do not is between 0.073 and -0.073 (which can be written as an absolute value of 0.073).

d.  We can infer that there is a statistically significant difference between the two groups in terms of the proportions of positive skin test results because the interval does not contain zero.

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It would take Kenny 5 seconds to run up the flight of stairs between the escalators without using the escalator.

Let's assume that the escalator has a certain height and Kenny needs to climb the same height by running up the flight of stairs between the escalators.

Let's say that the height of the escalator is h and the speed of Kenny's running is s (measured in units of height per second).

When Kenny runs up the escalator, he covers the same height h in two ways:

by running up the stairs, which takes him t seconds

by using the help of the moving escalator, which takes him 30 seconds

The speed of Kenny's running up the escalator is therefore:

s + h/30

Similarly, when Kenny runs up just the stairs, he covers the same height h in two ways:

by running up the stairs, which takes him t seconds

by running up the up escalator, which takes him 6 seconds

The speed of Kenny's running up the stairs is therefore:

s + h/6

Since the distances covered in both cases are the same, we have:

t(s + h/30) = h

t(s + h/6) = h

Dividing the second equation by the first one, we get:

(s + h/6)/(s + h/30) = 30/t

Simplifying and solving for t, we get:

t = 5 seconds

Therefore, it would take Kenny 5 seconds to run up the flight of stairs between the escalators without using the escalator.

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the probability that 7 to 9 women in the sample will hold the opinion is 0.1790

What is frequency distribution?

The gathered data is arranged in tables based on frequency distribution. The information could consist of test results, local weather information, volleyball match results, student grades, etc. Data must be presented meaningfully for understanding after data gathering. A frequency distribution graph is a different approach to displaying data that has been represented graphically.

a. To find the probability that at least 5 women in the sample will hold the opinion, we can use the complement rule and find the probability that less than 5 women will hold the opinion, and then subtract it from 1.

P(at least 5) = 1 - P(0) - P(1) - P(2) - P(3) - P(4)

where P(k) is the probability of k women holding the opinion in the sample.

Using the binomial probabilities table or technology, we can find:

P(at least 5) = 1 - P(0) - P(1) - P(2) - P(3) - P(4)

= 1 - 0.2037 - 0.3293 - 0.2836 - 0.1565 - 0.0626

= 0.9643

So the probability that at least 5 women in the sample will hold the opinion is 0.9643 (rounded to four decimal places).

b. To find the probability that 7 to 9 women in the sample will hold the opinion, we can use the binomial probabilities table or technology to find the individual probabilities of 7, 8, and 9 women holding the opinion, and then add them up.

P(7 to 9) = P(7) + P(8) + P(9)

Using the binomial probabilities table or technology, we can find:

P(7 to 9) = P(7) + P(8) + P(9)

= 0.1223 + 0.0440 + 0.0127

= 0.1790

So the probability that 7 to 9 women in the sample will hold the opinion is 0.1790.

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The width of the box is approximately 8.5 inches.

We have,

The equation to find the width of the box, w, is:

V = l × w × h

where V is the volume of the box, l is the length, w is the width, and h is the height.

Substituting the given values, we get:

357 = 10.5 × w × 4

Simplifying, we get:

357 = 42w

Dividing both sides by 42, we get:

w = 357/42

w ≈ 8.5

Therefore,

The width of the box is approximately 8.5 inches.

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Answer: i think it b

Step-by-step explanation:

b

The argument is not valid.

The argument commits a fallacy known as the false dilemma or false dichotomy, which presents only two options when there may be more. In this case, the argument assumes that if Superman does not prevent evil, then he must either be impotent or malevolent.

However, there could be other reasons why Superman does not prevent evil, such as a lack of knowledge or resources.

Furthermore, the argument assumes that if Superman exists, then he must either prevent evil or be impotent/malevolent, but this assumption is not necessarily true. It is possible for Superman to exist and not have the ability or inclination to prevent all evil.

Therefore, the conclusion that Superman does not exist does not necessarily follow from the premises. The argument is not valid.

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The surface area of the paper towel is determined as 212.1 in².

The surface area of the cylinder is calculated as follows;

S.A = 2πr (r + h )

where;

The radius of the cylinder = 5 in /2 = 2.5 in

The total surface area of the cylinder is calculated as follows;

S.A = 2πr (r + h )

S.A = 2π x 2.5 in ( 2.5 in + 11 in )

S.A = 212.1 in²

Thus, the surface area of the cylinder is equal to surface area of the paper towel.

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The distance from the corner of Oak and Ridgewood to the corner of Oak and Savannah is given as follows:

276 yd.

Suppose we have a triangle in which:

The lengths and the sine of the angles are related as follows:

[tex]\frac{\sin{A}}{a} = \frac{\sin{B}}{b} = \frac{\sin{C}}{c}[/tex]

Then the ratio for this problem is given as follows:

sin(38º)/d = sin(42º)/300

The distance is obtained as follows:

d = 300 x sine of 38 degrees/sine of 42 degrees

d = 276 yd.

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To show that the functions f(x) = x, g(x) = x - 1, and h(x) = x + 3 are linearly dependent, we need to find a non-zero linear combination of the three functions that equals zero.

Let's assume that a, b, and c are constants such that:

a*f(x) + b*g(x) + c*h(x) = 0

Substituting in the given functions, we get:

a*x + b*(x - 1) + c*(x + 3) = 0

Simplifying this equation, we get:

(a + b + c) * x + (-b + 3c) = 0

For this equation to hold true for all x, we must have:

a + b + c = 0

-b + 3c = 0

This is a system of two equations with three unknowns, which means that we have infinitely many solutions. For example, we could choose a = 1, b = -2, and c = 1, and the equation would hold true. Therefore, we have shown that the functions f(x) = x, g(x) = x - 1, and h(x) = x + 3 are linearly dependent.

Now, let's show that the functions f(x) = x^2, g(x) = x - 1, and h(x) = x + 3 are linearly independent.

We need to show that there are no non-zero constants a, b, and c such that:

a*f(x) + b*g(x) + c*h(x) = 0

Substituting in the given functions, we get:

a*x^2 + b*(x - 1) + c*(x + 3) = 0

This equation holds true for all x if and only if its coefficients are all zero. Therefore, we need to solve the system of three equations:

a = 0

-b + c = 0

3c = 0

The first equation tells us that a must be zero. The third equation tells us that c must be zero. Substituting c = 0 into the second equation, we get:

-b = 0

Therefore, we must have b = 0 as well.

Since a, b, and c are all zero, we have shown that the functions f(x) = x^2, g(x) = x - 1, and h(x) = x + 3 are linearly independent.

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The sample variance computed differently from the population variance is the calculation in the numerator is different and the calculation in the denominator is different

The sample variance is computed differently from the population variance in that the calculation in the numerator is different and the calculation in the denominator is different. Specifically, in the numerator, the sample variance formula includes a computation for SS (sum of squared deviations from the mean), while the population variance formula does not.

Additionally, in the denominator, the sample variance formula divides by n-1 (sample size minus one) instead of by the denominator (population size) in the population variance formula.

The sample variance is computed differently from the population variance in the following ways:

1. The calculation in the numerator is the same for both sample and population variance, as they both involve computing the sum of squared differences (SS) between each data point and the mean.

2. The calculation in the denominator is different. For the population variance, the denominator is the number of data points in the population (N), while for the sample variance, the denominator is the number of data points in the sample (n) minus 1.

So, the correct answer is: the calculation in the denominator is different (Option C).

Here are the formulas for each variance:

Population variance: σ² = Σ(x - μ)² / N
Sample variance: s² = Σ(x - X)² / (n-1)

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The  inequality equation is 15x - 120 ≥ 75.

The number of hours Alonzo must work to achieve his goal is 13 hours.

From the given question, let x = the number of hours Alonzo must work to achieve his goal.

Our inequality equation becomes the following;

15x - 120 ≥ 75

Now solve for x;

15x ≥ 75 + 120

15x ≥ 195

x ≥ 195/15

x ≥ 13

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Lily would need 40.64 centimeters of copper wire for her experiment.

Given data ,

We may use the conversion factor that 1 inch is equivalent to 2.54 centimeters to convert 16 inches to centimeters .

From the unit conversion ,

1 inch = 2.54 inches

Consequently, 16 inches is equivalent to :

40.64 centimeters are equal to 16 inches at 2.54 centimeters per inch.

Hence , Lily would thus want 40.64 centimeters of copper wire for her experiment.

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The probability of rolling an integer is

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

Sides = 6

Integer sides = 6

using the above as a guide, we have the following:

P(Integer) = Integer sides/Total sides

So, we have

P(Integer) = 6/6

Evaluate

P(Integer) = 1

Hence, the probability is 1

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The Laplace transform of tJo(t) is s / (s^2 - 1)^(3/2).

To find the Laplace transform of tJo(t), we can use the following formula:

L{t^n f(t)} = (-1)^n F^(n)(s)

where F(s) is the Laplace transform of f(t) and F^(n)(s) denotes the nth derivative of F(s) with respect to s.

Using this formula with f(t) = Jo(t), we have:

L{tJo(t)} = -d/ds [ L{Jo(t)} ]

We can find L{Jo(t)} by using the formula for the Laplace transform of Jo(t):

L{Jo(t)} = 1 / sqrt(s^2 - 1)

Taking the derivative of both sides with respect to s, we get:

d/ds [ L{Jo(t)} ] = d/ds [ 1 / sqrt(s^2 - 1) ]

= (-1/2) (s^2 - 1)^(-3/2) (2s)

= -s / (s^2 - 1)^(3/2)

Substituting this result back into our original equation, we get:

L{tJo(t)} = -d/ds [ L{Jo(t)} ]

= -d/ds [ 1 / sqrt(s^2 - 1) ]

= s / (s^2 - 1)^(3/2)

Therefore, the Laplace transform of tJo(t) is s / (s^2 - 1)^(3/2).

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Step-by-step explanation:

12 nickels out of (8+13+12+22 = 55) coins    12/55 chance of nickel

   now there are only 54 coins   and 13 are dimes  :   13/54 chance of dime

12/55 * 13/54 = 26/495 = .0525 chance

Answer:

Bellow

Step-by-step explanation:

(2x³ + 4x³ - ) - (-7x² + x -5)

= 6x³ + 7x² - x + 5

(-6y² + 2y - 2) - (y² - 3y +10)

= -6y² + 2y - 2 - y² + 3y - 10

= -7y² + 5y - 12

(5x² -4x +11) + (-12x² +4x -1)

= -7x² + 0x + 10

= -7x² + 10

(10x² -5x +3) - (8x² + 6x + 4)

= 10x² - 5x + 3 - 8x² - 6x - 4

= 2x² - 11x - 1

I hope this helps!

The expressions are s

6x³ + 7x² - x + 5

-7y² + 5y - 12

-7x² - 8x + 10

2x² - 11x -1

Algebraic expressions are defined as expressions that are composed of coefficients, variables, constants, terms and factors.

These algebraic expressions are also made up of some arithmetic operations. These operations are;

From the information given, we have that;

1. (2x3 + 4x3 - ) - (-7x2 + x -5)

expand the bracket

6x³ + 7x² - x + 5

2. (-6y2 + 2y - 2) - (y2 - 3y +10)

expand the bracket

-6y² + 2y -2 - y² + 3y - 10

collect the like terms

-7y² + 5y - 12

3. (5x2 -4x +11) + (-12x2 +4x -1)

expand the bracket

5x² - 4x + 11 - 12x² - 4x - 1

-7x² - 8x + 10

4. (10x2 -5x +3) - (8x2 + 6x + 4)

expand the bracket

2x² - 11x -1

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