9) all of the following are required of a binomial distribution except: a) each trial has exactly two outcomes. b) the number of trials is fixed. c) all trials have the same probability of success. d) there must be at least 30 trials.

The rate of change for the given table is 1.

For a function y = f(x), the rate of change in any interval (a, b) is:

R = (f(b) - f(a))/(b - a)

Here we can use any pair of values in the table, because it clearly is linear, so we can use the first two.

(4, 9) and (9, 14)

The rate of change is:

r = (14 - 9)/(9 - 4) = 5/5 = 1

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according to the question the probabilities of event can be P(s)= 14/2525, P(C) = 6/2525, P(S and C) = 5/2525, P(S or C) = 3/505

Probability theory, a subfield of mathematics, quantifies the likelihood that an event is going to happen or that a statement is true. The probability for an event is a number between 0 and 1, where 0 roughly denotes how probable the event is to occur and 1 denotes certainty. A probability is a numerical representation of the likelihood that a certain event will occur. In addition to numbers from 0 to 1, probability values can also be stated as percentages between 0% and 100%. the fraction of an entire set of equally likely possibilities that result in a certain occurrence out of all possible outcomes, expressed as a ratio.

given,

To solve the problem, we can use the formula:

P(A and B) equals P(A) plus P(B) minus P(A or B)

where P(A) is the probability of event A, P(B) is the probability of event B, and P(A or B) is the probability of either A or B occurring (including the case where both A and B occur).

P(S): the probability that a student writes steak is 14/2525.

P(C): the probability that a student writes chicken is 6/2525.

The likelihood that a student would write steak plus chicken equals 5/2525.A or B. P(A and B) Equals P(A) +P(B), which -P(P(S or C))

P(S or C): the probability that a student writes steak or chicken can be calculated as:

P(S or C) = P(S) + P(C) - P(S and C)

= (14/2525) + (6/2525) - (5/2525)

= 15/2525

= 3/505

Therefore, the answers to the questions are:

P(S) = 14/2525

P(C) = 6/2525

P(S and C) = 5/2525

P(S or C) = 3/505

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Use STDDEV.s function to find standard deviation and AVERAGE function to find mean years of maturity.

To answer this question, you would need to open the provided Excel file and input the data into a spreadsheet. Once the data is inputted, you can use Excel's built-in functions to calculate the mean and standard deviation.

To calculate the mean years to maturity, you would use the AVERAGE function and select the column of years to maturity data. The result will give you the average years to maturity for the sample of 40 corporate bonds.

To calculate the standard deviation, you would use the STDEV.S function and select the column of yield data. This will give you the sample standard deviation for the yield data.

Overall, your spreadsheet should have columns for years to maturity and yield, with 40 rows of data for each bond. The mean years to maturity and sample standard deviation for yield can then be calculated using Excel functions.

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The sample mean years to maturity for corporate bonds:

Type the following formula and press Enter:
=AVERAGE(A1 : A40).

The sample standard deviation:

Press Enter: = STDEV.S(A1 : A40).

To calculate the sample mean and sample standard deviation for years to maturity of the 40 corporate bonds, follow these steps:
Open the Excel online file provided.
Assuming that the years to maturity data is in column A, click on an empty cell (let's say B1) to find the sample mean.

Type the following formula and press Enter:
=AVERAGE(A1 : A40).

This will calculate the mean of the years to maturity for the 40 corporate bonds.
To find the sample standard deviation, click on another empty cell (let's say B2) and type the following formula and press Enter:
=STDEV.S(A1 : A40)
This will calculate the sample standard deviation of the years to maturity for the 40 corporate bonds.
Now, you should have both the sample mean years to maturity and the sample standard deviation in cells B1 and B2 respectively.

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The most appropriate measure to compare the frequency of hypertension in white and non-white populations is the relative risk.

To compare the frequency of hypertension between two populations, the most appropriate measure is the prevalence ratio or prevalence odds ratio. The prevalence ratio is the ratio of the prevalence of hypertension in the exposed group (e.g., non-white population) to the prevalence of hypertension in the unexposed group (e.g., white population). It is a measure of the strength of association between the exposure and the outcome.

The prevalence odds ratio is the ratio of the odds of hypertension in the exposed group to the odds of hypertension in the unexposed group. It is a commonly used measure in epidemiology and can be used to estimate the relative risk of hypertension in the exposed group compared to the unexposed group.

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The question "What are the prices of the computers?" is not a statistical question.

A statistical question is a question that can be answered by collecting and analyzing data. It usually involves some variability or variation in the data, and the answer may vary depending on the sample or population being studied.

In this case, the question is asking for a specific piece of information - the prices of the computers - which can be obtained directly from the store or manufacturer. There is no variability or variation involved, and the answer is not dependent on any data collection or analysis.

Therefore, this question is not a statistical question.

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Yes, a triangle can be constructed with sides of 2/3, 4/5, and 1/2. the value of x is 17.

Since a triangle is a polygon that has three sides and three vertices. It is one of the basic figures in geometry.

To determine if a triangle can be constructed, we need to check if the sum of the two smaller sides is greater than the largest side.

In this case, we can see that

2/3 + 1/2 > 4/5,

2/3 + 4/5 > 1/2,

1/2 + 4/5 > 2/3,

Therefore, a triangle can be formed.

The value of x can be calculated as;

45 + 68 + 3x + 16 = 180

3x = 51

x = 17

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Option b is correct.

The null hypothesis in the chi-square test of hypothesis states that the two categorical variables under consideration are independent of each other, meaning that there is no relationship or association between them.

In the chi-square test of hypothesis, the null hypothesis states that the variables under consideration are independent. That is, there is no relationship between the two variables being studied.

The chi-square test is a statistical method used to determine if two categorical variables are associated or independent. Categorical variables are those that take on values that are categories or labels.

For example, gender (male or female) or educational level (high school, college, graduate school) are categorical variables.

The chi-square test determines the expected frequency of each category based on the null hypothesis, which assumes independence between the two variables.

The observed frequency is then compared to the expected frequency, and if the difference is significant enough, it suggests that the null hypothesis should be rejected, and the two variables are considered to be associated or dependent.

Therefore, in summary, the null hypothesis in the chi-square test of hypothesis states that the two categorical variables under consideration are independent of each other, meaning that there is no relationship or association between them.

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As a result of probability, there is a 1/1326 chance of drawing a red 4 and selecting a queen of diamonds.

A measure of an event's likelihood is probability. It is represented by a number between 0 and 1, where 0 denotes the impossibility of an event and 1 denotes its certainty.

For instance, you can get either heads or tails when you flip a coin. Given that there is only one way to receive heads and a total of two outcomes, the chance of receiving heads is half (or 0.5).

Since there are two red fours in a deck of 52 cards, the likelihood of drawing one is one in every 52 draws.

Since there are 51 cards in the deck after drawing the red 4, the likelihood of getting a queen of diamonds is 1/51 if you decide to keep the red 4.

Since the outcomes of these two occurrences are interdependent (the first event's outcome influences the second event's outcome), we may multiply their probabilities to determine the likelihood that both events will occur:

(2/52)× (1/51) = 1/1326

As a result, there is a 1/1326 chance of drawing a red 4 and selecting a queen of diamonds.

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The surface area of the composite solid is 162 unit²

The area occupied by a three-dimensional object by its outer surface is called the surface area.

The composite solid has 6 faces . The area of each face is calculated as follows;

Face 1

area = 5×7 = 35 units²

face 2

area = 1/2bh + l×b

= 1/2 ×3×4 + 3×4

= 6+12 = 18units²

face 3 = face 2

area = 18units²

face 4

area = 3× 7 = 21units²

face 5

area = 4×7

= 28units²

face 6

area = 3×7 + 3×7

= 21+21 = 42units²

Therefore total surface area = 42+28+21+18+18+35

= 162 units²

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Mean = 13

Variance = 36.2

Independent variable is the variable that is being purposely changed by the researcher in an experiment to observe its effect on the dependent variable.

It is the variable that is manipulated or altered to test a hypothesis or research question.

The independent variable is the variable that you purposely change in an experiment to observe the effect it has on the dependent variable.

It is also known as the manipulated variable because it is the one that is manipulated or altered by the researcher in order to study the effect it has on the dependent variable.
Investigate the effect of fertilizer on plant growth, we would manipulate the amount of fertilizer that the plants receive. In this case, the amount of fertilizer would be the independent variable because it is the variable that we are purposely changing.

The dependent variable, in this case, would be the plant growth because it is the variable that we are observing and measuring to see if there is any change.
It is important to note that the independent variable is not always the only variable that can affect the dependent variable.

There may be other variables, known as extraneous variables, that could also have an effect on the dependent variable.

In order to control for these variables, researchers will often use control variables or hold them constant in their experiments.

This allows them to isolate the effect of the independent variable on the dependent variable.

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1745 packages of tennis balls can be made from 5235 balls.

Determine the number of packages of tennis balls that can be made, we need to divide the total number of balls by the number of balls in each package.

5235 tennis balls and each package contain 3 balls.

Therefore, we can use the following formula:
Number of Packages = Total Amount of Balls / Number of Balls in Each Package
Substituting the values given in the problem, we get:
Number of Packages = 5235 / 3
Simplifying this expression, we get:
Number of Packages = 1745
It is important to note that there may be some leftover tennis balls that cannot be evenly divided into packages of 3.

Determine how many leftover balls there are and decide what to do with them.

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The given 3D model is a trapezoidal pyramid.

A pyramid is a 3D polyhedron having three or more triangle-shaped faces that meet above the base and a polygonal base. The point above the base is referred to as the apex, while the three sides are referred to as faces. The base and apex are joined to form a pyramid. To distinguish them from the base, the triangular sides are also also referred to as lateral faces. In a pyramid, the apex, which creates the triangle face, is connected to each base edge.

Hence, the given 3D model is a trapezoidal pyramid.

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Answer: Option A) A 1-unit increase in the independent variable, number of lanterns, means a 5-unit increase in the dependent variable, total price.

The correct statement that describes the relationship between the number of lanterns purchased and the total price is Option A

A 5-unit increase in the independent variable, number of lanterns, means a 1-unit increase in the dependent variable, total price.

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This is because the graph shows a slope of 5/1, meaning that for every 5 lanterns purchased, the total price increases by 1 unit.

According to unitary method, there are 10 30¢ cards and 8 35¢ cards in the box, which adds up to a total of $5.80.

Let's start by defining our units. In this case, our units are the number of 30¢ cards and the number of 35¢ cards. We know that the box of cards is being sold for $5.80, which means the total value of all the cards in the box is $5.80. We can use this information to set up an equation:

0.30x + 0.35y = 5.80

where x is the number of 30¢ cards and y is the number of 35¢ cards.

Next, we are given the information that the number of 30¢ cards is six more than one half the number of 35¢ cards. Using the unitary method, we can set up an equation that relates the number of 30¢ cards to the number of 35¢ cards:

x = 0.5y + 6

Now we can use this equation to eliminate x from our first equation:

0.30(0.5y + 6) + 0.35y = 5.80

Simplifying this equation gives:

0.15y + 1.80 + 0.35y = 5.80

0.50y = 4.00

y = 8

So there are 8 35¢ cards in the box. We can use the unitary method again to find the number of 30¢ cards:

x = 0.5y + 6

x = 0.5(8) + 6

x = 10

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Formula:

98% Confidence Interval = (Mean - (2*Standard Deviation/√n), Mean + (2*Standard Deviation/√n))

98% Confidence Interval = ($775 - (2*$110/√45), $775 + (2*$110/√45))

98% Confidence Interval = ($735.56, $814.44)

The radius of the circle with a circumference of 15 ft is approximately

7.5 ft.

We have,

The circumference of a circle is the distance around its boundary. It is calculated by multiplying the diameter of the circle by π (pi), which is approximately 3.14159.

The formula for the circumference of a circle is:

Circumference = 2 π radius

To find the radius of a circle, we can rearrange the formula and solve for the radius:

Radius = Circumference / (2 π)

In this case, the given circumference is 15 ft.

Plugging this value into the formula:

Radius = 15 ft / (2 π)

Simplifying further:

Radius ≈ 7.5 ft

Therefore,

The radius of the circle with a circumference of 15 ft is approximately

7.5 ft.

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Mambo needs to save R2,322.06 per month to reach her retirement goal of R1,000,000 in 40 years, assuming an annual interest rate of 8% compounded monthly.

Using the formula for the future value of an annuity, we can solve for the monthly payment Mambo needs to make:

[tex]FV = P * [(1 + r/n)^{(nt)} - 1]/(r/n)[/tex]

where FV is the future value, P is the monthly payment, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.

Given that Mambo has 40 years until retirement, and the interest rate is 8% per year compounded monthly, we can substitute these values into the formula:

[tex]FV = 1,000,000 \\P = ?\\r = 0.08\\n = 12\\t = 40 \\1,000,000 = P * [(1 + 0.08/12)^(12*40) - 1]/(0.08/12)[/tex]

Solving for P, we get:

P = 2,322.06

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--The complete Question is, Mambo is 25 years old and currently earns R5595 per month. She wants to retire at age 65 and wishes to have R1,000,000 by then. Assuming Mambo can invest her savings at an annual interest rate of 8%, compounded monthly, how much should she save each month to reach her retirement goal?--

1. 1001 (in base 2) - 111 (in base 2) = 2 (in base 2).

2. 313 (in base 4) - 123 (in base 4) = 210 (in base 4).

3. 234 (in base 5) - 12 (in base 5) = 222 (in base 5).

What is arithmetic sequence?

An arithmetic sequence is a sequence of numbers in which each term after the first is found by adding a fixed constant number, called the common difference, to the preceding term.

To perform the subtractions in different bases, we need to convert the numbers to the same base and then subtract them.

1. 1001 (in base 2) - 111 (in base 2):

First, we need to align the two numbers by adding leading zeros to the second number:

1001

0111

0010

Therefore, 1001 (in base 2) - 111 (in base 2) = 2 (in base 2).

2. 313 (in base 4) - 123 (in base 4):

Again, we need to align the two numbers by adding leading zeros to the second number:

313

123

210

Therefore, 313 (in base 4) - 123 (in base 4) = 210 (in base 4).

3. 234 (in base 5) - 12 (in base 5):

Once again, we need to align the two numbers:

234

012

222

Therefore, 234 (in base 5) - 12 (in base 5) = 222 (in base 5).

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Answer:

y- coordinate = 4

Step-by-step explanation:

consider a right triangle formed by the x- axis, the radius (hypotenuse) of 5 and a vertical line drawn to the x- axis from the point ( 3, - )

using Pythagoras' identity in the right triangle

3² + y² = 5²

9 + y² = 25 ( subtract 9 from both sides )

y² = 16 ( take square root of both sides )

y = [tex]\sqrt{16}[/tex] = 4

the y- coordinate of the point is 4 , that is (3, 4 )

Answer:

y= coordinate 4

right triangle formed by the x- axis, the radius (hypotenuse) of 5 and a vertical line drawn to the x- axis from the point ( 3, - )

using Pythagoras' identity in the right triangle

3² + y² = 5²

9 + y² = 25 ( subtract 9 from both sides )

y² = 16 ( take square root of both sides )

y =

16

16

= 4

the y- coordinate of the point is 4 , that is (3, 4 )

The differential of the function Z is -4e⁻⁴ˣcos(4πt) - 4πsin(4πt)e⁻⁴ˣ

To find the differential function of Z = e⁻⁴ˣ cos(4πt), we will use the product rule of differentiation. The product rule states that the derivative of the product of two functions is equal to the first function multiplied by the derivative of the second function plus the second function multiplied by the derivative of the first function.

Let's apply the product rule to our function Z:

First, we differentiate the first function e⁻⁴ˣ with respect to x. The derivative of e⁻⁴ˣ is -4e⁻⁴ˣ.

Next, we differentiate the second function cos(4πt) with respect to t. The derivative of cos(4πt) is -4πsin(4πt).

Therefore, the differential function of Z is:

dZ/dt = -4e⁻⁴ˣcos(4πt) - 4πsin(4πt)e⁻⁴ˣ

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If the decision variables for a problem have to be integers, rounding the linear programming optimal solution for that problem will always result in a feasible solution.

However, this solution may not always be optimal. It may result in either a feasible or infeasible solution depending on the problem constraints.

Rounding may also result in an optimal solution if the optimal solution happens to already have integer values for the decision variables. Therefore, rounding may result in a feasible and optimal solution or just a feasible solution but not necessarily always optimal.

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To make the probability greater than 0.12 that there are at least two people born on the same day of the week, we need at least 21 people chosen at random.

To solve the problem, we can use the concept of the pigeonhole principle.

The probability that no two people share the same birth day of the week is given by:

P(No two people share the same birth day of the week) = 7/7 x 6/7 x 5/7 x … x [(7-(n-1))/7]

Here, n is the number of people chosen at random. The first person can be born on any day of the week. The probability that the second person is born on a different day of the week is 6/7. The probability that the third person is born on a day of the week different from the first two is 5/7, and so on.

The probability that at least two people share the same birth day of the week is

P(At least two people share the same birth day of the week) = 1 - P(No two people share the same birth day of the week)

We want to find the smallest value of n for which P(At least two people share the same birth day of the week) is greater than 0.12.

1 - P(No two people share the same birth day of the week) > 0.12

P(No two people share the same birth day of the week) < 0.88

Using a calculator or a spreadsheet, we can find that n = 21 is the smallest value that satisfies this inequality. Therefore, we need at least 21 people chosen at random to make the probability greater than 0.12 that there are at least two people born on the same day of the week.

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Natalie used for constructing the bar graph is type of writing utensil.

The representation of numerical data using rectangles (or bars) of equal width and varying height is known as a bar graph.

Depending on the distribution and nature of the data, various types of charts or graphs, such as scatter plots, histograms, or box plots, would typically be used to represent the mentioned quantitative variables, such as the price, volume, and weight of each writing utensil.

Natalie probably used the variable "type of writing utensil" for the bar graph based on the information provided. This is due to the fact that a bar graph is a type of chart that uses rectangular bars to represent categorical data. Each bar represents a distinct category or group.

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The constant of proportionality is $8.40

The constant of proportionality is a value that relates two quantities that are proportional to each other. It is represented by the letter k and is found by dividing the dependent variable by the independent variable. In this case, the constant of proportionality is $8.40 for the given data set.

According to the given information:

To find the constant of proportionality, we can use any two data points from the table and plug them into the equation y = kx.

Let's use the first and second data points: (0.75, $6.30) and (2.5, $21.00).

We can set up the equation as:

$6.30 = k(0.75)

Solving for k, we get:

k = $6.30/0.75 = $8.40

Now, we can check our work by using another data point. Let's use the third data point: (4, $33.60).

Plugging in the values, we get:

$33.60 = k(4)

k = $33.60/4 = $8.40

Since we get the same value for k, we can be confident that our answer is correct.

Therefore, the constant of proportionality is $8.40.

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If Taylor is proving the Pythagorean theorem.  Taylor can use the diagram to prove the Pythagorean theorem by: A. Taylor could set the area of a square with side length a + b equal to the sum of the areas of the 4 triangles and the square with side length c.

To prove the Pythagorean theorem, we want to show that in a right triangle with legs a and b and hypotenuse c, the square of the hypotenuse c^2 is equal to the sum of the squares of the legs a^2 + b^2.

From the given diagram, we can see that we have a square with side length a+b, which is divided into 4 congruent right triangles and a smaller square with side length c. Each of the 4 triangles has legs a and b, which are also the legs of the right triangle we want to prove the theorem for. The smaller square with side length c has an area equal to c^2, which is the square of the hypotenuse of the right triangle.

The area of the square with side length a+b is (a+b)^2 = a^2 + 2ab + b^2. The area of one of the congruent right triangles is (1/2)ab, so the sum of the areas of the 4 triangles is 2ab. Therefore, the sum of the areas of the 4 triangles and the smaller square is:

a^2 + 2ab + b^2 + c^2

But this is also equal to the area of the larger square with side length a+b, which is (a+b)^2. So we have:

a^2 + 2ab + b^2 + c^2 = (a+b)^2

Expanding the right-hand side gives:

a^2 + 2ab + b^2 + c^2 = a^2 + 2ab + b^2

Canceling the common terms on both sides gives:

c^2 = a^2 + b^2

This is the Pythagorean theorem, which we have proved using the given diagram.

Therefore, option A is the correct answer.

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Answer:   C

Step-by-step explanation:

hope this helped

Answer:

22√5

Step-by-step explanation:

√20=√4x5 = √4 x √5 = 2√5

√45 = √9 x 5 = √9 x √5 = 3√5

√80 = √16 x 5 = √16 x √5 = 4√5

4√20 = 6 √45 - √80 = 4(2√5) + 6(3√5)- 4√5

8√5 + 18√5 - 4√5 = 22√5

So its 22√5

Answer:

[tex]22 \sqrt{5} [/tex]

Step-by-step explanation:

the explaination is avaliable in the picture i sent you

and please give me branliest