based on historical data, the probability that a major league pitcher pitches a no-hitter in a game is about 1/1300. round your answers to three decimal places, if necessary. a. use the binomial distribution to determine the probability that in 650 games 0, 1, 2, or 3 no-hitters will be pitched. (find the separate probabilities of these four events.)

Answer:

b

Step-by-step explanation:

did the math?

8 is the best estimate of [tex]8\frac{1}{8}[/tex].

In simple words, the ratio of the two numbers is called a fraction.

Mixed fraction is a form of a fraction which is defined as the ones having a fraction and a whole number.

For example, 2 (1/3) is a mixed fraction, where 2 is the quotient, 1 is the remainder. So, a mixed fraction is a combination of a whole number and a proper fraction.

Step 1: Multiply the denominator with the whole number,

i.e. Multiply 8 with 8 in the given example, 8(1/8).

                                            8× 8  =64

Step 2: Add the numerator of the Fraction to the result in step 1. i.e.,             Add                                      1+ 64=65.

Step 3: Keep the Denominator same i.e. 8.

Step 4: The Improper fraction obtained is: 65/8.

Given number can be denoted as 8+[tex]\frac{1}{8}[/tex] = 8+0.15 = 8.15

So the number is nearest to 8 itself.

i.e. 8 is the best estimate.

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The given function models the amount in the account after t years is true.

What is compounded quarterly?

The process of calculating the interest earned quarterly on a fixed deposit or investment, computed based on the principal amount plus the interest earned for previous periods, is known as quarterly compounding.

Given:

Albert deposits $3250 in an account that earns 4.3% interest compounded quarterly.

P = $3250

r = 4.3% = 0.043

n = 4

t = t years

So, the function models the amount in the account after t years is,

[tex]A = P(1+\frac{r}{n})^n^t\\ A = 3250(1+\frac{0.043}{4})^4^t[/tex]

This equation is same as the given equation.

Hence, the given function models the amount in the account after t years is true.

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Complete question:

Complete question is attached below.

The line chart can be created using insert tab and then click line symbol in charts group.

Line chart is a type of chart with line visualization to show information of changing values over time.

Insert tab is tab in excel to insert object, symbol, chart, etc.

To create line chart,

I'm attaching a image for microsoft excel 365 version, your excel version may be different, but the line chart is still in the insert tab.

Thus, to create the line chart use insert tab and in chart group click line symbol.

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Answer:

3(13/2)+2y=9 the answer is y=-21/4

Statement on a population parameter that constitutes a statistical hypothesis. There's a chance it's true or not.

If the researchers predict a difference (or an impact) between two or more variables, this suggests that the observed pattern of the data is not the product of chance.

An equality declaration, such as =,, or, is present in a null hypothesis, which is a statistical hypothesis. A counterargument to the null hypothesis is an alternate hypothesis.  The likelihood of rejecting the null hypothesis when it is truly true is known as the level of significance. Error Type I is another name for it.

Determine the P-value for a Hypothesis Test

Find the P-value by choosing one of the following options: For a left-tailed test, P= (Area in left tail); For a right-tailed test, P= (Area in right tail); For a two-tailed test, P = 2. ( Area in tail of standardized test statistic)

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The best count on the tuition axis will be $5,000.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The senior counselor is making a histogram of the yearly cost of tuition of 20 colleges.

And, Tuition ranges from $5,000 to $51,000 a year.

Now,

Since, Tuition ranges from $5,000 to $51,000 a year.

And, There are 20 colleges.

Hence, We get;

The best count on the tuition axis will be $5,000.

Thus, he best count on the tuition axis will be $5,000.

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Proving  that the maximum spanning tree of g contains the widest paths between every pair of vertices .

Suppose now we were to add an edge from the widest path into the spanning tree in a place that it won't cause a cycle.

so every path between our two nodes must contain some edge between two previously unconnected nodes.

The weight of the edge we removed was equal to the width of the original path, and because the path was that every edge in the new path must have had more weight than that edge.

This means that our new spanning tree must have strictly more total weight than the original, which contradicts the definition of the original 'maximum' spanning tree.

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So option B. F(x)= 2x3/2- 3/2x² is the correct option of the given statement.

Using just the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables, a polynomial is an expression in mathematics made up of variables (also known as indeterminates) and coefficients.

The formulas that only contain addition, subtraction, multiplication, and non-negative integer exponents are those that can be used to identify the polynomials. The expressions with other operations will be non-polynomial expressions. Justify the expressions' lack of polynomial status.

A polynomial function is a function in an equation, such as the quadratic equation, cubic equation, etc., that only uses non-negative integer powers or only positive integer exponents of a variable. A polynomial with an exponent of 1 is, for instance, 2x+5.

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The vertex of the function g(x) = |x - 8| + 6 is (8, 6)

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

g(x) = |x - 8| + 6

The above equation is an absolute value function

An absolute value function represented as

y = a|x - h| + k

Where

Vertex = (h, k)

This means that the vertex is

Vertex = (8, 6)

Remove the x value

y = 6

Because the leading coefficient is positive, then the vertex is a minimum

i.e.

y ≥ 6

So, the range is y ≥ 6

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The best approximation to the solution of the system of equations is (2, 3)

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

Equation 1 is 5 x plus 2 y equals 16.

Equation 2 is x plus 3 y equals 12.

Rewrite the equations properly

So, we have the following representation

5x + 2y = 16

x + 3y = 12

Make x the subject in the second equation

So, we have

x = 12 - 3y

Substitute x =12 - 3y in the equation 5x + 2y = 16

So, we have

5(12 - 3y) + 2y = 16

Open the brakects

This gives

60 - 15y + 2y = 16

Evaluate the like terms

-13y = -44

Divide both sides by -13

y = 3.39

Substitute y = 3.39 in x = 12 - 3y

x = 12 - 3 * 3.39

Evaluate

x = 1.83

Approximate the solutions

x = 2 and y = 3

Hence, the solution is (2, 3)

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The width of the shape is 4.2 units

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

Surface Area = 54 square units

Length = 2 units

Height = 3 units

The surface area of the shape can be calculated using the following formula

Surface Area = 2 * (Length * Width + Length * Height + Width * Height)

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

2 * (2 * Width + 2 * 3 + Width * 3) = 54

Divide both sides by 2

So, we have

2 * Width + 2 * 3 + Width * 3 = 27

Subtract 6 from both sides

2 * Width + Width * 3 = 21

This gives

Width * 5 = 21

Divide both sides by 5

Width = 4.2

HEnce, the width is 4.2 units

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Answer:

------------------------------------

Average rate of change for this case is:

Answer:

The slope is [tex]\frac{-2}{3}[/tex]

Step-by-step explanation:

An order pair is in the form (x y).  The slope is the change in y over the change in x.  From the 2 points our y's are 2 and 4.  From the 2 points our x's are  1 and -2.  to find the change you subtract.

[tex]\frac{2-4}{1 - -2}[/tex] = [tex]\frac{-2}{1 + 2}[/tex] [tex]\frac{-2}{3}[/tex]

The expensive a car that you can afford is $42666.42.

What is interest rates?

The amount a lender charges a borrower is called an interest rate, and it is expressed as a percentage of the principal, or the loaned amount. Typically, a loan's interest rate is expressed as an annual percentage rate, or APR (APR).

Given that you can deposit $325 each month. The interest rates is 4.25%.

Future Value of an Ordinary Annuity

[tex]S = R[\frac{(1+i)^n-1}{i}][/tex]

where

S is the future value;

R is the periodic payment;

i is the interest rate per period;

n is the number of periods.

The value of R is $325, i = 0.0425/12 = 0.00354

n = (12 × 9) =108

The future value is

[tex]S = 325[\frac{(1+0.00354)^{108}-1}{0.00354}][/tex]

S = 42666.42

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Answer:

Step-by-step explanation:

it is C because 65 is a one Time thing and 30x means every month u rent it times the money.

The probability that the sample mean is less than 5, is 0.92135.

Let X1,X2,...,X32 be a random sample from an exponential distribution with a mean of 4.

We have to find an approximate probability that the sample mean is less than 5.

Let X = [tex]\frac{\Sigma_{i=1}^{n}x_{i}}{n}[/tex]

X = [tex]\frac{\Sigma_{i=1}^{32} x_{i}}{32}[/tex]

Then required probability is P(X<5).

Now we have to find the distribution of X where [tex]x_{i}[/tex]……. x_{32}.

Follow exponential with mean 4.

[tex]x_{i}[/tex]→exponent(λ=1/mean)

[tex]x_{i}[/tex]→exponent(λ=1/4)

[tex]x_{i}[/tex]→exponent(λ=0.25)

Now we have result:

If [tex]x_{1}[/tex] ………… x_{n} are exponential with α.

Then [tex]\Sigma{x_{i}}[/tex] has Gamma Distribution with (α=0.25, n=32)

Now we have result

X→G(α, λ) then c X→G(α/c, λ)

Here, we have

[tex]\frac{\Sigma x_{i}}{n}[/tex]→Gamma(α=0.25, n=32)

[tex]\frac{\Sigma x_{i}}{n}[/tex]→Gamma(α/(1/n), n)

[tex]\frac{\Sigma x_{i}}{n}[/tex]→Gamma(nα, n)

X→Gamma(32*0.25, 32)

X has Gamma distribution with α=8, λ=32.

Required probability is;

P(X<5) = [tex]\int_{0}^{5}f(x) dx[/tex]

P(X<5) =[tex]\int_{0}^{5}\frac{\alpha }{\sqrt{\lambda}}e^{-\alpha x}x^{\lambda-1} dx[/tex]

Now to approximate this probability using normal as

X-mean(X)/SD(X)  = N(0,1)

X→Gamma(α=8, λ=32)

E(X) = λ/α                                            Var(X)= λ/α^2

E(X) = 32/8                                          Var(X)= 32/(8)^2

E(X) = 4                                               Var(X)= 0.5

Now P(X<5)=P[{(X-E(X))/√Var(X)}<{ (5-4)/√0.5}]

P(X<5)=P[{z< 1/√0.5}]

P(X<5) = P(z<1.4142

From the normal probability table

P(X<5) = 0.92135

Hence, the probability that the sample mean is less than 5, is 0.92135.

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The value of f(-2) is -8 and the value of [tex]f(v+1)=\frac{3v+1}{|v+2|}[/tex] for the given function [tex]f(v)=\frac{3v-2}{|v+1|}[/tex].

Given function is

[tex]f(v)=\frac{3v-2}{|v+1|}[/tex]

To evaluate f(-2), we need to substitute v = -2 in the given function.

So, on substituting v = -2, we get

f(-2) = (3(-2) - 2)/|-2+1|

      = (-6 - 2)/|-1|

      = -8/1

Since we know that |-a| = a; we can write |-1| = 1.

Thus, f(-2) = -8

To evaluate f(v+1), we need to substitute v = v+1 in the given function.

So, on substituting v = v+1, we get

f(v+1) = (3(v+1) - 2)/|v+1+1|

        = (3v+3-2)/|v+2|

        = (3v+1)/|v+2|

Thus, f(v+1) = (3v+1)/|v+2|.

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The equation of the parabola that passes through the points (1,4) and (2,2) would be y = (-4)(x - 1.5)² + 3.

What is a parabola?

A parabola is defined as a collection of points such that the distance to a fixed point (the focus) and a fixed straight line (the directrix) are equal. But it's probably easier to remember it as the U-shaped curved line created when a quadratic is graphed.

To find the equation of the parabola that passes through the points (1,4) and (2,2), we can use the formula for the general form of the equation of a parabola:

y = a(x - h)² + k

where (h,k) is the vertex of the parabola, and a is a nonzero constant that determines the direction and shape of the parabola.

To find the values of a, h, and k that will give us the equation of the parabola that passes through the points (1,4) and (2,2), we can use the following steps:

Find the coordinates of the vertex of the parabola. The vertex of the parabola is the point where the parabola changes direction. In this case, the parabola changes direction at the midpoint of the two given points, which is the point (1.5,3).

Substitute the coordinates of the vertex into the formula for the general form of the equation of a parabola: y = a(x - h)² + k.

Substitute the coordinates of one of the given points into the equation to find the value of a. For example, if we substitute the coordinates of the point (1,4) into the equation, we get:

4 = a(1 - 1.5)² + 3

4 - 3 = a(-0.5)²

1 = a(-0.25)

a = -4

Substitute the values of a, h, and k into the formula for the general form of the equation of a parabola to find the equation of the parabola that passes through the points (1,4) and (2,2):

y = (-4)(x - 1.5)² + 3

Hence, the equation of the parabola that passes through the points (1,4) and (2,2) would be y = (-4)(x - 1.5)² + 3.

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The pattern that this system detects is a four-digit number that is divisible by 3.

1. The system starts by taking an input of a four-digit number.

2. It then checks if the last digit of the input number is divisible by 3.

3. If it is, the system continues to check if the sum of the remaining three digits is divisible by 3.

4. If this turns out to be true, the system will output a signal indicating that the input number is divisible by 3.

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Therefore the solution to the given problem is  the each of the congruent base angles is 70°

In Euclidean geometry, an angle is the figure generated by two rays, called the sides of the angle, sharing a common termination, called the vertex of the angle. Angles created by two rays are in the plane where the rays are located. The intersection of two planes also forms angles. We refer to these as dihedral angles.

Here,

As the triangle is an isosceles triangle therefore it will have 2 same angles

thus,

Sum of the 3 angles of a triangle=180°

Vertex angle =40°

Sum of two congruent angles=180°–40°=140°

Measure of each base angle=70°

Therefore the each of the congruent base angles is 70°

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The correct answer is (B) 99.73%..

For a process in control, we expect 99.73% of the points on a process control chart to fall within the upper control limit (UCL) and the lower control limit (LCL).

A process control chart is a tool used in statistics and quality control to monitor and analyze a process over time. It consists of a line graph that plots the measured values of a process variable, such as the temperature or weight of a product, over time. The UCL and LCL are horizontal lines that are drawn on the graph at a predetermined distance above and below the average value of the process variable.

The expected percentage of points within the UCL and LCL is determined by the chosen level of statistical significance and the distribution of the process variable. In this case, the expected percentage of points within the UCL and LCL is 99.73%.

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Complete Question:

For process in control, we expect Pfo of the points on process control chart to fall within the UCL and the LCL:

A)0.27

B)99.73

C)100

The number of aerobic classes would be 7 to make the cost of both gyms the same in the first month.

What are linear equations?

First-order equations include linear equations. In the coordinate system, linear equations are defined for lines. A linear equation in one variable is one in which there is a homogeneous variable of degree 1 (i.e., only one variable). Multiple variables may be present in a linear equation. Linear equations in two variables, for example, are those in which the linear equation contains two variables.

Let x= number of months, and a=no of aerobic classes.

Let Gym A charge a $10 membership fee plus $20.25 per month plus $5.50 per aerobics class.

So we get the equation:

y= 10+20.25x+5.50a

y=30.25+5.50a ------------ as (x=1)

Next, for Gym B, it charges $46 per month plus $3.25 per aerobics class.

So the equation is:

y=46x+3.25a

y=46+3.25a ------------------as (x=1)

Now since we need to find the number of aerobic classes, we equate both equations:

30.25+5.50a = 46+3.25a

2.25a = 15.75

a = 7

Therefore, there must be 7 aerobic classes that would make the cost of both gyms to be the same.

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There are total percentage of 56% of red gumballs and 44% of blue gumballs in 4000 gumball machine.

Percentage is a relative figure used to denote hundredths of any quantity. Since one percent (symbolized as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified.

Given,

Total gumballs in the machine = 4000

Red gumballs in the machine = 2240

Blue gumballs in the machine = 1760

Percentage of each gumballs,

Percentage of red gumballs,

Value/Total × 100%

2240/4000 × 100

0.56 × 100

56%

Percentage of blue gumballs,

1760/4000 × 100%

0.44 × 100%

44%

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Answer:

  73.3%

Step-by-step explanation:

You want to know the percentage adopted when 4 of 15 were not adopted.

The percentage can be found by multiplying the fraction by 100%. The fraction of dogs adopted was 11 out of 15, or 11/15. The percentage is ...

  11/15 × 100% ≈ 73.3%

About 73.3% of the dogs were adopted.

According to Ritchie et al., a typology is a set of ordered categories occurring at discrete positions along a continuum is a True statement. often helps researchers gain insight into the underlying dynamics of the items being studied.

A typology is an organized classification of distinct types of entities, such as people, places, or objects. It is used to create order and structure out of seemingly unrelated items and to identify relationships between them. According to Ritchie et al. (2015), a typology is a set of ordered categories occurring at discrete positions along a continuum. This allows for a more comprehensive understanding of the items being classified, as it allows for further comparison and contrast between the categories. This type of ordered structure often helps researchers gain insight into the underlying dynamics of the items being studied.

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Given the following sample of three data points: 3, 6, 9, calculate the (estimated) standard error for the sample mean. Round to 3 decimal places.

s = √((3 - 8)² + (6 - 8)² + (9 - 8)²) / (3 - 1) = 4

2. Calculate the standard error of the sample mean:

SE = s / √n = 4 / √3 = 2.45

3. Round the standard error to three decimal places:

SE = 0.567

The standard error of the sample mean can be calculated by first finding the standard deviation of the sample (s). This is done by taking the sum of the squared differences between each data point and the mean, divided by the number of data points minus one. In this case, the standard deviation is 4. The standard error is then calculated by dividing the standard deviation by the square root of the number of data points, which is 3. The result is 2.45, which can be rounded to 0.567.

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The graph of this inequality shows a region to the left at x = 12.

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

Given, An inequality (1/2)x < 6.

Multiplying both sides of the inequality by 2 we get,

2×(1/2)x < 2×6.

x < 12.

The graph of this inequality shows a dotted line at x = 12 and the region is left side to it.

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Hence, the earnings per share for Aware is [tex]0.25[/tex] $.

What is the ratio?

It is a term that is used to compare two or more numbers. It is used to indicate how big or small a quantity is when compared to another. In a ratio, two quantities are compared using division.

Here given that,

The stock of Aware is trading at $[tex]4.90[/tex]. The price-earnings ratio is [tex]4[/tex] times earnings.

So,

The price earning is four times the stock of aware trading is

[tex]4.90(4)=19.6[/tex] $

So, the earnings per share for Aware is

[tex]\frac{4.90}{19.6}=0.25[/tex] $

Hence, the earnings per share for Aware is [tex]0.25[/tex] $.

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The good practice to protect the classified information is labelling them with markings.

In the question ,

we have been asked about the good practice that can help in protecting the classified information .

we know that ,

the term Classified means when something is arranged in classes. and

the term Labeling means that when something is assign to a category.

So , the best practice is to Ensure the proper labeling by appropriately marking all the classified material and when required, sensitive material.

Therefore , the best practice is Ensure proper labeling by appropriately marking all classified material .

The given question is incomplete , the complete question is

What is a good practice to protect classified information ?

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Pedro earns $5.1 per hour more than Oliver

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

The hourly rate of Pedro is calculated using

Hourly rate = Amount earned/Number of hours

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

Hourly rate = 521.40/22

Evaluate

Hourly rate = 23.7

Using the points on Oliver's graph

The hourly rate of Oliver is calculated using

Hourly rate = Amount earned/Number of hours

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

Hourly rate = 186/10

Evaluate

Hourly rate = 18.6

The difference between these rates is

Difference = 23.7 - 18.6

Evaluate the difference

Difference = 5.1

Hence, the difference is $5.1

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