public transportation and the automobile are two methods an employee can use to get to work each day. samples of travel times recorded for each method are shown. times are in minutes.

Answers

Answer 1

a. The sample mean time to get to work for public transportation is 31.3 minutes and the sample mean time to get to work for the automobile is 32.1 minutes.

b. The sample standard deviation for public transportation is 4.2 minutes and the sample standard deviation for the automobile is 1.7 minutes.

c. Based on the results from parts (a) and (b), public transportation should be preferred. The sample mean time for public transportation is slightly lower than the sample mean time for the automobile, and the sample standard deviation for public transportation is much lower than the sample standard deviation for the automobile.

This indicates that public transportation is more consistent and reliable than the automobile, and therefore should be preferred as a method of transportation to get to work each day.

Complete question:

Public transportation and the automobile are two methods an employee can use to get to work.

each day. Samples of times recorded for each method are shown. Times are in minutes.

Public Transportation: 28 29 32 37 37 33 25 29 32 41 34

Automobile: 29 31 33 32 34 30 31 32 35 33

a. Compute the sample mean time to get to work for each method.

b. Compute the sample standard deviation for each method.

c. On the basis of your results from parts (a) and (b), which method of transportation should be preferred? Explain.

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Related Questions

Y=1+sinx/1-sinx find the derivative of this problem

Answers

The derivative of the problem is dy/dx = (2cosx)/(1-sinx)²

How to find the derivative of the function?

The given function is Y=1+sinx/1-sinx

d/dx (u/v) = [u (dy/dx) - v (dv/dx) ] / v²or less formerly

(u/v) =[ [(v (du) = u(dv)] / v²

(Remember the rule in word; " vdu minus udv all over v squared)

So with Y=1+sinx/1-sinx then,

Let u = 1+sin x ⇒du/dx= cos x and

v = 1-sin x⇒dv/dx = -cos x

Then, [d/dx(u/v) = u(dy/dx) - u(dv/dx)] / v²

dy/dx = [(1-sinx)(cosx) - (1+sinx)(-cosx)] / (1-xin x)²

This implies that dy/dx =[ cosx - sin x +cosx +sin xcosx] / (1-sinx)²

Therefore, dy/dx = (2cos x)/(1-sinx)²

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Question 15
Divide £65 in the ratio 11:2
Questic
Divide

Answers

Answer:

55 and 10

I hope this helps

the length of a shadow of a tree is feet when the angle of elevation of the sun is . approximate the height of the tree.

Answers

The approximate height of the tree is feet.

The exact height of the tree cannot be determined without additional information. However, a rough estimate can be made using the following formula:

Height of Tree = Length of Shadow / Tan(Angle of Elevation of Sun)

In this case, the estimated height of the tree would be: Length of Shadow / Tan( ) = feet/tan( ).

The formula to calculate the height of a tree is:

Height of Tree = Length of Shadow * Tan(Angle of Elevation of the Sun)

In this case, Length of Shadow = feet and Angle of Elevation of the Sun

Therefore, the height of the tree can be calculated as follows:

Height of Tree = feet * Tan( )

Height of Tree = feet * 0.839

Height of Tree = feet

Therefore, By  the angle of elevation the approximate height of the tree is feet.

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One factor of the function f(x) = x^3 - 6x^2 + 11x - 6 is (x-3)

Answers

The quotient of the polynomial division is x^2 - 3x + 2.

How to determine the quotient of the division?

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

f(x) = x^3 - 6x^2 + 11x - 6

Factor = (x-3)

One way to find the other factors of the function f(x) = x^3 - 6x^2 + 11x - 6 is to divide the polynomial by (x-3) and see what the quotient is.

To do this, we have

Quotient = f(x)/Factor

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

Quotient = (x^3 - 6x^2 + 11x - 6)/(x - 3)

Using a graphing calculator, we have

Quotient = x^2 - 3x + 2

Hence, the quotient is x^2 - 3x + 2

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Complete question

One factor of the function f(x) = x^3 - 6x^2 + 11x - 6 is (x-3)

Determine the quotient of the polynomial and the factor

Each cement block is 9 centimeters thick and each clay block is 5 centimeters thick. Xavier made a stack of 17 blocks that was 113 centimeters thick. How many of each type of block did Xavier use?

Answers

Using a system of equations, the number of each type of block Xavier used is as follows:

7 cement blocks10 clay blocks.

What is a system of equations?

A system of equations is two or more equations solved simultaneously or concurrently.

A system of equations is also described as simultaneous equations.

Let a represent the number of cement blocks and b the number of clay blocks.

9a + 5b = 113 ... Equation 1

a + b = 17 ... Equation 2

Multiply Equation 2 by 9:

9a + 9b = 153 ... Equation 3

Subtract Equation 1 from Equation 3:

9a + 9b = 153

-

9a + 5b = 113

4b = 40

b = 10

In Equation 2, substitute b = 10:

a + b = 17

a + 10 = 17

a = 7

Thus, Xavier used 7 cement blocks and 10 clay blocks to make the stack of 17 blocks that was 113 centimeters thick.

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Ina study, the sample is chosen by dividing the population into voting precincts, and sampling everyone in the precincts selected What is the sampling method? Simple Random Systematic Stratified Cluster Convenience

Answers

The sample is chosen by dividing the population into voting precincts, and sampling everyone in the precincts selected is cluster sampling.

As stated in the question statement, the sample was obtained by randomly selecting precincts from which to sample the entire population, which is known as cluster sampling.

A population is divided into clusters, such as districts or schools, and some of these clusters are randomly chosen as your sample via the probability sampling technique known as cluster sampling. In a perfect world, each cluster would be a tiny reflection of the whole population.

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HELPPPPPPPPPPPPPPPPPPPPPPP

Answers

Answer:

12π m²

Step-by-step explanation:

We are interested in calculating the area bounded by the given arcs .

we know that if [tex]\theta[/tex] is the angle subtended at the centre by the arc , then ; the area is given by ,

[tex]\longrightarrow Area =\dfrac{\theta}{360^o}\times \pi r^2 \\[/tex]

here we have ,

[tex]\theta = 120^o[/tex][tex] r = 6m [/tex]

Therefore on substituting the respective values, we have;

[tex]\longrightarrow Area =\dfrac{120^o}{360^o}\times \pi (6m)^2 \\[/tex]

Simplify,

[tex]\longrightarrow Area =\dfrac{1}{3}\times \pi \times 36m^2 \\[/tex]

[tex]\longrightarrow \underline{\underline{ Area = 12\pi \ m^2}} \\[/tex]

And we are done!

Answer: The result is 12π m²

Step-by-step explanation:

To solve, we must find the Area of the circle, for this we must do the following:

[tex] \: \sf{Area} = \cfrac{ \sf{θ} }{360 {}^{ \circ} } * \sf{\pi r {}^{2} }[/tex]

Once having the above, we must extract the results that we have to put in the fraction, where:

[tex] \theta = 120 {}^{ \circ} [/tex][tex]\sf{r = 6m}[/tex]

Once we have the above, we must substitute the respective values...

[tex] \sf Area = \cfrac{120 {}^{ \circ} }{360 {}^{ \circ} } * \pi(6m) {}^{2} [/tex]

Now to finish, let's simplify:

[tex] \sf{Area = \cfrac{1}{3}* \pi * 36m {}^{2} }[/tex]

[tex] \sf Area = 12 \pi \: m {}^{2} [/tex]

Rpt: The result is 12π m²

The depth D in inches, of snow in my yard t hours after it started snowing this morning is given by D=1.5t+4 If the depth of the snow is 7 inches now, what will be the depth one hour from now?

Answers

If the depth of the snow is 7 inches now, the depth one hour from now is equal to 8.5 Inches.

How to determine the depth one hour from now?

Based on the information provided above, a function which models the depth (D) in inches, of snow in a yard time (t) hours after it started snowing this morning is given by:

D = 1.5t + 4

where:

D represents the depth measured in inches.t represents the time measured in hours.

When the depth (D) in inches is equal to 7 inches now, the time measured in hours would be given by:

D = 1.5t + 4

7 = 1.5t + 4

1.5t = 7 - 4

1.5t = 3

Time, t = 3/1.5

Time, t = 2 hours.

One hour from now, the time measured in hours would be given by:

Time, t = 1 hour + 2 hours

Time, t = 3 hours.

At time, t = 3 hours, the depth can be calculated as follows;

Depth, D = 1.5t + 4

Depth, D = 1.5(3) + 4

Depth, D = 8.5 Inches.

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question content area top part 1 describe the three methods used to represent a set. give an example of a set represented by each method.

Answers

The three methods which are used to represent a set are word description, roster method and set-builder notation.

What is a set?

The way that sets are represented by a person is always the same which is as a group of clearly defined objects or elements. A capital letter designates a set. The cardinal number of a set is the number of elements in the finite set.

The three methods used to represent a set are as follows;

1. Word description

It is the method of representing a set under which we simply use words for describing the elements of the given set.

For example: A is the set of all natural numbers less than 8.

2. Roster method

It is the method of representing a set under which the elements of the set are listed by separating them with commas and in curly brackets.

For example: A = {1,2,3,4,5,6,7}

3. Set-builder notation

It is the method of representing a set under which only the property of the elements of the given set are written.

For example: A = {x ,x ∈ N and x<8}

Hence, the above stated methods are used to represent a set.

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Ronnie loaned her older brother $1500 and he offered to pay her 4% interest in three years. How much money will Ronnie have in three years when her brother pays her back

Answers

Answer: 1560

Step-by-step explanation:1500*1.04=1560

HELP ASAP it is TIMED

Answers

Answer:24

Step-by-step explanation:

When the function f(x) is divided by 2x + 3, the quotient is 2x² + 7x - 8 and the
remainder is-7. Find the function f(x) and write the result in standard form.

Answers

The function f(x) is 4x³ + 20x² + 5x - 31.

What is a function?

A function in mathematics from a set X to a set Y allocates precisely one element of Y to each part of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two changing quantities.

Here, we have

Given:  function f(x) is divided by 2x + 3, the quotient is 2x² + 7x - 8 and the remainder is -7.

When a polynomial f(x) is divided by any another polynomial d(x) and there is q(x) and r then it can be written as:

f(x) = d(x)q(x) + r

Now putting values of d(x) = 2x+3, q(x) = 2x² + 7x - 8 and r = -7, we get

f(x) = (2x+3)(2x² + 7x - 8) - 7

f(x) = 4x³ + 14x² - 16x + 6x² + 21x - 24 - 7

f(x) =  4x³ + 20x² + 5x - 31

Hence, the function f(x) is 4x³ + 20x² + 5x - 31.

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True or False: Scale factors figures must be the same proportions on all sides from the original figure.

Answers

The statement is true, the scale factor maintains the proportions between the sides.

Is the statement true or false?

We want to see if the statement "Scale factors figures must be the same proportions on all sides from the original figure." is true or false.

Suppose we have a polygon with N sides, such that the lengths of each side are:

{L₁, L₂, L₃,...}

If we apply a scale factor k, we just need to multiply each one of these lengths by k, then we will get:

{k*L₁, k*L₂, k*L₃,...}

Now, let's take the proportion between the new lengths for sides 1 and 2, we will get:

(k*L₁)/(k*L₂) = L₁/L₂

The scale factor disappears, then the proportions are maintained,

The statement is true.

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Writing and solving radical equations: Mastery Test
PLEASE HELP

Answers

The equation has 2 valid solutions; no extraneous solutions.

What are functions?

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.

What is factorization  and radicals?

Factorisation : The process of breaking or decomposing an entity (such as a number, a matrix, or a polynomial) into a product of another entity, or factors, whose multiplication results in the original number, matrix, etc., is known as factorisation or factoring.

Radicals :In the same way that addition is the opposite of subtraction in mathematics, a radical, also known as a root, is the opposite of an exponent. The square root, denoted by the symbol  is the smallest radical.

The given equation is:

First, we determine the solutions

Add 5 to both sides

Square both sides

Expand

Collect like terms

Expand again

Factorize

Factor out x - 2

Split

The above values are valid values of x.

Hence, the equation has 2 valid solutions; no extraneous solutions

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f (x) = log(x-1) +1
g(x) = log
What shifts occur for f(x)?

Answers

Answer:

f(x) shifts for log(DWX)

Step-by-step explanation:

The functions f and g are such that
f(x) = 6x+7 /2
g(x) = 3x - 5
Find the value of x that makes f^-1 g ^-1 (x) = 0.
Give your answer as an integer or as a decimal.

Answers

Using the inverse function method, the value of x should be x = 7/2 or x = -5

From the case, we know that:

f(x) = (6x + 7) / 2

g(x) = 3x - 5

f⁻¹.g⁻¹(x) ?

First, we need to find the inverse function of each given functions. We assume that:

f⁻¹(x) = p

g⁻¹(x) = q

f⁻¹(x) = (6x + 7) / 2

p = (6x + 7) / 2

2p = 6x + 7

2p - 7 = 6x

x = (2p - 7) / 6

f⁻¹(x) = (2x - 7) / 6

g⁻¹(x) = 3x - 5

q = 3x - 5

q + 5 = 3x

x = (q + 5) / 3

g⁻¹(x) = (x + 5) / 3

Next, we will try to find the value of x

f⁻¹.g⁻¹(x) = 0

(2x - 7) . (x + 5) = 0

     6           3

(2x² - 7x + 10x - 35) = 0

             15

2x² +3x - 35 = 0

(2x -7) (x+5) = 0

x = 7/2 ∨ x = -5

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Determine the vertex and the zeros of the function: y = (x – 1)2 – 25. Question 1 options: A) Vertex: (–1,25); zeros: (–6,0), (4,0) B) Vertex: (–1,25); zeros: (6,0), (–4,0) C) Vertex: (1,–25); zeros: (6,0), (–4,0) D) Vertex: (1,–25); zeros: (–6,0), (4,0)

Answers

The vertex for the given function is (1, -25) and the zeros are (6, 0)(-4, 0).

What is a quadratic function?

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of the second degree.

Given y = (x - 1)² - 25

converting the equation in form of y = ax² + bx + c

y = x² + 1 - 2x - 25

y = x² - 2x - 24

vertex of a quadratic equation is given by (-b/2a, -D/4a)

b = -2, a = 1, c = -24

D = b² - 4ac

D = (-2)² - 4(-24)

D = 4 + 96

D = 100

vertex is, -b/2a = -(-2)/2 = 1

and -D/4a = -100/4 = -25

vertex are (1, -25)

and for zeros put y = 0

y = x² - 2x - 24

x² - 2x - 24 = 0

x² - 6x + 4x - 24 = 0

x(x - 6) + 4(x - 6) = 0

(x - 6)(x + 4) = 0

x = 6 and x = -4

zeros are (6, 0)(-4, 0)

Hence option C is correct.

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Armando's workouts consist of kickboxing and swimming. While kickboxing, he burns 10 calories per minute and he burns 9 calories a minute while swimming. He wants to burn at least 450 calories each day.

a) If
x
is the number of minutes that Armando will kickbox and
y
is the number of minutes he will swim, write an inequality that would help Armando create a workout for today.

Answers

The inequality that models this scenario is given as 10x + 9y ≥ 450

What is an equation?

An equation is an expression showing the relationship between numbers and variables.

Let x represent the number of minutes that Armando will kickbox and y represent the number of minutes he will swim.

Kickboxing, he burns 10 calories per minute and he burns 9 calories a minute while swimming. He wants to burn at least 450 calories each day, hence:

10x + 9y ≥ 450

The inequality is given as 10x + 9y ≥ 450

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Liam has quarters, dimes, and nickels in his pocket. Liam says he has twice as many quarters as dimes and 3 more dimes than nickels. Liam also says he has the same amount of money in dimes as he has in quarters.

How many of each coin does Liam have in his pocket?

Answers

Liam has 5 quarters, 10 dimes and  and 7 nickels.

What is quarter and dime?

1 dollar is 100 cents - a full dollar, so 100 cents.

One dollar is written on one side of the coin, sometimes as "$1".

1 quarter dollar equals 25 cents - 1/4 of a dollar equals 25%, so 25 cents

On one side of the coin, a quarter dollar is written.

1 dime is 10 cents - 1/10th of a dollar, so 10%, so 10 cents, dime begins with d, decimal begins with, and decimal is base-10. One dime is written on one side of the coin.

1 nickel is 5 cents - made of nickel alloy, 1 cent/penny is possibly not made of nickel because it costs more than 1 cent, so it begins with 5 cents.

On one side of the coin, five cents are written.

Let d be the no. of dimes, n be the no. of nickels and q be the no. of quarters.

Given that

2q = d

n + 3 = d

money in dimes = money in quarters

10d = 25q

d can be written as

d = q/2

So

10(2q)  = 25q

2q/q = 25/10

q = 2.5

as 2.5 cant be a number for quarter, lets double it

q = 5

d = 2q

d = 2(5)

d = 10

n = d - 3

n = 10 - 3

n = 7

Thus, Liam has 5 quarters, 10 dimes and  and 7 nickels.

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Write the equation of the line that passes through the points (-3, 3) and (1, 2).

Answers

The equation of a line passing through the points (-3, 3) and (1, 2) is x + 4y = 9

What is line passing through the points?

When two points in a plane are given, a line passing through them can be determined. It is the set of all points in the plane that are equidistant from the two given points.

These points form a straight line, which can be represented by an equation with two variables.

The equation of the line can be found using the slope-intercept form or by solving a system of two equations.

The slope of the line is the ratio of the change in the y-coordinate of the two points over the change in the x-coordinate of the two points.

The y-intercept is the point where the line crosses the y-axis. The line can also be expressed in terms of its intercepts on the x and y-axes.

The x-intercept is the point where the line crosses the x-axis, and the y-intercept is the point where the line crosses the y-axis.

We know that the equation of a line passing through the points (x1, y1) and (x2 , y2) is given by y - y1 = m (x - x1).

m is the slope given by the formula m = (y2 - y1) / (x2 - x1)

Hence on substituting the given points in the equation of a line, we get

y - 3 = m ( x - (-3) ) -------(1)

m =  (y2 - y1) / (x2 - x1)

m = (2 - 3) / (1+3)

m = -1/4

Substituting value of m in equation (1), we get

y - 3 = -1/4 ( x + 3)

4(y - 3) = -x - 3

4y - 12 = -x - 3

x + 4y = -3 +12

x + 4y = 9

Therefore, the equation of a line passing through the points (-3, 3) and (1, 2) is x + 4y = 9

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A store sells a package of 25 trading cards for $5.25.

Answers

Ok what’s the question like how do you expect me to help

Plsss help and be legit I need help with this

Answers

On solving the provided question, we can say that the inequality we have ( -3, 2 ) => 2x - y>-8

What is inequality?

An inequality in mathematics is a relationship between two expressions or values that is not equal. Thus, imbalance leads to inequality. An inequality creates the link between two values that are not equal in mathematics. Egality is distinct from inequality. When two values are not equal, most commonly use the not equal sign (). Different inequalities are used to contrast values, no matter how little or large. Many simple inequalities may be resolved by modifying the two sides until the variables are all that remain. But a number of things contribute to inequality: Negative values on both sides are divided or added. Trade off the left and right.

here the inequality

we have ( -3, 2 )

y - 2 > 2(x+3)

y-2 > 2x +6

2x - y>-8

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can someone pleaseeeee help me???????

Answers

Answer:

Hello the vertex point is (4, -6)

this parabola opens upwards because the coefficient of x is positive.

The answer is B, good luck!

First, rewrite 2/7 and 3/10
so that they have a common denominator

Answers

Answer:

The common denominator will be 70

Step-by-step explanation:

To set the fractions to a common denominator, we need to know what number they both share. In this case, both 7 and 10 share the number 70, since 7 * 10 is 70.

Therefore, we can multiply 2/7 by 10/10 and 3/10 by 7/7:

[tex]\frac{2}{7}[/tex] * [tex]\frac{10}{10}[/tex] = [tex]\frac{20}{70}[/tex]

[tex]\frac{3}{10}[/tex] * [tex]\frac{7}{7}[/tex] = [tex]\frac{21}{70}[/tex]

Answer: Common denominator = 70

Step-by-step explanation: In order to find a common denominator, we need to find what number they have in common. That'd be 70. So, now rewrite the fractions like this:

[tex]\frac{2}{7} = \frac{?}{70}[/tex]

[tex]\frac{3}{10} = \frac{?}{70}[/tex]

Now, we need to find the equivalent fractions on the right. To do that, use this formula for part 1:

Right denominator / left denominator

Then, what you get after dividing those 2, you multiply by the left numerator.

So, let's plug the numbers in:

70 / 7 = 10

10 * 2 = 20

Therefore, [tex]\frac{2}{7} = \frac{20}{70}[/tex]

70 / 10 = 7

3 * 7 = 21

Therefore, [tex]\frac{3}{10} = \frac{21}{70}[/tex]

I hope this helped!

according to government data, 22 percent of children in the united states under the age of 6 years live in households with incomes that are classified at a particular income level. a simple random sample of 300 children in the united states under the age of 6 years was selected for a study of learning in early childhood. if the government data are correct, which of the following best approximates the probability that at least 27 percent of the children in the sample live in households that are classified at the particular income level? (note: z represents a standard normal random variable.)

Answers

The probability that at least 27 percent of the children in the sample live in households that are classified at the particular income level is approximately 0.04.

What is the binomial distribution?

In a binomial distribution, the probability of getting success must remain the same for the trials we are investigating. For example, when tossing a coin, the probability of flipping a coin is ½ or 0.5 for every trial we conduct, since there are only two possible outcomes.

To approximate the probability that at least 27 percent of the children in the sample live in households that are classified at the particular income level, we can use a normal approximation to the binomial distribution.

The sample size is n = 300 and the proportion in the population is p = 0.22. The standard deviation of the sample proportion is:

[tex]\sigma_{p}[/tex] = √(p(1-p)/n) = √(0.22(1-0.22)/300) = 0.0115

We can use the standard normal distribution to approximate the probability that the sample proportion is at least 0.27:

[tex]P(p_{hat} > = 0.27) \approx P( (p_{hat} - p) / \sigma_{p} > = (0.27 - 0.22) / 0.0115 )[/tex]

P(z >= 1.74)

where z is the standard normal variable.

We can use a standard normal table or calculator to find the probability for z >= 1.74 is about 0.04.

Hence, the probability that at least 27 percent of the children in the sample live in households that are classified at the particular income level is approximately 0.04.

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a student eats a dinner containing
[tex]8.0 \times 10 { }^{6} [/tex]
joules of energy. he wishes to do an equivalent amount of work in a nearby gym by lifting a 60kg object. how many times must he raise the object to expand this much energy? assume he raises it a distance of 2.0m each time

Answers

The number of times a student must raise the object to expand the given energy level is 6800 times.

What is work and energy?

Work is defined as transferring energy into an object so that there is some displacement. Energy is defined as the ability to do work. Work done is always the same. Energy can be of different types such as kinetic and potential energy.

Here, W=8.0×10⁶, m=60 kg, g=9.8 ms⁻² and h=2.0 m

We know that, W=mghn

Now, n=W/mgh

n=8.0×10⁶/(60×9.8×2)

= 6800 times

Therefore, the number of times a student must raise the object to expand the given energy level is 6800 times.

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enrique says 0.44444444 is a rational number. which of the following best describes whether enrique is correct and why? enrique is correct. repeating decimals are rational numbers because they can be written as fractions. the number is actually equivalent to 4/9. enrique is correct. repeating decimals are rational numbers because they can be written as fractions. the number is actually equivalent to 4/10. enrique is not correct. repeating decimals are never rational numbers. enrique is not correct. some repeating decimals are rational numbers, but this one is not.

Answers

Repeating decimals are never rational numbers. Hence the statement of enrique that "0.44444 is a rational number" is incorrect.

Rational numbers are those which can be expressed as the ratio of two integers, but the denominator should not be zero. Rational numbers can be expressed in p/q form. Rational numbers are never repeating decimals. For example 10/2, 3/2, 2/1 are rational numbers.

Irrational number are those which cannot be written in the form of p/q. They are repeating decimal and recurring decimals. The best example of irrational number is the value of π(pie). The value of π is 3.1415...with no repeating pattern of decimals.

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How do you solve this problem: you have a random number generator that in each trial generates a number in {1,2,…,n} uniformly at random. What’s the expected number of trials to see all of the n values at least k times? Specifically for k=log(n)

Answers

A base must be raised to a certain exponent or power, or logarithm, in order to produce a specific number.

How do you explain logarithm?

The exponent or power that must be added to a base to produce a particular number is called the logarithm. If bx = n, then the mathematical expression for x is x = logb n, where x is the logarithm of n to the base b. For instance, since 23 = 8, 3 is the logarithm of 8 in base 2, or 3 = log2 8.

The opposite of exponentiation in mathematics is the logarithm. The exponent to which b must be raised in order to obtain a number x is hence the logarithm of a number x to the base b. For instance, since 1000 = 103, log10 of 1000 is 3, or log10 = 3.

Common logarithms, with a base of 10, binary logarithms, with a base of 2, and natural logarithms, with a base of e 2.71828, are the four most popular varieties of logarithms.

Say you have n=4 and k=2. (Next, we might look at n=8 and k=3). Let f[(x-list_),y] be the expected value of the number of random trials needed to get from a list of thus and so many hits already, to completion with y or more hits in every slot. We want f[(0,0,0,0),2].

Note that f[anylist,0]=0, and that f[(0),1]=1.

Now f[0000,2]=1+f[0001,2], because the first random number has to go somewhere and whichever one it lands on is symmetric to the case where it lands on 4.

Next, f[0001,2]=1+(1/4)f[0002,2]+(3/4) f[0011,2]=1+(1/3)f[000,2]+(3/4)f[0011,2], the second step because once one slot is filled, it just takes 4/3 times as long to finish because 1/4 of your shots will be wasted on the saturated target.

By and by, you’ll encounter f[1111,2] among other situations, and this will be equal to f[0000,1].

It’s a finite calculation, it can be written up as a recursive program, and you’ll be able to get an exact answer for any f[(however many zeros), (whatever value counts as saturation)]. The calculation will, unfortunately, run into geometric expansion of time and space as there are going to be a lot of subcases to consider even for f[00000000,3]. Still, it’s nice to have the actual exact answer for a number of representative small cases.

As to the long term situation, once you’ve fired, say, n log n shots, you theoretically might be done, having `wasted no shots’. But consider the number of hits that “1” has got. This is a binomial distribution, with the probability of k hits out of n log n shots each at odds 1/n of hitting being Binomial[n log n, k](1/n)^k((n-1)/n)^(n log n-k). This should work out to roughly a Poisson distribution, with density something like (x/log n)e^{-x/log n} being the probability that you got x hits. The saturated targets would be the ones with x greater than log n, and you’d expect a typical target would need  ( log n - x )  e x / log n dx further hits.

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factorise the following:
11a - 11a^

i think ^ is squared

Answers

The factorization of the provided question is basically -11a(a-1).

What exactly is factorization?

The process of breaking or decomposing an entity (such as a number, a matrix, or a polynomial) into a product of another entity, or factors, whose multiplication results in the original number, matrix, etc., is known as factorization or factoring. You will mostly learn this idea in your lower secondary classes from grades 6 to 8.

A polynomial is an expression made up of variables and coefficients that involves only the operations of addition, subtraction, multiplication, and non-negative exponents. Polynomials are commonly used in algebra and in various mathematical disciplines.

Given,

11a-11a²

Taking common terms

-11a(a-1).

by factorizing 11a-11a²

we get -11a(a-1).

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In baseball, a ".300 hitter" gets a hit 30% of the time. (For those of you not well-versed in spiritual things like baseball: hitting .300 is pretty good.) Suppose a player has five times at bat in a game.

a) What is the probability of getting at least one hit in a game?

b) What is the probability of getting at least one hit, in ten consecutive games?


The answers are 0.8319, 0.1588, but I don`t understand how the textbook got them.

Answers

Step-by-step explanation:

a) The probability of getting at least one hit in a game can be found by using the complement rule, which states that the probability of an event happening is equal to 1 minus the probability of the event not happening.

In this case, the event of getting at least one hit in a game is the complement of getting no hits in a game.

To get no hits in a game, the player must get 0 hits out of 5 at bats.

The probability of getting no hits in a game is (1-.3)^5 = 0.168.

Therefore, the probability of getting at least one hit in a game is 1 - 0.168 = 0.832

b) The probability of getting at least one hit in ten consecutive games is found by multiplying the probability of getting at least one hit in one game by itself ten times.

So it would be (0.832)^10 = 0.1588

Alternatively, we could use the binomial distribution formula, where probability of getting a hit k times out of n trials is given by

P(k) = (n choose k) * p^k * (1-p)^(n-k)

If we want to find the probability of getting at least one hit in ten games, we need to find the probability of getting 0 hits in all ten games and subtract it from 1.

1 - (1 - 0.832)^10 = 0.1588

So the probability of getting at least one hit in ten consecutive games is 0.1588.

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