chapter 17 review questions how does a b-tree differ from a b -tree? why is a b -tree usually preferred as an access structure to a data file?

1) missing number is 7 (answer #2)

Each circles' numbers add up to 20. (the first one is 1 + 9 + 10, the second is 5 + 4 + 11.)

20 minus 10 minus 3 is 7, so that's the missing number.

2) missing number is 3 (answer #4)

This one's similar to the previous question. Each square's numbers have a sum of 10, this time. (First square is 2 + 7 + 1 + 0, second is 4 + 3 + 1 + 2.)

10 minus 6 minus 1 minus 0 is the same as 10 minus 7. This equals 3- so there's the number that's missing!

Hopefully this helps!

The area of the triangle as the function of x is [tex]x^2[/tex] / 2x - 4 and the domain of the function is  x∈(2, ∞)

The point on the line = (2, 1)

The give three points are (0, y), (2, 1) and (x, 0)

The slope of the line is the change in y coordinates with respect to the change in x coordinates of the line

Consider the point (0, y) and (2, 1)

Slope = (1-y) / (2-0)

= (1-y) /2

Consider the point (2, 1) and (x, 0)

Slope = (0-1) / (x-2)

= -1/x-2

Both slopes are equal

(1-y) /2 = -1/x-2

(1-y) = -2 / (x-2)

y = 1 + (2/(x-2))

y = x / (x-2)

The area of the triangle = (1/2)bh

Where b is the base

h is the height

The area of the triangle = (1/2) × x × (x / (x-2))

= [tex]x^2[/tex] / 2x - 4

The domain is x∈(2, ∞)

Hence, the area of the triangle is  [tex]x^2[/tex] / 2x - 4 and the domain of the function is x∈(2, ∞)

The complete question is

A right triangle is formed in the first quadrant by the x- and y-axes and a line through the point (2,1). Write the area of the triangle as a function of x, and determine the domain of the function.

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Answer:

The three numbers are 3, 7 and 13

Step-by-step explanation:

Considering the 3 numbers: x, y and z

x + z = 16

z=16-x

3x=z-4

3x=16-x-4

4x=12

x=3

3+z=16

z=16-3

z=13

3+13+y=23

y=23-13-3

y=7

Hope this helps :)

Answer: How Weather Exists

Step-by-step explanation:

~I think you mean, how weather exists.

You see, "Weather" exists because of the atmosphere. Evidently, weather  is the movement of the atmospheric gases around the planet that creates weather. Places like the Moon or Mercury do not have weather - only temperature changes.

~Hope this helped :)

The average rate of change over the interval x = -2 and x = 1 is 4

The equation is given as

f(x) = x² + 5x - 12

The interval is given as:

x = -2 to x = 1

Start by calculating the functions f(-2) and f(1)

So, we have

f(-2) = (-2)² + 5(-2) - 12 = -18

f(1) = (1)² + 5(1) - 12 = -6

So, the average rate over these intervals is calculated as:

Average rate = [f(1) - f(-2)]/[1 - -2]

This gives

Average rate = [-6 - -18]/[1 - -2]

Evaluate

Average rate = 4

Hence, the average rate of change is 4

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Answer:

12 miles

Step-by-step explanation:

72 x [tex]\frac{10}{60}[/tex] = 12

The speed of the current of the river will be 4.47 km per hour.

Speed is defined as the length traveled by a particle or entity in an hour. It is a scale parameter. It is the ratio of length to duration.

We know that the speed formula

Speed = Distance/Time

A riverboat goes at a normal of 14km each hour in still water. the riverboat voyages 110km east up the Ohio waterway and 110km west down a similar stream in a sum of 17.5 hours.

Let 'y' be the speed of the current of the river. Then the equation is given as,

T = T₁ + T₂

17.5 = [110 / (14 + y)] + [110 / (14 - y)]

17.5 / 110 = (14 - y + 14 + y) / (196 - y²)

196 - y² = 176

y² = 20

y = 4.47 km per hour

Then the speed of the current of the river will be 4.47 km per hour.

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A) 3x+9y-1 = 3(x+3y) -1, here distributive property is used the 3 is multiplied with each term inside the bracket.

What is algebraic operations?
Any of the common arithmetic operations, such as addi - tion, subtraction, multiplication, division, raising to a complete number power, and taking roots, are considered basic algebraic operations in mathematics (fractional power). These operations could be applied to numerical data, in which case people are frequently referred to as arithmetic operations. Similar operations can be carried out on factors, algebraic expressions, and, more generally, on components of algebraic structures like groups and fields. Another way to describe an algebraic operation is as a function from the Cartesian power of the a set to the same set. The dot product is an example of an operation that can be described by compounding simple algebraic operations, and is referred to as an algebraic operation.

b) 7x+5y-5y = 7x

Here the Additive inverse of 5y is used which is -5y .

c) (x-4)(x+3) = 0

here distributive property of addition over multiplication is used.

d) 4x+5x = 5x+4x

here commutative property is used.

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The angle ACB would be 80 degrees.

What is tangent to a circle?

The tangent always makes a single-point contact with the circle. It never intersects the circle twice. Tangents from an external point to a circle have the same length.

In the given figure,

angle AOB = 40.

So angle OBA = 40.

Then the angle AOB = 180 - 40 -40

                          AOB = 100.

By the theorem of circles,

          AOB + ACB = 180

          100 + ACB = 180

              ACB = 80.

Hence, the angle ACB would be 80 degrees.

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The solution is y will increase by 2 units with every unit increase in x1

A single dependent variable and several independent variables can be analyzed using the statistical technique known as multiple regression. In order to predict the value of the single dependent value, multiple regression analysis uses independent variables whose values are known.

X and Y variables are the sole ones in simple linear regression. Two or more x variables and one y variable make up multiple linear regression. For instance, basic linear regression is used when we forecast rent using only square footage.

In the above question:-

Interpretation of b1=2

it means that y will increase every 2 units for every unit increase in x1

holding x2 constant.

Hence option B is the correct answer.

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The simplest expression of the ratio of circles to squares is 5:3.

Describe ratio.

A relationship between two quantities is called a ratio, and it is expressed as one quantity divided by the other.

There are 6 circles and 10 squares.

These steps can be used to determine the ratio of two quantities:

Finding the quantities of both scenarios for which we are calculating the ratio is the first step. There are 10 squares and 6 circles in this instance.

It should be expressed as a fraction, a/b. Thus, we represent it as 10/6.

If you can, make the fraction even simpler. The ultimate ratio will be shown by the simple fraction.

In this case, 10/6 can be reduced to 5/3.

As a result, the simplest expression of the ratio of circles to squares is 5:3.

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The height of the kite assuming that there is no slack in the string is 86.6 m.

We have given that,

the string of a kite is 100 meters long and it makes an angle of 60°.

and we have to find the height of the kite.

So therefore we know the formula for right angled triangle,

i.e. sinθ = Opposite side/ Hypotenuse

Here θ = 60°

Opposite side = height of the kite = h (say)

Hypotenuse = length of string = 100 m

⇒ sin60° = [tex]\frac{h}{100}[/tex]

           h = 100sin60°

              = 100 × [tex]\frac{\sqrt{3} }{2}[/tex]

              = 50 × 1.732

           h = 86.6 m

Hence the height of the kite is 86.6 m.

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If x and y are independent variables such that x has uniform distribution (0,1) and y has exponential distribution means 1 then e (X+Y) is 3/2, E(XY) is 1/2, E (x-y)2 is 4/3 and E x2 e24 is -1/3

[tex]2^{2}[/tex][tex]e^{ty}[/tex]x ≈ u (0,1) > Independent

y ≈ exp (1) > Independent

E (x) = 0+1/2 = 1/2

v (x) = [tex][1- 0 ] ^{2}[/tex] / 12 = 1/12

E [tex]x^{2}[/tex] = v (x) + [tex][ E x]^{2}[/tex]

       = 1/12 + 1/4 = 1+3/12 = 4/12 = 1/3

E (y) = 1  v(y)=1  E [tex]y^{2}[/tex]= 1+1= 2

E[tex]e^{ty}[/tex] = [tex]\int\limits^_0[/tex][tex]e^{ty}[/tex][tex]e^{-y} dy[/tex]

E[tex]e^{ty}[/tex]  = [tex]\int\limits^_0[/tex][tex]e^{-y} (1-t)[/tex] dy

a : E (x+y) = E (x) + E(y)

       E (x+y) = 1/2+1 = 3/2

b: E (xy) = E (x) E(y) = 1/2 x 1 = 1/2

c: E [tex][x-y]^2[/tex] = E ([tex]x^{2}[/tex]-2xy+ [tex]y^{2}[/tex]

   = E [tex]x^{2}[/tex] - 2 Exy + E [tex]y^{2}[/tex]

  =  1/3 - 2 x 1/2 + 2

   = 1/3 + 1 = 4/3

d. E [tex]x^{2}[/tex] [tex]e^{24}[/tex]

   E ([tex]x^{2}[/tex] ) E [tex]e^{24}[/tex] = 1/3 x -1 = - 1/3

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Answer: 2/11

Step-by-step explanation: there are 11 letters and 2 of them are p so the chances of getting p is 2/11

Answer:

2/11

Step-by-step explanation:

The total amount of tiles is 11. There are only 2 tiles that have the letter P on them.

Theoretical probability is the probability that should occur over many, many trials.

Theoretical probability = favorable outcomes / total outcomes.

In this scenario, the favorable outcome is the letter P. which there are two of. The total outcomes would be all the letters that make up the word MISSISSIPPI, or 11.

So your theoretical probability would be 2/11.

By resolving an equation, we may determine that Uan needs to sell 12 or more goods in order to generate a profit of $60 or more.

A formula that describes how two expressions on each side of a sign are connected.

It typically has an equal sign and one variable.

Similar to this: 2x - 4 = 2.

Graphing, substitution, or elimination are the three methods that can be used to solve systems of equations.

To answer a problem by graphing, just plot the given equations on a graph and identify the point(s) where they all intersect.

So, a number of items Uan should sell to earn a profit of $60 or above:
We know that Uan earns $5 for each item he sells.

So, let x be the number of items Uan should sell.

Then, the equation will be:

5x = 60

Now, solve as follows:
5x = 60

x = 60/5

x = 12

Profit of $60: 12 items to sell

Profit more than $60: More than 12 items to sell

So, by resolving an equation, we may determine that Uan needs to sell 12 or more goods in order to generate a profit of $60 or more.

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The slope and y-intercept of this function is

B. The slope is 5/6, The y-intercept is (0, -3

Linear function is a function of the form y = mx + c

m = slope

c = intercept

The slope is represented as m, The slope by definition is the ratio change of the output values to the input values

the slope, m calculated using the points (0, -3) and  (6, 2)

m = (y₀ - y₁) / (x₀ - x₁)

m = (2 - -3) / (6 - 0)

m = (5) / (6)

m = 5/6

c = y intercept, from the table

c = -3

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The simplification of the expression (3√-5 + 2)(4√-5 -1) gives 5√-5 - 62

Simplification is a way of determining an answer for a complex calculation that may involve numbers on division, multiplication, square roots, cube roots, plus and minus, etc.

Given: the expression (3√-5 + 2)(4√-5 -1)

(3√-5 + 2)(4√-5 -1)

Clear the parenthesis:

(3√-5 + 2)(4√-5 -1) = 3√-5(4√-5) + 3√-5 (-1) + 2(4√-5) + 2(-1)

                             = -60 - 3√-5 + 8√-5 -2

                            = 5√-5 - 62

Therefore, the expression (3√-5 + 2)(4√-5 -1) simplifies to 5√-5 - 62

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A comparison of multiple treatments and the use of the double-blind method are two fundamental components of all statistically designed experiments. (6) Compare various treatments; assign patients to treatments at random.

What is double-blind method?

A kind of clinical experiment in which neither the participants nor the researcher is aware of the treatment or intervention that each participant is receiving until the trial is complete.

                      This reduces the likelihood of skewed study outcomes.

What is a sample of a double-blind study?

Imagine, for instance, that researchers are looking into the effects of a novel medication.

                            The participants in a double-blind study would not be aware of who was receiving the real medication and who was receiving a placebo, and neither would the researchers who interact with them.

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The complete question is -

Two essential features of all statistically designed experiments are (2 Points) O use enough subjects; always have a control groups O always have a placebo group; use the double - blind method O use a block design; use chance to assign subjects to treatments O compare several treatments; use the double - blind method O compare several treatments; use chance to assign subjects to treatments.

Answer:

Step-by-step explanation:

First of all let's look at the side lengths of both figures.

Let's see how the corresponding sides relate:-

[tex]\sf 6*\cfrac{1}{3} =3[/tex]

[tex]\sf 3*\cfrac{1}{3} =1[/tex]

We can see that all sides scale by the same factor of 1/3.

Therefore, YES A is a scaled copy of Figure B.

______________________

Hope this helps!

Have a great day!

The zeroes of the function f(x) = 28x² - 7 will be 1/2 and negative 1/2.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The quadratic equation is given as ax² + bx + c = 0. Then the degree of the equation will be 2.

The function is given below.

f(x) = 28x² - 7

For the zeroes of the function, put f(x) = 0, then we have

f(x) = 0

28x² - 7 = 0

x² = 1/4

x = ± 1/2

The zeroes of the function f(x) = 28x² - 7 will be 1/2 and negative 1/2.

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Rosie's statement about expecting a total of about 175 points over 100 turns is accurate.

Based on the expected value, Rosie's statement is correct.

The expected value, denoted as E(X), represents the average or mean value of a random variable, in this case, the sum of points in a given turn when rolling the five dice.

Tom's statement, "A player will most likely get 17.5 points in any given roll," is not accurate. The expected value of 17.5 points does not necessarily mean that a player is most likely to get exactly 17.5 points in any single roll. Instead, it indicates that over many rolls, the average value of points earned in a turn is 17.5 points.

On the other hand, Rosie's statement, "Over 100 turns, we can expect a total of about 175 points," is correct. Since the expected value is 17.5 points per turn, over 100 turns, we can expect the total sum of points to be approximately 100 turns × 17.5 points/turn = 1750 points.

In summary, the expected value of 17.5 points represents the average outcome over multiple rolls, and based on this value, Rosie's statement about expecting a total of about 175 points over 100 turns is accurate.

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The complete question:

Tom and Rosie are designing a game. In each turn, a player rolls five 6-sided dice and adds the numbers showing on each face to determine how many points they get that turn. For example, the lowest number of points in a given turn is 1+1+1+1+1=5 points, and the highest is 6+6+6+6+6=30 points.

They let X represent the sum in a given turn, and they find the expected value of X is E(X) = 17.5 points.

Tom says, "A player will most likely get 17.5 points in any given roll."

Rosie says, "Over 100 turns, we can expect a total of about 175 points."

Whose statement is correct based on the expected value?

The value of x for the given equation is 1.

What is solving an equation?

A General Rule for Equation Solving

Remove parentheses from each side of the equation and combine similar phrases to make it simpler.

To separate the variable term on one side of the equation, use addition or subtraction.

To find the variable, use division or multiplication.

Consider the given expression

0.2(x + 1) + 0.5x = -0.3(x - 4)

Simplifying,

0.2x + 0.2 + 0.5x = -0.3x + 1.2

0.7x + 0.2 = -0.3x + 1.2

Add 0.3x on both sides,

0.7x + 0.2 + 0.3x = -0.3x + 1.2 + 0.3x

x + 0.2 = 1.2

Subtract 0.2 from both sides,

x + 0.2 - 0.2 = 1.2 - 0.2

x = 1

Hence, the value of x for the given expression is, 1.

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The statement if true, for 95% of the samples from the population, the confidence interval we compute will contain the true mean.

In the given question we have to check whether the given statement is TRUE or FALSE.

The given statement is:

For 95% of the samples from the population, the confidence interval we compute will contain the true mean.

Because the underlying approach succeeds on 95% of random samples, we have a 95% confidence that this confidence interval contains the population mean.

Approximately 95% of the estimated intervals will contain the actual value of the population mean if samples are taken frequently and 95% confidence intervals are generated.

So the given statement is true.

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Answer:

[tex]\huge\boxed{\sf 3 \ baskets}[/tex]

Step-by-step explanation:

Let the baskets missed in game 2 be x.

Says that, the shooting of both the games were accurate.

So,

[tex]\displaystyle \frac{Baskets \ made \ in \ game \ 1}{Baskets \ missed \ in \ game \ 1 } =\frac{Baskets \ made \ in \ game \ 2}{Baskets \ missed \ in \ game 2} \\\\\frac{15}{5} =\frac{x}{1} \\\\Cross \ Multiply\\\\15 \times 1 = 5 \times x\\\\15 = 5x\\\\Divide \ 5 \ to \ both \ sides\\\\3 = x\\\\x = 3\\\\\rule[225]{225}{2}[/tex]

The had to wait for the second flight for 40 mins.

We know that sometimes when a person is travelling there may be need to have a flight that connects a person from one place to another and at times you would have to wait for a connecting flight and this wait would add to the total time that is required for the journey.

Now we are told in the question that it takes 8 hours and 5 minutes to travel from Hong Kong to Dubai and that they left Dubai at 2250 hrs but landed in Hong King at  1405 hrs. The time in between must be;  2250 hrs - 1405 hrs = 8: 45 hrs thus the time of waiting is 40 minutes.

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Answer:

[tex]S=\{-2,-3\}[/tex]

Step-by-step explanation:

Required integers are: -2 and -3

Answer:

Slope-intercept form: y = 3x + 5

Slope: 3

y-intercept: 5

Step-by-step explanation:

When the equation of a line is written in the slope-intercept form, we can easily identify the slope from the coefficient of x and the y-intercept from the constant.

The slope-intercept form is expressed as y = mx + c, where m is the slope and c is the y-intercept. Note that other textbooks might use y = mx + b instead, but both have the same meaning as both m and b or c will be replaced by a certain value.

To rewrite an equation in the slope-intercept form, isolate the y term on the right-hand side of the equation and divide the whole equation by the coefficient of y.

Working

[tex]y - ( - 7) = 3(x - ( - 4))[/tex]

Expand:

[tex]y + 7 = 3(x + 4)[/tex]

[tex]y + 7 = 3x + 12[/tex]

Subtract both sides by 7:

[tex]y = 3x + 12 - 7[/tex]

[tex]\bf{y = 3x + 5}[/tex]

Since the coefficient of y is already 1, we have arrived at our final answer.

When the equation is in the slope-intercept form, the slope can be identified from the coefficient of x. This refers to the number that comes before x which is multiplied to x.

Thus, the slope is 3.

The y-intercept is the value of the constant in the slope-intercept form. This refers to the number that is not attached to any variables.

Hence, the y-intercept is 5.

Note that the y-intercept can also be found by substituting x = 0 into the equation.

The x-intercept occurs at y = 0. Since we have the equation of the line, we can substitute y = 0 into the equation to find the value of x when y = 0.

Working

y = 3x + 5

When y = 0,

0 = 3x + 5

3x = -5

Divide both sides by 3:

[tex]x = - \frac{5}{3} [/tex]

I have attached the graph as an image. If only a sketch is required, there are 3 pieces of information that needs to be labelled on the graph:

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Answer:

For the first graph:

Domain: -∞ [tex]\leq[/tex] x [tex]\leq[/tex] ∞

Range: y [tex]\geq[/tex] 3

For the second graph:

Domain: 0 [tex]\leq[/tex] x [tex]\leq[/tex] 4

Range: y [tex]\leq[/tex] 64

Step-by-step explanation:

For the second graph, I'm assuming that that point are stopping at (0,0) and (4,0) that's why I wrote that for the domain. If it doesn't stop, then the domain would be the same and the first graph.