In statistics, a series of random events in which the probability of a given event is determined only by its predecessors is known as a "chain" named after what Russian mathematician?

Step-by-step explanation:

6 blocks ÷ 14 sudents =    6/14 =   3/7  of a block each

Here, we can use the fact that ln(x) grows slower than any positive power of x. That means that as x approaches infinity, ln(x) approaches infinity slower than x. Therefore, (ln(x))/x approaches zero as x approaches infinity. Using this fact, we can see that the entire expression approaches zero as x approaches infinity. Therefore, the limit is equal to zero.

To get  the limit of lim (ln(x))²/3x as x approaches infinity, we can use l'Hospital's Rule. Taking the derivative of the numerator and denominator separately, we get: lim 2ln(x) * 1/x / 3
x→[infinity]
Simplifying this expression, we get: lim 2ln(x) / (3x)
x→[infinity]
Using l'Hospital's Rule again, we take the derivative of the numerator and denominator separately: lim 2 * 1/x / 3
x→[infinity]
Simplifying further, we get: lim 2/ (3x)
x→[infinity]
Since the denominator approaches infinity as x approaches infinity, the limit is equal to zero.
Alternatively, we can use an elementary method to find the limit. We can rewrite the expression as: (ln(x))^2 = (ln(x)) * (ln(x))
Then we can use the fact that ln(x) grows slower than any positive power of x. That means that as x approaches infinity, ln(x) approaches infinity slower than x. Therefore, (ln(x))/x approaches zero as x approaches infinity. Using this fact, we can see that the entire expression approaches zero as x approaches infinity. Therefore, the limit is equal to zero.

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Answer:

The answer to your problem is, A. Larger

Step-by-step explanation:

First in order to know to the answer lets learn about different types of fractions:

For example, 1/4, 3/4, 3/8, are all proper fractions.

4/3, 5/2, are all improper fractions.

When we have to multiply a whole number with fractions less than 1, then the resulting number will be less the number originally

Example; 3 x [tex]\frac{3}{4}[/tex]

If we then multiplying numerators together and the denominators together.

3 x [tex]\frac{3}{4}[/tex] = [tex]\frac{3}{1}[/tex] x [tex]\frac{3}{4}[/tex] = [tex]\frac{9}{4}[/tex] = 2[tex]\frac{1}{4}[/tex] < 3

Example /\

Thus the answer to your problem is, A. Larger OR Multiply.

The percent of students in grade 8 those who like to join dance club is equal to 25%.

Total number of students in grade 8 = 20

Total number of students of grade 8  join in dance club = 5

Percent of students of grade 8 prefer to join dance club

= ( total number of students prefer dance club ) / ( Total number of students in grade 8 ) × 100

Substitute the value in the formula we get,

⇒ Percent of students of grade 8 prefer to join dance club

= ( 5 ) / ( 20 ) × 100

⇒ Percent of students of grade 8 prefer to join dance club  = 0.25 × 100

⇒ Percent of students of grade 8 prefer to join dance club  = 25%

Therefore, percent of grade 8 students who preferred to join dance club is equal to 25%.  

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The above question is incomplete, the complete question is:

What percent of students in grade 8 prefer to join a dance club?

                      Dance club      Hiking club     Total

Grade 7               15                       15                 30

Grade 8               5                        15                  20

Total                    20                     30                    50

The function that is shown in the graph is y = √(2x - 6) + 1

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

The graph

The parent function of the graph is

y = √2x

The graph is shifted right by 6 units

So, we have

y = √(2x - 6)

The graph is shifted up by 1 unit

So, we have

y = √(2x - 6) + 1

hence, the function is y = √(2x - 6) + 1

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Katy traveled more distance than Roger by 84.9 miles.

Subtraction is a basic arithmetic operation that involves finding the difference between two numbers, by taking away one number from another. It is denoted by the minus (-) sign and is the inverse operation of addition

To find out who traveled more distance, we need to calculate the difference between the distance traveled by Roger and Katy.

So, Katy traveled 205.65 miles and Roger traveled 120.75 miles.

To find out who traveled more, we subtract the distance traveled by Roger from the distance traveled by Katy

= 205.65 miles - 120.75 miles

Subtract the numbers

= 84.9 miles

Therefore, Katy traveled 84.9 miles more than Roger.

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Lakeside Olds should expect to have approximately 3 automobiles lined up at opening time on a typical day based on the probability distribution provided.

To find the expected number of automobiles lined up at the Lakeside Olds dealer at opening time, we use the concept of expected value. The expected value is the average value we would expect to see if we repeated the experiment many times. In this case, the experiment is the number of automobiles lined up at the dealer at opening time.

We are given the probability distribution for the number of automobiles, which tells us the probability of each possible outcome. We use these probabilities to calculate the expected value as the weighted average of all possible outcomes.

Expected number of automobiles = (1 x 0.05) + (2 x 0.30) + (3 x 0.40) + (4 x 0.25)

= 0.05 + 0.60 + 1.20 + 1.00

= 2.8

≈ 3

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The given question is incomplete, the complete question is:

The probability distribution for the number of automobiles lined up at a Lakeside Olds dealer at opening time (7:30 a.m.) for service is:

how many automobiles should Lakeside Olds expect to be lined up at opening time?

To compute the distance dd from yy to the line through uu and the origin, we can use the formula for finding the distance between a point and a line. The line through uu and the origin can be represented by the equation

y = (u2/u1)x, where u1 and u2 are the x and y coordinates of uu, respectively.
To find the distance dd, we first need to find the coordinates of the point where the line through uu and the origin intersects with the line perpendicular to it that passes through yy. Let (a,b) be the coordinates of this point. Then we have:
b = (u2/u1)a  (since (a,b) lies on the line through uu and the origin)
u1a + u2b = 0  (since (a,b) lies on the line perpendicular to it that passes through yy)
Solving these equations simultaneously, we get:
a = -u1u2/(u1^2 + u2^2)
b = u1^2/(u1^2 + u2^2) * y
Now we can use the distance formula to find dd:
dd = sqrt((x - a)^2 + (y - b)^2)
where x and y are the coordinates of yy.

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Equations in the system are accurate and coincident.

Solve the system using any approach, such as elimination or substitution, and then categorize the equations as consistent independent, inconsistent, or coincident.

Using the substitution technique:

x - 2y = -4 => x = 2y - 4

Substituting x = 2y - 4 into the first equation:

3x - 6y = -12

3(2y - 4) - 6y = -12

6y - 12 - 6y = -12

-12 = -12

Identity -12 = -12 is a constant. Since the two equations represent the same line and have an infinite number of solutions, the system of equations is consistent and coincident.

Any value of y can be chosen, and x = 2y - 4 can be used to calculate the equivalent value of x.

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Answer:

[tex]x = \sqrt{ {28.46}^{2} - {27}^{2} } = \sqrt{80.9716} = 9.00[/tex]

The absolute value of  |-8 +12| is number  4.

We have to find the value of |-8 +12|

The absolute value | x | of a real number x is the non-negative value of x without regard to its sign.

Let us solve the value inside the mod

When eight is subtracted from twelve we get 4

|-8 +12|

|4|

The absolute value is 4.

Hence, the absolute value of  |-8 +12| is 4.

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The value of expression is, 4

We have to given that;

The expression is,

⇒ | - 8 + 12 |

Now, We can simplify the expression as;

⇒ | - 8 + 12|

⇒ | 4 |

⇒ 4

Thus, The solution of expression is, 4

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Answer:

The original recipe calls for 1 1/4 cups of dip and 1/2 cup of veggies, so you + both together which is a total of 1 3/4 cups of ingredients.

If Austin wants to use 1 cup of veggies instead of 1/2 cup, he needs to double the recipe. To keep the same ratio of dip to veggies, he will also need to double the amount of dip.

1 3/4 cups (original recipe) x 2 = 3 1/2 cups

Therefore, Austin will need 3 1/2 cups of dip to make the recipe using 1 cup of veggies.

The breadth of the cuboid is 0.5 m

The volume of a cuboid is given by the formula:

V = l * b * h

Where l is the length, b is the breadth and h is the height of the cuboid

We have:

length (l) = 60 cm = 0.6 m

volume (V) = 1.2 m³

height (h) = 4 m

Substituting:

1.2 = 0.6 * b * 4

1.2 = 2.4b

b = 1.2/2.4

b = 0.5 m

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The value of x is 7.99 centimeters to the nearest hundredth.

As per the given diagram, the value of x sits as the base length of the triangle.

And it is given that the hypotenuse's side length is 10 cm.

As per the cosine function,

The adjacent side to hypotenuse ratio is known as the cos function.

Adjacent Side/Hypotenuse = CosA.

Here, A = 37 degrees, adjacent side = x, and hypotenuse = 10cm.

So,

cos37° = x/10

x = 10 × cos37°

x = 7.9863551

x ≈ 7.99 cm.

Therefore, the value of x to the nearest hundredth can be described as x = 7.99 cm.

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The complete question:

Solve for x. x = [ ? ] cm, round to the nearest hundredth.

The image is attached below.

The approximation of g(-1.2) using the line tangent to the graph of g at x=-1 is 3.6.

We can use the formula for the equation of a tangent line to approximate the value of g(-1.2) using the given information:

y - y1 = m(x - x1)

m = g'(-1) = 2 (since g'(-1) = 2)

Substituting these values into the formula, we get:

y - 4 = 2(x + 1)

Simplifying:

y = 2x + 6

Now we can use this equation to approximate g(-1.2) by plugging in x=-1.2:

g(-1.2) ≈ 2(-1.2) + 6

g(-1.2) ≈ 3.6

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Answer:

The cost is $115.20

Step-by-step explanation:

The locker is 8ft by 12ft by 9ft.

The volume is:

V = 8 × 12 × 9

V = 864 cubic feet

But the price is given by cubic yards so we need to find that first. (we have cubic feet)

A cubic yard is

1yd × 1yd × 1yd

And a yard is 3 feet, so that is the same as:

3ft × 3ft × 3ft

= 27cubic feet

Divide:

864/27

= 32

The locker is 32 cubic yards.

The price is $3.60 per cubic yard. Multiply.

32 × 3.60

= 115.2

The cost of the locker will be $115.20.

Answer:

6 cm

Step-by-step explanation:

let, missing side be x cm

then, x+x+3 = 15

=> 2x = 12

=> x = 6 cm

Thus, missing side is 6 cm long

To find the limit of ln(5x)/√5x as x approaches infinity, we can use l'Hospital's Rule since it is an indeterminate form of ∞/∞.

Taking the derivative of the numerator and denominator separately, we get: lim [(1/5x) / (1/2√5x)] x→[infinity]

Simplifying this expression, we get: lim 2/5√5x x→[infinity]

Since the denominator approaches infinity as x approaches infinity, the limit is equal to 0.

Therefore: lim ln(5x)/√5x = 0 x→[infinity]

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Answer:

This can be figured out from the equation:

2n = 11

If he walks 2 miles/hour, then you can just say "2n" to say the miles in the unknown variable for hours.  Set it to equal 11, the number of miles he will walk in n hours.

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The number of miles driven if the cost of renting a car is $130 with a cost function of c(m) = 0.05m + 30 is 2000 miles.

We can start by setting up an equation to solve for the number of miles driven, m

c(m) = 0.05m + 30 (where c(m) is the cost of renting a car)

We know that the cost is $130, so we can substitute that into the equation

130 = 0.05m + 30

Now we can solve for m

130 - 30 = 0.05m

Subtract the numbers

100 = 0.05m

m = 100/0.05

Divide the numbers

m = 2000 miles

Therefore, the number of miles driven is 2000 miles

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The given question is incomplete, the complete question is:

If c(m)=0. 05m + 30 represents the cost of renting a car, how many miles were driven if the cost is 130$?

There were 4 speed bumps installed on the road leading into the house development.

What is the formula of speed when time and distance have given?

The formula is speed = distance/time

Here given,

The length of the road is 3/4 miles or 12/16 miles and the distance between each speed bump is 3/16 miles.

Now we want to obtain the number of speed bumps,

So, Number of speed bumps = (Total distance of road) / (Distance between each speed bump)

Number of speed bumps = [tex] \frac{ \frac{12}{16} }{ \frac{3}{16} } [/tex]

Number of speed bumps = [tex] \frac{12}{16} \times \frac{16}{3} [/tex]

Number of speed bumps = 4

Therefore, there were 4 speed bumps installed on the road leading into the house development.

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The change in the allocation of congressional seats based on changes in the population is called redistricting.

The process of altering the borders of electoral districts or constituencies in response to population changes is known as redistricting. The census is taking a note of the population in an interval of ten years to check the population of the united states nationally and also in each and every state.

Further on the data from the census will be helping to calculate the number of the states in the house of representative from the states. This is done to make sure the one person one vote agenda. Redistricting has the potential to significantly affect political power and representation.

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The trigonometric ratios of the angle are given as follows:

The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:

Applying the Pythagorean Theorem to the terminal side, the hypotenuse is given as follows:

h² = 9² + 10²

h = square root(9² + 10²)

h = 13.45.

Hence the ratios are given as follows:

The inverse ratios are given as follows:

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An equation that can be used to determine how many months Ely will need to save money to reach his goal of a total of $1,550 in his savings account is 200 + 150x = 1,550.

An equation is a mathematical statement showing the equality or equivalence of two or more algebraic expressions.

Equations use the equal symbol unlike mathematical or algebraic expressions, which combine variables with numbers, constants, and values using mathematical operands.

The intended monthly savings = $150

The amount already in Ely's account = $200

The total amount Ely needs = $1,550

Let the number of months required to reach $1,550 = x

200 + 150x = 1,550

150x = 1,550 - 200

150x = 1,350

x = 9 months.

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If Hi, Leon Sargetta, do you promise to pay Patrick Amina the sum of $3500. the minimum amount of Leon’s monthly payment is: c. $104.84.

Using this formula

Monthly Payment = (P * r * (1 + r)^n) / ((1 + r)^n - 1)

where:

P = Principal = $3500

r = Monthly interest rate =  (5.5% / 12) = 0.00458333

n = Number of months in the loan term = 3 years 36 months.

Let plug in the formula

Monthly Payment = (3500 * 0.00458333 * (1 + 0.00458333)^36) / ((1 + 0.00458333)^36 - 1)

Monthly Payment  = 104.84

Therefore the correct option is C.

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Answer:

1760

Step-by-step explanation:

10 x 16 x 11

160 x 11 = 1760

Answer:

The surface area of the square pyramid is approximately 28.2 square units.

Explanation:

The base area and the areas of each triangle face must be determined to calculate the surface area of a square pyramid.

Since the base is a square with four units for each edge, its area is:

The base area equals 42 to 16 square units.

We must determine the length of the slant height, which is the height of each triangular face, to get the area of each triangle.

The Pythagorean theorem may be used to get the slant height: a2 + h2 = s2,

where an equals half the base's length (2 units), h is similar to the pyramid's size (3 units), and s is the slant height.

Inputting the values, we obtain:

2^2 + 3^2 = s^2

4 + 9 = s^2

13 = s^2 s = √13

Using the following formula, we can now get the area of each triangle face:

The area of the triangular face equals 0.5 base height, where the base is the slant height (13 units), and the size is the square base's edge length (4 units).

The triangular face area equals 0.5 x 4 x 13 = 213 square units.

Given that there are four triangular faces, their combined area is:

Units of area: 4 x 2 x 13 = 8 x 13

The total surface area is then calculated by summing the base and triangle face areas:

Base area plus triangle face area equals total surface area.

Surface area total = 16 + 8 x 13

28.2 square units total surface area (rounded to the nearest decimal point)

Therefore, the square pyramid's surface area is around 28.2 square units.

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The length of the arc shown in red is 5.2359 radians

We know that the formula for the length of the arc of a circle.

s = r × θ

where s represents the arc length (in radians)

r represents the radius

and θ is the central angle in radians

From the attached figure of the circle, the radius of the circle r is 10 cm.

Here, the arc length is given in degrees.

We know that central angle = arc measure

So, the central angle θ = 30°

θ = 0.52359 radians

Using above formula of the arc length,

s = r × θ

s = 10 × 0.52359

s = 5.2359 radians

Thus, the arc length = 5.2359 radians

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Grantly must place the chairs close enough so that people can easily speak with one another

Grantly is designing a sitting area that will be located outside of his client's master bedroom. He intends to furnish the area with a few rugs, an end table, and chairs.  The seats should be spaced apart just enough to allow for easy conversation while seated, but not too much that it seems crowded. For easy access, end table should be positioned close to the seats. The placement of rugs should be such that they both define seating area and add to overall attractiveness of the space.

To make sure that chairs, end table, and rugs fit properly without giving area a claustrophobic feeling, Grantly should take measurements of the available space in the sitting room. He should also consider how the master bedroom is organised as well as any existing furnishings or fixtures that could have an impact on how the sitting room furniture is arranged. Additionally, seating should be set up so that conversing with one another while seated is simple. Conversation can be facilitated and a cosy environment can be created by positioning chairs in a circula configuration, facing one another.

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