The value of China’ export of automobile and part i approximately F of X equal 1. 8208 to the E to the 0. 3387. Ak her ak equal zero correpond in 1998 and what year did will the oxford reach 5. 3 billion

when we pay n pesos, then recurrence relation for all the number are in a ways to pay a bill is in this order:[tex]a_{n} =a_{n-1}+a_{n-2}+2a_{n-5}+2a_{n-10}+ a_{n-20}+a_{n-50}+a_{n-100}[/tex]

A recurrence relation is an equation which represents a chain primarily based totally on a few rule. It enables in locating the following time period (subsequent time period) established upon the previous time period (preceding time period). If we recognise the preceding time period in a given series, then we will without difficulty decide the following time period.

Recurrence family members are used to lessen complex issues to an iterative procedure primarily based totally on less difficult variations of the trouble. An instance trouble wherein this technique may be used is the Tower of Hanoi puzzle. Recurrent is some thing that happens frequently or repeatedly. However, in case you are speakme approximately a recurrence relation, then you definitely have a mathematical shape which you are handling and it's miles really specific than a recursive formula. Recursion is the repeated use of a process or action.

pay 1 pesos coin , then n-1 pesos

pay 2 pesos coin , then n-2 pesos if n ≥ 2

pay 5 pesos coin , then n-5 pesos if n ≥ 5

pay 10 pesos coin , then n-10 pesos if n ≥ 10

pay 5 pesos bill , then n-5 pesos if n ≥ 5

pay 10 pesos bill , then n-10 pesos if n ≥ 10

pay 20 pesos bill , then n-20 pesos if n ≥ 20

pay 50 pesos bill , then n-50 pesos if n ≥ 50

pay 100 pesos bill , then n-100 pesos if n ≥ 100

a0=1

so i have recurrence relation as follows:

[tex]a_{n} =a_{n-1}+a_{n-2}+2a_{n-5}+2a_{n-10}+ a_{n-20}+a_{n-50}+a_{n-100}[/tex]

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a) Considering the scale factor, the height that she should build the model is of: 22.1 inches.

b) Essence has enough information to build the accurate scale model, as she needs only the scale and either the actual or the drawn model.

An scale is defined as the relation between the actual length of a segment and the length of drawn segment, as follows:

Scale = Actual length/drawn length

The scale for this problem is given as follows:

Scale factor = 300 ft/1 in.

Which means that each inch on the drawing represents an actual height of 300 ft.

The height of the Clingman Dome is given as follows:

6,643 feet.

Considering the scale factor of 300 ft/1 in, the height of the drawing is obtained as follows:

6643/300 = 22.1 inches.

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a) Probability model

P(40) = 1/6

P(0) = 5/36

P(-10) = 25/36

b)  E(X) = -5/18

standard deviation  = 18.331

c) standard deviation  = 91.65

d) Probability = 0.560

From the question, we have

a) X = -10, 0 or 40 for your winnings (or losses). The corresponding probabilities are:

P(40) = 1/6

P(0) = (5/6)(1/6) = 5/36

P(-10) = 1 - 1/6 - 5/36 = 25/36

b) E(X) = (-10)(25/36) + 0(5/36) + 40(1/6) = -5/18

E(X^2) = (100)(25/36) + 1600(1/6) = 3025 / 9

Var(X) = E(X^2) - [E(X)]^2 = 3025 / 9 - (-5/18)^2 = 108875 / 324

standard deviation = sqrt [Var X] = 119043 / 6494 =18.331

c) E(X) = (-10)(25/36) + 0(5/36) + 40(1/6) = -5/18

5 * E(X)  =  - 25/18

standard deviation = 5 * 18.331 = 91.65

d) Probability :

P(X < 0) = P{ z < [0 - (-5/18)] / [(119043 / 6494) / sqrt 100] } = P(z < 0.1515) = 0.560

Probability:

Possibility is referred to as probability. This branch of mathematics deals with the occurrence of a random event. The value's range is 0 to 1. Probability has been applied into mathematics to predict the likelihood of different events. Probability generally refers to the degree to which something is likely to occur. This fundamental theory of probability, which also applies to the probability distribution, can help you comprehend the possible outcomes for a random experiment. Gonna determine how likely something is to occur, use probability. Many things are hard to predict with 100% certainty. We can only anticipate the possibility of an event occurring using it, or how likely it is.

Complete question:

From the Data at Hand to the World at Large 4. New game You pay $10 and roll a die. If you get a 6, you win $50. If not, you get to roll again. If you get a 6 this time, you get your $10 back. a) Create a probability model for this game. b) Find the expected value and standard deviation of your prospective winnings. c) You play this game five times. Find the expected value and standard deviation of your average winnings. d) 100 people play this game. What's the probability the person running the game makes a profit?

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The time taken for Bob take to run one lap of the track is 69 seconds

Akira is running around a circular track. Akira runs counterclockwise.

It takes him 95 seconds to run one complete lap

Bob starts running at the same time as Akira

Bob and Akira pass each other for the first time after 26 seconds

It takes him 95 seconds to run one complete lap

In 26 seconds he covers 26/95 laps

In this time Bob must have covered 69/95 laps

An inverse relationship

c/95 = 69/95

c = (69/95) x 95

c = 69

Therefore, time taken for Bob take to run one lap of the track is 69 seconds.

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The expression in terms of x that represents the total amount that Zoe paid is 1.2075x.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

From the information, Zoe goes to a restaurant and the subtotal on the bill was x dollars. A tax of 5% is applied to the bill and Zoe decides to leave a tip of 15% on the entire bill.

The expression will be:

= x + (5% × x) + (15% × 1.05x)

= x + 0.05x + 0.1575x

= 1.2075x

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Answer: y= -4x -24

Step-by-step explanation:

The equation is y=mx + b

We know the b is -24 because it already tells us the coordinate of the y-intercept is (0, -24), so we only need to find x by looking at the rise over run.

The rise is -24, and the run is 6, so -24/6 = -4

So the equation is y= -4x -24

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The arrangements are there with no pair of consecutive letters the same is ∑ₐⁿ(−1)^k2^k(2n−k)!C(n,k).

The past step makes six void spots in which three Is might be sorted out, however just three spots should be picked. Request doesn't make any difference, as every one of the three Is are something similar. Along these lines, there are (63) approaches to picking those spots.

Given 2n letters, two of every one of n types. What number of courses of action of these letters are there without any sets of sequential letters something similar? Kindly look at my answer and let me know where my mix-up is!

So such plans where the sets of indistinguishable letters are discernable. Then, at that point, ∑ₐⁿ(−1)^k2^k(2n−k)!C(n,k) gives the quantity of such plans by incorporation avoidance (there are (2n−k)! ways for k given matches to be together (by combining the those sets into single components) and the rest randomly requested, 2k ways of requesting inside those given matches, and C(n,k) ways of picking those k pairs).So we can acquire the recipe

∑ₐⁿ(−1)^k2^k(2n−k)!C(n,k)

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the surface integral. s (x + y + z) ds, s is the parallelogram with parametric equations x = u + v, y = u − v, z = 1 + 2u + v is 10[tex]\sqrt{14}[/tex]

The surface element is

dS = || ∂r/∂u  x  ∂r/dv || du dv

where

r (u, v) = x (u, v) i + y (u, v) j + z (u, v) k

r (u, v) = (u + v) i + (u - v) j + (1 + 2u + v) k

is the vector parameterization for the surface S.

The normal vector to the surface is

∂r/∂u  x  ∂r/dv

… = (i + j + 2 k)  x  (i - j + k)

… = 3 i + j - 2 k

and has norm

|| ∂r/∂u  x  ∂r/dv || = √(3² + 1² + (-2)²) = √(14)

Now compute the integral:

∫∫ (x + y + z) dS = √(14) ∫₀¹ ∫₀² ((u + v) + (u - v) + (1 + 2u + v)) du dv

… = √(14) ∫₀¹ ∫₀² (3u + v + 1) du dv

… = √(14) ∫₀¹ (3/2 u² + uv + u) |₀² dv

… = √(14) ∫₀¹ (8 + 2v) dv

… = √(14) (8v + 2v²) |₀¹

… = 10 √(14)

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The required balance at the beginning of the incomplete register is $38.25.

Given that,
To determine the beginning balance in the incomplete register.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
In the table, in the register, the balance starts with an entry of $38.25 paycheck. So, the 1 st entry of the register shows the balance in the beginning.

Thus, the required balance at the beginning of the incomplete register is $38.25.

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Answer:

6

Explanation:

x = 3 /cos(60) = 6

The amount of sales Terry must make is $1667

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

Commission = 18% of sales

Commission = $300

These parameters mean that

Commission = 18% of sales

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

18% of sales = 300

Divide both sides by 18%

Sales = 1667

Hence, the amount is $1667

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{(- 8, 6), (- 4, 3), (0, 0), (4, - 3)}set of ordered pairs (x, y) could represent a linear function

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

Linear function is a function whose graph is a straight line

Slope of a line tells us how steep the line is . Slope of a line is same at all the points.

For option A:

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

m=3/2

m=7-4/8-5=3/3=1

Slopes are not same

For option B:

m=3-6/-3+6=-3/3=-1

m=0-3/0+3=-1

m=-4/3

Slopes are not same

For option C:

m=6-8/-1+2=-2

m=4-6/1=-2

m=-3/2

Slopes are not same

For option D:

m=3-6/-4+8=-3/4

m=-3/4

m=-3/4

Slopes are same at every point, so this set of ordered pairs could represent a  linear function

Hence, {(- 8, 6), (- 4, 3), (0, 0), (4, - 3)}set of ordered pairs (x, y) could represent a linear function

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Answer: At a small savings and loan company, you have to deal with your customers being victims of identity theft. This happens unpredictably to one of your customers once every 9 weeks; and no incident seems to have any connection to any other incident.

Step-by-step explanation:

Answer:

x = - 25

Step-by-step explanation:

the absolute value function always gives a positive value , however , the expression inside the bars can be positive or negative, that is

| - a | = | a | =a

given

| x + 10 | = 15 , then

x + 10 = 15 ( subtract 10 from both sides )

x = 5

OR

-(x + 10) = 15

- x - 10 = 15 ( add 10 to both sides )

- x = 25 ( multiply both sides by - 1 )

x = - 25

solutions are x = 5 , x = - 25

Answer: -25

Step-by-step explanation:

Using the percentage method, we know that the original price of the TV set was $400.

Percentages are just fractions with a denominator of 100.

To show that a number is a percentage, we place the percent sign (%) next to it.

For instance, if you properly answered 75 out of 100 questions on a test, you would have received a 75% grade (75/100).

So, we know that the percentage is always out of 100.

Then we automatically know that:

100% - 15% = 85%

We know:
85% = $340

15% = ?

Now, calculate the reduced price as follows:
85/340 = 15/x

85x = 15(340)

85x = 5,100

x = 5100/85

x = $60

Original price of the TV set:

Sold cost + Reduced cost

$340 + $60

$400

Therefore, using the percentage method, we know that the original price of the TV set was $400.

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Six candies would cost $1.44.

Answer:

$1.44

Step-by-step explanation:

We need to figure out how much one piece of candy costs. So you do .96/4, which is going to equal 0.24.

1 piece of candy = $0.24

So we do 0.24*6= 1.44

I hope this helps!!!

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The vertex and range of the function y = |x - 5| + 5 is (5, 4) and  [4, ∞) respectively

The vertex of the function is located at (h,k) of its vertex form, and will be located at the peak or trough of the parabola on a graph. This is the highest or lowest point of the function, depending on its direction.

The range of a function is the complete set of all possible resulting values of the dependent variable (y, usually), after we have substituted the domain.

In the given function;

y = |x - 5| + 4

Using a graph, the lowest point of the function is at x = 5 and y = 4 is the vertex of this function.

vertex = (5, 4)

Range = [4, ∞)

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The value of x in the given function, f(x) = 3/2x - 4 when f(x) = 5, is x = 6

From the question, we are to determine the value of x in the given function for the given value of f(x).

The given function is

f(x) = 3/2x - 4

and

f(x) = 5

Now, to determine the value of x, put f(x) = 5 in the given function

f(x) = 3/2x - 4

5 = 3/2x - 4

Add 4 to both sides of the equation

5 + 4 = 3/2x - 4 + 4

9 = 3/2x

Multiply both sides by 2

2 × 9 = 2 × 3/2x

18 = 3x

Divide both sides by 3

18/3 = 3x/3

6 = x

Therefore,

x = 6

Hence, the value of x is 6

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Answer: x=4

Step-by-step explanation:

6x + 10 = 5x + 14

x + 10 = 14

x = 4

Answer:

They took 3 vans and 3 buses.

Step-by-step explanation:

Given:

To find:

The number of vans and the number of buses they took.

Explanation:

Let the number of vans = v

Let the number of buses = b

The total number of vans and buses is 6:

[tex]v+b=6[/tex]

⇒[tex]v=6-b....[/tex]Equation(1)

Each van holds 6 students and each bus hold 50 students.

The number of students on the trip is 168.

[tex]6v+50b=168[/tex]....Equation(2)

Substitute equation (1) into equation (2):

[tex]6v+50b=168[/tex]

[tex]6(6-b)+50b=168[/tex]

Then solve the equation for b:

[tex]36-6b+50b=168[/tex]

[tex]44b=168-36[/tex]

[tex]44b=132[/tex]

[tex]\frac{44b}{44}=\frac{132}{44}[/tex]

[tex]b=3[/tex]

Then, solve for v:

[tex]v=6-b=6-3=3[/tex]

Answer:

They took 3 vans and 3 buses.

Answer:

628 m

Step-by-step explanation:

We need to find the circumference, C, of the circle.

C = πd

C = 3.14 × 100 m

C = 314 m

Walking around the circular path twice is twice the length of the circumference.

distance = 2C = 2 × 314 m = 628 m

The probability of getting exactly 0 heads is, 0.031.

What is probability?

The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a proposition to be true. A number between 0 and 1 is the probability of an event, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

Given:

A fair coin is tossed 5 times.

So, the the total number of possibilities are,

[tex]2^5= 32[/tex]

We have to find the probability of getting exactly 0 heads.

The only possible set of flips that yields 0 heads is {T, T, T, T, T}.

So,

The probability is, [tex]\frac{1}{32}=0.03125[/tex]

Probability ≈ 0.031

Hence, the probability of getting exactly 0 heads is, 0.031.

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Answer and explanation in one:

(4+9)/(-2-1) = 13/-3 = -13/3

y=-13x/3 + b

4=26/3 + b

b = 4-26/3 = (12-26)/3 = -14/3

y=-13x/3 -14/3 is the line through the two given points

find the line perpendicular and through (14,-6)

y=3x/13 + b, plug in the point to find b

-6 = 3(14)/13 + b

b = -6 -42/13 = -78/13 - 42/13 = -120/3

y= 3x/13 - 120/13

find the intersection point of the two lines, set them equal

3x/13 -120/13 = -13x/3 - 14/3

multiply by 39

9x - 360 = -169x - 182

178x = 360-182 = 178

x = 1

y= -27/3=-9

the point is (1,-9)

calculate the distance from (1,-9) to (14,-6)

d^2 = 9+169 = 178

d = sqr178 = about 13.34

The odds against selecting a history are 31/16.

Probability is the concept that describes the likelihood of an event occurring. In many situations, it is necessary to foresee how something will turn out in the actual world. We may be aware of the result of an event or not. When this occurs, we state that there is a possibility that the event will occur.

Probability is the ratio of the most likely outcomes to all other possible outcomes of an event. The number of successful outcomes for an experiment with 'n' outcomes may be expressed using the symbol x. The following formula can be used to determine the likelihood of an event.

Probability(Event) = favorable outcome/Total outcome = x/n

Number of playwrights = 47

Number of tragedies = 16

Therefore, the odds against selecting tragedies are

(47 - 16) / 16

= 31/16

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The complete question is:

Of the 47 plays attributed to a​ playwright, 11 are​ comedies, 16 are​ tragedies, 20 are histories. If one play is selected at​ random, find the odds against selecting a tragedy.

Answer:

You could divide 5 in half and then add that to the five to find the amount of flour to use in a triple recipe. Hope this helps.

Step-by-step explanation:

The number of total different outcomes are, 7,776.

What is rolling dice?

Every face of a cube known as a dice has a unique number.

By throwing a dice into the air, players can advance in any game by getting a certain number. Typically, this dice or dice has numbers from 1 to 6 written on each face or side of the cube-like shape.

Given:

Discrete 5 dice of different colors are rolled, and the number coming up on each dice is recorded.

Since all the dice are of different colors.

So any combination of the numbers on the dice is unique.

Dice has numbers 1 to 6.

So, for each dice there are 6 possibilities.

Since number coming on a dice is independent to the number coming on the another dice.

So, total different outcomes are = 6 x 6 x 6 x 6 x 6 = 6^5 = 7776.

Hence, the number of total different outcomes are, 7,776.

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Answer:

  remaining zeros: {-1/2, √3}

Step-by-step explanation:

Given the polynomial function f(x) = 2x³ +x² -6x -3 has one zero at x = -√3, you want the remaining zeros.

A polynomial with rational real coefficients and zeros that are roots or complex numbers will have all such roots in conjugate pairs.

The root that is the conjugate of -√3 is +√3.

The product of the roots of an odd-degree polynomial will be the opposite of the ratio of the constant to the leading coefficient. Here, that means the product of roots is ...

  -(-3/2) = 3/2

We already know that two of the three roots are ±√3, so their product is -3. The remaining root will be ...

  (3/2)/(-3) = -1/2

The remaining zeros of f(x) are √3 and -1/2.

__

Additional comment

When the degree of the polynomial is even, the constant term will be the product of the roots. This odd/negative, even/positive behavior comes from the fact that each zero (q) corresponds to a factor (x -q).

The product of these binomial factor constants is the constant in the standard-form polynomial. It will have a negative sign if there are an odd number of factors.

Answer:

9 + 4i

Step-by-step explanation:

5 + 4 + 9i - 5i

=> 9 + 4i