What five things happen when two parallel lines are cut by a transversal?.

The total of 4 players left after 5 rounds.

Given information,

Given that a neighborhood tennis club holds a fundraising competition every year. A total of 128 players are permitted to enter. In each round, half the participants are eliminated.

The function will be written as,

[tex]F(x) = 128e^x[/tex]

To know how many players left after 5 rounds,

Round 1 ⇒ 128/2 = 64

Round 2 ⇒ 64/2 = 32

Round 3 ⇒ 32/2 = 16

Round 4 ⇒ 16/2 = 8

Round 5 ⇒ 8/2 = 4

Hence, 4 players will be left after 5 rounds.

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The expectation of the required  random variable is Ex(r) for the given number of days when a relaxed student delays for laundry is Ex(r) = 5.

As given in the question,

6-sided fair die was rolled by relaxed student

Rolls of fair die represents  1  it mean laundry is done ( no delay in laundry)

Count the number of days when laundry gets  done = 1 / (1 /6)

                                                                                       = 6

Number of days when laundry gets delays = 6 - 1

                                                    = 5

Probability of laundry delay = 5/6

Expectation of the required number of random variables

Ex(r) = [tex]\sum\limits^\infty_0 {P_{r} } \,[/tex]

       = [tex]\frac{5}{6} + (\frac{5}{6}) (\frac{5}{6}) +....[/tex]

       = (5/6)( 1+ ( 5/6) + (5/6)(5/6) + (5/6)(5/6)(5/6) +...)

       =  [tex]( 5/ 6)[ \frac{1}{1- (\frac{5}{6} )}][/tex]

       = 5

Therefore, the number of days when relaxed student delays for laundry is equal to Ex(r) = 5.

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If there are 2. 2 pounds in 1 kilogram then there are 1.91 kilograms in 4.21 pounds.

We need to find how  many kilograms are there in 4. 21 pounds if there are 2. 2 pounds in 1 kilogram. This can be calculated by using unitary method.

There are 2. 2 pounds in 1 kilogram,

We need to find the kilograms are there in 4. 21 pounds

If there are 2. 2 pounds in 1 kilogram,

Then, 1 pound is 1/2.2 kilogram

1 pound = 0.4545

4.21 pound is (1/2.2) 4.21 kilogram

4.21 pound is 1.91 kilogram.

Therefore,  if there are 2. 2 pounds in 1 kilogram then there are 1.91 kilograms in 4.21 pounds.

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Option (d) is correct. Criteria for assigning fixed costs to sectors include relative utility, sustainability, and fairness.

Fixed cost and allocation:

Fixed costs are costs that are essentially constant and do not change with fluctuations in the output of the relevant sector. Fixed costs are borne by the company and exist independently of business activities. Rent, insurance, and depreciation are examples of fixed costs. Cost attributes help identify, total, and assign costs to cost objects.

Fixed cost allocation involves identifying the beneficiaries of outputs and allocating costs to beneficiaries in proportion to the benefits received. Fixed costs can also be allocated in relation to the payer's ability to bear the allocated costs. Fairness is a criterion met where cost allocation is the basis for determining a satisfactory price (such as government contracts).

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[tex]x=number\hspace{5em}x^2=\textit{squared number} \\\\\\ \stackrel{\textit{difference of }x^2\textit{ and 18}}{x^2~~ - ~~18}~~ = ~~\stackrel{\textit{three times }x}{3x} \\\\\\ x^2-3x-18=0\implies (x-6)(x+3)=0\implies x= \begin{cases} 6\\\\ -3 ~~ \checkmark \end{cases}[/tex]

Answer:

The base equals 4 units².

Step-by-step explanation:

Formula:

A = hbB/2

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Answer:

base = 4 units

Step-by-step explanation:

[tex]A=bh/2\\bh=2A[/tex]

[tex]b=2A/h[/tex]

Replace values:

[tex]b=2(24)/12=48/12[/tex]

[tex]b=4[/tex]

Hope this helps

In 120 ways 5 numbers can be arranged through permutations.

A permutation of a set in mathematics is, broadly speaking, the rearrangement of its elements if the set already has an ordered structure into a sequence or linear order. The act or procedure of altering the linear order of an ordered set is referred to as a "permutation." The number of possible arrangements for a given set is calculated mathematically, and this process is known as permutation. Simply said, a permutation is a term that refers to the variety of possible arrangements or orders. The arrangement's order is important when using permutations.

Given,

In following ways 5 numbers can be arranged through permutations,

5!

5 × 4 × 3 × 2×1

120

In 120 ways 5 numbers can be arranged through permutations.

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for point (1,4)

After 1 hour, Evelyn and her friends are 4 miles from shore.

for point (3,12)

After 3 hour, Evelyn and her friends are 12 miles from shore.

If banks' desired reserve/deposit ratio is 25.0 percent, deposits in macro land are $28800000 and the money supply is $36000000

The deposit ratio is the rate sum of money (stores) that commercial banks must not loan out or invest, the reserve ratio is as a rule fixed by the central banks to control inflation and the volume of cash in circulation inside a given country in a particular time.

Initial bank deposit= 60% of 12000000 = 7200000, The reserve/deposit will calculate as follows (25.0 /100%)=0.25 and If banks desired to keep 25.0  it deposit ratio will be : 1/0.25*7200000= 28800000

So the money supply will be the desired deposited :

=28800000+ 7200000 =36000000

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The number of apples that could be in the box is 180

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

Number of apples = Fewer than 200

Children that can share the apples evenly = 2, 3, 4, 5, or 6 children

This means that the number of apples that could be in the box can be a multiple of 2, 3, 4, 5, or 6

Also, the number must be less than 200

The highest number less than 200 that is a multiple of 2, 3, 4, 5, or 6 is 180

Hence, the possible number of apples is 180

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Answer:

Multiples of 60 under 200!

Step-by-step explanation:

A political party is made up of people who band together to run the government, win elections, and shape public policy. Currently, the two major parties in Congress are the Democratic and Republican.

Political parties act as a conduit between the governed and the ruling class. They educate the public, arouse inspiration, and pique interest in and engagement in public affairs. Their main duty is to suggest candidates for elected office.

Self-annuncation, in which a candidate for office only declares their candidacy, is the earliest method of nominating in American politics.

The national chairman, a national committee, the national convention, and two congressional campaign committees make up the party's overall organizational structure. The party is decentralized at the state level, and state legislation generally determines how it is structured.

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If you try to solve an equation and receive a variable or a number equal to itself, the problem has an unlimited number of solutions.

There are an infinite number of solutions to the equation system when two lines coincide with the same y-intercept. If the slope and y-intercept of the two lines coincide, they actually belong to the same line. Although a system of linear equations typically has a single solution, it occasionally may have infinite or no solutions (parallel lines) (same line). When the two lines that make up a linear system cross each other once, the system has a single solution. When the two lines are identical, as in the cases of y=x+3 and 2y=2x+6, a linear system has several (infinite) solutions. When the lines never cross (i.e., they are parallel and have the same slope), a linear system cannot be solved.

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The price per share of BBQ Corp. after there has been a stock split, or post - split, is $24. 15

When there is a stock - split, then each of outstanding shares that a company has, is divided into a number of shares that is determined by the stock split ratio.

The price of the individual shares are also divided into the same ratio as the shares.

This means that the price per share for BBQ Corp. post - split is:

= Price per share before split / 3

= 72. 45 / 3

= $24. 15

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a system of two linear equations is solved by combining the two equations to eliminate one of the variables.

Using the linear combination method, a system of two linear equations is solved by combining the two equations to eliminate one of the variables. Once one of the variables is eliminated, an equation with only one variable is left, e.g., 2x=2, and it is very simple to see that in this case, x=1

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The correct option is A. The formula for the mean absolute deviation over a range of forecasted values is  MAD t 1 t 1.

Forecasting is the method of creating predictions primarily based on past and gift information. Later these can be compared (resolved) against what occurs. for example, a company would possibly estimate their sales in the next yr, then examine it in opposition to the real results. Prediction is similar, but the more preferred time period. Forecasting would possibly confer with particular formal statistical methods using time series, pass-sectional or longitudinal information, or as an alternative to less formal judgmental strategies or the manner of prediction and resolution itself. utilization can range among regions of application:  

for example, in hydrology, the phrases "forecast" and "forecasting" are sometimes reserved for estimates of values at sure unique future instances, at the same time as the term "prediction" is used for extra widespread estimates, consisting of the wide variety of times floods will arise over an extended duration.

chance and uncertainty are vital to forecasting and prediction; it's miles generally taken into consideration as an excellent practice to indicate the diploma of uncertainty attached to forecasts. in any case, the information ought to be updated in order for the forecast to be as accurate as possible. In a few instances, the information used to are expecting the variable of the hobby is itself forecast

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Answer:

its A

Step-by-step explanation:

-x²+x+(4x²-x-1)

-x²+x+4x²-x-1

-x²+4x²-1

3x²-1

:: means average mean in mathematics.

A number system is defined as a system of writing to express numbers.

We need to find what is :: in maths

Mathematical notation consists of using symbols for representing operations, unspecified numbers, relations and any other mathematical objects, and assembling them into expressions and formulas.

: : is a mathematical notation, it is called as double colon and it is used to find the average mean.

a:b: : c:d

In the above expression it acts as an equivalent ration between a:b and c:d

Hence, :: means average mean in mathematics.

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You can buy car A, because the acceptable rate is 14% and here car A has a rate of 20%

Given,

There are three different cars that you could buy. They differ in initial cost, annual operating costs, and life. Your minimum acceptable rate of return is 14%. Use the ROR method to select the best alternative.

Alternative            A             B                 C

Initial Cost          10,000     8,000       5,000

Annual Cost       1,000       1,500        1,500

Life                     8 years    8 years     5 years

Here,

Rate of Return of car A = (10,000 - 1000 x 8) / 100 = 2000/100 = 20%

Rate of Return of car B = (8,000 - 1500 x 8) / 100 = -4000/100 = -40%

Rate of Return of car B = (5,000 - 1500 x 5) / 100 = -2500/100 = -25%

That is,

You can buy car A, because the acceptable rate is 14% and here car A has a rate of 20%

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Using the equation of the model:

a. About 150.4 thousand students studied in abroad in 2011.

b. About 467.5 thousand students would be studying in abroad in 2018.

An example of an equation of a model that can be used to make predictions or determine the value of one variable, is the equation that models the number of college students who studied abroad each year. This is given as y = 123.1(1.069)^x, here, we have:

Using the equation, y = 123.1(1.069)^x, we would solve the following:

a. 2001 after 1998 would be x = 3 years. Therefore, substitute x = 3 into the equation y = 123.1(1.069)^x to find the number of students that are studying abroad in 2001:

y = 123.1(1.069)^3 = 150.4

This implies that about 150.4 thousand students studied in abroad in 2001.

b. 2018 after 1998 would be x = 20 years. Therefore, substitute x = 20 into the equation y = 123.1(1.069)^x to find the number of students that would be studying abroad in 2018:

y = 123.1(1.069)^20 = 467.5

This implies that about 467.5 thousand students studied in abroad in 2018.

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The transtors produced by one machine have a lifetime which is Exponentially Distributed. let X be the lifetime of a transistor.

a) P(X≥200 hours) = 0.29

b) E(x) = 166.7

c) Var(x) = 12222.22

We have given the exponential distribution of lifetime of transtors produced by one machine

So, X∼Exp(x)

a) The probability density function is

f(x)=m × e⁻ᵐˣ

The number e = 2.71828182846e

we have , mean , u = 100 for first machine

and it follows that

P(X≥200) = e⁻²·⁴¹² + e⁻¹·⁸¹² = 2e⁻²≈0.29.

(b) By the tower property of conditional expectation, E(X) = E[E(X|Y)] = XyE(X|Y=y)

pY(y)=E(X|Y= 1)P(Y= 1) +E(X|Y= 2)P(Y= 2).

Again using the conditional distributions of X|Y, we have E(X|Y= 1) = 100, E(XY= 2) = 200.

Hence,E(X) = 100·412+ 200·812=5003≈166.7.

(c) The general formula for a random variable depending on a parameter is:

Var(X) = E(Var(X|Y)) + Var(E(X|Y))

In this case, Y is a random variable which is "100" with a probability of 1/3 and "200" with a probability of 2/3, and X is an exponential distribution with mean Y.

Var(X|Y) = Y² so E(Var(X|Y)) = (1/3)100² + (2/3) 200² = 90000/9

E(X|Y) = Y, so Var(E(X|Y)) = Var(Y) = E(Y²) - E(Y)² = 30000 - (500/3)² = (30000 * 9 - 250000)/9

= 20000/9

Var(X) = 110000/9 = 12222.22

Hence, a) the P(X≥200) = 0.29

b) E(x) = 166.7

c) var(x) = 12222.22

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After applying Baye's Rule , the value of P(A/B) is 1 , the correct option is (d) .

In the question ,

it is given that ,

probability of A is P(A) = 1/2 ,

P(B) is = 1/3 , and

P(A/~B) = 1/4

we know that Baye's Rule for any two events A and B is ,

P(A/B) = (P(B/A) × P(A))/ P(B)

Substituting the values of P(A) and P(B) from above in the Baye's Rule ,

we get ,

P(A/B) = 3/2 × P(B/A)

given that P(A/~B) = 1/4 ,

and we know that , P(B/A) = 1 – P(~B/A)      ....equation(1)

by Baye's rule ,

P(~B/A) = (P(A/~B) × P(~B)) / (P(A))

= (1/4 * 2/3 )/(1/2)

= 1/3

Substituting it in equation(1) , we get

P(B/A) = 1 - 1/3

= 2/3

Substituting the value of P(B/A) in P(A/B) = 3/2 × P(B/A) ,

we get ,

P(A/B) = 3/2 × 2/3

P(A/B) = 1

Therefore , the value of P(A/B) is 1 .

The given question is incomplete , the complete question is

Given two Boolean random variables, A and B, where P(A) = 1/2 , P(B) = 1/3, and P(A/~B) = 1/4 , Apply Baye's Rule and calculate the value of  P(A/B) ?

A. 1/6

B. 1/4

C. 3/4

D. 1

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Option c 15.8% is the required rate of return for Warp-O common stock.

Given,

The market price of share = $45

Beta = 1.4

The rate of return on Treasury bonds = 6%

Market rate of return = 13%

We have to find the required rate of return on Warp-O common stock;

Here,

Rate of return = The rate of return on Treasury bonds + beta × (market rate of return -The rate of return on Treasury bonds  )

= 6% + 1.4 × (13% - 6%)

= 6% + 1.4 ×7%

= 6% + 9.8%

= 15.8%

That is,

The required rate of return on Warp-O common stock is option c 15.8%

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The statements which are true is 4∈W, 7.5∈W and W= ∅

What does the term "universal set" mean?

A set that contains elements from all related sets, without any repetition of elements, is known as a universal set (typically denoted by the letter U). If A and B are two sets, for example, A = 1, 2, 3 and B = 1, a, b, c, then U = 1, 2, 3, a, b, c is the universal set that these two sets belong to.

What are the 8 different kinds of sets?

Empty set, finite set, singleton set, equivalent set, subset, power set, universal set, superset, and infinite set are the various types of sets.

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The upper sum is 24 and the lower sum is 8 for the given function

f(x) = 6 - x², -2 ≤x≤ 2.

A function from a set X to a set Y in mathematics assigns to each element of X exactly one element of Y. The domain of the function is the set X, and the codomain of the function is the set Y.

The first known approximation to the concept of function is attributed to the Persian mathematicians Al-Biruni and Sharaf al-Din al-Tusi. Functions were originally idealistic representations of how one variable quantity depended on another. The location of a planet, for example, changes throughout time. Historically, the concept was formed with infinitesimal calculus near the end of the 17th century, and the functions that were analyzed were differentiable until the 19th century.

Given,

f(x) = 6 - x²

-2 ≤x≤ 2

When n=2, partition of interval -2, 0, 2

When x=-2, f(-2)=6-4

f(-2)=2

x=0, f(0)=6-0

f(0)=6

x=2, f(2)=6-4

f(2)=2

Upper sum= M₁S₁+M₂S₂

=6(2)+6(2)

=24

Lower sum=m₁ s₁+m₂ s₂

=2(2)+2(2)

=8

Therefore, upper sum=24 and lower sum= 8

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Using the test statistic z, the value of z is 1.20.

In the given question,

Given:

Sample Size(n) = 12

Population Mean([tex]\mu[/tex]) = 25

Standard Deviation(S) = 4.6

Statistic of intereset(x) = 26.6

The test statistic z is

[tex]z=\frac{x-\mu}{\frac{s}{\sqrt{{n}}}}[/tex]

Putting the value

[tex]z=\frac{26.2-25}{4.6/\sqrt{12}}[/tex]

z = 1.6/(4.6/3.46)

z = 1.6/1.329

z = 1.20

Hence, the value of z is 1.20.

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Bisectors are the special segments that pass through the mid point of the lines or line segments.

A bisector is the line, line segment or ray that intercepts and/or divided lines or line segments into two equal line segments and thus passes through the midpoint of the given line segment or line segments.

There can be infinite bisector for one particular line or line segment at multiple angles.

The bisector that intercepts and/or cuts a line in half, passes through the midpoint when it is perpendicular (making an angle of 90°) to the line segment is known as the Perpendicular Bisector.

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The population mean strength of the components differs from 50 is 0.304.

In the  given question, an engineer selected 30 components at random and measure their strengths. 34,54,73,38,89,52,75,33,50,39,42,42,40,66,72,85,28,71,52,47,41,36,33,38,49,51,55,63,72,78

We have to check does this data suggest that the population mean strength of the components differs from 50 and we have to set up an appropriate hypothesis test to answer this question.

Sample size n = 30

Claim : The population mean strength of the components differs from 50.

Null and alternative hypothesis:

H(0): μ = 50

H(A): μ≠50

As the population standard deviation is unknown (not given) , t-test can be used .

Test Statistic :

t = (X-μ)/(S/√n)

To find the sample mean we find the average of the given sample.

So

X = 34 + 54 + 73 + 38 + 89 + 52 + 75 + 33 + 50 + 39 + 42 + 42 + 40 + 66 + 72 + 85 + 28 + 71 + 52 + 47 + 41 + 36 + 33 + 38 + 49 + 51 + 55 + 63 + 72 + 78/ 30

X = 53.267

Now finding the standard deviation using the excel.

SD = 17.1101

To find the SD we use the formula =STDEV(B1:C15)

Now putting the value in the formula of Test Statistic

t = (X-μ)/(S/√n)

t = (53.267-50)/(17.1101/√30)

After solving:

t=1.046

P-value :

As the alternative hypothesis H(A) is of not equal to type , this is two tailed test.

Degrees of freedom = n-1 = 30 -1 = 29

df =29

Using Excel function , =TDIST( t , df , number of tails )

=TDIST( 1.046 , 29 , 2 )

=0.304201657

Rounding to three decimal places

= 0.304

P-value = 0.304

Hence, the population mean strength of the components differs from 50 is 0.304.

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Answer:

shaded area

unlikely

Step-by-step explanation:

She should guess a shaded portion of a rectangle that has a height of 10 and a length of 8 to maximize her chances of winning. The unlikely word describes the likelihood of the ball stop.

First, we need to find the areas of all the regions.

The area of the shaded rectangle = Length x Breadth = 10 x 8 = 80 square units

Area of unshaded rectangle = Length x Breadth = 5 x 2 = 10 square units

Area of unshaded triangle = 1/2 x base x height = 1/2 x 4 x 8 = 32/2 = 16 square units

Area of unshaded square = Side^2 = 4^2 = 16 square units

The area difference between the shaded and unshaded areas = The area of the shaded rectangle - (Area of unshaded rectangle + Area of unshaded triangle + Area of the unshaded square)

The area difference between the shaded and unshaded areas = 80 - (10 + 16 + 16)

The area difference between the shaded and unshaded areas = 80 - 42 = 38

As we see that the area of the shaded region is 38 more than the unshaded region so to maximize her chances of winning she should guess the shaded region or area.

Probability percentage of the shaded rectangle = 80/122 x 100 = 65.57%

Probability percentage of an unshaded rectangle = 10/122 x 100 = 8.20%

Probability percentage of an unshaded triangle = 16/122 x 100 = 13.11%

Probability percentage of an unshaded square = 16/122 x 100 = 13.11%

The unlikely word describes the likelihood of the ball stopping in a square or rectangular-shaped area because one is shaded and unshaded and the other is only unshaded. So, both are having different probabilities because of shape, area, and portion.

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