let n be a positive integer and suppose n distinct lines are drawn in the plane. no two of these lines are parallel, and no three of these lines intersect at a common point. prove that these lines divide the plane into n 0 c n 1 c n 2 regions.

The expressions of the total cost are 1.15t and t * (1 + 0.15)

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

Cost of a ticket = t dollars

Amusement tax on each ticket = 15%

The above parameters mean that the total cost of a ticket can be calculated using the following equation

The total cost of a ticket = Cost of a ticket * (1 + Amusement tax on each ticket)

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

The total cost of a ticket = t * (1 + 15%)

Evaluate the percentage

The total cost of a ticket = t * (1 + 0.15)

So, we have

The total cost of a ticket = t * (1.15)

Evaluate the product

The total cost of a ticket = 1.15t

Hence, the expression is 1.15t

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We can prove that the given triangles GHL and KHJ are congruent using the ASA theorem. So, the second option is the correct answer.

We can say any two shapes are congruent if they have the same shape and size. For this, their sides and angles need to be mirror images of each other. We have four congruency theorems at hand here. These are side-side-side(SSS), angle-side-angle(ASA), side-angle-side(SAS), and angle-angle-side(AAS).

According to the ASA congruency theorem, one side and two angles of the triangles in question need to be similar. In the given image, we can see that two of the angles i.e., HGL and HKJ are congruent while GHL and KHJ are congruent. The sides GH and KH are also congruent. This makes the two triangles  △GHL ≅ △KHJ by the ASA theorem. So, the second option is the correct answer.

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The equation of circle for both the parts will be as,

(a)  (x-3)² +(y-2)²= 4

(b)   x²+y² = 1

What is circle?

A circle may be a form consisting of all purposes in a very plane that ar at a given distance from a given point, the centre. Equivalently, it's the curve copied out by a point that moves in a very plane so its distance from a given point is constant.

Main Body:

(a) When the circle is offset from the origin, the equation for the radius gets messy. In general, it will be the root of a quadratic equation in sine and cosine, not easily simplified. The Cartesian equation is easier to write.

Circle centered at (h, k) with radius r:

(x -h)² +(y -k)² = r²

The given circle is ...

(x -2)² +(y -2)² =2²

(x -2)² +(y -2)² = 4

__

(b) When the circle is centered at the origin, the radius is a constant. The desired circle is most easily written in polar coordinates:

x²+y² = 1

Hence the equation of circle is such.

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Answer:

34

Step-by-step explanation:

hope u new it have fun hsm s

The main difference between experiment and survey is that experiment is laboratory research and survey is field research. Experiments are used to prove theories or hypotheses. Surveys are used to understand the notions of a group of people.

The year in which the number of both jobs pharmacy technicians and network systems and data communication analysts is equal is 2008.

Considering the set of equations

7.3x - y = -256

12.1x - y = -234

where x represents the period of time since 2003.

y represents the quantity of jobs in thousands.

We have the answer after solving the system:

(x, y) ==> (4.5, 292)

Find the year where the total number of both jobs is equal.

At the solution point, the graphs of the two lines will collide.

The year in which the number from both jobs is equal will be 4.5 years after 2003, since x is the number of years after 2003.

So, here we are:

Year where the sum of the two jobs is equal:

2003 + 4.5 = 2007.5

= 2008 year

As a result, there will be an equal number of both jobs in 2008.

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Answer:

The letter [tex]r[/tex] in the given formula represents the rate of interest.

Explanation:

Where I is the amount of interest, P is the principal (amount of money borrowed), r is the interest rate (per year), and t is the time (expressed in years).

Hope this helps!

Answer:

You can draw a picture like this:

Step-by-step explanation:

If we are working with fractions, then think of it as a circle.

3 circles divided by 8 people

(Draw 3 circles divided into eighths)

Now, on the first circle, write the number one into one of the slices.

Do the same to the second circle.

Now the third.

How many slices have the number 1 in it?

3 slices have the number 1 in it.

And each whole circle has 8 pieces.

3 (slices) divided by 8 (People) = 3/8

lines a and d are neither parallel nor perpendicular.

What is the slope of line?

Given two line-side coordinates, use the slope formula to determine the slope of the line. The slope is defined as the ratio of the change in the y values to the change in the x values using the formula m=(y2-y1)/(x2-x1). x1 and y1 are represented by the first point's coordinates. The second points are located at x2, y2, and their locations. Whichever point you choose to classify as the first and which as the second doesn't matter.

The given points of line d is (3,5) and (10,1)

and line an of line a is (5, 8) and (2, 13).

The slope of line d is m 1 = [tex]\frac{1-5}{10-3}[/tex]

m1 = -4/ 7

The slope of line d is m2 = [tex]\frac{13-8}{2-5}[/tex]

m2 = -5/3

if the slope of two lines is equal that is m1 = m2 , then the lines are parallel and the relation m1*m2=−1, then the lines are perpendicular to each other.

Here both condition fails.

Hence, lines a and d are neither parallel nor perpendicular.

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An Endure chosen randomly the likelihood of any battery lasting longer than 550 hours is 10.56%.

These steps are used to determine the Z score:

z = (x - μ)/σ

As mentioned in question-

x > 550 and μ = 500, σ = 40:

z = 550 - 500 / 40

z = 1.25

Obtain the p-value from normal distribution chart,

P(z > 1.25) = 1 - P(z < 1.25)

P(z > 1.25) = 1 - 0.8944

P(z > 1.25) = 0.1056

Thus, an Endure chosen at random the likelihood of any battery lasting longer than 550 hours is 10.56%.

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To know the answer check the given file.

The number of tests that it would take for the probability of committing at least one type I error to be at least 0.7 is 118   .

In the question ,

it is given that ,

the probability of committing at least , type I error is = 0.7

we  have to find the number of tests ,

let the number of test be n ,

the above mentioned situation can be written as

1 - P(no type I error is committed) ≥ P(at least type I error is committed)

which is written as ,

1 - (1 - 0.01)ⁿ ≥ 0.7

-(0.99)ⁿ ≥ 0.7 - 1

(0.99)ⁿ ≤ 0.3

On further simplification ,

we get ,

n ≈ 118 .

Therefore , the number of tests are 118 .

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Fewer families with kids under 18 now have dinner together seven nights a week

Given,

Let p represent the percentage of households with kids under 18 that have supper together every night.

So, Null Hypothesis, : p 38%    (meaning that more or the same number of families with children under the age of 18 now have dinner together seven nights a week.)

Alternate Hypothesis, : p < 38%     {means that the proportion of families with children under the age of 18 who eat dinner together seven nights a week has​ decreased}

The test statistics that will be used here is One-sample z-test for proportions;

T.S.  =    ~  N(0,1)

Where,

p  = sample proportion of families = 403/1122 = 0.36

n = sample of adults with children under the age of 18 = 1122

So,

The test statistics =     -1.32

The value of z-statistics is -1.32.

Also, the P-value of the test statistics is given by;

 P-value = P(Z < -1.32) = 1 - P(Z  1.32)

= 1 - 0.9066 = 0.0934

We have enough data to reject our null hypothesis since the test statistics will fall in the rejection region because the P-value for our test statistics is less than the level of significance, which in this case is 0.0934 <  0.10.

As a result, we draw the conclusion that fewer families with children under the age of 18 now have supper together seven nights a week.

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It seems that there is perhaps some missing info here. Could you double check your question to validate the information being asked? Tysm!

Logarithmic function log₍ₓ₊₂₎(4) = 3x can be written in exponential form as  4 = 3x ⁽ˣ⁺²⁾

Which property of log function is used?

The properties of log are nothing but the rules of logarithms and these are derived from the exponent rules.

These properties of logarithms are used to solve the logarithmic equations and to simplify logarithmic expressions.

A log function can be written in exponential form using

logₐ m = x ⇒ m = ax

According to the given question:

The given logarithmic function is

log₍ₓ₊₂₎(4) = 3x

On applying the property we get

4 = 3x ⁽ˣ⁺²⁾

Hence the required exponential form is 4 = 3x ⁽ˣ⁺²⁾

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Under the Binomial and Poisson distributions gives approximate result is p → 0 n → ∞.

One of the common discrete distribution which is used in Statistics is the Binomial distribution. The Binomial distribution often deals with two types of situations, first, the occurring of an event and second, the non-occurring of an event termed respectively as success and failure. The Binomial distribution can be typically characterized by the two parameters namely “n” and “p” where “n” represents the number of trials and “p” represents the fixed probability of occurring of the desired event.

Further, the Binomial distribution can be visualized as an approach to determine the probability of observing a specified number of successes in a specified number of trials. The typical examples of Binomial distribution in our day-to-day life may include the survival of number of cancer patients, from the treatment offered, over a specified period of time;

Winning the number of seats against the number of candidates filed by a certain political party for an election;

Number of people benefiting from a certain house scheme when applied;

Number of covid patients discharged within three days from the hospital after their admission to a hospital for the treatment.

There is another discrete distribution which is equally popular as the Binomial distribution is the Poisson distribution. While the Binomial distribution deals with the number of trials and the probability of a success, Poisson distribution deals with the average number of successes per day or the number of successes observed per unit of time.

Unlike, in the case of a Binomial distribution, for a Poisson distribution, the knowledge of number of trials to get the observed number of successes is not required. The Poisson distribution has only one parameter namely “m” the mean number of successes per given unit of time.

The Poisson distribution is often taken as a limiting case of Binomial distribution, under the following conditions.

The number of trails is indefinitely large i.e., n → ∞

The probability of success, “p” is very small i.e., p → 0

np is finite i.e., np = m where p = m/n and q = 1 – m/n and m > 0.

However, it is not defined if “n” is large means how large and “p” is closed to zero means how small? It is left to the readers to assume how large n should be and how small p should be? As mentioned earlier, the Poisson distribution is often described as a limiting case of Binomial distribution.

Based on the results of the study , published by me clearly proves that even when 10 ≤ n ≤50 and p ≤ 0.2, the Poisson distribution can be a good approximation to Binomial distribution.

Hence the answer is Under the Binomial and Poisson distributions gives approximate result is p → 0 n → ∞.

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Answer:

8

Step-by-step explanation:

23:41

41+23=64

64/8=8

This table illustrates how many trials out of 100 resulted in each number of heads out of ten flips. Because it precisely depicts the possibility of each occurrence, this frequency table is the most likely to include the outcomes of the 100 trials.

The likelihood of receiving any number of heads out of ten flips is the same in a fair coin flip, therefore the table should show a fairly uniform distribution of trials across each number of heads. Overall, the frequency table most likely to capture the outcomes of the 100 trials has the number of heads out of 10 flips as rows and the number of trials out of 100 as columns.

This table may be used to precisely depict the data as well as determine the likelihood of each occurrence.

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Since , a researcher is attempting to determine which ethnic group is more likely to go to the movies at a movie theatre. The dependent variable is metric. Therefore, the Multiple Regression method will be more appropriate analysis of variance.

Multiple regression analysis is a statistical technique that analyzes the relationship between two or more variables and uses that information to estimate the value of the dependent variable. The goal of multiple regression is to develop a model that describes the dependent variable y with multiple independent variables. Linear regression has only one independent and dependent variable. But for multiple regression, there are many independent variables that help explain or predict the dependent variable y better.

The multiple regression equation is given by

y = a + b 1×1+ b2×2+……+ bk xk

where x1, x2, ….xk are the k independent variables and y is the dependent variable

Advantages of multiple stepwise regression:

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The correct option for the lines of symmetry of a regular pentagon-

An image of a pentagon's five lines of symmetry is included below.

We can observe from the following photo that the lines for symmetry cut through a vertex angle, a side, and are perpendicular to either a side.

Options C, D, and E are the appropriate choices.

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Complete question is;

Which statements are true about the lines of symmetry of a regular pentagon? Check all that apply.

A) Every line connects two vertices.

B) Every line connects the midpoints of 2 sides.

C) Every line bisects a vertex angle.

D) Every line bisects a side.

E) Every line is perpendicular to a side.

Answer: Identify the concluion of the tatement. If AB i a egment, then it ha two endpoint. O The egment ha two endpoint. O If AB i a egment. O

AB i a egment. O Then, the egment ha two endpoint

Step-by-step explanation: Identify the concluion of the tatement. If AB i a egment, then it ha two endpoint. O The egment ha two endpoint. O If AB i a egment. O

AB i a egment. O Then, the egment ha two endpointIdentify the concluion of the tatement. If AB i a egment, then it ha two endpoint. O The egment ha two endpoint. O If AB i a egment. O

AB i a egment. O Then, the egment ha two endpointIdentify the concluion of the tatement. If AB i a egment, then it ha two endpoint. O The egment ha two endpoint. O If AB i a egment. O

AB i a egment. O Then, the egment ha two endpointIdentify the concluion of the tatement. If AB i a egment, then it ha two endpoint. O The egment ha two endpoint. O If AB i a egment. O

AB i a egment. O Then, the egment ha two endpointvvIdentify the concluion of the tatement. If AB i a egment, then it ha two endpoint. O The egment ha two endpoint. O If AB i a egment. O

AB i a egment. O Then, the egment ha two endpointIdentify the concluion of the tatement. If AB i a egment, then it ha two endpoint. O The egment ha two endpoint. O If AB i a egment. O

AB i a egment. O Then, the egment ha two endpointIdentify the concluion of the tatement. If AB i a egment, then it ha two endpoint. O The egment ha two endpoint. O If AB i a egment. O

AB i a egment. O Then, the egment ha two endpointIdentify the concluion of the tatement. If AB i a egment, then it ha two endpoint. O The egment ha two endpoint. O If AB i a egment. O

AB i a egment. O Then, the egment ha two endpointIdentify the concluion of the tatement. If AB i a egment, then it ha two endpoint. O The egment ha two endpoint. O If AB i a egment. O

AB i a egment. O Then, the egment ha two endpointIdentify the concluion of the tatement. If AB i a egment, then it ha two endpoint. O The egment ha two endpoint. O If AB i a egment. O

AB i a egment. O Then, the egment ha two endpoint

Answer: X is equal to 21

Step-by-step explanation:

Answer:

25 degrees

Step-by-step explanation:

5x - 10 = 115

5x = 115 + 10

5x = 125

5/5 x = 125/5

x = 25

Answer: the one in blue

Step-by-step explanation:

The given expression can be simplified as (x³ + 3x + 5)/(x² - x).

If the fractions have the same denominators then their numerators are added keeping the denominators as the same.

For fractions with different denominators the LCM of the denominators are taken then that is divided by the numerators of each fraction and the number obtained is multiplied to each of them to get the equivalent fraction.

The given expression is as below,

(x² - 5)/x + (x + 8)/(x - 1)

It can be simplified as follows,

(x² - 5)/x + (x + 8)/(x - 1)

= ((x² - 5)(x - 1) + x(x + 8))/(x(x - 1))

= ((x³ - x² - 5x + 5) + x² + 8x)/(x² - x)

= (x³ + 3x + 5)/(x² - x)

Hence, the given expression can be written in the form of single fraction as (x³ + 3x + 5)/(x² - x).

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There are 207 students in the 9 classes at East Middle School. At this rate, how many students are in 6 classes?

1: 54 students

2: 138 students

3: 69 students

4: 250 students

207 / 9 = 23

23 * 6 = 138

The required number of ways to arrange the letters in the word mississippi so that either all the is are consecutive are 11!/4!2!4!..

factorial, in science, the result of all certain whole numbers not exactly or equivalent to a given positive whole number and meant by that whole number and an interjection point. Subsequently, factorial seven is composed 7!, meaning 1 × 2 × 3 × 4 × 5 × 6 × 7. Factorial zero is characterized as equivalent to 1.

We have,

All out no. of words = 11

Had all letters been unmistakable, the response would have been =11!. However, as it isn't the case we want a method for diminishing it to consider the way that a portion of its letter sets are same.

In each game plan of the expressions of "mississippi" :

Presently taking into truth the over three focuses decrease 11! by separating it by 4!2!4! also, you have your response.

Thus, required arrangement is 11!/4!2!4!.

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Sum of the 15 two elements subset of $\{1,2,3,4,5,6} = ( N-1) (N)(N+1)/2

Three elements....two at  time  (1,2) (1,3) (2,3)....sum  =   12

Four elements .... two at a time  (1,2) (1,3) (1,4) (2,3) (2,4) (3,4)  .....sum  =  30

Five elements....two at a time  (1,2) (1,3) (1,4) (1,5) (2,3) (2,4) (2,5) (3,4) (3,5) (4,5)

Note that for N elements taken 2 at a time....the pattern of sums seems to be

= (N-1)(N)(N+1) / 2

For taking 6 elements taking 2 at a time the sum should be

=(5)(6)(7) /2

=210 /2

=105

Therefore, total sum  of those 15 sums  of the elements of each of the 15 two-element subsets of $\{1,2,3,4,5,6\}$ = 105

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Answer:

no it wont

Step-by-step explanation:

Answer:

6, 7, 10

Step-by-step explanation:

7 > x - 4 ( add 4 to both sides )

11 > x , then

x < 11

the values from the table which are solutions are 6, 7, 10

Answer:

Answer is 11

Step-by-step explanation:

7+4>z-4+4

11>z