A vertical line passes through the point (2,7). What is the equation for this line

The justification of each step in solving the system of equations is below;

5x - y = 3

x + 2y = 5

multiply equation (1) by 2 (Multiplication Property of Equality)

10x - 2y = 6

x + 2y = 5

Add both equations (Addition Property of Equality)

11x = 11

divide both sides by 11

x = 1

Substitute x = 1 into (Substitution Property of Equality)

5x - y = 3

5(1) - y = 3

5 - y = 3

-y = 3 - 5

-y = -2

y = 2

Hence, the steps involved in solving the equation are; Multiplication Property of Equality, Addition Property of Equality, Substitution Property of Equality.

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The probability that the household has a dog given that the household has a cat is 37.5%

The probability that the household has a dog given that the household has a cat can be found using Bayes' Theorem.

Applying that, we have P(dog | cat) = P(cat and dog) / P(cat) = (P(cat) * P(dog | cat)) / P(cat) = (0.20 * P(dog | cat)) / 0.20 = P(dog | cat)

P(cat or dog) = P(cat) + P(dog) - P(cat and dog) = 0.45

P(cat and dog) = P(cat) * P(dog | cat) = 0.20 * P(dog | cat)

P(dog) = P(dog or cat) - P(cat) = 0.30

P(cat and dog) = P(dog or cat) - (P(dog) - P(cat and dog)) = 0.45 - (0.30 - P(cat and dog))

P(cat and dog) = 0.45 - 0.30 + P(cat and dog)

P(cat and dog) = 0.15 + P(cat and dog)

2 * P(cat and dog) = 0.15 + 2 * P(cat and dog)

P(cat and dog) = 0.15 / 2

P(dog | cat) = P(cat and dog) / P(cat) = 0.15 / (2 * 0.20) = 0.375

In conclusion, the probability that the household has a dog given that the household has a cat is 37.5%.

The results of the exponent expressions are;

5) 8

6) 125

7) 1

8) 1

9) 1/36

10) 1

11) 1/16

12) -27

13) 5 1/4

14) 1/243

15) 1/125

We know that the laws of exponents are also called the laws of indices these are the laws that can be used when we are trying to sort out a mathematical problem that involves the expoennets.

In this case we can see that we can use the laws of the exponents to determine the simple values of each of the expressions as we have been able to show above and then know what then value of the exponent is.

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an elevation of 3m is closer because it has a distance of 3 spaces from sea level, while -4 m has a distance of 4. Hope this helped =)

The variance is the correct option of property of Poisson distribution.

The Poisson distribution has the property that its mean is equal to its variance. This means that the average number of occurrences, represented by λ, is equal to the spread of the distribution.

The Poisson probability is calculated as P (x, λ) = (e^-λ * λ^x) / x! where e is approximately equal to 2.71828. The mean, represented as E(X), is equal to the variance, V(X). In a Poisson distribution, λ is the expected value of the distribution.

When certain conditions are met, there is a table available to make calculating probabilities easier using the Poisson distribution.

In Poisson distribution, the mean is known as E(X) = λ.

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The total number of students going for the weekend trip as per the given total cost and other charges is equal to 50.

Let us consider 'n' be the number of students going for trip.

Per student charge for food and lodging = $50

Total food and lodging charges = $50n

Bus charges per student = $25

Total bus charges = $25n

Bus cleaning fees = $15

Total cost for the trip = $3,765

Equation formed for the above condition is:

$ (50n + 25n + 15 ) = $3,765

⇒ $ ( 75n + 15 ) = $3,765

⇒ 75n = 3,765 - 15

⇒ n = 3,750/ 75

⇒ n = 50

Therefore, there are 50 students going on the weekend trip.

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Answer:

122

Step-by-step explanation:

We treat the estimated intercept and slope coefficients from the sample regression as normally distributed because of Central Limit Theorem .

The Central Limit Theorem is the reason is the estimated intercept and slope coefficients from a sample regression as normally distributed.

In the Regression Analysis, the intercept and slope coefficients are estimated using a sample of data, instead of  the entire population.

The Central Limit Theorem states that ; as sample size increases, the distribution of the sample mean approaches a normal distribution.

In the context of regression analysis, it means that, as sample size increases, distribution of estimated coefficients approaches a normal distribution.

The given question is incomplete , the complete question is

We treat the estimated intercept and slope coefficients from the sample regression as normally distributed because of _____  .

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Considering the distributive property, the factored expression is given as follows:

3/4(x + 3).

The expression for this problem is defined as follows:

3/4x + 9/4.

The common factor to both terms of the expression is given as follows:

3/4, as 3 x 3/4 = 9/4.

Hence the factored expression is given as follows:

3/4(x + 3).

Applying the distributive property, multiplying the outer term 3/4 by both of the inner terms and combining them, we go back to the original expression.

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The number of robberies in Colorado Springs per year is a ratio variable is 1/2

Ratio variables are a type of continuous variable in which the values have a meaningful order and can be compared in terms of their size.

In terms of mathematical expression, the number of robberies in Colorado Springs per year can be represented by the variable x.

The value of x can range from 0 to infinity, with 0 implying the absence of robberies and any value greater than 0 representing the number of robberies that have occurred. The mathematical expression for this ratio variable would be:

=> x = number of robberies in Colorado Springs per year.

Where the value of 4 and 2, then it can be written as,

=> 2/4 = 1/2

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Displacement of the truck is 5 km south.

Displacement is defined as the change in the position of an object. Displacement is a vector quantity since it has both direction and magnitude.

Given that A truck drives 8 km east, 5 km south, then 8 km west.

The figure representing the position of the truck is given.

Truck moves from A to B 8 km east.

Then move from B to C 5 km south.

Then move from C to D 8 km west.

Displacement of the truck is the shortest distance from A to D.

It is equal to 5 km and the direction is south.

Hence the displacement is 5 km south.

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If you wanted to visualize the change in the mean test score for the same exam over multiple semesters then you can bar chart for visualizations.

A bar chart would be a suitable visualization to see the change in the mean test score for the same exam over multiple semesters. These types of charts allow you to see trends and changes over time, making it easy to compare the mean test scores from one semester to the next.

A histogram is used to visualize the distribution of continuous data, while a pie chart is used to show the proportion of various categories, so they are not suitable for this type of data visualization.

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there is a 5% probability of rejecting a false null hypothesis and hence c is correct option

Simply put, probability is the likelihood that something will occur.

When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.

Testing hypotheses is a crucial component of empirical research and evidence-based medicine. A well-developed hypothesis is only half the solution to the research problem. Working understanding of fundamental statistical principles is preferred for this, as well as subject-specific knowledge gleaned through a thorough survey of the literature.

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The sum of two numbers is 13 more than twice the first number. Their difference is 14 less than twice the second number. Then each of these numbers are 1/2 and 13 1/2.

Create equations from statements

Suppose: x = the first number

                y = the second number

x + y = 2x + 13

⇔ y + x - 2x = 13

⇔ y - x = 13

⇔ y = x + 13    ... (1)

y - x = 2y - 14

⇔ y - 2y - x = -14

⇔ -y - x = -14  ... (2)

Solve the system of equations

-y - x = -14

- (x + 13) - x = -14

-x - 13 - x = -14

-2x = -1

  x = 1/2

y = x + 13

y = 1/2 + 13

y = 13 1/2

So, each of these numbers are 1/2 and 13 1/2.

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(a) The two expressions 3(m - 2)  +  2(m - 2)  and 5(m - 2 )  are equivalent.

(b) They are equivalent because  they will have equal values when we plug in the same variable.

Equivalent expressions are expressions that work the same even though they look different.

If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value(s) for the variable(s).

The given expression include the following;

3(m - 2)  +  2(m - 2)  

= 3m - 6 + 2m - 4

= 5m - 10

5(m - 2 )

= 5m - 10

Thus, we can conclude that the two expressions 3(m - 2)  +  2(m - 2)  and 5(m - 2 )  are equivalent.

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Answer: only to give the other brainlest

Step-by-step explanation:

The probability that no letters are repeated is 0.4121.

Divide the total number of outcomes by the entire number of different ways an event could happen to arrive at the probability. There are differences between probability and odds. The possibility of an event happening divided by the likelihood that it won't happen yields the odds. Probability is a metric used to assess the likelihood that a specific event will occur. The likelihood that the coin will land with the heads side up is measured using the probability concept when we toss it in the air. Here is an example of how probability is used in everyday life that you probably already know about. Prior to a major outing, we always consult the weather prediction.

So, the probability

Given, Number of letters=8

N[tex]=26*25*24*23*22*21*20*19[/tex]

P[tex]=\frac{25}{26}*\frac{24}{26}*\frac{23}{26}*\frac{22}{26}*\frac{21}{26}*\frac{20}{26}\\=0.96*0.92*0.88*0.85*0.81*0.77\\=0.4121[/tex]

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∠ XYQ is 122 degrees.

Angles are an important concept in mathematics and geometry. They are formed when two rays or line segments intersect at a common endpoint, known as the vertex. Angles can be measured in degrees, which is a unit of angular measure. A full circle is 360 degrees, and angles can be classified based on their measure relative to this standard. For example, an angle measuring less than 90 degrees is called an acute angle, while an angle measuring exactly 90 degrees is a right angle. An angle measuring between 90 and 180 degrees is an obtuse angle, and an angle measuring exactly 180 degrees is a straight angle. Angles are used in many applications, such as trigonometry, physics, and engineering. They are also important in everyday life, such as determining the direction of travel or the position of objects.

We can start by using the fact that angles XYQ and ZYQ are co-interior angles (also known as consecutive interior angles) and that they lie on a straight line, which means they add up to 180 degrees. So we have:

∠XYQ + ∠ZYQ = 180

Substituting the given values for ∠ZYQ and ∠XYQ, we get:

(10a + 2) + (5a - 2) = 180

Simplifying and solving for a, we get:

15a = 180

a = 12

Now we can substitute this value back into the expression for angle ∠XYQ to find its value:

∠XYQ = 10a + 2 = 10(12) + 2 = 122

Therefore, angle ∠XYQ is 122 degrees.

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Answer:

A

Step-by-step explanation:

because of the vertical line rule

for every other one when you draw vertical line you can get more values for y for the same x

The values of x in the circles and secant lines are 7 in all cases

To calculate x, we make use of the intersecting secant line theorem which stated that

a * c = b * d

Using the above as a guide, we have the following:

Shape (7)

4 * (4 + 2x) =3 * (3x + 1)

This gives

16 + 8x = 9x + 9

Collect and evaluate the like terms

x = 7

Shape (8)

20 * (20 + x) = 15 * (15 + 3x)

This gives

400 + 20x = 225 + 45x

Collect and evaluate the like terms

x = 7

Shape (9)

6 * (6 + 4) = 5 * (5 + x)

This gives

60 = 25 + 5x

Collect and evaluate the like terms

x = 7

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Yes, there are situations where the data may not be centered around the average or where the average is not the best representation of the data collected.

For example, in a positively skewed distribution, the mean is greater than the median, and the data is spread out more on the right side of the average. In this case, the average may not accurately represent the "typical" value in the data set. In addition, in cases where there are extreme outliers in the data, the mean can be greatly affected, making it a less representative measure of central tendency. In such cases, the median or mode may be a better representation of the data.

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a) The solution for x is obtained as follows: x = 5.

b) The vertical angles are not complementary, as the sum of the measures of the angles is different of 90º.

Vertical angles are angles that are opposite by the same vertex on crossing segments, hence they share a common vertex, thus being congruent, meaning that they end up having the same angle measure.

Considering the vertical angles, the value of x is obtained as follows:

8x + 3 = 9x - 2.

9x - 8x = 3 + 2

x = 5.

Hence the angle measures are of:

8 x 5 + 3 = 43º.

The sum of the measures is of 86º, which is different of 90º, hence the vertical angles are not complementary.

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If the population standard deviation of a sample decreases without other changes, then the confidence interval will also decrease or become narrower.

If the population standard deviation of a sample decreases without other changes, the standard deviation of the sample mean (known as the standard error of the mean) will also decrease. This will lead to a decrease in the width of the confidence interval, meaning that the interval will become more precise and the confidence level in the estimation of the population mean will increase.

A smaller standard deviation results in a smaller standard error, which in turn leads to a narrower confidence interval and a higher level of confidence in the estimation of the population mean.

This is because the confidence interval is calculated using the standard error and the sample mean, and the standard error is a measure of the variability in the sample mean. So, if the standard deviation decreases, the variability in the sample mean will decrease, resulting in a more precise estimation of the population mean.

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The median is the least appropriate measure of central tendency for a data set that contains outliers .

What does math's median mean?

When a data set's median value is used, 50% of the data points in the collection have values that are lower or equal to the median and 50% of them have values that are higher or equal to the median.

                                      When working with a small data collection, you must first count the number of data points (n) and organize them in ascending order.

What is the average succinct response?

The middle number, or median, is obtained by sorting all of the data points and choosing the center one (or if there are two middle numbers, taking the mean of those two numbers).

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The complete question is -

Generally, which one of the following is the least appropriate measure of central tendency for a data set that contains outliers? a. mean b. median c. 2nd quartile d. 50th percentile

The area of the prism A before dilation is 75 m²

Dilation means changing the size of an object without changing its shape. The size of the object may be increased or decreased based on the scale factor.

Given that, a triangular prism B is the image of triangular prism A after dilation by a scale factor of 1/5, the surface area of triangular prism B is 3 m²,

Since, the dilation transformation gives similar figures,

We know that, in solids that are similar, the ratio of their surface areas is equal to the square of the ratio of their scale factor.

Let the area of Prism A be x,

Therefore,

(1/5)² = 3/x

x = 75

Hence, the area of the prism A before dilation is 75 m²

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The new triangle is similar with original triangle.  By using this, the perimeter of the new triangle P₂ = 75 cm.

When applying a scale factor, similar shapes are enlarged versions of one another. All of the corresponding angles and lengths in related shapes are equal and in the same ratio.

We divide the length of the enlarged shape by the length of the original shape to calculate the length scale factor.

The ratio of perimeter of both shapes is same as the ratio their corresponding side.

Given that the sides of triangle are 9cm, 20cm, 21cm.

The perimeter of this triangle

P₁ = 9cm + 20cm + 21cm

P₁  = 50cm

As the lengths of triangle are multiplied by 150%. So the perimeter of new triangle is also 150% of original triangle.

Let the perimeter of new triangle is P₂

So that

150% = P₂ /  P₁

⇒ 150 / 100 =  P₂ / 50

Multiply both sides by 50 we get

⇒ (3/2)*50 =  P₂

⇒ P₂ = 150/2

⇒ P₂ = 75

So the perimeter of the new triangle P₂ = 75 cm.

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Answer:

22.3 x 1.8 = 40.14

Step-by-step explanation:

22.3

x  1.8  

________

1784

2230

________

40.14

Answer:

40.14

Step-by-step explanation:

22.3

× 1.8  ← Forget about the decimal places and multiply by the one's place.

1 7 8 4

2 2 3 0 ← Put a 0 to hold the one's place and multiply 223 by ten's place.

4 0 . 1 4 ← Add those 2 numbers and keep 2 decimal places.

Answer:

238 miles

Step-by-step explanation:

2cm=68 miles

2cm÷2=68 miles÷2

1cm = 34 miles

7cm x 34 miles

=238 miles

The rational functions that have an oblique asymptote are:

are:

f(x) = x^2 + 1/X

f(x) =4x^2 - 6/x + 1

f(x) =x^5/x^3 +1

f(x) =x² +2/ x^2+ 3x

The concept that will be used here is finding the function one after the other.

The first function:

f(x) = x^2 + 1/X

The degree of numerator is seen to be 2, which can be considered to be  is greater than the degree of denominator which is one, the, we can consider this function as oblique asymptote.

Second function:

f(x) =4x^2 - 6/x + 1

The degree of numerator which can be seen to be 2 is greater than the degree of denominator which is 1 and can be considered as  an oblique asymptote.

Third function:

f(x) =-x/x^2

The degree of numerator can be seen as 1 which can be considered to be less than the degree of denominator which is 2, and we can not considere this as  an oblique asymptote.

The fourth function:

f(x) =x^5/x^3 +1

The degree of numerator can be seen as 5 which can be considered to begreater than the degree of denominator which is 3 and this  function can be considered to be an oblique asymptote.

Fifth option:

f(x) =x² +2/ x^2+ 3x

The degree of numerator can be seen as 3 which can be considerd to be  greater than the highest degree of denominator which is seen as 2 and can be considered to be  oblique asymptote.

Therefore, the 1st, 2nd, 4th, and 5th options are correct.

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missing options:

f(x) = x^2 + 1/X

f(x) =4x^2 - 6/x + 1

f(x) =-x/x^2

f(x) =x^5/x^3 +1

f(x) =x² +2/ x^2+ 3x