For the points (3.1, -13.4) and (0.1, -9.4), (a) Find the exact distance between the points. (b) Find the midpoint of the line segment whose endpoints are the given points. Darts​

The new points when the triangle is rotated through 270°  counterclockwise are P = ( -4 , 4 ) ,Q = ( 2 , -2 ) and R = ( -3 ,-3 )

What are coordinates of triangle ?

The triangle's vertices' coordinates are (x1,y1), (x2,y2), and (x3,y3). The line that connects the first two is split in the ratio l:k, and the line that runs from the division point to the opposing angular point is divided in the ratio m:k+l.

According to the given information

Center = ( -5 , -4 )

Initial points of the triangle

P = ( -13 , -3 )

Q = ( -7 , 3 )

R = ( -6 , -2 )

Hence

CP = ( -8 , 1 )

CQ = ( -2 , 7 )

CR = ( -1 , 2 )

When the triangle is rotated through 270° counterclockwise

CP = ( 1 , 8 )

CQ = ( 7 , 2 )

CR = ( 2 , 1 )

Hence

The new points will be

P = ( -4 , 4 )

Q = ( 2 , -2 )

R = ( -3 ,-3 )

The new points when the triangle is rotated through 270°  counterclockwise are P = ( -4 , 4 ) ,Q = ( 2 , -2 ) and R = ( -3 ,-3 )

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Answer:

To do this, you need to multiply out the expressions. This is a bit tedious, but remember like FOIL for binomials, for these trinomials you must multiply each term. If you need a step-by-step, I'd be happy to provide it. Let me know.

Once you have simplified the expression, you get

-x-9/2x-4

But, the problem stipulates that a must equal 1. We can equivalently factor out the negative sign and put it on the denominator with no change to write

x+9/-(2x-4) = x+9/-2x+4

So, seeing where each coefficient corresponds between the two expressions, you get a = 1, b = 9, c = –2, and d = 4.

a) The process to find the limit is given as follows:

b) When a function does not have any discontinuity at x = 1, the procedure is the same as calculating f(1), however in the case of a discontinuity, such as for f(x), the discontinuity first has to be removed, if possible.

The first step in calculating the limit of a function is calculating the numeric value of the function at the value of x which the function approaches.

Hence:

For the case of g(x), there is a discontinuity, meaning that the function has to be factored to remove the discontinuity.

Applying the subtraction of perfect squares, we have that:

x² - 1 = (x - 1)(x + 1).

Then:

g(x) = (x - 1)(x + 1)/(x - 1) = x + 1.

Meaning that the limit is then calculated as follows:

lim x -> 1 g(x) = lim x->1 x + 1 = 1 + 1 = 2.

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What are you asking?

A study based on a population sample that includes 2000 respondents would be the most reliable out of the given options.

In statistical analysis, the reliability of a study depends on the representativeness and size of the sample.

A larger sample size generally provides more reliable results as it reduces the sampling error and increases the precision of the estimates.

Given that the population contains 20,000 people, we need to consider which number of respondents would yield the most reliable study.

Option A: 200 respondents

This represents only 1% of the population.

While it is better than having just 2 respondents, it may not be sufficient to accurately capture the characteristics of the entire population.

Option B: 20 respondents

This represents only 0.1% of the population.

With such a small sample size, the study would likely suffer from a high sampling error and may not provide reliable results.

Option C: 2000 respondents

This represents 10% of the population.

While it is a larger sample size compared to the previous options, it still only captures a fraction of the population.

The study may provide reasonably reliable results, but there is room for potential sampling error.

Option D: 2 respondents

This represents an extremely small sample size, accounting for only 0.01% of the population.

With such a small sample, the study would be highly susceptible to sampling bias and would likely yield unreliable results.

Based on the options provided, option C with 2000 respondents would be the most reliable study.

Although it does not include the entire population, a sample size of 2000 respondents provides a larger representation of the population and reduces the potential for sampling error.

However, it's important to note that the reliability of a study depends not only on sample size but also on the sampling method, data collection techniques, and other factors that ensure representativeness.

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Answer:

y = -3/5x - 5

Step-by-step explanation:

Slope intercept form: y = mx + b

We can subtract 3x from both sides to get:

5y = -3x - 25

Divide both sides by 5

y = -3/5x - 5

$2010.458 is her new balance after she makes one new transaction for $51.

What does a credit balance mean?

The amount that the credit card company owes you is shown as a credit balance on your billing statement. Each payment you make results in credits being added to your account.

                                   When you return something you purchased with your credit card, you can receive an additional credit.

Credit balance  = $1,603

   APR = 28.6%

        = 28.6%  * $1,603

         =   458.458

Credit balance  = $1,603 + 458.458

                        = $2061.458

  net balance =  $2061.458 - 51

                      = $2010.458

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Answer:

3x+9+4x+x = 8x+9

I hope this helps.

Me das mas información porfavor?

The box in the middle of the plot spans from the first quartile (Q1) to the third quartile (Q3), with a line inside representing the median.

A whisker plot, also known as a box and whisker plot, is a graphical representation of a set of numerical data through their quartiles. The plot consists of a box with whiskers extending from the top and bottom, showing the spread and distribution of the data. The five-number summary, which includes the minimum value, first quartile (Q1), median, third quartile (Q3), and maximum value, is used to create the whisker plot.

Here,

To create a box and whisker plot, we need to find the five-number summary of the data set, which includes:

Minimum value: the smallest value in the data set.

First quartile (Q1): the median of the lower half of the data set.

Median: the middle value in the data set.

Third quartile (Q3): the median of the upper half of the data set.

Maximum value: the largest value in the data set.

First, we need to put the data in order:

10, 12, 14, 15, 16, 18, 22, 24, 25, 28

The minimum value is 10 and the maximum value is 28.

The median is the middle value, which is 18.

To find the first quartile, we need to find the median of the lower half of the data set, which is:

10, 12, 14, 15, 16

The median of this lower half is 14.

To find the third quartile, we need to find the median of the upper half of the data set, which is:

22, 24, 25, 28

The median of this upper half is 24.

So, the five-number summary for this data set is:

Minimum value = 10

First quartile (Q1) = 14

Median = 18

Third quartile (Q3) = 24

Maximum value = 28

Now we can use this information to create the box and whisker plot:

      |          |      

 ----+----+----+----+----

    10   14   18   24   28

The box in the middle of the plot spans from the first quartile (Q1) to the third quartile (Q3), with a line inside representing the median. The whiskers extend from the box to the minimum and maximum values in the data set.

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Answer:

i tink its D

Step-by-step explanation:

Answer: C (-3, -2)

Step-by-step explanation: because it is

Answer:

Step-by-step explanation: evagline has 3/5 of box of nuts.she uses it to fill 6 bowls

Answer:

True

Step-by-step explanation:

∫₀°° f(x) dx = ∫₀¹ f(x) dx + ∫₁°° f(x) dx

We know that ∫₁°° f(x) dx converges, and we know that f(x) is continuous on [0, 1], inclusive.  Therefore, ∫₀¹ f(x) dx converges, so ∫₀°° f(x) dx converges.

The monthly cell phone bill when shared data equals zero is given as follows:

$26.

The slope-intercept representation of a linear function is given by the equation presented as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

The intercept of the line in this problem is given as follows:

b = 26.

Hence $26 is the monthly cell phone bill when shared data equals zero.

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\(\red{➤}\:\)\(\sf \dfrac{13}{5-i} \)

\(\\\)

\(\orange{☛}\:\)\(\sf Write \: given \: Quotient \:in \: a+bi \:form\)

\(\\\)

\(\begin{gathered}\\\quad\longrightarrow\quad\sf \frac{13}{5-i} \\\end{gathered} \)

Multiplaying denominator and numerator by 5+i to get denominator as real number

\(\begin{gathered}\\\quad\longrightarrow\quad\sf \frac{13(5+i)}{5-i(5+i)} \\\end{gathered} \)

\(\begin{gathered}\\\quad\longrightarrow\quad\sf \frac{65+13i}{5^2-i^2} \\\end{gathered} \)

\(\quad\quad\quad\quad\quad\sf ((a+b)(a-b)=a^2-b^2) \)

\(\begin{gathered}\\\quad\longrightarrow\quad\sf \frac{65+13i}{25-(-1)} \\\end{gathered} \)

\(\quad\quad\quad\quad\quad\sf (For\:Complex\: Number,i ; i^2 = -1) \)

\(\begin{gathered}\\\quad\longrightarrow\quad\sf \frac{65+13i}{25+1} \\\end{gathered} \)

\(\begin{gathered}\\\quad\longrightarrow\quad\sf \frac{65+13i}{26} \\\end{gathered} \)

\(\begin{gathered}\\\quad\longrightarrow\quad\sf \frac{\cancel{65}}{\cancel{26}}+\frac{\cancel{13}i}{\cancel{26}} \\\end{gathered} \)

\(\begin{gathered}\\\quad\longrightarrow\quad\boxed{\sf {\frac{5}{2} +\frac{1}{2} i}}\\\end{gathered} \)

Answer:

1.) 7x+5y

2.)-19m+14r

3.)22b+40c

4.)10x+25

5.)7m+7

Step-by-step explanation:

ez

Step-by-step explanation:

The definite integral of sin^5(x)dx from 0 to pi/2 can be evaluated using the method of substitution.

Let u = sin(x), then du = cos(x)dx

The integral becomes:

∫sin^5(x)dx = ∫u^5du from 0 to sin(π/2)

= (u^6)/6 evaluated at sin(π/2) and 0

= (sin^6(π/2))/6 - 0

= (1^6)/6

= 1/6

So, the definite integral of sin^5(x)dx from 0 to pi/2 is equal to 1/6.

Based on the information given, there are a total of 118 solutions.

This is a problem of solving a Diophantine equation subject to some conditions. Let's introduce a new variable y4 = 20 - (x1 + x2 + x3 + x4). Then the problem can be restated as finding the number of solutions to:

x1 + x2 + x3 + y4 = 20

Subject to the following conditions:

0 ≤ x1 < 3

0 ≤ x2 < 4

0 ≤ x3 < 5

0 ≤ y4 < 6

We can solve this problem using the technique of generating functions. The generating function for each variable is:

(1 + x + x^2) for x1

(1 + x + x^2 + x^3) for x2

(1 + x + x^2 + x^3 + x^4) for x3

(1 + x + x^2 + x^3 + x^4 + x^5) for y4

The generating function for the equation is the product of the generating functions for each variable:

(1 + x + x^2)^3 (1 + x + x^2 + x^3 + x^4 + x^5)

We need to find the coefficient of x^20 in this generating function. We can use a computer algebra system or a spreadsheet program to expand the product and extract the coefficient. The result is: 1118

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Answer: This problem involves finding the number of non-negative integer solutions to the equation x₁ + x₂ + x3 + x₁ = 20 subject to the given constraints. We can use the stars and bars method to solve this problem.

Suppose we have 20 stars representing the sum x₁ + x₂ + x3 + x₁. To separate these stars into four groups corresponding to x₁, x₂, x₃, and x₄, we need to place three bars. For example, if we have 20 stars and 3 bars arranged as follows:

**|**||

then the corresponding values of x₁, x₂, x₃, and x₄ are 2, 4, 6, and 8, respectively. Notice that the position of the bars determines the values of x₁, x₂, x₃, and x₄.

In general, the number of ways to place k identical objects (stars) into n distinct groups (corresponding to x₁, x₂, ..., xₙ-₁) using n-1 separators (bars) is given by the binomial coefficient (k+n-1) choose (n-1), which is denoted by C(k+n-1, n-1).

Thus, the number of non-negative integer solutions to the equation x₁ + x₂ + x3 + x₁ = 20 subject to the given constraints is:

C(20+4-1, 4-1) = C(23, 3) = 1771

However, this count includes solutions that violate the upper bounds on x₁, x₂, x₃, and x₄. To eliminate these solutions, we need to use the principle of inclusion-exclusion.

Let Aᵢ be the set of non-negative integer solutions to the equation x₁ + x₂ + x3 + x₁ = 20 subject to the given constraints, where xᵢ ≥ mᵢ for some integer mᵢ. Then, we want to find the cardinality of the set:

A = A₀ ∩ A₁ ∩ A₂ ∩ A₃

where A₀ is the set of all non-negative integer solutions to the equation x₁ + x₂ + x3 + x₁ = 20, and Aᵢ is the set of solutions that violate the upper bound on xᵢ.

To find the cardinality of A₀, we use the formula above and obtain:

C(20+4-1, 4-1) = 1771

To find the cardinality of Aᵢ, we subtract the number of solutions that violate the upper bound on xᵢ from the total count. For example, to find the cardinality of A₁, we subtract the number of solutions where x₂ ≥ 4 from the total count. To count the number of solutions where x₂ ≥ 4, we fix x₂ = 4 and then count the number of solutions to the equation x₁ + 4 + x₃ + x₄ = 20 subject to the constraints 0 ≤ x₁ < 3, 0 ≤ x₃ < 5, and 0 ≤ x₄ < 6. This count is given by:

C(20-4+3-1, 3-1) = C(18, 2) = 153

Similarly, we can find the cardinalities of A₂ and A₃ by fixing x₃ = 5 and x₄ = 6, respectively. Using the principle of inclusion-exclusion, we obtain:

|A| = |A₀| - |A

Step-by-step explanation:

The probability of pulling out a number which is divisible by 2 or 3 will be 7/10 which is not given here. So, option D will be the answer.

How do we find Probability?

The measurement through which we find the likelihood of an event to occur is called probability. We cannot predict a lot of events with total certainty. And thus, the chance of a event to occur (i.e. how likely they re going to happen) can be predicted using probability.

Probability of any event to happen can be find as: No of favorable outcomes/Total number of outcomes.

Here,

The total no of outcomes = 1,2,3,4,5,6,7,8,9,10

No of favorable outcomes ={2,3,4,6,8,9,10} = 7

Therefore, P(E) = 7/10

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Answer:  The last expression shows the result of 3  so it models the distance between x and y.

Step-by-step explanation:

First you will have to  find the distance between the two points by square the x coordinates and squaring the y coordinates to find their sum .  

-4 - (-1) = -3

-5 - ( -5) = 0

-3^2 + 0^2 = d^2   where d  is the distance

9  = d^2

d= 3  

The distance is 3 units  

Now evaluate which expression have a solution as 3.

The last expression is the answer

the absolute value for -4 is 4   , and the absolute value for -1 is 1  and 4 minus 1 is 3.

Answer:

Step-by-step explanation:

4.3 split into a certain equal number  

The product of -0.003 and a number

Answer:

4.3 split into a certain equal number 4.3/y The product of -0.003 and a number -0.003z

Step-by-step explanation:

\(5(n + 2) = \frac{3}{5} \cdot (5 + 10n)\\5n + 10 = \frac{3(5 + 10n)}{5}\\(5n + 10) \cdot 5 = 3(5 + 10n)\\25n + 50 = 15 + 30n\\25n - 30n = 15 - 50\\-5n = -35\\n = 7\)

Answer:

n = 7

Step-by-step explanation:

5(n+2)=3/5(5+10n)

Alright, remember PEMDAS (Parenthesis Exponent Multiplication Division Addition Subtraction).

What I do first is turn the fraction into a decimal, which is just numerator x denominator, aka 3 divided by 5, and that gives you 0.6, which you can put into the equation.

5(n+2)=0.6(5+10n)

Parenthesis is first, so you'll multiply the number before the parenthesis by each number and/or letter in the parenthesis. Do this for both sides.

5(n) + 5(2) = .6(5) + .6(10n)

5n + 10 = 3 + 6n

Next, you want to get just a number on one side and the letter on the other side. Subtract 5n from both sides.

(5n-5n) + 10 = 3 + (6n-5n)

10 = 3 + 1n which may also be written as just n

Do the same for 3.

(10-3) = (3-3) + n

7 = n

Normally if you had like 7 = 14n you'd divide both sides by 14 and get n = 7, but since it was 1n your answer is n = 7.

Hope this helped!! Sorry it was long!

The y-intercept of f(x + 4) + 8 is given as follows:

10.

A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.

The four translation rules for functions are defined as follows:

The parent function for this problem is given as follows:

\(f(x) = \log_2{x}\)

The translated function is then given as follows:

\(g(x) = \log_2{x + 4} + 8\)

The y-intercept of the function is the numeric value at x = 0, hence:

\(g(0) = \log_2{0 + 4} + 8\)

g(0) = 2 + 8 = 10.

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Answer:

gallons: 14, 21, 28, 35

time: 2, 3, 4, 5

Step-by-step explanation:

Answer:

D) 19

Step-by-step explanation:

4 + 5x

4 + 5(3)

4 + 15

19

Answer:

Step-by-step explanation:

Since x = 3, replace any x in the equation with 3.

4 + 5 (3) =

multiply 5 • 3

4 + 15 = 19

Answer: x=4

Step-by-step explanation:

The value of the function operation f - g(x) is 3x² + x

Function operations refer to mathematical operations that can be performed on functions, such as addition, subtraction, multiplication, and composition.

Addition and subtraction of functions:

A function can be added or subtracted with another function if both of them have the same domain. The result is a new function with the same domain as the original functions.

Multiplication of functions:

Two functions can be multiplied together to create a new function. The result is a new function whose value at each point in the domain is the product of the original functions' values at that point.

Composition of functions:

Function composition is the application of one function to the result of another function. The result is a new function that is the composition of the original functions. It is represented by (f ∘ g) (x) = f(g(x)) where f and g are the functions being composed.

In this problem, we have two functions which are;

The value of (f - g)(x) = 3x² + x

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