Line/has the equation y=1/3x. Find the equation of the image of/ after a dilation with a scale factor of 1/2, centered at the origin

The most appropriate choice for probability will be given by:

Probability that the number of households in these 4 who own homes is exactly 4 = [tex]\frac{42}{455}[/tex]

What is Probability?

Probability of an event is the chance of occurance of that event.

Probability can be obtained by Number of favourable outcomes divided by the total number of outcomes

Probability varies from 0 to 1.

Here,

Total number of households = 15

No of households to be selected = 4

4 households can be selected from 15 households in [tex]15 \choose 4[/tex] ways

                                                                                      = [tex]\frac{15!}{(15-4)! \times 4!}\\[/tex]

                                                                                      = [tex]\frac{15!}{11! \times 4!}[/tex]

                                                                                       [tex]=\frac{15 \times 14 \times 13 \times 12}{1 \times 2 \times 3 \times 4}[/tex]

                                                                                       = [tex]1365[/tex] ways

Now,

Number of households who own homes = 9

4 households can be chosen from 9 households in [tex]9 \choose 4[/tex] ways

                                                                                  [tex]\frac{9!}{(9-4)! \times 4!}\\[/tex]

                                                                                = [tex]\frac{9!}{5! \times 4!}[/tex]

                                                                                [tex]=\frac{9 \times 8 \times 7 \times 6}{1 \times 2 \times 3 \times 4}[/tex]

                                                                                = [tex]126[/tex]

Probability that the number of households in these 4 who own homes is exactly 4 = [tex]\frac{126}{1365}[/tex]

               = [tex]\frac{42}{455}[/tex]

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Answer:

9

Step-by-step explanation:

[tex]-5+(-18)+32 \\ \\ =-5-18+32 \\ \\ =-23+32 \\ \\ =9[/tex]

Answer: 6.809 < 6.812. 6.812 is greater.

Step-by-step explanation:

If you mean if...  

|-6.809| > |-6.812|

then, -6.812 will be bigger because when you absolute value an answer the number inside the | | will become positive. So the simplified equation will look like this:

6.809 > 6.812

So, the sign is wrong and should be flipped.

6.809 < 6.812

As per the given matrix [tex]A= \left[\begin{array}{ccc}2&2\\-1&1\end{array}\right][/tex], Option (C) is not true.

Matrix:

The matrix is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object.

Given,

[tex]A= \left[\begin{array}{ccc}2&2\\-1&1\end{array}\right][/tex]

Here we need to find which of the option is not true.

To find the incorrect options first we have to calculate the |A| and A⁻¹.

And we have also check whether is matrix has inverse or skew symmetric matrix.

First, we have to calculate the value of |A|,

|A| = (2 x 1) - (-1 x 2)

|A| = 2 - (-2)

|A| = 2 + 2 = 4

Therefore, option (A) is true.

Now we have to check this matrix has inverse,

It can be calculated using the formula,

[tex]A^{-1} =\frac{1}{|A|} \left[\begin{array}{ccc}d&-b\\-c&a\end{array}\right][/tex]

So, the inverse of the matrix is,

[tex]A^{-1} =\frac{1}{4} \left[\begin{array}{ccc}1&-2\\-(-1)&2\end{array}\right][/tex]

Which is equal to,

[tex]A^{-1} =\left[\begin{array}{ccc}1/4&-2/4\\1/4&2/4\end{array}\right][/tex]

When we simplify it then we get,

[tex]A^{-1} =\left[\begin{array}{ccc}1/4&-1/2\\1/4&1/2\end{array}\right][/tex]

Through this we have conclude that Option (B) and (D) are true.

We know that,

In the skew-symmetric matrix, a matrix whose transpose is equal to its negative.

So, the transpose of the given matrix is,

[tex]A^{T}=\left[\begin{array}{ccc}2&-1\\2&1\end{array}\right][/tex]

So, the given matrix is not a skew-symmetric matrix.

Therefore, the incorrect option is (c).

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Answer:

I'm not so very sure but I really need points

Answer:

Your leading coefficient is 2

Units change translation from cm to feets

1 cm is equivalent to 2.5 feets

triangle is a rectangular triangle suported with the bigger side

this means the height of triangle is 6cm

the base is 16 cm

the area is (base x height)/2

so then area= 16x 6/2= 48cm ^2

BUT because 1cm is equivalent to 2.5 feets then

multiply 48 x 2.5 x 2.5 = 48 x 6.25 = 300 ft^2

olution

or this case we have the following vectors:

u= -3i +2j, w= 4j, v= 6i -4j

And we can do the following:

art a

u*v= -3*6 + 2*-4= -18 -8= -26

Part b

w*v= 0*6 + 4*-4 =-16

The ratio of appaloosa to mustang horses is 12:40

The total number of horses is given as 52.

Number of white horses =12

Let the number of black horses be x

This means that ratio of white: black horses is 12 : x

Using the ratio above, we can find the number of black horses as follows:

[tex]\frac{x}{12+x} of 52 = x[/tex]

[tex]\frac{52x}{12+x} = x[/tex]

52x = x(12 + x)

[tex](12x + x^{2} ) = 52x[/tex]

[tex]x^{2}[/tex] + 12x - 52x = 0

[tex]x^{2}[/tex] - 40x = 0

Taking out the common factor x from equation we have:

x(x - 40) = 0

This gives us with two solution:

x = 0 and x = 40

Since the question said there are some black horses, the x=0 value can be ignored. So we have x = 40

Hence,  The ratio of appaloosa to mustang horses is 12:40

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Option E, the x-axis is the line of reflection used to map the preimage to its image.

The graph represents that if the graph is folded by an x-axis,

Point Y will cross-point Y', which is two coordinates away from the x-axis.

Point X will cross point X', which is five coordinates away from the x-axis.

Points W will cross-point W', which is eight coordinates away from the x-axis.

Points V will cross-point V', which is five coordinates away from the x-axis.

A mirror image is symmetric about the x or y-axis. Reflection is called "inverse geometry". A mirror reflector is a type of reflector. When the line reflects the image, the reflection line appears. A shape is said to reflect a different shape if a point on a shape is equidistant from a point on another shape.

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Given the expression:

Let's multiply the expression.

To multiply apply the distributive property of multiplication.

Distribute 4 to the values in the parentheses:

ANSWER:

Answer:

$5.19

Step-by-step explanation:

10.33 × $2.51 = $25.93

$25.93÷5=$5.19

Answer: D:-1

Step-by-step explanation: 11,9,7,5,3,-1,-3,... => dãy số trên có quy luật là số lẻ

Solution

(a) There are 9 students entering the school district science project:

medals for 1st, 2nd and 3rd

k1 = 1O ways to choose first person to be chosen from the group of 10.

99

k2 = 8 ways for the second person to be chosen from the remaining people(9–1).

k3 = 7 ways for the second person to be chosen from the remaining people(8–1).

then all you need to do is multiply these k1 * k2 * k3.

(b) There are 7 unique names in a bowl. In how many orders can 2 names be chosen:

This is a permutation problem in order

There are 7 names, and the 2 name have to be in same order

In order to find the slope between those two points, we can use the following formula for the slope:

Where m is the slope between the points (x1, y1) and (x2, y2).

So using the points (-4, 2) and (5, 6), we have:

So the slope is 4/9

Answer: 25 is divisible by 5, so it is composite

Step-by-step explanation:

Answer:

43a + c = 13.25

Step-by-step explanation:

A = 9

C = 81

If the following table summarizes the percent of U.S. who have diabetes and the accuracy of the current medical tests used to detect the disease.  The percent of those who do not have diabetes test negative for the disease is: B. 56.8%.

Probability can be defined as the tendency or likelihood that something will happen.

Hence,

Percentage of people  do not have diabetes and test positive is 5.2%

Percentage of people  do not have diabetes and test negative is  56.8%

Total percentage of people who tested positive and negative is 62%

Based on the above analysis for people who does not have a diabetes we can see that the Percentage of people  do not have diabetes and test negative is  56.8%.

Therefore the correct option  is B.

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The expression of the square walkway is (x + 4)² - (x - 5)² and the area of the square cement walkway is 135ft².

Area of square:

The area of a square is refers the place covered by the square.

The formula to calculate the area of square is,

Area = s²,

where, 's' refers the side of the square.

Given,

A square swimming pool is covered by a cement walkway with a uniform width.

Length of swimming pool = (x-5) feet.

Length of square walkway including the swimming pool = (x+4) feet

Here we need to find the area  of the cement walkway and when the value of x is 8 then the value of the cement walkway.

1) Here we have to write an expression for the area of the entire square minus area of the pool.

Remember the equation for the area of a square is , where

A = area of square and

s = side value of the square.

We are given that the side of the entire square including walkway and pool is s = (x+4)ft.

Apply the value of the side into the formula for the area of the square, then we get,

A = s²

A = (x + 4)² --------------(1)

We are also given that the side length of the swimming pool is s = (x-5)ft. Apply that into the equation for the area of a square to get the expression for the area of the pool:

A = s²

A = (x - 5)² --------------(2)

Now subtract the area of the pool (x - 5)² from the area of the entire square (x + 4)² to get your expression for the area of the walkway.

Expression for the area of the walkway:

=> (x + 4)² - (x - 5)²

2) Since you know that x = 8ft, you can solve your expression for the area of the walkway. Plug x into your expression:

=> (8 + 4)² - (8 - 5)²

=> (12)² - (3)²

=> 144 - 9

=> 135

The area of your walkway is 135ft².

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Step-by-step explanation:

domain = width

range = height

closed point (filled in) means the number is included and we use ()'s.

set builder nation format: (x,y)

domain: (-5, -1)

range: (3,3)

f(1) means what does y equal when x equals 1:

locate on the graph where y is when x = 1:

f(1) = 2

Given:

Center of circle: (-4, 7)

Endpoint on the circle: (8, -4)

Let's write the equation of the circle with the given information.

Apply the equation of a circle:

Where:

Center of circle: (h, k) ==> (-4, 7)

Radius = r

Substitute the values of (h, k) in the equation:

To find the radius, let's find the distance between the points (-4, 7) and (8, -4).

Apply the distance formula:

Given:

(x1, y1) ==> (-4, 7)

(x2, y2) ==> (8, -4)

Thus, we have:

Therefore, the radius is 16.3

Therefore, we have the equation of the circle as:

ANSWER:

The estimated value of 3√28 using linear approximation is 82/27 which is answered in form of fraction.

A general function can be approximated using a linear function in mathematics using the term "linear approximation" (more precisely, an affine function). They are frequently utilised in the finite difference method to create first order approaches for resolving or approximating solutions to equations.

We need to find the approximate value of ∛28 using linear approximation

Let f(a) =  ∛a

then F(27) =  ∛27 = 3

We compute the derivative of f(a) as being

[tex]f(a)=a^{\frac{1}{3}}[/tex]  ⇒  [tex]f'(a)=\frac{1}{3}a^{-\frac{2}{3}}[/tex]

Hence,

[tex]f'(a)=\frac{1}{3}a^{-\frac{2}{3}}[/tex] = [tex]\frac{1}{3}(3)^{-2}=\frac{1}{3}(\frac{1}{9})=\frac{1}{27}[/tex]

Recall the equation of a line is given by

⇒ y - b = m(x - a)

⇒ [tex]y-3=\frac{1}{27}(x-27)[/tex]

⇒ [tex]y=\frac{1}{27}x-1+3[/tex]

⇒ [tex]y=\frac{1}{27}x+2[/tex]

So the approximation at  x= 27.5 would be

⇒  [tex]y=\frac{1}{27}(28)+2[/tex]

⇒ y = 82/27

⇒ y = 3.037

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6 and -6

please give brainliest

Domain and Range of Functions

Given a function y = f(x), the domain of f is

The range of f is the

We are given the function:

It's required to find the domain and range of the inverse function.

We must recall that, if the inverse function exists, its domain is the range of f, and its range is the domain of f.

Since f(x) is a rational function, it may not exist for the values of x where the denominator is 0.

Concretely, for x=0, the denominator is 0 and the function does not exist, thus the domain of f consists of every real number except x=0.

This can be written as (-∞,0) U (0,∞). This is also the range of the inverse function.

Now let's find the inverse function. We must solve for x the equation:

Adding 3:

Multiplying by x and dividing by y+3:

Swapping letters:

This is the inverse function of f.

Thus the domain of the inverse is:

-3-3

And the range:

Answer: Choice d

Answer:  31y2 + 6

Step-by-step explanation:

61 y2 + 1 y2 = 62 y2  

7y + -7y = 0

6+6 =12

62y2 + 12  then divide by 2 and it's  31y2 + 6

1) Dividing the given formula by W we get:

2) We know that:

Therefore:

Then:

Substituting W=3/4ft and L=18ft in the given formula we get:

Answer:

1)

2)

Given equation [tex]x^{2} +2x+6=0[/tex]

we use in Quadratic formula

[tex]{\displaystyle x={\frac {-b\pm {\sqrt {b^{2}-4ac}}}{2a}}\ \ }[/tex]

So a=1, b=2, c=6

[tex]{\displaystyle x={\frac {-2\pm {\sqrt {2^{2}-4*1*6}}}{2*1}}\ \ }[/tex]

[tex]{\displaystyle x={\frac {-2\pm {\sqrt {4-24}}}{2}}\ \ }[/tex]

[tex]{\displaystyle x={\frac {-2\pm {\sqrt {20}}}{2}}\ \ }[/tex]

[tex]{\displaystyle x={\frac {-2\pm 2i{\sqrt {5}}}{2}}\ \ }[/tex]

[tex]{\displaystyle x= {-1\pm i{\sqrt {5}}}[/tex]

What is the Quadratic formula?

A second-degree equation is a quadratic equation. It implies that at least one term in which the variable is squared will be present. This equation's conventional form is:

ax²+ bx + c = 0

where a, b, and c are variables or coefficients.

X is also an unknowable variable.

The fact that the coefficient "a" cannot be 0 is one unbreakable law.

Two potential choices for its variable X will fulfill the equation because of the degree of 2. Quadratic equations may reflect a wide range of real-world scenarios, as is clear to observe. We'll now look at several solutions.

Quadratic is derived from the term "quad," which means square. Here, we'll create the formula for quadratic equations so that they may be solved.

The factorization approach fails to reduce a large number of equations. Such equations are solved using a more potent approach. Every quadratic problem may be solved using this technique. This is the formula for a quadratic equation in general.

This is how it is explained:

If ax2 + bx + c = 0, then

is a quadratic equation, then the following formula provides the value of x.

Simply enter the numbers for a, b, and c, and the computations will be performed.

The values of a, b, and c are extracted from the equation and entered into the quadratic equation formula.

A, B, and C in this case only numbers. These are the quadratic equation's numerical coefficients, which you must solve.

[tex]{\displaystyle x={\frac {-b\pm {\sqrt {b^{2}-4ac}}}{2a}}\ \ }[/tex]

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Polynomials are utilized in management, business, farming, computer science, and math-related fields.Expressions defining known and unknown numbers are created using variables and constants in all professions that need proficiency with polynomials.

where we can use Adding and Subtracting Polynomials in real life?

Electronics

Curve Fitting

Chemistry

Engineering and physics

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We can calculate the slope of a line segment by using the formula:

Where (x1,y1) and (x2,y2) are two points of the line.

In this case the side DF goes from the point D(-2,-2) to the point F(1,7), then its slope is:

For the side, CD, it goes from D(-2,-2) to C(0,4), then its slope is: