Of the 22 students in a classroom, 10 are transfer students, 7 are nursing students, 4 are AAS students and 1 student is undecided. If 5 students are chosen randomly, with replacement, find the probability that at least one student is a transfer student.

Answers

Answer 1
To solve this problem, we can use the complement rule, which states that the probability of an event occurring is equal to 1 minus the probability of the event not occurring. In this case, we want to find the probability that at least one student is a transfer student, so we can find the probability that no students are transfer students and subtract that from 1.

The probability that a randomly chosen student is not a transfer student is 12/22, since there are 12 students who are not transfer students out of a total of 22 students. Therefore, the probability that none of the 5 students chosen are transfer students is:

(12/22)^5 = 0.068

To find the probability that at least one student is a transfer student, we can subtract this from 1:

1 - 0.068 = 0.932

Therefore, the probability that at least one student is a transfer student is 0.932.

Related Questions

A pole that is 3m tall cast a shadow that is 1.15m long at the same time a nearby building cast a shadow that is 40.75m long. How tall is the building

Answers

Answer:

The heights and shadows of the objects are legs of similar right triangles. We can use these similar triangles to set up a proportion to solve for the height of the building.

2.9 / 1.26 = x / 47.25

x = 108.75 m

Find an equation of the tangent line to the curve x2/3 + y2/3 = 10 (astroid)at the point(−27 ,1)

Answers

The equation of the tangent line to the curve [tex]x^\((2/3) + y^\((2/3)[/tex]= 10 at the point (-27, 1) is  -(1/3)(x + 27).

How to find the equation of the tangent line?

First step is to take the  derivative of both sides of the equation

[tex](2/3 )x ^\((-1/3) + (2/3)y ^\((-1/3)*dy/dx = 0[/tex]

Solve for dy/dx

[tex]dy / dx = -(y ^\(1/3)/x ^(1/3))[/tex]

Substitution

[tex]dy /dx = -(1 ^\((1/3)/(-27) ^ \((1/3)) = -(1/3)[/tex]

Formulate a linear equation

y - y1 = m(x - x1)

Where:

m= slope

(x1, y1)= point (-27, 1):

So,

y - 1 = -(1/3)(x + 27)

Therefore the equation is y - 1 = -(1/3)(x + 27).

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Which statement correctly describes confidence level? A confidence level is the probability that a simple event will occur. A confidence level is a value that is added and subtracted from a given value to give an interval where something will likely happen. A confidence level is the probability that something will fall outside of a confidence interval. A confidence level is the probability that something will fall within a confidence interval.

Answers

The statement which correct describe "confidence-interval" is (d) confidence level is considered as probability that something will fall within "confidence-interval".

A "Confidence-Interval" is a statistical term used to describe the amount of uncertainty associated with a sample estimate. It refers to the percentage of all possible samples that can be expected to include the true population parameter being estimated.

For example, if a study reports a 95% confidence level, it means that 95% of all possible samples would contain the true population parameter. This can be considered as the probability that the estimate falls within a certain range or interval, called the confidence interval.

Therefore, option (d) is the correct statement.

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The given question is incomplete, the complete question is

Which statement correctly describes confidence level?

(a) A confidence level is the probability that a simple event will occur.

(b) A confidence level is a value that is added and subtracted from a given value to give an interval where something will likely happen.

(c) A confidence level is the probability that something will fall outside of a confidence interval.

(d) A confidence level is the probability that something will fall within a confidence interval.

Answer:

A confidence level is the probability that something will fall within a confidence interval.

Step-by-step explanation:

Plato/Edmentum

Each of 6 students reported the number of movies they saw in the past year. Here is what they reported. 14, 9, 9, 6, 10, 19 Find the mean number of movies that the students saw. If necessary, round your answer to the nearest tenth.

Answers

The answer is 11.2

The mean is the sum of all numbers divided by how many there is. So 14+9+9+6+10+19 is 67. 67 divided by 6 is 11.1667. But it says round to the nearest tenth which would make it 11.2

College Level Trigonometry Question!

Answers

The force parallel to the incline that would be required to hold the monolith on this causeway is 32, 120.52 Newtons.

How to find the force ?

The formula for finding the force parallel to the incline:

= mass of the monolith x acceleration due to gravity x sin( slope angle )

Mass in kg :

=  57 tons x 1000

= 57, 000 kg

Force parallel to the incline:

= 57, 000 kg x 9. 81 m/s² * sin ( 1.4 degrees )

= 57, 000 kg x 9.81 m/s² x sin ( 0.0244 radians )

= 32, 120.52 Newtons

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Solve for x. Round to the nearest tenth, if necessary.

Answers

Answer:

x = 16.2

Step-by-step explanation:

Using trig functions:

cos theta = adjacent side/ hypotenuse

cos 72 = 5/x

Solving for x

x = 5 /cos 72

x=16.18033

Rounding to the nearest tenth

x = 16.2

Answer: x = 16.2 units

Step-by-step explanation:

     We are given an angle (72°), the adjacent side (5), and the hypotenuse (x). We will use the cosine function to solve.

cos(θ) = [tex]\frac{adjacent}{hypotenuse }[/tex]

cos(72°) = [tex]\frac{5}{x }[/tex]

xcos(72°) = 5

x = [tex]\frac{5}{cos(72\°)}[/tex]

x = 16.1803398 ≈ 16.2

Solve for measure of angle a.
a
96°
140°
a = [?]°
If 2 secant lines intersect outside a circle: Enter
2-b

Answers

The measure of angle a is solved to be 22 degrees

How to find angle a

When two secant lines intersect outside a circle the formula for the vertex angle at a is

To find the vertex angle at point A where two secant lines intersect outside a circle, you can use the following formula:

angle A = 1/2 * (measure of arc 1 - measure of arc 2)

let arc 1 = 140 degrees

arc 2  = 96 degrees

plugging in the values

angle A = 1/2 * (140 - 96)

angle A = 1/2 * 44

angle A = 22 degrees

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find area of the triangle help please

Answers

The calculated area of the triangle is 7.5 square inches

Finding the area of the triangle

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

The triangle with the following dimensions

base = 6 inches

height = 2.5 inches

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

Area = 1/2 * base * height

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

Area = 1/2 * 6 * 2.5

Evaluate

Area = 7.5

Hence, the area of the triangle is 7.5 square inches

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answer: 7.5

because: 1/2 base * height

I really need help I will give you points

A.
x = 60; m∠ROS = 28°
B.
x = 62; m∠ROS = 31°
C.
x = 28; m∠ROS = 60°
D.
x = 31; m∠ROS = 62°

Answers

Answer:

D.

x = 31; m∠ROS = 62°

Step-by-step explanation:

we know that a right angle is always 90 degrees, so we subtract 90° by ∠QOR:

[tex]90 - 28 = 62[/tex]

Then we insert the 62 with the (2x)

[tex]62 = 2x[/tex]

we divide both sides by 2 and we get:

[tex]31 = x[/tex]


so the answer is D

x is equal to 31 and we can multiply 31 by 2 and we can get 62°

The rectangles in the figure below are folded along the dotted lines at 90 * angles to make a completely closed rectangle box with no overlap. What is the volume of the resulting box?

Answers

The Volume of the resulting rectangular box is calculated as: 72 cubic units.

What is the Volume of a Rectangular Box?

A rectangular box's volume can be calculated using the formula expressed below:

Volume = length * width * height.

Using the image of the net of the rectangular box, when folded, the dimensions of the box would be:

Length = 6 units

Width = 10 - 6 = 4 units

Height = 11 - 4 - 4 = 3 units

Plug in the values:

Volume of rectangular box = 6 * 4 * 3 = 72 cubic units.

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1. Convert the following Mayan numbers to decimal (base 10).
b)
||:
:|| || ()

Answers

The given Mayan number which is: :|| :|| in decimal (base 10) is 42.

How to solve

The Mayan number system is a base-20 system that uses three symbols: a dot (.), a horizontal bar (|), and a shell-like symbol (:). The symbol for zero is a shell-like symbol (:).

In order to obtain the decimal equivalent (base 10) of a Mayan numeral, it is imperative to comprehend the positional significance of each constituent symbol.

The numerical system employed here assigns a weight to each digit that corresponds to a certain power of 20. Specifically, the weight associated with the least significant digit is 20 raised to the exponent of 0, while the weight of the digit to its immediate left is 20 raised to the exponent of 1, and so forth.

The Mayan number given, : :|| :||, can be broken down as follows:

The leftmost position has no symbol, which represents a value of 0.

The second position from the left has two shell-like symbols (:), which represent a value of 2x20¹ = 40.

The third position from the left has two horizontal bars (||), which represent a value of 2x20⁰ = 2.

The given Mayan number in decimal (base 10) is 40 + 2 = 42.

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Find the length of the missing side

Answers

Answer:

24

Step-by-step explanation:

10^2+x^2=26^2

x^2=26^2-10^2

x^2=576

x=[tex]\sqrt{576}[/tex]=24

A card is picked from a standard deck of 52 cards. Determine the odds against and the odds in favor of selecting a diamond

Answers

Answer: The odds against selecting a diamond are 3:1 (or 3/4)

Step-by-step explanation: Which means that there are 3 ways to not select a diamond and only 1 way to select a diamond. The odds in favor of selecting a diamond are 1:3 (or 1/4), which means that there is only 1 way to select a diamond and 3 ways to not select a diamond.

Kyle submits a design for the contest, but his explanation was misplaced. How can figure A be mapped onto figure B? Can any other transformation be used to map figure A onto figure B

Answers

Answer:

A

Step-by-step explanation:

ita a bc i know its I did this before

Select the correct answer.
Consider functions f and g.
f(z) = log (x - 1)
g(x)
²-4
Which statement gives the best approximation of the solutions of the equation f(x) = g(z)?
OA. The solutions are where the graphs of the functions intersect at ≈ 1 and ≈ 3.642
-3.464 and z≈ 3.642.
OB.
The solutions are where the graphs of the functions cross the x-axis at z
O C.
The solutions are where the graphs of the functions intersect at
-3.464 and z≈ 3.464
O D.
The solutions are where the graphs of the functions cross the x-axis at z ≈ -4 and ≈ 0.422

Answers

The statement that gives the best approximation of the solutions of the equation f(x) = g(x) is:

option A. The solutions are where the graphs of the functions intersect at ≈ 1 and ≈ 3.642.

How did we get the value?

To find the solutions of the equation f(x) = g(x), set f(x) = g(x) and then solve for x. Using the given functions, we have:

log(x - 1) = (⅓x² - 4)

Exponentiating both sides:

x - 1 = e^(⅓x²-4)

Solve for x:

x = e^(⅓x²-4) + 1

Therefore, the solutions to the equation f(x) = g(x) are given by the values of x for which the graphs of the functions intersect. To find these points of intersection, plot the graphs of the functions and look for the points where they intersect. In other way round, solving for x numerically:

Based on the given functions, it is clear that g(x) is an upward-facing parabola with its vertex at (0, -4) and x-intercepts at (-2√3, 0) and (2√3, 0). The function f(x) is defined only for x > 1, and its graph is a monotonically increasing curve that approaches infinity as x approaches 1 from the right.

Therefore, there is only one point of intersection between the graphs of f(x) and g(x), which occurs to the right of x = 1. This point of intersection can be found numerically using a calculator or computer software, and it is approximately x ≈ 3.642.

Thus, the statement that gives the best approximation of the solutions of the equation f(x) = g(x) is:

OA. The solutions are where the graphs of the functions intersect at ≈ 1 and ≈ 3.642.

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A side of an equilateral triangle is 20 cm long. What is the area of the triangle

Answers

Should be 60 cm long in total. All sides are equal and it’s a triangle, so 20+20+20. Hope this helps

A triangle has side lengths of (6.2x - 9.4y) centimeters, (6.2x - 2.5z)
centimeters, and (8.3z + 1.4y) centimeters. Which expression represents the
perimeter, in centimeters, of the triangle?
O-3.2xy +3.7xz +9.7yz
O 12.4x8y + 5.8z
O-10.5yz +20.7xz
O-1.1z + 12.4x - 1.1y
Submit Answer

Answers

The perimeter of the given triangle is 12.4x-8.0y+5.8z. Therefore, option C is the correct answer.

Given that, triangle has sides of lengths of (6.2x-9.4y) centimeters, (6.2x-2.5z) centimeters and (8.3z+1.4y) centimeters.

We know that, perimeter of triangle is sum of all the sides.

Now, perimeter = 6.2x-9.4y+6.2x-2.5z+8.3z+1.4y

= (6.2x+6.2x)+(-9.4y+1.4y)+(-2.5z+8.3z)

= 12.4x-8.0y+5.8z

Therefore, option C is the correct answer.

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Algebra substitution y=-3x+5 2x+y=6

Answers

The solution to the system of equations y=-3x+5 and 2x+y=6 is (x,y) = (-1,8).

To solve the system of equations using substitution, we can substitute the expression for y in the second equation with the expression for y in the first equation:

2x + y = 6

2x + (-3x + 5) = 6 (substitute y = -3x + 5)

2x - 3x + 5 = 6

-x + 5 = 6

-x = 1

x = -1

Now that we have found the value of x, we can substitute it back into either of the original equations to find the value of y:

y = -3x + 5

y = -3(-1) + 5

y = 8

We can check our solution by verifying that it satisfies both equations:

y = -3x + 5 => 8 = -3(-1) + 5 => 8 = 8 (true)

2x + y = 6 => 2(-1) + 8 = 6 => 6 = 6 (true)

Thus, our solution is correct.

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I need help with this please

Answers

The matrix formed by performing R2 -> 4R1 + R2 on M is given as follows:

[tex]\left[\begin{array}{ccc}-4&3&1\\-18&9&8\end{array}\right][/tex]

How to do the row operation?

The matrix in the context of this problem is defined as follows:

[tex]\left[\begin{array}{ccc}-4&3&1\\-2&-3&4\end{array}\right][/tex]

The rows are given as follows:

R1: -4, 3 and 1.R2: -2, -3 and 4.

Hence the row 2 of the resulting matrix has the elements given as follows:

Column 1: 4 x -4 - 2 = -18.Column 2: 4 x 3 - 3 = 9.Column 3: 4 x 1 + 4 = 8.

Thus the resulting matrix is:

[tex]\left[\begin{array}{ccc}-4&3&1\\-18&9&8\end{array}\right][/tex]

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Which of the following is not a linear transformation?
Select one:
Rotation in geometry
Projection in geometry
None of the options
Reflection in geometry​

Answers

Answer is None of the options

The question asks which of these is NOT a linear transformation.

dilations, shears, rotations, reflections and projections are all linear.

Translation is NOT a linear transformation.

Mia is designing a cake for a birthday party. She plans for a total of 20 guests, each of whom may eat a piece of cake that has a volume of 8 cubic inches. Which of the following cakes would provide enough cake for each guest to have one piece of cake, with the least amount left over?

Answers

The square cake can be distributed in such a way that each person out of 15 guest may get 8  , with the least amount left over .

The Correct option is (1).

What is Volume of any shape?

The volume of an object is the amount of space occupied by the object or shape, which is in three-dimensional space. It is usually measured in terms ofof cubic units.

First find the volume of square cake,

Volume = l x b x h

= 8 x 8 x 2

=128

Now there are total 15 guests, Each of get

=

=  8.533

2.Volume of round cake (d= 6 inch, r=3 inch, h= 3 inch)

Volume=

=

=

=28.26  

Now there are total 15 guests, Each of get

=

= 1.884

3.Volume of round cake (d= 8 inch, r=4inch, h= 3 inch)

Volume=

=

=

=50.24  

Now there are total 15 guests, Each of get

=

=  3.349

4. Volume = l x b x h

= 6 x 9 x 2

=108

Now there are total 15 guests, Each of get

=

=  7.2

According to question each person may get 8 .

Only the square cake can be distributed in such a way that each person may get 8 , with the least amount left over .

help pleaseeeeeeee

here is the picture is about Row Ops

Answers

The result of adding -4 (row 1) to row 3 is determined as (0  - 9   2)|12.

What is the result of the row multiplication?

The resultant of the row multiplication in the Matrice is calculated by applying the following method;

row 1 in the given matrices = [1  2  1] | -5

To multiply row by -4, we will multiply each entity by 4 as shown below;

= -4(1 2  1) | -5

= (-4  -8  - 4) |20

To add the result to 3;

(-4  -8  - 4)|20 + (4  - 1   6) | -8

= (0  - 9   2)|12

Thus, the result of the row multiplication is determined by multiplying each entry in row 1, by - 4.

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‼️‼️WILL MARK BRAINLIEST IF HELPFUL‼️‼️

Answers

The area of the composite figure is equal to 75.5 square meters

How to calculate for the area of the figure

The composite figure can be observed to be made up of a big rectangle, a smaller rectangle, a triangle and a smaller triangle. We calculate for the area of the four shapes and sum the results to get the total area of the composite figure as follows:

area of the big rectangle = 6 m × 4 m = 24 m²

area of the smaller rectangle = 7 m × 2 m = 14 m²

area of the big triangle = 1/2 × 10 m × 6 m = 30 m²

area of the smaller triangle = 1/2 × 5 m × 3 m = 7.5 m²

total area of the composite figure = 24 m² + 14 m² + 30 m² + 7.5 m²

total area of the composite figure = 75.5 m²

Therefore, the area of the composite figure is equal to 75.5 square meters

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A survey asked students whether they have any siblings and pets. The survey
data are shown in the relative frequency table.
Pets
No pets
Total
Siblings
0.3
0.45
0.75
OA. 30%
OB. About 67%
O C. 75%
D. 40%
Given that a student has a sibling, what is the likelihood that he or she also
has a pet?

Answers

The likelihood that he or she has a pet given that a student does not have a sibling is 60%. Therefore, the correct option is option D.

Let A denote the event that a student does not have a sibling.

Let B denote the event that a student has a pet.

Then A∩B will denote the event that the student does not have a sibling but he has a pet.

Let P denote the probability of an event in this question.

Then, we have to find the conditional probability of event B which means the likelihood of event B occurring based on the occurrence of event A.

P(B|A)

We know that:

[tex]P(B|A) = \frac{P(A\cap B)}{P(A)}[/tex]

Also from the table, we have:

P(A)=0.25

and P(A∩B)=0.15

Hence,

[tex]P(B|A) = \frac{0.15}{0.25}[/tex]

[tex]P(B|A) = \frac{3}{5}[/tex]

[tex]P(B|A) = 0.6[/tex]

which in percentage is:

0.6 * 100 = 60 %

Therefore, the likelihood that he or she has a pet too is 60% and the correct option is option D.

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please I need help in this one​

Answers

Answer: 55

Step-by-step explanation:

can someone help me do these qustions ( sorry if its hard to see) -(geometric sequence)​

Answers

1. The geometric sequence is B. -1, 2, -4, 8.

2. The sixth term is 8192.

3. The next three terms are 1, 1/2 and 1/4.

4. The 10th term is 4374.

5. The eight term is 1/16.

6. The next three terms in the geometric sequence are -1/36 1/216, and - 1/1296

7. The 8th term or the sequence will be 4.

8. The 6th term of the geometric sequence is 2048.

How to calculate the value

The 6th term of the sequence is:

a₆  = -2 * 4⁵ = -2 * 1024 = -2048

The common ratio of the sequence is:

r = 8/16 = 4/8 = 2/4 = 1/2

16 * (1/2) = 8

8 * (1/2) = 4

4 * (1/2) = 2

Therefore, the next three terms in the geometric sequence are 8, 4, and 2.

The common ratio of the sequence is:

r = 6/(-36) = -1/6

-1/6 * (1/6) = 1/36

1/36 * (1/6) = 1/216

-1/216 × 1/6 = -1 /1296

Therefore, the next three terms in the geometric sequence are -1/36, 1/216 and 1/1296.

The 8th term or the sequence will be:

= 512 × 0.5 × 0.5 × 0.5 × 0.5⁴

= 4

The 6th term of the geometric sequence is:

= 2 × 4 × 4 × 4 × 4 × 4

= 2048

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Pleas help and I will mark your brainliest. It is simple matrix work!

Answers

The inverse of matrix C is C⁻¹ = [1/9 4/27] [1/27 -5/27].

How to determine inverse of matrix?

To find the inverse of matrix C, use the following formula:

C⁻¹ = 1/det(C) × adj(C)

where det(C) = determinant of matrix C and adj(C) = adjugate of matrix C.

To find the determinant of C, use the following formula for a 2x2 matrix:

|a b|

|c d| = ad - bc

So:

det(C) = |5 1|

|12 -3| = (5)(-3) - (1)(12) = -27

Find the adjugate of C, which is the transpose of the matrix of cofactors of C, which is:

|-3|

| 1| = -(-3) = 3

So the upper left cofactor is 3, which is:

|12|

|-3| = -(12) = -12

So the upper right cofactor is -12, which is:

| 1|

|-3| = -(1) = -1

So the lower left cofactor is -1, which is:

|5|

|1| = 5

So the lower right cofactor is 5. Putting the cofactors into a matrix and transposing it gives the adjugate of C:

adj(C) = [ 3 -12]

[-1 5]

Now find the inverse of C:

C⁻¹ = 1/det(C) × adj(C)

= -1/27 × [ 3 -12]

[-1 5]

= [1/9 4/27]

[1/27 -5/27]

So the inverse of matrix C is:

C⁻¹ = [1/9 4/27]

[1/27 -5/27]

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During a sale, a store offered a 25% discount on a bed that originally sold for $800. After the sale, the discounted price of the bed was marked up by 25%. What was the price of the bed after the markup? Round to the nearest cent.

Answers

The price of the bed after mark up is $475.00

What is discount?

Discount results in the reduction of the selling price of the product, which makes it more attractive for the customer.

The first discount given is 25% , therefore the price of the bed before mark up is

25/100 × 800

= 25×8

= 200

the price before mark up = 800-200 = $600

Another 25% is given after the first sale, there the price of the bed after mark up is

25/100 × 600

=$ 125

price after markup = 600-125

= $475.00

therefore the price of the bed after markup is $475.00

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What is the domain indicated on the graph for each portion of the piecewise function?
f(x) = StartLayout enlarged left-brace 1st Row 1st column negative 2, 2nd column Domain 1st piece 2nd row 1st column 2 x + 1, 2nd column Domain 2nd piece Third row 1st column negative one-half x, 2nd column Domain 3rd piece EndLayout

Answers

The domain of the 1st piece is -10 < x < 0, for 2nd piece is 0 < x < 4, and for 3rd piece is 4 < x < 8.

What is a function?

A function is a particular kind of relationship where there is a set domain and range, and every input value in the domain is associated with a single output value in the range.

We have a piecewise function shown in the picture:

From the graph:

f(x) = -2, Domain: -10 < x < 0

f(x) = 2x + 1, Domain: 0 < x < 4

f(x) = (-1/2)x, Domaim: 4 < x < 8

Thus, the domain of the 1st piece is -10 < x < 0, for 2nd piece is 0 < x < 4, and for 3rd piece is 4 < x < 8.

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Question 6(Multiple Choice Worth 5 points)
(Reflections MC)

Triangle NMO has vertices at N(−5, 2), M(−2, 1), and O(−3 , 3). Determine the vertices of image N′M′O′ if the preimage is reflected over y = −2.

N′(−3, 2), M′(0, 1), O′(−5, 3)
N′(−5, 0), M′(−2, −1), O′(−3, 1)
N′(−5, 1), M′(−2, 0), O′(−3, 2)
N′(−5, −6), M′(−2, −5), O′(−3, −7)



Please Fast only have 10 minutes.

Answers

The image coordinates of NMO after the translation is option d: N′(−5, −6), M′(−2, −5), and O′(−3, −7).

What is the  image coordinates?

To get the image coordinates of the preimage translated -2 units to the left, we simply subtract -2  from the y-coordinates of each vertex:

N' = (Nx - (-2), Ny) = (−5 , 2- (-2)) = (−5, 4)

M' = (Mx - (-2), My) = (−2 , 1 - (-2)) = (−2, 3)

O' = (Ox - (-2), Oy) = (−3 , 3- (-2)) = (−3, 5)

Therefore, based on the above, the image coordinates of NMO after the translation are N′(−5, 4), M′(-2,3 ), O′(−3, 5)

So the reflected vertices are:

The distance from N to the line y = -2 is 4, and -6 - (-2) = -4, so one need to move down 4 units to have  a y-coordinate of -6.

The distance from M to the line y = -2 is 3, and -5 - (-2) = -3, so  one need to move down 3 units to have a y-coordinate of -5.

The distance from O to the line y = -2 is 5, and -7 - (-2) = -5, so  one need to move down 5 units to have  a y-coordinate of -7.

So it will be: N′ (−5, −6), M′(−2, −5), O′(−3, −7)

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Answer:

D) N′(−5, −6), M′(−2, −5), O′(−3, −7)

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Given triangle MNO with vertices:

N = (-5, 2), M = (-2, 1) and O = (-3, 3)

It is reflected in line y = - 2.

This reflection doesn't affect the x-coordinates of the vertices and the y-coordinates change.

Since y = - 2 is the line of symmetry,  it also represents midpoints of the segments formed by corresponding endpoints of image and preimage.

Using midpoint equation, find the y-coordinates.

Point N'(2 + y)/2 = - 2 ⇒ 2 + y = - 4 ⇒ y = - 6Point M'(1 + y)/2 = - 2 ⇒ 1 + y = - 4 ⇒ y = - 5Point O'(3 + y)/2 = - 2 ⇒ 3 + y = - 4 ⇒ y = - 7

So the coordinates of the image are:

N′(−5, −6), M′(−2, −5), O′(−3, −7)

This is matching the option D.

See attached for visual representation of the problem.

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