The average time between accidents in a factory is 5 weeks.
Find the probability that more than 7 weeks pass between accidents.

Answers

Answer 1

Answer:

The probability that more than 7 weeks pass between accidents is 4.0551 .

Step-by-step explanation:

Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e. how likely they are to happen, using it.

The probability formula is defined as the possibility of an event to happen is equal to the ratio of the number of favorable outcomes and the total number of outcomes

A Poisson distribution is a probability distribution that is used to show how many times an event is likely to occur over a specified period.

mean = 5 weeks

rate = 1/5 = 0.2

x = average time

 P(x > 7) = e^(0.2×7) = 4.0551

The probability that more than 7 weeks pass between accidents is 4.0551 .

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Related Questions

5. Walker is reading a book that is 792 pages. He reads
15 pages a day during the week, and 25 pages a day
during the weekend. After 5 weeks of reading, how
many pages does Walker still have left to read before
he finishes the book?
Let r represent the pages left to read.
Equation:
Walker has
to read.
pages left

Answers

Forming Equations from Word Problems

To form equations from word problems, we can derive mathematical operations as well as variables from the given information.

In this case, each time Walker reads a certain number of pages, we subtract that from the total number of pages left to know how many pages is left to read.

Solving the Question

Let r represent the pages left to read.

792 pages in total

r = 792

Walker reads 15 pages a day during the week and 25 pages a day during the weekend.

There are 5 weekdays, and he reads 15 pages each of those days. ⇒ r = 792 - 5×15There are 2 weekend days, and he reads 25 pages each of those days.
r = 792 - (5×15 + 2×25)

5 weeks have passed

Multiply the terms representing the number of pages he reads a week by 5, for 5 weeks.
r = 792 - (5×15 + 2×25)×5

Answer

r = 792 - (5×15 + 2×25)×5

The domain of the function

Answers

Step-by-step explanation:

[-5, 4] because it is an empty circle, meaning less than

The number of bacteria in a culture is increasing according to the law of exponential growth. The initial population is 240 bacteria, and the population after 9 hours is double the population after 1 hour. How many bacteria will there be after 4 hours? (Round your answer to the nearest whole number.)

Answers

Answer:

339

Step-by-step explanation:

Exponential Function

General form of an exponential function: [tex]y=ab^x[/tex]

where:

a is the initial value (y-intercept)b is the base (growth/decay factor) in decimal formx is the independent variabley is the dependent variable

If b > 1 then it is an increasing function

If 0 < b < 1 then it is a decreasing function

Given information:

a = 240 (initial population of bacteria)x = time (in hours)y = population of bacteria

Therefore:  [tex]y=240b^x[/tex]

To find an expression for the population after 1 hour, substitute x = 1 into the found equation:

[tex]\implies y=240b^1[/tex]

[tex]\implies y=240b[/tex]

We are told that the population after 9 hours is double the population after 1 hour.  Therefore, make y equal to twice the found expression for the population after 1 hour, let x = 9, then solve for b:

[tex]\implies 2(240b)=240b^9[/tex]

[tex]\implies 480b=240b^9[/tex]

[tex]\implies 480=240b^8[/tex]

[tex]\implies 2=b^8[/tex]

[tex]\implies b=\sqrt[8]{2}[/tex]

[tex]\implies b=2^{\frac{1}{8}}[/tex]

Therefore, the final exponential equation modelling the given scenario is:

[tex]\implies y=240(2^{\frac{1}{8}})^x[/tex]

[tex]\implies y=240(2)^{\frac{1}{8}x}[/tex]

To find how many bacteria there will be after 4 hours, substitute x = 4 into the found equation:

[tex]\implies y=240(2)^{\frac{1}{8}(4)}[/tex]

[tex]\implies y=240(2)^{\frac{1}{2}}[/tex]

[tex]\implies y=339 \:\: \sf (nearest\:whole\:number)[/tex]

Therefore, there will be 339 bacteria (rounded to the nearest whole number) after 4 hours.

Do you know how fast last year's winner was traveling? san francisco laser boat.

Answers

The average speed of the Australian team's laser boat in the San Francisco final was 68.81 km/h.

What is the laser boat?

The laser boat is a type of boat that uses the wind to move on the water. This type of boat is used in the SailGP Championship.

In the phase of San Francisco, the United States the winner was the team of Australia that had an average speed of 68.81 km/h and a maximum of more than 90 km/h.

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PLEASE HELP!!! I will give brainliest pleasee help. each question has to be solved, there are no options for answers.

Answers

The intersecting secant theorem states the relationship between the two intersecting secants of the same circle. The given problems can be solved using the intersecting secant theorem.

What is Intersecting Secant Theorem?

When two line secants of a circle intersect each other outside the circle, the circle divides the secants into two segments such that the product of the outside segment and the length of the secant are equal to the product of the outside segment other secant and its length.

a(a+b)=c(c+d)

1.)

6(x+6) = 5(5+x+3)

6x + 36 = 25 + 5x + 15

x = 4

2.)

4(2x+4)=5(5+x)

8x + 16 = 25 + 5x

3x = 9

x = 3

3.)

8x(6x+8x) = 7(9+7)

8x(14x) = 112

112x² = 112

x = 1

4.)

(x+3)² = 16(x-3)

x² + 9 + 6x = 16x - 48

x² - 10x - 57 = 0

x = 14.0554

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Variables y and x have a proportional relationship, and y = 21 when x = 14.

What is the value of x when y = 12?

Enter your answer in the box.

x =
please help

Answers

Answer:

18

Step-by-step explanation:

We know that y is 1.5 times x, so when x = 12, y = (1.5)(12)=18

This directly proportional relationship between p and q is written as p∝q  where that middle sign is the sign of proportionality. The value of x is 8, when the value of y is 12.

What is the directly proportional and inversely proportional relationship?

Let there are two variables p and q

Then, p and q are said to be directly proportional to each other if

 p = kq

where k is some constant number called the constant of proportionality.

This directly proportional relationship between p and q is written as p∝q  where that middle sign is the sign of proportionality.

In a directly proportional relationship, increasing one variable will increase another.

Now let m and n be two variables.

Then m and n are said to be inversely proportional to each other if

[tex]m = \dfrac{c}{n} \\\\ \text{or} \\\\ n = \dfrac{c}{m}[/tex]

(both are equal)

where c is a constant number called the constant of proportionality.

This inversely proportional relationship is denoted by

[tex]m \propto \dfrac{1}{n} \\\\ \text{or} \\\\n \propto \dfrac{1}{m}[/tex]

As visible, increasing one variable will decrease the other variable if both are inversely proportional.


Given Variables y and x have a proportional relationship, therefore, we can write,

y ∝ x

y = k × x

21 = k × 14

21/14 = k

k = 1.5

Therefore, the equation for the relationship between x and y can be written as,

y = 1.5x

now, the value of x when the value of y is 12 is,

12 = 1.5 × x

x = 8

Hence, the value of x is 8, when the value of y is 12.

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17. Find the height of a rectangular room that
measures 4.7 m long and 3.2 m wide, if
the space within it is 33.84 m³.

Answers

Answer:

the height: h=2,25

Step-by-step explanation:

volume of rectangular box = wide*long*the height

----> the height = volume of rectangular box / ( wide*long) = 2,25

give me 5 stars and hearts^^

the answer is going to be h = 2 ,25

Please help!!!!
A triangular patch of grass in a park is bordered by walking paths. The longest path bordering the patch of grass measures 135 feet. The smallest path bordering the patch of grass measures 60 feet. The smallest angle formed by the paths measures 26°. What is the measure of the largest angle of the triangular patch of grass? Round your answer to the nearest degree. Show all your work.

Answers

The measure of the largest angle of the triangular patch of grass is 81 degrees

Application of sine rule

In order to determine the measure of the largest angle, we will use the expression below;

[tex]\frac{60}{sin26^0} =\frac{135}{sinx^0}[/tex]

Cross multiply

135sin26 = 60sinx

sinx = 135sin26/60

sinx = 59.18/60
sinx = 0.986

x = 80.5 degrees

Hence the measure of the largest angle of the triangular patch of grass is 81 degrees

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How do the graph of f(x) and f^(-1)(x) relate?
A.They are rotations of each other.
B.They are reflections of each other.
C.They are the exact same graph.
D.They are translations of each other.

Answers

The correct option regarding the inverse function is given by:

B.They are reflections of each other.

What is the relation between the graphs of the original function and it's inverse?

The inverse function is the reflection of the original function over the line y = x, that is, they are reflections of each other, hence option B is correct.

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Please help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! i will give u brainliest

Answers

Answer: The answer is x = +/- [tex]\sqrt{y+1}[/tex].

Step-by-step explanation: You can solve this by simply rearranging the equation to make x by itself.

-[tex]x^{2}[/tex] = -y - 1

Then cancel out the -1 by dividing it through to obtain.

[tex]x^{2} =y+1[/tex]

The final step is to square root both sides to get rid of the exponent.

x = [tex]\sqrt{y+1}[/tex]

This should be the answer since square roots have a +/-.

If x^2 = y
x = +- y

So y = x^2 - 1
x^2 = y+1
x = +- square root (y+1)

Solve for x in the diagram below.

Answers

Answer:

x = 20°

Step-by-step explanation:

x° + 2x°+ (x+10)° = 90°

4x° + 10° = 90°

4x° = (90 -10)°

x° = (80/4)°

x = 20°

Hope this helps

Answer:

x = 20

Step-by-step explanation:

Key points:

understanding diagram notationunderstanding the Angle Addition Postulate

Diagram notation

In the diagram, there are three angles, each with an expression representing the measure of their angle (in degrees).  Angles are adjacent (next to each other with the same vertex) such that collectively they form one large angle.

The small square in the lower left corner means that the large angle is a right angle.  All right angles are 90°.

Note:  The expressions for each angle all have a degree marking, so each angle is measured in degrees.  The unknown value x, is a number without any units, the expression is simplified, and then the units "degrees" are applied.  So in the end, the answer for "x" will not have units; "x" will just be a number.

Angle Addition Postulate

The Angle Addition Postulate states that the sum of the measures of two adjacent angles is equal to the measure of the large angle formed by those adjacent angles.  

[tex](\text{measure of first angle})+(\text{measure of second angle})=(\text{measure of the combined angle})[/tex]

Solving the given problem

By applying the Angle Addition Postulate a couple times, the sum of the measures of all three angles in the diagram is equal to the measure of the large angle formed by those three angles.

[tex](\text{measure of first angle})+(\text{measure of second angle})+(\text{measure of third angle})=(\text{measure of the large right angle})[/tex]

or

[tex](x)+(2x)+(x+10)=(90)[/tex]

From here, to solve for x, we'll need to combine like terms, isolate x, and simplify.

Start with the Associative Property of Addition to combine like terms:

[tex](x+2x+x)+10=90\\4x+10=90[/tex]

To isolate x, subtract 10 from both sides and simplify...

[tex](4x+10)-10=(90)-10\\4x=80[/tex]

... then divide by 4 on both sides and simplify.

[tex]\dfrac {4x}{4}=\dfrac {80}{4}\\x=20[/tex]

So, x=20

What are the y-intercept and the asymptote of g(x) = 4x – 6?

(0, –5); y = –6
(0, –2); y = –4
(0, 4); y = 6
(0, 6); y = 4

Answers

The y-intercept of the line is (0 -6). The given function has no vertical and horizontal asymptotes

y-intercept and asymptotes of an equation

A linear equation is an equation that has a leading degree of 1. Given the equation

g(x) = 4x - 6

The y-intercept occurs at a point where x = 0

g(0) = 4(0) - 6

g(0) = -6

Hence the y-intercept of the line is (0 -6)

The given function has no vertical and horizontal asymptotes

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Which point is on the graph of f(x) = 3.4^x
O A. (1, 12)
OB. (0, 12)
O C. (12, 1)
O D. (0,0)

Answers

simply plug in each x-value and see if the y-value matches the one in the pair.

if the equation above is 3.4 to the power of x, then there is none of these are on the graph of f(x)

but if the equation that you are trying to convey is f(x) = 3 * (4^x), then the answer is "a", since f(1) = 3* (4^1) which is the same as 3* 4, which equals 12.

The point on the graph f(x) = 3.4ˣ is (0, 1)

None of the given options is correct.

What is a function?

A function is a relationship between a number of inputs and outputs. A function is an association of inputs where each input is coupled with exactly one output. There is a range, co-domain, and domain for every function.

To determine which point is on the graph of f(x) = 3.4ˣ, we need to substitute the given x-coordinate into the function and see if we get the given y-coordinate.

Let's try each option:

A. (1, 12): f(1) = 3.4¹ = 3.4, so this point is not on the graph of f(x) = 3.4ˣ.

B. (0, 12): f(0) = 3.4⁰ = 1, so this point is not on the graph of f(x) = 3.4ˣ.

C. (12, 1): f(12) = 3.4¹² ≈ 108089.7, so this point is not on the graph of f(x) = 3.4ˣ.

D. (0, 1): f(0) = 3.4^0 = 1, so this point is on the graph of f(x) = 3.4ˣ.

Therefore, the point (0, 1) is on the graph of f(x) = 3.4ˣ. The answer is option D.

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In the triangle above, what is the measure of A.
M B.
M C.
M D
, cannot be determined

Answers

B. 45. The two angles B and A are both 45 to make 90 and angle C is a 90 degree angle so they come together for 180 degrees total

For an each situation, it begin with the square field, measuring X centimetres by X centimetres. The dimensions of this square are to be changed. How do you write an expression for the area of the new square field, and then expand, and simplify? :/

A). The length of a side is being increased by 8 cm.
B). The length is being increased by 12 cm and the width is being decreased by 7 cm.

Answers

#A

New side

X+8

Area

(x+8)²x²+16x+64 cm²

#2

Now it has turned rectangle

Sides

x+12 and x-7

Area

(x+12)(x-7)

Answer:

A)  (x + 8)² cm² = (x² + 16x + 64)  cm²

B)  (x + 12)(x + 7) cm² = (x² + 19x + 84) cm²

Step-by-step explanation:

Formula

Area of a square = s²  (where s is the side length)

Given side length of square field:

x cm

⇒ Area of field = x² cm²

Part A

If the side length of the square field is increased by 8 cm then:

⇒ new side length = (x + 8) cm

Substitute the new side length into the formula for the area of a square:

Area of field = (x + 8)² cm²

Expand and simplify:

Area = (x + 8)²

Area = (x + 8)(x + 8)

Area = x(x + 8) + 8(x + 8)

Area = x² + 8x + 8x + 64

Area = (x² + 16x + 64)  cm²

Part B

If the side length of the square field is increased by 12 cm and the width is decreased by 7 cm then:

⇒ new side length a = (x + 12) cm

⇒ new side length b = (x - 7) cm

Substitute the side lengths into the formula for area of a square:

⇒ Area of a square = s × s

⇒ Area of a square = a × b

Area of the field = (x + 12)(x + 7) cm²

Expand and simplify:

⇒ Area = (x + 12)(x + 7)

⇒ Area = x(x + 7) + 12(x + 7)

⇒ Area = x² + 7x + 12x + 84

Area = (x² + 19x + 84) cm²

Select the correct answer.
Gas station A has posted a chart that shows the price of gasoline in terms of the number of gallons.

Answers

The correct answer is option C which is Gas station A is selling gasoline at a lower rate its price is $3.05 per gallon.

What is an expression?

Expression in maths is defined as the collection of numbers, variables, and functions using signs like addition, subtraction, multiplication and division.

Here we have two pieces of information

Gas station A:-

3 gallons for $9.15

1 gallons for  $9.15 / 3 = $ 3.05

Gas station B:-

P = 3.08g

It means that station B is selling the gasoline at a higher price.

Therefore the correct answer is option C which is Gas station A is selling gasoline at a lower rate its price is $3.05 per gallon.

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which of the following is a rational number
a.√5
b.π
c.1/2
d.√(77)

Answers

c. 1/2

the quotient of two integers

Write the equation of the line that passes through the points (8,-1) and (2,-5) in standard form, given that the point-slope form is y+1=3/3(x-8)

Answers

The equation of the line that passes through the points (8,-1) and (2,-5) is 2x - 3y = 19.

The given coordinate are (8, -1) and (2, -5).

What is the slope of an equation?

In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line.

The slope of the equation is [tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex].

The standard form of an equation is Ax + By = C.

The given the point-slope form is [tex]y+1=\frac{2}{3} (x-8)[/tex].

Multiply each term by 3 of the equation.

[tex](y+1) \times3=\frac{2}{3} (x-8) \times3[/tex]

⇒3y + 3 = 2x - 16

Subtract 2x from both sides of a equation.

That is, -2x + 3y + 3 = - 16

Subtract 3 from both sides of a equation.

That is, -2x + 3y = - 19

Multiply each term by - 1 from both sides of an equation.

That is, 2x - 3y = 19

Therefore, the equation of the line that passes through the points (8,-1) and (2,-5) is 2x - 3y = 19.

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3.5 decimals to mixed numbers

Answers

1 2/3
It’s one and two thirds written out

Mike has 21 pounds of tomatoes and 9 pounds of mixed peppers from his garden that he will use to make salsa and tomato sauce. The graph represents the system of equations shown.

A system of equations. x plus 5 y equals 21. x plus y equals 9.

The variable x represents the number of batches of salsa that can be made and y represents the number of batches of tomato sauce that can be made.

Answers

Answer:

x= 6 , y = 3

Step-by-step explanation:

x + 5y = 21

i am using trail and error method and i got the answer easily

the logic behind this is simple

the first equation is x + 5y = 21 so we can say that y  will be 5 x 1 , 5 x 2 , 5 x  3 , 5 x 4

first i did 5 x 4 = 20

x + 5 x 4 = 21

x= 1 but the equation x + y = 1 + 4 = 5  which is not equal to 9

second i tried with 5 x 3 =15

and the equation will be

x + 5 x 3 = 21

6 + 15 = 21

this time the second equation became true

x + y = 9

6 + 3 = 9

the no of pounds of salsa = 6

no of pounds of tomato = 3

Change the decimal to a fraction. (Use the “/“ in your fraction.) 0.45454545….

Answers

The decimal: 0.4545...

Can be written in fraction form as 45/99.

How to write the number as a fraction?

Here we have the number:

N = 0.4545...

Notice that the repeating digits are two, 4 and 5.

Then we can multiply our number by 100 (same number of zeros as repeating digits) so we get:

100*0.4545... = 45.4545...

Now if we subtract the original number, we get:

45.4545... - 0.4545... = 45

This means that:

(100 - 1)*0.4545... = 99*0.4545... = 45

Then we can multiply and divide our number by 99, so we get:

[tex]0.4545... = 0.4545...\frac{99}{99} = \frac{45}{99}[/tex]

So the fraction is 45/99

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what is the answr to -5(b + 1) = 8

Answers

[tex] - 5(b + 1) = 8 \\ - 5b - 5 = 8 \\ - 5b = 8 + 5 \\ - 5b = 13 \\ b = \frac{ - 13}{5} [/tex]

PLEASE GIVE BRAINLIEST

\\\///\\\///\\\///\\\///\\\///\\\///\\///\\\///\\\///\\\///\\\///\\\//\\//\\//\\//\\\///\\//\\\///\\\///\\\///\

                                      [tex]\Rsh[/tex] Hey! [tex]\Lsh[/tex]

[tex]\Rsh[/tex]Let's solve this! We can do this! [tex]\Lsh[/tex]

>>> First, let's multiply -5 by b and 1. Then we obtain

[tex]\pmb{-5b-5=8}[/tex].

>>> Now we add 5 to both sides.

[tex]\pmb{-5b=13}[/tex]

>>> And then, divide both sides by -5.

[tex]\pmb{b=-\dfrac{13}{5}}[/tex]

>>> That is the value of b.

><><><><><<><><><><><><><><><><><><><><><><><><><><><><><><><><>

Hope the answer - and explanation - assisted you!

Happy studies! :)

The median height of 11 footballers is 1.85m.
Only one footballer has a height of 1.85m
How many footballers have a height under 1.85m

Answers

5 footballers because if 1.85 is the median, or the middle number, there has to be five players above that height and 5 players below.

find sizes of unknown angles​

Answers

Answer:

a=75

b=70

c=110

d=105

e=110

f=105

Step-by-step explanation:

For any positive numbers a, b, and d, with b 1,


A.
logb a logb d

B.
logb a + logb d

C.
d logb a
done

D.
logb a - logb d

Answers

Answer:

D

Step-by-step explanation:

using the rule of logarithms

log x - log y ⇔ log ( [tex]\frac{x}{y}[/tex] )

then

[tex]log_{b}[/tex] ( [tex]\frac{a}{d}[/tex] ) = [tex]log_{b}[/tex] a - [tex]log_{b}[/tex] d

Find the greatest common factor of these two expressions.
28y^7x^2 and 8y^8v^4x^6

Answers

Answer:

4y⁷x²

Step-by-step explanation:

Finding GCF:

    Prime factorize each expression.

28y⁷x² = 2 * 2 * 7 * y⁷ * x²

8y⁸v⁴x⁶ = 2 * 2 * 2 * y⁸ * v⁴ * x⁶

GCF = 2 * 2 *y⁷*x²

        = 4y⁷x²

Hey can I have help with this question. An explanation would be great as I find things difficult to understand :)

Answers

Answer:

[tex](0, -\frac{15}{2} )[/tex]

Step-by-step explanation:

When a straight line crosses the y-axis, the point that touches it is called the y-intercept. We can find the y-intercept by plugging in zero as the value for 'x', as any x value on the y-axis is zero. So plugging in x = 0 into the equation '3x - 2y = 15', we get -2y = 15, so y = -15/2. The point would be [tex](0, -\frac{15}{2} )[/tex], as x = 0 when y = -15/2.

Timothy is 13 5/6 years old. Camden is 1 1/3 years younger than Timothy and Jane is 1 1/4 years younger than Camden. How old is Jane?

Answers

Answer:

Jane is 11 1/4 years old.

Step-by-step explanation:

Subtract all of the numbers given.

[tex]13\frac{5}{6} -1\frac{1}{3} -1\frac{1}{4}[/tex].

To subtract this, we need to find a common denominator.

A common denominator in this situation is 12. To do this multiply the 5 and the 6 of 5/6 by 2. Multiply the 1 and the 3 of 1/3 by 4. And multiply the 1 and the 4 1/4 by 3.

The new expression will look like this:

[tex]13\frac{10}{12} -1\frac{4}{12} -1\frac{3}{12}[/tex].

Now we can subtract.

[tex]13\frac{10}{12} -1\frac{4}{12} -1\frac{3}{12}=11\frac{3}{12}[/tex]

Reduce the answer.

[tex]11\frac{3}{12}=11\frac{1}{4}[/tex]

In decimal form 11.25

Hope this helps!

If not, I am sorry.

2(2x – 1) + 7 < 13 or –2x + 5≤-10

Answers

Answer:

2, 7.5

Step-by-step explanation:

2(2x - 1) + 7 < 13

4x - 2 + 7 < 1

4x + 5 < 13

4x < 8

x < 2

-2x + 5 ≤ -10

-2x ≤ -10 - 5

-2x ≤ -15

x ≤ -15 / -2

x ≤ 7.5

Planes X and Y and points J, K, L, M, and N are
shown.
X
L
K
M
Y
Exactly how many planes contain points J, K, and N?
0000
O
1
O2
3

Answers

0 planes contain points J, K, and N.

Given that, planes X and Y and points J, K, L, M and N.

We need to find exactly how many planes contain points J, K, and N.

From the figure, we can see Point J doesn't belong to the planes X and Y and Point K and N belong to the plane X.

Since, points J, K, and N together do not belongs to any single plane, the planes contain points J, K, and N is 0.

Therefore, 0 planes contain points J, K, and N.

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Answer:

2 planes.

Step-by-step explanation:

The third option is correct.

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