Find the slope using the formula.
(-2, -8) and (4, -6)

Complete Question

The amounts a soft drink machine is designed to dispense for each drink are normally distributed, with a mean of 12.1 fluid ounces and a standard deviation of 0.3 fluid ounce. A drink is randomly selected.

Required:

a) Find the probability that the drink is less than 11.9 fluid ounces

b) Find the probability that the drink is between 11.6 and 11.9 fluid ounces

c) Find the probability that the drink is more than 12.6 fluid ounces. Can this be considered an unusual​ event? Explain your reasoning.

Answer:

a

  [tex] P(X < 11.9 ) =  0.25239  [/tex ]  

b

  [tex]P(  11.6 < X < 11.9 ) =  0.20463 [/tex]

c

  [tex] P(X > 12.6 ) =  0.047757  [/tex ]  

Yes  It is an unusual event

Step-by-step explanation:

From the question we are told that

   The mean is  [tex]\mu = 12.1[/tex]

   The standard deviation is  [tex]\sigma =0.3[/tex]

Generally the probability that the drink is less than 11.9 fluid ounces is mathematically represented as

      P(X < 11.9 ) =  P(\frac{X -\mu}{\sigma } < \frac{11.9 - 12.1}{0.3} )

   [tex]\frac{X -\mu}{\sigma }  =  Z (The  \ standardized \  value\  of  \ X )[/tex]

      [tex] P(X < 11.9 ) =  P(Z< -0.667 ) [/tex ]

From the z table  the area under the normal curve to the left corresponding to -0.667  is

P(Z< -0.667 ) = 0.25239

So

[tex] P(X < 11.9 ) =  0.25239  [/tex ]  

Generally the  probability that the drink is between 11.6 and 11.9 fluid ounces is mathematically represented as

[tex] P(  11.6 < X < 11.9 ) =  P(  \frac{11.6 -12.1}{0.3} < \frac{X -\mu}{\sigma } < \frac{11.9 - 12.1}{0.3} ) [/tex]

   [tex]P(  11.6 < X < 11.9 ) =  P( -1.667 < Z < -0.667 ) [/tex]

=> [tex]P(  11.6 < X < 11.9 ) =  P( Z < -0.667) -  P ( Z < -1.667 ) [/tex]

From the z table  the area under the normal curve to the left corresponding to  -1.667  is

  P(Z< -1.667 ) = 0.047757

So

       [tex]P(  11.6 < X < 11.9 ) =  0.25239  - 0.047757 [/tex]

=>      [tex]P(  11.6 < X < 11.9 ) =  0.20463 [/tex]

Generally the probability that the drink is more than 12.6 fluid ounces is mathematically represented as

         P(X > 12.6 ) =  P(\frac{X -\mu}{\sigma } > \frac{12.6 - 12.1}{0.3} )

      [tex] P(X >12.6 ) =  P(Z> 1.667 ) [/tex ]

From the z table  the area under the normal curve to the right corresponding to 1.667  is

P(Z> 1.667 ) = 0.047757

So

[tex] P(X > 12.6 ) =  0.047757  [/tex ]        

Given that this probability is less than 0.05 , it mean it is an unusual​ event

Answer: 12/28

Explanation: I got this right years ago my man.

Answer:

5200

Step-by-step explanation:

STEP 1: The discriminant of a quadratic is the expression inside the radical of the quadratic formula.

[tex]b^2-4(ac)[/tex]

STEP 2: Substitute in the values of a, b, and c.

[tex](-10)^2-4(5)(-255)[/tex]

STEP 3: Evaluate the result to find the discriminant.

[tex]5200[/tex]

Answer:

x = 12

Step-by-step explanation:

[tex] \because BD \perp AC... (given) \\\\

\therefore m\angle DBA =90\degree... (1)\\\\

\because m\angle DBA=(7x + 6)\degree... (2)\\[/tex]

From equations (1) & (2)

[tex](7x + 6)\degree= 90\degree \\\\

7x + 6 =90\\\\

7x = 90 - 6\\\\

7x = 84\\\\

x = \frac{84}{7}\\\\

\huge \orange {\boxed {x = 12}} [/tex]

(3) Differentiating both sides of

[tex]2x^{3/2} + y^{3/2} = 29[/tex]

with respect to x gives

[tex]3x^{1/2} + \dfrac32 y^{1/2} \dfrac{\mathrm dy}{\mathrm dx} = 0[/tex]

Solve for dy/dx :

[tex]\dfrac32 y^{1/2} \dfrac{\mathrm dy}{\mathrm dx} = -3x^{1/2} \\\\ \dfrac{\mathrm dy}{\mathrm dx} = \dfrac{-3x^{1/2}}{\frac32y^{1/2}} = \dfrac{-2x^{1/2}}{y^{1/2}} = -2\sqrt{\dfrac xy}[/tex]

Then the slope of the tangent line to the curve at (1, 9) is

[tex]\dfrac{\mathrm dy}{\mathrm dx} = -2\sqrt{\dfrac19} = -\dfrac23[/tex]

The equation of the tangent line would then be

y - 9 = -2/3 (x - 1)   ==>   y = -2/3 x + 29/3

(4) The slope of the tangent line to

[tex]y=\dfrac{ax+1}{x-2}[/tex]

at a point (x, y) on the curve is

[tex]\dfrac{\mathrm dy}{\mathrm dx} = \dfrac{a(x-2)-(ax+1)}{(x-2)^2} = -\dfrac{2a+1}{(x-2)^2}[/tex]

When x = -1, we have a slope of 2/3, so

-(2a + 1)/(-1 - 2)² = 2/3

Solve for a :

-(2a + 1)/9 = 2/3

2a + 1 = -18/3 = -6

2a = -7

a = -7/2

Answer:

7.17

Step-by-step explanation:

sorry for the first answer

7.17 kilometres is Michael's journey in total.

Given that, the number of kilometres Michael travelled on motorcycle =3.85 kilometres and on a horse 3.32=kilometers.

Total distance means the actual distance between the places from which the material is transported to the destination place.

The total distance travelled is the path taken by a body to get from an initial point to an endpoint in a given period of time.

Now, total distance travelled=3.85+3.32=7.17 kilometres.

Therefore, the distance travelled is 7.17 kilometres.

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https://brainly.com/question/15172156.

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Answer:

7.75

Step-by-step explanation:

The total number of ways could the guests be arranged on a four person couch is 31465.

Given is that there are 31 guests at your home for a dinner party.

The total number of ways could the guests be arranged on a four person couch is -

C{31, 4} = 31!/{(31 - 4)!4!}

C{31, 4} = (31 x 30 x 29 x 28 x 27!/27! x 4!) = (31 x 30 x 29 x 28)/24 = 31465

C{31, 4} = 31465

Therefore, the total number of ways could the guests be arranged on a four person couch is 31465.

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brainly.com/question/17421223

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Answer:

Uhm answer what? there is no picture nor question.

Step-by-step explanation:

theres nothing there

Step-by-step explanation:

do u play among us

Answer:

see explanation

Step-by-step explanation:

The rectangle has the following properties

• Opposite sides are parallel and congruent

• All angles are right angles

• The diagonals are congruent

• The diagonals bisect each other

Thus

They are quadrilaterals

Opposite sides are equal in length

All angles are 90°

Opposite sides are parallel

Rectangles are not parallelograms ( the angles of a parallelogram are not necessarily right and diagonals are not congruent )

Answer:

Kite

Step-by-step explanation:

Def of kite has no parallel sides

Answer:

Step-by-step explanation:

Each of them do not have any parallel lines or sides

Answer:

24 i think if im wrong im sorry :(

Step-by-step explanation:

Answer:

62/9

Step-by-step explanation:

Answer:

D. should be the answer

Ha, Asa and Aas are correct because there is only one known side, and two known angles, making these postulates correct.

Answer:

Step-by-step explanation:

If A, B and C are integers, according to distributive property;

A(B+C) = AB+AB

A is distributed over B and C

Given

9×6 = 5 sixes +4 sixes

5 sixes = 5(6) =30

4 sixes = 4(6) =24

9×6 = 5(6)+4(6)

9×6 = 30+24

9×6 = 54

Hence ? =5,?? =24 ??? = 54

Answer:

2 tickets because round

Step-by-step explanation:

make an equation: 100=40x+2 and solve

2.45 tickets so only two

40+40 =80

100-80=20

but 100-2=98 so there is only 18$ left so not enough for another ticket

Answer:

30 Tickets

Step-by-step explanation:

In the question, it said that $40 is the entrance fee. Then, it said that visitors purchase additional tickets for rides, games, and food. This means that EACH ticket is 2 dollars.

Hence, $40 (entrance fee) + $2 (each ticket price) x (the number of tickets spent) = 100 (total amount of money).

So, the equation should be 40 + 2x = 100, which means x = 30.

100 - 40 = 60

60/2 = 30

30 tickets can be purchased

Answer:

b = 4,

m = 4/3,

y = 4x/3 + 4

Step-by-step explanation:

We can see the line intercepts the x-axis in (-3,0) and the y-axis in (0,4). So, using the fact that the line equation in the slope-intercept form is:

[tex]y = mx+b[/tex]

We can substitute the points we know:

→ (0,4):

[tex]y = mx+b\\\\4 = m\cdot0+b\\\\4 = 0+b\\\\\boxed{b=4}[/tex]

→ (-3,0):

[tex]y = mx+b\\\\0 = -3m + 4\\\\3m = 4\\\\\boxed{m = \dfrac{4}{3}}[/tex]

So, the line equation in form requested is:

[tex]\boxed{y=\dfrac{4}{3}x+4}[/tex]

Answer:

250/475

Step-by-step explanation:

Answer:

A) 4

Step-by-step explanation:

Plug in the value for x and y.

(4 x 3) - 2(4)

12 - 8 = 4

Answer:

(3,-2), (-3,-7), 2nd one is x2,y2

Step-by-step explanation:

Answer:

the answer is 1.5 of course because converting them into their fractional form indeed informs u that 1.5 is the solely answer

Answer:

i am going to work it out

Step-by-step explanation:

i am to ask my mom for help and tell you the answer

Answer:

when u search it one by one

Answer:

this is the answer

Step-by-step explanation:

[tex]12(2(16) - 4) =336 [/tex]

336

Step-by-step explanation:

12(2×16-4) =12(32-4)=12×28=336

Answer: 90.2

Step-by-step explanation:

Answer:

100 digits

Step-by-step explanation:

One trillion is 10¹², so it adds 12 zeros.

8000 adds 4 digits.

8 trillions add 8·12 = 96 zeros.

So in total you have 96+4 = 100 digits

This number would also be called 8 googol, since 1 googol is 10¹⁰⁰

Answer:

The correct answer (B)

Answer:

Step-by-step explanation:

y = 4x is proportional and linear ( y = coffienient(x) )

y = -4x - 3 is not proportional because it has a costant ( -3 )

They are both an equation, they have a coffienient, and a value like (x)

9514 1404 393

Answer:

Step-by-step explanation:

The slope of the first line is 4; the slope of the second line is -4, so the slopes are opposites of each other. (The lines are not perpendicular.)

The y-intercept of the first line is 0; that of the second line is -3, so they cross the y-axis in different places.

Since the slopes are opposites of each other, one line is a reflection of the other about the horizontal line through the point where the lines meet. That point is ...

  4x = -4x -3

  8x = -3

  x = -3/8

  y = 4x = -3/2

The point of intersection (common to both lines) is (-3/8, -3/2).

Answer:

i wont give u a direct answer but i will tell u this.. Look up Mt. Mights height  and subtract 8,678.37 with a cauculator. The answer will tell you

Answer: 28,979.87

Step by step explanation: I GOT THE ANSWER CORRECT!!!!!! For any one wondering I am doing this question right no and what the other guy said about subtracting is wrong because i tried doing tat and it said it was wrong.

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[tex](A + B)(A + B) = [/tex]

[tex] {A}^{2} + 2AB + {B}^{2} [/tex]

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