Express these system specifications using the propositions p “The user enters
a valid password,” q “Access is granted,” and r “The user has paid the
subscription fee” and logical connectives (including negations).
a) “The user has paid the subscription fee, but does not enter a valid
password.”
b) “Access is granted whenever the user has paid the subscription fee and
enters a valid password.”
c) “Access is denied if the user has not paid the subscription fee.”
d) “If the user has not entered a valid password but has paid the subscription
fee, then access is granted.”

Answers

Answer 1

Answer:

a) r ⋀~p

b)(r⋀p)⟶q

c) ~r ⟶ ~q

d) (~p ⋀r) ⟶q

Step-by-step explanation:

To solve this question we will make use of logic symbols in truth table.

We are told that;

p means "The user enters

a valid password,”

q means “Access is granted,”

r means “The user has paid the

subscription fee”

A) The user has paid the subscription fee, but does not enter a valid

password.”

Fist part of the statement is correct and so it will be "r". Second part of the statement is a negation and will be denoted by ~p. Since both statements are joined together in conjunction, we will use the conjuction symbol in between them which is "⋀" Thus, we have; r ⋀~p

B) Still using logic symbols, we have;

(r⋀p)⟶q

⟶ means q is true when r and p are true.

C) correct symbol is ~r ⟶ ~q

Since both statements are negation of the question. And also, if ~r is true then ~q is also true.

D) Similar to answer A to C above, applying similar conditions, we have (~p ⋀r) ⟶q


Related Questions

Ray is constructing a flower bed

Answers

Answer:

41 feet

Step-by-step explanation:

12 +12 + [tex]\sqrt{144+144}[/tex]

Answer:

Perfilar. Comienza por delimitar la forma y dimensión del macizo. ...

Cavar y abonar. ...

Enmarcar y rastrillar. ...

Distribuir y plantar.

Step-by-step explanation:

after buying 55 books for Rs 50 each a man has rupees 3/4 of his money left how much he had at first?​

Answers

Answer:

916.67 (corrected to 2 decimal places)

Hope I'm right, fingers crossed

Step-by-step explanation:

[tex]55 \times 50 = 2750 \div \frac{3}{4 } = 916.6666667[/tex]

Necesito ayuda con esto

Answers

Answer:

La suma de las dos matrices cuadradas de dimensión 2 es [tex]\vec U = \left[\begin{array}{cc}-1&11\\2&5\end{array}\right][/tex].

Step-by-step explanation:

Considerando que se tratan de dos matrices de igual dimensión y cuyos elementos son números reales, conocemos que la adición entre dos matrices consiste en las sumas de los elementos de igual posición, esto es, los elementos que están localizados en las mismas filas y columnas, entonces, la suma es:

[tex]\vec A = \left[\begin{array}{cc}1&2\\-1&0\end{array} \right][/tex], [tex]\vec B = \left[\begin{array}{cc}-2&9\\3&5\end{array}\right][/tex]

[tex]\vec U = \vec A + \vec B = \left[\begin{array}{cc}1 + (-2)&2+9\\-1 + 3&0 + 5\end{array}\right][/tex]

[tex]\vec U = \left[\begin{array}{cc}-1&11\\2&5\end{array}\right][/tex]

La suma de las dos matrices cuadradas de dimensión 2 es [tex]\vec U = \left[\begin{array}{cc}-1&11\\2&5\end{array}\right][/tex].

What is AD/AB in simplest form?

Answers

Answer:

3

Step-by-step explanation:

From the diagram

AD = 9 units and AB = 3 units , then

[tex]\frac{AD}{AB}[/tex] = [tex]\frac{9}{3}[/tex] = 3

Given that Q(x)=2x^2 +5x-3 find and simplify Q(a+h)-Q(a-h)

Answers

Answer:

[tex]Q(a+h)-Q(a-h)=8ah+10h[/tex]

Step-by-step explanation:

We are given the function:

[tex]Q(x)=2x^2+5x-3[/tex]

And we want to find and simplify:

[tex]Q(a+h)-Q(a-h)[/tex]

Substitute:

[tex]=[2(a+h)^2+5(a+h)-3]-[2(a-h)^2+5(a-h)-3][/tex]

Expand:

[tex]\displaystyle =[2(a^2+2ah+h^2)+5a+5h-3]-[2(a^2-2ah+h^2)+5a-5h-3][/tex]

Distribute:

[tex]=[2a^2+4ah+2h^2+5a+5h-3]-[2a^2-4ah+h^2+5a-5h-3][/tex]

Distribute:

[tex]=(2a^2+4ah+2h^2+5a+5h-3)+(-2a^2+4ah-2h^2-5a+5h+3)[/tex]

Rewrite:

[tex]=(2a^2-2a^2)+(4ah+4ah)+(2h^2-2h^2)+(5a-5a)+(5h+5h)+(-3+3)[/tex]

Combine like terms:

[tex]=8ah+10h[/tex]

Hence:

[tex]Q(a+h)-Q(a-h)=8ah+10h[/tex]

The height and base radius of a cone are increased by a factor of 2 to create a similar cone. How is the slant height of the cone affected? The slant height of the larger cone is equal to the slant height of the smaller cone. The slant height of the larger cone is double the slant height of the smaller cone. The slant height of the larger cone is 4 times the slant height of the smaller cone. The slant height of the larger cone is 8 times the slant height of the smaller cone.

Answers

Answer:

The slant height of the cone affected is two times the slant height of original cone

Step-by-step explanation:

we know that

If the height and base radius of a cone are increased by a factor of  to create a similar cone

then

the scale factor is equal to  

therefore

the slant height of the cone affected is equal to the slant height of the original cone multiplied by the scale factor

Find the slant height of the original cone

Let

l-----> slant height of original cone

la-----> slant height of the cone affected

Applying the Pythagoras theorem

so

The slant height of the cone affected is two times the slant height of original cone

(I GOT THIS FROM SOMEONE ELSES ANSWER IN 2017 SO I HOPE THIS HELPS)

The slant height of the larger cone is double the slant height of the smaller cone.

Option B is the correct answer.

What is a cone?

It is a shape of a Christmas tree where there is a base of radius r and a top point called the apex.

The volume of a cone is 1/3 πr²h

We have,

The slant height of the cone is affected by a factor of 2.

When the height and base radius of a cone are multiplied by 2, the dimensions of the new cone are doubled.

Therefore,

The slant height of the larger cone is double the slant height of the smaller cone.

Learn more about cones here:

https://brainly.com/question/13798146

#SPJ5

A ball is thrown vertically upward with an initial velocity of 19 m/s. Its height, h(t)metres after t seconds, is given by the equation h(t) = -3t2 + 20t + 2.0.

The time taken by the ball to reach the maximum height is ________ seconds. Round your answer to the nearest tenth.

Answers

Answer:

Step-by-step explanation:

There are 2 different ways to do this: calculus and by completing the square. In this particular instance, calculus is WAY easier, and since I don't know for what class you are doing this, I'll do both ways. First the calculus way. We know the position equation, and the first derivative of the position is velocity. We also know that when the velocity is equal to 0 is when the object is at its max height. So we'll find the derivative first, then solve it for t:

If [tex]s(t)=-3t^2+20t+2[/tex] then the first derivative is

v(t) = -6t + 20 Solving for t requires that we set the velocity equal to 0 (again, this is where the object is at its max height), so

0 = -6t + 20 and

-20 = -6t so

t = 3.3 seconds. Now that we know that at 3.3 seconds the object is at its highest point, we sub that time into the position function to see where it is at that time:

s(3.3) = [tex]-3(3.3)^2+20(3.3)+2[/tex] and

s(3.3) = 35.3 meters.

Now onto the more difficult way...completing the square. Begin by setting the position function equal to 0 and then move over the constant to get:

[tex]-3t^2+20t=-2[/tex] Since the leading coefficient is not a 1 (it's a 3), we have to factor out the 3, leaving us with:

[tex]-3(t^2-\frac{20}{3}t)=-2[/tex] Now the rule is to take half the linear term, square it, and add it to both sides. Our linear term is [tex]\frac{20}{3}[/tex] and half of that is [tex]\frac{20}{6}[/tex]. Squaring that:

[tex](\frac{20}{6})^2=\frac{400}{36}=\frac{100}{9}[/tex]. We will add that in to both sides. On the left it's easy, but on the right we have to take into account that we still have that -3 sitting out front, refusing to be ignored. So we have to multiply it in when we add it to the right. Doing that gives us:

[tex]-3(t^2-\frac{20}{3}t+\frac{100}{9})=-2-\frac{100}{3}[/tex] We will clean this up a bit now. The reason we do this is because on the left we have created a perfect square binomial which will give us the time we are looking for to answer this question. Simplifying the right and at the same time writing the perfect square binomial  gives us:

[tex]-3(t-\frac{20}{6})^2=-\frac{106}{3}[/tex] Now the last step is to move the constant back over and set the quadratic back equal to y:

[tex]y=-3(t-\frac{20}{6})^2+\frac{106}{3}[/tex].  The vertex of this quadratic is

[tex](\frac{20}{6},\frac{106}{3})[/tex] where

[tex]\frac{20}{6}=3.3[/tex] as the time it takes for the ball to reach its max height of

[tex]\frac{106}{3}=35.3[/tex] meters.

I'd say if you plan on taking calculus cuz you're not there yet, you'll see that many of these types of problems become much simpler when you know it!

The following formula gives the area A of a trapezoid with base lengths b1 and b2, and height h.
A=12(b1+b2)h
Find the area of a trapezoid with base lengths 3 and 6 and a height of 8.

Answers

1/2 (3+6) x8
1/2 (9)x8
4.5 x 8
=36

I need help with this question

Answers

Answer:

A=W, B=X, C=Y, D=Z, AB=WX, BC=XY, CD=YZ, AD=WZ

(The second answer down)

Step-by-step explanation:

Match each equation with its graph.


Answers

1. 1
2.2
3.3


Good luck:)

In any triangle ABC,Prove by vector method c^2=a^2+b^2-2abcosC​

Answers

Answer:

Let be [tex]\vec A[/tex], [tex]\vec B[/tex] and [tex]\vec C[/tex] the vector of a triangle so that [tex]\vec C = \vec A + \vec B[/tex]. By definition of Dot Product:

[tex]\vec C \,\bullet\,\vec C = (\vec A + \vec B) \,\bullet \vec C[/tex]

[tex]\vec C \,\bullet \,\vec C = (\vec A\,\bullet \,\vec C) + (\vec B \,\bullet \,\vec C)[/tex]

[tex]\|\vec C\|^{2} = [\vec A \,\bullet \,(\vec A + \vec B)] + [\vec B\,\bullet \,(\vec A + \vec B)][/tex]

[tex]\|\vec C\|^{2} = \vec A \,\bullet \, \vec A + \vec B\,\bullet \vec B + 2\cdot (\vec A \,\bullet \, \vec B)[/tex]

[tex]\|\vec C\|^{2} = \|\vec A\|^{2} + \|\vec B\|^{2} + 2\cdot \|\vec A\|\cdot \|\vec B\|\cdot \cos\theta_{C}[/tex]

Step-by-step explanation:

Let be [tex]\vec A[/tex], [tex]\vec B[/tex] and [tex]\vec C[/tex] the vector of a triangle so that [tex]\vec C = \vec A + \vec B[/tex]. By definition of Dot Product:

[tex]\vec C \,\bullet\,\vec C = (\vec A + \vec B) \,\bullet \vec C[/tex]

[tex]\vec C \,\bullet \,\vec C = (\vec A\,\bullet \,\vec C) + (\vec B \,\bullet \,\vec C)[/tex]

[tex]\|\vec C\|^{2} = [\vec A \,\bullet \,(\vec A + \vec B)] + [\vec B\,\bullet \,(\vec A + \vec B)][/tex]

[tex]\|\vec C\|^{2} = \vec A \,\bullet \, \vec A + \vec B\,\bullet \vec B + 2\cdot (\vec A \,\bullet \, \vec B)[/tex]

[tex]\|\vec C\|^{2} = \|\vec A\|^{2} + \|\vec B\|^{2} + 2\cdot \|\vec A\|\cdot \|\vec B\|\cdot \cos\theta_{C}[/tex]

What is the rate of change of the line on the graph

Answers

Answer:

A. ¼

Step-by-step explanation:

Rate of change (m) = [tex] \frac{y_2 - y_1}{x_2 - x_1} [/tex]

Using two points on the line, (4, 1) and (-4, -1), find the rate of change using the formula stated above:

Where,

[tex] (4, 1) = (x_1, y_1) [/tex]

[tex] (-4, -1) = (x_2, y_2) [/tex]

Plug in the values

Rate of change (m) = [tex] \frac{-1 - 1}{-4 - 4} [/tex]

= [tex] \frac{-2}{-8} [/tex]

= [tex] \frac{1}{4} [/tex]

Rate of change = ¼

The point-slope form of the equation of a line that passes through points (8, 4) and (0, 2) is y -4 = %(x -8). What is
the slope-intercept form of the equation for this line?
O y = ÷x-12
O y= x-4
O y= =x+2
O y= =x +6

Answers

Answer:

y= x-4

Step-by-step explanation:

PLEASE HELP ASAP! What is the value of x in the inequality start fraction seven plus two x over five end fraction minus three less than x ?

A. x greater than negative start fraction eight over three end fraction
B. x less than negative start fraction eight over three end fraction
C. x greater than start fraction eight over three end fraction
D. x less than negative start fraction three over eight end fraction

Answers

Answer:

A

Step-by-step explanation:

the first one in the picture

Can someone help me please..

Answers

D, company b has a larger mean than company a

What is the greatest common factor of 3^3 x 5^4 and 2 x 5^3 x 11?

Answers

[tex]\huge\textsf{Hey there!}[/tex]

[tex]\mathsf{3^3 \times 5^4}[/tex]

[tex]\mathsf{3^3}[/tex]

[tex]\mathsf{= 3\times3\times3}[/tex]

[tex]\mathsf{= 9\times3}[/tex]

[tex]\mathsf{= \bf 27}[/tex]

[tex]\mathsf{5^4}[/tex]

[tex]\mathsf{= 5\times 5\times5\times 5}[/tex]

[tex]\mathsf{= 25\times25}[/tex]

[tex]\mathsf{= \bf 625}[/tex]

[tex]\mathsf{27 \times625}[/tex]

[tex]\mathsf{= \bf 16,875}[/tex]

[tex]\mathsf{2\times5^3\times11}[/tex]

[tex]\mathsf{5^3}[/tex]

[tex]\mathsf{= 5\times 5\times5}[/tex]

[tex]\mathsf{= 25\times 5}[/tex]

[tex]\mathsf{\bf = 125}[/tex]

[tex]\mathsf{2\times125\times11}[/tex]

[tex]\mathsf{= 250\times11}[/tex]

[tex]\mathsf{\bf = 2,750}[/tex]

[tex]\large\textsf{Find the Greatest Common Factor (GCF) of 16,875 \& 2,750}[/tex]

[tex]\large\textsf{16,875: 1, 3, 5, 9, 15, 25, 27, 45, 75, 125, 135, 225, 375, 625, 675, 1,125,}\\\\\large\textsf{1,875, 3,375, 5,625, \& 16,875}[/tex]

[tex]\large\textsf{2,750: 1, 2, 5, 10, 11, 22, 25, 50, 55, 110, 125, 250, 275, 550, 1,375, \& 2,750}[/tex]

[tex]\boxed{\boxed{\huge\textsf{Answer: the GCF is \bf 125 }}}\huge\checkmark[/tex]

[tex]\large\textsf{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Please explain absolute values?

Answers

Answer:

the magnitude of a real number without regard to its sign.

Step-by-step explanation:

For example, |-3| would just be a 3 in general, no negative sign in the front.

hope this answers your confusion.

Absolute value describes the distance from zero that a number is on the number line, without considering direction. The absolute value of a number is never negative.

Weatherwise magazine is published in association with the American Meteorological Society. Volume 46, Number 6 has a rating system to classify Nor'easter storms that frequently hit New England states and can cause much damage near the ocean coast. A severe storm has an average peak wave height of 16.4 feet for waves hitting the shore. Suppose that a Nor'easter is in progress at the severe storm class rating.
(A) Let us say that we want to set up a statistical test to see if the wave action (i.e., height) is dying down or getting worse. What would be the null hypothesis regarding average wave height?
a) μ < 16.4.
b) μ > 16.4.
c) μ = 16.4.
d) μ ≠ 16.4.
(B) If you wanted to test the hypothesis that the storm is getting worse, what would you use for the alternate hypothesis?
a) μ < 16.4.
b) μ = 16.4.
c) μ ≠ 16.4.
d) μ > 16.4.
(C) If you wanted to test the hypothesis that the waves are dying down, what would you use for the alternate hypothesis?
a) μ < 16.4.
b) μ ≠ 16.4.
c) μ > 16.4.
d) μ = 16.4.
(D) Suppose you do not know if the storm is getting worse or dying out. You just want to test the hypothesis that the average wave height is different (either higher or lower) from the severe storm class rating. What would you use for the alternate hypothesis?
a) μ > 16.4.
b) μ = 16.4.
c) μ ≠ 16.4.
d) μ < 16.4.
(E) For each of the tests in parts (b), (c), and (d), would the area corresponding to the P-value be on the left, on the right, or on both sides of the mean?
a) left; right; both.
b) left; both; right.
c) both; left; right.
d) right; left; both.

Answers

Answer:

a)  c) μ = 16.4.

b)  d) μ > 16.4.

c) a) μ < 16.4.

d) c) μ ≠ 16.4.

e)  d) right; left; both.

Step-by-step explanation:

Question a:

Test if it is getting worse, so at the alternative hypothesis we test if the mean is of greater than 16.4 inches, but at the null hypothesis we test if it is still of 16.4 options, so option C.

Question b:

At the alternative hypothesis we test if the mean is of greater than 16.4 inches, as said above, so the answer is given by option d.

Question c:

Dying down, so if the mean is lower than 16.4 inches, so option a.

Question d:

Don't know, so just test if it is different, which includes both lower or greater, so the correct answer is given by option c.

Question e:

Test if more -> right, so on question b) is a right tailed test.

Test if less -> left, so on question c) is a left tailed test.

Different -> both sides, so on question d) it is a two-tailed test.

Thus the correct answer is given by option d.

Which proportion resulted in the equation 3a = 7b?

StartFraction 3 over a EndFraction = StartFraction 7 over b EndFraction
StartFraction 3 over b EndFraction = StartFraction 7 over a EndFraction
StartFraction a over b EndFraction = StartFraction 3 over 7 EndFraction
StartFraction 3 over 7 EndFraction = StartFraction 3 over b EndFraction

Answers

Answer:

The correct one is 3 over b equals 7 over a

Answer:

3/b = 7/a

Step-by-step explanation:

I took it on Edge

HELP ASAP?

the two answers not showing on screen are



C:y<6x-3
D:y<6-3

Answers

Answer:

A is that answer

A) y<2x-3

A car originally costs $20,000. Its price went up by 20% and then by another $8,000. How much did the price go up as a percentage of the original price?

Answers

Answer:

60%

Step-by-step explanation:

20,000

we can move the decimal place one to the left to find 10 percent

2,000

multiply 10 x 2 to find twenty percent or 4,000

we add this to the original total. 24,000

then add the 8,000

32,000

we know find one percent of the original total

200

and find the difference between the two totals

32000-20000 = 12,000

12000 divided by 200 which is 6

multiply six by ten to get

60 percent

Which of the following is true?
1. The scale factor is 5/2 with a center of dilation at point B. The image of AB is on the same line because it passes through the center of dilation and CD is parallel to its image because it does not pass through the center of dilation.

2. The scale factor is 5/2 with a center of dilation at point B. The image of AB is on the same line because it does not pass through the center of dilation and CD is parallel to its image because it does pass through the center of dilation.

3. The scale factor is 2/5 with a center of dilation at point B. The image of AB is on the same line because it does not pass through the center of dilation and CD is parallel to its image because it does pass through the center of dilation.

4. The scale factor is 2/5 with a center of dilation at point B. The image of AB is on the same line because it passes through the center of dilation and CD is parallel to its image because it does not pass through the center of dilation.

Answers

Answer:

Option A

Step-by-step explanation:

If the quadrilateral ABCD is dilated by a scale factor 'k' to form quadrilateral A'B'C'D',

Scale factor = [tex]\frac{\text{Length of one side of the Image}}{\text{Length of one side of the original}}[/tex]

k = [tex]\frac{BA'}{BA}[/tex]

Distance between B(2, -5) and A(-1, -1) = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

                                                               = [tex]\sqrt{(2+1)^2+(-5+1)^2}[/tex]

                                                               = 5 units

Distance between B(2, -5) and A'(-5.5, 5) = [tex]\sqrt{(-5.5-2)^2+(5+5)^2}[/tex]

                                                                    = [tex]\sqrt{(-7.5)^2+(10)^2}[/tex]

                                                                    = 12.5 units

Scale factor 'k' = [tex]\frac{12.5}{5}[/tex]

k = [tex]\frac{5}{2}[/tex]

Therefore, ABCD is dilated by a scale factor [tex]\frac{5}{2}[/tex] about point B.

BA and it's image BA' are on the same line and passes through center of dilation B.

Similarly, lines CD and C'D' will be parallel because they do not pass through center of dilation.

Therefore, Option (A) will be the correct option.

Please answer for me ! And if you do answer Tysm please show your work also! ❤️

Answers

4 is the answer
Divide by negative 5 on the right

I am Your Crush boy you have never seen a boy like me if you will see me you will fall in my love. come zom Id- 6622308635 pas- 6UC3yE​

Answers

Answer:

I don't know the answer to ur question. LOL

Answer:

stop being desperate

nobody is gonna fall in love with some desperate weirdo

QUICK PLEASE
Factor 2x^2+19x+12

Answers

Answer:

39

Step-by-step explanation:

you just put it in a calculator

Answer:

The expression is not factorable with rational numbers.

2x^2+19x+12

Step-by-step explanation:

Write an equation that expresses the following relationship.

d varies directly with w and inversely with p.

In your equation, use k as the constant of proportionality.

Answers

9514 1404 393

Answer:

  d = kw/p

Step-by-step explanation:

When d varies directly with w, the equation is ...

  d = kw

When d varies inversely with p, the equation is ...

  d = k/p

When d does both, the equation is ...

  d = kw/p

x^2-9x+20 the factor of this trinomial are(____)(___)

Answers

Answer:

(x-4) (x-5)

Step-by-step explanation:

* means multiply

first you figure out what 2 numbers

when added make 9

when multiplied make 20

those are 4 and 5

(x  4) (x  5)

in this case

-4 -5 make -9

-4 * -5 make 20

(x-4) (x-5)

Answer:

(x-4)(x-5)

Step-by-step explanation:

Firstly you need to use the second equation formula to get the value of x.

x= [tex]\frac{-(-9)+- \sqrt{(-9)^{2}-4*1*20 } }{2*1}[/tex]

x= [tex]\frac{9+- \sqrt{81-80 } }{2}[/tex]

x= [tex]\frac{9+-1}{2}[/tex]

so,

x=[tex]\frac{9+1}{2}[/tex]      x=5

and

x=[tex]\frac{9-1}{2}[/tex]      x=4

When writing the factor, we have to change signs of 5 and 4. So it will be -5 and -4.

That's why the awnser is (x-4)(x-5)

Hope it helps!

A paddleboat can move at a speed of 4 ​km/h in still water. The boat is paddled 12 km downstream in a river in the same time it takes to go 6 km upstream. What is the speed of the​ river?

Answers

Answer:

Speed of the river = [tex]\frac{4}{3}[/tex] km per hour

Step-by-step explanation:

Speed of the boat in still water = 4 km per hour

Let the speed of the river = v km per hour

Speed of the boat upstream = (4 - v) km per hour

Time taken to cover 6 km = [tex]\frac{\text{Distance}}{\text{Speed}}[/tex]

                                           = [tex]\frac{6}{4-v}[/tex] hours

Speed of the boat downstream = (4 + v) km per hour

Time taken to cover 12 km = [tex]\frac{12}{4+v}[/tex] hours

Since, time taken by the boat in both the cases is same,

[tex]\frac{6}{4-v}= \frac{12}{4+v}[/tex]

6(4 + v) = 12(4 - v)

24 + 6v = 48 - 12v

12v + 6v = 48 - 24

18v = 24

v = [tex]\frac{24}{18}[/tex]

v = [tex]\frac{4}{3}[/tex] km per hour

It has a time to failure distribution which is normal with a mean of 35,000 vehicle miles and a standard deviation of 7,000 vehicle miles. Find its designed life if a .97 reliability is desired.

Answers

Answer:

The designed life should be of 21,840 vehicle miles.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean of 35,000 vehicle miles and a standard deviation of 7,000 vehicle miles.

This means that [tex]\mu = 35000, \sigma = 7000[/tex]

Find its designed life if a .97 reliability is desired.

The designed life should be the 100 - 97 = 3rd percentile(we want only 3% of the vehicles to fail within this time), which is X when Z has a p-value of 0.03, so X when Z = -1.88.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-1.88 = \frac{X - 35000}{7000}[/tex]

[tex]X - 35000 = -1.88*7000[/tex]

[tex]X = 21840[/tex]

The designed life should be of 21,840 vehicle miles.

Which proportion resulted in the equation 3a = 7b?

Answers

Hello!

3a = 7b =>

=> 3 × a = 7 × b =>

=> a/b = 7/3

Good luck! :)

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