Suppose a device has three independent components, all of whose lifetimes (in months) are modeled by the exponential pdf, fY (y) = e−y, y > 0. What is the probability that all three components will fail within two months of one another?
Please note the question is asking for the probability that they all fail within 2 months of each other, not within the first two months.

The roots of the equation x^2 - 14x + 24 = 0 are x1 = 2 and x2 = 12, obtained using the quadratic formula.

To find the roots of the equation x^2 - 14x + 24 = 0, we can use the quadratic formula. The quadratic formula states that for an equation in the form ax^2 + bx + c = 0, the roots can be found using the formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 1, b = -14, and c = 24. Plugging these values into the quadratic formula, we get:

x = (-(-14) ± √((-14)^2 - 4(1)(24))) / (2(1))

x = (14 ± √(196 - 96)) / 2

x = (14 ± √100) / 2

x = (14 ± 10) / 2

Simplifying further, we have:

x1 = (14 + 10) / 2 = 24 / 2 = 12

x2 = (14 - 10) / 2 = 4 / 2 = 2

Therefore, the roots of the equation x^2 - 14x + 24 = 0 are x1 = 2 and x2 = 12.

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Answer:

My answer is 1170 but the way I figured out the problem was by listing numbers 1-30. the problem state that the 1st row had 10, 2nd row had 12, and 3rd row had 14 and so forth. So I basically did the same method till I got to 30 and then add up all the numbers which gave me the answer of 1170.

Step-by-step explanation:

Answer:

1170

Step-by-step explanation:

hey there,

(the other person just calculated each number themselves then added them up which i guess is okay but not in the long term for when you're taking a test for example or your teacher asks you this kind of question so it's better to memorize a formula.)

< There are two types of sequences: arithmetic and geometric. So also two formulas for finding sums of each. This situation is an arithmetic sequence.

Formula for the sum of an arithmetic sequence: \(S_n=\frac{n}{2} (a_1+a_n)\)

We know there are 30 total rows so n = 30. a1 is the very first term of a sequence so this is 10 in this situation. Before we fill in the formula, we should find what an is equal to.

For this, we will use the basic formula you learned previously: \(a_n=dn+c\)

d (the common difference) = a2-a1 = 12-10=2

c (the common ratio) = a1-d = 10-2 = 8

an = dn + c = 2(30) + 8 = 68

Now that we have found what a_n is equal to, we can plug everything into the sum equation.

\(S_n = \frac{30}{2} (10+68)=1170\)

So 1170 is your final answer. >

Hope this helped! Feel free to ask anything else.

Answer:

D. 31°C

Step-by-step explanation:

I hope it helps you

Answer:

z=-300

Step-by-step explanation:

Answer:

c and d

Step-by-step explanation:

c) Housing, savings and food = 54%

d) Housing, food and transportation = 60%

Answer:

c and d

Step-by-step explanation:

Answer:

Option B

Step-by-step explanation:

Given the corrected equations from the comment:

Y = -1/2x - 1

Y = 1/4x - 4

(I am assuming from the answer choices  that the 1/2 is negative)

Use a graphing tool to graph the given equations.

When graphed, the lines pass the point (4, -3).

See graph below.

Option B should be the correct answer.

Hope this helps.

The perimeter of a kite is the sum of all sides of the kite. In this case, the perimeter is 24 inches (in.). Therefore, we can find the length of the other set of equal sides (a) by subtracting the known length (7 in.) from 24 in.:
a = 24 - 7 = 17 in.


A kite is a geometric shape with four sides and two pairs of equal sides (a and b). The perimeter of a kite is the sum of all four sides. In this case, the perimeter is given as 24 in. We can find the length of the other set of equal sides (a) by subtracting the length of one of the pairs (7 in.) from the perimeter (24 in.):
a = 24 - 7 = 17 in.
Therefore, if the perimeter of the kite is 24 inches and the length of one pair of equal sides (b) is 7, the length of the other set of equal sides (a) is 17.

To better visualize this, consider a kite with side lengths of 7 in. and 17 in. The perimeter of this kite is equal to the sum of all its sides: 7 in. + 7 in. + 17 in. + 17 in. = 48 in.

Thus, the perimeter of the kite is 24 inches and the length of one pair of equal sides (b) is 7, so the length of the other set of equal sides (a) is 17.

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(a) The parametric equations for the line of intersection of the given planes 2x − y + z = 3 and x + y − z = 6 are x = 3 - 2t, y = 3t, z = -3 + 3t.

(b) The parametric equations of the line segment between the points P(5, 4, −7) and Q(−3, 6, 2) are x = 5 - 8t, y = 4 + 2t, z = -7 + 9t where 0 ≤ t ≤ 1.

(a) Find the direction vector of the line of intersection by taking the cross product of the normal vectors of the two planes:

<2, -1, 1> x <1, 1, -1> = <-2, 3, 3>

Find a point on the line of intersection by solving the system of equations formed by the two planes:

2x − y + z = 3

x + y − z = 6

Adding the two equations gives:

3x = 9

So, x = 3. Plugging this value of x back into either equation gives us:

2(3) − y + z = 3

y − z = 3

Let's set y = 0 and z = -3. Then the point on the line of intersection is (3, 0, -3).

Write the parametric equations for the line of intersection using the direction vector and the point on the line:

x = 3 - 2t, y = 3t, z = -3 + 3t

(b) Find the direction vector of the line segment.

The direction vector of the line segment is the vector pointing from point P to point Q. This can be found by subtracting the coordinates of P from the coordinates of Q:

<−3, 6, 2> − <5, 4, −7> = <-8, 2, 9>

Find a point on the line segment.

Any point on the line segment can be used as the starting point. Here we can use point P, whose coordinates are given as (5, 4, -7).

Write down the parametric equations of the line segment.

The parametric equations of the line segment can be written as:

x = 5 - 8t, y = 4 + 2t, z = -7 + 9t

where 0 ≤ t ≤ 1.

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Answer:I think its 5.25 if im wrong sorry

Answer:

I got 25.6cm² but I could be wrong

The expected value of the number of marbles Zuri removes from the bag is the sum of the number of red marbles plus the number of blue marbles.

The expected value of the number of marbles Zuri removes from the bag is the sum of the number of red and blue marbles. This is because the expected value of an event is the sum of the probability of each outcome multiplied by the associated outcome. Since Zuri is randomly removing marbles from the bag, one at a time and without replacement, the probability of each outcome (red or blue) is equal. Therefore, the expected value of the number of marbles Zuri removes from the bag is the sum of the number of red marbles plus the number of blue marbles. This is because each marble has an equal chance of being removed and, therefore, each marble has the same expected value.

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According to the US Geological Survey (USGS), the total copper contained in world reserves as of 2018 was estimated to be approximately 830 million metric tons.

The USGS gathers and analyzes data on global mineral reserves, including copper. In their 2018 report, they estimated that the total identified copper resources worldwide were approximately 2.2 billion metric tons. However, not all of these resources are economically recoverable. To determine the amount of copper in world reserves, the USGS considers factors such as geology, mining methods, and economic viability.

Based on their analysis, the USGS estimated that around 38% of the identified copper resources were classified as reserves in 2018. Therefore, the calculated amount of copper in world reserves was approximately 830 million metric tons (2.2 billion metric tons x 38%).

In 2018, the USGS estimated that the world's copper reserves contained approximately 830 million metric tons. It is important to note that these estimates are subject to change as new discoveries are made, mining technologies evolve, and economic factors fluctuate. The USGS plays a crucial role in providing reliable and up-to-date information on global mineral resources to aid in resource planning and decision-making.

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Answer: Hope this helps:)

Step-by-step explanation:

The probability that a student participates in clubs, the student is a girl, is approximately 0.588.

Let's define:

G:

The circumstance a pupil is a female.

C:

The activity in a student engages with clubs.

In the event G, 17 students are female, 11 students are club members, and 10 students are female and club members in the event G and C.

Calculate P(C|G), or the probability of event C provided that event G has occurred, to determine if a student joins clubs given that she is a girl.

Using the conditional probability formula, we have:

P(C and G) / P(G) = P(C|G)

P(C and G) = 10/32 because 10 students are both ladies and take part in

clubs (events G and C).

Additionally, according to event G, there are 17 girls in the class.P(G) = 17/32.

The probability that a student participates in clubs, given that the student is a girl, is:P

(C|G) = (10/32) / (17/32)

= 10/17

≈ 0.588

Answer:

0.588

trying my best to help.

Answer:

12 inches

Step-by-step explanation:

Answer:

Step-by-step explanation:

Each person will Share 1/3 of an gallon of orange juice

In a report of a quantitative research study, a nurse would expect to find the gaps or conflicts about the phenomenon being studied to be identified in: D. Review of the literature.

A research report can be defined as a publication that is used by a researcher to provide data about a research work after analyzing the information gathered on a particular subject, especially in a summarized or condensed format..

In Science, there are three main types of research report and these include the following:

A review of the literature is also referred to as literature review and it is typically used by a researcher to describe what's known and what isn't known about a phenomenon that is being studied.

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Complete Question:

Where in a report of a quantitative research study would a nurse researcher expect the gaps or conflicts about the phenomenon studied to be identified?

a. Analysis of data

b. Research design

c. Problem statement

d. Review of the literature

Hello, I am Alyssa Ann Verrett.

Put the numbers in order:

City A: {2, 3.5, 4, 4, 5, 5.5}

City B: {3.5, 4, 5, 5.5, 6, 6}

a)

The mean monthly rainfall amount for city A: 4 in;

The mean monthly rainfall amount for city B: 5 in;

b)

The MAD monthly rainfall amount for city A: 0.8 in;

The MAD monthly rainfall amount for city B: 0.8 in;

c)

The median monthly rainfall amount for city A: 4 in;

The median monthly rainfall amount for city A: 5.25 in;

Step-by-step explanation:

a) The general definition of mean of a set X is:

mean = (x₁ + x₂ + x₃ + ... xₙ)/n

For City a:

mean = (4+3.5+5+5.5+4+2)/6 = 4

For City b:

mean = (5+6+3.5+5.5+4+6)/6 = 5

b) The general definition of mean absolute deviation of a set X is:

MAD = (|x₁-mean| + |x₂-mean| + |x₃-mean| + ... + |xₙ-mean|)/n

For City a:

MAD = ( |4-4| + |3.5-4| + |5-4| + |5.5-4| + |4-4| + |2-4| )/6 = (0 + 0.5 + 1 + 1.5 + 0 + 2)/6 = 5/6 =0.8

For City b:

MAD = ( |5-5| + |6-5| + |3.5-5| + |5.5-5| + |4-5| + |6-5| )/6 = (0 + 1 + 1.5 + 0.5 + 1 + 1)/6 = 5/6 = 0.8

c) The general definition of median depends on the quantity of elements in the set X and it represents the middlemost value of the set:

When the quantity is odd:

median= x₍ₙ₊₁₎/₂

When the quantity is even:

median= (xₙ/₂ + x ₙ₊₂/₂) /2

For City A:

median = 2, 3.5, 4, 4, 5, 5.5 = (4 + 4) / 2 = 4

For City B:

median = 3.5, 4, 5, 5.5, 6, 6 = (5 + 5.5) / 2 = 5.25

Answer:

1 is  6.45

Step-by-step explanation:

3.25+1.55+1.65=6.45

Bottom left as it's measurements and shape are the closest to the one Jan has

Answer:

Ask her out and make her the happiest girl in the world.

Answer:

26 ft

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean theorem

a^2 + b^2 = c^2

10^2+24^2 = c^2

100 +576 = c^2

676 = c^2

Take the square root of each side

sqrt(676) = sqrt(c^2)

26 = c

Answer:

26 ft

Step-by-step explanation:

Pythagoras theorem

a^2+b^2=c^2

10^2+24^2=676

square root of 676= 26

Answer:

41 inches

Step-by-step explanation:

p = 2l + 2w

p=perimeter

l= length

w=width

110 = 2l + 2(14)

110 = 2l + 28  Subtract 28 from both sides

82 = 2l  Divide both sides by 2

41 = l

Answer:28

Step-by-step explanation:

Break it up! 6x3 is 18. Then 18 + 10 is 28 :P

Hope this helps :D

Check the picture below.

so the area of it, is really the area of a 16x16 square and four triangles with a base of 16 and a height of 15.

\(\stackrel{ \textit{\LARGE Areas}}{\stackrel{ square }{(16)(16)}~~ + ~~\stackrel{ \textit{four triangles} }{4\left[\cfrac{1}{2}(16)(15) \right]}}\implies 256~~ + ~~480\implies \text{\LARGE 736}~cm^2\)

9514 1404 393

Answer:

  254.0 cm³

Step-by-step explanation:

The formula for the volume of a sphere in terms of its radius is ...

  V = (4/3)πr³

Then the formula for the volume of a hemisphere in terms of its diameter is ...

  V = (1/2)(4/3)π(d/2)³ = (π/12)d³

The volume of the hemisphere is ...

  V = (π/12)(9.9 cm)³ ≈ 254.024 cm³

The volume is about 254.0 cm³.

Answer:

\(\frac{19}{7}\)x+\(\frac{11}{7}\)y+5=0

Step-by-step explanation:

the intersection of x-2y=0 and 3x+y+5 is (\(\frac{-10}{7}\);\(\frac{-5}{7}\))

=> the line : \(\frac{19}{7}\)x+\(\frac{11}{7}\)y+5=0

Answer:

\(Point \ of \ intersection = (\frac{-10}{7} , \frac{-5}{7})\\\\Equation \ of \ line : y = -\frac{19}{11}x - \frac{35}{11}\)

Step-by-step explanation:

Find intersection of the given lines :

x - 2y = 0 => x = 2y ----------- ( 1 )

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

Substitute ( 1 ) in ( 2 ) :

                               3x + y = - 5

                               3 ( 2y ) + y = - 5

                                6y + y = - 5

                                  7y = - 5

                                    \(y = -\frac{5}{7}\)

Substitute y in ( 1 ) :

                            x = 2y

                           \(x = 2 \times \frac{-5}{7} = - \frac{10}{7}\)

\(Therefore , \ point \ of \ intersection\ is ( -\frac{10}{7}, -\frac{5}{7} )\)

To find the equation of the line passing through ( - 3, 2) and point of intersection :

Standard equation of a line : y = mx + b , where m is the slope, b is the y intercept.

So step 1 : Find slope , m:

 \(slope, m = \frac{y_2 - y_1}{x_2 - x_1}\)       \([ \ where \ (x_1, y_ 1 ) = ( -3, 2 ) \ and \ (x_2, y_ 2 ) = ( \frac{-10}{7} , \frac{-5}{7}) \ ]\)

              \(= \frac{\frac{-5}{7}-(2)}{\frac{-10}{7} - (-3)}\\\\= \frac{-5- 14}{-10 + 21}\\\\=\frac{-19}{11}\\\\=-\frac{19}{11}\)

Step 2 : Equation of the line :

\((y - y _1) = m (x - x_1)\\\)

\((y - 2 ) = -\frac{19}{11}(x -( -3))\\\\(y - 2 ) = -\frac{19}{11} (x+ 3)\\\\y = -\frac{19}{11} (x+ 3) + 2\\\\ y = -\frac{19}{11}x +(-\frac{19}{11} \times 3) + 2\\\\y= - \frac{19}[11}x +(\frac{-57}{11} + 2)\\\\y= - \frac{19}{11}x +(\frac{-57+ 22}{11})\\\\y= - \frac{19}{11}x +(\frac{-35}{11})\\\\\)

The equilibrium number of firms will be the smallest integer such that the price is 6 or higher. This occurs when n = 2. At this equilibrium, the price is P = 6, the output of each firm is y = 3/2, the industry's output is Y = 3, and the profit of each firm  = -2.

a) Supply curve of an individual firm

The price received by the individual firm will be P. Its demand curve is given by

D(p) = 20 - p.

Each firm chooses output to maximize its profit. Profit maximization occurs when the price is equal to the marginal cost. Mathematically,

P = MC(y)

4y = P

y = P/4

Thus the supply curve of the firm is y = P/4

b) The smallest price at which the product can be sold. The product can be sold at the minimum of the supply curve, which is y = 0, given P ≥ 0. Therefore the smallest price is P = 0.

c) Equilibrium price and output

Equilibrium occurs when each firm is producing at its profit-maximizing output given the output of other firms. Let the number of firms in the industry be n. The output of the industry is Y = ny. The industry supply curve is given by

S(P) = nP/4

The equilibrium price intersects the industry supply curve with the demand curve. Thus the equilibrium price satisfies

S(P) = Y

nP/4 = 20 - P

=> P = 80/(4 + n).

The equilibrium number of firms is the number that makes the industry supply curve equal to the demand curve. Thus

20 - P = nP/4

=> P = 80/(4 + n)

=> n = (80 - 20P)/P

= 20/P - 4.

Thus the equilibrium number of firms is a function of P and can range between 1 and infinity, but it must be an integer. The equilibrium output of each firm is given by

y = P/4 = 20/(4n + n²)

The equilibrium output of the industry is given by

Y = n

y = 5/P = (n² + 4n)/80.

d) Equilibrium number of firms with new demand curve D(p) = 21 - p.

The intersection of this curve with the marginal cost curve is at p = 21/5. This is greater than the minimum possible price of 0. Thus there is a positive profit to be earned in this industry, and new firms can enter the market.

e) Equilibrium price and output with new demand curve with the new demand curve D(p) = 21 - p, the industry supply curve and the equilibrium price are as given in part (d). The equilibrium output of each firm is given by y = P/4 = 21/20, and the equilibrium output of the industry is given by Y = 21/4.

f) Equilibrium number of firms, price, output, and profit with demand curve D(p) = 24 - p. This demand curve intersects the marginal cost curve at p = 6. The minimum possible price is P = 0. Thus there is a range of prices from 0 to 6 where firms can profit positively.

The equilibrium number of firms will be the smallest integer such that the price is 6 or higher. This occurs when n = 2. At this equilibrium, the price is P = 6, the output of each firm is y = 3/2, the output of the industry is Y = 3, and the profit of each firm is (6)(3/2) - (2)(2(3/2)² + 8) = -2.

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There are many possible answers for this.

One example is below.

S = the number of stations included when a person orders basic cable, write an expression for the number of stations a person has if he ordered basic cable and 7 premium channels.

We can represent this as s + 7.

The value that we don't know is the number of

stations included when a person orders basic cable.

So we can represent that as s.

Then, since the person ordered 7 premium channels, that means he

is adding an additional 7 channels to his basic cable plan.

So we can represent this as s + 7.

Answer:

a number plus 7

Step-by-step explanation:

s+7

Let s represent an unknown number

a number plus 7

It takes 40 seconds (400 / 10) for the entire caravan to line up before the second toll booth.

It takes 100 seconds (20 * 5) for the entire caravan to receive service at the first toll booth.

Assuming that the cars line up at the second toll booth right after receiving service at the first toll booth, the time it takes for the entire caravan to line up before the second toll booth depends on the speed of the cars.

Since the speed of the cars is 10 kilometers per second, in the 100 seconds it takes for the entire caravan to receive service at the first toll booth, the entire caravan travels a distance of 1000 kilometers (100 * 10).

Since the distance between the first and second toll booths is 400 km, it takes 40 seconds (400 / 10) for the entire caravan to line up before the second toll booth.

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It takes 40 seconds (400 / 10) for the entire caravan to line up before the second toll booth.

It takes 100 seconds (20 * 5) for the entire caravan to receive service at the first toll booth.

Assuming that the cars line up at the second toll booth right after receiving service at the first toll booth, the time it takes for the entire caravan to line up before the second toll booth depends on the speed of the cars.

Since the speed of the cars is 10 kilometers per second, in the 100 seconds it takes for the entire caravan to receive service at the first toll booth, the entire caravan travels a distance of 1000 kilometers (100 * 10).

Since the distance between the first and second toll booths is 400 km, it takes 40 seconds (400 / 10) for the entire caravan to line up before the second toll booth.

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