Find the gradient of the line y - x = 2

Q.3

(a) The probability of the chosen hard drive to fail within one year is 0.005.

(b) The probability that the hard drive was manufactured by company C is 3.95%.

(a) The probability that a randomly chosen computer purchased from this manufacturer will experience a hard drive failure within one year is:

Probability of choosing hard drive from company A and failure within one year + Probability of choosing hard drive from company B and failure within one year + Probability of choosing hard drive from company C and failure within one year

P(A and F) = P(A) x P(F|A) = 0.5 x 0.001 = 0.0005

P(B and F) = P(B) x P(F|B) = 0.3 x 0.002 = 0.0006

P(C and F) = P(C) x P(F|C) = 0.2 x 0.005 = 0.0010

The probability that a randomly chosen computer purchased from this manufacturer will experience a hard drive failure within one year is:

0.0005 + 0.0006 + 0.0010 = 0.0021 (or 0.21%)

(b) Let F be the event that the hard drive fails within one year and C be the event that the hard drive is manufactured by company C.

We want to calculate P(C|F), the probability that the hard drive was manufactured by company C, given that it failed within one year;

P(C|F) = P(C and F) / P(F) = [P(C) x P(F|C)] / [P(A) x P(F|A) + P(B) x P(F|B) + P(C) x P(F|C)]

P(C|F) = (0.2 x 0.005) / (0.5 x 0.001 + 0.3 x 0.002 + 0.2 x 0.005)

P(C|F) = 0.083 / 0.0021 = 0.0395 (or 3.95%)

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The probability that the hard drive in my computer is manufactured by company C given that my computer experiences a hard drive failure within one year is approximately 0.74.

(a) Let the random variable X denote the number of hard drives in the computer manufacturer's hard drives that fail within one year. The probability distribution of X can be found as follows:

\(P(X = 0) = 0.5(1 - 0.001) + 0.3(1 - 0.002) + 0.2(1 - 0.005) = 0.9957\)

\(P(X = 1) = 0.5(0.001) + 0.3(0.002) + 0.2(0.005) = 0.0016\)

Thus, the probability that a randomly chosen computer purchased from this manufacturer will experience a hard drive failure within one year is 0.0016.

(b) Let the event H denote that the computer I buy experiences a hard drive failure within one year. Let the event Ci denote that the hard drive in my computer is manufactured by company

i. Then, using Bayes' theorem, we have:

\(P(C3 | H) = P(H | C3)P(C3) / P(H)\)

We can find the values of the three probabilities in the above formula as follows:

P(H | C1) = 0.001

P(H | C2) = 0.002

P(H | C3) = 0.005

P(C1) = 0.5

P(C2) = 0.3

P(C3) = 0.2

\(P(H) = P(H | C1)P(C1) + P(H | C2)P(C2) + P(H | C3)P(C3)≈ 0.00135\)

Thus, P(C3 | H) = 0.005(0.2) / 0.00135 ≈ 0.74

Therefore, the probability that the hard drive in my computer is manufactured by company C given that my computer experiences a hard drive failure within one year is approximately 0.74.

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The absolute value of -3/2 represents 3 units of the total circumference of the unit circle.

The absolute value of -3/2 is 3/2, which represents a positive value. To determine what portion of the total circumference of the unit circle this value represents, we need to consider the ratio between the absolute value and the circumference.

The total circumference of the unit circle is given by the formula C = 2πr, where r is the radius of the circle. In this case, the radius is 1 since we are dealing with the unit circle. Therefore, the circumference of the unit circle is C = 2π.

To find the portion that represents the absolute value of -3/2, we can set up the following proportion:

(3/2) / (2π) = x / 1,

where x represents the portion of the circumference we are trying to find.

By cross-multiplying, we get:

3 / (2π) = x.

To simplify, we can multiply both sides by (2π):

x = (3 / (2π)) * (2π).

The (2π) terms cancel out, leaving us with:

x = 3.

Therefore, the absolute value of -3/2 represents 3 units of the total circumference of the unit circle.

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The number of hours for both the motorcycles to meet is given by the equation T = 4 hours

Speed is defined as the rate of change of position of an object in any direction. Speed is measured as the ratio of distance to the time in which the distance was covered. Speed is a scalar quantity as it has only direction and no magnitude

Speed = Distance / Time

Given data ,

Let the speed of the motorcycle 1 = 55 mph

Let the speed of the motorcycle 2 = 70 mph

Let the total distance between them be D = 500 miles

Now , the number of hours for them to meet be T

So , the distance traveled by motorcycle 1 d = 55T

The distance traveled by motorcycle 2 = ( 500 - d ) = 70T

Substituting the values in the equation , we get

( 500 - d ) = 70T

500 - 55T = 70T

Adding 55T on both sides of the equation , we get

500 = 125T

Divide by 125 on both sides of the equation , we get

T = 500/125

T = 4 hours

Hence , the number of hours is 4 hours

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Step-by-step explanation:

5x +4×3x=34

5x+12x=34

17x=34

×=2

y=3×2=6

y=6

Answer:

First should get $220, other two should get $140 each.

Step-by-step explanation:

The ratio of hours the friends worked is 11:7:7. Say that they are paid 11x, 7x, and 7x respectively, therefore:

11x + 7x + 7x = 500

25x = 500

x = 20 so the first friend should get 11 * 20 = $220 and the other two should get 20 * 7 = $140 each.

Question:

According to the behavior of integer division, when an integer is divided by an integer, the result will be a float. True or false?

Answer: False

The water where the submarine reaches the bottom is approximately 212.43 meters deep.

To determine the depth of the water where the submarine reaches the bottom, we can use trigonometry.

The angle of depression of 13° tells us that the submarine is diving at an angle below the horizontal line.

The distance traveled diagonally, which is 890 meters, represents the hypotenuse of a right triangle.

Using trigonometric functions, we can find the length of the adjacent side, which represents the depth of the water.

In this case, we can use the tangent function:

tan(13°) = opposite/adjacent

We know the opposite side is the depth we're trying to find, and the adjacent side is the distance traveled diagonally.

Solving for the depth:

\(depth = 890 \times tan(13) \approx 212.43 meters\).

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Answer: -3r³s⁶

Step-by-step explanation:

\((-r^2s)(-3rs^3)(-s^2)=\\\\(-3)(-r^2)(r)(s)(s^3)(-s^2)=\\\\-3(-r^{2+1})(-s^{1+3+2})=\\\\-3(-r^3)(-s^6)=\\\\-3r^3s^6\)

The width of the new rectangular field would be 0 meters, which means it would essentially be a line segment.

To find the length and width of another rectangular field that has the same perimeter but a larger area, we can use the following steps:

1. Calculate the perimeter of the given rectangular field:

  Perimeter = 2 * (Length + Width)

            = 2 * (120 meters + 80 meters)

            = 2 * 200 meters

            = 400 meters

2. Divide the perimeter by 2 to find the equal sides of the new rectangular field. Since the perimeter is divided equally into two sides, each side would be half of the perimeter length:

  Side length = Perimeter / 2

             = 400 meters / 2

             = 200 meters

3. Now, we have the side length of the new rectangular field. However, we need to determine the length and width that would yield a larger area. One way to achieve this is to make one side longer and the other side shorter.

4. Let's assume the length of the new rectangular field is 200 meters. Since both sides have the same length, the width can be calculated using the formula for the perimeter:

  Width = Perimeter / 2 - Length

        = 400 meters / 2 - 200 meters

        = 200 meters - 200 meters

        = 0 meters

5. Therefore, the width of the new rectangular field would be 0 meters, which means it would essentially be a line segment. However, note that the question asks for a rectangular field with a larger area. Since the width cannot be zero, we can conclude that it is not possible to have a rectangular field with the same perimeter but a larger area than the given field.

In summary, it is not possible to find another rectangular field with the same perimeter but a larger area than the rectangular field with dimensions 80 meters wide and 120 meters long.

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Answer:

\(sin(x)\,cos(x)-cos^2(x)=\frac{\sqrt{3} -3}{4}\)

Step-by-step explanation:

Recall the Pythagorean identity for cotangent:

\(1+cot^2(x)=csc^2(x)\)

where the cosecant is the reciprocal of the sine function. So, since we know the value of the cotangent of the angle, we can derive the value of the square of the sine:

\(1+cot^2(x)=csc^2(x)\\1+(\sqrt{3})^2=\frac{1}{sin^2(x)} \\1+3=\frac{1}{sin^2(x)} \\4=\frac{1}{sin^2(x)}\\sin^2(x)=\frac{1}{4}\\ sin(x)=+/-\frac{1}{2}\)

We can also use the Pythagorean identity for sin and cos, to find the value of \(cos^2(x)\) and of cos(x):

\(cos^2(x)=1-sin^2(x)\\cos^2(x)=1-\frac{1}{4} \\cos^2(x)=\frac{3}{4}\\cos(x)=+/-\frac{\sqrt{3}}{2}\)

We also notice that since the cotangent is positive, the angle "x" must be located in either the firs or the third quadrant, where both sine and cosine have the same sign (both positive in the first quadrant, and both negative in the third quadrant.

Then the requested quantity can be written as:

\(sin(x)\,cos(x)-cos^2(x)=(\frac{1}{2}) \,\frac{\sqrt{3} }{2} -\frac{3}{4} =\frac{\sqrt{3} }{4} -\frac{3}{4}=\frac{\sqrt{3}-3 }{4}\)

Answer:

here man let me is 1 im sure the answer is =((1))

Step-by-step explanation:

6^(-3 * 10^(-10 * 27 * 25 / 5^(-8 * 3^(4 * 2^-3))))

The average of A and B is 7.

From the information given, we know that AB = 48 and A - B = 2. We can use algebra to solve for A and B, and then find their average.

We can start by adding B to both sides of the equation A - B = 2, which gives us A = B + 2. We can substitute this expression for A into the equation AB = 48, which gives us (B + 2)B = 48. Simplifying this equation, we get B^2 + 2B - 48 = 0. We can factor this equation as (B + 8)(B - 6) = 0, which gives us two solutions: B = -8 and B = 6. Since A and B both represent lengths, we can disregard the negative value of B and take B = 6.

Now that we know B = 6, we can use the expression A = B + 2 to find that A = 8. The average of A and B is (A + B)/2 = (8 + 6)/2 = 7.

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Answer:

79°

Step-by-step explanation:

Remember, the sum of all the angles in a triangle is 180

So 180-RST-RTS=180-53-48=79

There are 40,320 ways to line up the 8 people in a row for the photograph.

To determine the number of ways to line up the 8 people in a row for a photograph, we can use the concept of permutations.

Since the order of the members matters (i.e., the arrangement is distinct based on the order), we can calculate the number of permutations using the formula for permutations of n objects, which is n!.

In this case, we have 8 members, so the number of ways to line them up is:

8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40,320

Therefore, there are 40,320 ways to line up the 8 people in a row for the photograph.

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Answer:

b I think is the right answer.

The skip interval should be 40 if the sampling frame has 2000 names and the desired sample size is 50.

Systematic sampling is a type of sampling which uses the probability method where researchers select members of the group or population at a regular interval.

To determine the skip interval, it is necessary to first determine the sample size. Then the skip interval can be determined by dividing the total population by the target/desired sample size. Therefore;

skip interval = population / target sample size

Substituting the given values;

skip interval = 2000 / 50

skip interval = 40

Hence, the skip interval is calculated to be 40 if the frame has 2000 names and the desired sample size is 50.

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18.3 < d < 18.5, this set of ordered pairs could be the endpoints of the hypotenuse of a right triangle with a hypotenuse of approximately 18.4 units long.

We know that the hypotenuse of a right triangle is the longest side and it is opposite to the right angle. We also know that the Pythagorean Theorem states that in a right triangle, the sum of the squares of the lengths of the legs (the two shorter sides) is equal to the square of the length of the hypotenuse.

Let's assume that the endpoints of the hypotenuse are (x1, y1) and (x2, y2). Then, using the distance formula, we can calculate the length of the hypotenuse:

d = √\(((x2 - x1)^2\) +\((y2 - y1)^2\)

If we know that the length of the hypotenuse is approximately 18.4 units, we can set up an inequality:

18.3 < d < 18.5

Substituting the distance formula, we get:

18.3 < \(((x2 - x1)^2\)+\((y2 - y1)^2)\)< 18.5

Squaring both sides, we get:

335.89 < \((x2 - x1)^2\)+\((y2 - y1)^2\) < 342.25

Now we need to find a set of ordered pairs that satisfies this inequality. There are many possible solutions, but one example is:

(x1, y1) = (0, 0)

(x2, y2) = (6, 18)

Using the distance formula, we can verify that the length of the hypotenuse between these two points is approximately 18.4 units:

d =  √\((6^2 + 18^2)\)≈ 19.21

The hypotenuse of a right triangle is approximately 18.4 units long. Which set of ordered pairs could be the endpoints of the hypotenuse?

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Answer:

144 calories

Step-by-step explanation:

12%(1200)=

0.12(1200)=144

Answer:

Step-by-step explanation:

17f+1i

6f+5f+4f=15f

11i+4i+10i=25i     ---------> 2f+1i

1feet=12inch

The triangle ABC is right angled triangle as product of slope of line AB and line AC is equal to -1.

Slope of line AB = 4 /6

Slope of line AC = - 3/2

Slope of line BC = -5/12

Two lines are perpendicular to one another when the product of their slopes is equal to -1.

Slope of line AB × Slope of line AC

= ( 4/6 ) × ( -3/2 )

= (-12 / 12 )

= -1

Thus, the sides AB and AC are perpendicular.

This implies that ,

Triangle ABC is a right triangle.

Therefore, the product of the slope of line AB and AC is -1 and triangle ABC is right triangle.

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Answer:

natatae ako shuta hehhe

de joke lang

Answer: C: An odd number of factors were negative.

Step-by-step explanation:

a positive number being the answer an odd number number of factors would be needed for it to be

All of the aforementioned equations have the same solution except: C. y/3 - 5 = -5.

In Mathematics, an equation is said to have zero solution or no solution when the left hand side and right hand side of the equation are not the same or equal when simplified.

This ultimately implies that, an equation would have zero solution or no solution when both sides of the equal sign are not the same and the variables cancel out when simplified.

From the information provided, we have the following equation:

y/-1 - 6 = -5        

Adding 6 to both sides of the equation, we have:

y/-1 - 6 + 6 = -5 + 6

y/-1 = -1

Multiplying both sides of the equation, we have:

-1 × (y/-1) = 1 × -1

y = -1.

-y + 4 = 5

Rearranging the equation by collecting like terms, we have:

y = 4 -5

y = -1

y/3 - 5 = -5

Adding 5 to both sides of the equation, we have:

y/3 - 5 + 5 = -5 + 5

y/3 = 0

y = 0 (different solution).

2y - 5 = -7

Adding 5 to both sides of the equation, we have:

2y - 5 + 5 = -7 + 5

2y = -2

Dividing both sides of the equation by 2, we have:

y = -2/2

y = -1.

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The sample's standard deviation is equal to 12. Thus, choice B is the right choice.

The variance of a sample of 144 observations equals 576.

Variance S² = 144

The standard deviation is a measure of how spread out a set of data is. It is calculated by taking the square root of the variance, which is the average of the squared differences from the mean.

The standard deviation can be used to measure the amount of variation or dispersion of a set of data values from the mean.

Standard Deviation = √Variance

Standard Deviation = √144

Standard Deviation = 12

The standard deviation of the sample equals 12. So the option B is correct.

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The complete question is:

The variance of a sample of 144 observations equals 576. The standard deviation of the sample equals:

A. 441

B. 12

C. 63,504

D. 21

a) Diminishing returns start at x = 1,  where the marginal revenue will be less than the marginal cost

b)At x = 1, the company will earn R(1) = -32 + 6 + 18 + 4 = -4,000 dollars.

c) 0 ≤ x ≤ 25 implies that the Coffee Junction company has the capacity to spend a maximum of 25,000 dollars per month on advertisements.

a) At what level of advertising spending does diminishing returns start?

Diminishing returns refers to a situation when the marginal return on investment decreases as more resources are devoted to it. For instance, in case of Coffee Junction, increasing the advertising expenditure may lead to higher revenue, but the marginal revenue (revenue generated by each additional dollar spent) will gradually decrease.

b) How much revenue will the company earn at that level of advertising spending?

At x = 1, the company will earn R(1) = -32 + 6 + 18 + 4 = -4,000 dollars.

c) What does 0≤x≤25 tell us with respect to this problem?

In this problem, 0 ≤ x ≤ 25 implies that the Coffee Junction company has the capacity to spend a maximum of 25,000 dollars per month on advertisements.

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Answer:

$160

Step-by-step explanation:

Diane sold some stuffs at a garage sale.

Let the total value of the money Diane made = x

She spent one-half of the money she made on a new bicycle.

Amount spent on a Bicycle = 1/2 × x = 1/2x

Next,

Amount left

= x - 1/2x = 1/2x

She spent one-half of what was left on a portable stereo.

Amount spent spent on Portable stereo

= 1/2 × 1/2x

= 1/4x

If Diane had $40.00 left,

Hence:

The fraction of what was left is calculated as:

= x - (1/2x + 1/4x)

= x - (3/4x)

= 1/4x

Hence:

1/4x = $40

We can find the value of x now.

1/4 × x = $40

x/4 = $40

x = $40 × 4

x = $160

Therefore, the amount she made from the garage sale is $160

Answer:

Hey hey guys, it is 160.00

Step-by-step explanation:

Answer:

506π ft^2

Step-by-step explanation:

here's your solution

=> height of cylinder = 12 ft

=> radius of cylinder = 11 ft

=> surface area of cylinder = 2πr(h+r)

=> SA = 2*11(12+11)*π

=> SA = 22*23π

=> SA = 506π ft^2

hope it helps

259 pieces of candy can be distributed in 80 bags to give 3 candy per bag and there will be 19 candies remaining

The concept for distributing the required candies is achieved by the mathematical operation called division.

Division is an inverse of multiplication. With division we can share and determine number of candy per bag

The question is solved by

= 259 ÷ 80

= 259 / 80

= 3 19/80

This means that there will be 3 candies per bag and after sharing among the nags there will be 19 candies remaining.

Putting this in decimal gives

= 3.2375 ≅ 3.24

In a situation where we are to count the candies if they are 3.25 pieces per bag the we multiply as follows

= 3.25 * 80

= 260

in this case the total number of candies should be 260

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Answer:

-1/2

Step-by-step explanation: