In a support system in the U.S. space program, a single crucial component works only 85% of the time. In order to enhance the reliability of the system, it is decided that 3 components will be installed in parallel such that the system fails only if they all fail. Assume the components act independently and that they are equivalent in the sense that all 3 of them have an 85% success rate. Consider the random variable X as the number of components out of 3 that fail a) Write out a probability function for the random variable X b) What is E[X] (i.e., the mean number of components out of 3 that fail)? c) What is var(X)? d) What is the probability that the entire system is successful? e) What is the probability that the system fails?

Answer:

hi

Step-by-step explanation:

i am not sure but i think Aristotle

hope it helps

have a great day

The Binomial probability of x = 3 for the given parameters is 0.2048

The Binomial probability relation can expressed as :

\(P(x) = nCx * p^{n} * q^{n-x}\)

where :

for x = 3

We substitute x into the equation thus :

P(x = 3) = 17C3 * (1/8)³ * (1 - 1/8)¹⁴

P(x = 3) = 0.2048

Therefore, the probability of x = 3 in the scenario given is 0.2048

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Foreign direct investment helps improve the economic situation of a recipient country by increasing employment opportunities in the country that the company invests in.

When foreign companies invest in a recipient country, they often establish or expand their operations, which requires hiring local workers. This leads to job creation and reduces unemployment rates in the recipient country.

Increased employment opportunities result in more individuals having access to income and improved standards of living.

Foreign direct investment also contributes to the transfer of technology, knowledge, and skills to the recipient country. Multinational companies often bring advanced technologies, production techniques, and management practices that may not have been available or widely adopted in the recipient country.

Furthermore, foreign direct investment stimulates domestic investment and encourages the growth of local businesses. When foreign companies invest in a recipient country, they often form partnerships or engage in supply chain relationships with local firms.

Overall, foreign direct investment increases employment opportunities, fosters technology transfer, and stimulates domestic investment, all of which contribute to improving the economic situation of a recipient country.

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From the percentage of the coffee bags with 10.9 ounces, we can see that it is unlikely that the company's claim is true because 20% of the bags in the sample contain 10.9 ounces.

What is meant by percentage?

A figure or ratio stated as a fraction of 100 is called a percentage. Frequently, it is indicated with the per cent sign, "%". If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The percentage, therefore, refers to a component per hundred. Per 100 is what the word per cent means. As there is no unit of measurement for percentages, they are dimensionless numbers. This is because we divide numbers with the same units in percentage calculation.

Given,

Amount of coffee in A bag of ground coffee = 11 ounces

Number of bags = 250 bags

Number of bags which contain 10.9 ounces of coffee = 50

The percentage of bags which contain 10.9 ounces of coffee

= (50/250) × 100 = 20%

This percentage shows that the company's claim is not true because they claim every bag contains 11 ounces of coffee.

Therefore from the percentage of the coffee bags with 10.9 ounces, we can see that it is unlikely that the company's claim is true because 20% of the bags in the sample contain 10.9 ounces.

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Answer:

the width is 15

Step-by-step explanation:

Answer:

wish i could

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

.

rate = distance / time Ok, part a is correct, try writing the answer as 2/5

rate = 2/5 = 0.4 in/s

rate = 0.4 in/s

Hi, I'm here is just that the pictures are small, I'm trying to read them

b)

Please upload a picture of part b like the last picture you sent of part a

2/5 = x/ 15

x = 15 x 2 / 5

x = 30/5

x = 6 inches

The result is 6

Answer:

1/6 becomes 4/24 and 3/8 becomes 9/24.

Step-by-step explanation:

The LCD of the denominators is 24 because that is the lowest number that 6 and 8 are both related too (6 times 4 is 24, and 8 times three is 24). Since 6 goes into 24 4 times, multiply 1 (the numerator) by 4 and you get 4. Since 8 goes into 24 3 times, multiply 3 (the numerator) by 3 and you get 9.

G(x) is defined instead of F(x) because the property of memoryless is expressed in terms of G(x). Next, professor refers that there is rational numbers in the set of real numbers, so rational number is dense.  G(x) is an exponential distribution with some rate parameter λ because G(x) has the memoryless property.

The reason why the function G(x) is defined as G(x) = P(X > x) = 1 - F(x) instead of just F(x) is because the memoryless property is expressed in terms of G(x).

Specifically, the memoryless property says G(s+t) = G(s)G(t), which means that the probability of X being greater than s+t is equal to the probability of X being greater than s multiplied by the probability of X being greater than t. This property is easier to work with when expressed in terms of G(x) rather than F(x).

When the professor says that taking the limit of rational numbers gives you real numbers, he is referring to the fact that the set of rational numbers is dense in the set of real numbers. This means that between any two real numbers, there exists a rational number.

In the context of the proof, this means that if G(mn) = G(t)^mn holds for all rational numbers mn, then it also holds for all real numbers x = mn, where mn is the limit of a sequence of rational numbers.

To see why G(x) = G(1)x looks like an exponential function, we can rewrite it as G(x) = e^(ln(G(1))x). Now, suppose we define λ = -ln(G(1)). Then we have G(x) = e^(-λx), which is the probability density function of an exponential distribution with rate parameter λ.

Thus, the assumption that G(x) has the memoryless property implies that G(x) is an exponential distribution with some rate parameter λ.

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The missing values in the quantitative reasoning given are : -2, 13 and 9

Given the rule :

We can deduce that :

For the left circle :

circle = -6 - (-4) = -6 + 4 = -2

For the right circle :

circle = 11 - (-2) = 11 + 2 = 13

For the left square :

square = 13 + (-4)

square = 13 -4 = 9

Therefore, the missing values are : -2, 13 and 9

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Answer:

390 runners are women

Step-by-step explanation:

1. 1430/11=130

2. 130+130+130=390

The domain is all real numbers, and the range is all real numbers greater than or equal to -4.

From the question, we have the following parameters that can be used in our computation:

f(x) = (x + 2)(x + 6)

The above equation is a quadratic function

The rule of this function is that

The domain is the set of all real numbers

For the range, we expand and calculate the vertex

So, we have

f(x) = x² + 8x + 12

The x-coordinate of the vertex is

x = -8/(2 * 1)

x = -4

The x-coordinate of the vertex is

f(-4) = (-4)² + 8(-4) + 12

f(-4) = -4

So, the range is

y ≥ -4

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By finding all the four slopes, we can see that the word is ECHA.

We know that the general linear equation can be written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

We know that if the line passes through (x₁, y₁) and (x₂, y₂) then the slope is:

s = (y₂ - y₁)/(x₂ - x₁)

With that formula we can get the slopes.

1) Using the points (0, 3) and (2, 4).

m = (4 - 3)/(2 - 0) = 1/2, so the letter is E.

2)Using (-1, -12) and (1, -8)

m = (-8 + 12)/(1 + 1) = 4/2 = 2, so the letter is C.

3) We have (2, -6) and (-4, -3) so:

m = (-3 + 6)/(-4 - 2) = 3/-6 = -1/2, so the letter is H

4)we can use the points (0, 3) and (1, 1), so:

m = (1 - 3)/(1 - 0) = -2, so the letter is A

Then the word is ECHA

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Yes, there are several ways to understand the concept of a limit in calculus without going into the details of a formal proof. One way to understand the concept of a limit is to think of it as a way to measure how close a function gets to a particular value as the input to the function gets closer and closer to a certain number. For example, if we have a function f(x) and we want to find the limit of the function as x approaches 2, we can think of this as asking "how close does f(x) get to a certain number as x gets closer and closer to 2?"

Another way to understand the concept of a limit is to think of it as a way to describe the behavior of a function as the input gets very large or very small. For example, if we have a function f(x) and we want to find the limit of the function as x approaches infinity, we can think of this as asking "how does f(x) behave as x gets very large?"

Overall, the concept of a limit is a fundamental concept in calculus that allows us to describe and analyze the behavior of functions as the input to the function changes. While a formal proof of the limit can be quite complex, there are several intuitive ways to understand the concept without going into the details of the proof.

As per the given data, to enable the drain pipe to carry 60 liters per second, there needs to be a 66.67% increase in the diameter of the drain pipe.

We must comprehend the link between the carrying capacity and the area of the pipe's cross-section in order to calculate the percentage increase in the drain pipe's diameter required to make it capable of carrying 60 litres per second.

The cross-sectional area of the pipe directly relates to its carrying capacity. This implies that the carrying capacity will grow if the cross-section's area increases.

Q ∝ A

Q1/A1 = Q2/A2

A2 = (Q2/Q1) * A1

A2 = (60/36) * A1

A2 = (5/3) * A1

Percentage increase = (A2 - A1)/A1 * 100

Percentage increase = [(5/3) * A1 - A1]/A1 * 100

Percentage increase = (2/3) * 100

Percentage increase = 66.67%

Thus, the answer is 66.67%.

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Answer:

T-intercept = 67

Step-by-step explanation:

Given

T = 44m + 67

Required

Calculate and interpret the t-intercept

To calculate the t-intercept, we simply set the number of minutes (m) to 0

i.e. substitute 0 for m in T = 44m + 67

T = 44 * 0 + 67

T = 0 + 67

T = 67

Hence, the T-intercept is 67

The interpretation is that the initial temperature when the oven is turned on is 67 degrees

Answer:

a. A data set with ​14, ​68, and s41.

Step-by-step explanation:

For a normally distributed data set; Q₁ and Q₃ will be 0.6745 × 2 = 1.349 standard deviation.

The interquartile range IQR = Q₃ -  Q₁ = 1.349 × \({\sigma}\)

              Q₁        Q₃          \({\sigma}\)         IQR = Q₃ -  Q₁             1.349 × \({\sigma}\)

a.            14        68          41               = 68 - 14              1.349 × 41

                                                            = 54                   = 55.309

b.         1330      2940      2440         = 2940 - 1330      1.349 × 2440

                                                           = 1610                  = 3291.56

c.         2.2         7.3          2.1            = 7.3 - 2.2             1.349 × 2.1

                                                           = 5.1                   = 2.8329

d.         105        270          33           = 270 - 105          1.349  × 33

                                                          = 165                   = 44.517

From the above calculation, we will see that option a have a data set that is approximately normal.

The two cars must be approximately 177.34 feet apart from each other for Spiderman to have different depression angles to each car.

To find the distance between the two cars, we can use trigonometry and the concept of similar triangles. Let's denote the distance between Spiderman and the nearest car as d1 and the distance between Spiderman and the farther car as d2.

In a right triangle formed by Spiderman, the height of the hotel, and the line of sight to the nearest car, the tangent of the depression angle (52 degrees) can be used:

tan(52) = 600 / d1

Rearranging the equation to solve for d1:

d1 = 600 / tan(52)

Similarly, in the right triangle formed by Spiderman, the height of the hotel, and the line of sight to the farther car, the tangent of the depression angle (46 degrees) can be used:

tan(46) = 600 / d2

Rearranging the equation to solve for d2:

d2 = 600 / tan(46)

Using a calculator, we can compute:

d1 ≈ 504.61 feet

d2 ≈ 681.95 feet

The distance between the two cars is the difference between d2 and d1:

Distance = d2 - d1

Plugging in the values, we have:

Distance ≈ 681.95 - 504.61

Distance ≈ 177.34 feet

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Answer:

1. b_ 2. a_ 3. c_ 4. d

Step-by-step explanation:

1 is b mainly because it is marked that way. Your picture doesn't show all of d so not really sure about it, but I used the process of elimination. Picture c is side angle side b/c of the vertical angles.

The function that would have the greatest value at x = 16 include the following: B. y = x² - 17x + 182.

In Mathematics and Geometry, a function is a mathematical equation which defines and represents the relationship that exists between two or more variables such as an ordered pair in tables or relations.

In this exercise, we would determine the corresponding output value for this function of y based on the x-value (x = 16) in simplified form as follows;

\(y = 10^{16}\)

y = 10,000,000,000,000,000.

y = x² - 17x + 182

y = 16² - 17(16) + 182

y = 256 - 272 + 182

y = 166.

\(y = 1.17^x\\\\y = 1.17^{16}\)

y = 12.330304108137675851908392069373.

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Answer:

12 1/3 + 13 1/3 + 14 1/3 = 40

Step-by-step explanation:

Here we will use algebra to find three consecutive integers whose sum is 40. We start by assigning X to the first integer. Since they are consecutive, it means that the 2nd number will be X + 1 and the 3rd number will be X + 2 and they should all add up to 40. Therefore, you can write the equation as follows:

we know angle RLP= 100⁰

also

angle RLP+ angle RLB=180⁰(Linear pair)

=>100⁰+angleRLB= 180⁰

=> angle RLB=80⁰

since BR and LR are equal, angle RBL and angle RLB are equal

therefore angle RBL is also equal to 80⁰

using angle sum property of triangles we know that the sum of all angles in a triangle is equal to 180⁰

=>angle BRL+angle RBL+angle RLB= 180⁰

=> angle BRL+80⁰+80⁰=180⁰

=>angle BRL = 180⁰-160⁰

=>angle BRL= 20⁰

I'm sorry it took me some time I'm a slow typer

Answer:

I think its c i'm not sure though i'm so sorry if i'm wrong I would recommend waiting for another answer if u don't trust me but good luck !

3.43 liters of Can A, and 4.57 liters of Can B  should be used from each can to obtain 5 liters of paint which is half blue and half yellow.

A word problem is a few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.

From the question,

Can A is 9 parts of blue  1 part yellow= 90% blue, 10% yellow

Can B is 20% blue, 80% yellow.

let

A + B = 8 Liters

90% A + 20% B = 50% (Blue)

10% A + 80% B = 50% (Yellow)

resolving

90% A + 20% B = 10% A + 80% B

80% A = 60% B

Go back to A + B = 8 and solve for one of the variables.

B = 8 - A

80% A = 60% (8 - A)

80% A = 480% - 60% A

140% A = 480%

A = 3 43 liters

B = 8 - A = 4.57 liters

Hence, 3.43 liters of Can A, and 4.57 liters of Can B should be used.

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Answer: