You get a bag of 30 components. And you know that, with probability 0. 1, there is one faulty component in the bag, and with probability 0. 9, all the components are in good working. You are not sure you have a faulty component in the bag, so you propose to test k of the components. (a) How many ways are there of selecting k out of the 30 components? (b) Assume the bag has a faulty component. How many ways are there of selecting k out of the 30 components that include the faulty component? (c) Use your answers from parts (a) and (b) to determine a formula for the probability of including a faulty in the k selected ones, if there was a faulty component in the bag. (d) Evaluate your answer from part (c) for k = 5. (e) Assume now that you did select a batch of 5 components, measured each of them and found that none were faulty. What is the probability that there is a faulty component left in the bag? Remember that there were two original possibilities for the bag: all the components could be good, or one component could be faulty

The value of the given expression is 31/6.

What is the equivalent expression?

Equivalent expressions are expressions that perform the same function despite their appearance. If two algebraic expressions are equivalent, they have the same value when we use the same variable value.

We can simplify the given expression using the order of operations (PEMDAS):

First, we evaluate the expression inside the parentheses:

9 - 3/4 = 35/4

Next, we simplify the multiplication by 2/3:

2/3 * 35/4 = 35/6

Now we substitute the above values in the expression and simplify:

-1/6 + 35/6 - 1/2 = (-1 + 35 - 3)/6

= 31/6

Therefore, the value of the given expression is 31/6.

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Answer:

In a bubble sort, on each pass through the list that must be sorted, the largest value "bubbles" to the end of the list. Therefore, after each pass, the end of the list is guaranteed to be sorted. This means that we can stop making pair comparisons one comparison sooner, which is option B.

Step-by-step explanation:

Bubble sort works by repeatedly comparing and swapping adjacent elements in the list if they are in the wrong order. During each pass through the list, the largest unsorted element "bubbles up" to its correct position. As a result, after the first pass, the largest element is in its correct position, after the second pass, the two largest elements are in their correct positions, and so on.

Therefore, with each subsequent pass, you can stop making pair comparisons one comparison sooner because the elements at the end of the list are already sorted.

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However, 2/7 is not equivalent to any fraction with denominator 6. Therefore, Maria's claim is incorrect.

A fraction is a way of representing a part of a whole or a ratio between two quantities. It consists of two numbers, the numerator (located above the fraction line) and the denominator (located below the fraction line), separated by a horizontal fraction bar. The numerator represents the number of parts of the whole or the ratio, while the denominator represents the total number of equal parts or the denominator of the ratio.

For example, the fraction 3/4 represents three out of four equal parts or three parts out of a total of four parts. It can also be interpreted as a ratio of three to four. Fractions can be simplified by dividing both the numerator and denominator by their greatest common factor. For instance, the fraction 6/8 can be simplified to 3/4 by dividing both the numerator and denominator by 2.

A counterexample to Maria's claim is the fraction 2/7.

To see this, note that 1/5 is equivalent to 14/70 and 1/7 is equivalent to 10/70. Therefore, any fraction between 1/5 and 1/7 can be expressed in the form n/70, where 10 < n < 14.

However, 2/7 is not equivalent to any fraction with denominator 6. Therefore, Maria's claim is incorrect.

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The complete chart here is

|---Simplify the Polynomial---|--Degree--|--Leading Coefficient--|--Constant--|

|------7a^4 - 3a^3 - 2a + 2------|------4-------|---------------7----------------|--------2-------|

Explain polynomial

A polynomial is a mathematical expression consisting of variables, coefficients, and exponents, combined using mathematical operations such as addition, subtraction, multiplication, and exponentiation. Polynomials can have one or more terms and are commonly used to model relationships in science and engineering.

What is meant by coefficient?

The coefficient is a numerical factor that is multiplied by a variable or a product of variables in an algebraic expression or equation.

According to the given information

To add the two polynomials, we combine like terms. That is, we add the coefficients of terms that have the same degree.

(7a⁴ - 6a³ + 1) + (3a³ - 2a + 1)

= 7a⁴ + (-6a³ + 3a³) + (-2a) + (1 + 1)

= 7a⁴ - 3a³ - 2a + 2

So, the simplified polynomial is `7a⁴ - 3a³ - 2a + 2`.

The degree of this polynomial is `4` since the term with the highest degree is `7a⁴`.

The leading coefficient of this polynomial is `7` since it is the coefficient of the term with the highest degree.

The constant term of this polynomial is `2` since it is the term with a degree of `0`.

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Answer:4*10^28, I MAY BE WRONG! perhaps wait for others to answer

Step-by-step explanation:

Planet A has a mass of 4 * 10^28 kilograms, and Planet B has a mass of 5 * 10^26 kilograms. To determine which planet has a larger mass, we can compare the exponents of 10, as the larger exponent indicates a larger value.

In this case, the exponent of 10 for Planet A is 28, and the exponent of 10 for Planet B is 26. Since 28 is larger than 26, we can conclude that Planet A has a larger mass.

To fill in the blanks with a number written in standard notation, we can simply write the mass of Planet A as:

4 * 10^28 kilograms (in standard notation)

The probability that the student picked at random from the graduating class will be a male would be = 0.51

The probability that the student picked at random from the graduating class will be receiving an education degree = 0.3.

To calculate the probability of the given variables, the formula given below is used.

Probability = Possible outcome/sample space.

For question 1.)

Possible outcome = 4057

sample space = 7909

probability = 4057/7909 = 0.51

For question 2.)

Possible outcome = 2700

sample space =7909

probability = 2700/7909= 0.3

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The measures of the indicated angles are YUZ = 105 and WUZ = 75

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

The circle

From the circle, we hae

2x + 31 + 5x - 5 = 180

Evaluate

x = 22

Next, we have

YUZ = 5x - 5

YUZ = 5(22) - 5 = 105

WUZ = 180 - 105 = 75

XUV = cannot be determined and YWZ = cannot be determined

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The only restriction on the domain of the expression is that x cannot be equal to -3. In interval notation, the domain is:

(-∞, -3) U (-3, ∞)

In mathematics, the domain of a function is the set of all possible input values (often x-values) for which the function is defined. It is the set of values that can be plugged into the function to produce a valid output (often y-values).

The expression [tex](x^2 + 3x - 5) / (x^2 + 6x + 9)[/tex] can be simplified as:

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

The denominator is [tex](x + 3)^2[/tex], which is always positive. Therefore, the expression is defined for all real values of x except when the denominator is zero, which occurs when:

x + 3 = 0

Solving for x, we get:

x = -3

Therefore, the only restriction on the domain of the expression is that x cannot be equal to -3. In interval notation, the domain is:

(-∞, -3) U (-3, ∞)

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We got x = 84.50 by using Pythagorean theorem.

angle of semicircle is always be 90°.

[tex]115^2 = 78^2 + x^2[/tex]

[tex]13225 = 6084 + x^2[/tex]

[tex]x^2 = 13225- 6084[/tex]

[tex]= 7141[/tex]

[tex]x = \sqrt{7141}[/tex]

[tex]x = 84.50[/tex]

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It will take approximately 268.08 cubic feet of air to fill the giant beach ball.

A sphere is a three-dimensional geometric shape that is perfectly round in shape, with every point on its surface equidistant from its center. It is a type of round solid figure that has no edges or vertices. The surface of a sphere is continuous, and it encloses a fixed volume of space.

The formula for the volume of a sphere is:

V = (4/3) × π × r³

where r is the radius of the sphere.

In this case, the radius of the beach ball is 4 feet, so we can substitute this value into the formula:

V = (4/3) ×π × (4)³

V = (4/3) × π × 64

V = 268.08 cubic feet (rounded to two decimal places)

Therefore, it will take approximately 268.08 cubic feet of air to fill the giant beach ball.

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The average value of a necklace at Julie's shop is $57.19.

For the gold necklaces, she has 15 of them worth $120 each. So the total value of the gold necklaces is:

15 x $120 = $1,800

For the silver necklaces, she has 9 of them worth $90 each. So the total value of the silver necklaces is:

9 x $90 = $810

For the plated necklaces, she has 10 of them worth $60 each. So the total value of the plated necklaces is:

10 x $60 = $600

Finally, for the beaded necklaces, she has 30 of them worth $15 each. So the total value of the beaded necklaces is:

30 x $15 = $450

To find the total value of all the necklaces, we add up the value of each type of necklace:

$1,800 + $810 + $600 + $450 = $3,660

Now that we know the total value of all the necklaces at Julie's shop, we can find the average value of a necklace by dividing the total value by the total number of necklaces:

Average value of a necklace = Total value of all necklaces / Total number of necklaces

There are a total of 15 + 9 + 10 + 30 = 64 necklaces at Julie's shop. So the average value of a necklace is:

$3,660 / 64 = $57.19

This means that if you were to randomly select a necklace from her shop, the typical value you could expect it to have is $57.19.

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Answer:

Set your calculator to degree mode.

1) sin(X)/x = sin(Z)/z

sin(57.5°)/15 = sin(Z)/13

sin(Z) = 13sin(57.5°)/15

Z = 47.0°

2) sin(M)/m = sin(L)/l

sin(32°)/9 = sin(L)/12

sin(L) = 12sin(32°)/9

L = 45.0°, so N = 180° - (32° + 45°)

= 103.0°

3) sin(Q)/q = sin(P)/p

sin(48°)/19 = sin(P)/17

sin(P) = 17sin(48°)/19

P = 41.7°, so R = 180° - (48° + 41.7°)

= 90.3°

4) sin(A)/a = sin(B)/b

sin(85°)/8 = sin(B)/7

sin(B) = 7sin(85°)/8

B = 60.7°

5) sin(D)/d = sin(F)/f

sin(D)/24 = sin(56°)/23

sin(D) = 24sin(56°)/23

D = 59.9°

6) sin(U)/u = sin(V)/v

sin(U)/30 = sin(130°)/45

sin(U) = 30sin(130°)/45

U = 30.7°

To determine how fast the height of the pineapple juice is increasing in a cylindrical can with radius 1 inch and filling rate of [tex](2)^{\frac{3}{s} }[/tex], we can use the formula for the volume of a cylinder and then differentiate it with respect to time.

The formula for the volume of a cylinder is [tex]V = πr^2h[/tex], where V is the volume, r is the radius, and h is the height. In this case, r = 1 inch.

Now, we are given [tex]\frac{dV}{dt}= (2)^{\frac{3}{s} }[/tex], which is the rate at which the volume of pineapple juice is increasing.

1. Plug in the radius value into the volume formula: [tex]V=π(1)^{2h}=πh[/tex].
2. Differentiate both sides of the equation with respect to time: [tex]\frac{dV}{dt} = π(\frac{dh}{dt})[/tex].
3. Plug in the given value of [tex]\frac{dV}{dt} :2 =  π \frac{dh}{dt}[/tex].
4. Solve for [tex]\frac{dh}{dt} : \frac{dh}{dt} = \frac{2}{π}[/tex].

So, the height of the pineapple juice is increasing at a rate of [tex]\frac{2}{π}[/tex]  inches per second.

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Angle m1 has a value of 113 degrees.

Angles that are vertical (opposite in a vertical direction) Vertical angles, also known as vertically opposite angles, are the opposing angles formed when two lines converge. Angles that are vertically opposite one another are always equal to one another.

Alternate interior angles are made when a transversal joins two coplanar lines. They can be found on the inner side of the parallel lines, but on their transverse sides. The transversal goes through the two coplanar lines at two separate points.

According to the statement, it is creating a pair of linear angles whose sum is 180.

m1 + 67° = 180°

m1 = 113°

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Answer: Line AB

Hope this helps

Sam completed more of his science fair project than Paul.

To determine who completed more of their science fair project, we can compare the completion percentages of Paul and Sam.

Paul completed 65% of his science fair project, which can be expressed as 0.65 or 65/100.

Sam completed 17/24 of his science fair project, which can also be expressed as a decimal by dividing 17 by 24, which is approximately equal to 0.7083 or 70.83%.

Comparing the two completion percentages, we can see that Sam completed a higher percentage (70.83%) of his science fair project compared to Paul (65%). Therefore, Sam completed more of his science fair project than Paul.

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As per the mentioned informations, the cash paid for rent during 2014 is calculated to be  $395,000. So, the correct  answer is option (C) i.e. $395,000.

To calculate the cash paid for rent during 2014, we need to use the information given in the problem and apply the following formula:

Cash paid for rent = Rent expense + Prepaid rent at the beginning of the period - Prepaid rent at the end of the period

Substituting the values given in the problem, we get:

Cash paid for rent = $420,000 + $70,000 - $95,000

Cash paid for rent = $395,000

Therefore, it can be concluded that the correct answer is (C) $395,000.

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The probability that Cherish, Taffy, Haunter, and Maverick are chosen is 1/126

The total number of ways to choose 4 dogs out of 9 is given by the combination formula:

9Cr4 [this reads "nine combination four"]

9Cr4 = 9! / (4! 5!)

        = 126

This means there are 126 possible outcomes, each equally likely.

The number of ways to choose Cherish, Taffy, Haunter, and Maverick out of the 9 dogs is:

5Cr0 * 4Cr4 = 1

This means there is only 1 favourable outcome.

Therefore, the probability of choosing Cherish, Taffy, Haunter, and Maverick is:

1/126

So the answer is 1/126.

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Water vapor is an important component of the Earth's atmosphere, and it plays a crucial role in regulating the climate. water vapor makes up about 0-4% of the Earth's atmosphere by volume . So the correct option is A.

It is a greenhouse gas, which means that it can trap heat in the atmosphere and contribute to global warming. The amount of water vapor in the atmosphere can vary depending on location, temperature, and weather conditions. On average, water vapor makes up about 0-4% of the Earth's atmosphere by volume. This may seem like a small amount, but it has a significant impact on weather patterns and climate. As temperatures rise due to climate change, the amount of water vapor in the atmosphere is expected to increase, which could have further impacts on global climate.

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The values of x and y for the tangent segments to the circle A are: 4 and 8.899 respectively.

A theorem of tangents to a circle states that if from one exterior point, two tangents are drawn to a circle then they have equal tangent segments.

KJ = K L

6x - 3 = 5x + 1

6x - 5x = 1 + 3 {collect like terms}

x = 4

IJ = IH = 11

y² - 10 = 4y + 2

y² - 4y - 2 - 10 = 0

y² - 4y - 8 = 0 {quadratic equation}

using the quadratic formula

y = 8.899 or y = -0.898

Therefore, the values of x and y for the tangent segments to the circle A are: 4 and 8.899 respectively.

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The graph of the data from the table is added as an attachment

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

Jerome is a photographer. He earns $125 per hour

This means that the equation of the function is

f(x) = 125x

Where x is the number of hours he works

Using the above as a guide, we have the following table of values

x    f(x)

1     125

2    250

3    375

4    500

5    625

6     750

Next, we plot the graph from the table of values and the function f(x) = 125x

The graph of the function is added as an attachment

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Answer:

y=2/3x-6 1/3

Step-by-step explanation:

y+1=2/3(x-8)

first do the distributive property.

2/3*x=2/3x

2/3*-8= -5 1/3

2/3x-5 1/3

then we subtract 1 from both sides

y=2/3x-6 1/3

The total area of the four offices in the building is 1296 square feet.

When we talk about the area of a shape, we are referring to the amount of space that it occupies. In this case, since the offices are squares, we can find the area of each office by multiplying the length of one side by itself. This is represented by the formula A = s², where A is the area and s is the length of one side.

So, if each office has a side length of 18 feet, we can find the area of one office by plugging that value into the formula: A = 18² = 324 square feet.

Since there are four offices, we can find the total area of all four offices by multiplying the area of one office by 4: 324 square feet x 4 = 1296 square feet.

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If Robert ate lunch at 11:am and he ate a snack 4and a half hours later, Robert ate his snack at 3:30 pm

To find out what time Robert ate his snack, we need to add 4 and a half hours to the time he ate lunch.

Since he ate lunch at 11:00 am, we can convert this time to 24-hour format by adding 12 hours to get 11:00 + 12:00 = 23:00.

Next, we add 4 and a half hours to 23:00 by converting the half hour to minutes and adding it to the minutes portion of the time:

23:00 + 4 hours + 30 minutes = 27:30

However, since there are only 24 hours in a day, we need to convert this time back to 12-hour format. To do this, we subtract 12 hours from 27:30 to get 15:30.

Therefore, Robert ate his snack at 3:30 pm (or 15:30 in 24-hour format).

In summary, we added 4 and a half hours to the time Robert ate lunch, converted the resulting time to 24-hour format, subtracted 12 hours to account for the excess of 24 hours, and then converted the time back to 12-hour format to obtain the time Robert ate his snack.

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To price the derivative using the two-period binomial model, we need to calculate the expected payoff of the derivative using the risk-neutral probabilities.

The possible outcomes for the two-period binomial model are H and T,  there are four possible states of the world: HH, HT, TH, and TT.

To calculate the expected payoff we need to calculate the probability of each state occurring. The probability of HH occurring is pp=0.60.6=0.36, the probability of HT and TH occurring is pq+qp=0.60.4+0.40.6=0.48, and the probability of TT occurring is qq=0.40.4=0.16.

Next, we can calculate the expected payoff in HH and TT states, the derivative pays off 1, and in the HT and TH states, the derivative pays off 0. The expected payoff of the derivative in the HH and TT states is 10.36=0.36, and the expected payoff in the HT and TH states is 00.48=0.

We need to discount the expected payoffs back to time 0 using the risk-neutral probabilities.

The probability of that state occurring multiplied by the discount factor, which is 1/(1+r), where r is the risk-free interest rate.

Since this is a risk-neutral model, the risk-free interest rate is equal to 1. Therefore, the risk-neutral probability of each state occurring is

HH: 0.36/(1+1) = 0.18

HT/TH: 0.48/(1+1) = 0.24

TT: 0.16/(1+1) = 0.08

Finally, we can calculate the price of the derivative

Price = 0.181 + 0.240 + 0.240 + 0.081 = 0.26

Therefore, the price of the derivative is 0.26.

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Answer:

A) 11.66190379

B) 9.74679

C)10.24695

D)6.32455532

Step-by-step explanation:

All of these are done by using the equation A^2 + B^2 = C^2, C being the long side and a and b being the short side.

Answer:

Great, based on the provided dimensions for Object 1 (the cereal box), here are the formulas and calculations for:

Area of the entire rectangular prism:

A = lw + lh + wh

A = 128 + 121.75 + 8*1.75

A = 96 + 21 + 14 = 131 square inches

Base area:

The base of a rectangular prism is a rectangle. So the base area formula is:

Base area = Length * Width

= 12 inches * 8 inches = 96 square inches

So the formulas are:

Area (entire prism): A = lw + lh + wh

Base area: Base area = Length * Width

In this case:

Length = 12 inches

Width = 8 inches

Height = 1.75 inches

Step-by-step explanation:

The value of one square in each sample is:

(a) 2

(b) 6

(c) 3

(d) 5

Let x represent the value one square. Thus, the value of one square in each sample can be determined as follow.

(a) 2x + 1 = 5        (Left side is equal to right side)

2x = 5 - 1

2x = 4

x = 4/2

x = 2

(b) 10 = x + 2 + 2

10 = x + 4

x = 10 - 4

x = 6

(c) 5 + 1 + x = 9

6 + x = 9

x = 9 - 6

x = 3

(d) 25 = 5x

x = 25/5

x = 5

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With the probability that 75% of students favor a difficult final exam, the 95% confidence interval based 60 students for sample proportion is ( 0.64, 0.86).

We have to investigate the believability of my results.

Sample size, n = 60

Confidence nterval = 95%

Sample proportion for students who favour the difficulty of exam, [tex] \hat p[/tex] = 75% = 0.75

We have to determine 95% confidence interval based 60 students. Using the confidence interval formula or sample proportion, [tex]CI = \hat p ± z^* \sqrt{\frac{\hat p ( 1 - \hat p )}{n}}[/tex]

Now, using the Z-distribution table, the value z- score for 95% of confidence interval is equals to 1.96.

Substitute all known values in above formula, [tex]= 0.75 ± 1.96 \sqrt{ \frac{ 0.75( 1- 0.75)}{60}}[/tex]

= 0.75 ± 0.11

= ( 0.64, 0.86)

Hence, required value of interval is ( 0.64, 0.86), i.e., 0.64 < p < 0.86.

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