A box contains 16 transistors, 3 of which are defective. If 3 are selected at random, find the probability of the statements below.a. All are defectiveb. None are defectiveWith, and without replacement

The measure of arc BC in circle E, inscribed in triangle BCD with angle DBC measuring 51 degrees, is 102°.

In a circle, an inscribed angle is equal to half the measure of its intercepted arc. Since BD is a diameter, angle DBC is a right angle, and the intercepted arc BC is a semicircle. Therefore, the measure of arc BC is 180°.

However, we are given that angle DBC measures 51 degrees. In an inscribed triangle, the measure of an angle is equal to half the measure of its intercepted arc. So, angle DBC is half the measure of arc BC, which means arc BC measures 2 times angle DBC, or 2 * 51° = 102°.

Hence, the measure of arc BC is 102°.

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Inscribed circle E is formed by triangle BCD, with BD as the diameter. DC and CB are secants, and angle DBC is 51 degrees. We need to find the measure of arc BC.

When a triangle is inscribed in a circle, the measure of an angle formed by two secants that intersect on the circle is half the measure of the intercepted arc.

In this case, angle DBC is 51 degrees, which means the intercepted arc BC has twice that measure. Therefore, the measure of arc BC is 2×51=102 degrees.

To understand why this relationship holds, we can use the Inscribed Angle Theorem. According to this theorem, an angle formed by two chords or secants that intersect on a circle is equal in measure to half the measure of the intercepted arc.

In our scenario, angle DBC is formed by secants DC and CB, and it intersects the circle at arc BC. According to the Inscribed Angle Theorem, angle DBC is equal to half the measure of arc BC.

Hence, if angle DBC is 51 degrees, the measure of arc BC is twice that, which gives us 102 degrees.

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Answer:

A and e

Step-by-step explanation:

Answer:

75°

Step-by-step explanation:

B=105° (corresponding angles)

Straight line=180°

180°-105°=75°

The interest earned after 10 years is $2000

When you invest money in a savings account that earns simple interest, the interest earned is calculated based on the initial principal amount, the interest rate, and the time period for which the money is invested.

In this problem, we are given that we invest $4000 in an account that pays simple interest of 5% per year, and we want to find out how much interest is earned after 10 years.

Using the simple interest formula, we can calculate the interest earned as the product of the principal amount, the interest rate, and the time period. In this case, the principal amount is $4000, the interest rate is 5% (or 0.05 as a decimal), and the time period is 10 years.

Substituting these values into the formula, we get:

I = P * r * t

= $4000 * 0.05 * 10

= $2000

Therefore, the interest earned after 10 years is $2000. This means that at the end of 10 years, the value of the investment will be $4000 + $2000 = $6000.

It is important to note that in simple interest, the interest earned remains constant over time and is calculated only on the principal amount, whereas in compound interest, the interest earned is added to the principal amount, and future interest is calculated on the new total.

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Answer:

rrfgggefgegeegfegefegegeegfgfgfdfefdfefgdfdfdddgedgdfdgedfgfedffdddfgfdgddfddfgdfdgdf

Therefore, the correct option is (b) 46 that is the number of students who like Twix and Reese's peanut butter cups only (region D) by principle of inclusion-exclusion, we need to subtract the number of students who like Snickers, as well as the number of students who like all three kinds of candy, from the number of students who like Twix and Reese's peanut butter cups along with one or both of the other kinds of candy.

We can start by using the principle of inclusion-exclusion, which tells us that:

|A ∪ B ∪ C| = |A| + |B| + |C| - |A ∩ B| - |A ∩ C| - |B ∩ C| + |A ∩ B ∩ C|

where |X| denotes the number of elements in set X.

Using the numbers given in the problem, we have:

|A| = 129

|B| = 118

|C| = 145

|A ∩ B| = 22

|B ∩ C| = 54

|A ∩ C| = 55

|A ∩ B ∩ C| = 8

Substituting these values into the formula, we get:

|A ∪ B ∪ C| = 129 + 118 + 145 - 22 - 55 - 54 + 8 = 269

This tells us that 269 students like at least one of the three kinds of chocolate candy.

To find the number of students who like Twix and Reese's peanut butter cups only (region D), we need to subtract the number of students who like Snickers, as well as the number of students who like all three kinds of candy, from the number of students who like Twix and Reese's peanut butter cups along with one or both of the other kinds of candy:

|D| = |B ∩ C| - |A ∩ B ∩ C|

= 54 - 8

= 46

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Answer:

g(-3) = 16

Step-by-step explanation:

To find g(-3), we need to plus -3 into the given function. So, g(-3) = |2(-3) - 10|. Now we solve using PEMDAS. Two times -3 is -6, then we have g(-3) = |-6-10| which is essentially g(-3) = |-16|. Lastly, we take the absolute value of |-16| which is just 16, therefore g(-3) = 16.

The value of the equation is P ( x ) = 60 + 2.50x , where x is the number of computers sold

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number of computers sold be represented as x

Now , the equation will be

Now , the total pay Ian received be represented as P ( x )

Let the base pay of Ian be = $ 60

The commission amount for selling one computer = $ 2.50

So , the commission amount for selling x computers = 2.50 ( x )

Substituting the values in the equation , we get

P ( x ) = base pay of Ian + commission amount for selling x computers

P ( x ) = 60 + 2.50x   be equation (1)

Now , when x = 0

On simplifying the equation , we get

P ( 0 ) = $ 60

when x = 1

On simplifying the equation , we get

P ( 1 ) = $ 60 + $ 2.50 ( 1 )

P ( 1 ) = $ 62.50

when x = 2

On simplifying the equation , we get

P ( 2 ) = $ 60 + $ 2.50 ( 2 )

P ( 2 ) = $ 60 + $ 5

P ( 2 ) = $ 65.00

when x = 3

On simplifying the equation , we get

P ( 3 ) = $ 60 + $ 2.50 ( 3 )

P ( 3 ) = $ 60 + $ 7.50

P ( 3 ) = $ 67.50

Hence , the equation is P ( x ) = 60 + 2.50x

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The solution of the system, x' y = t 16x y' = 0 x(0) = 1, y(0) = 3 using laplace transform is

Y(s) = [16 ± sqrt(192s^4 + 256)] / 32

To solve the given system using Laplace transforms, we'll apply the Laplace transform to each equation separately.

1. Taking the Laplace transform of the first equation:
L(x' y) = L(t)
sX(s) - x(0) * y(0) + Y(s) = 1/s^2

2. Taking the Laplace transform of the second equation:
L(16x y') = L(0)
16X(s) * sY(s) - y(0) = 0

Now, we'll substitute the initial conditions into the Laplace transforms:

1. Substituting x(0) = 1 and y(0) = 3 into the first equation:
sX(s) - 1 * 3 + Y(s) = 1/s^2
sX(s) + Y(s) = 1/s^2 + 3

2. Substituting y(0) = 3 into the second equation:
16X(s) * sY(s) - 3 = 0
16X(s) * sY(s) = 3

Now, we'll solve for X(s) and Y(s):

From equation (2), we have:
16X(s) * sY(s) = 3
X(s) = 3 / (16sY(s))

Substituting this into equation (1), we get:
s * (3 / (16sY(s))) + Y(s) = 1/s^2 + 3
3 / (16Y(s)) + Y(s) = 1/s^2 + 3
(3 + 16Y^2(s)) / (16Y(s)) = 1/s^2 + 3
3 + 16Y^2(s) = (16Y(s)) / s^2 + 3s^2
16Y^2(s) - (16Y(s)) / s^2 = 3s^2

Now, we'll solve for Y(s) using quadratic equation:
16Y^2(s) - (16Y(s)) / s^2 - 3s^2 = 0
Multiplying through by s^2:
16Y^2(s) - 16Y(s) - 3s^4 = 0

Using quadratic formula:
Y(s) = [16 ± sqrt((16)^2 - 4 * 16 * (-3s^4))] / (2 * 16)
Y(s) = [16 ± sqrt(256 + 192s^4)] / 32
Y(s) = [16 ± sqrt(192s^4 + 256)] / 32

Therefore, the solution for the Laplace transform of the given system is:
Y(s) = [16 ± sqrt(192s^4 + 256)] / 32

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The standard deviation of x when the variable is normally distributed is 19.53125 .

Let X be the random variable.

Here, random variable X is normally distributed with mean 1000.

As 40% area is left of the mean and remaining 40% area is right side of the mean, we can say that the probability that the value of the random variable is lied between 925 and 1000 is 0.4 .

The area under normal curve is evenly distributed with respect to the mean (0).

So, 80% of area around the mean is evenly distributed with mean that mean 40% area is left of the mean and 40% area is right of the mean.

By using one of the above, the value of the standard deviation can be obtained.

As the probability that the value of the random variable X is lies between (1000 , 1025 ) is 0.8 .

From the z-table of P(0<Z<z), it can be fount that in the row 1.2 and column 0.08, value is 0.4.

So, by looking in z-table, it is found that the value of P(0<Z<1.28) is 0.4.

By comparing equation (i) and (ii), we have,

Hence, the value of the standard deviation is 19.53125 .

Given that the 80 % confidence interval around X is given by (975 , 1025). That means there are 80% chances that value of the random variable X lies between (975 , 1025).

So, the probability that the value of the random variable X is lies between (975 , 1025) is 0.8.

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Area of a square = x² ( x is the length of a side)

Area = 36cm² = x² = 6²

length of one side of the square in the scale drawing = 6cm

since the diagram is scaled to 1cm : 3ft

the actual length = 6 × 3 ft = 18ft

the actual area = x² = 18² = 324 ft²

the ratio of the area in the drawing to the

actual area is

36 cm² : 324 ft²

to get the simplest ratio we divide both sides by 36 ( as 36 is the factor they both share in common)

the simplest ratio of the area in the drawing to the

actual area is

1 : 9

Hope you understood :)

Answer:

A' (3,1)

Step-by-step explanation:

You start with (-3,5)

Translation Down 4: (-3,1), just subtract 4 from the y-coordinate

Reflection over the y-axis: (3,1), multiply -1 to the x-coordinate

Answer:

The answer is D I think :)))

a) The set Z (integers) is not open.

b) The set O = ∩(i=1 to ∞)Oi, where Oi = (-1/i, 1/i), is open.

a) The set Z (integers) is not open.

An open set is a set that does not contain its boundary points.

In the case of the set of integers, every point in the set is a boundary point since there are no open intervals around any integer that lie entirely within the set.

Therefore, the set Z is not open.

b) The set O = ∩(i=1 to ∞)Oi, where Oi = (-1/i, 1/i), is open.

Each individual interval Oi = (-1/i, 1/i) is an open interval, and the intersection of open sets is also an open set.

This means that for any point x in O, there exists an open interval around x that is entirely contained within O.

Therefore, O is an open set.

Neither set Z nor set O is closed.

In the case of set Z, it does not contain all of its boundary points since the boundary points include all non-integer numbers.

set O is not closed since it does not contain its boundary points, which include the points -1 and 1.

Neither set Z nor set O is compact.

A compact set is a set that is both closed and bounded. As mentioned earlier, neither set Z nor set O is closed.

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Answer:

5 hours

Step-by-step explanation: in 5 hours 60 degrees would become 50 degrees and so wold the 35 degrees.

The button's radius is 5 millimeters.

The button's diameter is given as 10 millimeters. The diameter of a circle is the distance across the circle passing through its center. To find the button's radius, we need to divide the diameter by 2 since the radius is the distance from the center to any point on the circle's circumference.

So, the formula to calculate the radius is:

Radius = Diameter / 2

Plugging in the given diameter:

Radius = 10 mm / 2 = 5 mm

Therefore, the button's radius is 5 millimeters. The radius is a fundamental property of a circle, and it helps determine other important aspects such as the area and circumference of the circle. In this case, knowing the radius can be useful for various calculations or measurements related to the button's size or any other geometric considerations involving the circle.

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What am I supposed to help with. You didn't put anything.

The three angle bisector of a triangle intersect at a single point that point of concurrency of the angle of bisectors is called the incenter.

Given:

the 3 angle bisectors of a triangle intersect.

when three angle bisector of a triangle intersect then that point of concurrency is called incenter.

Incenter:

The incenter of a triangle is the intersection point of all the three interior angle bisectors of the triangle. In other words, it can be defined as the point where the internal angle bisectors of the triangle cross. This point will be equidistant from the sides of a triangle, as the central axis’s junction point is the center point of the triangle’s inscribed circle.

Incenter formula:

= (ax1+bx2+x3 / a+b+c  , ay1+by2+y3 / a+b+c).

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a. The price of the consol is approximately $133.33.

b. The new price of the consol would be $100. The price of the consol falls by 24.99% and the interest rate rises by 1%.

c. Your holding period return is approximately -49.99%.

a. The price of the consol can be calculated using the formula for the present value of a perpetuity:

Price = Annual Payment / Interest Rate

In this case, the annual payment is $4 and the interest rate is 3%. Substituting these values into the formula:

Price = $4 / 0.03 ≈ $133.33

Therefore, the price of the consol is approximately $133.33.

b. To calculate the new price of the consol if the interest rate rises to 4%, we use the same formula:

New Price = Annual Payment / New Interest Rate

Substituting the values, we get:

New Price = $4 / 0.04 = $100

The percentage change in the price of the consol can be calculated using the formula:

Percentage Change = (New Price - Old Price) / Old Price * 100

Substituting the values, we have:

Percentage Change in Price = ($100 - $133.33) / $133.33 * 100 ≈ -24.99%

The percentage change in the interest rate is simply the difference between the old and new interest rates:

Percentage Change in Interest Rate = (4% - 3%) = 1%

Comparing the two percentages, we can see that the price of the consol falls by approximately 24.99%, while the interest rate rises by 1%.

c. The holding period return can be calculated using the formula:

Holding Period Return = (Ending Value - Initial Value) / Initial Value * 100

The initial value is the purchase price of the consol, which is $133.33, and the ending value is the price of the consol after one year with an interest rate of 6%. Using the formula for the present value of a perpetuity, we can calculate the ending value:

Ending Value = Annual Payment / Interest Rate = $4 / 0.06 = $66.67

Substituting the values into the holding period return formula:

Holding Period Return = ($66.67 - $133.33) / $133.33 * 100 ≈ -49.99%

Therefore, the holding period return is approximately -49.99%.

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Answer:

C

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

(27) ^1/3

We want to know what number times itself 3 times is equal to 27

3*3*3 = 27

(3^3)^1/3

3

Answer:

\(\Huge \boxed{3}\)

Step-by-step explanation:

\(\sqrt[3]{27}\)

27 is a perfect cube.

A number when multiplied by itself 3 times gives 27.

\(\sqrt[3]{3 \times 3 \times 3}\)

\(\sqrt[3]{3^3 }=3\)

The cube root of 27 is 3.

To evaluate \(8^{\frac{2}{3} }\) first find the square of 8 and then take the cube root.

The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself.

Depending on the powers they possess, many rules of exponents are given.

Law of Multiplication: Exponents should be added while keeping the base constant when multiplying like bases.

Exponents should be multiplied while bases are kept constant when bases are raised by a power of two or more.

Division Rule: When dividing like bases, maintain the base constant and deduct the exponent of the denominator from the exponent of the numerator.

The given value can be written as:

\(8^{\frac{2}{3} } = \sqrt[3]{8^{2} }\)

Hence, to evaluate \(8^{\frac{2}{3} }\) first find the square of 8 and then take the cube root.

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To find the probability that at least 2 of the comments are positive, we can use the concept of complementary probability. We'll find the probability that fewer than 2 comments are positive and then subtract it from 1 to get the desired probability.

Let's consider the following scenarios:

1. No comments are positive (all 10 comments are negative).

2. Exactly 1 comment is positive.

Let's calculate the probability of each scenario:

1. Probability of no comments being positive:

P(No positive comments) = (0.9)^10 = 0.3487 (rounded to four decimal places)

2. Probability of exactly 1 comment being positive:

P(Exactly 1 positive comment) = 10 * (0.1)^1 * (0.9)^9 ≈ 0.3874 (rounded to four decimal places)

To find the probability that at least 2 comments are positive, we subtract the sum of the above probabilities from 1:

P(At least 2 positive comments) = 1 - P(No positive comments) - P(Exactly 1 positive comment)

                             = 1 - 0.3487 - 0.3874

                             ≈ 0.2639 (rounded to four decimal places)

Therefore, the probability that at least 2 of the comments are positive is approximately 0.2639 or 26.39%

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The solution to the equation does not exist

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

2x - 3 = 0

2x - 3 = 3

Also from the question, we understand that the graph is given as

3 = 0

The above equation is false, and cannot be represented on a graph

This is so because 0 and 3 do not have the same value

Similarly, we have 2x - 3 = 0 and 2x - 3 = 3

By substitution, the equations becomes

0 = 3

Hence, the equation has no solution

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Complete question

Graph of 3=0

Solve the equation 2x - 3 = 0 and 2x - 3 = 3 graphically

1.Understand the problem

2.Gather your resources

3.Come to answer

4.Check your answer and present solution

In a study conducted by the Centers for Disease Control and Prevention (CDC) during the early 1990s, the homicide rate for children (under the age of 15) in the United States was found to be higher compared to 25 other high income countries.

This study aimed to analyze and compare the rates of child homicides across different nations.

The findings of the study indicated that the United States had a disproportionately higher rate of child homicides when compared to its economic peers.

The specific numerical value for the homicide rate in the United States during this period was not provided in the information provided. However, the study established that the United States ranked among the highest in child homicide rates among the countries examined.

It is important to note that this information is based on a study conducted during the early 1990s, and the specific numbers and rankings may have changed since then.

To obtain the most up-to-date and accurate information on the current homicide rates for children in the United States, it is advisable to consult the latest reports and studies published by reputable sources such as the CDC or other relevant research institutions.

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The probable question may be:

In a study of 26 high-income countries during the early 1990s, the Centers for Disease Control and Prevention found that the homicide rate for children (under age 15) in the U.S. was the highest among the countries surveyed.

To find the probability distribution for Y, the number of errors detected by the auditor, we can use the binomial distribution formula. The binomial distribution is used when there are only two possible outcomes, success or failure, and each trial is independent.

In this case, the probability of success (detecting an error) is 5% or 0.05, and the probability of failure (not detecting an error) is 1 - 0.05 = 0.95.

a. To find the probability distribution for Y, we can use the formula for the binomial distribution:

P(Y = y) = (nCk) * p^k * (1-p)^(n-k)

where n is the number of trials (3 in this case), k is the number of successes (errors detected), p is the probability of success (0.05), and (nCk) is the combination formula.

For y = 0:
P(Y = 0) = (3C0) * (0.05)^0 * (0.95)^(3-0) = (1) * (1) * (0.95)^3 = 0.857375

For y = 1:
P(Y = 1) = (3C1) * (0.05)^1 * (0.95)^(3-1) = (3) * (0.05) * (0.95)^2 = 0.135375

For y = 2:
P(Y = 2) = (3C2) * (0.05)^2 * (0.95)^(3-2) = (3) * (0.05)^2 * (0.95)^1 = 0.007125

For y = 3:
P(Y = 3) = (3C3) * (0.05)^3 * (0.95)^(3-3) = (1) * (0.05)^3 * (0.95)^0 = 0.000125

So the probability distribution for Y is:
Y = 0 with probability 0.857375
Y = 1 with probability 0.135375
Y = 2 with probability 0.007125
Y = 3 with probability 0.000125

b. To construct a probability histogram for p(y), you can create a bar graph where the x-axis represents the number of errors detected (Y) and the y-axis represents the probability (P(Y = y)). Each bar will have a height corresponding to the probability.

c. To find the probability that the auditor will detect more than one error, we need to calculate the sum of the probabilities for Y = 2 and Y = 3:

P(Y > 1) = P(Y = 2) + P(Y = 3) = 0.007125 + 0.000125 = 0.00725

Therefore, the probability that the auditor will detect more than one error is 0.00725.

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