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The probability of selecting a defective bulb is 0.16.

Given: 8 Bulbs are defective out of 50 bulbs. To find the probability that a randomly selected item is defective.

What is probability?

Probability shows the possibility of how likely an event is happening to occur out of all the possibilities.

Let’s solve the problem:

Total number of video recorders: 50

The sample space n(S) = 50

Number of defective bulbs: 8

Let E be the event of selecting a defective bulb.

Then n(E) = 8

Therefore, the probability of selecting a defective bulb: Number of defective bulbs / Total number of bulbs

=> n(E) / n(S)

=> 8 / 50

=> 0.16

Hence the probability of selecting a defective bulb is 0.16.

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Answer:

CCCC YES BY SASA

Step-by-step explanation:

Answer:

x : y

2   0

3   1

4   2

5   3

Step-by-step explanation:

you just subtract two from whatever number is on the left, for example 2-2=0, 3-2=1, and so on :)

Step-by-step explanation:

Because

3×4=12

and

3+3+3+3=12

are same. For easy calculations we use 3×4

There is a loss of $14500 and 30 units are required to be made to break- even. The solution has been obtained using profit function.

What is profit function?

A relationship that depicts the difference created by subtracting the cost function from the revenue function is called a profit function. The ideal pairing of revenues and expenses to generate the greatest possible profit can be seen on the graph of a profit function.

a. The fixed cost of the factory is $5000 + $10000 = $15000

The variable cost of the factory is $700 + $800 = $1500

The revenue of the factory is $2000x.

We need to find profit after 1 unit is made i.e. x = 1

So, TC= FC + VC(x)

⇒ TC = $15000 + $1500(1)

⇒ TC = $16500

Therefore, the profit will be

⇒Profit = R(x) - TC

⇒Profit = $2000(1) - $16500

⇒Profit = -$14500

Hence, there is a loss of $14500.

b. For break even, the total cost must be equal to the revenue

So, TC = R(x)

⇒ FC + VC(x) = R(x)

⇒ $15000 + $1500(x) = $2000(x)

⇒ $15000 = $500(x)

⇒ x=30

Hence, 30 units are required to be made to break- even.

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Option D has a non-zero component function in the y-direction and a zero component function in the x-direction.

The vector field →F is normal to the line x=2, so it must be tangent to the line y-axis at every point. This means that the component function of →F in the x-direction should be 0 and the component function of →F in the y-direction should be non-zero.

Option D has a non-zero component function in the y-direction and a zero component function in the x-direction, so it satisfies the given property. Therefore, the answer is: D. →F=(0,y)

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The given point is P (3, 3, 4), and the plane is 9y + 6z = 0. We will find the distance between the point and the plane using the formula of the distance from the point to the plane.

The formula for the distance from the point to the plane is given by:
d(P, π) = | ax + by + cz + d | / √(a² + b² + c²)
Where (x, y, z) is a point on the plane π, a, b, and c are the coefficients of x, y, and z respectively in the plane's equation, and d is the constant term in the equation.
Substitute the values in the given formula
d(P, π) = | (0) + (9)(3) + (6)(4) + (0) | / √(9² + 6² + 0²)
= | 27 + 24 | / √(81 + 36)
= 51 / √117
= 4.67 (rounded to two decimal places)
Therefore, the distance between the point P(3, 3, 4) and the plane 9y + 6z = 0 is 4.67 units.
To find the distance from the point to the plane, the formula d(P, π) = | ax + by + cz + d | / √(a² + b² + c²) is used. The coefficients of x, y, and z, and the constant term in the plane's equation are used to find the values of a, b, c, and d. The formula is then applied to calculate the distance between the given point and the plane. In this problem, the distance between the point P(3, 3, 4) and the plane 9y + 6z = 0 is 4.67 units.

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On evaluating the given data, sum of all the angles of the traingle is equal to 102°. While angle of a is 46° and b is 22°

Given the values provided, we can determine the answers as follows:

To find the length of side CC, we need additional information about the triangle. Please provide the lengths of two sides or the necessary angles to calculate it.

Angle of a: a∘ = AA = 46

Angle of b: b∘ = BB = 22

Sum of all the angles of the triangle: a∘ + b∘ + c∘ = 46 + 22 + 34  = 102°

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Approximately 330.7 grams of the element remain after 8 minutes.

We can use the exponential decay formula to solve this problem

A = A0 * \((1-r)^{t}\)

Where A0 is the initial amount, r is the decay rate (expressed as a decimal), t is the time elapsed, and A is the amount remaining.

In this problem, we have

A0 = 640 grams

r = 0.073 (since the element decays by 7.3% per minute, the decay rate is 0.073 per minute)

t = 8 minutes

Plugging these values into the formula, we get

A = 640 * \((1 - 0.073)^{8}\)

A = 640 * 0.516289

A = 330.65136

Rounding this to the nearest tenth of a gram, we get

A ≈ 330.7 grams

Therefore, approximately 330.7 grams of the element remain after 8 minutes.

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Answer:

$8.40

Step-by-step explanation:

Price in England = 1.4 pounds per Litre

Current exchange rate : 1 pound = 1.65 dollars

1 Litre = 0.26 gallons

If 1 Litre = 0.26 gallons

1 gallon = (1 / 0.26) litres = 3.8461538 litres

Therefore, cost per gallon in England = (1.4 × 3.8461538)

= 5.3846153 pounds

Then ;

If 1 pound = 1.56 dollars

Then cost per gallon in dollars equals

5.3846153 * 1.56 = 8.399999868 dollars

$8.40

To convert the integral to cylindrical coordinates, we use the following conversions:

x = r cos(theta)

y = r sin(theta)

z = z

And we also replace dV with r dz dr d(theta).

The limits of integration are:

0 ≤ r ≤ 2 (since the bounds on x and y are from 0 to 2)

0 ≤ theta ≤ 2pi (since we integrate over the entire circle)

0 ≤ z ≤ 16 - r^2 (since the bounds on z are from 0 to 16 - x^2 - y^2, which in cylindrical coordinates is 16 - r^2)

Thus, the integral becomes:

∫^(2pi)_0 ∫^2_0 ∫^(16-r^2)_0 r dz dr d(theta)

Integrating with respect to z, we get:

∫^(2pi)_0 ∫^2_0 (16 - r^2)r dr d(theta)

Integrating with respect to r, we get:

∫^(2pi)_0 [8r^2 - (1/3)r^4]∣_0^2 d(theta)

= ∫^(2pi)_0 (32/3) d(theta)

= (32/3) ∫^(2pi)_0 d(theta)

= (32/3)(2pi)

= (64/3)pi

Therefore, the value of the iterated integral in cylindrical coordinates is (64/3)pi.

The solution to the system of equations as an ordered pair is (4, -3).

We are given a system of linear equations in two variables. The first equation is y = (-1/2)x-1. The second equation is (-1/4)x+y+4 = 0.

We need to find the solution of the system of equations. We will use the substitution method to solve for the values of "x" and "y".

y = (-1/2)x - 1

(-1/4)x + y + 4 = 0

Substitute the value of "y" from the first equation into the second equation.

(-1/4)x + (-1/2)x - 1 + 4 = 0

(-3/4)x+3 = 0

(3/4)x = 3

x = 4

Substitute the value of "x" back into the first equation to get the value of "y".

y = (-1/2)x - 1

y = (-1/2)4 - 1

y = -2 - 1

y = -3

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The inverse is y = x/2 - 4

Steps involved are -

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Answer:

Explanation:

Given the expression:

This can be written as a difference of two squares. But before that, we can rewrite the expression as:

So, as a different of two squares, we write:

In inferential statistics, the objective is to determine the probability of the alternative hypothesis being true or the null hypothesis being true.

This involves using sample data to make inferences and draw conclusions about a larger population. By analyzing the data and performing statistical tests, we assess the likelihood of the alternative hypothesis or the null hypothesis being accurate.

The alternative hypothesis represents a claim or statement that contradicts the null hypothesis and suggests that there is a significant relationship or difference between variables. To determine its probability, statistical methods such as hypothesis testing and p-values are employed. These methods evaluate the strength of evidence against the null hypothesis and support the alternative hypothesis when the evidence is substantial.

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Answer:

132 cm squared

Step-by-step explanation:

6x5=30

6x5=30

6x8=48

1/2(8x3)=12

1/2(8x3)=12

Total added together is 132 cm squared

The probability of not repeating any letter when choosing a password of 7 letters from the alphabet is approximately 2.14%.

The total number of possible 7-letter passwords from the alphabet (repetition allowed) is 26^7 = 8,031,810,176. To calculate the number of passwords with no repeated letters, we can use the permutation formula nPr = n!/(n-r)!, where n is the number of items to choose from (26 letters in the alphabet) and r is the number of items to choose (7 letters for the password).

Therefore, the number of 7-letter passwords with no repeated letters is 26P7 = 6,634,204,312. The probability of choosing such a password is the number of desired outcomes (6,634,204,312) divided by the total number of possible outcomes (8,031,810,176), which is approximately 0.0214 or 2.14%.

Therefore, the probability of not repeating any letter when choosing a password of 7 letters from the alphabet (repetition allowed) is approximately 2.14%

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The standard error of the mean for this sample of information systems managers is $0.90.

To find the standard error of the mean, we use the formula:
Standard Error of the Mean = standard deviation / square root of sample size

In this case, the standard deviation is $9.00 and the sample size is 100, so we can plug in these values:

Standard Error of the Mean = 9 / √100

Standard Error of the Mean = 0.9

Therefore, the standard error of the mean for this sample of information systems managers is $0.90.

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The maximum period of time they could reserve the meeting space is 9 hours.

Mathematical expressions with the symbols > and are known as inequality. Finding a range, or ranges within ranges, of values that an unknown x can have while still satisfying the inequality is referred to as "solving" an inequality. In this lesson, inequalities are resolved using graphs and algebra.

An algebraic inequality expression is a mathematical statement that uses the it as a sign to connect an expression to a value, a variable, or another expression. One type of variable inequalities can have solutions that can be graphed either in a coordinate plane or on a number line.

Inequality expression is 31 + 5.9*t < 84.10.

To understand it, collect all constant on the right side:

5.9*t < 84.10 - 31 = 53.10,

Hence, t < 53.10 % 5.9 = 9 hours.

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Correct Question:

To rent a certain meeting room, a college charges a reservation fee of $31 and an additional fee of $5.90 per hour. The chemistry club wants to spend less than $84.10 on renting the meeting room. What are the possible amounts of time for which they could rent the meeting room? Use t for the number of hours the meeting room is rented, and solve your inequality for t.

Answer:

Postulate definition ⇔ suggest or assume the existence, fact, or truth of (something) as a basis for reasoning, discussion, or belief.

Step-by-step explanation:

I hope this helps and have a good day!

As a verb, postulate is usually defined as to ask, demand or claim. In other words: To claim or assume the existence or truth of, especially of a basis for reasoning or arguing.

As a noun, postulate is usually defined as something taken as self-evident or assumed without proof as a basis for reasoning. In other words, a proposition that requires no proof, being self-evident, or that is for a specific purpose assumed true, and this is used in the proof of other propositions, axioms.

Answer:

26

Step-by-step explanation:m a t h w a y

Answer:

26

Step-by-step explanation:

Using an exponential function, it is found that 0.08 ml of the will be in the body in 30 hours.

The amount of a decaying substance is modeled by an exponential function in the following format:

\(A(t) = A(0)e^{-kt}\)

In which:

In this problem, the half-life is 6 hours, which means that \(A(6) = 0.5A(0)\), and this is used to find k.

\(A(t) = A(0)e^{-kt}\)

\(0.5A(0) = A(0)e^{-6k}\)

\(e^{-6k} = 0.5\)

\(\ln{e^{-6k}} = \ln{0.5}\)

\(-6k = \ln{0.5}\)

\(k = -\frac{\ln{0.5}}{6}\)

\(k = 0.11552453009\)

Hence:

\(A(t) = A(0)e^{-0.11552453009t}\)

2.5 ml injection, hence \(A(0) = 2.5\)

After 30 hours, we have to find A(30), hence:

\(A(t) = 2.5e^{-0.11552453009t}\)

\(A(30) = 2.5e^{-0.11552453009(30)}\)

\(A(30) = 0.08\)

0.08 ml of the will be in the body in 30 hours.

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Slopes of all four sides are 1, -2/3, 1 and -2/3.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

The given points are J(-4,-1), K(-7,-4), L((2, -10), M(5, -7)

For JK, Slope=-4 - (-1)) / (-7 - (-4)) = -3 / -3 = 1

For KL, slope= (-10 - (-4)) / (2 - (-7)) = -6 / 9 = -2/3

For LM, slope= (-7 - (-10)) / (5 - 2) = 3 / 3 = 1

For MJ, Slope=(-1 - (-7)) / (-4 - 5) = 6 / -9 = -2/3

Hence, slopes of all four sides are 1, -2/3, 1 and -2/3.

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Answer:

The rule is. the nth term  aₙ is given by

aₙ = n² + 1

Step-by-step explanation:

The following is the summary of n, aₙ

n            aₙ      In terms of n

1             2        1² + 1

2            5        2² + 1

3            10       3² + 1

4            17        4² + 1

5            26       5² + 1

6            37       6² + 1

So the nth term is given by
n² + 1

The statement "the standard errors should not always be included along with the estimated coefficients" is false.

False

Therefore, if the standard error is not included, it would not be possible to construct the confidence interval.

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Answer:

The answer that you have highlighted is correct.

Step-by-step explanation:

When you are dividing, you divide the exponents

-10 - (-4)

-10 + 4

-6

Answer:

(x + 10)^2 + (y - 5)^2 = r^2

Three statements are correct: B, C, and D.

Statement A is incorrect. The technique of blocking is not indicated when only a random component is present.

Blocking is a statistical method used to remove or reduce the effects of nuisance factors or sources of variation in a dataset. Random components alone do not require blocking.

Statement B is correct. Blocking is indicated when both random and trend components are present. Trend refers to a systematic change in the data over time, and blocking can help separate the trend from other factors.

Statement C is correct. Blocking is also indicated when both random and seasonal components are present. Seasonality refers to regular patterns or cycles in the data, such as monthly or yearly variations. Blocking can help account for these seasonal effects.

Statement D is correct. Blocking is generally indicated when a dataset contains a combination of random, trend, and seasonal components.

In such cases, blocking can be used to extract each component separately and analyze their individual effects on the data.

In summary, statements B, C, and D correctly describe the situations in which the technique of blocking is indicated, while statement A is incorrect.

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