A manufacturer of compact fluorescent light bulbs advertises that the distribution of the lifespans of these light bulbs is nearly normal with a mean of 9,000 hours and a standard deviation of 1,000 hours.
(a) What is the probability that a randomly chosen light bulb lasts more than 10,500 hours?
(b) Describe the distribution of the mean lifespan of 15 light bulbs.
(c) What is the probability that the mean lifespan of 15 randomly chosen light bulbs is more than 10,500 hours?
(d) Sketch the two distributions (population and sampling) on the same scale.
(e) Could you estimate the probabilities from parts (a) and (c) if the lifespans of light bulbs had a skewed distribution?

The product of two random variables that follows the normal distribution with mean 0 and variance 1 is expected 0.

To compute the product of two random variables that are normal distributed with a mean of 0 and a variance of 1, the following procedure can be employed:

Thus, we can write the probability density function of the normal distribution as:

f(x) = (1/√2π) * e^(-x^2/2)

E[X] = ∫x * f(x) dx, where the integral is taken over the entire range of X.

E[Y] = ∫y * f(y) dy, where the integral is taken over the entire range of Y.

E[XY] = E[X] * E[Y]

E[X] = ∫x * f(x) dx = ∫x * (1/√2π) * e^(-x^2/2) dx = 0

E[Y] = ∫y * f(y) dy = ∫y * (1/√2π) * e^(-y^2/2) dy = 0

E[XY] = E[X] * E[Y]

= 0 * 0 ⇒ 0

Therefore, the product of two random variables that follow a normal distribution with mean 0 and variance 1 has an expected value of 0.

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The probability that a randomly selected finishing time is greater than 87 seconds is 14.08%. This can be calculated using the empirical rule.

The empirical rule states that for any data that is normally distributed, about 68% of the data will fall within one standard deviation of the mean (in this case, within 69 ± 6 seconds). Approximately 95% of the data will fall within two standard deviations (in this case, within 69 ± 12 seconds), and about 99.7% of the data will fall within three standard deviations (in this case, within 69 ± 18 seconds).Given the mean and standard deviation given, we can calculate the probability that a randomly selected finishing time is greater than 87 seconds.

We can do this by subtracting the area under the curve from the mean to the value we are interested in (in this case, 87 seconds). Since the total area under the curve is 1, subtracting the area from the mean to 87 seconds will give us the desired probability.To calculate the area under the curve, we need to calculate the Z-score, which is the number of standard deviations away from the mean a particular value is. In this case, the Z-score is (87 - 69) / 6, which is 2.16. Using a Z-table, the probability of a Z-score of 2.16 or higher is 0.8592. Therefore, the probability that a randomly selected finishing time is greater than 87 seconds is 1 - 0.8592, which is 0.1408. Rounding to two decimal places, this is 14.08%.

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Answer:

In the picture.

34 ft.

The probability that a randomly selected firm will earn less than 96 million dollars is 0.8907

The given data is that the mean income of firms in the industry for a year is 80 million dollars with a standard deviation of 13 million dollars. Now, it is required to find the probability that a randomly selected firm will earn less than 96 million dollars if incomes for the industry are distributed normally.

The probability is calculated by the Z-score formula which is given as below:

z = (x - μ) / σ

Where,μ = 80 (Mean),  x = 96 (Randomly selected firm income),  σ = 13 (Standard deviation)

Putting the values in the formula we have,

z = (96 - 80) / 13z = 1.23

Now we will use the Z-table to find the probability value. From the Z-table, we can say that the probability of Z-score = 1.23 is 0.8907.

Therefore, the probability that a randomly selected firm will earn less than 96 million dollars is 0.8907 (approx) when rounded off to four decimal places.

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Answer:

the value of x is 3

Step-by-step explanation:

6/3-3=6/0

which is undefinied

Answer:

3

Step-by-step explanation:

Answer:

[tex]y=-3,\:x=6[/tex]

Step-by-step explanation:

hope this helped :P

In response to the stated question, we may state that As a result, there equation are 55 Democrats in the Senate.

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x + 3" equals the number "9". The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. In the equation "x2 + 2x - 3 = 0," for example, the variable x is raised to the second power. Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.

Let's call "x" the number of Republicans in the Senate.

According to the problem, Democrats outnumber Republicans by ten. Therefore "x + 10" represents the number of Democrats in the Senate.

Because the Senate has a total of 100 senators, we may formulate an equation:

x + (x + 10) = 100

To simplify this equation:

2x + 10 = 100

Taking 10 off both sides:

2x = 90

Divide all sides by two:

x = 45

As a result, there are 45 Republicans in the Senate.

To get the number of Democrats, we may insert x = 45 into the following expression:

x + 10 = 45 + 10 = 55

As a result, there are 55 Democrats in the Senate.

Therefore:

Democrats have 55 seats.

Republicans have 45 seats.

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The correct answer is option (a) Not quite - it is a more complicated method than a SRS, but the data is representative of all American adults.

The General Social Survey (GSS) is a nationally representative survey of the adult population of the United States. The GSS uses a multistage area probability sample design, which means that the sample is selected in two or more stages, with the first stage being the selection of primary sampling units (PSUs) and the second stage being the selection of households or individuals within PSUs.

While the GSS does not use a simple random sampling method, the survey design is intended to provide a representative sample of the U.S. adult population. The GSS employs a complex sampling design that takes into account stratification, clustering, and oversampling of certain groups, such as African Americans, Hispanics, and Asian Americans. This design is intended to improve the precision of estimates for these groups, which may be small in number in the overall population.

Therefore, the correct option is (a) Not quite - it is a more complicated method than a SRS, but the data is representative of all American adults.

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Figure SPOT is translated unit(s) right and unit(s) up to the right move 8 and to the up move 9.

An effective method for beginning to make this idea clear for translating squares is to give them a slice-out shape to get across the page truly.

Afterward, kids need to figure out how to have the option to interpret a shape without this support.

while doing the above task, ideally, let's begin by putting the effective method for beginning making this idea clear for translating square is to give them a slice out shape to get across the page truly.

Afterward, kids need to figure out how to have the option to interpret a shape without this support.

while doing the above task, ideally, let's begin by putting the mark of your pencil on the upper left-hand corner of the shape and afterward dropping your pencil down 1 and right 2, then, at that point, plotting the primary place of your new shape with a dab.

You would then have to do likewise with the upper right-hand corner of the shape, the bottom left, and afterward the bottom right.

To respond to this, they would have to interpret the square and afterward give the directions of point An on the new shape, which would be (8, 9).  mark your pencil on the upper left-hand corner of the shape and afterward drop your pencil down 5 and right 6, then, at that point, plot the primary place of your new shape with a dab.

You would then have to do likewise with the upper right-hand corner of the shape, the bottom left, and afterward the bottom right.

To respond to this, they would have to interpret the square and afterward give the directions of point An on the new shape, which would be (5, 4), (6, 3), (5, 2), and (4, 3).

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The product of any two invertible matrices is invertible that is (BC) = A⁻¹

Now, let's consider the product of two invertible matrices, say A and B. Since A and B are invertible, they both have an inverse, denoted by A⁻¹ and B⁻¹, respectively.

To show that the product AB is also invertible, we need to find a matrix that satisfies the definition of an inverse. Let's call this matrix C.

If C is the inverse of AB, then we should have:

(AB)C = C(AB) = I

where I is the identity matrix.

Now, we can use the associativity of matrix multiplication to expand the left-hand side of the equation:

(AB)C = A(BC)

Notice that B and C are both matrices, so their product BC is also a matrix. Thus, we can write:

A(BC) = I

Since A is invertible, we can multiply both sides by A⁻¹ to get:

A⁻¹A(BC) = A⁻¹I

The left-hand side simplifies to:

(BC) = A⁻¹

Now, we have found a matrix C that satisfies the definition of an inverse for AB, which means that AB is invertible.

To summarize, the product of two invertible matrices is invertible, and the proof relies on the fact that the inverse of a matrix is unique and the associativity of matrix multiplication.

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The probability that student A or B can solve a problem chosen at random is 0.95.

Probability is calculated by dividing the number of favourable outcomes by the number of possible outcomes.

Random: An event is referred to as random when it is not possible to predict it with certainty. The probability that either student A or B will be able to solve a problem chosen at random can be calculated as follows:

P(A or B) = P(A) + P(B) - P(A and B) where: P(A) = probability of A solving a problem = 0.75, P(B) = probability of B solving a problem = 0.7, P(A and B) = probability of both A and B solving a problem. Since A and B are independent, the probability of both solving the problem is:

P(A and B) = P(A) x P(B) = 0.75 x 0.7 = 0.525

Now, using the above formula: P(A or B) = P(A) + P(B) - P(A and B) = 0.75 + 0.7 - 0.525 = 0.925

Therefore, the probability that student A or B can solve a problem chosen at random is 0.95 (or 95%).

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The solution of the equation 7x² - 6x + 11 = 0 is x = 1 or x = 11/7.

In order to solve quadratic equations of the type ax2 + bx + c = 0, the quadratic formula is utilised. The equation is:

x = (-b ± √(b² - 4ac)) / 2a

where a, b, and c are constants, x is the variable we're trying to solve for, and sqrt() stands for square root. By solving the quadratic equation's square, one may deduce the quadratic formula. Any quadratic equations, whether they have real or complex roots, may be solved using the same formula.

The given equation in standard form is:

7x² - 6x + 11 = 0

The quadratic formula is given as:

x = (-b ± √(b² - 4ac)) / 2a

Substituting the values a = 7, b = -6, and c = 11.

x = (-(-6) ± √((-6)² - 4(7)(11))) / 2(7)

x = (6 ± √(196)) / 14

x = (6 ± 14) / 14

x = 1 or x = 11/7

Hence, the solution of the equation 7x² - 6x + 11 = 0 is x = 1 or x = 11/7.

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The required value of EC is 5 units.

Since DE is parallel to BC, we can use the property of similar triangles to set up a proportion:

AD/DB = AE/EC

We know that AD + DB = AB = x + 5. Since D is a point on AB, we can express AD and DB in terms of x:

AD = x, DB = x + 5 - x = 5

We also know that AE = 3 and ED = x + 1. Using these values, we can express AD in terms of ED:

AD = ED - AE = (x + 1) - 3 = x - 2

Substituting these values into the proportion, we get:

(x - 2)/5 = 3/EC

Multiplying both sides by 5EC, we get:

x - 2 = 15/EC

Multiplying both sides by EC, we get:

EC(x - 2) = 15

Expanding the left side, we get:

ECx - 2EC = 15

Solving for EC, we get:

EC = 15/(x - 2)

We are given that EC = x, so we can set these expressions equal to each other:

x = 15/(x - 2)

Multiplying both sides by (x - 2), we get:

x(x - 2) = 15

Expanding the left side, we get:

x² - 2x = 15

Bringing all terms to one side, we get:

x² - 2x - 15 = 0

We can factor this quadratic equation:

(x - 5)(x + 3) = 0

Therefore, x = 5 or x = -3. We reject x = -3 since we are given that EC > 0. Thus, the length of EC is: EC = x = 5.

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24% of the students bought their lunch on Monday. Therefore, the number of students in the 6th grade is 190

Step-by-step explanation:

Answer: 8

Step-by-step explanation:

6 + 2 is a simple arithmetic operation, which results in 8. When adding 6 and 2, you are combining two numbers to find their total. In other words, you are asking "if I have 6 items and someone gives me 2 more, how many items do I have in total?" The answer is 8, because you would have a total of 8 items.

Answer:

8

Step-by-step explanation:

[tex]6+2[/tex]

We can find the value of this by counting up 2 from 6.

7, 8

So the answer is 8

The average rate of change for the exponential function over the interval from x = 3 to x = 5 is 12.

The average rate of change for an exponential function can be found by dividing the change in y-values over the change in x-values for the given interval.

For the interval from x = 3 to x = 5, the change in x-values is 5 - 3 = 2.

The corresponding y-values for x = 3 and x = 5 are

y = 8 and y = 32, respectively.

Therefore, the change in y-values over the interval is 32 - 8 = 24.

The average rate of change for the exponential function over the interval from x = 3 to x = 5 is:

Average rate of change = Change in y-values / Change in x-values

Average rate of change = 24 / 2

Average rate of change = 12

Hence, the average rate of change for the exponential function over the interval is 12

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The percentage of the teenagers who purchased something with their parents' money can be calculated from the two-way frequency table. About 38.64% of the teenagers purchased something with their parents' money.

There were a total of 88 teenagers who were surveyed by Alexis. 38 of them completed the purchase, and out of these 38 teenagers, 34 of them used their parents' money. So, the percentage of teenagers who purchased something with their parents' money can be calculated as follows:

Percent of teenagers who purchased something with their [tex]parents' money = \frac{Frequency of completed purchase}{Total Number of teenagers surveyed} *100[/tex]

Percent of teenagers who purchased something with their parents' money = [tex]\frac{34}{88} * 100%[/tex]%

Therefore percent of teenagers who purchased something with their parents' money = 38.64%

Therefore, about 38.64% of the teenagers purchased something with their parents' money.

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Answer:

D. The electrician charges $23 per hour.

Step-by-step explanation:

C(h)= 23h+30 is in the form y=mx +b

$30 is the initial fee (b)

$23 is the amount charged per hour (h)

Probability of getting a prime number=7/7=1

Probability of getting 4 tens place=2/7

Probability of getting “3” in either it’s tens or one place=3/7

Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. For an experiment containing 'n' number of outcomes, the number of favorable outcomes can be denoted by x. The formula for calculate the probability of an event is as follows.

Probability(Event) = Favorable Outcomes/Total Outcomes = x/n

Number of Occurence= 7

Number of Occurence that prime number will come = 7

Probability of getting a prime number=7/7=1

Number of Occurence that 4 will come in tens place=2

Probability of getting a tens place=2/7

Number of Occurence that has a “3” in either it’s tens or one place=3

Probability of getting “3” in either it’s tens or one place=3/7

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Adam needs to show that the diagonals are perpendicular, congruent, and bisect each other.Therefore Option D is correct.

To prove that PQRS is a square, Adam needs to show that all four sides are congruent and that all four angles are right angles.

One way to do this is by showing that the diagonals of PQRS are perpendicular, congruent, and bisect each other.

If the diagonals are perpendicular, then opposite angles are congruent and the quadrilateral is a kite.

If the diagonals bisect each other, then opposite sides are congruent and the kite is a rhombus.

If the diagonals are also congruent, then all sides are congruent and the rhombus is a square.

Therefore, He needs to show that the diagonals of PQRS are perpendicular, congruent, and bisect each other to prove that PQRS is a square.

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-5x^2 - 20x- 30, the equation from vertex form to standard form.

An equation is a mathematical statement containing two algebraic expressions flanked by equal signs (=) on either side.

It shows that the relationship between the left and right printed expressions is equal.

All formulas hav LHS = RHS (left side = right side).

You can solve equations to determine the values ​​of unknown variables that represent unknown quantities.

If a statement does not have an equals sign, it is not an equation. A mathematical statement called an equation contains the symbol "equal to" between two expressions of equal value.

Hence, -5x^2 - 20x- 30, the equation from vertex form to standard form.

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Answer: The two triangles are congruent by axiom AAS as the opposite side of equal angles are also equal.

The perimeter of the figure with dimensions (4cm, 5cm, 8cm, and 3cm) is 20 cm

What is the perimeter?

The entire length of a shape's boundary is referred to as the perimeter in geometry. A shape's perimeter is calculated by combining the lengths of all of its sides and edges. Its dimensions are expressed in linear measures like centimeters, meters, inches, and feet.

Why is a perimeter important?

They help you to quantify physical space and also provide a foundation for more advanced mathematics found in algebra, trigonometry, and calculus. Perimeter is a measurement of the distance around a shape and area gives us an idea of how much surface the shape covers.

What is the formula for the perimeter of a rectangle?

The formula for the perimeter of a rectangle is,

P = length + breadth + length + breadth.

Perimeter of given figure(4cm, 5cm, 8cm, and 3cm) = 4 + 5 + 8 + 3

                                                                                      = 20

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The contrapositive of the zero product property is that if neither of the two real numbers is 0, then the product of the two numbers will not be 0. In plain language, this means that if neither of the two numbers are 0, then the product of the two numbers cannot be 0.

In an informal version, this can be stated as "if neither number is 0, then their product cannot be 0". This can be understood as "if neither number is 0, the result of multiplying them together cannot be 0". In other words, the product of two real numbers will not be 0 if neither of them is 0.

The two triangles have to have two equal angles that's congruent and one set of corresponding sides who are congruent or adjacent to the angles in order to satisfy the AAS (Angle-Angle-Side) a triangle congruence theory.

A right triangle's hypotenuse is its longest side, its "opposite" side was the one that faces a specific angle, and its "adjacent" side is the one that faces the angle in question. To define the edges of right triangles, we use specific terminology.

A triangle represents a closed, three-sided object in two dimensions. The various kinds of circles go by various titles. Three different kinds of triangles—scalene, isosceles, and equilateral—are distinguished by the lengths of their sides.

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The correlation coefficient may assume any value between -1 and 1. Correct answer option A.

This means that the coefficient might be negative, zero, or positive, with -1 being a perfect negative correlation, 0 representing no connection, and 1 representing a perfect positive correlation.

The correlation coefficient is a numerical measure of two variables' linear connection. It is a measure of the strength of the link between two variables. A correlation coefficient of 1 indicates that there is a perfect positive connection, a coefficient of -1 indicates that there is a perfect negative correlation, and a coefficient of 0 shows that there is no correlation between the two variables.

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Answer:

[tex] 900^5x^{25} [/tex]

Step-by-step explanation:

[tex] (900x^5)^5 = [/tex]

[tex] = 900^5(x^5)^5 [/tex]

[tex] = 900^5x^{25} [/tex]

If the midpoint of AB is =M(−6, 2) and one endpoint is =A(−8, 7), then the coordinates of the other endpoint B is (-4, -5)

To find the coordinates of endpoint B, we can use the midpoint formula, which states that the midpoint of a line segment is the average of the coordinates of its endpoints.

The midpoint formula is

Midpoint = ((x1 + x2)/2, (y1 + y2)/2)

where (x1, y1) and (x2, y2) are the coordinates of the endpoints.

We know the coordinates of point M, which is the midpoint of the line segment AB:

M = (-6, 2)

We also know the coordinates of one endpoint of the line segment, A:

A = (-8, 7)

Let's use the midpoint formula to find the coordinates of endpoint B:

Midpoint = ((x1 + x2)/2, (y1 + y2)/2)

Substituting the values we know:

(-6, 2) = ((-8 + x2)/2, (7 + y2)/2)

Simplifying

-6 = (-8 + x2)/2 and 2 = (7 + y2)/2

Multiplying both sides of each equation by 2:

-12 = -8 + x2 and 4 = 7 + y2

Adding 8 to both sides of the first equation:

-4 = x2

Subtracting 7 from both sides of the second equation:

-5 = y2

Therefore, the coordinates of endpoint B are B = (-4, -5)

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The slope between the points (-3, 0) and (0, -1) is -1/3.

The slope of a line serves as a gauge for its steepness. It may be calculated by dividing the difference in y-coordinate by the difference in x-coordinate between any two points on a line. A line's slope might be zero, positive, negative, or undefinable. A line with a positive slope is moving upward from left to right, a negative slope is moving downward from left to right, and a line with a zero slope is level. The line is vertical if the slope is undefinable.

Let us consider the first two points (-3, 0) and (0, -1).

The slope of the line is given as:

m = (y2 - y1) / (x2 - x1)

Substituting the values we have:

m = (-1 - 0) / (0 - (-3)) = -1/3

Hence, the slope between the points (-3, 0) and (0, -1) is -1/3.

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