Find the solution to each of these recurrence relations with the given initial conditions. use an iterative approach such as that used in example 10 d) an =2an-1-3, ao =-1 e) an-(n + 1)aa-1, ao 2

The probability that a randomly chosen light bulb lasts more than 10,500 hours is 0.0668 (rounded to four decimal places).

The probability that a randomly chosen light bulb lasts more than 10,500 hours is 0.0668(rounded to four decimal places).Here's how to calculate it:Given data mean μ = 9,000 and standard deviation σ = 1,000.To calculate the probability that a random light bulb lasts more than 10,500 hours, convert the problem to a standard normal distribution.

z = (10,500 - μ)/σ = (10,500 - 9,000)/1000 = 1.50

Here's the standard normal distribution curve with the shaded area representing the probability required: Standard normal distribution curve with the shaded area

Now, the area under the curve to the right of z = 1.5 is the probability that a randomly chosen light bulb will last more than 10,500 hours.

Using the Z table, we can look up the value corresponding to a z-score of 1.5. The table gives us a value of 0.9332.Now, the area to the left of z = 1.5 is 1 - 0.9332 = 0.0668, which is the probability that a randomly chosen light bulb lasts more than 10,500 hours, rounded to four decimal places.

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The value of the angle x using trigonometric ratio is: x = 53.13°

Some of the trigonometric ratios in mathematics based on a right angle triangle are:

Sin x = opposite/hypotenuse

cos x = adjacent/hypotenuse

tan x = opposite/adjacent

Similarly:

cot x = 1/tan x

sec x = 1/cos x

cosec x = 1/sin x

We are given that:

sin x = 12/15

Thus:

x = sin⁻¹(12/15)

x = 53.13°

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According to the information, each of the cases of equations has a different solution depending on the value that is given to the unknown or x.

Let p = √(x - 3), then the equation becomes p^2 - 2p - 3 = 0. This is a quadratic equation that can be factored as (p - 3)(p + 1) = 0. Therefore, p = 3 or p = -1. Since p = √(x - 3) and we want real solutions, we have two cases:

Case 1: p = √(x - 3) = 3. Squaring both sides, we get x - 3 = 9, so x = 12.

Case 2: p = √(x - 3) = -1. This case gives no real solution, since the square root of a real number cannot be negative. Therefore, the only real solution is x = 12.

Let p = √(x - 5), then the equation becomes p^2 - 4p - 12 = 0. This is a quadratic equation that can be factored as (p - 6)(p + 2) = 0. Therefore, p = 6 or p = -2. Since p = √(x - 5) and we want a real solution, we have only one case:

Case 1: p = √(x - 5) = 6. Squaring both sides, we get x - 5 = 36, so x = 41. However, we need to check that this solution is valid. Since p = √(x - 5) = 6 > 0, we have x - 5 > 0, so x > 5. Therefore, the only real solution is x = 41.

Let p = 3^x, then the equation becomes p^2 + 11p - 12 = 0. This is a quadratic equation that can be factored as (p + 12)(p - 1) = 0. Therefore, p = -12 or p = 1. Since p = 3^x and we want a real solution, we have only one case:

Case 1: p = 3^x = 1. This gives x = 0. However, we need to check that this solution is valid. Since 3^x > 0 for all x, we have x > -∞. Therefore, the only real solution is x = 0.

There is only one real solution because the function 9^x + (11x3^x) - 12 is continuous and strictly increasing for all x, which means that it can cross the x-axis at most once. Since we have found one real solution, there cannot be any others.

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Answer:

3/7

Step-by-step explanation:

A ratio has two or more numbers that symbolize relation to each other. Ratios are used to compare numbers, and you can compare them using division.

Let’s assume that we have 7 units of paint in total. Then, we have 3 units of green paint and 4 units of red paint. When we mix them together, we get 7 units of brown paint.

Because 3 out of the 7 units of paint are green, the fraction of the brown paint that is green paint is [tex]\frac{3}{7}[/tex].

Therefore, [tex]\frac{3}{7}[/tex] of the brown paint is green.

The length of the segment SR for the given pentagons is 9 units.

A polygon having 5 sides and 5 angles is called a pentagon. The words "pentagon" (which implies five angles) are formed up of two other terms, namely Penta and Gonia. End to end, the sides of a pentagon come together to form a shape. Hence, there are 5 sides in a pentagon.

The pentagon is a polygon with five sides and five angles, just like other polygons including triangles, quadrilaterals, squares, and rectangles. There are several sorts of pentagon forms, including regular and irregular pentagons as well as convex and concave pentagons, depending on the sides, angles, and vertices.

We know that, for similar figures the length of the ratios of their corresponding segments are equal.

Thus,

NM/TS = ML/SR

4/7.2 = 5/x

Using cross multiplication we have:

4x = 5(7.2)

4x = 36

x = 9

Hence, the value of the segment SR for the given pentagons is 9 units.

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April has six pieces of paper, each measuring 8 inches in length which can be calculated using fractions.

April starts with a sheet of paper that is 4 feet long, which is equivalent to 48 inches since there are 12 inches in a foot. She then cuts the length of paper into halves, which gives her two pieces, each of them 24 inches long.

Next, she cuts the length of each of these 24-inch pieces into thirds, which gives her six pieces in total. Each of these pieces is 8 inches long, since 24 divided by 3 equals 8. Therefore, April has six pieces of paper, and each piece is 8 inches long.

It's worth noting that April's process of cutting the paper into halves and then into thirds is an example of how fractions can be used to divide a whole into equal parts. In this case, cutting the paper into halves means dividing it into two equal parts, and cutting each of these halves into thirds means dividing each half into three equal parts.

Overall, April has six pieces of paper, each measuring 8 inches in length. These pieces could be useful for various purposes, such as for creating small origami figures, for making decorations, or for use in a crafting project.

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Answer:

144

Step-by-step explanation:

The angles on the line next to the big c must add up to 180, and 180-58=122, so the space next to the 58 must be 122

The interior angles of a polygon can be calculated with 180(n-2) where n is the sides, so a pentagon has 540 degrees of interior angles

540 - 96 - 88 - 90 - 122 = 144

Answer:

Step-by-step explanation:

90+96+88+180-58=540-k

k=540-396

k = 144

The value of x is 8

The theorems of triangle are the rules that governs solving mathematical problems. Part of this theorem is a theorem that states that: The line joining the midpoint of the two sides of a triangle is parallel to the base.

Therefore ;

If we represent a side by y, using similar triangle,

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

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

3x +8 = 2(x+8)

3x +8 = 2x +16

collect like terms

3x-2x = 16-8

x = 8

therefore the value of x is 8

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In order for ΔCAM≅ΔCOM to be proved, all three sides and all three angles must be equal. So the correct answer is E. ΔCAM≅ΔCOM.

Corresponding sides are two sides in a polygon that are directly across from each other. This can be seen when two sides are connected by a line that is perpendicular to the other two sides.

ΔCAM≅ΔCOM can be proved when the two triangles have three corresponding sides and three corresponding angles that are equal.

However, option E does not provide proof of this as it only states that two angles are equal.

The other four options provide such proof.

Option A states that two angles are equal, Option B states two lines are equal and two angles are equal, Option C states two lines are equal and two angles are equal, and Option D states two lines are equal and two lines are equal. All of these provide the proof that ΔCAM≅ΔCOM.

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In order for ΔCAM≅ΔCOM to be proved, all three sides and all three angles must be equal. Option E does not provide proof of this as it only states that two angles are equal. So the correct answer is E. ΔCAM≅ΔCOM.

Corresponding sides are two sides in a polygon that are directly across from each other. This can be seen when two sides are connected by a line that is perpendicular to the other two sides.

ΔCAM≅ΔCOM can be proved when the two triangles have three corresponding sides and three corresponding angles that are equal.

However, option E does not provide proof of this as it only states that two angles are equal.

The other four options provide such proof.

Option A states that two angles are equal,

Option B states two lines are equal and two angles are equal,

Option C states two lines are equal and two angles are equal, and Option D states two lines are equal and two lines are equal.

All of these provide the proof that ΔCAM≅ΔCOM.

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If at least 3 of 4 balls must be blue then the number of possible selections = 462

Let us assume that m represents the number of red balls in a bowl.

So, m = 7

And n  represents the number of blue balls in a bowl.

So, n = 8

A woman selects 4 balls at random from the bowl.

We need to find the number of possible selections if at least 3 balls must be blue.

The first combination would be 4 blue balls + 0 red balls

And the second combination would be 3 blue balls + 1 red ball

so, using combination formula the number of possible selecctions:

(⁸C₄ × ⁷C₀) + (⁸C₃ ×  ⁷C₁)

= (70 × 1) +(56 × 7)

= 462

Therefore, the number of possible selections: 462

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Answer:

7.81 units

Step-by-step explanation:

To find the distance between two points, we can use the distance formula:

d = √((x2 - x1)^2 + (y2 - y1)^2)

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

Using the coordinates given in the problem, we can plug in the values into the formula:

d = √((4 - (-2))^2 + (1 - (-4))^2)

Simplifying this expression, we get:

d = √((6)^2 + (5)^2)

d = √(36 + 25)

d = √61

Therefore, the distance between the two points (-2,-4) and (4,1) is √61 (square root of 61), which is approximately 7.81 units.

The coordinates of the vertices of the enlarged shape A are (3, -3), (7, -3), (1, -6), and (0, -6).

In mathematics and geometry, a scale factor is a numerical factor that describes how much a figure or object has been enlarged or reduced in size. It is the ratio of any two corresponding lengths in the original figure and the scaled figure.

In geometry, a vertex (plural vertices) is a point where two or more line segments, lines, or rays meet to form an angle. In other words, a vertex is a point where two or more edges of a polygon, polyhedron, or any other geometrical shape meet.

In the given question,

To enlarge the shape A by a scale factor of 2 with a centre of enlargement of (-3, -5), we need to:

Translate the centre of enlargement to the origin (0, 0) by adding 3 to the x-coordinates and 5 to the y-coordinates of all points.

Apply the enlargement by multiplying the coordinates of each point by 2.

Translate the centre of enlargement back to its original position by subtracting 3 from the x-coordinates and 5 from the y-coordinates of all points.

So, the coordinates of the vertices of the enlarged shape A are:

Vertex 1:

Original coordinates: (0, -4)

Translate to origin: (3, 1)

Enlarge: (6, 2)

Translate back: (3, -3)

Final coordinates: (3, -3)

Vertex 2:

Original coordinates: (2, -4)

Translate to origin: (5, 1)

Enlarge: (10, 2)

Translate back: (7, -3)

Final coordinates: (7, -3)

Vertex 3:

Original coordinates: (1, -6)

Translate to origin: (4, -1)

Enlarge: (8, -2)

Translate back: (1, -6)

Final coordinates: (1, -6)

Vertex 4:

Original coordinates: (0, -6)

Translate to origin: (3, -1)

Enlarge: (6, -2)

Translate back: (0, -6)

Final coordinates: (0, -6)

Therefore, the coordinates of the vertices of the enlarged shape A are (3, -3), (7, -3), (1, -6), and (0, -6).

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Additionally, please note that offering a "brainiest" reward for assistance is not necessary.

Hello! I'd be happy to help you with your question, but please refrain from using excessive capitalization or urgency in your request. It can come across as rude and disrespectful to others who are also seeking assistance.

Regarding your question, I'll do my best to answer it to the best of my abilities. However, I need you to provide me with more details on what specifically you need help with. Without this information, it's difficult for me to provide you with an accurate answer.

Our goal is to provide helpful and informative responses to all users, regardless of any potential rewards.

Thank you for reaching out, and I look forward to hearing back from you with more information on your question.

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As the angle ∠c in a triangle increases, the length of the middle section on line p decreases.

Conversely, as the angle ∠c decreases, the length of the middle section on line p increases. This is because the middle section on line p is a portion of the altitude of the triangle, which is the perpendicular segment from the vertex of the angle to the opposite side. As the angle ∠c increases, the altitude of the triangle gets shorter, resulting in a shorter middle section on line p. Similarly, as the angle ∠c decreases, the altitude of the triangle gets longer, resulting in a longer middle section on line p. Examples of triangles can include equilateral, isosceles, scalene, acute, right, and obtuse triangles, among others.

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The solution to the system of inequalities is:

x > 10/3 and x > 0

What is inequality?

In mathematics, an inequality is a statement that shows the relationship between two values, expressions or quantities using inequality symbols such as <, >, ≤, or ≥. Inequalities convey that one value is not the same as the other, but rather is either greater than or less than the other value.

The system of inequalities is:

3x-10 > 0

2x > 0

To solve this system, we need to find the values of x that satisfy both inequalities at the same time.

From the first inequality, we can isolate x by adding 10 to both sides:

3x - 10 + 10 > 0 + 10

3x > 10

Then, we can divide both sides by 3:

x > 10/3

So we know that x is greater than 10/3.

From the second inequality, we know that x must be greater than 0.

Therefore, the solution to the system of inequalities is:

x > 10/3 and x > 0

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The average mother stays in the maternity ward when local maternity ward delivers 1,500 babies per year is equal to 1.22 days.

Total number of babies delivered by maternity ward per year = 1,500

⇒ Total number of patients = 1,500

On average number of beds filled in the maternity ward at any given time = 5

Total patient days per year is,

⇒ Total patient days = Average number of beds filled x Number of days in a year

Since there are 365 days in a year,

⇒Total patient days = 5 x 365

                                 = 1,825

Use the formula,

Average length of stay = Total patient days / Total number of patients

⇒Average length of stay = 1,825 / 1,500

⇒Average length of stay = 1.22 days

Therefore, the average mother stays in the maternity ward for 1.22 days.

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Answer: the answer is x < 2.80

Step-by-step explanation: can i get brainliest pls

Using functions, we can find that the population of Smalltown reached its minimum in year 1995.

Functions are the central idea of calculus in mathematics. The functions are special types of relations. A function is a rule that generates a unique outcome for each input x in mathematics.

A mapping or transformation in mathematics represents a function.

The minimum point of this function corresponds to the vertex of the upward-opening parabola it creates.

You must consider the sign of the coefficient of the quadratic term, "a," in order to calculate the direction of the parabola without graphing it.

The parabola widens if the value of "a" is positive.

The parabola begins at the bottom if "a" is negative.

Now, you must use the following formula to find the x-coordinate of the vertex of a quadratic function represented in standard form:

x = -b/2a

a = 0.34

b = -4.08

x = -(-4.08)/2 × 0.34

= 4.08/0.68

= 6

Now, f (6) = 0.34 × 6² - 4.08 × 6 + 16.2

= 12.24 - 24.48 + 16.2

= 3.96

≈ 4

So, coordinates of the vertices are: (6,4)

If x = 0 is year 1989

Then, x = 6 is year 1989 + 6 = 1995.

This means that the population of Smalltown reached its minimum in year 1995.

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The surface area of the composite figure is; SA = 224 in.²

From the composite figure attached, we can find the surface area of each of the rectangular/square external face seen as:

[tex]SA= 2(10 \times 2) + 2(4 \times 7) + 2(4 \times 4) + 2(4 \times 2) + (4 \times 7) + (10 \times 4) + (3 \times 4)[/tex]

[tex]SA = 40 + 56 + 32 + 16 + 28 + 40 + 12[/tex]

[tex]SA = 224 \ \text{in}.^2[/tex]

Thus, we can conclude that the surface area of the composite figure is:

[tex]SA = 224 \ \text{in}.^2[/tex]

Answer:26

Step-by-step explanation:

Answer: 96 in squared.

First find the area of the whole triangle:

= 1/2(24+6)(8)

= 1/2(30)(8)

= 120

Then, find the area of the triangle formed by dotted lines:

= 1/2(6)(8)

= 24

Subtract the two areas:

= 120 - 24

= 96

The expression [tex]\mathbf{\frac{\left(x^2\:-\:\frac{1}{y^2}\right)^x\cdot \left(x\:-\:\frac{1}{y}\right)^{y-x}}{\left(y^2\:-\:\frac{1}{x^2}\right)^y\cdot \left(y\:+\:\frac{1}{x}\right)^{x-y}}}[/tex] when simplified to the simplest form is [tex]\frac{x^{x+y}}{y^{x+y}}}[/tex]

From the question, we have the following expression to be used in our computation:

[tex]\mathbf{\frac{\left(x^2\:-\:\frac{1}{y^2}\right)^x\cdot \left(x\:-\:\frac{1}{y}\right)^{y-x}}{\left(y^2\:-\:\frac{1}{x^2}\right)^y\cdot \left(y\:+\:\frac{1}{x}\right)^{x-y}}}[/tex]

Simplifying the numerator, we get

[tex]\mathbf{\frac{\left(x^2\:-\:\frac{1}{y^2}\right)^x\cdot \left(x\:-\:\frac{1}{y}\right)^{y-x}}{\left(y^2\:-\:\frac{1}{x^2}\right)^y\cdot \left(y\:+\:\frac{1}{x}\right)^{x-y}} = \frac{\left(x^2y^2 - 1\right)^x\cdot \left(xy - 1\right)^{y-x}/y^{x+y}}{\left(y^2\:-\:\frac{1}{x^2}\right)^y\cdot \left(y\:+\:\frac{1}{x}\right)^{x-y}}}[/tex]

Simplifying the denominator, we get

[tex]\mathbf{\frac{\left(x^2\:-\:\frac{1}{y^2}\right)^x\cdot \left(x\:-\:\frac{1}{y}\right)^{y-x}}{\left(y^2\:-\:\frac{1}{x^2}\right)^y\cdot \left(y\:+\:\frac{1}{x}\right)^{x-y}} = \frac{\left(x^2y^2 - 1\right)^x\cdot \left(xy - 1\right)^{y-x}/y^{x+y}}{\left(x^2y^2 - 1}\right)^y\cdot \left(xy\:+\:1\right)^{x-y}/x^{y+x}}}[/tex]

Applying the following fraction rule:

(a/b)/(c/d) = (a * d)/(b * c)

So, we have

[tex]\mathbf{\frac{\left(x^2\:-\:\frac{1}{y^2}\right)^x\cdot \left(x\:-\:\frac{1}{y}\right)^{y-x}}{\left(y^2\:-\:\frac{1}{x^2}\right)^y\cdot \left(y\:+\:\frac{1}{x}\right)^{x-y}} = \frac{\left(x^2y^2 - 1\right)^x\cdot \left(xy - 1\right)^{y-x} \cdot x^{x+y}}{\left(x^2y^2 - 1}\right)^y\cdot \left(xy\:+\:1\right)^{x-y} \cdot y^{x+y}}}[/tex]

Cancel the common factors

So, we have

[tex]\mathbf{\frac{\left(x^2\:-\:\frac{1}{y^2}\right)^x\cdot \left(x\:-\:\frac{1}{y}\right)^{y-x}}{\left(y^2\:-\:\frac{1}{x^2}\right)^y\cdot \left(y\:+\:\frac{1}{x}\right)^{x-y}} = \frac{x^{x+y}}{y^{x+y}}}[/tex]

Hence, the expression when simplified is [tex]\frac{x^{x+y}}{y^{x+y}}}[/tex]

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Answer:

0.0234189518

Step-by-step explanation:

The y-coordinate of the solution of the system is -10.

What is the linear equation?

A linear equation is an equation that describes a straight line in a two-dimensional space. It is a mathematical expression that relates two variables, usually x and y, such that one variable is a function of the other. The general form of a linear equation is:

y = mx + b

To find the y-coordinate of the solution of the system:

3x - y = 22 ...(1)

y = x - 14 ...(2)

We can substitute the expression for y from equation (2) into equation (1) to eliminate y:

3x - (x - 14) = 22

Simplifying this equation:

3x - x + 14 = 22

2x + 14 = 22

Subtracting 14 from both sides:

2x = 8

Dividing both sides by 2:

x = 4

Now we can substitute x = 4 into equation (2) to find the corresponding value of y:

y = x - 14

y = 4 - 14

y = -10

Therefore, the y-coordinate of the solution of the system is -10.

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Answer:

  (B) one

Step-by-step explanation:

You want to know how many points on the interval [0, 5] the function f(x) = e^(2x) have a slope equal to the average slope.

The instantaneous rate of change of function f(x) is its derivative:

  f'(x) = 2e^(2x)

This is a continuously increasing function (as is f(x)), so in any given interval there will be only one point that has any given slope.

The Mean Value Theorem says there is at least one point in the interval with the same slope as the average slope. The nature of the derivative tells you there is exactly one point with the same slope as the average slope.

The average rate of change on [0, 5] is ...

  AROC = (e^(2·5) -e^(2·0))/(5 -0) = (e^10 -1)/5

The instantaneous rate of change will have that value where ...

  f'(x) = 2e^(2x) = (e^10 -1)/5

  2x = ln((e^10 -1)/10)

  x = ln((e^10 -1)/10)/2 ≈ 3.84868475302

For this value of x, f'(x) = AROC

Answer:

i believe its D

im sorry if i am incorrect

Answer:

D is the answer

Step-by-step explanation:

Answer:

a = 12

Step-by-step explanation:

Pythagorean theorem states that the the square value of hypotenuse is equal to the sum of the squares of two legs.

Now, according to this statement:

15² = 9² + a²

225 = 81 + a²

144 = a²

12 = a