Pablo is 4 feet 10 inches tall. what is his height in inches?

From the observations, we can conclude that the probabilities form a geometric sequence, where each subsequent probability is a constant factor smaller than the previous one. Let's call this constant factor "q".

(i) Pn > Pn+1 for n = 0,1,2,3,4 means that Pn = P0 * q^n for some value of q such that 0 < q < 1.

(ii) The difference between Pn and Pn+1 is the same for n = 0,1,2,3,4 means that

Pn - Pn+1 = P0 * q^n - P0 * q^(n+1)

= P0 * q^n (1 - q) is the same for all n.

Let's call this difference "d".

d = P0 * q^n (1 - q) for all n.

We know that exactly 40% of policyholders file fewer claims during a given year, so P0 = 0.4.

Using this information, we can find q:

d = P0 * q^n (1 - q)

= 0.4 * q^n (1 - q)

= 0.4 * q^n - 0.4 * q^n * q

= 0.4 * q^n (1 - q)

= d.

So,

0.4 * q^n = d

And

q = d / (0.4 * q^n)

Substituting n = 0:

q = d / (0.4)

Now we can find P3 and P4:

P3 = P0 * q^3

P4 = P0 * q^4

Finally, the probability that a random policyholder will file more than three claims during a given year is

1 - (P0 + P1 + P2 + P3)

= 1 - (0.4 + 0.4 * q + 0.4 * q^2 + 0.4 * q^3).

Substituting the values we found for P0, q, and P3:

= 1 - (0.4 + 0.4 * q + 0.4 * q^2 + 0.4 * q^3)

= 1 - (0.4 + 0.4 * (d / 0.4) + 0.4 * (d / 0.4)^2 + 0.4 * (d / 0.4)^3)

= 1 - (1 + (d / 0.4) + (d / 0.4)^2 + (d / 0.4)^3)

This is the probability that a random policyholder will file more than three claims during a given year.

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Answer:

Slope of the line = 8

Step-by-step explanation:

Slope of a line = (y2-y1)/(x2-x1)

Slope = -1 - (-9)/4 - 4

= -1 + 9/0

= 8

Therefore the slope of the line is 8

Answer:

It looks like you are trying to solve some math problems and are looking for help filling in some information on a geometry reference sheet. Here are the answers to the questions you provided:

A Median:

Originates at the vertex of the triangle.

Connects the vertex to the midpoint of the opposite side.

Divides the side into two equal parts.

To solve for x in the equation 2x + 1 = 0, you can subtract 1 from both sides to get 2x = -1. Then divide both sides by 2 to get x = -1/2.

To solve for x in the equation 3x - 31 = 0, you can add 31 to both sides to get 3x = 31. Then divide both sides by 3 to get x = 31/3 = 10 1/3.

An Altitude:

Originates at the vertex of the triangle.

Connects the vertex to the line containing the opposite side.

Divides the opposite side into two equal parts.

To solve for x in the equation 10x + 9 = 6x + 21, you can subtract 6x from both sides to get 4x + 9 = 21. Then subtract 9 from both sides to get 4x = 12. Finally, divide both sides by 4 to get x = 3.

Without more context, it is not possible to solve for x in the equation (pa + 53)*(5x + 2) = 0. Please provide more information about the problem you are trying to solve.

Step-by-step explanation:

Answer:

We can start by using the second equation to eliminate x:

2x + 5y - 2z = 3

2x = -5y + 2z + 3

x = (-5/2)y + z + 3/2

Now we can substitute this expression for x into the first and third equations:

x + y + z = 4

(-5/2)y + z + 3/2 + y + z = 4

(-5/2)y + 2z = 5/2

x + 7y - 7z = 5

(-5/2)y + z + 3/2 + 7y - 7z = 5

(9/2)y - 6z = 7/2

Now we have a system of two equations with two variables, (-5/2)y + 2z = 5/2 and (9/2)y - 6z = 7/2. We can use any method to solve for y and z, such as substitution or elimination. However, we will find that the system is inconsistent, meaning there is no solution that satisfies both equations.

Multiplying the first equation by 9 and the second equation by 5 and adding them, we get:

(-45/2)y + 18z = 45/2

(45/2)y - 30z = 35/2

Adding these two equations, we get:

-12z = 40/2

-12z = 20

z = -5/3

Substituting z = -5/3 into (-5/2)y + 2z = 5/2, we get:

(-5/2)y + 2(-5/3) = 5/2

(-5/2)y - 10/3 = 5/2

(-5/2)y = 25/6

y = -5/12

Substituting y = -5/12 and z = -5/3 into any of the original equations, we get:

x + y + z = 4

x - 5/12 - 5/3 = 4

x = 29/12

Therefore, the solution is (x, y, z) = (29/12, -5/12, -5/3). However, if we substitute these values into any of the original equations, we will find that it does not satisfy the equation. For example:

2x + 5y - 2z = 3

2(29/12) + 5(-5/12) - 2(-5/3) = 3

29/6 - 5/2 + 5/3 ≠ 3

Since there is no solution that satisfies all three equations, the system is inconsistent.

Step-by-step explanation:

Answer:

See below for proof.

Step-by-step explanation:

A system of equations is not consistent when there is no solution or no set of values that satisfies all the equations simultaneously. In other words, the equations are contradictory or incompatible with each other.

Given system of equations:

\(\begin{cases}x+y+z = 4\\2x+5y-2z =3\\x+7y-7z =5\end{cases}\)

Rearrange the first equation to isolate x:

\(x=4-y-z\)

Substitute this into the second equation to eliminate the term in x:

\(\begin{aligned}2x+5y-2z&=3\\2(4-y-z)+5y-2z&=3\\8-2y-2z+5y-2z&=3\\-2y-2z+5y-2z&=-5\\5y-2y-2z-2z&=-5\\3y-4z&=-5\end{aligned}\)

Subtract the first equation from the third equation to eliminate x:

\(\begin{array}{cccrcrcl}&x&+&7y&-&7z&=&5\\\vphantom{\dfrac12}-&(x&+&y&+&z&=&4)\\\cline{2-8}\vphantom{\dfrac12}&&&6y&-&8z&=&1\end{aligned}\)

Now we have two equations in terms of the variables y and z:

\(\begin{cases}3y-4z=-5\\6y-8z=1\end{cases}\)

Multiply the first equation by 2 so that the coefficients of the variables of both equations are the same:

\(\begin{cases}6y-8z=-10\\6y-8z=1\end{cases}\)

Comparing the two equations, we can see that the coefficients of the y and z variables are the same, but the numbers they equate to is different. This means that there is no way to add or subtract the equations to eliminate one of the variables.

For example, if we subtract the second equation from the first equation we get:

\(\begin{array}{crcrcl}&6y&-&8z&=&-10\\\vphantom{\dfrac12}-&(6y&-&8z&=&\:\:\;\;\:1)\\\cline{2-6}\vphantom{\dfrac12}&&&0&=&-11\end{aligned}\)

Zero does not equal negative 11.

Since we cannot eliminate the variable y or z, we cannot find a unique solution that satisfies all three equations simultaneously. Therefore, the system of equations is inconsistent.

Answer: The width is 15 yards and the length is 24 yards

Step-by-step explanation:

Let x represent the width of the parking lot in yards

Let the length of the parking lost be (x + 9) as the length is 9 yards greater than the width

So, area = width * length

i.e. 360 = x(x + 9)

360 = x2 + 9x

x2 + 9x - 360 = 0

x2 + 24x - 15x - 360 = 0

x(x + 24) - 15(x + 24) = 0

(x + 24)(x - 15) = 0

Either x = -24 or, x = 15

But as width can not be negative, so we can not have, x = -24

So, we have, x = 15

Therefore, (x + 9) = (15 + 9) = 24

So, we have the following answers.

Width : 15 yards

Length : 24 yards

Answer:

C

Step-by-step explanation:

The equation of the parabola that opens to the right, has a focus (-1, -3), and a focal diameter of 8 is y = (1/16)x²+ (10/16)x - (23/16)

To determine the equation of a parabola that opens to the right, has a focus at (-1, -3), and a focal diameter of 8

we can use the standard form of the equation for a parabola with a horizontal axis:

(x - h)² = 4p(y - k)

Where (h, k) is the vertex of the parabola and p is the distance from the vertex to the focus.

Since the parabola opens to the right, the vertex will be to the left of the focus.

Therefore, the vertex will be at (-1 - p, -3).

The focal diameter is given as 8, which means the distance between the vertex and the focus is p = 8/2 = 4.

Plugging these values into the equation, we have:

(x - (-1 - 4))² = 4 × 4 × (y - (-3))

Simplifying:

(x + 5)² = 16(y + 3)

x² + 10x + 25 = 16y + 48

Rearranging to isolate y:

16y = x² + 10x + 25 - 48

16y = x² + 10x - 23

Dividing by 16:

y = (1/16)x² + (10/16)x - (23/16)

Therefore, the equation of the parabola that opens to the right, has a focus (-1, -3), and a focal diameter of 8 is y = (1/16)x²+ (10/16)x - (23/16)

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Answer:

since n is an integer you substitute n with all the integers. But since that is too much you should use infinity.

n=[-∞,+∞] where -∞ is a negative infinity which stands for negative numbers and +∞ is a positive infinity where it stands for positive numbers.

an integer contains negative and positive numbers so above is the answer.

Step-by-step explanation:

Answer:

12x2

Step-by-step explanation:

The explicit formula of the geometric sequence is given as follows:

\(a_n = 100(4)^{n-1}\)

The recursive formula of the geometric sequence is given as follows:

A geometric sequence is a sequence of numbers where each term is obtained by multiplying the previous term by a fixed number called the common ratio (q). In other words, a geometric sequence is a sequence where each term is a fixed multiple of the previous term.

The explicit formula of the sequence is given as follows:

\(a_n = a_1q^{n-1}\)

In which \(a_1\) is the first term.

For the recursive formula, we just take the first term and each consecutive term is the previous term multiplied by the common ratio.

There are 100 views in day one, hence the first term is given as follows:

\(a_1 = 100\)

The number of viewers is multiplied by 4 each day, hence the common ratio is given as follows:

q = 4.

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Answer:

C.

Step-by-step explanation:

When you replace x with x - h, the graph shifts h units horizontally.

Here, x is replaced by x - 12.

Compare x - 12 to x - h.

h = 12

The graph shifts 12 units to the right.

Answer:

answer maybe A..not sure but it might be in my opinion..

The weight on the inflation gap has increased from 0.5 to 0.75. The real interest rate is 16.86% and Nominal interest rate is 20%

a. In the base scenario, the real interest rate will be 20%, and the nominal interest rate will be 20%.

b. In scenario B, inflation rate will be higher (4%) compared to the base scenario (3.14%).

Output gap is 0% in both the scenarios, however, in the base scenario inflation gap is 0% (3.14 - 3.14) and in scenario B, inflation gap is 0.86% (4 - 3.14).

Now, let's calculate the real interest rate.

Real interest rate in base scenario = 20% - 3.14%

= 16.86%.

Real interest rate in scenario B = 20% - 3.14% + 1.5 + 0.5 (4-3.14) + 0.5 (0-0/0)

= 19.22%.

The real interest rate has moved in the direction to move inflation rate towards its target.

c. In scenario C, the output gap will be 20% compared to 0% in the base scenario.

Inflation gap is 0% in both the scenarios

Inflation rate is 3.14% and in scenario C, inflation rate is 2%.

Let's calculate the real interest rate. Real interest rate in the base scenario = 20% - 3.14%

= 16.86%.

Real interest rate in scenario C = 20% - 2% + 1.5 + 0.5 (3.14 - 3.14) + 0.5 (20-0/20)

= 20.15%.

Real interest rate in scenario C = 20% - 2% + 1.5 + 0.75 (3.14-3.14) + 0.25 (20-0/20) = 18.78%.

The new policy rule has changed the weight of the output gap in the Taylor Rule from 0.5 to 0.25.

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Answer:

A = 3

B = 1

C = 2

D = 10

E = 2

F = Not listed

G = 1

Step-by-step explanation:

\(\sqrt[3]{270x^5y^7} =\sqrt[3]{27*10x^5y^7}=3xy^2\sqrt[3]{10x^2y}\)

The Solution:

Given:

We are asked to solve for x.

Writing the given equation in exponential form, we get:

Dividing both sides by 11, we get:

Therefore, the exact answer is:

So, the correct answer is [option A]

Answer:

864 in^2

Step-by-step explanation:

Area of triangle

15 x 18 x 1/2 = 135

Area of Square

18 x 18 = 324

There are 4 triangles so...

135 x 4 = 540

Therefore the area is

540 + 324 = 864

Answer:

k=172.2

Step-by-step explanation

When you search up (0.6888) into a fraction calculator you get (861/1250),

which clearly needs to be simplified. Easy find the LCD. We already know that 1250 needs to be 25. So, divide (1250/25=50)

So know we know that the LCD is 50. Now we need to divide 861 by the LCD.  (861/50=172.2)

k=172.2

Answer:

\(2x + y \leq 8\)

Step-by-step explanation:

since potatoes cost $2 they are represented as 2x

Carrots cost $1 and are simply y

Answer:

2/5 or 0.4.

Step-by-step explanation:

6/15 = 2/5

Answer:

Bottom left

Step-by-step explanation:

The point of reflection is the bottom left one because when reflecting a figure in a line or in a point, the image is congruent to the preimage. A reflection maps every point of a figure to an image across a fixed line. The fixed line is called the line of reflection.

The picture that shows the line of reflection is the image in the bottom left. The correct option is C.

There are four pictures given in the image below A, B, C, and D.

In image A:

The line of reflection goes through the first image and therefore its reflection is not matched.

In image B:

The line of reflection B is available but there is no reflection image present.

In image C:

This picture shows a figure and its reflection.

In image D:

This picture shows a figure but this does not represent its reflection.

Therefore, the correct image is C.

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Step-by-step explanation:

50× 6/ 100=3 that will be your answer

Answer:

x=10 I am pretty sure

Step-by-step explanation:

Answer:

yh the answer is x=10

Step-by-step explanation:

The coordinates of point B =(5,10)

what is coordinates?

Coordinates are a set of values which helps to show the exact position of a point in the coordinates plane.

step - by - step  explanation

5-2 = 3

2-3= -1 = the x coordinate of B

-7-3= -10

-7-10 = -13 = the y coordinate of B

(-1, -13) is the point B

A is 3 to the right of the midpoint ,so B is 5 to the left to the midpoint

A is 10 up from the midpoint so B is 10 down from the midpoint.

so the coordinates of point B is (5,10)

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Answer: The formula for the mathematical function that takes as input an RGB color vector ⟨r,g,b⟩ and yields as output the RGB color vector that is the unique shade of gray whose total amount of light (r+g+b) is equal to that of the input is:

(r+g+b)/3, (r+g+b)/3, (r+g+b)/3

Step-by-step explanation: RGB color space is a way to represent colors digitally, where each color is represented by a combination of red, green, and blue values ranging from 0 to 255. To obtain a unique shade of gray whose total amount of light (r+g+b) is equal to that of the input color, we have to set all three color channels to the average value of the red, green and blue values.

To calculate this average value we use the formula: (r+g+b)/3

So the output of the function is ⟨(r+g+b)/3, (r+g+b)/3, (r+g+b)/3⟩ which is the unique shade of gray whose total amount of light is equal to that of the input color.

Note: This is one way to convert color to gray, other methods exist like using luminosity or other weights to RGB channels.

Answer:

It results in no solution.

Step-by-step explanation:

If you subtract x on both sides, this will leave you with 0 ≠ 3. The result is no solution. This is why it is contradictory.

Answer:

The area of the shaded region is 27 units^2.

Step-by-step explanation:

Area of outer square = 6^2 = 36 units^2

Area of inner square = 3^2 = 9 units^2

Area of shaded region

= 36 units^2 - 9 units^2 = 27 units^2

The area of a shaded region in a unit grid can be found either by subtracting the area of unshaded regions from the total grid area or by adding up the areas of identifiable shapes within the shaded region.

To find the area of the shaded region without counting every square, you can use a few different strategies, such as identifying and subtracting the area of unshaded regions from the total grid area, or recognizing and adding together larger, easily countable shapes within the shaded region.

For example, if your grid is 10x10 units, the total area would be 100 square units. If, within that grid, there are 20 unshaded squares, you can subtract this from the total area to find the area of the shaded region. So, 100 total square units - 20 unshaded square units = 80 shaded square units. This approach works best when the number of unshaded squares is relatively small or easily countable.

Alternatively, if the shaded region forms easily identifiable shapes (like a 5x5 square or a 3x10 rectangle), you can add the areas of these shapes together to get the total shaded area. This approach works best when the shaded region forms a few large, simple shapes.

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Answer:

10.63

Step-by-step explanation:

To find the Hypotenuse we need to use Pythagorean Thereom. So plugging in the formula the square root of A squared plus B squared you get 10.63

Answer:

Step-by-step explanation:

To solve the triangle means to find ALL unknown elements of Δ ( sides and angles )

JH² = 8² + 7² = 113

JH = √113 ≈ 10.63 m

m∠H = β

\(\frac{8}{7}\) = tan β ; β = arctan \(\frac{8}{7}\) = \(tan^{-1}\) \(\frac{8}{7}\) ≈ 48.814°

m∠H ≈ 49 °

m∠J = 90° - 49° = 41 °

Answer: 23.404

Step-by-step explanation:

Answer:

y=x+5

Step-by-step explanation:

Plug in -1 for x to find the tangent point:

y = (-1)^3 - 2(-1) + 3 = 4

y = 4

So, the tangent point is (-1,4)

Then find the slope:

take the derivative of y = x^3 - 2x + 3

3x^(3-1) - 2x^(1-1) + 0 (power rule)

dy/dx = 3x^2 - 2

then plug in x= -1 to find the slope...

m = 3(-1)^2-2 = 1

m=1

now we find the line with the slope m=1 passing through the points (-1,4)

using the equation of a line: (y-y₁) = m*(x-x₁)

So,

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

[Answer] y = x+5

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