Given the sequence: 125, 25, 5, ....
Write the recursive formula

The converted value of the units 3000 meters to the required miles is given by 1. 8641 miles ( round up to four decimal places ) .

Standard form to Convert meters and miles is equal to :

1 meter = 0.000621371 miles

Now,  the value of 3000 meters in miles we get by multiplying it by 0.000621371 we get,

3000 meters = ( 3000 ) × ( 0.000621371 ) miles

                      = ( 1.864113 ) miles

                      = ( 1.8641 ) miles ( round up to four decimals places )

Therefore, the value of 3000 meters to miles is equal to ( 1.8641 ) miles ( round up to four decimals places ) .

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Answer:

151 m^2

Step-by-step explanation:

Given,

Height ( h ) = 10 m

Radius ( r ) = 2 m

To find : Surface Area

Here, the shape is cylinder.

Formula : -

Surface area of cylinder = 2πr ( r + h )

Note : -

The value of π is 3.14

Surface area of cylinder

= 2πr ( r + h )

= 2 x 3.14 x 2 ( 2 + 10 )

= 12.56 ( 12 )

= 12.56 x 12

= 150.72

= 151 m^2 ( approximately )

False , the variance and standard deviation are not measures of central location

Given data ,

The variance and standard deviation are not measures of central location but measures of dispersion or spread of a dataset

Measures of central location include the mean, median, and mode, which represent the typical or central value of a dataset

The variance and standard deviation are measures of dispersion or spread in a dataset. They provide information about how the values in a dataset are spread out around the mean.

In order to understand the variability or dispersion of data points within a dataset, one must take into account both the variance and standard deviation. They provide information on the range of values and aid in calculating how far away from the mean certain data points are. In statistics and data analysis, these metrics are frequently used to comprehend and evaluate the variance of various datasets.

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The true statement is (b) Xavier used 15 oz of pineapple to with 24 oz of orange juice

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

The graph that represents the ratio of orange juice to pineapple juice

The graph passes through the origin

So, we have

slope = 16/10

Evaluate

slope = 1.6

When pineapple juice is 15, we have

orange = 15 * 1.6

orange = 24

Hence, the true statement is b

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Okay, here we have this:

Considering the provided information, we are going to calculate the requested probability, so we obtain the following:

Let us remember that in a 6-sided dice, the numbers it contains are (1,2,3,4,5,6), and of those 3 are odd, then we are going to substitute in the following formula of the simple probability of an event :

Probability of an event=Favorable Cases/Possible Cases

Probability of tossing an odd number with 6 sided number cube =3/6

Probability of tossing an odd number with 6 sided number cube =1/2

Finally we obtain that the probability of tossing an odd number with 6 sided number cube is 1/2.

The number of maximum terms in an nth degree polynomial can be found by adding 1 to the degree of the polynomial.

The number of maximum terms in an nth degree polynomial can be determined using the formula (n+1). This means that the maximum number of terms in a polynomial of degree 3 would be (3+1) = 4, in degree 5 it would be (5+1) = 6, and so on. So, the number of maximum terms in an nth degree polynomial can be found by adding 1 to the degree of the polynomial.

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Answer:

-54

Step-by-step explanation:

Please write this sequence in the following form:  a(n) = (-2)*3^(n- 1)

Then a(1) = -2*3^0  =  -2

         a(2) = -2*3^(2 - 1) = -6

          a(3) = -2*3^(3 - 1) = -2*9 = -18

          a(4) = -2*3^(4-1) = -2*27 = -54

The evaluation of ∫30(4f(t) - 6g(t)) dt given that ∫150f(t) dt = -7, ∫30f(t) dt = -8, ∫150g(t) dt = 4, and ∫30g(t) dt = 8 is -80.

Given that ∫150f(t) dt = -7, ∫30f(t) dt = -8, ∫150g(t) dt = 4, and ∫30g(t) dt = 8.

Let us evaluate ∫30(4f(t) - 6g(t)) dt.

Therefore,∫30(4f(t) - 6g(t)) dt = ∫30(4f(t) dt - 6g(t) dt) = 4 ∫30f(t) dt - 6 ∫30g(t) dt

Now, using the given values in the question we can say that,∫30(4f(t) - 6g(t)) dt = 4 ∫30f(t) dt - 6 ∫30g(t) dt = 4 (-8) - 6(8) = -32 - 48 = -80

Therefore, the evaluation of ∫30(4f(t) - 6g(t)) dt given that ∫150f(t) dt = -7, ∫30f(t) dt = -8, ∫150g(t) dt = 4, and ∫30g(t) dt = 8 is -80.

Note: The given integrals ∫150f(t) dt, ∫30f(t) dt, ∫150g(t) dt, and ∫30g(t) dt are only intermediate steps in order to evaluate the final integral.

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Answer:

Step-by-step explanation:

1 side = 2.5y - 3

8 sides = 8(2.5y - 3)

8 sides = 20y - 24

Perimeter = 20y - 24

The information that describes the line plot is

A line plot is said to be symmetric when the data points on one side of the center line (usually the median) mirror the data points on the other side. In other words, if you fold the line plot in half at the center line, the two halves would overlap perfectly.

Symmetry can be determined visually by looking at the line plot and assessing whether the data points appear to be evenly distributed on either side of the center line.

If the line plot is symmetric, it suggests that the data is evenly distributed around the center, and there are no significant outliers or biases in the data. If the line plot is not symmetric, it suggests that there may be some skewness or asymmetry in the data, and further analysis may be needed to understand the underlying patterns and trends.

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Based on the numbers that Joe selected, the people selected were D) Alan, Eugene, Martin, Sam.

The 17th person was selected and if we assigned numbers from 1 to 20 to the alphabetized list, we would find that number 17 is Sam.

The 5th person is Eugene and the 1st person is Alan. The 12th person is Nathan.

In conclusion, option D is correct.

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Answer:

Step-by-step explanation:

Base of triangle = b = 8 cm

Height of triangle = h = 6 cm

Length of rectangle = l = 6 cm

Sides of the triangle :  S1 = 6 cm ;  S2 = 8 cm and S3 = 10 cm

Surface area of triangular prism= bh + l *(s1+ S2 + S3)

                                                    = 8 * 6 + 6*(6+8+10)

                                                    = 48 + 6*24

                                                     = 48 + 144

                                                     = 192 square cm

The range of the function g(x) = |x - 12| - 2 is {y | y > -2}, indicating that the function can take any value greater than -2.

To find the range of the function g(x) = |x - 12| - 2, we need to determine the set of all possible values that the function can take.

The absolute value function |x - 12| represents the distance between x and 12 on the number line. Since the absolute value always results in a non-negative value, the expression |x - 12| will always be greater than or equal to 0.

By subtracting 2 from |x - 12|, we shift the entire range downward by 2 units. This means that the minimum value of g(x) will be -2.

Therefore, the range of g(x) can be written as {y | y > -2}, which means that the function can take any value greater than -2. In other words, the range includes all real numbers greater than -2.

Visually, if we were to plot the graph of g(x), it would be a V-shaped graph with the vertex at (12, -2) and the arms extending upward infinitely. The function will never be less than -2 since we are subtracting 2 from the absolute value.

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60% of the flanges will exceed 0.99 millimeters. 90% of the flanges will exceed a thickness of 1.04 millimeters. The mean is 1.000000 millimeters and the variance is 0.008333 millimeters^2.

To determine the proportion of flanges that exceed 0.99 millimeters, we need to calculate the probability that a randomly selected flange has a thickness greater than 0.99 millimeters. Since the thickness is uniformly distributed between 0.95 and 1.05 millimeters, the proportion can be found by calculating the ratio of the length of the interval above 0.99 to the total length of the interval.

Proportion = (1.05 - 0.99) / (1.05 - 0.95) = 0.06 / 0.1 = 0.6

Therefore, 60% of the flanges will exceed 0.99 millimeters.

To find the thickness that is exceeded by 90% of the flanges, we need to determine the value at which the cumulative distribution function (CDF) reaches 0.9. Since the distribution is uniform, the CDF increases linearly.

Let's denote the thickness as x. The CDF is given by (x - 0.95) / (1.05 - 0.95). We set this equal to 0.9 and solve for x:

(x - 0.95) / (1.05 - 0.95) = 0.9

x - 0.95 = 0.9 * (1.05 - 0.95)

x - 0.95 = 0.9 * 0.1

x - 0.95 = 0.09

x = 0.95 + 0.09

x = 1.04

Therefore, 90% of the flanges will exceed a thickness of 1.04 millimeters.

The mean and variance of the flange thickness can be calculated using the formulas for a uniform distribution. The mean is given by the average of the minimum and maximum values:

Mean = (0.95 + 1.05) / 2 = 1.00 millimeters

The variance is calculated using the formula:

Variance = ((1.05 - 0.95)^2) / 12 = 0.008333 millimeters^2

Rounded to 6 decimal places, the mean is 1.000000 millimeters and the variance is 0.008333 millimeters^2.

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The value of MN is 3.05

Along with arithmetic, geometry is one of the earliest subfields of mathematics. It is concerned with spatial characteristics like the separation between objects, their shape and size, and their relative positions.

Since MN=NK,

draw an isosceles triangle (two sides are equal).

Mark the angle N as 110 degrees.

Now, draw a line from N to the opposite side at a right angle. This line will divide MK=5 in half since MN = NK.

It will also divide angle N into half. So, we will end up with a right triangle with one side 5/2 = 2.5 and the opposite angle 55 degrees.

sin(55) = opposite / hypotenuse = 2.5 / MN = 0.82

MN = 2.5 / 0.82 = 3.05

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The figure that is part of ray AB is BA (ray). It represents the portion of the line that extends infinitely in the direction from point B towards point A.

Among the given choices, the figure that is a part of ray AB is BA (ray).

In geometry, a ray is a part of a line that has one endpoint and extends infinitely in one direction.

In this case, the ray AB would start at point A and extend infinitely in the direction of point B.

Similarly, the ray BA would start at point B and extend infinitely in the direction of point A.

So, the figure that is part of ray AB is BA (ray). It represents the portion of the line that extends infinitely in the direction from point B towards point A.

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Answer:

A lot

Step-by-step explanation:

A lot

Answer:

2x+y=-2

-9x-3y=18

So what you would do is see which one you would like to get rid of (either x, or y in this situation get rid of y)

multiply y by postive 3

3(2x+y=-2)

6x+3y=-6

-9x-3y=18          (both y's cross out since 3y+-3y is equal to zero)

-----------------

-3x=-24 (divide both sides by -3)

---     ---

-3      -3

x= 8 (neg/neg=positive)

Then figure out the x so use either the first or second equation

so in this case I will use the first equation (plug in the x for 8)

2(8)+y=-2

16+y=-2

-16    -16

---------------

y=-18

Check:

2x+y=-2

2(8)+y(-18)=-2

16+-18=-2

-2=-2 (therfore you know that you are right)

Ansers:

y=-18

x=8

Hope this helps!

The area of the triangle PQR that has a side length of p = 14 inches, q = 37 inches, and r = 38 inches is 257.2 inches².

area of triangle = √s(s - a)(s - b)(s - c)

where

Therefore,

s = 14 + 37 + 38  / 2 = 89 / 2 = 44.5

area of triangle = √44.5(44.5 - 14)(44.5 - 37)(44.5 - 38)

area of triangle = √44.5 × 30.5 × 7.5 × 6.5

area of triangle = √66165.9375

area of the triangle = 257.227404255

area of the triangle ≈ 257.2 inches²

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Positive

Negative

Sorts Explanation

Lines which go / are positive.

Lines which go \ are negative.

That's the best explanation I could do. (Sorry)

Answer:

f(x) = -3x + 6

Step-by-step explanation:

The general linear function is;

y = mx + b

it can also be written as (x , f(x))

f(x) = mx + b

where m is the slope and b is the y-intercept

so we have the points ;

(0,6) and (4,-6)

So we have;

for f(0) to be 6, it means that the y-intercept b is 6

This is because the value of x at the y-intercept is 0

So we have this as;

f(x) = mx + 6

Now, let’s substitute the other point so as to get m

For the other point;

x = 4 and f(x) = -6

that means;

-6 = 4m + 6

4m = -6-6

4m = -12

m = -12/4

m = -3

So we have the equation as;

f(x) = -3x + 6

Based on the information given the real interest rate is 1.75%.

Using this formula

Real interest rate =Nominal interest rate − Inflation rate

Where:

Nominal interest rate=4.00%

Inflation rate=2.25%

Let plug in the formula

Real interest rate=4.00%-2.25%

Real interest rate=1.75%

Inconclusion the real interest rate is 1.75%.

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Answer: 46.619 units.

Step-by-step explanation:

To find the length of the spiraling polar curve, we need to use the formula:

L = int_a^b sqrt[r^2 + (dr/d\theta)^2] d\theta

where r is the polar curve, dr/d\theta is its derivative with respect to theta, and a and b are the limits of integration.

In this case, we have:

r = 7 e^{4 \theta}

dr/d\theta = 28 e^{4 \theta}

And the limits of integration are a = 0 and b = 2\pi.

Substituting these into the formula, we get:

L = int_0^(2\pi) sqrt[(7e^{4\theta})^2 + (28e^{4\theta})^2] d\theta

Simplifying this expression using algebra, we get:

L = int_0^(2\pi) 7e^{4\theta} sqrt[1 + 16e^{8\theta}] d\theta

This integral cannot be solved analytically, so we need to use numerical methods to approximate its value. One way to do this is to use a numerical integration technique such as the trapezoidal rule or Simpson's rule.

Using Simpson's rule with a step size of h = \pi/1000, we get:

L \approx 46.619

Therefore, the length of the spiraling polar curve r = 7 e^{4 \theta} from 0 to 2 \pi is approximately 46.619 units.

a)The industry output will be: Q = qA + qB.

b) The industry output will be: Q = qA + qB.

c) Both firms would earn a higher profit if they agree on the industry output.

a) Bertrand Model:

In the Bertrand Model, both firms produce the same quality products at a constant marginal cost of X. Both companies attempt to maximize their own profits by selecting the lowest price. Firm A produces qA, while firm B produces qB. The firms would earn no profits if they set the same price.

Assume that each firm offers the same price P. The industry supply will be Q = qA + qB. The market demand is given by Q = Y - P. Substituting the value of Q, we get: Y - P = qA + qB.

The industry price is given by: P = (Y - Q)/2 = (Y - qA - qB)/2. Putting the value of Y and Q, we have: P = [(B + C) - (A + D/2) - qA - qB]/2 = (B + C - A - D/2)/2 - qA/2 - qB/2.

The industry output will be: Q = qA + qB.

Consumer surplus is given by the difference between what consumers are willing to pay and the market price of a good, summed over all customers. The consumer surplus is calculated by taking the area between the demand curve and the market price up to the equilibrium output.

Consumer Surplus = 1/2 (B + C - A - D/2 - P) * Q = 1/2 (B + C - A - D/2 - [(qA + qB)/2]) * [(qA + qB)].

Industry profit is given by: π = qA * P + qB * P - X(qA + qB) = qA * qB / 2Q - X(Q/2).

Deadweight Loss (DWL) is the loss of economic efficiency that occurs when the equilibrium output is not achieved. DWL is given by: DWL = [1/2 (qa + qb) - Q]/2.

b) Cournot Model:

In the Cournot Model, both firms produce identical products with a constant marginal cost of X. Both firms attempt to maximize their profits by selecting their output levels qA and qB. Let Q = qA + qB be the industry's output.

Substituting the value of Q, we get: Y - P = qA + qB.

The industry price is given by: P = (Y - qA - qB)/2 = (B + C - A - D/2)/2 - qA/2 - qB/2.

The industry output will be: Q = qA + qB.

Consumer surplus is given by the difference between what consumers are willing to pay and the market price of a good, summed over all customers. The consumer surplus is calculated by taking the area between the demand curve and the market price up to the equilibrium output.

Consumer Surplus = 1/2 (B + C - A - D/2 - P) * Q.

Industry profit is given by: π = (qA + qB) * (P - X) - (qA^2 + qB^2)/2.

Deadweight Loss (DWL) is the loss of economic efficiency that occurs when the equilibrium output is not achieved. DWL is given by: DWL = [(qa - qb)^2 - (qA + qB)^2]/2.

c) Tacit Collusion Model:

In the tacit collusion model, both firms in the industry aim to maximize their collective profits. Both firms would earn a higher profit if they agree on the industry output. The firms produce identical products at a constant marginal cost

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The two-dimensional shape which could be created by a plane slicing vertically through the hexagonal pyramid is Square. The correct option is B.

When vertically intersecting the given pyramid, the base of which is a hexagon, such two-dimensional figures are formed at its base. As can be seen at the attached picture of Hexagon ABCDEF.

CEFD and ACDB are quadrangles, which are squares. So, the shape which could be created by slicing vertically the hexagonal pyramid is square.

Squares are quadrilaterals that have 4 congruent sides and 4 right angles, and also, they have two sets of parallel sides. Meanwhile, parallelograms are quadrilaterals that have two sets of parallel sides. Since squares have to be quadrilaterals with two sets of parallel sides, this means all squares are parallelograms.

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Although part of your question is missing, you might be referring to this full question: Which two-dimensional shape could be created by a plane slicing vertically through this hexagonal pyramid? (Picture attached)

A. Octagon

B. Square

C. Hexagon

D. Pentagon

To find the total number of balloons used, we need to add the quantities of white, yellow, blue, and red balloons together.

Let's break down the given information:
- The number of white balloons used is 1243.
- There are 7559 more yellow balloons than white balloons.
- The number of blue balloons is 1138 more than the number of white balloons.
- The number of red balloons is equal to the combined quantity of yellow and blue balloons.

First, let's determine the number of yellow balloons. Since there are 7559 more yellow balloons than white balloons, we add 7559 to the quantity of white balloons:
1243 + 7559 = 8802 yellow balloons.

Next, let's determine the number of blue balloons. As there are 1138 more blue balloons than white balloons, we add 1138 to the quantity of white balloons:
1243 + 1138 = 2381 blue balloons.

Now, let's calculate the number of red balloons. The number of red balloons is equal to the sum of yellow and blue balloons:
8802 + 2381 = 11183 red balloons.

Finally, to find the total number of balloons used, we add the quantities of white, yellow, blue, and red balloons:
1243 + 8802 + 2381 + 11183 = 23609 balloons in total.

In total, 23609 balloons were used for the party. For the party, a total of 23609 balloons were used. The breakdown of balloon colors is as follows: 1243 white balloons, 8802 yellow balloons, 2381 blue balloons, and 11183 red balloons. To arrive at these numbers, we followed the given information step by step. First, we determined the quantity of yellow balloons by adding 7559 (the number of yellow balloons that exceeded the white balloons) to the initial quantity of white balloons (1243). This gave us a total of 8802 yellow balloons. Then, we calculated the quantity of blue balloons by adding 1138 (the number of blue balloons that exceeded the white balloons) to the initial quantity of white balloons (1243). This resulted in 2381 blue balloons. Finally, we found the quantity of red balloons by adding the number of yellow balloons (8802) and the number of blue balloons (2381), resulting in 11183 red balloons. Adding up the quantities of white, yellow, blue, and red balloons, we obtained a total of 23609 balloons for the party.

In conclusion, the total number of balloons used for the party was 23609, consisting of 1243 white balloons, 8802 yellow balloons, 2381 blue balloons, and 11183 red balloons.

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