Find the thirty-fourth term of the sequence defined by a = 146, a₁ = an-1+ 36.

The new weight of wrestler 1 is w_{(n+2)/2} = w_{(n+3)/2} - 1

The new weight of wrestler 2 is w_{(n+4)/2} = w_{(n+3)/2} + 2.

Let's suppose the weights of the wrestlers before the two new wrestlers joined the team are arranged in increasing order as follows:

w_1 ≤ w_2 ≤ w_3 ≤ ... ≤ w_n

where;

Since the mean weight remains unchanged, we have:

(w_1 + w_2 + w_3 + ... + w_n) / n = (w_1 + w_2 + w_3 + ... + w_n + x + y) / (n+2)

where x and y are the weights of the two new wrestlers.

Simplifying the above equation, we get:

2(w_1 + w_2 + w_3 + ... + w_n) = nw_1 + nw_2 + nw_3 + ... + nw_n + 2x + 2y

which can be further simplified as:

2(w_1 + w_2 + w_3 + ... + w_n) - 2nw_n = (n-2)w_1 + (n-2)w_2 + (n-2)w_3 + ... + (n-2)w_{n-1} + 2x + 2y

Since the median weight increases by 3 pounds, the new median weight is the weight of the (n+3)/2-th wrestler.

where;

We can express this in terms of the weights of the original wrestlers and the weights of the new wrestlers as follows:

If n+2 is even, then the new median weight is the average of the (n+2)/2-th and (n+4)/2-th weights.

If n+2 is odd, then the new median weight is the (n+3)/2-th weight.

In either case, we have:

w_{(n+2)/2} + w_{(n+4)/2} = 2(w_{(n+3)/2} - 3)

Substituting the weights of the original wrestlers and the new wrestlers using the equation we derived earlier, we get:

[(n-1)w_{(n+2)/2} + (n-1)w_{(n+4)/2} + 2x + 2y] + [(n-1)w_{(n+2)/2} + (n-1)w_{(n+4)/2}] = 2[(n+2)w_{(n+3)/2} - 6]

Simplifying and rearranging the terms, we get:

4w_{(n+3)/2} - 2w_{(n+2)/2} - 2w_{(n+4)/2} = x + y - 3

Substituting x + y = 2w_{(n+3)/2} - 3, we get:

w_{(n+4)/2} - w_{(n+2)/2} = 3 - w_{(n+3)/2}

Since the weights are arranged in increasing order, we have:

w_{(n+2)/2} ≤ w_{(n+3)/2} ≤ w_{(n+4)/2}

Therefore, the only possible solution is:

w_{(n+2)/2} = w_{(n+3)/2} - 1

w_{(n+4)/2} = w_{(n+3)/2} + 2

Learn more about weights here: https://brainly.com/question/2337612

#SPJ1

The probability of Jose being the president and Ellen being the vice president in a committee of eight people choosing leaders at random is 1/56.

The probability of Jose being chosen as the president and Ellen being chosen as the vice president is:

P(Jose as president and Ellen as vice president) = P(Jose as president) * P(Ellen as vice president | Jose as president)

Since the assignments are made at random and there are no restrictions on who can be chosen for each position, the probability of Jose being chosen as president is 1/8, and the probability of Ellen being chosen as vice president, given that Jose is president, is 1/7 (since there are 7 remaining people who can be chosen for the position of secretary).

Therefore,

P(Jose as president and Ellen as vice president) = (1/8) * (1/7) = 1/56

So the probability that Jose is president and Ellen is vice president is 1/56.

To know more about Probability:

https://brainly.com/question/11234923

#SPJ4

_____The given question is incomplete, the complete question is given below:

A committee of eight people must choose a president, a vice president, and a secretary.

Two of the committee members are Ellen and Jose. Assume the assignments are made at random. What is the probability that Jose is president and Ellen is vice president?

Answer:

[tex]y = - 5x - 4[/tex]

Step-by-step explanation:

[tex] - 9 = - 5(1) + b[/tex]

[tex] - 9 = - 5 + b[/tex]

[tex]b = - 4[/tex]

[tex]y = - 5x - 4[/tex]

Answer: 40 degrees

Step-by-step explanation:

There are 9 sides in a nonagon and 360 degrees make the shape up.

360 degrees divided by  9 EQUAL SIDES of a nonagon = 40 degrees

Answer:

(x,y) = (-5,-8)

Answer:

Step-by-step explanation:3x+7=x-3. 3x-x=-3-7. 2x=-10. X=-5. but y=x-3. So. Y=-5-3=-8

The equation whigh relates x and y points along the incline is: y = 2x - 3

We know that the general form of a slope - intercept form of equation of line is :

y = mx + c

m = slope

and c = y-intercept

We know that slope is nothing but angle of incline.

From figure we can observe that the line passes through points (3, 3) and (6, 9)

Using the formula of slope,

m = (9 - 3) / (6 - 3)

m =  6/3

m = 2

So the equation of line would be

y = 2x + c

As line passes though point (3, 3),

3 = 2(3) + c

3 = 6 + c

c = - 3

So, the equation that relates x and y for points along the incline is:

y = 2x - 3

Learn more about an equation here:

https://brainly.com/question/28243079

#SPJ4

The complete question is:

All three points displayed are on the line. you'll need to write an equation that relates x and y for points along the incline. what is this equation?

Answer:

Step-by-step explanation:

when i got it it was d

The answer option to the above question is The 3 ordered pairs are B, (4,10),(4,11),(4,12).

In this context, the word "equation" refers to the equation of the line that best fits a certain set of data points. A straight line that most accurately depicts the trend or pattern in a collection of data points is called the line of best fit. Predictions or estimations for additional data points that might not be a part of the initial set can be made using the equation of the line of best fit.

According to the given information:

To determine which three ordered pairs are most likely the added data points, we need to consider the slope and y-intercept of the original line of best fit. Since the equation of the line of best fit remains unchanged, the new points must lie on the original line.

The original line of best fit can be determined using a linear regression algorithm. However, we can estimate the slope and y-intercept of the line by simply finding the coordinates of two points on the line.

We can use the first and last points in the original set of data to estimate the slope and y-intercept. Using these points, we find that the equation of the line of best fit is:

y = -0.84x + 10.8

Now we can check which of the given sets of points lie on this line:

A: (4,4), (5,5), (6,6)

For (4,4), y = -0.84(4) + 10.8 = 7.56, which is not equal to 4. So (4,4) is not on the line.

Similarly, (5,5) and (6,6) are not on the line.

Therefore, A is not the correct answer.

B: (4,10),(4,11),(4,12)

For (4,10), y = -0.84(4) + 10.8 = 7.56, which is equal to 10. So (4,10) is on the line.

Similarly, (4,11) and (4,12) are also on the line.

Therefore, B is a possible answer.

C: (8,9),(8,10),(8,11)

For (8,9), y = -0.84(8) + 10.8 = 4.32, which is not equal to 9. So (8,9) is not on the line.

Similarly, (8,10) and (8,11) are not on the line.

Therefore, C is not the correct answer.

D: (10,10),(10,11),(10,12)

For (10,10), y = -0.84(10) + 10.8 = 3.96, which is not equal to 10. So (10,10) is not on the line.

Similarly, (10,11) and (10,12) are not on the line.

Therefore, D is not the correct answer.

Therefore, the answer is B, (4,10),(4,11),(4,12).

To know more about equation:

https://brainly.com/question/29657983

#SPJ1

Answer:

20cm

Step-by-step explanation:

90cm ÷ 1/2 the length 90 = 20cm

Answer:

experimental probability approaches theoretical probability when the sample size is large.

Step-by-step explanation:

This illustrates that experimental probability approaches theoretical probability when the sample size is large. As the number of tosses increases, the experimental probability of both coins being heads for both Deena and Jackson approaches the theoretical probability of 1/4 (since the probability of getting heads on a single coin toss is 1/2, and the probability of getting heads on two coin tosses is (1/2) * (1/2) = 1/4). This is because the law of large numbers states that as the sample size increases, the experimental probability approaches the theoretical probability. Therefore, the more tosses that are performed, the closer the experimental probability will be to the theoretical probability.

I remember doing this but I don’t seem to remember

The equation of the line passing through the two given points in slope-intercept form is: y = (-5 / 6)x - 1/6

To find the equation of the line passing through the two given points (–6, 1) and (6, –9) in slope-intercept form, we need to first find the slope of the line.

The slope of a line passing through two points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is given by:

[tex]m = (y_2 - y_1) / (x_2 - x_1)[/tex]

Substituting the values of the given points, we get:

m = (-9 - 1) / (6 - (-6))

m = -10 / 12

m = -5 / 6

Now that we know the slope of the line, we can use the point-slope form of the equation of a line to find its slope-intercept form. The point-slope form of a line passing through a point [tex](x_1, y_1)[/tex] with slope m is given by:

[tex]y - y_1 = m(x - x_1)[/tex]

Substituting the values of the slope and one of the given points (–6, 1), we get:

y - 1 = (-5 / 6)(x - (-6))

y - 1 = (-5 / 6)(x + 6)

Simplifying this equation, we get:

y = (-5 / 6)x - 1/6

Therefore, the equation of the line passing through the two given points in slope-intercept form is: y = (-5 / 6)x - 1/6

Learn more about slope-intercept :

https://brainly.com/question/29146348

#SPJ1

The quadratic equation 2x^2 - x + 10 = 0 can be solved using the quadratic formula, which is:

x = [-b ± sqrt(b^2 - 4ac)] / 2a

Here, a = 2, b = -1, and c = 10. Substituting these values, we get:

x = [-(-1) ± sqrt((-1)^2 - 4(2)(10))] / 2(2)

x = [1 ± sqrt(1 - 80)] / 4

x = [1 ± sqrt(-79)] / 4

Since the square root of a negative number is not a real number, there are no real solutions to this equation. Therefore, the answer is "No solution".

The total area of the rectangle and square joined together is 27 cm².

First, let's find the area of the rectangle. The formula for the area of a rectangle is A = L x W, where A is the area, L is the length, and W is the width.

In this case, the length of the rectangle is 6 cm and the width is equal to the length of the square, which is also 3 cm. So, the area of the rectangle is:

A = 6 cm x 3 cm

A = 18 cm^2

Now let's find the area of the square. The formula for the area of a square is A = s^2, where A is the area and s is the length of a side.

In this case, the length of the side of the square is also 3 cm. So, the area of the square is:

A = 3 cm x 3 cm

A = 9 cm^2

To find the total area of the rectangle and square joined together, we simply add the two areas together:

Total area = area of rectangle + area of square

Total area = 18 cm^2 + 9 cm^2

Total area = 27 cm^2

Learn more about area here: https://brainly.com/question/25292087

#SPJ1

To convert 1/5 to a decimal number by long division, we divide 1 by 5 and keep adding 0s to the dividend until we have enough decimal places and 1/5 as a decimal number is 0.2.

0.2 | 1.0000

   |-------

   | 0

   |----

     1

So, 1/5 as a decimal number is 0.2.

Part O:

If we keep repeating the division process in part N, we will get the same result of 0.2 because 1/5 has a finite decimal representation.

Part P:

From the three long-division calculations we have completed, we can conclude that the quotient, or result, from the long-division process can either end or continue indefinitely.

In part N, we found that 1/5 has a finite decimal representation, so the long division process ended.

However, for other fractions, such as 1/3, the long division process will continue indefinitely because the quotient has a repeating pattern of digits.

Read more about long division here:

https://brainly.com/question/25289437

#SPJ1

The measure of the angle of elevation is 58°( nearest degree)

The angle of elevation is an angle that is formed between the horizontal line and the line of sight. If the line of sight is upward from the horizontal line, then the angle formed is an angle of elevation.

The height of the pole will represent the opposite to the angle of elevation and the length of the shade will be the adjascent to the angle of elevation.

Represent the angle of elevation by x

Tan x = opp/adj

Tan x = 8/5

Tan x = 1.6

x = tan^-1(1.6)

x = 58° ( nearest degree)

learn more about angle of elevation from

https://brainly.com/question/88158

#SPJ1

Thus, the angle of depression from the plane to the building is found as:

Ф = 27.90°.

The angle of depression is indeed the angle formed by a line drawn from the observer's line of sight down to an object below it.

It is frequently used in navigating, surveying, and trigonometry to describe its position of an object in relation to an observer's point of view. Degrees are used to express the depression's angle.

Give data:

Let the height  h = 420 ft.

Let the distance x = 896 ft.

angle of depression is found using the trigonometric formula:

tan Ф = height/distance

tan Ф = h/x

tan Ф = 420/896

tan Ф = 0.46875

Ф = tan⁻¹(0.46875)

Ф = 27.90°.

Thus, the angle of depression from the plane to the building is found as:

Ф = 27.90°.

Know more about the angle of depression

https://brainly.com/question/17193804

#SPJ1

A sufficient estimator is the distributions of exponential.The correct answer to this question is (c) exponential.

An estimator is a rule or procedure that is used to determine an estimate of a parameter based on observed data. A statistic is used to estimate a parameter, and it is computed from the observed data. An estimator is a random variable that computes a statistic from the data.

The following distributions have a sufficient estimator:

Poisson Distribution with parameters λ and x is a Poisson distribution.

The rate of the occurrence is λ.

Exponential Distribution with parameters λ and x is an exponential distribution.

The mean waiting time is 1/λ.

Bernoulli The Bernoulli distribution is not sufficient for an estimator, but the binomial distribution, which generalizes the Bernoulli distribution, is. In the context of the binomial distribution, p is a parameter Exponential

The exponential distribution is a continuous probability distribution that describes the time between events in a Poisson process, such as the amount of time until the next vehicle arrives at a traffic intersection or the amount of time a particular component lasts in a manufacturing process.

for such more question on estimator

https://brainly.com/question/31141387

#SPJ11

Answer:

  40 seconds

Step-by-step explanation:

You have a Ferris wheel such that the height of a rider is modeled by d=30sin(πt/20)+15, and you want to know the time it takes for one revolution.

The sine function has a period of 2π. The value of the function when the argument is 2π is the same as when it is zero. The period is the time difference between those argument values. Since the argument is 0 when t=0, we only need to find the value of t that makes the argument 2π:

  2π = πt/20

  40 = t . . . . . . . multiply by 20/π

The Ferris wheel makes one revolution in 40 seconds.

The critical value t for constructing a 99% confidence interval for a  with 11 degrees of freedom is approximately 3.106.

A t-distribution table is a table of values that shows the critical values for the t-distribution, which is a probability distribution used in statistics.

The table is typically organized by degrees of freedom and the level of significance (α) for a two-tailed test.

To find the critical value t* for a 99% confidence interval for a mean with 11 degrees of freedom, we can use a t-distribution table or a calculator.

Using a t-distribution table, we can find the critical value that corresponds to a 99% confidence level and 11 degrees of freedom.

The table shows that the critical value is approximately 3.106.

Alternatively, we can use a calculator that has a t-distribution function.

For example, using the function (0.005, 11) in Microsoft Excel will give us the same result of approximately 3.106.

To know more about critical value visit:

https://brainly.com/question/29095707

#SPJ1

Therefore, each bus can hold 22 students if there were 12 students per van.

In mathematics, an equation is a statement that asserts the equality of two expressions. Equations typically contain one or more variables, which are symbols that can represent different values. Solving an equation means finding the value or values of the variable(s) that make the equation true.

Here,

a) Let V be the number of vans and B be the number of buses. We know that there were 8 vans and 12 buses, so we can write:

V + B = 20 (the total number of vehicles)

We also know that there were 360 students in total. If we assume that each van can hold 12 students, and each bus can hold some number of students, we can write:

12V + bB = 360 (the total number of students)

where b is the number of students that each bus can hold.

b) We can use the equation we derived in part a) and substitute V = 8 to solve for B:

V + B = 20

8 + B = 20

B = 12

So there were 12 buses in total. We can then use the equation 12V + bB = 360 and substitute V = 8 and B = 12 to solve for b:

12V + bB = 360

12(8) + b(12) = 360

96 + 12b = 360

12b = 264

b = 22

To know more about equation,

https://brainly.com/question/28243079

#SPJ1

The answer of the given question based on Quadrilateral ABCD is inscribed in the circle on finding the measure of the angle ∠B is  70°.

A quadrilateral is a geometric shape that consists of four straight sides, connected end-to-end to form a closed figure. Examples of the quadrilaterals are rectangles, squares, parallelograms, trapezoids, and rhombuses. In a quadrilateral, the interior angles add up to 360° degrees. Quadrilaterals can have opposite sides parallel (as in parallelograms) or opposite sides equal in length (as in kites). They are widely used in geometry and mathematics in general.

In a circle, the opposite angles of a quadrilateral inscribed in the circle are supplementary. Therefore, we have:

m∠B + m∠D = 180°

We are given that B = (4x - 20)°, so we can substitute this into the equation above and solve for x:

m∠B + m∠D = 180°

(4x - 20)° + 115° = 180° (Note that m∠D is given as 115° in the diagram)

4x - 20 + 115 = 180

4x + 95 = 180

4x = 85

x = 21.25

Now that we know x, we can find the measure of angle ∠B:

m∠B = 4x - 20°

m∠B = 4(21.25) - 20°

m∠B = 70°

Therefore, the measure of angle ∠B is 70°.

To know more about Equation visit:

https://brainly.com/question/9312365

#SPJ1

The scale factor of the two rectangles show a common ratio of 4/5

A scale factor in geometry is a ratio that indicates how much a figure has been extended or shrunk.

When two figures are comparable, the scale factor is the ratio of any matching lengths in the two figures.

A scale factor of higher than 1 indicates expansion, whereas a scale factor of less than 1 indicates decrease. The figure is the same size as the original when the scale factor is 1.

The dimensions of comparable figures can be calculated using scale factors. For instance, we can use the scale factor to determine the length of the corresponding side of the smaller rectangle if we know the scale factor between two identical rectangles and the length of one of its sides of the larger rectangle.

In the given figure;

12/15 = 36/45

Let's find the ratio here;

4/5 =4/5

The scale factor is 4/5

Learn more on scale factor here;

https://brainly.com/question/10891847

#SPJ1

Answer:

The expression you use to find the amount of miles would be 5xT=X miles.

or 5t

The sum that shows how many concert tickets were sold using the given parameters is: ²/₅x + 60

Algebraic expressions are defined as the simple idea of expressing numbers with the aid of letters or alphabets without even specifying their actual values.

Let the total number of tickets available for sale be denoted as x.

We are told that 100 tickets were sold last week. Thus:

Amount of tickets left unsold = (x - 100)

We are now told that 2/5 of the remaining tickets were sold this week. Thus:

Number of tickets sold this week = ²/₅(x - 100)

Thus:

Total Number of Tickets sold = 100 + ²/₅(x - 100)

= 100 + ²/₅x - 40

= ²/₅x + 60

Read more about Algebraic Expressions at: https://brainly.com/question/4344214

#SPJ1

which is approximately 3.864 times the length of QS.the circle is approximately 4 times the length of QS, or approximately 4 times 0.966 times the length of QS,

An angle is a measure of the amount of turn between two lines or rays that meet at a common point, known as the vertex of the angle. The angle is typically measured in degrees or radians. In a Euclidean plane, an angle can range from 0 degrees (corresponding to two lines that are parallel to each other) to 180 degrees (corresponding to two lines that form a straight line). An angle greater than 180 degrees is called a reflex angle. Angles are used in many areas of mathematics and physics, such as geometry, trigonometry, and calculus, as well as in real-world applications such as navigation, architecture, and engineering.

by the question.

The ratio of the central angle ZQTS to the whole circle is 1/12, or 0.0833 (rounded to four decimal places). This is because there are 360 degrees in a circle, and 75 is 1/12 of 360.

QS represents 1/4 of the circle's circumference. This is because the central angle ZQTS is 75 degrees, which is 1/3 of a right angle (90 degrees). An inscribed angle that intercepts the same arc as a 1/3 angle will have twice the measure of the 1/3 angle, or 150 degrees. Thus, angle QTS is 150 degrees. Angle QOS is also 150 degrees, since it intercepts the same arc as QTS. Therefore, angle QOT is 60 degrees, since the angles in triangle QOT add up to 180 degrees. Since triangle QOT is an equilateral triangle, QT and QS are equal in length, and angle QTS is 75 degrees, we can use the sine function to find the length of QS. The sine of 75 degrees is approximately 0.966, so QS represents approximately 0.966 times the circumference of the circle. Since QS represents 1/4 of the circumference, the circumference of the circle is approximately 4 times the length of QS, or approximately 4 times 0.966 times the length of QS,

To learn more about circumference:

https://brainly.com/question/28757341

#SPJ1

The best description of the roots of the equation [tex]x^2 - 4x + 4 = 0[/tex]  is that it has two equal or identical real roots.

Identical real roots are solutions to a quadratic equation in which both roots have the same value. In other words, if a quadratic equation has identical real roots, it means that there is only one solution to the equation, and that solution is repeated twice.

To use the discriminant to describe the roots of equation [tex]x^2 - 4x + 4 = 0[/tex] we need to first identify the coefficients of the quadratic equation:

[tex]a = 1\\b = -4\\c = 4[/tex]

The discriminant is given by the expression [tex]b^2 - 4ac[/tex].  Substituting the values of a, b, and c, we get:

[tex]b^2 - 4ac\\ = (-4)^2 - 4(1)(4)\\ = 16 - 16 = 0[/tex]

Since the discriminant is equal to zero, this tells us that the quadratic equation has two equal roots. In other words, the equation has a single root with a multiplicity of two.

The best description of the roots of equation x^2 - 4x + 4 = 0 is that it has two equal or identical real roots.

To know more about identical real roots visit:

brainly.com/question/13580012

#SPJ1

An equation that can be used to find the lightest and heaviest acceptable weights, x, for the filled canister include the following: B. |x − 42| = 0.9.

In Mathematics, an absolute value function is a type of function that is composed of an algebraic expression, which is placed within absolute value symbols and measures the distance of a point on the x-coordinate to the x-origin (0) of a cartesian coordinate (graph).

Mathematically, an absolute value function can be represented by the following mathematical equation:

|x| = x, x ≥ 0.

|x| = x, x < 0.

Based on the information provided about the desired weight of the canister and the popcorn, an equation that models the situation is given by;

|x − 42| = 0.9.

Read more on absolute value function here: brainly.com/question/28308900

#SPJ1

Keelin's hourly rate increased by 7.89%. To calculate the percentage increase in Keelin's hourly rate, we need to determine the difference between the new and old rates and express that difference as a percentage of the old rate.

First, we find the difference between the two rates:

$10.25 - $9.50 = $0.75

This means that Keelin's hourly rate increased by $0.75 per hour.

Next, we need to express this increase as a percentage of the old rate:

($0.75 / $9.50) x 100% = 7.89%

Therefore, Keelin's hourly rate increased by 7.89%.

A percent increase is a measure of the increase in a quantity compared to the original value. In this case, the original value is Keelin's hourly rate of $9.50, and the new value is $10.25. The percentage increase is calculated by finding the difference between the new and old values and expressing that difference as a percentage of the original value.

A percentage increase is useful in analyzing changes over time or comparing changes in different variables. In this case, knowing the percentage increase in Keelin's hourly rate can help her understand how much her pay has increased and plan for future financial goals. It can also be helpful for an employer to calculate percentage increases in employee salaries when determining raises or promotions.

To know more about Keelin's hourly rate,  click here:

brainly.com/question/19454366

#SPJ4