MATHEMATICS COLLEGE

Identify the recursive formula for the sequence 900, 850, 800, 750,…

Answers

Answer 1

Answer:

The recursive formula for the given sequence as required in the task content is; f(n) = f (n - 1) - 50.

What is the recursive formula for the given sequence?

It follows from the task content that the recursive formula for the given sequence is to be determined.

By observation, the sequence is an arithmetic progression and the common difference, d can be evaluated as;

d = 750 - 800 = 800 - 850 = 850 - 900 = -50

Also, since the recursive formula for an arithmetic sequence takes the form;

f(n) = f (n - 1) + d.

Hence, since the recursive formula as required is;

f(n) = f (n - 1) - 50.

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A certain analytical method for the determination of lead yields masses for lead that are low by 0.5 g. Calculate the percent relative error caused by this deviation for each measured mass of lead. Report the percent relative error with the correct number of significant figures.

Sin2x/1+cos2x=tanx
How do I prove this with the double angle law

Answers

$sin(2x) = 2 sin x cos x \n \n cos(2x) = cos^2 x - sin^2 x$
After Substituting:
$(2 sin x cos x)/(1+cos^2 x - sin^2 x)$
Use pythagorean thm:
$1 - sin^2 x = cos^2 x$
......................
$(2 sin x cos x)/(2cos^2 x) \n \n = (sinx )/(cos x) \n \n = tan x$

the perimeter of a triangle is 47.678cm two of the sides have lengths of 15.463cm and 11.34cm what is the length of the other side?

Answers

Answer:

20.875

Step-by-step explanation:

47.678-(15.463+11.34) =20.875

20.875 is the answer

What are the factors of the product represented below?TILES
A. (2x2 + 1)(3x2 + 1)
+
B. (5x + 1)(x+1)
C. (2x + 1)(3x + 1)
O D. (3x + 1)(2x+2)

Answers

Answer:

Step-by-step explanation:

The top is 2x + 1 and the left is 3x + 1

Answer:

The top is 2x + 1 and the left is 3x + 1

Problem 8-19 Because of high tuition costs at state and private universities, enrollments at community colleges have increased dramatically in recent years. The following data show the enrollment (in thousands) for Jefferson Community College for the nine most recent years. Click on the datafile logo to reference the data. Year Period (t) Enrollment (1,000s) 1 1 6.5 2 2 8.1 3 3 8.4 4 4 10.2 5 5 12.5 6 6 13.3 7 7 13.7 8 8 17.2 9 9 18.1 Use simple linear regression analysis to find the parameters for the line that minimizes MSE for this time series.If required, round your answers to two decimal places.
y-intercept, b0 = 4.7.17
Slope, b1 = 1.46
MSE = ???????? NEED THIS
What is the forecast for year 10? 19.283
Round your interim computations and final answer to two decimal places.

Answers

Answer:

a) find the attached graph

b) find the attachment no 4 and 5

c) $T_(10)= 4.72+1.46(10) = 19.28$

Step-by-step explanation:

a) A trend pattern exist if the time series plot gradually shifts to higher or lower values over a long period of time

find the attached graph

b) Liner Trend Equation

$T_(1) =b_(0) +b_(1)t$

Where $T_(1)$ is the linear trend forecast in period t , $b_(0)$ is the intercept of the linear trend time, $b_(1)$ is the slope of the linear trend line, t is the time period

now computing the slope and intercept

formula is attached ( 3 no attachment)

$Y_(t)$ is the value of the time series in period t, n is the number of time periods

Y(bar) is the average value and t(bar) is the average value of t

due to unavailability of equation in math-script i attached the calculation part of this question( 4th and 5th no attachment)

thus the linear trend equation is $T_(t)= 4.72+1.46t$ (1)

$T_(10)= 4.72+1.46(10) = 19.28$

Final answer:

To find the Mean Squared Error (MSE), you can calculate the difference between the actual and predicted values, square these differences, and find their average. To forecast for a specific year, you can insert the year as the 'x' value into the simple linear regression equation.

Explanation:

The question is asking for the Mean Squared Error (MSE) for a simple linear regression model based on the enrollment data of Jefferson Community College. This involves using the y-intercept (b0) and slope (b1) values provided, and the given data points. You can calculate the MSE by taking the difference between the actual and predicted values (errors), squaring these differences, and then finding the average of these squared differences for the entire dataset.

Then, to forecast for year 10, you use the simple linear regression model equation, y = b0 + b1*x, where y represents the predicted enrollment. So, for year 10, you would insert 10 as your 'x' value into the equation, which results in the forecast value provided which is 19.283.

Learn more about Simple Linear Regression here:

brainly.com/question/33168340

#SPJ12

Evaluate the given integral by changing to polar coordinates. sin(x2 y2) dA R , where R is the region in the first quadrant between the circles with center the origin and radii 2 and 4

Answers

Answer:

I = 1.47001

Step-by-step explanation:

we have the function

$f(x,y)=sin(x^2y^2)\n$

In polar coordinates we have

$x=rcos\theta\ny=rsin\theta$

and dA is given by

$dA=rdrd\theta$

Hence, the integral that we have to solve is

$I=\int \limt_2^4 \int \limit_0^(\pi /2)sin(r^4cos^2\theta sin^2\theta)rdrd\theta$

This integral can be solved in a convenient program of your choice (it is very difficult to solve in an analytical way, I use Wolfram Alpha on line)

I = 1.47001

Hope this helps!!!

Solve for x Write both solutions, seperated by a comma 4x^2+5x+1=0

Answers

Answer:

-1/4 , -1

Step-by-step explanation:

I solved it using Factorization method and Quadratic Equation .

Factorization Method

$4x^2+5x+1=0\nWrite +5x- as- a -difference(write+5x-using- two- numbers -in-which-their-sum-is ; 5-and-their-product-is ; 4)\n4x^(2) +4x+1x+1=0\nFactorize-out-common-terms\n4x(x+1)+1(x+1)=0\nFactor-out-(x+1)\n(4x+1)(x+1)=0\n4x+1 =0 \nx+1=0\n4x=0-1\nx =0-1\n4x =-1\nx =-1\n4x=-(1)/(4) \n\nAnswer = -1/4 , -1$

Quadratic Equation

$4x^2+5x+1=0\na = 4\nb =5\nc = 1\n\nx =(-b\±√(b^2 -4ac) )/(2a) \n\nx = (-(5)\±√((5)^2-4(4)(1)) )/(2(4)) \n\nx = (-5\±√(25-16) )/(8) \n\nx = (-5\±√(9) )/(8) \n\nx = (-5\±3)/(8) \n\nx =(-5+3)/(8) \n\nx = (-5-3)/(8) \n\nx = (-2)/(8) \n\nx = (-8)/(8) \n\nx = -(1)/(4) \nx=-1$

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