Answer:
C) English
Step-by-step explanation:
I don't really know how to explain it, so I'll show you instead.
For science, there are 6 of 6 correct answers with a 0.5 chance of answering correctly.
So,
0.5 x 0.5 x 0.5 x 0.5 x 0.5 x 0.5 = 0.016
For English, there are 4 of 4 correct answers with a 0.25 chance of answering correctly.
So,
0.25 x 0.25 x 0.25 x 0.25 = 0.004
They will have to study English (0.004) because it is lower than science (0.016).
The trapezoidal approximation will be the average of the left- and right-endpoint approximations.
Let's consider a simple example of estimating the value of a general definite integral,

Split up the interval
![[a,b]](https://tex.z-dn.net/?f=%5Ba%2Cb%5D)
into

equal subintervals,
![[x_0,x_1]\cup[x_1,x_2]\cup\cdots\cup[x_{n-2},x_{n-1}]\cup[x_{n-1},x_n]](https://tex.z-dn.net/?f=%5Bx_0%2Cx_1%5D%5Ccup%5Bx_1%2Cx_2%5D%5Ccup%5Ccdots%5Ccup%5Bx_%7Bn-2%7D%2Cx_%7Bn-1%7D%5D%5Ccup%5Bx_%7Bn-1%7D%2Cx_n%5D)
where

and

. Each subinterval has measure (width)

.
Now denote the left- and right-endpoint approximations by

and

, respectively. The left-endpoint approximation consists of rectangles whose heights are determined by the left-endpoints of each subinterval. These are

. Meanwhile, the right-endpoint approximation involves rectangles with heights determined by the right endpoints,

.
So, you have


Now let

denote the trapezoidal approximation. The area of each trapezoidal subdivision is given by the product of each subinterval's width and the average of the heights given by the endpoints of each subinterval. That is,

Factoring out

and regrouping the terms, you have

which is equivalent to

and is the average of

and

.
So the trapezoidal approximation for your problem should be
Answer: b
Explanation:
The line of best fit to a scattergram is obtained in linear regression analysis by minimizing the sum of the squared errors.
For example, in the diagram shown below, there are n data points in the scattergram.
The error for the i-th data point is

.
The coefficients (a and b) for the line of best fit are determined using calculus, to minimize

.
The production of health drink cans at a warehouse can be represented by the equation below, where x represents the hours of production, and y the total supply of items in the warehouse, in hundreds.
Which of the following graphs represents this situation?
the equation is y= 3/5x+2
I drew the graph.
3/5 is the slope, and 2 is the y-intercept. So you start at (0,2), and go up 3 units, then right 5.
---
hope it helps
Answer:
A 3x^12 - 2x^8 + x^5
Step-by-step explanation:
Degree of a polynomial:
The degree of a polynomial is given by the highest exponent of x.
In this question:
Option A: 12th degree
Option B: 1st degree
Option C: 3rd degree
Option D: 3rd degree
So the answer is given by option A.