Answer:
Step-by-step explanation:
The first differences of the sequence are ...
- 5-2 = 3
- 10-5 = 5
- 17-10 = 7
- 26-17 = 9
- 37-26 = 11
Second differences are ...
- 5 -3 = 2
- 7 -5 = 2
- 9 -7 = 2
- 11 -9 = 2
The second differences are constant, so the sequence can be described by a second-degree polynomial.
We can write and solve three equations for the coefficients of the polynomial. Let's define the polynomial for the sequence as ...
f(n) = an^2 + bn + c
Then the first three terms of the sequence are ...
- f(1) = 2 = a·1^2 + b·1 + c
- f(2) = 5 = a·2^2 +b·2 + c
- f(3) = 10 = a·3^2 +b·3 +c
Subtracting the first equation from the other two gives ...
3a +b = 3
8a +2b = 8
Subtracting the first of these from half the second gives ...
(4a +b) -(3a +b) = (4) -(3)
a = 1 . . . . . simplify
Substituting into the first of the 2-term equations, we get ...
3·1 +b = 3
b = 0
And substituting the values for a and b into the equation for f(1), we have ...
1·1 + 0 + c = 2
c = 1
So, the formula for the sequence is ...
f(n) = n^2 + 1
__
The 20th term is f(20):
f(20) = 20^2 +1 = 401
_____
<em>Comment on the solution</em>
It looks like this matches the solution of the "worked example" on your problem page.
Answer:
(a) The probability that a single randomly selected value lies between 158.6 and 159.2 is 0.004.
(b) The probability that a sample mean is between 158.6 and 159.2 is 0.0411.
Step-by-step explanation:
Let the random variable <em>X</em> follow a Normal distribution with parameters <em>μ</em> = 155.4 and <em>σ</em> = 49.5.
(a)
Compute the probability that a single randomly selected value lies between 158.6 and 159.2 as follows:
*Use a standard normal table.
Thus, the probability that a single randomly selected value lies between 158.6 and 159.2 is 0.004.
(b)
A sample of <em>n</em> = 246 is selected.
Compute the probability that a sample mean is between 158.6 and 159.2 as follows:
*Use a standard normal table.
Thus, the probability that a sample mean is between 158.6 and 159.2 is 0.0411.
(For question 1 you have to do it yourself, get a ruler and measure the actual length of the drawing, then multiply it by 8 to get the actual dimensions in the exercise. )
Example, if you measure 4 inches, the actual dimension will be 4 x 8 = 32 ft
2. (Scale drawing 1:5 is that every 1 (length units) will be equal to 5(length units) in the actual dimensions)
Model : 3ft ; 7m
Actual : 15ft ; 35m (corresponding)
Actual : 20yd ; 12.5 cm
Model : 4yd ; 2.5 cm
6. 1.5 ft = 1.5 x 12 = 18 inches.
The model is 3 inches, and the actual rose is 18 inches -> The scale of the drawing is 6. (enlargement)
Same goes to the scale factor, but this time is the quotient of the corresponding side -> 3 : 18 = 1:6.
(If I got any parts wrong just tell me, I actually kinda forgot these kind of stuff)
Answer:
398,765 books were sold
Step-by-step explanation:
How to get the answer:
1) Identify the given
32,300 is percentage
8.1 % is rate
base (b) is missing
2) Solve
b= p/r
b= 32,300 / 8.1% or 0.081
b= 398,765
3) Check
398,765 x 8.1% = 32,299.97 or 32,300
Answer:
f(-1) = 15
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
<u>Algebra I</u>
- Functions
- Function Notation
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify</em>
f(x) = 5(2 - x)
<u>Step 2: Evaluate</u>
- Substitute in <em>x</em> [Function f(x)]: f(-1) = 5(2 - -1)
- (Parenthesis) Subtract: f(-1) = 5(3)
- Multiply: f(-1) = 15
