Compute the standard deviation of the data set. Round to the nearest hundredth, if needed.

Proof by mathematical induction

Ghella [55]

Answer:

See below.

Step-by-step explanation:

I will assume that 3n is the last term.

First let n = k, then:

Sum ( k terms) = 7k^2 + 3k

Now, the sum of k+1 terms = 7k^2 + 3k + (k+1) th term

= 7k^2 + 3k + 14(k + 1) - 4

= 7k^2 + 17k + 10

Now 7(k + 1)^2 = 7k^2 +14 k + 7 so

7k^2 + 17k + 10

= 7(k + 1)^2 + 3k + 3

= 7(k + 1)^2 + 3(k + 1)

Which is the formula for the Sum of k terms with the k replaced by k + 1.

Therefore we can say if the sum formula is true for k terms then it is also true for (k + 1) terms.

But the formula is true for 1 term because 7(1)^2 + 3(1) = 10 .

So it must also be true for all subsequent( 2,3 etc) terms.

This completes the proof.

5 0

3 years ago

Choose the point-slope form of the equation of this line.

igor_vitrenko [27]

Answer:

y= -5x +7

Step-by-step explanation:

We can see points on the graph:

(2, -3) and (3, -8)

The function in general form is:

y= mx+b

Let's find the slope and y-intercept as per identified points on the graph:

m= (y1-y1)/(x2-x1)

m= (-8+3)/(3-2)= -5

b= y- mx

b= - 3 -(-5)*2= -3 +10= 7

Based on the found values of m and b, the given line is:

y= -5x +7

4 0

3 years ago

Read 2 more answers

What is the simple interest on $2500 invested at an interest rate of 6% for 2 years?

Brrunno [24]

Answer:

The simple interest is $300.

Step-by-step explanation:

Find the Interest amount.

I: Interest ?

P: Principle Amount $2500

R: Rate 6% = .06

T: Time Period (in years) 2 Years

Convert into equation to find Simple Interest

I = Prt

I = (2500)(.06)(2)

Calculate

I = 300

4 0

3 years ago

Read 2 more answers

What term describes a pair of vertical angles that are also supplementary: acute obtuse right straight?

IgorC [24]

Your answer would be straight!!

7 0

3 years ago

Read 2 more answers

There are 2504 computer science students at a school. Of these, 1876 have taken a course in Java, 999 have taken a course in Lin

Y_Kistochka [10]

Answer:

492

Step-by-step explanation:

As per the given data of the question:

Total number of students = 2504

Number of students in Java (J) = 1876

Number of students in Linux (L) = 999

Number of students in C = 345

J∩L = 876

L∩C = 231

C∩J = 290

L∩J∩C = 189

Now according to Venn-diagram as drawn below:

Number of students haven taken courses in Java and Linux both only

= J∩L - L∩J∩C

= 876 - 189

= 687

Number of students haven taken courses in Java and C both only

= C∩J - L∩J∩C

= 290 - 189

= 101

Number of students haven taken courses in C and Linux both only

= L∩C - L∩J∩C

= 231 - 189

= 42

Therefore,

Number of students only in Java = 1876 - 687 - 189 - 101 = 899

Number of students only in Linux = 999 - 687 - 189 - 42 = 81

Number of students only in C = 345 - 42 - 189 - 101 = 13

So,

Number of students who have not taken a course in any of these three subjects

= 2504 - 899 - 81 - 13 - 687 - 189 -101 - 42

= 492

Hence, the students who have not taken a course in any of these three subjects = 492.

6 0

3 years ago