Rite an inequality for the phrase ''two more than three times a number is at most 53.''

Maurinko [17]

In linear algebra, the rank of a matrix

A

A is the dimension of the vector space generated (or spanned) by its columns.[1] This corresponds to the maximal number of linearly independent columns of

A

A. This, in turn, is identical to the dimension of the vector space spanned by its rows.[2] Rank is thus a measure of the "nondegenerateness" of the system of linear equations and linear transformation encoded by

A

A. There are multiple equivalent definitions of rank. A matrix's rank is one of its most fundamental characteristics.

The rank is commonly denoted by

rank

⁡

(

A

)

{\displaystyle \operatorname {rank} (A)} or

rk

⁡

(

A

)

{\displaystyle \operatorname {rk} (A)}; sometimes the parentheses are not written, as in

rank

⁡

A

{\displaystyle \operatorname {rank} A}.

4 0

3 years ago

8,-67, -99, -91, -59, -81, 46<br> find the average of the following set of integers

konstantin123 [22]

Answer:

The average is -49.

Step-by-step explanation:

You add all numbers and then divide by the numbers that your adding:

8+-67+-99+-91+-59+-81+46= -252

-252/7= -49

7 0

3 years ago

A jury pool consists of 50 potential jurors and how many ways can a jury of 12 be selected

bija089 [108]

Solution:

we are given that

A jury pool consists of 50 potential jurors.

Wee have been asked to find the number of ways can a jury of 12 be selected.

As we know from the concept of combination that r person can be selected out of n in ncr ways. where

$n_C_r=\frac{n!}{r!(n-r)!}$

Now substitute the values we get

${50}_C_{12}=\frac{50!}{12!(50-12)!}\\
\\
{50}_C_{12}=\frac{50!}{12!38!}\\
\\
{50}_C_{12}=121399651100\\$

Hence the required number of ways is 121399651100

5 0

3 years ago

A science test, which is worth 100 points, consists of 24 questions. Each question is worth either 3 points or 5 points. If x is

Brilliant_brown [7]

The solution to the system of equations is (x, y) = (10, 14), where x is the number of 3-point questions and y is the number of 5-point questions. The appropriate choice is ...
The test contains 10 three-point questions and 14 five-point questions. (2nd selection)

6 0

3 years ago

Two integers, a and b, have a product of 36. What is the least possible sum of a and b?

Minchanka [31]

<h3>Answer: 12</h3>

==============================================================

Explanation:

The two integers multiply to 36, so,

ab = 36

which solves to

a = 36/b

Then we want to add the numbers such that we get the smallest possible result.

a+b = (36/b)+b

So we want (36/b)+b to be as small as possible.

Let's say we replace b with x and we consider this function

f(x) = (36/x) + x

The goal is to find when f(x) is smallest, ie, we want to minimize the function.

If we were to graph out the function, we get the curve shown below.

To make things easier, we'll only focus on positive values of x.

The lowest part of the curve is what we're after. Using the "minimum" function/feature on the graphing calculator, we would then find the lowest point occurs at (6,12). This point is considered a local minimum because it's the lowest point in that given neighborhood of x values.

So the input x = 6 leads to the smallest output f(x) = 12.

This in turn means b = 6 is going to pair with a = 36/b = 36/6 = 6.

In short, a = 6 and b = 6.

----------------------

As a check,

a*b = 6*6 = 36

a+b = 6+6 = 12

We can make a table of various values to help confirm that 12 is the smallest sum.

Side note: If you're not allowed to use a graphing calculator, then you'll need to use calculus.

8 0

2 years ago