A machine costs 7500. Its value decreases by 5% every year due to usage. what will be its price after 1 year?

Amir invests $4,000 in a 5-year cd paying 3.5% interest. How much interest will he make on the cd in 5 years? The simple interes

Sholpan [36]

Answer: $700

Step-by-step explanation:

First, convert the rate into a decimal

r = R/100 = 3.5%/100 = 0.035 per year,

then, solving our equation

I = 4000 × 0.035 × 5 = 700

I = $ 700.00

5 0

2 years ago

[ MATLAB] Check some linear algebra rules: Enter the following matrices:

lana66690 [7]

Answer:

Step by step explanation along with Matlab code and output is provided below.

Step-by-step explanation:

We are given three matrices A, B, and C of size 2x2

A = [0 1; 0 0]

B =[1 2; -3 -6]

C =[4 -2; -2 1]

Output:

A = 0 1

0 0

B = 1 2

-3 -6

C = 4 -2

-2 1

Let us first check if the given matrices A, B, and C are singular or not

% the Matlab function det( ) calculates the determinant of a matrix

det_A=det(A)

det_B=det(B)

det_C=det(C)

Output:

det_A = 0

det_B = 3.3307e-16 (its practically zero)

det_C = 0

So the given matrices are singular which means that the determinant of the matrix is zero so inverse of these matrices is not possible.

Rule I:

a1=B*C

Output:

a1 = 0 0

0 0

In Matrix theory, if BC=0 then B=0 or C=0 doesn't hold true

For matrices B*C=0 does not imply that either B or C is zero matrix but rather it implies that at least one of them is singular. In this case we know that both B and C are singular matrices therefore, BC=0

Rule II:

a2=A^2

Output:

a2= 0 0

0 0

In Matrix theory, if A^2=0 then A=0 doesn't hold true

For matrices A^2=0 does not imply that A is zero matrix but rather it implies that A is singular. We already know that A is singular therefore, A^2=0

Rule III:

a3_L=(A+B)^2

a3_R=A^2+2*A*B+B^2

Output:

a3_L = -8 -15

15 27

a3_R = -11 -22

15 30

In Matrix theory, (A + B)^2 = A^2 + 2AB + B^2 doesn't hold true.

(A + B)^2 = A^2 + 2AB + B^2 might hold true if AB = BA, but generally, AB≠BA in matrix algebra.

Rule IV:

a4_L=(A-B)*(A+B)

a4_R=A^2-B^2

Output:

a4_L = 2 3

-15 -27

a4_R = 5 10

-15 -30

In Matrix theory, (A-B)(A+B) = A^2-B^2 doesn't hold true.

Rule V:

a5_L=A*(B+C)

a5_R=A*B+A*C

Output:

a5_L = -5 -5

0 0

a5_R = -5 -5

0 0

In Matrix theory, A(B+C) = AB+AC holds true.

Rule VI:

a6_L=A*(B+C)

a6_R=B*A+C*A

Output:

a6_L = -5 -5

0 0

a6_R = 0 5

0 -5

In Matrix theory, A(B+C) = BA+CA doesn't hold true.

on a side note; (B+C)A = BA+CA holds true

Rule VII:

a7_L=(A*B)^2

a7_R=A^2*B^2

Output:

a7_L = 9 18

0 0

a7_R = 0 0

0 0

In Matrix theory, (AB)^2 =A^2*B^2 doesn't hold true.

(AB)^2 =A^2*B^2 might hold true if and only if BA=AB which is not true in general.

3 0

2 years ago

Consider the function represented by 9x + 3y = 12 with x as the independent variable. How can this function be written using

Viktor [21]

Answer:

f(x) = -3x + 4

Step-by-step explanation:

3y = -9x + 12

y = -3x + 4

3 0

2 years ago

1 (06.06 LC

Anika [276]

The question is incomplete. Here is the complete question.

A cell phone company is interested in the relationship between the number of texts per minute for their customers (y) and customer age. Based on the data collected, the least-squares regression line is $y=3.27+2.14x$ , where x is the number of years by which age exceeds 12. Which of the following statements best describes the meaning of the slope of the least-squares regression line?

a. For each increase in age of 1 year, the estimated number of texts per minute increases by 3.27.

b. For each increase in age of 1 year, the estimated number of texts per minute increases by 2.14.

c. For each increase of one text per minute, there is an estimated increase in age of 3.27 years.

d. For each increase of one text per minute, there is an estimated increase in age of 2.14 years.

e. The slope has no meaning because the units of measure for x and y are not the same.

Answer: b. For each increase in age of 1 year, the estimated number of texts per minute increases by 2.14.

Step-by-step explanation: The least-squares regression is a method of fitness, i.e., it fits a data set of number into an equation.

In this case, the relationship between number of texts per minute and customer age is given by a line equation:

$y=3.27+2.14x$

in which, y represents the number of texts per minute and x is the age.

In a line equation, slope is the measure of steepness, i.e., how inclined the line is.

In the least squares regression line, slope is 2.14 and it means, in each additional year, the number of texts increase by a factor of 2.14, which is the correct alternative.

5 0

2 years ago

Verify the identity sec^2(x)tan^2(x)+sec^2(x)=sec^4(x)

Natalija [7]

Answer:

see explanation

Step-by-step explanation:

Using the trigonometric identity

tan²x + 1 = sec²x ⇒ tan²x = sec²x - 1

Consider the left side

sec²x × tan²x + sec²x

= sec²x(sec²x - 1) + sec²x ← distribute and simplify

= $sec^{4}$ x - sec²x + sec²x

= $sec^{4}$ x = right side ⇒ verified

6 0

3 years ago

A machine costs 7500. Its value decreases by 5% every year due to usage. what will be its price after 1 year?​

A machine costs 7500. Its value decreases by 5% every year due to usage. what will be its price after 1 year?