All categories

3 years ago

Determine if the linear system

Mathematics

1 answer:

zubka84 [21]3 years ago

4 0

Answer:

b. The system is not in echelon form because the system is not organized in descending "stair step" pattern so that the index of the leading variables increases from the top to bottom.

Step-by-step explanation:

The given linear system has a equation which is not in echelon form. The echelon is a system which divides the data into rigid hierarchal groups. The given linear equation in not in echelon form as the leading variables are increased from top to bottom indicating descending stair step pattern.

You might be interested in

Emma invested $41,000 in an account paying an interest rate of 2.6% compounded monthly. Assuming no deposits or withdrawals are

kvasek [131]

Answer: it will take 7 years for the value of the account to reach $49,300

Step-by-step explanation:

We would apply the formula for determining compound interest which is expressed as

A = P(1 + r/n)^nt

Where

A = total amount in the account at the end of t years

r represents the interest rate.

n represents the periodic interval at which it was compounded.

P represents the principal or initial amount deposited

From the information given,

P = $41000

A = $49300

r = 2.6% = 2.6/100 = 0.026

n = 12 because it was compounded 12 times in a year.

Therefore,

49300 = 41000(1 + 0.026/12)^12 × t

49300/41000 = (1 + 0.0022)^12t

1.2024 = (1.0022)^12t

Taking log of both sides of the equation, it becomes

Log 1.2024 = 12t × log 1.0022

0.08 = 12 × 0.00095 = 0.0114t

t = 0.08/0.0114

t = 7 years

8 0

3 years ago

What is the volume of a box with 385 cubes and 11/3 x 5/3 x 7/3

Aleks04 [339]

Answer:

−

Step-by-step explanation:

7 0

2 years ago

A business executive bought 40 stamps for

alekssr [168]

Answer:

32 33-cent stamps, 8 23-cent stamps

Step-by-step explanation:

In order to solve this question, we need to set up a system of equations. Also known as solving for two variables (the number of each stamp).

Let's set x to be the number of 33-cent stamps. Similarly, let's set y to be the number of 23-cent stamps.

To make our first equation, let's think about the number of stamps total we have. We can say:

$x + y =40$

<em>(AKA - The number of 33-cent stamps, plus the number of 23-cent stamps, equals 40 stamps.)</em>

Now, let's make an equation for the cost of these stamps.

$0.33x + 0.23y = 12.40$

<em>(AKA - The cost of the stamps in total, should equal $12.40).</em>

So now, we have our two equations:

$x + y =40\\0.33x+0.23y=12.40$

If you have a TI-84 graphing calculator, you can go to apps -> polysmlt2 -> simultaneous eqn solver, and then input these equations into the menu. This will solve the problem for you.

If you need to do this manually, let's use substitution. Condense our first equation to make it more substitutable.

$x+y=40\\x=40-y$

Now, let's put this into our second equation.

$0.33x+0.23y=12.40\\0.33(40-y)+0.23y=12.40$

Distribute, and solve for y.

$13.2-0.33y +0.23y =12.40\\13.2-0.1y=12.40\\-0.1y=-0.8\\y=8$

Now, we plug this into one of our equations.

$x+y=40\\x+8=40\\x=32$

In the end, we have thirty-two 33-cent stamps, and eight 23-cent stamps.

3 0

1 year ago

Marine scientists categorize signature whistles of bottlenose dolphins by typelong dash—type a, type b, type c, etc. In one s

r-ruslan [8.4K]

Answer:

The 95% confidence interval for the true proportion of bottlenose dolphin signature whistles that are type a whistles is (0.4687, 0.6123).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.