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vitfil [10]
2 years ago
14

Find each product. 1) (5n - 5)(4n - 4)

Mathematics
1 answer:
Paraphin [41]2 years ago
6 0

Answer:

20n² - 40n + 20

Step-by-step explanation:

(5n - 5)(4n - 4)

= 5n(4n) + 5n(-4) - 5(4n) - 5(-4)

= 20n² - 20n - 20n + 20

= 20n² - 40n + 20

Another way to do this:

(5n - 5)(4n - 4)

= 5(n - 1) * 4(n - 1)

= 20(n - 1)(n - 1)

= 20(n - 1)²

= 20(n² - 2n + 1)

= 20n² - 40n + 20

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1. Contaminated water is subjected to a cleaning process. The concentration of the pollutants is initially 5 mg per liter of wat
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Answer:

C(t)=5\cdot(0.9)^t

Step-by-step explanation:

The exponential function is often used to model natural growing or decaying processes, where the change is proportional to the actual quantity.

An exponential decaying function is expressed as:

C(t)=C_o\cdot(1-r)^t

Where:

C(t) is the actual value of the function at time t

Co is the initial value of C at t=0

r is the decaying rate, expressed in decimal

The concentration of the pollutants starts at Co=5 mg/lt. We also know the pollutant reduces its concentration by 10% each hour. This gives us a value of r = 10% / 100 = 0.1

Substituting into the general equation:

C(t)=5\cdot(1-0.1)^t

Operating:

\boxed{C(t)=5\cdot(0.9)^t}

7 0
2 years ago
On a sheet of paper, you have 100 statements written down. the first says, "at most 0 of these 100 statements are true." the sec
Yuki888 [10]
I would go with the second statement is true because if all of the other ones mentioned in the problem had something that would not work either the one before or after would make the statement false excepted for statement two
4 0
2 years ago
Nine new employees, two of whom are married to each other, are to be assigned nine desks that are lined up in a row. If the assi
meriva

Answer:

The probability is 0.8

Step-by-step explanation:

The key to answering this question is considering the fact that the two married employees be treated as a single unit.

Now what this means is that we would be having 8 desks to assign.

Mathematically, the number of ways to assign 8 desks to 8 employees is equal to 8!

Now, the number of ways the couple can interchange their desks is just 2 ways

Thus, the number of ways to assign desks such that the couple has adjacent desks is 2(8!)

The number of ways to assign desks among all six employees randomly is 9!

Thus, the probability that the couple will have adjacent desks would be ;

2(8!)/9! = 2/9

This means that the probability that the couple have non adjacent desks is 1-2/9 = 7/9 = 0.77778

Which is 0.8 to the nearest tenth of a percent

4 0
2 years ago
Researchers are assessing a new screening tool (blood-based assay) for early identification of prostate cancer. The test is run
natima [27]

Answer: B. Accurate but not reliable

Step-by-step explanation:

An experiment is said to be "reliable" when it consistently gives the same answers when done repeatedly, when the experiment is carried out several times it gives the same result each times.

An experiment is said to be " accurate "

when it produce a correct result using the right procedure and method .

In this case the research assessing a new screening tools for early identification of prostate cancer, test result is "accurate but not reliable ", since the consistent test result was not accurate.

7 0
2 years ago
Find the perimeter of $\triangle CDE$ . Round your answer to the nearest hundredth. A trapezoid A B C D is plotted on a coordina
guapka [62]

Answer:

The answer is below

Step-by-step explanation:

We are asked to find the perimeter of triangle CDE. The perimeter of a shape is simply the sum of all its sides, hence:

Perimeter of tiangle CDE = |CD| + |DE| + |CE|

Given that C(4, -1), D(4, -5), E(2, -3).

The distance between two points X(x_1,y_1)\ and\ Y(x_2,y_2) is given as:

|XY|=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

Therefore the lengths of the triangle are:

|CD|=\sqrt{(4-4)^2+(-5-(-1))^2} =4\ units\\\\|DE|=\sqrt{(2-4)^2+(-3-(-5))^2} =2.83\ units\\\\|CE|=\sqrt{(2-4)^2+(-3-(-1))^2} =2.83\ units

Perimeter of CDE = 4 + 2.83 + 2.83 = 9.66 units

8 0
2 years ago
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