MATHEMATICS COLLEGE

2. Use the binomial theorem to expand the expression. (а — 2b)^5

Answers

Answer 1
Answer:

Answer:

(a-2b)^(5)=-32b^(5)+80ab^(4)-80a^(2)b^(3)+40a^(3)b^(2)-10a^(4)b+a^(5)

Step-by-step explanation:

The binomial expansion is given by:

(x+y)^(n)=_(0)^(n)\textrm{C}x^{^(0)}y^(n)+_(1)^(n-1)\textrm{C}x^(1)y^(n-1)+...+_(n)^(n)\textrm{C}x^(n)y^(0)

In our case we have

x=a\ny=-2b\nn=5

Thus using the given terms in the binomial expansion we get

(a-2b)^(5)=_(0)^(5)\textrm{C}a^(0)(-2b)^(5)+_(1)^(5)\textrm{C}a^{^(1)}(-2b)^(4)+{_(2)^(5)\textrm{C}}a^(2)(-2b)^(3)+_(3)^(5)\textrm{C}a^(3)(-2b)^(2)+_(4)^(5)\textrm{C}a^(4)(-2b)^(1)+_(5)^(5)\textrm{C}a^(5)(-2b)^(0)

Upon solving we get

(a-2b)^(5)=-32b^(5)+5* a*16b^(4)+10* a^(2) * (-8b^(3))+10* a^(3)* 4b^(2)+5* a^(4)* (-2b)+a^(5)\n\n(a-2b)^(5)=-32b^(5)+80ab^(4)-80a^(2)b^(3)+40a^(3)b^(2)-10a^(4)b+a^(5)

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Organizers of an outdoor summer concert in Toronto are concerned about the weather conditions on the day of the concert. They will make a profit of $31,000 on a clear day and $10,000 on a cloudy day. They will make a loss of $5,000 if it rains. The weather channel has predicted a 47% chance of rain on the day of the concert. Calculate the expected profit from the concert if the likelihood is 14% that it will be sunny and 39% that it will be cloudy.

Which of the following ratios is equivalent to 12/20? Answers A. 3/10 B. 5:3 c. 120 to 200 D. 60/80

Answers

A is 3/10 , if we multiply top and bottom by 4 we get 12/40 , which is not equivalent to 12/20.


B is 5:3 , it cannot be equivalent to 12/20.

C is 120 to 200 , if we divide both numerator and denominator by 10 we get 12/20, So option C is correct.


D is 60/80 , if we divide both numerator and denominator by 5, we get 12/16 , which is not equivalent to 12/20.



Hence option C is the correct answer.
12 : 20
12 x 10  : 20 x 10
120 : 200 (Answer C)

Can someone explain how to do it aswell please and thank you

Answers

Answer:

B: 24ft^2

Step-by-step explanation:

Area of triangle = (base x height)/2

Step 1: form an equation

a = (12ft x 4ft)/2

Step 2: solve equation

a = 48ft^2 / 2

a = 24ft^2

*the base is the measurement for the bottom of a triangle while height is the measurement of the length from the bottom to the top of a triangle*

Solve the quadratic equation by factoring.
x^2 - 4x - 12 = 0​

Answers

Answer: x=6, -2

Step-by-step explanation:

I'm pretty sure that's it if its not i apologize

A computer manufacturer built a new facility for assembling computers. There were construction and new equipment costs. The company paid for these costs and made combined profits of $40 million after 4 years, while profits increased $30 million per year. Select the correct graph of this function. (2 points)A)There is a graph of a line that has a y intercept that is approximately $80 million and passes through the point of approximately x equals 2 years and y equals $140 million.

B)There is a graph of a line that has a y intercept that is approximately negative $80 million and an x intercept that is approximately 2.7 years.

C)There is a graph of a line that has a y intercept that is approximately negative $45 million and an x intercept that is approximately 2 years.

D)There is a graph of a line that has a y intercept that is approximately negative $45 million and an x intercept that is approximately 0.6 years.

Answers

Answer:

I am not really good at this but...if I had to choose the ones that make sense

A and B

Step-by-step explanation:

Your are incresing the amount is going up, so if you go backwards you woild have to the negatuves.

Then again I woild not trust my math for the second answer cause I am no good at math.

Jon Ericson bought a home with a 11.5% adjustable rate mortgage for 20 years. He paid $10.67 monthly per thousand on his original loan. At the end of 2 years he owes the bank $50,000. Now that interest rates have gone up to 13%, the bank will renew the mortgage at this rate or Jon can pay $50,000.
Jon decides to renew and will now pay $11.72 monthly per thousand on his loan. You can ignore the small amount of principal that has been paid.

What is the amount of the old monthly payment? $ ____
What is the amount of the new monthly payment? $ ____
What is the percent of increase in his new monthly payment? ____ %

Answers

Remark

The first fact you need to know is that the bank has taken money from you and nothing has been reduced from the principle. Crafty people those bankers; you are going to pay off the interest before touching the principle. They're like you to refinance for the rest of your life at the rates you currently have.

Point. You started out with a 50k debt. You still have that same debt.

Solution

Givens

number of thousands (n) = 50000/1000 = 50

Amount paid per thousand (A) = 10.67

Total monthly payments (T) = ?

Part A

T = n * A

T = 50 * 10.67

T = 533.50 is the old monthly payment

Part B

T = n * A

T = 50 * 11.72

T = 586.00  new monthly payment.

Part C

This is a notes question. What have you been told in your notes on this question. You can find the raw amount just by subtracting 586 - 533.50 = 52.50

But how do you find the % increase. Which one of the payments do you use as your base?

In point of fact, you should be using the first number 533.5

What % will you get when you multiply that by 533.5 and get 52.50?

You are not trying to find 586. You are trying to find the number that you add to 533.5 to get to 586

The answer is (52.50 / 533.5)*100% = 9.84% is the % increase.

You are told to ignore the amount of principal paid, so you are apparently to assume the loan amount was for $50 thousand.

a) The old monthly payment was $10.67×50 = $533.50

b) The new monthly payment is $11.72×50 = $586.00

c) The increase in monthly payment is figured in the usual way:

... (new/old -1)×100% = (1.0984-1)×100% = 9.84%

_____

In reality, about 3% of the loan will have been paid at the end of 2 years. Thus, the original loan amount may have been near $51,500. This problem is telling you to ignore the difference.

A coral reef grows 0.14 m every week. How much does it grow in 14 weeks? Write your answer in millimeters.​

Answers

Answer:

0.14*14= 1.96

Step-by-step explanation:

Must multiply 0.14 times 14 for the answer.
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