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3 years ago

Help ASAP.

1 answer:

4 0

$1.\\A(n)=-2\cdot5^{n-1}\\\\\text{Find the first, fourth, and eighth terms}\\\text{It means}\ A(1),\ A(4)\ \text{and}\ A(8).\\\\\text{Substitute}\ n=1,\ n=4\ \text{and}\ n=8\ \text{in}\ A(n):\\\\A(1)=-2\cdot5^{1-1}=-2\cdot5^0=-2\cdot1=-2\\\\A(4)=-2\cdot5^{4-1}=-2\cdot5^3=-2\cdot125=-250\\\\A(8)=-2\cdot5^{8-1}=-2\cdot5^7=-2\cdot78,125=-156,250\\\\\boxed{Answer:\ a)\ -2,\ -250,\ -156,250}.$

$2.\\a_1=-6,\ r=2\\\\\text{The formula of a n-th term of geometric sequence}\\\\a_n=a_1r^{n-1}\\\\\text{Substitute:}\\\\a_n=-6\cdot2^{n-1}=-6\cdot2^n\cdot2^{-1}=-6\cdot2^n\cdot\dfrac{1}{2}=-3\cdot2^n\\\\\boxed{Answer:\ A(n)=a_n=-3\cdot2^n}$

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A bank loaned out $17,500, part of it at the rate of 12% annual interest, and the rest at 10% annual interest. The total interes

professor190 [17]

Answer: $9500 was loaned at 12% and $8000 was loaned at 10%

Step-by-step explanation:

Let x represent the amount that the

bank loaned out at the annual rate of 12%.

Let y represent the amount that the

bank loaned out at the annual rate of 10%.

The bank loaned out $17,500, part of it at the rate of 12% annual interest, and the rest at 10% annual interest.. It means that

x + y = 17500

The interest on $x after 1 year would be

12/100 × x = 0.12x

The interest on $y after 1 year would be

10/100 × y = 0.1y

The total interest earned for both loans was $1,940.00. . It means that

0.12x + 0.1y = 1940- - - - - - - - - 1

Substituting x = 17500 - y into equation 1, it becomes

0.12(17500 - y) + 0.1y = 1940

2100 - 0.12y + 0.1y = 1940

- 0.12y + 0.1y = 1940 - 2100

- 0.02y = - 160

y = - 160/ - 0.02

y = 8000

x = 17500 - y = 17500 - 8000

x = $9500

7 0

4 years ago

Suppose ABC is a right triangle with sides of lengths a, b, and c and right angle at C. Find the unknown side length using the P

Oxana [17]

Answer:

<h2>Unknown side = 28</h2><h2>tan B = 7/24</h2>

Step-by-step explanation:

The question is incomplete. Here is the complete question.

Suppose ABC is a right triangle with sides of lengths a, b, and c and right angle at C. Find the unknown side length using the Pythagorean theorem and then find the value of the indicated trigonometric function of the given angle. Rationalize the denominator if applicable. Find tan B when a = 96 and c = 100.

Pythagoras theorem states that the square of the hypotenuse side of a right angled triangle is equal to the sum of the square of its other two sides. Mathematically c² = a²+b² where c is the hypotenuse and a,b are the other two sides.

From the question, we are given a = 96 and c = 100, to get the unknown side 'b', we will substitute the given values into the formula above;

c² = a²+b²

100² = 96² +b²

b² = 100² - 96²

b² = 10,000 - 9216

b² = 784

b = √784

b = 28

Hence, the unknown length is 28.

To get tanB, we will use the SOH, CAH, TOA trigonometry identity

According to TOA, tan B = opposite/adjacent

tan B = b/a (note that side b is the opposite in this case since the angle we are considering is B)

Given b = 28 and a = 96

tan B = 28/96

tan B = 4*7/4*24

tan B = 7/24

8 0

3 years ago

A machine can reshape the body of a flattened can to a round shape. The machine can reshape 75 cans in 5 minutes. At what rate p

nignag [31]

The answer is 15 cans per minute. Here is how I did it: I know that you need to find how many cans per minute so I divided 5 by itself to get one because you are finding out how many cans per one minute then I did the same to 75 because when doing this type of problem you have to divide the first number which in this case is 75 by the second number which in this case is 5. And when I divided 75 by 5 I got fifteen so 15 cans per minute is the answer. Hope I helped!

7 0

3 years ago

On a 30-day easy-access loan, $1350 is borrowed at a 20% monthly fee. What is the total cost to repay the easy-access loan?

dmitriy555 [2]

To repay the easy access loan you will repay the borrowed amount and 20% of it.

You can show this in math terms by multiplying the borrowed amount of $3500 by 120%. (This includes all of the original amount plus the 20% monthly fee).

3500 x 1.2 = $4200

7 0

4 years ago

20. A frock is marked Rs. 228 at a discount of 20% is given on it. What is the discount and

Darina [25.2K]

Answer and step-by-step explanation:

20. Because the discount is 20% of the given price so the discount would be"

228/100*20

= 45.6 Rs

Its selling price would be:

228 + 45.6 = 273.6 Rs

21. Sales tax would be:

450/100*5

= 22.5 Rs

Total price in bill = 22.5 + 450 = 472.5 Rs

22. 10% tax of 3300 would be:

3300/100*10 = 330 Rs

Price before tax = 3300 - 330 = 2970 Rs

23. He spent in total of:

2500 + 500 = 3000Rs

He sold for 3300 Rs

He gain 3300 - 3000 = 300 Rs profit

His loss gain percent = 3300/3000 * 100 = 110%

24. On the first bike, he earn:

2500/100*20 = 500 Rs

On the second bike, he lose:

2500/100*25 = 625 Rs

He lose in total of 625 -500 = 125 Rs

his loss percentage = (2500+500) + (2500 - 625) / 5000* 100

= 100% - (2500+500) + (2500 - 625) / 5000* 100

= 100% - 97.5%

He lose 2.5% money

Hope this helped :3

5 0

3 years ago