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2 years ago

A list of consecutive integers begin withs with m and ends with n. If n-m = 66, how many integers are in the list?

Mathematics

1 answer:

malfutka [58]2 years ago

5 0

Answer:

Step-by-step explanation:

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Write out the first few terms of the series Summation from n equals 0 to infinity (StartFraction 2 Over 3 Superscript n EndFract

anyanavicka [17]

Answer:

$\sum\limits_{n=0}^{\infty} \frac{2}{3^n}\frac{(-1)^n}{5^n} = 15/8$

Step-by-step explanation:

The sum you are trying to understand is this.

$\sum\limits_{n=0}^{\infty} \frac{2}{3^n}\frac{(-1)^n}{5^n}$

Remember that in general when you have a geometric series

$\sum\limits_{n = 0}^{\infty} a*r^n$ you have that

$\sum\limits_{n = 0}^{\infty} a*r^n = \frac{a}{1-r}$ and that equality is true as long as $|r| < 1$ .

Therefore here we have

$\sum\limits_{n=0}^{\infty} \frac{2}{3^n}\frac{(-1)^n}{5^n} = \sum\limits_{n=0}^{\infty} 2* \big(\frac{-1}{3*5} \big)^n = \sum\limits_{n=0}^{\infty} 2* \big(\frac{-1}{15} \big)^n$ and $\big|\frac{-1}{15} \big| = \frac{1}{15} < 1$

Therefore we can use the formula and

$\sum\limits_{n=0}^{\infty} 2* \big(\frac{-1}{15} \big)^n = \frac{2}{1-(-1/15)} = \frac{2}{1+1/15} = 30/16 = 15/8$

5 0

2 years ago

3x+1 = y 2x+3y = 14<br> please explain the steps if you can as well

Likurg_2 [28]

3x + 1 = y
2x + 3y = 14

To solve this system of equations, we are going to use the substitution method. Substitution the equation where the variable is isolated into the second equation. In this system of equations, y is isolated, so we will replace y in the second equation with 3x + 1.

2x + 3y = 14
2x + 3(3x + 1) = 14
2x + 9x + 3 = 14
We will add the like terms and subtract 3 from both sides of the equation.
11x + 3 = 14
11x = 11
x = 1
In this system of equations, x is equal to 1. Now we will go back and solve for y, plugging in 1 for x.
3(1) + 1 = y
2(1) + 3y = 14

3 + 1 = y
2 + 3y = 14

4 = y
3y = 2

4 = y
4 = y

The solution to this system of equations is (1, 4).

8 0

3 years ago

How do u solve using the ratios !

Bingel [31]

Check the picture below.

surely you know how much that is.

6 0

3 years ago

A copier prints 80 pages in 5 minutes.

DochEvi [55]

The correct answer is D, 16 pages per minute. A unit rate is a ratio of something to one; in this case, the ratio is 16:1, or 16 pages to 1 minute. To get the unit rate for this problem, divide both numbers by 5 to get how many pages will be printed per 1 minute. 80/5 = 16, so the copier prints 16 pages in 1 minute. Answer choices A and B are not unit rates, and answer choice C is the incorrect unit rate.

Hope this helps!

7 0

2 years ago

1. "Fasting blood sugar" is a lab test usually done six to eight hours after eating. The normal range for this test is 70

Ilya [14]

Answer:

1. "Fasting blood sugar" is a lab test usually done six to eight hours after eating. The normal range for this test is 70

Step-by-step explanation:

6 0

2 years ago