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3 years ago

Please help show that the following are TRUE.

Mathematics

1 answer:

mafiozo [28]3 years ago

7 0

Answer:

see below

Step-by-step explanation:

The formula for the sum of an infinite geometric series with first term a1 and common ratio r (where |r| < 1) is ...

sum = a1/(1 -r)

Applying this to the given series, we get ...

a. sum = 5/(1 -3/4) = 5/(1/4) = 20

b. sum = d/(1 -1/t) = d/((t-1)/t) = dt/(t-1)

_____

The derivation of the above formula is in most texts on sequences and series. In general, you write an expression for the difference of the sum (S) and the product r·S. You find all terms of the series cancel except the first and last, and the last goes to zero in the limit, because r^∞ → 0 for |r| < 1. Hence you get ...

S -rS = a1

S = a1/(1 -r)

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Suzi bought 5 packages of M&M's, and each package contained 18 candy pieces. She opened the first package and counted 4 gree

Leni [432]

Answer: The correct answer is option B: There are between 15 and 20 green pieces in all 5 packages

Step-by-step explanation: The most important factor has been given which is, "Which statement about the candy pieces in the remaining packages is best supported by this information."

The information given is such that, the first package she opened had 4 green pieces and on this basis we can safely assume that all other packages have 4 green pieces as well. The second package had 3 green pieces and this based on this too we can safely assume that all other packages had 3 green pieces. Hence, all 5 packages can either have a total of 4 x 5 green candies which equals a total of 20 green pieces or, all 5 packages can have a total of 3 x 5 green candies which equals a total of 15 green pieces.

So according to Suzi's experiment, there are between 15 and 20 green pieces in all 5 packages.

7 0

3 years ago

Erik and Nita are playing a game with numbers. In the game, they each think of a random number from zero to 20. If the differenc

Mademuasel [1]

Let X is the random number Erik thinks of, and Y is the random number Nita thinks of.
Both X and Y are in the range from 0 to 20.
X<=20
Y<=20
If the difference between their two numbers is less than 10, then Erik wins.
The difference between the two numbers can be written X-Y, or Y-X depending on which number (X or Y) is greater. But we do not know that. In order not to get negative value, we calculate absolute value of X-Y, written |X-Y| which will give positive value whether X is greater than Y or not.
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If the difference between their two numbers is greater than 10, then Nita wins.
If |X-Y|>10 Nita Wins

6 0

3 years ago

Select from the drop-down menus to correctly complete each statement. −20>−21 −19>−20 −21 is located to the of −20 on a nu

LekaFEV [45]

Answer:

left, right

Step-by-step explanation:

If you use the < or ≤ symbol to compare the numbers, their left-right order is the same as on the number line. Here, we would write the ordering as ...

-21 < -20 < -19

So, we see that ...

-21 is left of -20 on the number line

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4 0

3 years ago

Read 2 more answers

What is the inverse of this function? f(x)=x−7

viva [34]

Answer:

Step-by-step explanation:

Replace f(x) with y. y = x − 7

Interchange the variables. x = y − 7

Solve for y. y = x + 7

Solve for y and replace with f^−1 (x). f^−1(x) = x + 7

I hope this helps have a great day :)

4 0

2 years ago

What is the x-intercept of the line with this equation −5x+1/5y=15 ?

bulgar [2K]

Step-by-step explanation:

I don't no but 5 and 1 is 6 so add 9 more and you have 15

6 0

3 years ago