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KiRa [710]
3 years ago
5

The letters from the word "alert" are used to form a password into a school computer system. How many 5-letter passowrds can be

formed if the letters can be used more than once?
a. 3125
b. 50
c. 120
d. 625
Mathematics
1 answer:
Sliva [168]3 years ago
6 0
The correct answer is a. 3125

That's because the letter can be used more than once, so if you start and try everything from aaaaa, to ttttt, the possibilities are huge and much larger than any of the lower numbers.
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A cyclist rides a bike at a rate of 24 miles per hour. What is this rate in miles per minute? How many miles will the cyclist tr
BlackZzzverrR [31]

there are 60 minutes per hour

24/60 = 0.4 miles per minute

0.4*5 = 2

they will ride 2 miles in 5 minutes

4 0
3 years ago
Consider the following series. 1 9 1 18 1 27 1 36 1 45 Determine whether the series is convergent or divergent. Justify your ans
Vedmedyk [2.9K]

Answer:

<em>Diverges; the limit of the terms, an, is not 0 as n goes to infinity</em>

Step-by-step explanation:

<u>Convergence of Infinite Series</u>

The series is given as the terms

1 , 9 , 1 , 18 , 27 , 1 , 36 , 1 , 45 ...

For a series to be convergent, the limit of the general term an when n goes to infinity must be 0. In such cases, the sum of all terms tends to a fixed value.

Our series has two clearly different sequences, which define it as a piecewise general term:

If n is odd, then

a_n=1

Otherwise, an is an arithmetic series starting from 9 with a common difference of 9, that is

a_n=9+9(n/2-1)=4.5n

if n is even.

If we take the limit as n goes to infinity, we don't know which one should be selected, thus we must assume that any of them is a correct option, therefore both of them should converge.

The limit of the function

a_n=1

is 1 when n goes to infinity. Since it's not 0, this piece is not convergent and the entire series isn't either.

But it goes worse because of the limit of the second piece

a_n=4.5n

when n goes to infinity is infinite.

The answer is

<em>Diverges; the limit of the terms, an, is not 0 as n goes to infinity</em>

8 0
3 years ago
Please help! I cant afford to fail.. PLEASE NO LINKS
vova2212 [387]

Answer:  The answer that I got was J.

7 0
3 years ago
Rectangle GHIJ is dilated to be a smaller shape. What is the name of the image after the dilation?
prisoha [69]
To know whether the shape is the pre-image or the resulting shape, we need to look at its name.

In this instance, the name of the pre-image is GHIJ.

The resulting name of the shape would be G'H'I'J'.

An apostrophe is placed after every letter to signify that it is the resulting coordinate of the original.
8 0
3 years ago
Read 2 more answers
Multiply the following binomials:<br> (x + 10)(x - 5)
SCORPION-xisa [38]

Answer:

X^2+5x-50

Step-by-step explanation:

X^2-5x+10x-50

8 0
3 years ago
Read 2 more answers
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