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3 years ago

Help me please with math

Mathematics

1 answer:

fomenos3 years ago

4 0

Let's make a table of differences

0 3 8 15 24

3 5 7 9

2 2 2

Constant second difference means a quadratic polynomial,

f(n)=an² + bn +c

f(1)=0, f(2)=3, f(3)=8

0 = a+b+c

3 = 4a + 2b + c

8 = 9a + 3b + c

Subtracting pairs

3 = 3a+b

5 = 5a + b

Subtracting,

2 = 2a

a = 1

b = 5 - 5a = 0

c = -a-b = -1

f(n)=n² -1

Duh, shoulda noticed that at the beginning.

f(17)=17²-1 = 288

a₁ =5

aₙ = aₙ₋₁ - 7

aₙ = a₁ + d(n-1)

aₙ = 5 - 7(n-1)

a₇ = 5 - 7(6) = -37

Answer: -37

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Answer:

Alfred can create the password in 9,360,000 possible ways

Step-by-step explanation:

Given the data in the questions;

Password of five characters must contain; three letters and 2 digits

[][][][][]

Now, using the five boxes above which as to be filled with three letters and two digits, such that; The first character of the password must be a letter and repetition of the same letter in the password is not allowed while repetition of digits is allowed.

Now,

we know that there are 26 alphabets in English language, so the first box can be filled in 26 ways { must be a letter }

next four will be filed with two letters and two digits

so two boxes from the four can be chosen in the following ways;

⇒ ⁴C₂ = 4! / ( 2!(4-2)! = 24 / 4 = 6 { ways }

now for each choice, we can fill the chosen two boxes with letters in;

⇒ 25 × 24 = 600 { ways}

and the next two by digits; ( 0, 1, 2, ..... 9)

⇒ 10 × 10 = 100 { ways }

So in total, the possible number of ways he can create a password is;

⇒ 26 × 6 × 600 × 100

= 9,360,000 possible ways

Therefore, Alfred can create the password in 9,360,000 possible ways

8 0

3 years ago

Mike drank more than half the juice in his glass. what fraction of the juice could Mike have drunk?

maxonik [38]

He drank more than half of his drink... So we need to look for fractions greater than 1/2.

First, lets find equivalents of 1/2

$\frac{1}{2}= \frac{2}{4} = \frac{3}{6}= \frac{4}{8}$

If all of these fractions are equal to 1/2, then by adding to the numerator of these fractions, we'l have fractions greater than 1/2.

2 +1 3
__= ___
4 4

3/4 is greater than 1/2

Mike could have drunken 3/4 of the juice

4/6>1/2 Mike could have drunken 4/6 of the juice

5/8 is greater then 1/2 Mike could have drank 5/8 of the drink.

Answer=3/4, 4/6, 5/8 and many more possible fractions

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