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Wewaii [24]
2 years ago
15

Prove that the value of the expression:

Mathematics
1 answer:
katrin2010 [14]2 years ago
7 0

Answer:

Step-by-step explanation:

5^{2} - 1 = 25 - 1 = 24

24 is divisible by 3.

So, (125² +25²)*(5²- 1)   is also divisible by 3

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Please solve the following question.
mylen [45]

Answer:

103, 776

Step-by-step explanation:

There are 48 possibilities, and you are picking 3.

Now, the order does matter (aka, if the same 3 athletes won but got different places, we would still consider it to be a separate possibility)

(this is considered "without repetitions")

the number of permutations (arrangement combinations where the order does matter) without repetitions formula:

Number of permutations

without <em>repetitions </em>= nPr

= \frac{n!}{(n-r)!}

(

[the P is for combinations [where the order does matter, if the order didn't matter then it would be C, and it would be a different formula.]

n is the total number of objects.

r is the number of objects selected]

<em>(a repetition would be like two versions of the same person competing, which doesn't make sense)</em>

{the ! means factorial:

5! = 5 x 4 x 3 x 2 x 1}

{for example, if there are 5 people to give a presentation, and they can go in any order [but cannot repeat their presentation], so they all must fill 5 slots}

{for the first slot there are 5 choices, the second slot there are 4 choices...}

)

So, if we follow this formula:

\frac{n!}{(n-r)!}

n: 48

r: 3

\frac{48!}{(48-3)!}

= \frac{48!}{45!}

=\frac{48 * 47*46*45!}{45!}

(the 45! cancel out)

= 48 * 47 * 46

= 103, 776

(or, without the formula:

for the first choice (lets say of gold), there are 48 options

for the second choice (lets say silver), there are 47 options left to choose from

for the third choice (lets say bronze), there are 46 options left to choose from

)

3 0
2 years ago
Apply the markup for each item. Then, find the retail price. Round to two decimals places when necessary.
Alborosie

Answer:

$45 with 20% markup = $45 + $9 for a new total = $54

$7.60 with a 50% markup = $7.60 + $3.80 for new total = $11.40

Step-by-step explanation:


7 0
3 years ago
Melissa made 15,000 in taxable income last year. Suppose the income tax rate is 15% for the first $9000 plus 19% for the amount
alisha [4.7K]
She must pay atless 20,00 a year
5 0
3 years ago
What is 5 divided by 4/9
Maslowich

The answer is 11 1/4

5 0
3 years ago
Read 2 more answers
Help me pweasee
lorasvet [3.4K]

Answer:

211 / 41 = 5 hours

Step-by-step explanation:

the total was 211 dollars, so you can add 25 dollars and 16 dollars together. That gives us 41 dollars. 211 divided by 41 is approximately 5 hours.

Hope it helps!

8 0
3 years ago
Read 2 more answers
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