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katovenus [111]
3 years ago
6

jody wants to figure out how he spends his time. currently, he spends 12 days out of a 30-day month practicing the piano. How mu

ch of the month does he spend practicing in terms of percent, decimal. and fraction?
Mathematics
1 answer:
shtirl [24]3 years ago
3 0

Answer:

percent- 40%

decimal- 0.4

percent- 2/5

Step-by-step explanation:

you divide 30 by 12 because he practices piano 12/30 days of the month

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If Beth has 5 books and Tom has 3 how many do they have in all?
aalyn [17]

Answer:

8 books

Step-by-step explanation:

5+3=8

4 0
3 years ago
Read 2 more answers
A shipment of 105 Otter box covers for I-phones has arrived. The total invoice (excluding tax, shipping, etc.) is $3,849.75.
bezimeni [28]
<span>3,849.75 </span>÷ 49.95 = 77 (Calculator)

Sense you would like it explained than the question is asking how many otter box Defender Covers where shipped in that price. So when you have that they want the amount of Otter Box Defenders than you divide the amount paid for the shipment with the amount of the otter box defender price.

I hope this is helpful.
3 0
4 years ago
Which ordered pair is a solution of the equation y = x - 2?
Liula [17]

Answer:

One order pair is  

( 2,0)

Step-by-step explanation:

What ordered pairs are the options?

Pick a value for  

x

and solve for  

y

. Or find the intercepts.

If  

x

=

2

, then:

y

=

2

−

2

⇒

y

=

0

So we have  

(

2

,

0

)

If  

x

=

0

, then:

y

=

0

−

2

⇒

y

=

−

2

Here we have  

(

0

,

−

2

)

You can simply use  

0

for both  

x

and  

y

(intercept) to get the same answer.

8 0
3 years ago
Prove that $5^{3^n} + 1$ is divisible by $3^{n + 1}$ for all nonnegative integers $n.$
Viktor [21]

When n=0, we have

5^{3^0} + 1 = 5^1 + 1 = 6

3^{0 + 1} = 3^1 = 3

and of course 3 | 6. ("3 divides 6", in case the notation is unfamiliar.)

Suppose this is true for n=k, that

3^{k + 1} \mid 5^{3^k} + 1

Now for n=k+1, we have

5^{3^{k+1}} + 1 = 5^{3^k \times 3} + 1 \\\\ ~~~~~~~~~~~~~ = \left(5^{3^k}\right)^3 + 1^3 \\\\ ~~~~~~~~~~~~~ = \left(5^{3^k} + 1\right) \left(\left(5^{3^k}\right)^2 - 5^{3^k} + 1\right)

so we know the left side is at least divisible by 3^{k+1} by our assumption.

It remains to show that

3 \mid \left(5^{3^k}\right)^2 - 5^{3^k} + 1

which is easily done with Fermat's little theorem. It says

a^p \equiv a \pmod p

where p is prime and a is any integer. Then for any positive integer x,

5^3 \equiv 5 \pmod 3 \implies (5^3)^x \equiv 5^x \pmod 3

Furthermore,

5^{3^k} \equiv 5^{3\times3^{k-1}} \equiv \left(5^{3^{k-1}}\right)^3 \equiv 5^{3^{k-1}} \pmod 3

which goes all the way down to

5^{3^k} \equiv 5 \pmod 3

So, we find that

\left(5^{3^k}\right)^2 - 5^{3^k} + 1 \equiv 5^2 - 5 + 1 \equiv 21 \equiv 0 \pmod3

QED

5 0
2 years ago
Rapheal paid $624 for a camera during a 60% off sale. What was the cameras regular rice?
Nostrana [21]
$1040.00
______________________________________________
Raphael paid $624

624/.60= 1040.00
4 0
3 years ago
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