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OLEGan [10]
2 years ago
14

The number 2^1993 + 3^1993 is a multiple of 5. What is the units digit of the quotient (2^1993 + 3^1993)/5?

Mathematics
1 answer:
Ad libitum [116K]2 years ago
3 0

Answer: The unit digit of the quotient is 1.

Step-by-step explanation:

Since the number 2^1993 + 3^1993 is a multiple of 5, this means that no matter the value of the answer to the equation, the last digit will be 5 (we call the last digit of any number its "unit digit").

Since the unit digit of 2^1993 + 3^1993 is 5, if the unit digit is divided by 5 i.e 5/5, it will give us 1.

We will only consider the last digits of the multiple of 5 as our numerator

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Jason Witten's Salary Negotiation Let's say that tight end Jason Witten (a football player) was given two options when negotiati
Leokris [45]

Answer:

Option 1: It is better for him to be paid per catch, starting with 1 cent and doubling with each catch up to 110

Explanation:

If Jason were to be paid per catch given that he makes a total of 110 catches for the 2017 season in his new contract, he would make a total of :

0.01 × 2^109 = $6.4903711e+30(calculator result, means 6 then 30 digits after)

Therefore it is better for Jason to be paid per catch and not a flat fee of $2000000

3 0
1 year ago
At a certain company, the annual winter party is always held on the second of Friday of December. What is the latest possible da
vitfil [10]

Answer:

The latest possible date is December, 14th.

Step-by-step explanation:

Notice that the second Friday of December is n+7, where n is the date for the first Friday of December. So, the latest the first Friday, the latest the second. As the weeks have seven days, the first Friday will be between 1st and 7th of each month. So, the latest first Friday will be 7th. Therefore, the latest second Friday will be 14th.

7 0
2 years ago
A student wants to know how far above the ground the top of a leaning flagpole is. At high​ noon, when the sun is almost directl
MariettaO [177]

Answer:

15.43 ft

Step-by-step explanation:

To solve this question, one should use the concept of similar triangles.

The pole's shadow and the distance to the ground (x) form a similar triangle to the distance of the plumb bob from the base and the length of the plumb bob, respectively. Note that we do not need to know the measurements of the third side of the triangles to solve the problem.  Therefore, the distance of the top of the pole to the ground is:

14 in = 1.1667 ft

1.1667x=6*3\\x = 15.43

The distance of the top of the pole to the ground is 15.43 ft.

4 0
2 years ago
Nuri joins a game for a car. The rule is that Nuri pick one key from box either A, B, or C. A box has two keys but only one can
jek_recluse [69]

Answer:

0.278

Step-by-step explanation:

Given that Nuri joins a game for a car. The rule is that Nuri pick one key from box either A, B, or C. A box has two keys but only one can be used. B box has three keys but only one can be used. C box has two keys but none of them can be used.

Each box is equally likely to be selected.

In other words

P(A) = P(B) = P(C)=\frac{1}{3}

If A is selected then probability of winning is using the correct key out of two keys i.e. 0.5

If B is selected then probability of winning is using the correct key out of three keys i.e. 0.333

If c is selected then probability of winning is using the correct key out of two keys i.e. 0.00

So the probability that Nuri can win the car

= \frac{1}{3} *0.5+\frac{1}{3} *0.333+\frac{1}{3} *0\\= 0.278

6 0
2 years ago
Lenny sold 576 tacos in 48 hours what was lenny's average rate of tacos sales
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If your looking for hourly they sold a total of 12 tacos per hour.
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4 0
2 years ago
Read 2 more answers
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