All categories

2 years ago

The sum of the first 1 million primes is N. Without knowing N's value, one can determine that the ones'digit of N cannot be

1 answer:

3 0

All primes are odd, except two. Therefore the sum of the first million primes is one even number plus 999999 odd numbers. Since odd*odd = odd, the first million primes must be even + odd = odd.

An odd number obviously has an odd final digit, so the only option that can be firmly rules out is b (which is even).

You might be interested in

Use the binomial theorem to show that 7^n + 2 is divisible by 3, where n is a positive integer.

masha68 [24]

By the binomial theorem,

$7^n=(6+1)^n=6^n+n6^{n-1}+\dbinom n26^{n-2}+\cdots+\dbinom n{n-2}6^2+n6^1+1$

Each term containing a factor 6 is divisible by 3, since 3 divides 6. The remaining 1 and 2 sum to 3, which is also divisible by 3.

7 0

1 year ago

Jake went on a riverboat tour. After returning from the tour, he was curious to know the speed at which the boat was going. Duri

atroni [7]

I'm sorry I'm too lazy to read all of that. However, I did get the main point. The river was going at 3 mph. Since he wanted to travel 10 miles upstream and downstream, you would have to subtract 20 by 3. This would mean he was going at a speed of 17 mph.

4 0

2 years ago

7526.442 rounded to the nearest hundredth

AlladinOne [14]

Number > 5 - round up
Number = 5 - round up
Number < 5 - round and keep the number the same

7526.442

Hundredth = 2nd decimal place = 4

2 < 5
Round and keep the number the same

7526.44

3 0

2 years ago

7 people out of the 99 visitors bought a gift. About ___% of the visitors bought a gift.

ArbitrLikvidat [17]

Answer:

About 7.07% of the visitors bought a gift.

Step-by-step explanation:

7/99 = 0.0707

0.0707 *100 = 7.07%

then:

About 7.07% of the visitors bought a gift.

5 0

2 years ago

Between 1896—when the Dow Jones index was created— and 2012, the index rose in 65% of the years. Based on this information, and

forsale [732]

Answer:

a) P(x) = 0.67

b) P(y) = 0.67

c) P(x=4) = 0.3325

d) P( x = 0 ) = 0.0039

e) The fact that the rise and fall of the stock market relies on market sentiments violates independence used in Binomial distribution and the years are independent

Step-by-step explanation:

A) The probability that the stock market will rise next year = P(x) = 0.67

assuming next year to be X

B) Probability that the stock market will rise the year after next year

= P(y) = 0.67 and this is because the probability is independent of that of the previous years

C) Probability that the stock market will rise in four of the next five years

= P(x=4) = 0.3325

D) probability that the stock market will rise in none of the next five years

= P( x = 0 ) = 0.0039

E) The fact that the rise and fall of the stock market relies on market sentiments violates independence used in Binomial distribution and the years are independent

4 0

2 years ago