All categories

2 years ago

How many natural numbers N have the property among 1,2,..........,N exactly 30% are divisible by 3?

Mathematics

1 answer:

k0ka [10]2 years ago

4 0

Answer:

The answer is B. 2.

Step-by-step explanation:

We know that for N = 1 and N = 2, none of them are divisible by 3.

For N = 3, 33.33% are divisible by 3. For N = 4, 25% (which is already less than 30%), so N = 5 would also be less.

At N = 6, we're back up to 33.33%. N = 7 is already less than 30%.

At N = 9, you guessed it, 33.33%. N = 10 is 30% (3, 6, and 9). So we have one case.

Moving along, at N = 18, 33.33%. N = 20 is again 30% (3, 6, 9, 12, 15, and 18). Two cases now.

Finally, at N = 21, again 33.33%. N = 22 and N = 23 are both greater than 30%. As we continue this, for any N after 20, we will always be greater than 30%.

You might be interested in

How do you do this question?

Bess [88]

"The function is decreasing":

This means the slope of the function will be negative at the given point. Anywhere the line is going down, from left to right, is decreasing. This eliminates choices A and C.

"The function is concave down":

This means the curve of the function will be open down (think of an upside down u). This eliminates choice E.

"f(x)>0":

This is anywhere the curve is above the x axis. This eliminates choice D.

The answer is Choice B) x=2.

Hope this helps!!

3 0

3 years ago

Can someone help please

elena-s [515]

Answer:

I'm sorry I can help you maybe a little bit if that's okay. Btw what grade are you in?

Step-by-step explanation:

3 0

3 years ago

Josie buys a scoop of dried cranberries and a scoop of dried bananas to make trail mix. The

iris [78.8K]

Answer:

4.65

Step-by-step explanation:

7 0

2 years ago

Read 2 more answers

2) A fair coin was tossed 75 times. The coin landed on Heads 42 times and Tails 33 times. What is the experimental probability o

coldgirl [10]

Answer:

$\frac{11}{25}$

Step-by-step explanation:

In the experiment that was conducted the coin was tossed a total of 75 times and out of those times it only landed on tails 33 times. Therefore the experimental probability of the coin landing on tails can be calculated by the dividing the times it landed on tails by the total number of times it was tossed. Like so...

$\frac{33}{75}$ or 0.44

This fraction can also be simplified to its simplest form of $\frac{11}{25}$ which is obtained by dividing both the numerator and denominator by 3

5 0

2 years ago

A mother invests $7000 in a bank account at the time of her daughter's birth. The interest is 18) compounded quarterly at a rate

Alex

well, from birth to your twentieth birthday that'll just be 20 years, so

$~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$7000\\ r=rate\to 8\%\to \frac{8}{100}\dotfill &0.08\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &20 \end{cases} \\\\\\ A=7000\left(1+\frac{0.08}{4}\right)^{4\cdot 20}\implies A=7000(1.02)^{80}\implies A\approx 34128.07$

5 0

1 year ago