Answer:
So there are 500 pairs of numbers that have a sum of 1001. Thus, the sum of numbers from 1 to 1000 is 500*1001 = 500,500.
Step-by-step explanation:
I can’t really see what it says but it it’s total surface area it’s 9044.3 but it it’s lateral surface are it’s 7840
It's clear that for x not equal to 4 this function is continuous. So the only question is what happens at 4.
<span>A function, f, is continuous at x = 4 if
</span><span>
</span><span>In notation we write respectively
</span>
Now the second of these is easy, because for x > 4, f(x) = cx + 20. Hence limit as x --> 4+ (i.e., from above, from the right) of f(x) is just <span>4c + 20.
</span>
On the other hand, for x < 4, f(x) = x^2 - c^2. Hence
Thus these two limits, the one from above and below are equal if and only if
4c + 20 = 16 - c²<span>
Or in other words, the limit as x --> 4 of f(x) exists if and only if
4c + 20 = 16 - c</span>²
That is to say, if c = -2, f(x) is continuous at x = 4.
Because f is continuous for all over values of x, it now follows that f is continuous for all real nubmers 
Answer:
1/12
Step-by-step explanation:
He has a 1/4 pan left and wants to divide that into 3 equal pieces. So in night he will eat 1/3 of what he has left from the 1/4 pan. To figure out how much one slice is from an entire pan:
1/4 * 1/3 = 1/12
1 / 12 is the probability that you'll end up with an orange hat.
<u>Step-by-step explanation:</u>
Given that,
- There are 4 piece of clothing ⇒ shirt, pants, socks, or hat
- There are 3 possible colors ⇒ purple, blue, or orange
<u>To find the total number of outcome :</u>
Total outcomes ⇒ (number of clothes) × (number of colors)
⇒ 4 × 3 = 12
Therefore, there will be 12 different possibilities.
<u>The 12 different outcomes are :</u>
⇒ Purple shirt, blue shirt, orange shirt
⇒ Purple pants, blue pants, orange pants
⇒ Purple socks, blue socks, orange socks
⇒ Purple hat, blue hat, and orange hat.
Now, the probability that you'll end up with an orange hat if you choose on random of 12 possibilities ⇒ No.of orange hats / Total no.of outcomes.
∴ P(orange hat) = 1 / 12
