9514 1404 393
Answer:
8.6
Step-by-step explanation:
The growth factor per year is 1.012, so in 500 years is ...
1.012^500
The number of doublings is the solution to ...
2^n = 1.012^500
Taking logarithms, we have ...
n·log(2) = 500·log(1.012)
n = 500·log(1.012)/log(2) ≈ 8.6046
About 8.6 doublings will take place in 500 years.
Answer:
Subtracting 7
Step-by-step explanation:
<u><em>Given:</em></u>
<em>Clara is stacking cups; she put 45 plastic cups in the first stack, 38 plastic cups in the second stack, 31 plastic cups in the third stack, and 24 plastic cups in the fourth stack. </em>
<u><em>To Find:</em></u>
<em>What kind of sequence is this?</em>
<u><em>Solve:</em></u>
<em>Let's make a table:</em>
<em />
<em>[1 stack] 45 </em>
<em>[2 stack] 38</em>
<em>[3 stack] 31</em>
<em>[4 stack] 24</em>
<em />
<em>Now all we have to do is subtract to see what each is:</em>
<em>45 - 38 = 7</em>
<em>38 - 31 = 7</em>
<em>31 - 24 = 7</em>
<em>Thus,</em>
<em>[1 stack] 45 ⇒ 7</em>
<em>[2 stack] 38 ⇒ 7 </em>
<em>[3 stack] 31 ⇒ 7 </em>
<em>[4 stack] 24 ⇒ 7 </em>
<em>Hence, each stack is going down by 7.</em>
<em />
<u><em>Kavinsky</em></u>
<em />
Answer:
D, 
Step-by-step explanation:
Separate -1, 2, and 100 from each other inside the radical. You can take out -1 as <em>i</em>, and 100 as 10. You now have 10<em>i</em> on the outside of the radical and 2 on the inside. Hope this helps.
Start by dividing all terms by 4, to reduce this expression: |x+1| < 3.
Case 1: x+1 is already positive. The abs. val. operator does not change
anything. Then x+1<3, or x<2.
Case 2: (x+1) is negative. The abs. val. operator, in effect, puts a - sign in
front of (x+1): -(x+1)<3. Distributing the - sign: -x - 1 < 3. Adding 1 to both sides: -x < 4. We want to solve for positive x, so we mult. both sides of
-x<4 by -1 AND change the direction of the inequality symbol:
x > -4
Thus, the solution set is (-4,2): All real numbers between -4 and 2.
