Answer:
Step-by-step explanation:
Maybe the big numbers make it confusing, so let's look at something simpler. If you start with 5 marbles and every day you add one marble to it how many will you have x days after startign the collection? Well on day 0 it's 5, on day 1 it's 6, because 5+1, on day 2 it's 5+2=7, and so on. You can write this as an equation, y = 5+x, where y is the new total and x is the number of days.
So let's move that thinking to this problem. 1990 is day 0 and you start with 3,500,000. Each year now instead of day you add 38,500. So year 0 has 3,500,000. year 1 has 3,500,000+38,500 = 3,538,500 and so on, where each year we add another 38,500. So just like in the simpler example we can rewrite this. y = 3,500,000 + 38,500x. Linear means that the x is just an x instead of something like x^2, or 1/x or something else. Just normal x.
Direct variation is y=kx where k is a constant
the fiest way to see if it is direct or not, is if x increases, then y increases as well,
then we see if y=kx is valid, basically if we have a constant of variation
the first one x increase and y increase
see if same constant
y=kx
-4.5=-3k
1.5=k
so
see next one
-1 and 3
-3=-1(k)
-3=-1(1.5)
-3=-1.5
false
not it
2nd is increase and y decrease, so not direct variation
3rd is x is same but y increase so nope
4th is x increase and y increase, now test the constant
-7.5=-3k
2.5=k
-1 and -2.5
-2.5=-1k
-2.5=-1(2.5)
-2.5=-2.5
true
answer is last option
Given :
Levi answered 8 questions correctly out of 10 turns in the game.
Then answered the next three questions correctly.
He reasoned that because he added 3 to both the total questions and his correct responses, that the ratio of correct answers to total questions remained the same.
To Find :
Is he correct or not .
Solution :
Initially total number of questions are 10 and he answered 8 of them correctly .
So , ratio of correct ans to total ans is :
Now , he added more three questions and able to solve all of them .
So , new ratio is :
Therefore , the ratio of correctly answered and and total questions will not remain same .
Hence , this is the required solution .
So , total number of questions now are 13 and correctly answered are 11 .
Answer: About 16 years
Step-by-step explanation:
The formula to find the compound amount if compounded continuously is given by :-
, where P is Principal amount, r is the rate of interest ( in decimal) and t is time ( in years).
Given : P= $1000 ; r= 4.6%=0.046
let t be the time it will take to double the amount, the we have
Dividing 1000 both sides, we get
Taking natural log on each side, we get
Hence, it will take about 16 years to double the amount.
Answer:
138,706 typewriters
Step-by-step explanation:
290,000(0.9)^7
=138,706