John has 3 pencils. He gives 1 to Abbie how much does John have now?
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The time for the village to dig the new well is about 7 1/2 years. At this time the population doubles from its current size.
<h3>How to graph a function?</h3>For a function f(x) = y, the steps to draw a graph for the given function are as follows:
- Consider certain values of x
- Substitute x values in the given function to obtain y values
- Plot the x and y values in the graph
- Join the points to know the variation.
It is given that,
f(x) = 200 ×
Village's population growing rate = 9.8%
Creating a table for x and f(x) values:
x: 0 2 4 6 8 10
f(x = 0) = f(0) = 200 × = 200
f(x = 2) = f(2) = 200 × = 241
f(x = 4) = f(4) = 200 × = 291
f(x = 6) = f(6) = 200 × = 350
f(x = 8) = f(8) = 200 × = 423
f(x = 10) = f(10) = 200 × = 509
So,
(x, f(x)): (0, 200) (2, 241) (4, 291) (6, 350) (8, 423) (10, 509)
Plotting these points in the graph and joining the points, the graph is shown below.
Finding the time for the village to dig a new well:
It is given that the population doubled from its current size, the village will need to dig new water well.
The current size of the village = 200
If it doubles for a certain time 't' = 400
So,
400 = 200 ×
⇒ = 2
⇒ log = log 2
⇒ t log(1.098) = 0.301
⇒ t × 0.04 = 0.301
∴ t = 7.525 years
Therefore, the village's population becomes double at the time 7 and half years from now. So, after 7 1/2 years, the village needs to dig a new well.
Learn more about the function and its graph here:
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A 52-card deck is made up of an equal number of diamonds, hearts, spades, and clubs. Because there are 4 suits, there is a 1/4 chance to draw one of them, in our case, spades.
There are 4 aces in a 52-card deck, so the chance of drawing one is 4/52, or 1/13.
The question asks for the probability of drawing an ace or a spade. Because it uses the word "or," we add the probabilities together. This is because there is a chance of drawing either of the cards; it doesn't have to meet both requirements to satisfy the statement.
However, if the question were to say "and," we would multiply the two probabilities.
Let's add 1/4 and 1/13. First, we can find a common denominator. We can use 52 because both fractions can multiply into it (since the ratio came from a deck of 52 cards as well).
Now we can add them together.
This cannot be simplified further, so the probability is 17 in 52, or 33%.
hope this helps!